Drinking Water Treatment: An Introduction 9783110551556

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Eckhard Worch Drinking Water Treatment

Also of Interest Adsorption Technology in Water Treatment Fundamentals, Processes, and Modeling Worch, 2012 ISBN 978-3-11-024022-1, e-ISBN 978-3-11-024023-8

Hydrochemistry Basic Concepts and Exercises Worch, 2015 ISBN 978-3-11-031553-0, e-ISBN 978-3-11-031556-1

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Eckhard Worch

Drinking Water Treatment | An Introduction

Author Prof. Dr. Eckhard Worch Technische Universität Dresden Institut für Wasserchemie 01062 Dresden [email protected]

ISBN 978-3-11-055154-9 e-ISBN (PDF) 978-3-11-055155-6 e-ISBN (EPUB) 978-3-11-055166-2 Library of Congress Control Number: 2019941243 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2019 Walter de Gruyter GmbH, Berlin/Boston Cover image: WLADIMIR BULGAR / Science Photo Library / Getty Images Typesetting: le-tex publishing services GmbH, Leipzig Printing and binding: CPI books GmbH, Leck www.degruyter.com

Preface Water is the basis of all life. For humans, water is essential for survival and therefore irreplaceable. Unfortunately, the water that can be taken from the available water resources is frequently not clean and thus it needs to be treated before use. The good news is that specific treatment technologies are available for all requirements. The purpose of this textbook is to give an introduction to the common methods of drinking water treatment. It is intended to meet the needs of readers who are new to the subject and are looking for a compact textbook that provides a concise and easy to understand introduction to the topic, requires little prior knowledge, and facilitates an easier access to more comprehensive monographs and handbooks. The textbook is based on 25 years of experience in teaching hydrochemistry and water treatment at a beginner level in various science and engineering study courses. The scope of the text was chosen to be suitable study material for a one- or twosemester lecture. Of course, that required a certain restriction to the essentials and the courage to omit some topics. Accordingly, the focus of this textbook is on the theoretical basics and practical aspects of the various technologies that are available for solving drinking water quality problems. By contrast, the inclusion of economic aspects and national regulations as well as the discussion of problems of water distribution and water-treatment residuals were largely dispensed with. The introductory Chapter 1 gives an overview of the water cycle, water resources, water quality, and general treatment options. The following Chapter 2 intends to provide some basic knowledge on chemical reactions and process engineering that is necessary to understand the basics of the treatment processes presented in the following chapters. This chapter is aimed primarily at readers who are not so familiar with these basics. Other readers may skip this chapter. From Chapter 3 to 14, all important processes that are used in drinking water treatment are presented: riverbank filtration (Chapter 3), filtration and sedimentation (Chapter 4), membrane separation processes (Chapter 5), gas–liquid exchange (Chapter 6), coagulation and flocculation (Chapter 7), deacidification (Chapter 8), softening and dealkalization (Chapter 9), deironing and demanganization (Chapter 10), ion exchange (Chapter 11), adsorption (Chapter 12), oxidation (Chapter 13), and disinfection (Chapter 14). The text is supplemented by numerous figures and tables. The attached glossary explains a large number of scientific terms related to drinking water treatment. I would be pleased if this book would find a broad acceptance by students and other readers who are interested in the basics of drinking water treatment. Last but not least I would like to thank all those who contributed in some way to this book. Special thanks to my wife Karola for her patience during the times of inten-

https://doi.org/10.1515/9783110551556-201

VI | Preface

sive writing. Thanks to my students and colleagues whose questions and discussions were an important source of inspiration. Thanks to the staff of the publishing house De Gruyter. I appreciate the useful support and the fruitful cooperation during the work on this book. Dresden, March 2019

Eckhard Worch

Contents Preface | V 1 1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.3 1.3.1 1.3.2 1.3.3

Introduction | 1 Natural and urban water cycle | 1 Water constituents and water quality | 4 Introduction | 4 Freshwater resources | 4 Microorganisms | 6 Abiotic particulate matter | 8 Dissolved inorganic water constituents | 9 Dissolved organic water constituents | 13 Treatment options | 15 Introduction and overview | 15 Brief characterization of the most important treatment processes | 17 Treatment train examples | 19

2 2.1 2.2 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.4 2.5 2.6 2.6.1 2.6.2 2.6.3 2.6.4

Some basics of hydrochemistry and process engineering | 25 Introduction | 25 Concentrations and activities | 25 Chemical equilibria | 27 General aspects | 27 Gas–water partitioning | 29 Acid/base equilibria | 30 Precipitation/dissolution equilibria | 33 Redox reactions | 35 Sorption/adsorption | 38 Reaction kinetics | 40 Mass transfer | 42 Reactor types | 45 Introduction | 45 Reactors for homogeneous reactions | 46 Reactors for gas–liquid exchange | 48 Reactors for liquid–solid transfer | 51

3 3.1 3.2 3.3

Riverbank filtration | 57 Introduction | 57 Attenuation processes during riverbank filtration | 59 Simplified mass transport modeling under consideration of sorption and biodegradation | 60

VIII | Contents

3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5 3.5 3.6

General assumptions | 60 Mass transport influenced by sorption | 61 Mass transport influenced by biodegradation | 63 Mass transport influenced by sorption and biodegradation | 63 Laboratory-scale simulation of riverbank filtration processes | 64 Assessment of organic substances with respect to their fate during riverbank filtration | 64 Biodegradation | 65 Sorption | 66 Sorption and biodegradation | 68 Special case: NOM breakthrough curves | 68 Prediction of model parameters | 70 Practical aspects | 71

4 4.1 4.2 4.2.1 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.3.4

Sedimentation and filtration | 75 Introduction | 75 Sedimentation | 76 Theoretical basics | 76 Sedimentation basins | 79 Design considerations | 80 Filtration | 83 Filtration processes: classification and basic principles | 83 Filtration mechanisms | 86 Depth filtration theory | 87 Practical aspects | 92

5 5.1 5.2 5.2.1 5.2.2 5.2.3 5.3 5.3.1 5.3.2 5.3.3

Membrane separation processes | 97 Introduction | 97 General aspects | 100 Operational modes | 100 Basic process parameters | 101 Fouling and scaling | 104 Microfiltration and ultrafiltration | 105 Membrane materials | 105 Membrane modules and membrane operation | 105 Combination of microfiltration/ultrafiltration with other treatment techniques | 108 Nanofiltration and reverse osmosis | 108 Osmosis and osmotic pressure | 108 Mass transfer | 110 Concentration polarization and scaling | 111

5.4 5.4.1 5.4.2 5.4.3

Contents | IX

5.4.4 5.4.5

Membrane materials | 113 Membrane modules and operation | 114

6.2.3 6.2.4 6.3 6.3.1 6.3.2 6.3.3 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5 6.5

Coagulation and flocculation | 117 Introduction and treatment objectives | 117 Coagulation | 118 Stability of colloidal solutions | 118 The zeta potential as a characteristic parameter of the electric double layer | 122 Destabilization of colloidal solutions by coagulation processes | 123 Coagulants | 125 Flocculation | 128 Principle | 128 Flocculants | 129 Kinetic aspects | 130 Important influence factors and process conditions | 132 General aspects | 132 pH value | 133 Temperature | 135 Type and dosage of coagulants and flocculant aids | 135 Preozonation | 136 Coagulation/flocculation systems | 137

7 7.1 7.2 7.2.1 7.2.2 7.2.3 7.3

Gas–liquid exchange | 141 Introduction | 141 Theoretical basics | 142 Gas–water partitioning | 142 Mass transfer | 146 Design equations for counterflow packed columns | 149 Reactors for gas–liquid exchange | 153

8 8.1 8.2 8.2.1 8.2.2 8.3 8.3.1 8.3.2 8.3.3 8.3.4

Deacidification | 157 Introduction and treatment objective | 157 The calco–carbonic equilibrium | 157 Basics | 157 Tillmans curve and Langelier equation | 160 Deacidification processes | 163 Treatment options | 163 Mechanical deacidification | 163 Chemical deacidification | 166 Practical aspects | 169

6 6.1 6.2 6.2.1 6.2.2

X | Contents

9 9.1 9.2 9.3 9.3.1 9.3.2 9.3.3 9.3.4 9.3.5 9.4

Softening and dealkalization | 171 Introduction and treatment objectives | 171 Hardness of water: definitions and units | 172 Softening and dealkalization processes | 175 Overview | 175 Precipitation processes | 176 Acid addition | 181 Ion exchange processes | 182 Membrane processes | 185 Special case: hardening of water | 187

10 Deironing and demanganization | 189 10.1 Introduction and treatment objectives | 189 10.2 Basics of deironing and demanganization | 192 10.2.1 General considerations and thermodynamic aspects | 192 10.2.2 Oxidation mechanisms and kinetic aspects | 195 10.3 Practical aspects | 197 11 Ion exchange | 203 11.1 Types and applications of ion exchange resins | 203 11.2 Selectivity of ion exchange resins | 207 11.3 Hydrochemical effects of ion exchange processes | 208 11.4 Practical applications of ion exchange resins | 211 11.4.1 General considerations | 211 11.4.2 Softening and dealkalization | 214 11.4.3 Demineralization | 219 11.4.4 Removal of nitrate | 223 11.4.5 Removal of humic substances | 224 11.4.6 Removal of heavy metals | 225 12 Adsorption | 227 12.1 Introduction | 227 12.2 Activated carbons | 228 12.2.1 Production | 228 12.2.2 Adsorption properties | 229 12.3 Theoretical basics of the adsorption process | 230 12.3.1 Adsorption equilibrium | 230 12.3.2 Adsorption kinetics | 234 12.3.3 Adsorption dynamics in fixed-bed adsorbers | 236 12.4 Practical aspects of activated carbon adsorption | 240 12.4.1 Application of powdered activated carbon in slurry reactors | 240 12.4.2 Application of granular activated carbon in fixed-bed adsorbers | 242

Contents | XI

12.4.3 12.4.4

Fixed-bed versus batch adsorber | 246 Biologically active carbon filters | 248

13 Oxidation processes | 251 13.1 Introduction | 251 13.2 Ozonation | 252 13.2.1 Oxidation mechanisms | 252 13.2.2 Ozone generation and introduction | 254 13.2.3 Oxidation byproducts | 257 13.3 Advanced oxidation processes | 259 13.3.1 Definition and classification | 259 13.3.2 Mixing of O3 and H2 O2 : the peroxone process | 260 13.3.3 H2 O2 and UV irradiation | 260 13.3.4 O3 and UV irradiation | 261 13.3.5 Photocatalysis | 261 13.3.6 Fenton reaction | 264 13.3.7 The EE/O concept | 265 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7

Disinfection | 267 Introduction | 267 Disinfection efficiency | 268 Disinfection with chlorine | 270 Disinfection with combined chlorine | 274 Disinfection with chlorine dioxide | 275 Disinfection with ozone | 277 UV disinfection | 277

Appendix: Glossary | 281 Nomenclature | 291 Abbreviations | 301 Bibliography | 305 Index | 307

1 Introduction 1.1 Natural and urban water cycle Water is the basis of all life. For humans, water is essential for survival and therefore irreplaceable. Ensuring water availability and quality belongs to the most important goals of sustainable development. The quality of water is determined by its constituents, which is the totality of the substances dissolved or suspended in water. Although water with a total mass of about 1.38×1018 t is the most common molecular substance on Earth, its distribution between the individual environmental compartments is strongly unbalanced (Table 1.1). Approximately 97% of the total water is salt water of the oceans that cannot be consumed by humans directly. Although the production of drinking water from ocean water is, in principle, possible (e.g., by reverse osmosis), it is unfavorable due to the high energy demand for the necessary treatment processes. Therefore, freshwater is typically used as the raw water resource for drinking water production. The most important freshwater resources are the polar ice caps and the glaciers as well as groundwater and surface water. From these resources, only parts of surface water and groundwater can be utilized to produce drinking water with an acceptable technical effort. It is estimated that less than 1% of the huge water resource is actually available for human use. Tab. 1.1: Global water resources. Data from Trenberth et al. (2007). Water resource

Volume (103 km3 )

Portion (%)

Oceans Polar ice caps and glaciers Groundwater Lakes and rivers Soil moisture Permafrost Atmosphere Total

1 335 040 26 350 15 300 178 122 22 12.7 1 377 024.7

96.95 1.91 1.11 0.013 0.009 0.0016 0.0009 100.0

However, the usable freshwater inventories are constantly renewed by the hydrological water cycle. Figure 1.1 shows the global water cycle in a very simplified form. Approximately 400 000 km3 of water are transferred by evaporation from the sea into the atmosphere each year and the same volume is returned by precipitation to the mainland and to the oceans. The cycle thus resembles a distillation plant whose energy demand, covered by the sun, can be calculated from the enthalpy of vaporization of water to be about 1021 kJ/a. For the renewal of freshwater resources, the proportion of evaporated water from the oceans that is transported through the atmosphere to the https://doi.org/10.1515/9783110551556-001

2 | 1 Introduction

Atmosphere

Transport to the land

40 Precipitation 113

Evaporation 73

Precipitation 373

Evaporation 413

Land Rivers and lakes Transport to the sea

Ocean

Groundwater

Fig. 1.1: The global hydrological water cycle. Volumetric flow rates in 103 km3 /a. Data from Trenberth et al. (2007).

land is of particular importance. At 40 000 km3 /a, this proportion is approximately one tenth of the water evaporated from oceans. A part of the rainwater is added directly to the surface water bodies (streams, rivers, lakes, reservoirs) or flows on the land surface into the surface water. Another part of the precipitate, the seepage water, infiltrates into the soil. There it is absorbed by plants or further transported into the ground where it finally reaches the groundwater level. Surface water can also infiltrate into the subsurface where it becomes groundwater. After more or less long residence times and flow paths, groundwater returns to the surface in the form of springs or directly by exfiltration into surface water. The hydrological cycle is completed by evaporation processes and water runoff to the sea. The evaporation can take place both from the ground and from the water surfaces as well as from plants. The runoff to the sea occurs via creeks, rivers, and streams. Despite the fact that only water is evaporated from the oceans and the dissolved substances remain as ‘distillation residual’ within the aqueous phase, naturally occurring freshwater water is never pure H2 O but contains dissolved, colloidal, and coarsely dispersed constituents that are introduced into the water in the different stages of the hydrological cycle by natural processes and anthropogenic activities. Nevertheless, the concentrations of the major components (i.e., inorganic ions) are much lower in freshwater than in ocean water. The highest ion concentrations in freshwater are in the mg/L range, whereas the highest ion concentrations in seawater are in the g/L range. In contrast to seawater, with a relatively constant composition, the composition of natural freshwaters varies strongly. It is influenced by a variety of physical, chemical,

1.1 Natural and urban water cycle | 3

Natural water cycle Wastewater disposal

Raw water abstraction (groundwater, surface water)

Urban rainwater runoff

Wastewater treatment

Direct use Wastewater recycling and reuse

Wastewater collection

Drinking water treatment

Drinking water distribution

Water use

Fig. 1.2: The urban water cycle.

and biological processes, which often act in a very complex manner inside the water phase but also at the boundaries with other environmental compartments such as the atmosphere or solid phases like soils or sediments. Therefore, the composition of freshwater not only varies depending on the type of the water body (e.g., groundwater, lakes, rivers, reservoirs) but also within a considered water body type. Every river, every lake, or every groundwater has an individual composition, determined by the natural environment and further modified by anthropogenic inputs. Consequently, when drinking water is produced from freshwater, which is the typical case, the treatment technology has to be adapted to the present raw water quality. Accordingly, there is no universal treatment technology, as will be further discussed in the following sections. Drinking water treatment is part of the urban water cycle (Figure 1.2), which is strongly connected with the natural water cycle presented above. Raw water for drinking water production can be taken from different parts of the natural water cycle. If possible, groundwater is used as raw water because it is better protected against the input of anthropogenic contaminants than surface waters are. However, anthropogenic inputs into the groundwater via seepage water are also possible, in particular under agricultural or industrial areas. Furthermore, natural constituents in the groundwater (e.g., reduced iron and manganese species, carbon dioxide) can cause problems and have to be removed from drinking water if their concentrations exceed specific limit values. Out of the available surface water resources, in particular water from wellprotected reservoirs and from weakly polluted rivers or lakes are used as raw water sources for drinking water production. If stronger polluted river water has to be used, a near-natural pretreatment by riverbank filtration is often reasonable. The use of spring water or rainwater is also possible but the available quantities are mostly not very large. In the last decades, drinking water production from seawater with membrane processes has gained importance, in particular for regions where no or not

4 | 1 Introduction

enough freshwater is available. However, the energy demand for such processes is relatively high. In contrast to its name, drinking water is not only used for drinking but also for many other purposes, for instance for cooking, dish washing, toilets, bathtubs, showers, room cleaning, laundry, and others. However, independent of the kind of use, all water that is distributed to consumers has to fulfill the quality standards of drinking water. After its use, the water becomes wastewater, which is collected in a sewer system and treated in a wastewater treatment plant (WWTP) to remove solids, organic substances, nutrients, and – to an increasing degree – also micropollutants. The WWTP effluent is disposed of by reintroducing into the natural water cycle, typically into rivers. Accordingly, the efficiency of the wastewater treatment strongly influences the quality of natural water bodies and therefore also the effort required for drinking water production from these water bodies.

1.2 Water constituents and water quality 1.2.1 Introduction As mentioned before, there is no absolutely pure water within the water cycle. In particular, surface water and groundwater, the most important drinking water resources, contain higher amounts of suspended, colloidal, and dissolved compounds. These substances can be introduced into the water body from natural or anthropogenic sources. Dissolution of minerals, humic substances, or atmospheric gases as well as biological transformation processes are important natural sources, whereas wastewater effluents and runoff from agricultural areas are typical anthropogenic sources. Often, natural and anthropogenic substances are introduced on the same pathway, for instance with surface runoff to the rivers, lakes, or reservoirs or with seepage water to the groundwater. The quality of a water resource is determined by the kind and concentration of these constituents. In the following sections, a brief characterization of the most important freshwater resources and a short introduction to the different groups of water constituents will be given.

1.2.2 Freshwater resources The main freshwater resources with respect to drinking water production are: groundwater, river water, lake water, and reservoir water. The composition of groundwater is mainly influenced by the geological background. It is dominated by the cations Ca2+ , Mg2+ , Na+ and K+ and the anions HCO−3 , − SO2− 4 and Cl . These major ions typically occur in the lower mmol/L or higher μmol/L

1.2 Water constituents and water quality |

5

range. Dissolved gases such as carbon dioxide and oxygen play a significant role in the interaction of water with solid phases. When seepage water on its way to the groundwater level flows through the soil layers, it is enriched with carbon dioxide, which is a product of biological degradation processes in the soil. This carbon dioxide in seepage and groundwater can enhance and accelerate the dissolution of minerals, in particular carbonates. Dissolved oxygen determines the redox intensity (or the redox potential) and thus the dissolution or precipitation of certain ions (such as iron or manganese ions). The solid layers above the groundwater protect it largely from pollutants. However, in recent years, anthropogenic influences, for instance through input of nitrate, pesticides, and chlorinated hydrocarbons, have increased. The composition of spring water is initially the same as that of the groundwater from which it is originated, but is then (as a creek or river) subject to extensive changes due to natural and anthropogenic inputs as well as through gas exchange with the atmosphere. Especially in urban areas, the rivers receive substantial amounts of inorganic and organic wastewater constituents. Also, runoff from agricultural areas (fertilizers, pesticides) and input from other diffuse (nonpoint) sources can contribute to the pollution of rivers and lakes. Rivers have a biological self-cleaning force, mainly based on the oxidative degradation of organic water constituents by microorganisms. These oxidation processes require an adequate oxygen supply. Although the oxygen uptake from the atmosphere by rivers is favored through the turbulence of the flowing water, an excessive organic load can increase the risk of widespread oxygen depletion coupled with a decrease in the water quality. Sediments in rivers and lakes act as pollutant sinks, for example for heavy metals, and thus are often heavily loaded. The introduction of complexing agents or changes in the redox potential can remobilize the heavy metals from the sediments. Frequently, the concentrations of anthropogenic pollutants are too high for the direct use of river water as raw water for drinking water supply. In such cases, riverbank filtrate, extracted from wells that are located at a certain distance from the river bank, can be used as the raw water source. During the subsurface transport of the river water from the river to the extraction wells, the pollutants are eliminated to some extent by filtration, biodegradation, and sorption processes. The material balances of standing water bodies are strongly influenced by biological processes and, in moderate (temperate) latitudes, also influenced by the change of stagnation and circulation phases, resulting from the density anomaly of water. For the stagnation periods in summer and winter, vertical concentration profiles are typical. In contrast, the circulation in spring and autumn leads to a uniform distribution of the dissolved substances. In the summer stagnation period, the photosynthetic production of biomass and oxygen from inorganic substances (water, carbon dioxide, nitrate, phosphate) dominates in the upper water layers (epilimnion). The dissolved oxygen, however, cannot be transferred into the deeper water layers (hypolimnion) due to the formation of a layer where temperature and density strongly change (thermocline, metalimnion),

6 | 1 Introduction

whereas dead biomass particles are transported to the bottom of the lake by sedimentation. During the following microbial mineralization of the biomass, in reverse to its production, organic substances are converted back to inorganic material, which is associated with a depletion of dissolved oxygen in the lower layers of the lake. Since oxygen is not replenished during the stagnation phase, the redox state in the hypolimnion often changes with the result that reduced compounds, such as NH+4 , Mn2+ , Fe2+ , H2 S/HS− , or CH4 , increasingly occur. During the reduction and dissolution of manganese (IV) oxide and iron (III) oxide hydrate under reducing conditions, substances bound to these solid substances (e.g., other metals, phosphate) are also remobilized from the sediment. In particular, high inputs of anthropogenic nutrients (especially phosphorus) intensify the photosynthetic production and the subsequent mineralization and oxygen consumption with the abovementioned negative impacts on the water quality. This intensified process is known as eutrophication of lakes and reservoirs. Limitation of nutrient input is therefore a crucial factor for securing the water quality of lakes and reservoirs. Reservoirs, which are intended for the drinking water supply, are usually well protected against anthropogenic inputs due to their location and/or designation of drinking water safeguard zones. However, some of the natural constituents of reservoir waters can also be problematic with respect to drinking water production, for instance humic substances, reduced iron and manganese ions, taste and odor substances produced by bacteria, and cyanotoxins released from cyanobacteria (formerly referred to as blue-green algae). The water constituents occurring in the different water resources can be subdivided into four groups: microorganisms, abiotic particulate matter, dissolved inorganic substances, and dissolved organic substances. These groups will be briefly characterized in the following sections.

1.2.3 Microorganisms Pathogenic bacteria, viruses, protozoa, and helminths may cause infectious diseases and are therefore considered the most common health risk associated with drinking water. Accordingly, the removal or inactivation of these microorganisms has priority in drinking water treatment, in particular when surface water is used as the raw water source. Microorganisms belong to the particulate matter that can be removed – at least partially – by filtration processes. Figure 1.3 shows the typical sizes ranges of microorganisms. Additionally, disinfection by chemicals or by ultraviolet (UV) irradiation has to be applied to inactivate the microorganisms. Since it is not possible to monitor all microbiological species in the raw water and during drinking water treatment, indicator pathogens are selected to assess the microbiological water quality. The background to this approach is the idea that when the

1.2 Water constituents and water quality |

7

Protozoa Algae Viruses

10-8 10-5 10-2

10-7 10-4 10-1

Bacteria

10-6 10-3 100

10-5 10-2 101

10-4 10-1 102

10-3 m 100 mm 103 µm

Fig. 1.3: Size ranges of microorganisms.

indicator organisms are detected, also other, possibly more harmful, organisms can be expected in the water and suitable measures against the microbiological contamination have to be taken. However, indicator organisms are not only measured to get information about the raw and product water quality, but some of them are also monitored in order to evaluate the efficiency of physical removal processes or disinfection. Criteria that are used to select such indicator organisms are health risk, frequency of occurrence, detectability, indicator function, persistence, and behavior during water treatment. Typical indicator organisms that are often used to characterize the drinking water quality are Escherichia coli (E.coli) and other coliforms as well as Enterococci. Since they are intestinal inhabitants, they are well suited as indicators for fecal pollution, for instance as a result of wastewater introduction into the water source. Clostridia (e.g., Clostridium perfringens) are ever-present in nature and can occur, for instance, in soil and surface waters but also in the intestinal tract of humans and animals. Under unfavorable environmental conditions they are able to form resistant endospores. Clostridium perfringens is therefore considered to be a suitable model for robust pathogens, including viruses and protozoa. Pseudomonas aeruginosa occurs in small numbers in the intestinal flora of humans and animals but only seldom in water bodies. Since it colonizes biofilms, it is considered a good indicator for pollution in the water distribution system or in water treatment installations. Other indicator microorganisms of concern to health risk are the protozoan parasites Gardia lamblia and Cryptosporidium parvum. Gardia lamblia can occur in a trophozoite (free swimming) or in a cyst (dormant) form. The latter facilitates survival during unfavorable environmental conditions. Since Gardia lamblia is excreted by the host animal in the cyst form, this form is particularly relevant with respect to drinking water quality. Cryptosporidium parvum is excreted as oocysts, which are thick-walled cells formed during the life cycle. Since filtration removes these cysts and oocysts better than conventional disinfection with chlorine, these microorganisms can also be used as indictors to validate the water treatment efficiency, in particular with respect to filtration processes. Table 1.2 lists some microorganisms together with their indicator functions. The heterotrophic plate count (HPC) is also frequently used to monitor the overall bacteriological water quality. HPC is an analytic method that measures the colony for-

8 | 1 Introduction

Tab. 1.2: Indicator organisms used to characterize the microbial water quality with respect to water treatment and distribution. Indicator organisms

Indicator function

Escherichia coli (E.coli) Total coliforms

Fecal indicator Fecal indicator

Enterococci

Fecal indicator

Clostridium perfringens

Indicator for past fecal contamination, indicator for robust pathogens (viruses and protozoa), indicator for pollution of the distribution system (biofilm growth)

Pseudomonas aeruginosa

Indicator for pollution of the distribution system (biofilm growth)

Gardia and Cryptosporidium, in particular their cysts and oocysts

Indicators for filtration efficiency

mation of heterotrophic bacteria on culture media. It has to be noted that HPC results are not a direct indicator of water safety, because there is a site-specific baseline range of the bacteria level. Abnormal deviations from this baseline range, however, indicate problems with the raw water quality, the treatment efficiency, or the integrity of the distribution system.

1.2.4 Abiotic particulate matter In this section, we want to restrict our discussion to solid particles that are small enough to be suspended throughout the bulk of the aqueous phase, because these particles are of special relevance with respect to raw water quality and water treatment. The main sources of abiotic particles in water are soil weathering, runoff from terrestrial environments, and precipitation processes. Weathering and surface runoff lead to the introduction of clay, silt, sand, metal oxides (e.g., aluminum oxide, ferric oxide, manganese oxide), and particulate organic matter (humic substances) into water bodies. The formation of calcium carbonate from calcium and hydrogencarbonate (bicarbonate) ions is an example of precipitation as particle source. Besides abiotic particles, particulate matter in a wider sense also comprises microorganisms, such as algae, protozoa, bacteria, and viruses (Section 1.2.3). The primary property of all particles is that they are, in contrast to ions and molecules, not dissolved in water but form heterogeneous or microheterogeneous systems. Suspended particles with particle sizes from 1 μm to about 100 μm form heterogeneous systems where the particles are visible to the naked eye. Smaller particles with sizes in the range from about 1 nm to 1 μm are referred to as colloids. They form socalled microheterogeneous systems (colloidal solutions), in which the particles cannot be seen with the naked eye but can be made visible by optical effects (e.g., light

1.2 Water constituents and water quality | 9

scattering). Generally, the boundaries between suspensions and colloidal solutions are fluid. It has to be noted that filtration through a 0.45 μm filter, which is widely used in water analytics to separate dissolved from particulate organic matter, includes most of the colloids with the dissolved species even though they behave in some ways as particles. Abiotic particles in water are mainly an aesthetic problem. Drinking water containing particles is not accepted by the consumers. The majority of natural abiotic particles found in raw waters are not hazardous; however, some of the solids may be problematic, for instance when they contain heavy metal compounds or when they are carriers of harmful substances that are sorbed to the surface of the solid material. Typically, the content of particles in surface water is higher than in groundwater. The total particle concentration can be measured as total suspended solids (TSS), which is the dry weight of suspended particles trapped by a filter. In drinking water treatment, the turbidity is often measured instead of TSS. The turbidity is an indirect measure of the content of smaller particles, which do not settle instantaneously, and also colloids. This parameter is therefore particularly relevant for the process control during drinking water treatment. Turbidity can also be used as an indicator for the occurrence of bacteria, Gardia cysts, and Cryptosporidium oocysts (Section 1.2.3). The turbidity can be measured with a special instrument called a nephelometer. It utilizes the property of particles to scatter a light beam, where the extent of light scattering is measured by a detector arranged at a right angle to the light beam. The units of turbidity measured with a calibrated nephelometer are referred to as nephelometric turbidity units (NTU). The World Health Organization (WHO) recommends that the turbidity of drinking water should ideally be below 1 NTU.

1.2.5 Dissolved inorganic water constituents Inorganic substances in natural waters mainly occur in the form of ions or as dissolved inorganic gases. Some of these species are components of acid-base or redox systems with the consequence that their occurrence is strongly influenced by the pH or the redox state of the water. The basics of acid-base and redox equilibria can be found in Chapter 2. The major ions in natural waters are the cations of sodium (Na+ ), potassium (K+ ), calcium (Ca2+ ), and magnesium (Mg2+ ) and the anions hydrogencarbonate (HCO−3 ), − sulfate (SO2− 4 ), and chloride (Cl ). Hydrogencarbonate is the anion of carbonic acid (more exactly dissolved carbon dioxide, CO2 ) that dominates in the medium pH range (Figure 1.4). According to this acid-base equilibrium, hydrogencarbonate is introduced into the water by dissolution of carbon dioxide or carbonates and subsequent transformation of the introduced species. One of the most relevant reaction equilibria in natural waters, the calco–carbonic equilibrium, links the major ions Ca2+ and HCO−3 as well as the dissolved gas CO2 with

10 | 1 Introduction

Fig. 1.4: Carbonic acid speciation as a function of pH.

the dissolution or precipitation of calcium carbonate, CaCO3 : CaCO3(s) + CO2 + H2 O 󴀕󴀬 Ca2+ + 2 HCO−3

(1.1)

The relevance of the calco–carbonic equilibrium with respect to water quality and water treatment is discussed in more detail in Chapter 8. Silica occurs in water in the hydrated form H4 SiO4 , which is a weak acid that only dissociates at relatively high pH values. Accordingly, the neutral form dominates under most practice-relevant conditions. Due to condensation reactions, molecules with sizes in the colloidal range can be formed. Besides dissolved CO2 , water typically contains other gases, in particular the atmospheric gases O2 and N2 , which can be introduced by absorption from the air or by biochemical transformation processes in the aqueous phase. Under strongly reducing conditions, dihydrogen sulfide, H2 S, can occur, which is in a pH-dependent acid-base equilibrium with its anion hydrogensulfide, HS− (Figure 1.5). Note that in practice the name hydrogen sulfide (with a space between the components) is often used for H2 S, which can lead to confusion with hydrogensulfide, HS− . Due to the high pK a value of HS− , the fraction of sulfide, S2− , in the medium pH range is very small. Nevertheless, it may be sufficient to form sulfides with heavy metals because theses sulfides have very low solubility products (see also Chapter 2, Section 2.3.4). Dissolved ammonia, NH3 , is part of the natural nitrogen cycle (Figure 1.6) and is in an acid-base equilibrium with the ammonium ion, NH+4 (Figure 1.7). Nitrate, NO−3 , occurs in many water bodies, but in strongly varying concentrations. In particular, under the influence of anthropogenic inputs (e.g., from agriculture), the

1.2 Water constituents and water quality |

11

Fig. 1.5: H2 S speciation as a function of pH. Oxidation state

+5

Assimilative nitrate reduction

NO3-

+3

NO2-

+1

N2O

±0

N2 Biological N fixation Ammonification

-3

Organic N compounds

NH3 / NH4+ NH3 assimilation

Fig. 1.6: Biogeochemical nitrogen cycle.

concentration can reach values that are comparable with the concentrations of the major ions. In well-protected water resources, however, the concentrations are typically much lower. NO−3 is also part of the nitrogen cycle shown in Figure 1.6. − Br− , Fe2+ , Mn2+ , HPO2− 4 /H2 PO4 and aluminum species are also found in natural waters with lower concentrations than those of the major ions. Aluminum occurs in the medium pH range in form of hydroxo complexes. The dissolved iron and manganese species Fe2+ and Mn2+ can only be found under reducing conditions. The an− ions of the phosphoric acid, HPO2− 4 and H2 PO4 , are the dominant phosphate species in the medium pH range (Figure 1.8). Increased phosphate concentrations in a water

12 | 1 Introduction

Fig. 1.7: Ammonium/ammonia speciation as a function of pH.

Fig. 1.8: Phosphoric acid speciation as a function of pH.

body are an indicator for anthropogenic inputs (e.g., from wastewater or from agricultural areas). Bromide (Br− ) frequently occurs along with the major ion chloride, but in lower concentrations. Heavy metals often form hardly soluble hydroxides and sulfides. Accordingly, they are frequently found in the sediments of rivers and lakes or as part of the suspended matter. However, some of them can also occur in the aqueous phase as cations (e.g., Cd2+ , Ni2+ ) or anions (CrO−4 ) or as coordination complexes with inorganic or or2− ganic ligands, such as OH− , CO2− 3 , SO4 , humic substances, and synthetic complexing

1.2 Water constituents and water quality | 13

Tab. 1.3: Problematic inorganic water constituents. Problematic water constituents

Problems

High salinity

Salty taste, corrosion

CO2 excess (in comparison to the calco–carbonic equilibrium)

Corrosion

Hardness (Ca2+ + Mg2+ )

High detergent consumption, scaling (CaCO3 precipitation)

Carbonate hardness (Ca2+ + equivalent amount HCO−3 )

Scaling (CaCO3 precipitation)

Fe2+ and Mn2+

Oxidation by air or other oxidants → formation of strongly colored precipitates

H2 S

Odor, indicator for reducing conditions

NO−3

Transformation to nitrite → formation of carcinogenic nitrosamines, inducing methemoglobinemia

Heavy metals

Toxicity

Br−

Formation of harmful transformation products (bromate, brominated organic compounds) during ozonation and disinfection

agents. In some regions of the Earth (e.g., Bangladesh and Pakistan), geogenic arsenic is a serious problem for the quality of ground and surface waters. Not all of the mentioned inorganic water constituents are of equal relevance for drinking water treatment and quality. Many of them are not harmful or their concentrations in the raw waters are much lower than the limit values. Moreover, some of the problematic water constituents have only regional relevance and an impact on the water supply can be avoided by changing the raw water source or by blending raw waters from different sources. Therefore, the main focus in drinking water treatment is only on a limited number of problematic inorganic water constituents. The most relevant substances or substance groups are listed in Table 1.3. Here, it has to be noted that often not a total removal but only a reduction of the inorganic water constituents during water treatment is necessary or wanted. This aspect will be discussed in the respective chapters where the treatment processes are presented. In particular, the removal of excess CO2 , hardness, Fe2+ , and Mn2+ are widely used processes in drinking water treatment. Nitrate removal has gained importance in the last decades due to the increasing pollution of groundwater resources as a result of intensive agriculture.

1.2.6 Dissolved organic water constituents According to conservative estimates more than 100 000 organic substances occur in the hydrosphere. The largest fraction of organic material in water is of natural ori-

14 | 1 Introduction

Total organic carbon TOC

0.45 µm filtration Residual

Particulate organic carbon POC

Filtrate

Dissolved organic carbon DOC

Fig. 1.9: Classification of organic matter.

gin, so-called natural organic matter (NOM), which consists of about 50% humic substances (humic and fulvic acids). The rest are low-molecular acidic and neutral substances and other compounds. It has to be noted that the term NOM in its general meaning includes also particulate organic matter. Nevertheless, it is also used for the dissolved fraction alone. To indicate the difference, the abbreviation DOM (dissolved organic matter) can be used instead of NOM. Due to the complex composition of NOM, no individual species can be identified and analytically determined. Therefore, the collective parameters TOC (total organic carbon) or DOC (dissolved organic carbon) are used to characterize the considered water with respect to its content of organic substances. The analytical method is based on an oxidation of the organic matter to CO2 (after removing the inorganic carbon species) and a subsequent detection of the formed CO2 . The result is reported as mg C/L. To determine the DOC, the sample has to be filtrated through a 0.45 μm membrane, whereas the analysis of an unfiltered sample gives the TOC including the particulate organic matter (Figure 1.9). Although the parameter DOC, according to its definition, comprises all kinds of dissolved organic substances, the contribution of the anthropogenic (synthetic) organic substances can be neglected due to their much lower concentrations. Therefore, the DOC can be considered a measure of the content of dissolved natural organic substances. The DOC of water resources varies depending on the water type. The typical range is from < 1 mg/L to > 10 mg/L, where the lower concentrations are typically found in groundwater (from < 1 mg/L to about 2 mg/L), whereas higher concentrations occur in surface water (from about 2 mg/L to > 10 mg/L). Natural organic matter does not pose a direct health risk, but it is relevant with respect to the water quality due to its indirect effects and its impact on the water treatment. NOM is a precursor for the formation of halogenated disinfection byproducts upon disinfection (chlorination). Furthermore, it reduces the adsorption capacity of

1.3 Treatment options

| 15

activated carbon for trace organic compounds due to competitive adsorption and it also leads to organic fouling on membrane surfaces. Due to its ability to form complexes with metals it can cause problems for the removal of iron, manganese, or heavy metals. Dissolved methane gas, CH4 , is formed within the natural carbon cycle by biological processes under reducing conditions and has to be removed from the water because it may disturb other treatment processes. Dissolved organic substances released by bacteria occur seasonally, mainly in lakes and reservoirs. The most relevant substances are cyanotoxins and taste and odor compounds. In the last decades, an increasing number of anthropogenic organic substances, also referred to as synthetic organic substances (SOCs), have been found in raw waters from different sources, in particular in surface water, but more and more also in groundwater. The concentrations of anthropogenic organic substances found in groundwaters and surface waters range from ng/L to μg/L. These compounds are therefore also referred to as micropollutants or trace pollutants. Important anthropogenic substance groups are halogenated solvents, pesticides, polycyclic aromatic compounds (PAHs), petroleum derived hydrocarbons, BTEX aromatics, phenols, synthetic complexing agents, pharmaceuticals, personal care products, sweeteners, and corrosion inhibitors. Some of these synthetic substances are harmful. In other cases, the health risk is not yet known exactly. However, for prevention reasons, such anthropogenic organic chemicals are generally unwanted in drinking water.

1.3 Treatment options 1.3.1 Introduction and overview The general objective of drinking water treatment is to provide a product that is microbiologically and chemically safe for the consumers. However, the site-specific requirements to reach this general objective may be very different and depend on the kind of water resource and its quality. Consequently, there is no universal treatment technology that is suitable for all sites and raw water conditions. By contrast, an optimal combination of available treatment processes has to be found for each local situation. Such a sequence of treatment processes is referred to as a treatment train. Some examples of treatment trains for different water sources are given in Section 1.3.3. A modern water supply is based on the multibarrier principle. That means that several barriers are established to limit the occurrence of contaminants in the treated water. These barriers include not only the processes in the waterworks but also the protection of raw water sources and the safety of the treated water during distribution.

16 | 1 Introduction

Tab. 1.4: Drinking water treatment: objectives and available processes. Treatment objective

Treatment processes

Chapter

Particle removal

Bank filtration and infiltration Coagulation and flocculation

3 6

Sedimentation

4

Removal or inactivation of microorganisms

Removal of dissolved inorganic compounds

Removal of dissolved organic compounds

Filtration

4

Microfiltration and ultrafiltration

5

Bank filtration and infiltration

3

Disinfection with chemicals (chlorine, chlorine dioxide, ozone)

14

Disinfection by UV irradiation

14

Ultrafiltration

5

Deacidification (removal of CO2 )

8

Softening (removal of hardness)

9

Dealkalization (removal of carbonate hardness)

9

Deironing and demanganization (removal of Fe2+ and Mn2+ )

10

Ion exchange (desalination or removal of specific ions, e.g., hardness, heavy metal ions, nitrate)

11

Adsorption (removal of specific ions, e.g., arsenate, phosphate)

12

Aeration/desorption (removal of dissolved gases)

7

Reverse osmosis and nanofiltration (total or partial removal of ions)

5

Bank filtration and infiltration

3

Coagulation and flocculation

6

Adsorption

12

Biofiltration

4, 12

Aeration/desorption (removal of volatile substances or dissolved gases)

7

Oxidation by ozone or reactive radicals

13

Reverse osmosis and nanofiltration

5

The general objective of drinking water treatment defined above can be further subdivided into four subgoals: particle removal, removal/inactivation of microorganisms, removal of dissolved inorganic substances, and removal of dissolved organic substances. Generally, efficient treatment techniques for all specific requirements are available. Some of them are able to remove groups of water constituents (e.g., suspended solids, natural organic matter), whereas others are very specific (e.g., removal of CO2 , Ca2+ /Mg2+ , or Fe2+ /Mn2+ ). Table 1.4 gives an overview of the available treatment techniques that can be applied to reach the four abovementioned subgoals, together with the reference to the book chapters in which the treatment processes are discussed in detail. It has to be noted that some of the treatment techniques are able

1.3 Treatment options

| 17

to contribute to the achievement of more than one subgoal. On the other hand, some of the goals can only be reached when different techniques are combined.

1.3.2 Brief characterization of the most important treatment processes In this section, the most important treatment processes will be briefly characterized with respect to their principles and effects. Riverbank filtration (more general: bank filtration) and infiltration use natural processes during a subsurface water transport to improve the raw water quality by mixing, filtration, biodegradation, and sorption. In particular, particles and dissolved organic substances are removed. Bank filtration is typically used in cases where polluted river water serves as the raw water source for drinking water production. Infiltration of surface water is used for groundwater recharge and sometimes applied in combination with bank filtration. The attenuation processes during infiltration are, in principle, the same as in riverbank filtration. Filtration processes are used to remove solid particles that are present in the raw water or are produced during other treatment processes (e.g., deironing/demanganization). Sand and gravel are the typical filter media. In slow sand filters, biological processes that reduce the content of organic water constituents also take place. Sedimentation can also be used to remove particles. Since the required sedimentation time strongly depends on the particle size, sedimentation is particularly suitable for larger particles. Coagulation and flocculation are chemical processes that lead to an increase of the particle size of colloids and small suspended solids by different mechanisms (destabilization of the colloidal solution, particle aggregation). To initiate these processes, inorganic coagulants (aluminum or iron salts) and organic polymer flocculants have to be added to the water. Coagulation/flocculation is used as a pretreatment step to improve the efficiency of a subsequent filtration or sedimentation step. The membrane processes microfiltration and ultrafiltration, which are able to remove particles, are modern alternatives to the conventional filtration or sedimentation techniques. Gas–liquid exchange processes are used for different purposes. They can be further subdivided into absorption and desorption (stripping) processes, where absorption is the introduction of gases into the aqueous phase and desorption is the removal of dissolved gases (or volatile substances) from the aqueous phase. The introduction of air (aeration) or ozone gas into the water by absorption is necessary for oxidation processes (e.g., deironing/demanganization, oxidation of organic water constituents), whereas the gases chlorine or chlorine dioxide are introduced as disinfectants. Air can also be used as a stripping gas to remove dissolved gases or volatile substances from the water (e.g., CO2 , H2 S, CH4 , and volatile organic compounds).

18 | 1 Introduction

The objective of deacidification is to remove excess concentrations of the corrosive carbon dioxide and to achieve the state of calco–carbonic equilibrium. This can be done mechanically by stripping with air or chemically by conversion of the CO2 to hydrogencarbonate by hydroxides or carbonates. Softening comprises all measures that are applied to reduce the hardness of water, where the focus can be on the total hardness (Ca2+ and Mg2+ ) or especially on the carbonate hardness (fraction of the total hardness that is equivalent to the hydrogencarbonate concentration). Often, reducing the carbonate hardness (also referred to as dealkalization) is the primary goal, because the carbonate hardness is responsible for scale formation during water heating (precipitation of calcium carbonate). A number of different treatment techniques can be used to reduce the hardness, in particular chemical precipitation (e.g., with hydroxides), ion exchange, or membrane processes (nanofiltration). The objective of deironing and demanganization is to remove dissolved iron and manganese (Fe2+ , Mn2+ ), which occur under reducing conditions, in particular in groundwater but sometimes also in reservoir waters (e.g., during stagnation periods). The ions have to be removed because they form colored precipitates (Fe(OH)3 , MnO2 ) if the redox intensity (or redox potential) of the water increases (e.g., due to the introduction of air). Since an uncontrolled oxidation in the waterworks or in the distribution system is unwanted, this oxidation coupled with a filtration has to be carried out under controlled conditions during drinking water treatment. In most cases, air is used as the oxidant; under unfavorable conditions, the use of ozone may be reasonable. Ion exchange processes are used to remove unwanted ions, for instance hardness-causing ions, nitrate, or heavy metal ions. In ion exchange, a solid exchanger material (ion exchange resin) binds the unwanted ions on its functional groups by replacing the originally bound ions (e.g., H+ , Na+ , OH− ). A combination of cation and anion exchange resins can also be applied to decrease the total salinity by the complete demineralization of a substream with subsequent blending of the treated and untreated water. Ions, as well as dissolved organic substances, can also be removed by the membrane processes nanofiltration and reverse osmosis. In contrast to the abovementioned membrane processes microfiltration and ultrafiltration, the membranes used here are dense membranes that are able to reject not only solid particles but also dissolved species. Typical applications are softening (nanofiltration) and desalination of freshwater substreams or seawater (reverse osmosis). Adsorption onto activated carbon is an efficient treatment process to remove dissolved organic substances. Although in most cases the trace organic substances are the target compounds, natural organic matter is always adsorbed in parallel. This competitive adsorption of natural organic matter reduces the capacity for the trace

1.3 Treatment options

| 19

compounds, but has also a positive effect, because NOM adsorption means a reduction of the precursor for the formation of disinfection byproducts during disinfection with chlorine. The activated carbon is applied either as powdered activated carbon in slurry adsorbers or as granular activated carbon in fixed-bed adsorbers. Adsorption processes can also be used to remove some inorganic ions, such as arsenate. In this case, special adsorbents (e.g., granular ferric hydroxide) have to be applied instead of activated carbon. Oxidation with ozone (ozonation) or with reactive radicals (advanced oxidation processes) is applied to oxidize the organic substances completely or at least partially. In particular, natural organic matter is often not completely oxidized but transformed into smaller and more polar compounds, which is beneficial for the efficiency of subsequent processes (e.g., biodegradation in sand filters or in biologically active adsorbers). Strongly oxidizing reactive radicals (e.g., ∙ OH) are partly formed from ozone during ozonation or can be produced by special processes. Disinfection is typically the last treatment step before the drinking water is distributed. The objective is to produce microbiologically safe water, which means that harmful microorganisms have to be removed or inactivated. Disinfection is frequently carried out with chlorine as the disinfectant. Alternative disinfectants are chlorine dioxide, chloramines, and ozone. The common problem of all these disinfectants consists in the formation of disinfection byproducts, although the extent of the formation and the kinds of byproducts are different for the different disinfectants and are also influenced by the water composition. UV irradiation is an alternative disinfection method that does not require the addition of chemicals but has no depot effect. The application of membrane filtration, in particular ultrafiltration, is a further alternative.

1.3.3 Treatment train examples As already mentioned, an optimal combination of treatment processes has to be found for each individual situation. Consequently, no universal treatment scheme can be given here. Instead, some selected examples for typical treatment trains are presented below with special regard to the different raw water sources. As a rule, the schemes show only a minimum configuration that is typical for the considered water source. Depending on the local requirements, deviating sequences of the treatment processes and/or additional stages may be necessary. Figure 1.10 shows a simple treatment scheme for groundwater. Groundwater often contains excess concentrations of carbon dioxide, which originates from biological processes in the soil layer and is introduced via seepage water. Therefore, a deacidification process is necessary in many waterworks that use groundwater as raw water source. Furthermore, reducing conditions are frequently found in groundwater with

20 | 1 Introduction

Groundwater

Aeration (Deacidification, Deironing, Demanganization)

Filtration Disinfection Drinking water

Fig. 1.10: Treatment of groundwater.

the consequence that dissolved iron and manganese (as Fe2+ and Mn2+ ) occur in the raw water and have to be removed by a deironing and demanganization process. Under strongly reducing conditions also methane and hydrogen sulfide can occur, which can be removed by aeration. Since aeration is also necessary for deironing and demanganization as well as for stripping of CO2 , aeration has a central relevance for groundwater treatment. Filtration after aeration is necessary to remove the oxidized iron and manganese species (Fe(OH)3 and MnO2 ). Since groundwater is typically of high microbiological quality, disinfection can be dispensed with in many cases. If necessary, UV disinfection can be used. Possible further treatment stages could be softening (in the case of very hard water) or pH adjustment with limewater (in the case of soft and acidic water). Reservoir water is often of good quality, in particular if it comes from wellprotected reservoirs, for instance from dams located in mountain regions. In this case, mainly particles and natural organic matter have to be removed by coagulation/ flocculation and filtration. Reservoir water is surface water and therefore not protected against the introduction of microorganisms. Accordingly, a final disinfection is necessary. Figure 1.11 shows a minimal configuration of a treatment train for reservoir water. Further treatment stages that have to be added if necessary are for instance adsorption (to remove biogenic taste and odor compounds), pH adjustment (in the case of very soft and acidic water as often found in woodlands), and deironing and demanganization (depending on the redox state at the water extraction level). Figure 1.12 shows an example for the treatment of lake water. As in the case of reservoir water, particle removal (here by microsieving and filtration), removal of organic substances (here by ozonation) and disinfection are of particular relevance. Ultrafiltration instead of conventional filtration and activated carbon adsorption instead of, or in addition to, ozonation are also frequently used.

1.3 Treatment options

| 21

Reservoir water

Coagulation/Flocculation

Filtration

Disinfection

Drinking water

Fig. 1.11: Treatment of reservoir water.

Lake water

Microsieving Ozonation Filtration Disinfection Drinking water

Fig. 1.12: Treatment of lake water.

Due to the strongly varying composition and quality of river water, the treatment technologies also show strong differences. Figures 1.13 to 1.15 present some typical examples. If the river water is strongly polluted and the hydrogeological conditions comply with the requirements (permeability of the subsurface), a natural pretreatment by riverbank filtration and/or infiltration is recommended to reduce the effort for the subsequent engineered treatment. Figure 1.13 shows a simple treatment train for riverbank filtrate. Deacidification is frequently necessary because bank filtrate often contains excess concentrations of CO2 due to biological processes during the subsurface transport or due to mixing with CO2 -rich groundwater from the land side. Since in most cases riverbank filtration is not able to completely remove all organic substances by biodegradation and/or sorption, the treatment train typically includes an additional adsorption and/or ozonation step. In all cases where river water or riverbank filtrate is used for drinking water production, an efficient disinfection with chlorine or chlorine dioxide is indispensable.

22 | 1 Introduction

Riverbank filtrate Ozonation Deacidification Filtration Adsorption Disinfection Drinking water

Fig. 1.13: Treatment of riverbank filtrate.

River water

Riverbank filtration

Coagulation/Flocculation

Infiltrate + Riverbank filtrate

Sedimentation Filtration

Aeration (Deacidification) Adsorption

Infiltration Disinfection Drinking water

Fig. 1.14: Treatment of bank filtrate and infiltrate.

Riverbank filtrate Aeration (Deironing/Demanganization) Coagulation/Flocculation Filtration Adsorption Disinfection Drinking water

Fig. 1.15: Treatment of riverbank filtrate containing reduced iron and manganese species.

1.3 Treatment options

|

23

Sometimes, bank filtration and infiltration are combined as shown in Figure 1.14. A specific particle removal step before infiltration is reasonable in order to avoid the filtration capacity of the infiltration pathway being exhausted too quickly. If the redox state of the water changes from oxidizing to reducing conditions during bank filtration, for instance as a result of strong oxygen consumption by biodegradation processes, iron and manganese are mobilized and have to be removed by deironing and demanganization (Figure 1.15).

2 Some basics of hydrochemistry and process engineering 2.1 Introduction For a better understanding of the theoretical basics of the various processes used in drinking water treatment, it is useful to recapitulate some fundamental definitions, laws, and relationships. This will be done in brief in the following sections. Section 2.2 gives an overview of the concentration measures used to describe the water composition and introduces the terms activity and ionic strength. Chemical reactions typically end in a state of equilibrium, which can be described by the law of mass action with the equilibrium constant as a characteristic parameter. The laws of mass action for the different types of reactions are presented in Section 2.3. Comparing the actual state of a system with the equilibrium state gives information on the possibility of a reaction. The rate of chemical reactions (reaction kinetics) can be described by different rate laws. The most important rate laws that play a role in water treatment processes are summarized in Section 2.4. The rate of many physical processes, in particular phase transfer processes, is determined by the mass transfer between the phases (e.g., water/gas, water/solid). The basics of mass transfer are discussed in Section 2.5. Section 2.6 finally presents different reactor types and some basics of process engineering.

2.2 Concentrations and activities In the practice of drinking water treatment mass concentrations are often used to describe the content of water constituents. The mass concentration of a component X, ρ ∗ (X), is defined by: m(X) (2.1) ρ ∗ (X) = VL where m(X) is the mass of X and V L is the volume of the aqueous phase. Typical units are g/L, mg/L (10−3 g/L), μg/L (10−6 g/L), and ng/L (10−9 g/L). For hydrochemical calculations, in particular equilibrium calculations, the use of molar concentrations is necessary. The molar concentration (also referred to as molarity), c(X), is defined by: n(X) (2.2) c(X) = VL where n(X) is the substance amount (number of moles). The common units are mol/L and mmol/L (10−3 mol/L). Often the abbreviation M is used for mol/L (1 M = 1 mol/L). https://doi.org/10.1515/9783110551556-002

26 | 2 Some basics of hydrochemistry and process engineering

The relationship between mass and molar concentration is given by: c(X) =

ρ ∗ (X) M(X)

(2.3)

where M(X) is the molecular weight of X (in g/mol or in mg/mmol). For establishing ion balances, it is reasonable to use the equivalent concentration. An equivalent (more precisely ion equivalent) can be thought of as that fraction of a real ion that carries the charge +1 or −1. In other words, the number of equivalents is the number of ions divided by their charge number. As a consequence, each positive equivalent compensates exactly one negative equivalent. The definition of the equivalent concentration reads: 1 n ( X) 1 z c ( X) = (2.4) z VL where z is the (absolute) charge number of the considered ion and n(1/z X) represents the amount of equivalents. The equivalent concentration can be found by multiplying the molar concentration by the charge number: 1 c ( X) = z c(X) z

(2.5)

To characterize the content of ions in a given water under consideration of their charges, the parameter ionic strength can be used. The ionic strength, I, is defined by: I = 0.5 ∑ c i z2i

(2.6)

i

In real aqueous solutions, the dissolved species are not isolated from each other but are subject to interactions. This is of particular relevance for ions, which are subject to electrostatic interactions. Due to the interactions, the species cannot act in reactions as strongly as can be expected from their measured concentration. Therefore, there is a need to distinguish between the measured concentration that is completely active in reactions only under ideal conditions (i.e., without any interactions) and an effective concentration that acts under real conditions. This effective concentration is referred to as activity. Consequently, exact hydrochemical equilibrium calculations have to be done on the basis of activities rather than concentrations. The activity, a, can be found by multiplying the molar concentration with a correction factor that is referred to as the activity coefficient, γ: a = γc

(2.7)

Note that this is a simplified definition that is suitable for practical purposes. A more rigorous thermodynamic definition requires the consideration of a standard state. In real aqueous solutions (e.g., natural waters) the activity coefficient, γ, is lower than 1 and approaches 1 with decreasing concentration. In the limiting case of an ideal

2.3 Chemical equilibria |

27

dilute solution without any interactions, the activity coefficient is 1 and the activity equals the concentration: c→0,

γ→1,

a→c

(2.8)

Activity coefficients can be calculated from the ionic strength, which summarizes the effects of concentration and charge. For the concentration range of freshwater, the Güntelberg equation is frequently used: log γ z = −0.5 z2

√I 1 + 1.4√I

(2.9)

where γ z is the activity coefficient of an ion with the charge z. In many practical cases, in particular if the concentrations are not very high (as in freshwater) and only a rough calculation is to be carried out, it is sufficient to use the concentrations instead of the exact activities.

2.3 Chemical equilibria 2.3.1 General aspects Many processes in drinking water treatment are based on phase transfer or chemical reactions, such as partitioning between the aqueous and the gas phase, acid/ base reactions, precipitation, redox reactions, and sorption/adsorption. The endpoint of these processes is an equilibrium state, where the involved compounds no longer change their concentrations. The equilibrium state is typically expressed by the law of mass action with the equilibrium constant as a characteristic parameter. The only exception are sorption/adsorption processes, where special equilibrium relationships have to be used. The following sections present the basic facts of the different reactions and their specific equilibrium relationships in a condensed form. The text is based on the respective chapters of the author’s hydrochemistry textbook (Worch, 2015), which should be consulted for more detailed information. If we consider a general reaction with the reactants A and B and the products C and D, we can write the reaction equation as: νA A + νB B 󴀕󴀬 νC C + νD D

(2.10)

where νA , νB , νC , and νD are the respective stoichiometric factors. The corresponding law of mass action reads: ν ν (aC )eqC (aD )eqD K∗ = (2.11) νA νB (aA )eq (aB )eq where K ∗ is the thermodynamic equilibrium constant. K ∗ depends on the temperature and is often given for a standard temperature of 25 °C.

28 | 2 Some basics of hydrochemistry and process engineering Given that the activities are related to the molar concentrations by a = γ c (Section 2.2) with γ as the activity coefficient, Equation (2.11) can be rewritten in a form that allows the use of measurable concentrations in equilibrium calculations: ν

K∗

ν

(cC )eqC (cD )eqD (γA )νA (γB )νB = K = ν ν (γC )νC (γD )νD (cA )eqA (cB )eqB

(2.12)

The constant K is referred to as the conditional constant, because it is valid only for a specific condition characterized by specific values of the activity coefficients or, due to the relationship between ionic strength and activity coefficients, by a specific ionic strength. Accordingly, the conditional equilibrium constant K depends not only on the temperature but also on the ionic strength of the aqueous solution. With decreasing concentrations (c → 0, γ → 1), the difference between K ∗ and K vanishes. If approximate solutions are sufficient, ideal conditions can be assumed and concentrations can be used in the law of mass action together with the thermodynamic constant. With respect to the formulation of the law of mass action, the following rules have to be considered: – The concentrations of dissolved species are written as molar concentrations or as respective activities. – If gases are involved, it may sometimes be reasonable to use the partial pressure of the gas over the solution instead of the molar concentration in the solution. Both are related by Henry’s law (Section 2.3.2). – Pure solid phases in contact with water do not have to be considered in the law of mass action. – Water as the solvent is the excess component in aqueous systems. Its concentration does not change markedly, even if it takes part in a reaction. By convention, this constant concentration is included in the equilibrium constant and does not therefore have be written in the law of mass action. If a considered system is not in the state of equilibrium, the direction in which the reaction has to proceed to reach the equilibrium can be found by comparing the so-called reaction quotient with the equilibrium constant. The reaction quotient is defined formally in the same way as the equilibrium constant, but in contrast to the equilibrium constant, it is more general and not restricted to equilibrium activities (or concentrations). Instead, it includes the actual activities or concentrations that are measured in the considered system. For the general reaction given in Equation (2.10), the reaction quotient reads: (aC )νC (aD )νD Q= (2.13) (aA )νA (aB )νB In nonequilibrium states, Q is higher or lower than K ∗ . In the state of equilibrium, the actual activities equal the equilibrium activities and Q equals K ∗ . The different cases and the resulting consequences for the direction of the reaction are listed in Table 2.1.

2.3 Chemical equilibria | 29

Tab. 2.1: Assessment of aqueous systems with respect to the establishment of equilibrium by comparison of Q and K ∗ . Condition Q
K∗

Direction of reaction Reaction proceeds spontaneously in the direction as written in the reaction equation (from left to right) Equilibrium state, no reaction Reaction proceeds spontaneously in the reverse direction (from right to left)

2.3.2 Gas–water partitioning Gas–water partitioning plays an important role in all water treatment processes, where gases have to be introduced into the water (e.g., during deironing/demanganization, ozonation, disinfection) or dissolved gases or other volatile substances have to be stripped (e.g., during deacidification, stripping of methane and H2 S, stripping of volatile organic compounds). Although gas–water partitioning is not a real chemical reaction but a phase transfer process, its equilibrium state can be formally described as a reaction equilibrium by using the law of mass action. Taking an arbitrary gas A as an example, the dissolution of A in the aqueous phase (absorption) can be written as: A(g) 󴀕󴀬 A(aq) (2.14) If the content of the gas A in the gas phase is expressed by its partial pressure, and the concentration of the dissolved gas is given as the molar concentration, the formal law of mass action reads: c(A) H(A) = (2.15) p(A) This law is also known as Henry’s law and, accordingly, the equilibrium constant in this special case is referred to as the Henry constant and abbreviated with H instead of the common K for equilibrium constants. Typically, Henry’s law is written in the form: c(A) = H(A) p(A) (2.16) The unit of H in this case is mol/(L ⋅ bar). If Henry’s law is written in the form of Equation (2.16), increasing Henry constants indicate an increasing solubility. As with other equilibrium constants, the Henry constant depends on the temperature. Generally, the solubility of gases increases with decreasing temperature. Alternatively, the reaction equation can be formulated for the reverse process (desorption) in the form: A(aq) 󴀕󴀬 A(g) (2.17) In this case, the law of mass action has to be written as: Hinv (A) =

p(A) c(A)

(2.18)

30 | 2 Some basics of hydrochemistry and process engineering

or p(A) = Hinv (A) c(A)

(2.19)

where Hinv (A) is the inverse of the equilibrium constant H(A): Hinv (A) =

1 H(A)

(2.20)

In contrast to H, increasing Hinv indicates increasing volatility. It has to be noted that both ways of writing Henry’s law can be found in the literature and often the same abbreviation H (without a qualifier) is used, which may cause confusion. It is therefore important to notice the unit when Henry constants are taken from literature or databases. For some applications (e.g., establishing of mass balances), it is reasonable to use the same concentration unit for the gas and the aqueous phase, for instance molar or mass concentrations. The partial pressure of a gas A in a gas mixture is related to its molar concentration in the gas phase, c g , by the following equation that can be derived from the state equation of an ideal gas: p(A) =

n g (A) R T = c g (A) R T Vg

(2.21)

where n g is the substance amount in the gas phase, V g is the gas phase volume, R is the universal gas constant (8.3145 × 10−2 L ⋅ bar/(mol ⋅ K)), and T is the absolute temperature. Substituting the partial pressure in Equation (2.16) by Equation (2.21) and introducing the subscript aq for the aqueous phase gives: caq (A) = H(A) R T c g (A) = K c (A) c g (A)

(2.22)

where K c is a dimensionless distribution constant that is related to H by: K c (A) = H(A) R T

(2.23)

With the molecular weight, M(A), of the gas A, we can also write: K c (A) =

caq (A) caq (A) M(A) ρ ∗aq (A) = = ∗ c g (A) c g (A) M(A) ρ g (A)

(2.24)

Accordingly, the value of K c is not only valid for the ratio of the molar concentrations but also for the ratio of the mass concentrations.

2.3.3 Acid/base equilibria The relevance of acid/base equilibria for aqueous systems results from the fact that numerous water constituents are acids or bases according to Brønsted’s acid/base theory. Moreover, water and its dissociation products H+ and OH− are involved in acid/

2.3 Chemical equilibria | 31

base reactions as well. Functional groups on solid surfaces (e.g., natural minerals, ion exchange resins) can also react as acids or bases. Since, according to Brønsted’s acid/base theory, the definition of acids and bases is based on the capability to donate or accept protons (H+ ), the pH as a measure of the proton activity (or concentration) plays an important role in all acid/base systems. The pH determines the concentration distribution of conjugate acid/base pairs. This is particularly relevant for weak acids and bases, which are not completely deprotonated or protonated over the whole pH range. In water treatment, a controlled pH change can be utilized to influence the water quality by shifting acid/base equilibria. According to Brønsted’s acid/base theory, acids are defined as species that are able to donate protons, whereas bases are defined as species that are able to accept protons. Accordingly, acids are proton donors and bases are proton acceptors. The process of proton release is also referred to as deprotonation, whereas the process of proton acceptance is referred to as protonation. According to the general equation Acid 󴀕󴀬 H+ + Base

(2.25)

an acid is always related to a base and vice versa. The dissociation of an acid HA (where A stands for an arbitrary anion) can be written as: HA 󴀕󴀬 H+ + A− (2.26) and the respective law of mass action reads: K ∗a =

a(H+ ) a(A− ) a(HA)

(2.27)

where K ∗a is the (thermodynamic) acidity constant. Introducing the conditional acidity constant, K a , the law of mass action can be written using concentrations instead of activities: c(H+ ) c(A− ) Ka = (2.28) c(HA) Note that for dilute solutions the difference between K ∗a and K a diminishes. Since the acidity constants extend over a wide range, a logarithmic notation (p notation) is frequently used: pK ∗a = − log K ∗a (2.29) It follows from Equation (2.29) that a large value of the acidity constant, K ∗a , corresponds to a low value of pK ∗a and vice versa. The acidity constant quantifies the degree of dissociation. The larger the value of K ∗a , the higher the degree of dissociation or, in other words, the more the equilibrium described by Equation (2.25) is shifted to the right and the more protons are released. Weak and strong acids can be distinguished by the value of K ∗a . Strong acids are characterized by large values of the acidity constant, K ∗a and low values of pK ∗a . Very strong acids dissociate completely. In contrast,

32 | 2 Some basics of hydrochemistry and process engineering weak acids with low values of K ∗a (high values of pK ∗a ) show only a partial dissociation, the extent of which depends on the pH. As a consequence, the undissociated acid and the anion (the dissociation product) coexist in the solution over a wide pH range. The pH-dependent acid/base speciation for a monoprotic acid HA (an acid that releases only one proton) can be found by rearranging the law of mass action. For the fraction of the anion, f(A− ), we find: f(A− ) =

c(A− ) 1 = + c(HA) 10pK a −pH + 1

c(A− )

(2.30)

The fraction of the undissociated acid is given by f(HA) = 1− f(A− ). The NH+4 /NH3 speciation shown in Chapter 1 (Section 1.2.5, Figure 1.7) is an example of the application of Equation (2.30). In the case of polyprotic acids, the laws of mass action for the different dissociation steps have to be combined with a material balance equation. For an acid H2 A that can release two protons, the material balance equation reads: ctotal = c(H2 A) + c(HA− ) + c(A2− )

(2.31)

After introducing the laws of mass action for the first and the second dissociation step, we get: c(H2 A) K a1 c(H2 A) K a1 K a2 ctotal = c(H2 A) + + (2.32) c(H+ ) c2 (H+ ) The fraction of the undissociated acid (f = c(H2 A)/ctotal ) can be found from Equation (2.32) after factoring out c(H2 A) and rearranging the equation. The fractions of the other species are available in an analogous manner. In the same way, the speciation of acids with more than two protons can also be calculated. Examples are shown in Figures 1.4, 1.5, and 1.8 (Chapter 1, Section 1.2.5). For a base B, we can write: B + H2 O 󴀕󴀬 BH+ + OH−

(2.33)

where BH+ stands for the protonated base. According to the conventions mentioned in Section 2.3.1 (inclusion of c(H2 O) in the constant), the law of mass action related to Equation (2.33) reads: a(BH+ ) a(OH− ) K ∗b = (2.34) a(B) or c(BH+ ) c(OH− ) (2.35) Kb = c(B) where K ∗b is the thermodynamic basicity constant and K b is the conditional basicity constant. Analogous to the acidity constant, a logarithmic form of the basicity constant can be defined by: pK ∗b = − log K ∗b (2.36)

2.3 Chemical equilibria | 33

Water itself dissociates to a small extent into protons and hydroxide ions: H2 O 󴀕󴀬 H+ + OH−

(2.37)

The law of mass action for the water dissociation is given by: K ∗w = a(H+ ) a(OH− )

(2.38)

where K ∗w is the dissociation constant of water, which has a value of 1 × 10−14 mol2 /L2 at 25 °C. The constant K ∗w , also referred to as ion product of water, is frequently given in logarithmic form as: pK ∗w = − log K ∗w (2.39) If the activities (or, simplifying, the concentrations) of the protons and the hydroxide ions are described by the parameters pH and pOH according to: pH = − log a(H+ ) ≈ − log c(H+ )

(2.40)

pOH = − log a(OH− ) ≈ − log c(OH− )

(2.41)

and then Equation (2.38) can also be written in the form: pK ∗w = pH + pOH

(2.42)

with pK ∗w = 14 at 25 °C. Combining the laws of mass action (Equations (2.27) and (2.34)), a relationship between the acidity constant and the basicity constant of the conjugate base (B = A− ) can be derived: K ∗a K ∗b =

a(H+ ) a(A− ) a(HA) a(OH− ) = a(H+ ) a(OH− ) = K ∗w a(HA) a(A− )

(2.43)

This relationship can also be expressed in logarithmic form as: pK ∗a + pK ∗b = pK ∗w

(2.44)

2.3.4 Precipitation/dissolution equilibria Precipitation processes can be used in drinking water treatment to remove unwanted ions. The reaction equation for the precipitation/dissolution equilibrium of a solid Cm A n consisting of the cation Cn+ and the anion Am− is: Cm An(s) 󴀕󴀬 m Cn+ + n Am−

(2.45)

where m and n are the stoichiometric factors. Due to the electroneutrality condition, the charges of the ions must be reflected in the opposite stoichiometric factors. The

34 | 2 Some basics of hydrochemistry and process engineering

reaction from left to right describes the dissolution, whereas the reaction from right to left describes the precipitation. The law of mass action related to Equation (2.45) reads: ∗ Ksp = a m (Cn+ ) a n (Am− ) (2.46) ∗ is the thermodynamic solubility product constant. As mentioned in Secwhere Ksp tion 2.3.1, the solid does not occur in the law of mass action. After introducing the conditional solubility product constant, the law of mass action can be rewritten as:

Ksp =

∗ Ksp

γ m (Cn+ ) γ n (Am− )

= c m (Cn+ ) c n (Am− )

(2.47)

∗ ; otherwise K ∗ has to be corrected by the acIn ideal dilute solutions, Ksp equals Ksp sp ∗ (or K ), often the solubility exponent is tivity coefficients to find Ksp . Instead of Ksp sp used which is defined by: ∗ ∗ = − log Ksp pKsp

pKsp = − log Ksp

(2.48)

The solubility product depends on the temperature, but in a nonuniform manner. Often, but not always, the solubility product increases with increasing temperature. The solubility product as an equilibrium constant should not be confused with the solubility, csat , which describes the amount of a solid that can be dissolved (saturation concentration). A relationship between both parameters can be derived from the law of mass action and material balance equations. For an arbitrary solid with the composition C m An , this relationship reads: csat =

√

m+n

Ksp mm nn

(2.49)

∗ (or K ) and the lower the value of pK ∗ , the Generally, the greater the value of Ksp sp sp higher is the solubility of the considered solid. The precondition for precipitation can be derived from Equation (2.46) or Equation (2.47). Precipitation is possible if the product of the actual activities (or concentrations) in the aqueous phase is higher than the solubility product (Table 2.1). Two points with relevance for practical processes are noteworthy. First, the solubility increases with increasing ionic strength, which means that at higher ionic strengths higher amounts of precipitation agent are necessary to get the same degree of precipitation. This can be derived from the trends of the activity coefficients and conditional constants with increasing ionic strength. If the ionic strength increases, the values of the respective activity coefficients decrease (γ < 1). Accordingly, Ksp and csat increase (Equations (2.47) and (2.49)). Second, the solubility increases if a side reaction consumes the anion or the cation on the right-hand side of Equation (2.45). According to Le Chatelier’s principle, the decrease of the concentration of a product component will shift the equilibrium to the product side to compensate for the

2.3 Chemical equilibria | 35

concentration decrease. As a consequence, more solid is dissolved. In this case, the relationship between solubility and solubility product is more complex than given in Equation (2.49) and additionally requires consideration of the law of mass action for the side reaction. Carbonate ions released during dissolution of solid carbonates, as an example, are subject to acid/base reactions (transformation of CO2− 3 into HCO−3 and CO2 dependent on pH; see also Figure 1.4 in Chapter 1). Accordingly, the solubility of carbonates increases strongly with decreasing pH (increasing degree of transformation of CO2− 3 ).

2.3.5 Redox reactions With respect to the quantitative description of redox equilibria, we have to distinguish between half-reactions (or half-cell reactions) and complete redox reactions. Half-reactions describe the electron transfer between the components of a redox couple according to: Ox + n e e− 󴀕󴀬 Red (2.50) where Ox is the oxidant, Red is the reductant and n e is the number of the transferred electrons. The oxidant (or oxidizing agent) gains electrons and will be reduced during the reaction, whereas the reductant (or reducing agent) loses electrons and will be oxidized. Accordingly, the reaction from left to right is a reduction (gain of electrons, decrease of oxidation state), whereas the reaction from right to left is an oxidation (loss of electrons, increase of oxidation state). Oxidant and reductant are also referred to as electron acceptor and electron donor, respectively. The degree of oxidation of an atom in a pure substance or in a compound is characterized by the oxidation state, also referred to as the oxidation number. This number, which can be positive, negative, or zero, is assigned to the atom either as an Arabic numeral over the atom symbol in the chemical formula or as a Roman numeral in brackets behind the atom symbol. Although half-reactions with free electrons do not reflect the real situation in water where free electrons do not occur, this formal approach provides the basis for the definition of the master variable redox intensity, which gives information about the redox state and the ratio of oxidants and reductants in a considered aqueous system. A complete redox reaction describes the electron transfer from one redox couple to another. Therefore, a complete redox system consists of two redox couples where the electrons released in one half-reaction are accepted by the other half-reaction according to: Ox1 + Red2 󴀕󴀬 Red1 + Ox2 (2.51) The law of mass action related to the half-reaction (Equation (2.50)) reads: K∗ =

a(Red) a(Ox) a n e (e− )

(2.52)

36 | 2 Some basics of hydrochemistry and process engineering

For the negative logarithm of the activity of the electrons, a new parameter is introduced that is referred to as the redox intensity, pe: pe = − log a(e− )

(2.53)

Writing Equation (2.52) in a logarithmic form and applying the definition of the redox intensity gives, after rearrangement: pe =

1 1 a(Ox) log K ∗ + log ne ne a(Red)

(2.54)

After introducing the standard redox intensity, pe0 , according to: pe0 =

1 log K ∗ ne

(2.55)

1 a(Ox) log ne a(Red)

(2.56)

we finally find: pe = pe0 +

From this equation, we can derive that the parameter pe is directly related to the activities of the components of the redox couple. For a given pe0 (or equilibrium constant), the value of pe determines the activity ratio of oxidant and reductant in a considered aqueous system. It has to be noted that Equation (2.56) was derived on the basis of Equation (2.50), which describes the simplest case of a redox system. However, redox half-reactions are frequently more complex and include, besides the oxidant and the reductant, also water and water related species (H2 O, H+ , OH− ), for instance: +2

+3

Fe(OH)3(s) + 3 H+ + e− 󴀕󴀬 Fe2+ + 3 H2 O

(2.57)

The law of mass action is given here by: K∗ =

a(Fe2+ ) a3 (H+ ) a(e− )

(2.58)

and after introducing the definitions of pe0 and pe, we find: pe = pe0 + log

a3 (H+ ) a(Fe2+ )

(2.59)

Two points are noteworthy. First, not only the reductant and the oxidant but also other species taking part in the reaction have to be considered in the formulation of the equation for pe, because the latter is a derivate of the law of mass action. Second, according to the rules for establishing the law of mass action (Section 2.3.1), H2 O and solids (even if they are reductant or oxidant) are not considered in the equation. To generalize Equation (2.56), we can write: pe = pe0 +

1 Πa ν (Ox) log ne Πa ν (Red)

(2.60)

2.3 Chemical equilibria | 37

where Πa ν (Ox) and Πa ν (Red) are the products of the activities of all relevant species on the oxidant side and on the reductant side of the reaction equation, with the respective stoichiometric factors,ν, as exponents of the activities. As with other laws of mass action, the activities can be replaced by the concentrations in the case of dilute solutions. The standard redox intensities, pe0 , are well known for all relevant redox couples in aqueous systems. The redox intensity is an important water quality parameter, because it is related to the redox state of the water. Low values of pe indicate reducing conditions under which the reduced partners of redox couples (the reductants) dominate, whereas high values of pe indicate oxidizing conditions under which the oxidized partners (the oxidants) dominate. In practice, often the directly measurable redox potential (in volts) is given instead of the redox intensity. The relation between the redox potential and the activities of the oxidant and the reductant is given by the Nernst equation: E H = E0H +

Πa ν (Ox) 2.303 R T log ne F Πa ν (Red)

(2.61)

where E0H is the standard redox potential, R is the universal gas constant (8.3145 J/(mol ⋅ K)), T is the absolute temperature, n e is the number of the transferred electrons, and F is the Faraday constant (F = 96 485 C/mol). To quantify potentials, a reference state is needed. By definition, the potentials E H and E0H are potentials relative to the standard hydrogen electrode (proton activity of 1 mol/L and hydrogen partial pressure of 1 bar) as reference. This reference electrode corresponds to the half-reaction: +1 +

±0

H + e− 󴀕󴀬 1/2 H 2(g)

(2.62)

for which it holds that E0H = 0 and, accordingly, log K ∗ = pe0 = 0. If we compare Equation (2.60) with Equation (2.61), we can easily derive a relationship between the redox intensity, pe, and the measurable redox potential, E H : pe =

F EH 2.303 R T

(2.63)

The same relationship holds for the standard values, pe0 and E0H : pe0 =

F E0 2.303 R T H

(2.64)

The conversion factors for 25 °C and 10 °C are: 1 EH 0.059 V 1 EH pe = 0.056 V

pe =

T = 298.15 K

(2.65)

T = 283.15 K

(2.66)

38 | 2 Some basics of hydrochemistry and process engineering

A complete redox reaction combines two half-reactions in such a manner that free electrons no longer occur in the overall reaction equation: Ox1 + n e e− 󴀕󴀬 Red1

(2.67) −

(2.68)

Ox1 + Red2 󴀕󴀬 Red1 + Ox2

(2.69)

Red2 󴀕󴀬 Ox2 + n e e

The law of mass action for the complete redox reaction reads: K∗ =

a(Ox2 ) a(Red1 ) a(Red2 ) a(Ox1 )

(2.70)

The equilibrium constant K ∗ of the complete redox reaction is related to the standard redox intensities of the half-reactions as can be easily derived from the equilibrium condition (pe1 = pe2 ) and the redox intensity equations for both half-reactions: pe01 +

1 a(Ox1 ) 1 a(Ox2 ) log log = pe02 + ne a(Red1 ) ne a(Red2 )

(2.71)

Here, it is assumed that the half-reactions are written in such a manner that the same number of electrons, n e , is transferred. Rearranging Equation (2.71) leads to: n e (pe01 − pe02 ) = log

a(Ox2 ) a(Ox1 ) a(Ox2 ) a(Red1 ) − log = log a(Red2 ) a(Red1 ) a(Red2 ) a(Ox 1 )

(2.72)

Given that the quotient on the right-hand side equals the equilibrium constant (Equation (2.70)), we receive the following relationship that links the equilibrium constant of the complete redox reaction with the standard redox intensities of the halfreactions: log K ∗ = n e (pe01 − pe02 ) (2.73) Accordingly, the equilibrium constant (and therefore the degree of conversion) of a complete redox reaction is greater the greater the difference between the standard redox intensities of the half-reactions is. For the oxidation processes in water treatment, we can conclude that the standard redox intensity (or standard redox potential) of an appropriate oxidant should be much higher than the standard redox intensities of the substances to be oxidized. Efficient oxidizing agents are therefore characterized by high standard redox intensities (see for instance Table 13.1 in Chapter 13).

2.3.6 Sorption/adsorption The term sorption is a generic term that describes the accumulation of dissolved species on a solid surface or within the solid material. It includes the surface processes adsorption and ion exchange as well as the uptake within the interior of the solid phase (absorption). The latter is of minor relevance and occurs only in some

2.3 Chemical equilibria |

39

specific cases (e.g., uptake of dissolved species within natural solid organic material). Therefore, sorption is mainly a surface process. Natural sorbents are often referred to as geosorbents. Accordingly, the term geosorption is sometimes used for natural sorption processes. Sorption is one of the attenuation processes that play a role in riverbank filtration and surface water infiltration where the water comes into contact with natural solid material. For engineered processes that take place only on the surface of a solid material, the term adsorption is typically used, where ‘surface’ explicitly includes the internal surface within a pore system of the solid. The typical example for an engineered adsorption process in drinking water treatment is the application of activated carbon to remove organic substances from the water. Although chemical reactions are possible between functional groups of the solid material (sorbent/adsorbent) and dissolved substances (sorbate/adsorbate), often physical processes act in parallel or even dominate the overall accumulation process. The latter is particularly true for activated carbon adsorption, which is mainly a nonstoichiometric physical adsorption. Since mixed mechanisms or pure physical interactions cannot be described by the law of mass action, other equations, such as the well-known isotherm equations, are typically used to describe sorption/adsorption equilibria. Sorption onto natural sorbents in the relevant concentration range is characterized by relatively weak interactions and can be described in many cases by a simple linear relationship between the sorbed amount, qeq , and the concentration, ceq : qeq = K d ceq

(2.74)

with K d as the characteristic isotherm parameter. K d is referred to as the distribution or partition coefficient. The common unit is L/g. There is obviously an analogy to the gas/water partitioning (Section 2.3.2). Equation (2.74) is therefore often referred to as the Henry isotherm. Adsorption onto engineered adsorbents, such as activated carbon, is much stronger than geosorption and is typically characterized by nonlinear equilibrium relationships. The isotherm equation, which is most frequently used to describe the adsorption from aqueous solutions, is the Freundlich isotherm: n qeq = K F ceq

(2.75)

where K F is the Freundlich coefficient and n is the Freundlich exponent. The parameter K F characterizes the adsorption strength (the greater the K F the stronger the sorption). The exponent n describes the curvature of the isotherm. n values much lower than 1 are typical for favorable isotherms, which are isotherms that show relatively high adsorption even at low concentrations. In some cases, the use of the Langmuir isotherm may be suitable. The Langmuir isotherm equation reads: q m K L ceq qeq = (2.76) 1 + K L ceq

40 | 2 Some basics of hydrochemistry and process engineering

where K L is the Langmuir coefficient and q m is the maximum value of the adsorbed amount. As a rule, sorption or adsorption equilibrium data have to be determined experimentally. Only under special conditions can K d be predicted from empirical correlations (Chapter 3). In contrast to adsorption, engineered ion exchange is a stoichiometric reaction that can be described with the law of mass action (Chapter 11). Nevertheless, sometimes also isotherm equations are used to describe ion exchange equilibria.

2.4 Reaction kinetics The term reaction kinetics comprises the study and mathematical description of the rate of chemical reactions. Reaction kinetics plays an important role in reactor design, because it determines the residence time of the reacting species in a reactor that is necessary to reach a certain degree of conversion. The general definition of the reaction rate, r i , of the considered reactant or product reads: 1 dc i ri = (2.77) ν i dt where dc i / dt is the change of concentration over time and ν i is the stoichiometric factor of the reactant or product in the reaction equation. The stoichiometric factor can be positive or negative depending on whether the substance is produced or consumed. The reaction rate, r i , can be expressed by the respective rate laws. The different forms of rate laws are classified by their order, which is the sum of the exponents of the concentration terms occurring in the rate law. With respect to water treatment processes, the most important rate laws are the first-order rate law and the second-order rate law. Other rate laws, such as zero-order or third-order rate laws as well as rate laws for complex reactions (parallel or sequential reactions) will not be discussed here. If necessary, special textbooks on chemical kinetics should be consulted. Generally, a reaction mechanism can either consist of only one elementary reaction, or of a number of coupled elementary reactions. For elementary reactions, simple rate laws can be derived directly from the stoichiometry of the reaction equation. For overall reactions based on complex reaction mechanisms, it is not easy to derive rate laws only from theoretical considerations. Here, appropriate rate laws can be found by kinetic experiments and testing of different equations. However, it has to be noted that complex reactions can often be described by simple rate laws. Accordingly, the applicability of the rate laws discussed in the following paragraphs is not restricted to the simple elementary reactions from which they were derived. First-order rate laws can be found for elementary reactions of the type: A → Product(s)

(2.78)

2.4 Reaction kinetics

| 41

The corresponding first-order rate law that describes the decrease of the concentration of A with time reads: dc(A) = k 1 c(A) (2.79) r(A) = − dt Accordingly, the concentration decrease of A depends on the actual concentration of A at the time t. The constant k 1 is the first-order rate constant, which has the unit 1/s. Integration with the initial condition t = 0, c(A) = c0 (A) leads to the equation: c(A) = e−k1 t c0 (A)

(2.80)

The half-life, t0.5 , which is the time required to reduce the concentration to the half of its initial value, is then: t0.5 =

ln 2 0.693 1 c0 (A) = ln = k1 0.5 c0 (A) k1 k1

(2.81)

A number of reactions relevant for water treatment, such as degradation or transformation reactions, follow a first-order rate law. Second-order rate laws are related to elementary reactions of the type: 2 A → Products

(2.82)

A + B → Products

(2.83)

or The respective rate laws with respect to the consumption of A are: 1 dc(A) = k 2 c2 (A) 2 dt

(2.84)

dc(A) = k 2 c(A) c(B) dt

(2.85)

r(A) = − and r(A) = −

The second-order rate constant, k 2 , has the unit L/(mol ⋅ s). It has to be noted that the constant stoichiometric factor (νA = 2 in Equation (2.84)) is often included in the rate constant. Integration of Equation (2.84) gives: 1 1 − = 2 k2 t c(A) c0 (A)

(2.86)

with the corresponding expression for the half-life: t0.5 =

1 2 k 2 c0 (A)

(2.87)

Integration of Equation (2.85) leads to: ln

c(A) c0 (B) = (c0 (A) − c0 (B)) k 2 t c(B) c0 (A)

(2.88)

42 | 2 Some basics of hydrochemistry and process engineering

with the respective expressions for the half-lives related to A or B: c0 (A) ) c0 (B) t0.5 (A) = k 2 (c0 (B) − c0 (A)) ln (2 −

c0 (B) ) c0 (A) t0.5 (B) = k 2 (c0 (A) − c0 (B))

(2.89)

ln (2 −

(2.90)

In the reaction described by Equation (2.83), both reactants A and B are consumed. A special case of this reaction type occurs when one of the reactants (e.g., B) is not consumed or consumed only to a negligible extent. This could be the case, for instance, if B is a catalyst that is not consumed during the reaction or B is an excess component whose consumption is negligible in comparison to its total concentration in the system. In such cases, the constant concentration of B can be included in the rate constant with the result that the rate law becomes a pseudo-first-order rate law: r(A) = −

dc(A) = k 2 c(A) c(B) = k ∗1 c(A) dt

(2.91)

with k ∗1 = k 2 c(B)

(2.92)

Finally, it has to be noted that comparable rate laws can also be formulated for the change of the concentration of particles or microorganisms with time (given as number per volume or mass per volume), for instance to describe coagulation/flocculation, filtration, or disinfection kinetics.

2.5 Mass transfer Several processes used in drinking water treatment include the transfer of a substance from one phase to another (e.g., gas to liquid, liquid to gas, liquid to solid). Typical examples are gas/water exchange (e.g., aeration, ozonation, chlorination, stripping of CO2 and other dissolved gases) as well as adsorption and ion exchange. The rate of such phase transfer processes is typically determined by mass transfer across the interface. In the most general sense, mass transfer is defined as the transport of a substance from one point to another caused by a driving force. In most cases, the mass transfer is based on diffusion and the driving force is given by a concentration difference. That means that the mass transfer proceeds from the location with the higher concentration to the location with the lower concentration. The mass transfer of a solute is typically expressed by the mass flux, N, which is the substance amount, n (in moles), transferred in a given time, t, across an area, A: n N= (2.93) At

2.5 Mass transfer

| 43

The flux is related to the molar flow rate, ṅ (= n/t), by: N=

ṅ A

(2.94)

Given that the driving force is a concentration difference, a general mass transfer equation can be written as: ṅ (2.95) N = = k m ∆c A where k m is the mass transfer coefficient. The mass transfer coefficient (unit: m/s) is a reciprocal measure of the mass transfer resistance. That means, the lower the mass transfer resistance, the greater k m , and the higher the flux at a given driving force, ∆c, and area, A. Mass transfer coefficients for different reactors and process conditions have to be determined experimentally or can be estimated from empirical correlations. To calculate the molar flow rate, the flux has to be multiplied with the area available for the mass transfer. It is common practice to normalize the area available for the mass transfer, A, by the reactor volume, V R : ṅ = k m

A ∆c V R = k m aVR ∆c V R VR

(2.96)

In the case of mass transfer from one phase to another, mass transfer equations have to be formulated for both sides of the interface. In the donor phase, the driving force is the difference between the higher concentration in the bulk phase and the lower concentration at the interface, which is a result of the mass transfer to the other phase. In the receiving phase, the driving force is the concentration difference between the higher concentration at the interface, resulting from the mass uptake from the other phase and the lower concentration in the bulk phase. The change of the concentrations over the distance from the interface is assumed to be linear and to be concentrated in a small boundary layer (film). Furthermore, the concentrations at the interface are assumed to be equilibrium concentrations that are linked by the equilibrium relationship. This model, schematically shown in Figure 2.1a, is referred to as the two-film model. Given that the total substance amount that leaves phase 1 must be received by phase 2 (continuity of the substance flow), the following relationship results: N = N1 = N2 = k m,1 (c1 − c∗1 ) = k m,2 (c∗2 − c2 )

(2.97)

where c1 and c2 are the bulk concentrations and c∗1 and c∗2 are the equilibrium concentrations at the interface. In the general case, the mass transfer in both phases has to be considered, which complicates the modeling. However, often the mass transfer is much faster in one phase than in the other. For the side of the fast mass transfer, it can be assumed that there is no difference between the bulk concentration and the equilibrium concentration at the interface. Accordingly, only the slower mass transfer determines the rate of the overall process (Figures 2.1b and 2.1c).

44 | 2 Some basics of hydrochemistry and process engineering Donor phase

Receiving phase

Receiving phase

Donor phase Interface

Interface

c1 c 1 = c 1*

c1* c2*

c 2* c2

(a)

Boundary layer

c2

Boundary layer

Boundary layer

(b)

Donor phase

Boundary layer

Receiving phase Interface

c1

c 1* c 2* = c 2

(c)

Boundary layer

Boundary layer

Fig. 2.1: Graphical representation of the two-film model: general form (a) and simplified forms with negligible mass transfer resistance in the donor phase (b) or in the receiving phase (c).

(c∗2

Given that the mass transfer resistances in the receiving phase 2 can be neglected = c2 ), Equation (2.97) simplifies to: N = k m,1 (c1 − c∗1 )

(2.98)

Mass transfer equations can also be used to describe the mass transfer through membranes (Chapter 5). It has to be noted that in membrane process modeling the symbol J is commonly used for the flux instead of N. Here, we want to follow this practice. For the water transport, the flux is typically defined on the basis of volume instead of substance amount (volumetric flux, J w ): Jw =

V̇ V = AM t AM

(2.99)

where A M is the membrane area. The respective unit for J w is m3 /(m2 ⋅ s). For porous membranes as used in microfiltration and ultrafiltration, the driving force for the water flux is given by the pressure difference over the membrane (trans-

2.6 Reactor types |

45

membrane pressure), ∆p: J w = k w ∆p

(2.100)

where k w is the mass transfer coefficient, which, in this case, has the unit m/(s ⋅ bar). It is also referred to as the membrane constant. For dense membranes as used in nanofiltration and reverse osmosis, the osmotic pressure, π, influences the water flux and has to be considered in the mass transfer equation: J w = k w (∆p − ∆π) (2.101) where ∆π is the difference in the osmotic pressures on both sides of the membrane. The osmotic pressure depends on the concentration of the solutes (Chapter 5, Section 5.4.1). For solute transport through dense membranes, the common form of the mass transfer equation can be used: J s = k s ∆c (2.102) where J s is the solute flux in mol/(m2 ⋅ s) and k s is the respective mass transfer coefficient in m/s.

2.6 Reactor types 2.6.1 Introduction For the different processes in drinking water treatment, a wide variety of reactors is applied. The following section gives an overview of the most important reactor types together with some fundamental equations necessary for process modeling and reactor design. The reactors that will be described in this section are subdivided into three classes: i) reactors for homogeneous aqueous-phase reactions, ii) reactors for gas–liquid exchange, and iii) reactors for liquid–solid transfer. It has to be noted that only basic types are discussed here. Special forms and modifications are presented in context with the respective processes. One of the fundamental equations needed for process modeling is the material balance equation (MBE). Material balance equations can be established for the whole reactor volume or for finite volume elements. Which variant is suitable depends on the reactor type. The volume that is considered in the material balance is referred to as the control volume. The general form of a MBE reads: Mass change within the control volume = Mass inflow − Mass outflow + Mass change due to reaction

(2.103)

The mass change due to reaction can be positive or negative, depending on whether the component under consideration is produced or consumed.

46 | 2 Some basics of hydrochemistry and process engineering

To establish a model for the reactor design, the MBE has to be combined with an equation that describes the process rate (kinetic or mass transfer equation) and, if necessary, the equilibrium relationship. Since reaction kinetics, mass transfer, and equilibrium relationships are typically described on a molar basis, it is reasonable to establish material balance equations also on a molar basis.

2.6.2 Reactors for homogeneous reactions Following the common classification, there are three basic types of ideal reactors: the completely mixed batch reactor (CMBR), the completely mixed flow reactor (CMFR), and the plug flow reactor (PFR). A schematic representation of the reactor types with the related hydraulic and concentration characteristics is given in Figure 2.2. In this section, these basic reactor types are discussed with a focus on homogeneous liquidphase reactions. However, these reactors can also be used for heterogeneous liquid– gas, gas–liquid, or liquid–solid transfer processes as will be shown in Sections 2.6.3 and 2.6.4. A CMBR is a discontinuously operated reactor, which has no continuous inflow or outflow. Therefore, the mass change within a control volume equals the mass change CMBR c0 VR, c = f(t) t CMFR  V, cin

cin

VR, cR = cout

 V, cout

cout t

PFR dz

 V, cin

AR

 V, cout

VR, cz 0

z dV = AR dz

L

cin cout z

Fig. 2.2: Schematic representation of the three types of ideal reactors and their characteristic concentration curves. The quantities that are used to describe the hydraulic conditions are explained within the text.

2.6 Reactor types | 47

due to reaction. The concentrations of the reactants decrease and the concentrations of the products increase with time. Taking the reactor volume, V R , as the control volume, the MBE reads: dc (2.104) VR = r VR dt where the left-hand side represents the mass change in the control volume and the right-hand side represents the mass change due to the reaction with the rate r. The reaction time, t R , needed to decrease the initial concentration from c0 to an appropriate value c t , can be found by integrating Equation (2.104): ct

tR = ∫ c0

dc r

(2.105)

For instance, for a first-order degradation process with r = −k1 c, the reaction time is given by: 1 ct (2.106) t R = − ln k1 c0 In drinking water treatment, completely mixed batch reactors are seldom used within the treatment train. They are mainly applied for special purposes (e.g., preparation of solutions) or for lab-scale experiments. In contrast, completely mixed flow reactors (CMFR) are more frequently used. Under normal conditions, the rates of inflow and outflow can be assumed to be equal. Given that the mixing is perfect, the outflow concentration equals the uniform concentration in the reactor. The mean residence time, t r , equally valid for the water and the reacting species, is given by: VR tr = (2.107) V̇ where V̇ is the volumetric flow rate. Taking the reactor volume, V R , as the control volume, the general form of the material balance equation for a CMFR reads: VR

dcout = V̇ cin − V̇ cout + r V R dt

(2.108)

Typically, it is assumed that steady-state conditions exist in the reactor. That means that there is no net change in the system content and the rate of accumulation (the term on the left-hand side of Equation (2.108)) is zero: 0 = V̇ cin − V̇ cout + r V R

(2.109)

Combining Equations (2.107) and (2.109) leads to an expression that can be used to find the mean residence time that is necessary for a given reduction of the concentration: VR 1 (2.110) = − (cin − cout ) tr = ̇ r V

48 | 2 Some basics of hydrochemistry and process engineering For a first-order degradation reaction with r = −k 1 cout , we can find the following expression that relates the concentration change with the residence time: 1 cin tr = ( − 1) (2.111) k 1 cout A plug flow reactor (PFR) is a tubular reactor for which it is assumed that the residence time of each fluid element is equal. Accordingly, the fluid velocity is uniform across any cross section orthogonal to the flow direction. This assumption is approximately fulfilled under turbulent flow conditions rather than under laminar flow conditions. In a plug flow reactor, the mean residence time and therefore also the reaction time is proportional to the reactor length. The reactant concentration decreases along the reactor length. Accordingly, in all cases where the reaction rate depends on the concentration (e.g., first-order or second-order reaction), the rate also changes with the reactor length. Therefore, the material balance equation has to be formulated for a differential volume element as the control volume instead of the total reactor volume. The material balance equation for a differential volume element in a PFR, which considers the spatial and temporal changes of the concentration, reads: dc dc = −v z +r dt dz

(2.112)

where the first term on the right-hand side describes the concentration change over the differential length dz of the volume element and v z is the flow velocity in the z direction (axial direction). If the rate of the concentration change due to transport equals the rate of the concentration change due to reaction (steady state), Equation (2.112) simplifies to: − vz

dc +r=0 dz

(2.113)

Separation of the variables and integration between z = 0 (c = cin ) and z = L (c = cout ) gives: L

cout

0

cin

dz dc L VR ∫ = = tr = = ∫ ̇ vz vz r V

(2.114)

where L is the length of the reactor. For a first-order degradation reaction with r = −k 1 c, we finally get: 1 L VR cin tr = (2.115) = = ln ( ) vz k1 cout V̇ Equation (2.115) relates the degree of conversion to the residence time in the reactor.

2.6.3 Reactors for gas–liquid exchange Gas–liquid exchange plays an important role in drinking water treatment. Generally, there are two types of gas–liquid exchange processes: i) absorption (introduction of

2.6 Reactor types |

49

gases into the liquid phase) and ii) desorption or stripping (transfer of dissolved gases or volatile substances from the liquid phase to the gas phase). Absorption is typically followed by a chemical reaction in the liquid phase. The introduction of air (to oxidize Fe2+ and Mn2+ ), ozone (to oxidize organic water constituents), and chlorine or chlorine dioxide (to disinfect the water) are examples of absorption processes. Desorption (stripping) is typically carried out by means of a stripping gas (typically air) that flows through the liquid phase and receives the unwanted dissolved gases or volatile substances from the water. Examples of desorption processes are the stripping of CO2 , CH4 , H2 S, and volatile synthetic organic chemicals. The most important reactors, which are used for absorption or stripping, are shown in Figure 2.3. It has to be noted that in gas–liquid exchange sometimes the term contactor is used instead of reactor.

CMFR

 VL, cl,in

 VG, cg,out  VL, cl,out

 VG, cg,in

 VL, cl,in

 VG, cg,out

Bubble column

CMFR

 VL, cl,in

 VL, cl,in

 VL, cl,out

 VG, cg,out

Packed-bed contactor

 VG, cg,in  VL, cl,out

 VG, cg,in

 VL, cl,out

Fig. 2.3: Reactors (contactors) for gas–liquid exchange.

Completely mixed flow reactors (CMFRs) can be used to introduce gases (e.g., ozone, chlorine) but also for stripping of gases and volatile substances with air as the stripping gas. Surface aerators, a special form of CMFRs, can be used to introduce air into the liquid phase for oxidation or stripping purposes. Here, water is mechanically dispersed in the space above the liquid phase from where the formed water droplets can receive air.

50 | 2 Some basics of hydrochemistry and process engineering

Packed-tower contactors (packed-bed contactors) are columns filled with packing material. The packing material (e.g., ceramic rings or saddles) extends the contact time between the liquid and the gas phase and improves the mass transfer. Bubble contactors are columns without packing material, in which the gas streams in the form of bubbles through the liquid phase. Both types of contactors can be used for several absorption or desorption processes. The reactor operation is possible under cocurrent as well as countercurrent flow conditions. The latter is shown in Figure 2.3. Establishing material balances and design equations for the different types of reactors for gas–liquid exchange is more complex than in the cases shown in Section 2.6.2, in particular if both reaction kinetics and mass transfer are relevant (e.g., absorption followed by reaction). Within the scope of this chapter, only some simple examples will be shown to demonstrate the general principles of modeling. The liquid-phase material balance equation for gas sparging in a CMFR under steady-state conditions can be found by extending Equation (2.109). For the general case, where both mass transfer and reaction are relevant, we get: V̇ L c l,in − V̇ L c l,out + ṅ + r V R = 0

(2.116)

The molar flow, n,̇ into or out of the liquid phase has to be expressed by the respective mass transfer equation with ∆c as the difference between the equilibrium concentration and the outlet concentration, c l,out (Section 2.5). As already mentioned in Section 2.6.2, the outlet concentration, c l,out , in a CMFR equals the mean concentration in the reactor. For the reaction rate, r, the respective rate law for the reaction in the liquid phase has to be introduced. This term can be omitted in the case of stripping, where no reaction takes place. In some special cases, the balance equation can be further simplified. In the case of absorption of ozone or chlorine, it can be assumed that the liquid feed stream does not contain the gas (c l,in = 0). Accordingly, the first term can be omitted. In the case of stripping in a surface aerated CMFR, the gas phase concentration of the stripped compound can be assumed to be zero due to the large dilution. Thus, the corresponding equilibrium concentration in the liquid phase, which occurs in the mass transfer equation, must also be zero. The development of design equations for bubble contactors is even more complicated, particularly if the rate of mass transfer between the fluid and the gas bubbles has to be considered. The modeling can be simplified if it is assumed that the equilibrium between the gas phase and the liquid phase, given by Henry’s law, is established within the column. In this case, the liquid-phase material balance equation for stripping in a countercurrent flow bubble contactor is given by: c l,out V̇ L c l,in − V̇ L c l,out = V̇ G c g,out = V̇ G Kc

(2.117)

where K c is the distribution constant that is related to the Henry constant, H, by K c = H R T (Equations (2.23) and (2.24) in Section 2.3.2).

2.6 Reactor types |

51

For countercurrent packed-tower contactors, the material balance equation has to be written for a differential control volume, A R dz, where A R is the cross-sectional area of the column and dz is the differential height of the volume element. For desorption under steady-state conditions, the liquid-phase material balance equation reads: vz

dc l − k m aVR (c l − c∗l ) = 0 dz

(2.118)

where aVR is the total area available for mass transfer related to the reactor volume and c∗l is the liquid-phase concentration at the liquid/gas interface. v z is the superficial flow velocity in the z direction: v z = V̇ L /A R (2.119) More details on packed-tower contactor design can be found in Chapter 7.

2.6.4 Reactors for liquid–solid transfer Liquid–solid transfer occurs in particular during ion exchange (Chapter 11) and adsorption (Chapter 12). It also plays a role in lab-scale experiments for simulating bank filtration processes, such as sorption and sorption plus biodegradation (Chapter 3). In these processes, the dissolved species are transported from the bulk liquid to the adsorption sites or ion exchange sites within the porous solid material where they are bound. In these processes, the actual adsorption or reaction step is typically fast, and the overall process rate is determined by the mass transfer. In the most general case, both the external and internal mass transfer has to be taken into account for process modeling. This can be done, for instance, by using the two-film model approach, where one film is the boundary layer in the fluid phase and the second film is thought of as solid-phase film that represents the mass transfer resistances within the pore system of the solid particle. The reactors that can be used for liquid–solid transfer are shown in Figure 2.4. In the following paragraphs, the basic equations necessary for modeling of liquid–solid transfer are formulated independent of the specific transfer processes in a very general manner with universal symbols for the relevant quantities (concentration, mass, volume). It has to be noted that for special processes (e.g., adsorption), different symbols are more common, for instance m A (adsorbent mass) instead of the general term mass of solid, m S , or q (adsorbed amount) instead of solid-phase concentration, c s . The specific nomenclature will be introduced in the respective chapters. In practice, completely mixed batch reactors are only used for lab-scale or pilotscale experiments (e.g., determination of adsorption isotherms or ion exchange equilibria). The material balance equation for liquid–solid transfer in a CMBR reads: m S (c s − c s,0 ) = V L (c l,0 − c l )

(2.120)

where c s is the solid-phase concentration, c l is the liquid-phase concentration, m S is the solid mass and V L is the volume of the liquid phase. The solid-phase concentration

52 | 2 Some basics of hydrochemistry and process engineering

CMBR

VL, ms, c = f(t)

CMFR

  VL, ms, cl,in

  VL, ms, cl,out

 VL, cl,out

 VL, cl,in

FBR

Fluidized-bed reactor

 VL, cl,out

 VL, cl,in

Fig. 2.4: Reactors for liquid–solid transfer.

is related to the solid mass and has the dimension substance amount per mass, for instance mmol/g or μmol/g. Generally, Equation (2.120) is valid at any time t of the process. If the residence time in the CMBR is long enough, the equilibrium is established and Equation (2.120) becomes: m S (c s,eq − c s,0 ) = V L (c l,0 − c l,eq ) (2.121) Equations (2.120) and (2.121) can be further simplified if the solid concentration at the beginning of the process is zero (c s,0 = 0). If the equilibrium relationship between c s,eq and c l,eq is known, the solid dose m S /V L necessary for a desired removal rate can be calculated. Inversely, equilibrium data points for a given dose can be found by measuring the concentration decrease during the process and applying Equation (2.121). In a completely mixed flow reactor, the mean hydraulic residence time is given by: tr =

VR V̇ L

(2.122)

The material balance equation can be found from Equation (2.120) by setting c l,0 = c l,in and c l = c l,out and replacing the mass, m S , and the volume, V L , by the respective flow rates, ṁ S and V̇ L : V̇ L (c l,in − c l,out ) (2.123) cs = ṁ S In Equation (2.123), it is assumed that the solid used in the process is initially free of the substance to be removed (c s,0 = 0).

2.6 Reactor types | 53

The degree of the substance accumulation on the solid phase at a given time related to the equilibrium state can be expressed by the mean fractional uptake, F: F=

cs c s,eq

(2.124)

After introducing Equation (2.124) into Equation (2.123) and rearranging, we get the following equation for the outflow concentration: c l,out = c l,in − c s,eq

ṁ S F V̇ L

(2.125)

To apply Equation (2.125), the solid-phase equilibrium concentration has to be substituted by means of the equilibrium relationship and F has to be expressed by an appropriate mass transfer equation. If the residence time in the CMFR is long enough to reach the equilibrium state, F becomes 1 and Equation (2.125) simplifies to: c l,out = c l,in − c s,eq

ṁ S V̇ L

(2.126)

Fixed-bed reactors (FBRs) are frequently used in adsorption and ion exchange processes. The liquid–solid transfer in a fixed-bed reactor is a semicontinuous process, where a mass transfer zone travels slowly through the adsorbent or ion exchange resin bed. When the mass transfer zone reaches the end of the bed, a concentration breakthrough occurs. The breakthrough curve (BTC), c l,out = f(t), which can be measured at the reactor outlet, shows a S-shaped form starting from the breakthrough time t b and ending at the saturation time, t s , where the total capacity of the bed is exhausted and the outlet concentration equals the inlet concentration. In the most general case, the spreading of the breakthrough curve depends on the mass transfer rate and the axial dispersion. The faster the mass transfer and the lower the extent of dispersion are, the steeper the breakthrough curve is. The ideal limiting case would be a concentration step from zero to c l,in at the so-called ideal breakthrough time, tid b . Figure 2.5 shows a typical breakthrough curve of a single solute. Ideal BTC

1

cl /cl,in

Real BTC

Real breakthrough time

Time

tb

tbid

Ideal breakthrough time

Fig. 2.5: Schematic representation of a breakthrough curve (BTC).

ts Saturation time

54 | 2 Some basics of hydrochemistry and process engineering

The differential material balance equation for a fixed-bed reactor reads: vF

∂c l ∂c l ∂c s ∂2 c l + εB + ρB − D εB =0 ∂z ∂t ∂t ∂z2

(2.127)

where c l is the liquid-phase concentration, c s is the mean solid-phase concentration, z is the spatial variable in flow direction, t is the time, v F is the filter velocity, ε B is the bed porosity, ρ B is the bed density, and D is the dispersion coefficient. The terms from left to right describe the processes advection, accumulation in the liquid phase, accumulation on the solid phase (e.g., adsorption), and dispersion in the axial direction. In engineered processes with relatively high flow rates, the dispersion term can usually be neglected, because under these conditions its impact on the spreading of the breakthrough curve is negligible in comparison to the influence of slow mass transfer processes: ∂c l ∂c l ∂c s vF + εB + ρB =0 (2.128) ∂z ∂t ∂t Sometimes, the accumulation term ε B ∂c l /∂t can also be neglected. This is in particular possible when the accumulation in the liquid phase can be assumed to be small in comparison to the accumulation on the solid phase. To model the liquid–solid transfer in fixed-bed reactors, Equation (2.128) has to be combined with mass transfer equations for the external and internal mass transfer and with an equilibrium relationship that relates the solid-phase concentration to the liquid-phase concentration. This approach leads to very complex models, in particular when the frequently occurring competition effects between different solutes have to be considered. Some more detailed information on this issue is given in Chapter 12. An estimate of the ideal breakthrough time can be made on the basis of an integral material balance if the equilibrium relationship is known. If the impact of the mass transfer rate is neglected (ideal BTC), the substance amount that is fed to the reactor until the ideal breakthrough time is achieved equals the substance amount that is accumulated at the solid particles and the substance amount that is still present in the liquid phase between the solid particles: c l,0 V̇ L tid b = c s,0 m s + c l,0 ε B V R

(2.129)

where c l,0 is the inlet concentration and c s,0 is the equilibrium solid-phase concentration related to c l,0 . The filter velocity (also referred to as superficial velocity) that occurs in Equations (2.127) and (2.128) is given by: vF =

V̇ L AR

(2.130)

where A R is the cross-sectional area of the reactor. This is a formal definition based on the assumption of an empty adsorber. The effective flow velocity (interstitial velocity), u F , can be found by dividing the volumetric flow rate by the cross-sectional area

2.6 Reactor types |

55

available for water flow, which is given by the product of the cross-sectional area, A R , and the bed porosity, ε B : vF V̇ L uF = = (2.131) AR εB εB According to the different velocity definitions, different definitions for the residence time are in use. The residence time for an empty reactor with the height h is referred to as empty bed contact time, EBCT, and is given by: EBCT =

h AR VR h = = vF V̇ L V̇ L

(2.132)

The effective residence time, t r , related to the effective flow velocity, u F , is lower than the EBCT and is given by: tr =

h h AR εB VR εB = = = EBCT ε B uF V̇ L V̇ L

(2.133)

For special applications fluidized-bed reactors are also in use. Fluidized-bed reactors are operated under upstream conditions. If the upstream flow velocity of the liquid phase is slightly greater than the terminal settling velocity of the solid material, a fluidized bed is formed within the reactor. To calculate the upstream flow velocity, u F , according to Equation (2.131), the void fraction (bed porosity) of the fluidized bed has to be known. The terminal settling velocity, v s , can be calculated by: v2s =

4 (ρ P − ρ F ) d P g 3 Cd ρF

(2.134)

where ρ P is the particle density, ρ F is the fluid-phase density, d P is the particle diameter, g is gravitational acceleration (9.81 m/s2 ), and C d is the drag coefficient. For more details on particle settling see Chapter 4. The drag coefficient depends on the Reynolds number, Re, which is defined by: Re =

dP vs ν

(2.135)

where ν is the kinematic viscosity of the fluid phase. In the range 2 < Re < 500, it holds that: 18.5 C d = 0.6 (2.136) Re Equations for other ranges of Re can be found in Chapter 4, Secion 4.2.1. Fluidized-bed reactors are used in water treatment in particular for ion exchange processes (Chapter 11) or for rapid lime dealkalization (Chapter 9). In both cases, modified versions of the ideal fluidized-bed reactor are used. In ion exchange reactors, the upstream flow velocity is adjusted in such a manner that the reactor contains a fixed-bed section (in the upper part of the reactor) as well

56 | 2 Some basics of hydrochemistry and process engineering

as a fluidized-bed section (in the lower part). The fluidized-bed section enables a fast mass transfer, whereas the fixed-bed section reduces the ion leakage. Rapid lime dealkalization (removal of carbonate hardness) is based on the precipitation of calcium carbonate. Here, the growing crystals constitute the solid phase. The initially formed small crystals have a lower settling velocity in comparison to the water velocity and are transported upstream together with the water and the precipitation agent. Due to the crystal growth, the settling velocity increases (Equation (2.134)). As long as the settling velocity is lower than the flow velocity of the water, the particles are kept in a fluidized state. If the crystals further grow, the settling velocity exceeds the flow velocity and the particles begin to settle and can be removed from the bottom of the reactor. An exact modeling of the abovementioned processes in fluidized-bed reactors is quite complicated and will not be further considered here.

3 Riverbank filtration 3.1 Introduction Generally, groundwater is used as raw water for drinking water production whenever possible, because it is much better protected against pollution than surface water. However, if the groundwater resources are limited, surface water (water from lakes, reservoirs, or rivers) has to be used. Among the different types of surface water, river water is often the most problematic raw water resource, because rivers, particularly in urban and industrialized regions, are exposed to pollutants from wastewater, nonpoint (diffuse) sources (e.g., rainwash from roads and agricultural areas), and inland waterway traffic. If, in the absence of other water resources, polluted river water has to be used for drinking water production, a pretreatment by riverbank filtration can be a reasonable option. Riverbank filtration is a near-natural treatment process that leads to a significant improvement of the raw water quality. It can support or replace other drinking water treatment steps and provides an additional safeguard for drinking water in emergency situations. Riverbank filtration utilizes natural attenuation processes during a subsurface water transport from the river to extraction wells located at a certain distance from the river. This water transport is induced by a hydraulic gradient resulting from lowering the water table by well-field pumping (induced infiltration). The most important attenuation processes during the subsurface water transport are mechanical filtration, biodegradation, and sorption. Additionally, mixing with groundwater decreases the pollutant concentrations, because the absolute pollutant mass is distributed in a larger water volume. Furthermore, the subsurface transport leads to a homogenization of the concentrations and temperatures. However, it has to be noted that riverbank filtration does not always have only positive effects. Under certain conditions, the redox state of the water can change from oxidizing to reducing conditions during the subsurface transport due to oxygen depletion by biodegradation processes. This change of the redox state has mainly negative effects, which will be further discussed in Section 3.2. Nevertheless, the positive effects typically outweigh the negative effects so that riverbank filtration is considered a reasonable pretreatment step in surface water treatment. However, the prerequisite is that the subsurface has sufficient permeability (Section 3.6). The general principle of riverbank filtration is shown in Figure 3.1. It has to be noted that the principle of subsurface filtration can also be applied to pretreat polluted lake water. Therefore, sometimes the more general term bank filtration is used instead of riverbank filtration. However, these cases are comparatively

https://doi.org/10.1515/9783110551556-003

58 | 3 Riverbank filtration Precipitation/Infiltration Extraction well River Mixing Filtration Biodegradation Sorption Redox processes

Bank filtrate Mixing

Groundwater Mixing

Fig. 3.1: Schematic representation of riverbank filtration.

Pretreatment

Post-treatment

River

Bank filtration

Infiltration

Extraction well Fig. 3.2: Riverbank filtration in combination with artificial surface water infiltration.

seldom and therefore the more common term riverbank filtration will be used throughout this chapter. Artificial infiltration of pretreated river water is another process that utilizes attenuation processes during the subsurface transport. Here, the water is directly taken from the river and then pretreated by engineered processes, in particular coagulation/flocculation and sedimentation. Sometimes also physicochemical processes, such as ozonation or activated carbon filtration, are additionally applied as pretreatment steps. The pretreated water is then infiltrated through artificial infiltration basins filled with sand. During the following subsurface transport the water quality is further increased due to attenuation processes such as biodegradation and sorption. In the subsurface, the infiltrated water is mixed with groundwater and/or bank filtrate. The blended water is extracted by the production wells of the waterworks and further treated by engineered processes. Figure 3.2 shows the combined application of riverbank filtration and artificial surface water infiltration as pretreatment steps in drinking water production.

3.2 Attenuation processes during riverbank filtration

|

59

3.2 Attenuation processes during riverbank filtration The attenuation processes involved in riverbank filtration can be classified into four groups: hydrodynamic, mechanical, biological, and physicochemical processes. Convective–dispersive transport and dilution are the relevant hydrodynamic processes. The dispersion effects during the transport lead to a concentration and temperature leveling and protect the water to be extracted by the wells from peak loads. Dilution with groundwater, which is typically of higher quality than river water, reduces the level of the pollutant concentrations in the riverbank filtrate. Mechanical filtration removes inorganic particles, particulate organic matter, and pathogens. Together with the particles, the substances sorbed on their surfaces are removed. Most of the particle removal takes part in the first few meters of the flow path from the river to the well. However, if too many fine particles are accumulated, clogging of the porous media takes place with the consequence that the infiltration rate of the water decreases. The biological processes that are possible during the subsurface transport depend on the kind of microorganisms that occur in the water and their environmental requirements. The most important biological process is the aerobic degradation of natural organic matter and synthetic organic chemicals. A precondition for aerobic degradation is the availability of oxygen. Therefore, aerobic degradation takes place in particular in the first part of the flow path where the oxygen concentration in the water is still relatively high. If the content of degradable organics in the water is not too high, the oxygen will not be totally consumed and oxidizing conditions will exist over the whole transport path. However, if the concentration of degradable organic substances in the river water is very high and/or the oxygen content of the water is low, a situation can occur where the oxygen is totally consumed during the transport, whereas degradable organics are still available. In this case, other oxidants such as nitrate, ferric hydroxide, manganese dioxide, or sulfate can be used by specialized microorganisms to oxidize organic substances. This sequence of oxidation processes that can be observed in the flow direction is accompanied by a continuous decrease of the redox potential. Accordingly, the redox state changes from oxidizing to reducing conditions. Although it could be shown that some synthetic chemicals can also be degraded under reducing conditions, the negative effects of the strong decrease of the redox potential predominate. The transformation of the oxidants and the associated decrease of the redox potential lead to the formation of substances that are not wanted in drinking water. Iron hydroxide and manganese oxide are reduced and mobilized as Fe2+ and Mn2+ ions. Under strongly reducing conditions, sulfate is transformed into sulfides (H2 S, HS− ) and methane formation begins. If these compounds occur in the riverbank filtrate, they have to be removed by specific treatment processes in the waterworks, such as deironing, demanganization, and gas–liquid exchange (Chapters 7 and 10).

60 | 3 Riverbank filtration

Among the possible physicochemical processes, sorption is the most important. In particular, natural organic matter and synthetic organic chemicals can be sorbed onto the aquifer material. The sorption preferentially takes place on the organic fractions of the solid material, the so-called solid organic matter (SOM). Inorganic water constituents are sorbed, if any, mainly onto inorganic solid matter. Relevant inorganic sorption has been observed, for instance, for phosphate and arsenate onto iron (hydr)oxides. Although the sorption processes in the aquifer are, in principle, comparable with adsorption processes in engineered systems, there are some relevant differences that have to be considered in transport modeling approaches. In contrast to adsorption processes onto engineered adsorbents such as activated carbons (Chapter 12), the sorption onto natural aquifer material (also referred to as geosorption) is not as strong and the sorption isotherms are often linear or only weakly nonlinear. A further difference consists of the relative impact of (ad)sorption kinetics and dispersion in flow-through systems (fixed-bed adsorber or aquifer). Due to the lower internal porosity of the geosorbents and the much lower flow velocities in the natural systems, the impact of sorption kinetics is lower and the impact of dispersion is higher in comparison to engineered adsorption processes.

3.3 Simplified mass transport modeling under consideration of sorption and biodegradation 3.3.1 General assumptions The substance transport in the subsurface from the riverbank to the extraction well is a very complex process. In particular, the different processes involved in the transport and their interactions, the heterogeneity of the aquifer material, and the complicated hydrodynamic conditions make an exact description of the transport quite difficult. Therefore, it is common practice to make simplifying assumptions in the development of transport models. A number of more or less complex model approaches can be found in the literature. Here, only a simple model will be discussed to demonstrate some general modeling basics. The model focuses on the fate of organic water constituents. The simplifying assumptions used in this model approach are: – one-dimensional transport, – consideration of either sorption or biodegradation, or a combination of both processes as the dominating processes in the subsurface, – linear sorption isotherm (Chapter 2, Section 2.3.6): q = Kd c

(3.1)

where q is the sorbed amount (sorbent loading), c is the concentration, and K d is the linear sorption (distribution) constant,

3.3 Simplified mass transport modeling |

– –

61

instantaneous establishment of the sorption equilibrium (sorption kinetics is neglected), and description of the biodegradation by a simple first-order rate law (Chapter 2, Section 2.4): dc − = λc (3.2) dt where λ is the degradation rate constant.

In the following sections, model solutions for different cases are presented. Details of the model development can be found elsewhere (Worch, 2012). Whereas this model allows only a rough estimate of the transport under field conditions, it has been shown to be suitable to describe laboratory-scale simulations of the reactive transport processes (Section 3.4) and to determine the characteristic process parameters for sorption and biodegradation.

3.3.2 Mass transport influenced by sorption Models that describe the solute transport in the subsurface or during column experiments can be derived from the differential material balance equation of a flowthrough system (Chapter 2, Section 2.6.4), which is, particularly in hydrogeological literature, also referred to as the advection–dispersion equation, or ADE. For the one-dimensional transport influenced by sorption, the ADE reads: ∂c ∂c ∂q ∂2 c + εB + ρB = D εB 2 ∂z ∂t ∂t ∂z

vF

(3.3)

where v F is the superficial velocity (Darcy velocity, filter velocity), c is the concentration, z is the distance in flow direction, ε B is the bulk porosity, ρ B is the bulk density, q is the sorbed amount, and D is the longitudinal dispersion coefficient. Here, it is assumed that the filter velocity, the bulk density, the porosity, and the dispersion coefficient are constant over time and space. The four terms in Equation (3.3) describe, from left to right, the processes of advection, accumulation in the void volume, sorption onto the solid material, and dispersion. Dividing Equation (3.3) by the bulk porosity, ε B , and introducing the mean pore water velocity, v w (= v F /ε B ), gives: vw

∂c ∂c ρ B ∂q ∂2 c + + =D 2 ∂z ∂t ε B ∂t ∂z

(3.4)

The derivatives with respect to time can be combined after applying the chain rule: vw

∂c ρ B ∂q ∂c ∂2 c + (1 + =D 2 ) ∂z ε B ∂c ∂t ∂z

(3.5)

62 | 3 Riverbank filtration

The term within the brackets is referred to as the retardation factor, R d . According to Equation (3.1), R d is related to the linear sorption constant by: Rd = 1 +

ρ B ∂q ρB Kd = 1+ ε B ∂c εB

(3.6)

An alternative but equivalent definition of R d can be derived from the mean travel velocity of the sorbing substance, v c : vc =

vF ∂q εB + ρB ∂c

=

vw vw = ρ B ∂q Rd 1+ ε B ∂c

(3.7)

Accordingly, R d describes the ratio of the pore water velocity and the mean velocity of the retarded (sorbing) substance: vw Rd = (3.8) vc It can be derived from the Equations (3.7) and (3.8) that in the case where no sorption takes place (K d = 0), R d is 1 and the substance velocity equals the pore water velocity. By contrast, in the case of strong sorption (K d ≫ 0), R d is much higher than 1 and v c is much lower than v w . Thus, the retardation factor is a parameter that shows how strong the solute is retarded in comparison to the pore water velocity or the velocity of nonsorbable species. Introducing R d into Equation (3.5) gives: vw

∂c ∂c ∂2 c + Rd =D 2 ∂z ∂t ∂z

(3.9)

Dividing Equation (3.9) by R d , introducing D∗ (= D/R d ), and rearranging the equation gives finally: ∂2 c ∂c ∂c = D∗ 2 − v c (3.10) ∂t ∂z ∂z The solution to Equation (3.10) is: c(z, t) =

z + vc t c0 z − vc t vc z (erfc ( ) + exp ( ∗ ) erfc ( )) 2 D 2 √D∗ t 2 √D ∗ t

(3.11)

Equation (3.11) describes the transport of a sorbing substance as a function of distance and time. The breakthrough behavior for a given transport distance L can be found by setting z = L = constant. The operator erfc in Equation (3.11) is the complementary error function. The parameters in Equation (3.11) are v c and D∗ , which include the retardation factor R d (v c = v w /R d ) and the dispersion coefficient (D∗ = D/R d ) as the characteristic transport parameters. It has to be noted that the hydrodynamic dispersion (characterized by the dispersion coefficient, D) summarizes the effects of mechanical dispersion and diffusion, which can be expressed by: D = vw α +

DL ≈ vw α εB

(3.12)

3.3 Simplified mass transport modeling

| 63

where α is the dispersivity (dispersion length) and D L is the liquid-phase diffusion coefficient. The terms v w α and D L /e B describe the contribution of the mechanical dispersion and the diffusion, respectively. Since the second term in Equation (3.12) is relatively low in most cases, it is usually neglected. Accordingly, the dispersivity can be used instead of D as the characteristic dispersion parameter in the transport modeling.

3.3.3 Mass transport influenced by biodegradation In cases where only biodegradation but no sorption takes place, R d becomes 1. Accordingly, v w equals v c and D∗ equals D. Additionally, the biodegradation has to be considered in the ADE by the respective rate law. If we assume that a first-order rate law can be used to describe the degradation rate, Equation (3.2) has to be introduced. Considering these changes in Equation (3.10), we get: ∂c ∂c ∂2 c = D 2 − vw −λc ∂t ∂z ∂z

(3.13)

The solution to Equation (3.13) is: c(z, t) =

c0 vw z zF z−Ft z+Ft zF exp ( ) {exp [− ] erfc [ ] erfc [ ] + exp [ ]} 2 2D 2D 2D 2 √D t 2 √D t (3.14)

with F = √v2w + 4 λ D

(3.15)

3.3.4 Mass transport influenced by sorption and biodegradation The equations for combined sorption and biodegradation are similar to the equations given in Section 3.3.3 with the only difference that the ‘retarded’ parameters have to be used. Introducing D∗ (= D/R d ), v c (= v w /R d ), and λ∗ (= λ/R d ), we find: ∂c ∂2 c ∂c = D∗ 2 − v c − λ∗ c ∂t ∂z ∂z

(3.16)

and c(z, t) =

zF z−Ft z+Ft vc z zF c0 ) {exp [− ] erfc [ exp ( ] + exp [ ]} ∗ ] erfc [ ∗ 2 2 D∗ 2 D∗ 2 D √ 2 D t 2 √D∗ t (3.17)

with F = √v2c + 4 λ∗ D∗

(3.18)

64 | 3 Riverbank filtration

3.4 Laboratory-scale simulation of riverbank filtration processes 3.4.1 Assessment of organic substances with respect to their fate during riverbank filtration In experimental studies at riverbank filtration sites with the special focus on anthropogenic organic water constituents it was found that the percentage elimination varies over a wide range from nearly 0% to a complete elimination of 100%, depending on the chemical nature of the substance under consideration, the water composition, the aquifer material, the traveling time in the subsurface, the redox conditions, and further factors. To get an insight into the elimination processes and their contribution to the overall attenuation effect, laboratory-scale experiments can be a helpful tool. Since biodegradation and sorption are the most relevant attenuation processes, the experiments are frequently focused on these processes. Figure 3.3 shows a respective assessment scheme. Since, in view of the removal of organic substances, biodegradation is the most relevant process, the biodegradability has to be studied first. In a second step, the substances that are nondegradable or only poorly degradable have to be assessed with respect to their sorption strength. With regard to the bank filtrate quality, the substances that are neither biodegradable nor sorbable deserve particular attention. Such substances have to be removed during the subsequent engineered water treatment. Substance degradable

Biodegradation?

Low relevance

poorly degradable or nondegradable

Sorption?

strong

Low relevance

weak

High relevance

Fig. 3.3: Assessment scheme for organic substances with respect to their relevance for the riverbank filtrate quality.

3.4 Laboratory-scale simulation of riverbank filtration processes

| 65

3.4.2 Biodegradation Biodegradability can be studied by using a circulation batch reactor system with a biologically active test filter (Figure 3.4). The filter column is filled with an inert solid material (glass beads, pumice stone) that serves as a carrier for the biofilm that is formed on the surface of the solid material during the filter conditioning with river water from the riverbank filtration site. The biofilm that develops during the conditioning contains microorganism populations that are typical for the considered river water. After the conditioning phase (about one month), the reservoir bottle is filled with a solution of the test compound in river water. The spiked river water is then percolated through the filter and the concentration decrease is measured as a function of time. The resulting kinetic curve can be used to determine the degradation rate constant. It has been shown that in many cases the overall degradation follows a pseudo-first-order rate law (Equation (3.2)) despite the complex nature of biodegradation. This is especially true if the electron acceptor (oxidant) concentration is not rate limiting and the number of microorganisms is constant over time. These conditions are assumed to be fulfilled in an open test filter system with relatively short test periods. For a first-order reaction in a completely mixed batch system (Chapter 2, Section 2.6.2), we get the following equation that can be used to determine the degradation rate constant, λ, from the experimental kinetic curve: ln

c = −λ t c0

(3.19)

The half-life that corresponds to the first-order degradation rate constant, λ, is given by: ln 2 t0.5 = (3.20) λ

Sampling

Testfilter

Reservoir Circulating pump

Fig. 3.4: Biologically active test filter.

66 | 3 Riverbank filtration

3.4.3 Sorption Sorption processes can be studied in column experiments with solid material from the bank filtration site as the sorbent (Figure 3.5). Here, a breakthrough curve, c/c0 = f(t), is measured in a flow-through experiment with a solution of the test substance. The time at the center of the real S-shaped breakthrough curve is referred to as the ideal breakthrough time, which corresponds to the breakthrough of an ideal concentration wave, which is not influenced by dispersion or sorption kinetics (Chapter 2, Section 2.6.4). For a symmetrical breakthrough curve, the ideal breakthrough time equals the time at the relative concentration c/c0 = 0.5. The ideal breakthrough time is indirectly proportional to the mean travel velocity of the sorbing substance, v c . By contrast, the residence time, t r , (or the ideal breakthrough time of a nonsorbing tracer) is indirectly proportional to the pore water velocity, which corresponds to the effective filter velocity. If using a normalized time axis, t/t r , for the breakthrough curve, the retardation factor R d (= v w /v c , Equation (3.8)) can be directly read from the normalized time at the center of the breakthrough curve, which is the normalized time at c/c0 = 0.5 for a symmetrical breakthrough curve (Figure 3.6): Rd =

id vw tb = vc tr

(3.21)

Knowing R d , the sorption coefficient, K d , can be found by Equation (3.6). Conductivity detector Sampling

Sorption column (Aquifer material) Reservoir

Conductivity detector

Pump

Fig. 3.5: Sorption column setup.

A more exact determination of R d is possible by applying a fitting procedure on the basis of a breakthrough curve model (e.g., Equation (3.11)). This is particularly recommended for breakthrough curves that are not symmetrical and where the curve center cannot be easily found.

3.4 Laboratory-scale simulation of riverbank filtration processes | 67

Fig. 3.6: R d determination from a normalized breakthrough curve.

Application of Equation (3.11) also allows for determination of the dispersion coefficient, D, or the dispersivity, α. However, the transferability of the dispersion parameters to field conditions is limited due to the so-called dispersion scale effect. For both methods of R d determination, the pore water velocity (or the residence time) has to be known. To determine v w or t r , a breakthrough curve of a conservative (nonsorbing) tracer has to be measured. Frequently, sodium chloride is used as tracer, because its concentration can be easily determined by measuring the electrical conductivity. Given that the residence time in a column of the height h equals the ideal breakthrough time, tid b , of the nonsorbing tracer, the mean pore water velocity, v w , can be calculated from: h h vw = (3.22) = id t r t (tracer) b

Knowing v w , the porosity, ε B , of the sorbent bed in the column can be found from the volumetric flow rate, V,̇ and the cross-sectional area of the column, A R (Chapter 2, Section 2.6.4): vw =

vF V̇ = AR εB εB

(3.23)

εB =

vF vw

(3.24)

68 | 3 Riverbank filtration

3.4.4 Sorption and biodegradation The same experimental setup as shown for sorption studies can also be used for substances that show biodegradation in addition to sorption. In this case, the breakthrough curves have a different shape in comparison to pure sorption. Due to the substance loss during biodegradation, the breakthrough curves do not reach the inlet concentration but end with a concentration plateau at c/c0 < 1. At a given column length, the final concentration level depends on the residence time and the degradation rate constant (Figure 3.7).

Fig. 3.7: Combined sorption and biodegradation: influence of the degradation rate constant, λ, on the breakthrough curve at constant hydraulic residence time.

Equation (3.17) can be used to model this type of breakthrough curve in order to determine the characteristic parameters R d , D, and λ.

3.4.5 Special case: NOM breakthrough curves Natural organic matter (NOM) is a multicomponent mixture of unknown composition, where only the total concentration can be measured by means of collective parameters, such as DOC (dissolved organic carbon). Accordingly, only total DOC breakthrough curves can be determined in experiments. Modeling of such DOC breakthrough curves and determination of the characteristic model parameters requires specific model approaches.

3.4 Laboratory-scale simulation of riverbank filtration processes

| 69

A simple approach is based on the definition of fictive components that stand for fractions with different sorption and biodegradation properties. This fictive component approach allows description of the sorption and biodegradation of the complex NOM system on the basis of an experimental DOC breakthrough curve. In this approach, it is further assumed that the different fictive components travel independently from each other, which has been shown to be a reasonable assumption for components that exhibit linear sorption isotherms. At first, a limited number of fictive components is defined, each of them characterized by a set of the following parameters: retardation factor, R d , dispersivity, α, biodegradation rate, λ, and initial concentration, c0 . After that, the values of these parameters have to be found by breakthrough curve fitting. Due to the high number of fitting parameters, the number of fictive components should be not higher than three. For a fictive three-component system, the number of fitting parameters would be 11 (nine process parameters and two concentrations; the third concentration is given as difference from the total DOC). The number of parameters can be further reduced if the components are characterized in such a manner that they represent limiting cases. For instance, one fictive component can be considered a conservative component (R d = 1, λ = 0), the second can be assumed to show sorption but no degradation (λ = 0), and the third can be treated as subject to sorption as well as to biodegradation. For α, the separately determined tracer dispersivity can be used. Despite the large number of remaining parameters (five), curve fitting is in principle possible because the parameters R d , and λ affect shape and location of the breakthrough curve in different ways. R d determines the location on the time axis, whereas λ determines the final concentration level (Figure 3.7). Due to the independent transport of the different components, the individual breakthrough curves ci = f(t) (3.25) c0,i can be calculated by using Equation (3.17). The concentrations as well as the initial concentrations have then to be added according to: ctotal = c1 + c2 + c3 c0,total = c0,1 + c0,2 + c0,3

(3.26) (3.27)

in order to receive the total breakthrough curve: ctotal = f(t) c0,total

(3.28)

Despite the strong simplifications, this fictive component approach is appropriate to describe the NOM breakthrough behavior at an acceptable quality as shown in Figure 3.8. The parameters found from the breakthrough curve modeling can then be used to approximately predict the NOM behavior under field conditions.

70 | 3 Riverbank filtration

Fig. 3.8: Modeling a NOM breakthrough curve using the fictive component approach (Worch, 2012).

3.5 Prediction of model parameters In view of the high effort needed for sorption and biodegradation experiments, it is reasonable to look for methods that allow prediction of the parameters required for transport modeling. However, the possibilities to predict transport parameters are limited. Prediction tools are only available for the sorption coefficient and the dispersivity. The biodegradation rate constant cannot be predicted. Thus, the possibility of a priori prediction of the transport behavior is restricted to systems where only sorption but no degradation is relevant. A further restriction exists concerning the sorption mechanism. Up until now, feasible prediction tools were developed only for the interaction of organic solutes with organic solid matter. Under the assumption that interaction between the organic solute and the organic fraction of the solid is the dominating sorption mechanism, it is reasonable to normalize the sorption coefficient, K d , to the organic carbon content, foc , of the sorbent: Koc =

Kd foc

(3.29)

In this way, the sorption coefficient becomes, to the greatest possible extent, independent of the specific sorbent. Given that the sorption of organic solutes onto an organic sorbent material is dominated by hydrophobic interactions, it can be expected that the sorption increases with increasing hydrophobicity of the solute. The hydrophobicity can be characterized by the n-octanol-water partition coefficient, Kow , which is available for many organic substances from databases or can be estimated using specific prediction methods. Correlations between Koc and Kow were found in numerous studies. The general form of all

3.6 Practical aspects | 71

Tab. 3.1: Selection of log Koc -log Kow correlations. Correlation log Koc log Koc log Koc log Koc

= 0.544 log Kow + 1.377 = 0.909 log Kow + 0.088 = 0.679 log Kow + 0.663 = 0.903 log Kow + 0.094

Authors Kenaga and Goring (1980) Hassett et al. (1983) Gerstl (1990) Baker et al. (1997)

these correlations is: log Koc = a log Kow + b

(3.30)

where a and b are empirical parameters. Table 3.1 shows some examples. The dispersivity, α, determines the steepness of the breakthrough curve. Since the dispersivity was found to be scale dependent, α (or the dispersion coefficient, D) determined in lab-scale experiments cannot be easily transferred to field conditions. Therefore, different empirical equations were developed that allow a rough estimate of the dispersivity as a function of the transport length, L. The equation proposed by Xu and Eckstein (1995) is given here as an example: α = 0.83 (log L)2.414

(3.31)

3.6 Practical aspects Riverbank filtration is used to pretreat polluted river water with the objective of reducing the effort for the subsequent engineered water treatment. Riverbank filtration wells are typically located in alluvial aquifers along the riverbanks. In Europe, riverbank filtration sites can be found for instance along the rivers Danube, Rhine, Elbe, and Seine. In the United States, riverbank filtration is applied along the rivers Mississippi, Missouri, Ohio, Colorado, and others. Less commonly, bank filtration is also used to pretreat water from lakes. In this case, the wells are located in the unconsolidated sand and gravel sediments along the lakeshores. Generally, the subsurface at riverbank filtration sites must be porous and permeable. Sufficient extraction capacities can be expected at bank filtration sites with hydraulic conductivities in the range of 10−4 –10−2 m/s, which corresponds to coarse grained and medium grained sand material. During the infiltration, a clogging layer is often formed on top or within the riverbed as a result of physical, chemical, and biological processes. Physical clogging results from the deposition and accumulation of fine grained suspended material. Chemical clogging includes different precipitation processes resulting from changes in the hydrochemical conditions and can occur not only at the infiltration site but also along the further flow path. Biological clogging results from the accumulation of

72 | 3 Riverbank filtration

bacterial cells and extracellular substances and leads to a biologically active clogging layer. Clogging can have positive and negative effects on the efficiency of riverbank filtration. On the one hand, clogging reduces the permeability with the result that the extraction capacity decreases. On the other hand, the biodegradation is enhanced in the biologically active clogging layer. Furthermore, as long as the pores are not totally blocked, the accumulation of small amounts of fine grained material can enhance the filtration effect. Typically, the growth of the clogging layer is limited by streambed scouring resulting from the water motion and the related shear forces. The self-cleaning effects are particularly high during flood events. As already mentioned in Section 3.2, mechanical filtration, biodegradation, and sorption are the main attenuation processes during bank filtration. In principle, two stages of the subsurface transport can be distinguished: i) infiltration through the biologically active clogging zone, where filtration, intensive biodegradation, and sorption take place; and ii) the subsequent subsurface transport over longer distances where sorption and slower degradation processes take place together with dilution by mixing with groundwater. In the second stage, changes of the redox state from oxidizing to reducing conditions can also occur due to the depletion of oxygen and possibly also nitrate. In riverbank filtration, horizontal as well as vertical extraction wells are in use. The wells are typically arranged in groups or galleries. The selection of the type of extraction wells and their distance from the riverbank depends on the primary goals of the application of riverbank filtration. Horizontal wells at a shorter distance from the river (with laterals beneath the river bed) as shown in Figure 3.9 are mainly used if the primary goals are filtration of particles, including pathogens, and removal of rapidly degradable substances. River

Horizontal extraction well

Horizontal collector arms River

Fig. 3.9: Schematic representation of a horizontal extraction well (elevation and plan).

3.6 Practical aspects | 73

Vertical wells (Figure 3.10) are often located at a larger distance from the river (up to 300 m, sometimes also more). This kind of arrangement is typically chosen when an advanced improvement of the water quality is pursued (e.g., additional degradation of weaker degradable substances, utilization of the sorption capacity of the aquifer material, degradation under reducing conditions). In this case, as a rule, the travel time of the water in the subsurface should be at least 50 days. Since the pore water velocities between the river and the vertical wells are often in the range of about 1 m/day, the 50 days rule corresponds to a distance of about 50 m between riverbank and extraction wells. River Vertical extraction well

River Well gallery

Fig. 3.10: Schematic representation of a vertical extraction well (elevation and plan).

Besides the primary treatment goal, a number of other factors influence the decision to use specific types of wells and their location, for instance the hydrogeological conditions, the required production capacity, the raw water quality, and operation and maintenance costs, as well as the demand for land.

4 Sedimentation and filtration 4.1 Introduction Both sedimentation and filtration belong to the standard processes used for particle removal during drinking water treatment. There are diverse reasons for particle removal from raw waters: aesthetic reasons (drinking water should be clear), hygienic reasons (removal or at least partial removal of bacteria, viruses, and also protozoa, such as Cryptosporidium and Giardia), and reduction of the health risk caused by inorganic or organic substances sorbed on the particles. Particle removal is particularly necessary for the treatment of surface water, which contains larger amounts of biotic and abiotic colloidal and suspended material. Since colloids (particle sizes between 1 nm and 1 μm) or small suspended particles (particle sizes in the lower μm range) are too small for an efficient separation by filtration or sedimentation, upstream particle aggregation by coagulation/flocculation is typically applied. Coagulation and flocculation processes are discussed separately in Chapter 6. If the particle concentration is not very high (< 50 mg/L), a direct filtration without sedimentation is often sufficient. Otherwise, sedimentation is applied prior to filtration to relieve the filters and to extend the filter run time. Particles do not only occur in the raw water but are also formed during several treatment processes. In particular, particle removal is always necessary as a final stage of treatment processes that are based on precipitation, such as softening/dealkalization (Chapter 9) or deironing/demanganization (Chapter 10). Since these precipitation processes are often used for groundwater, particle removal is

Groundwater

Reservoir water

River water

River water

Deironing Demanganization

Coagulation Flocculation

Coagulation Flocculation

Coagulation Flocculation

Filtration

Filtration

Sedimentation

Sedimentation

Infiltration

Filtration

Fig. 4.1: Typical arrangements of sedimentation and filtration steps within the treatment trains for different types of raw water.

https://doi.org/10.1515/9783110551556-004

76 | 4 Sedimentation and filtration

also a common treatment step in the drinking water production from groundwater, although groundwater itself contains only small amounts of pristine colloidal and suspended material. Figure 4.1 shows some typical examples for the arrangement of sedimentation and filtration steps within the treatment trains for different types of raw water. As shown in Chapter 3, riverbank filtration is also able to remove particles from the river water. A pretreatment of surface water by riverbank filtration can significantly reduce the effort for the engineered particle removal. Membrane processes, in particular microfiltration and ultrafiltration, are alternative processes that can be used for particle removal in addition to or instead of filtration. Microfiltration and ultrafiltration are described separately in Chapter 5 together with other membrane processes.

4.2 Sedimentation 4.2.1 Theoretical basics Sedimentation is the sinking of particles in liquids under the influence of gravity as a function of size, density, and shape. If balancing the forces acting on a settling particle (Figure 4.2), we have to write: Fd = Fg = Fw − Fb

(4.1)

where F g is the force acting downwards under the influence of gravity. It is given by the difference of weight (F w ) and buoyancy (F b ), both depending on gravity. F d is the frictional force (also referred to as drag force) acting in resistance to the fall. Fd = Fg Fd vs

Fg = Fw - Fb

Fg

Fg

Fw

Fb

Fig. 4.2: Forces acting on a particle that settles with the velocity v s . F b – buoyancy, F d – drag force, F g – force by gravity, F w – weight.

The force by gravity, F g , is given by: F g = F w − F b = ρ P V P g − ρ F V P g = (ρ P − ρ F ) V P g

(4.2)

where ρ P is the particle density, ρ F is the fluid density (here the density of water), V P is the particle volume, and g is the gravitational acceleration (9.81 m/s2 ). Assuming

4.2 Sedimentation | 77

a spherical shape of the particles, Equation (4.2) becomes: F g = (ρ P − ρ F )

4 π r3P π d3P g = (ρ P − ρ F ) g 3 6

(4.3)

where r P is the particle radius and d P is the particle diameter. The frictional force (drag force) for a spherical particle with the diameter d p is given by: π 1 1 (4.4) F d = C d ρ F A p v2s = C d ρ F d2P v2s 2 2 4 where C d is the drag coefficient, A p is the projected area of the sphere, and v s is the settling velocity (terminal velocity). Setting Equation (4.3) equal to Equation (4.4) gives: 4(ρ P − ρ F ) d P g 3 Cd ρF

v2s =

(4.5)

The drag coefficient, C d , depends on the Reynolds number, Re, which characterizes the streaming conditions. The Reynolds number is defined as: Re =

vs dP ν

(4.6)

where ν is the kinematic viscosity. The relationships between C d and Re for different flow conditions are summarized in Table 4.1 and graphically represented in Figure 4.3. It has to be noted that the relationship between C d and Re in the transition range is very complex. The simplified equation given in Table 4.1 is an approximation that is appropriate for practical purposes. Tab. 4.1: Drag coefficients for different flow regimes (Clark, 1996). Flow conditions

Reynolds number

Drag coefficient

Laminar flow (Stokes flow) Transition flow Turbulent flow

500

C d = 24/Re C d = 18.5/Re0.6 C d = 0.44

Introducing the equations given in Table 4.1 into Equation (4.5) gives the relationships that can be used to calculate the terminal settling velocity, v s , for the different flow conditions. For laminar flow (Re < 2), we get: vs =

(ρ P − ρ F ) d2P g 18 η

(4.7)

where η is the dynamic viscosity that is related to the kinematic viscosity by the fluid density (η = ν ρ F ). Equation (4.7) is also known as Stokes’s law.

78 | 4 Sedimentation and filtration

Fig. 4.3: Drag coefficient as a function of the Reynolds number.

For the transition flow regime (2 < Re < 500), the settling velocity, v s , is given by: vs = (

(ρ P − ρ F ) d1.6 P g 13.875 η0.6 ρ 0.4 F

1/1.4

)

(4.8)

For turbulent flow, we find: v s = √3.03

(ρ P − ρ F ) dP g ρF

(4.9)

Since the calculation of the Reynolds number (by means of Equation (4.6)) requires knowledge of the settling velocity, it is not possible to decide a priori which of the equations applies for the given process conditions. Therefore, one of the three equations has to be chosen to find v s , and after that, the Reynolds number has to be calculated. If Re is outside of the validity range of the chosen equation, a recalculation with another equation has to be carried out. It has to be noted that Equations (4.7)–(4.9) are strictly valid only for spherical particles. To calculate settling velocities for nonspherical particles, the equivalent diameter can be used as a rough approximation. Figure 4.4 shows the terminal settling velocity of spherical particles as a function of the particle diameter. It has to be noted that the well-known Stokes’s law is only valid for low Reynolds numbers (Re < 2, laminar flow). At higher Reynolds numbers, the settling is increasingly disturbed by turbulences. As a consequence, the settling velocity increases slower with the particle diameter as calculated from Stokes’s law. As can be seen from Figure 4.4, the settling velocity for a given particle diameter is higher the greater the particle density is.

4.2 Sedimentation

| 79

Fig. 4.4: Settling velocity of spherical particles as a function of the particle diameter.

4.2.2 Sedimentation basins In practice, two types of sedimentation basins (also referred to as settling tanks) are widely used: rectangular basins and circular basins (Figure 4.5). In a rectangular sedimentation basin, the water flows with a relatively slow velocity in horizontal direction through the basin, allowing the particles to settle. The bottom of the basin is typically sloped towards a sludge hopper where the particles are collected. The sludge hopper is located near to the water inlet where most of the particles settle. To support particle collection, mechanical collectors are used. The most frequently used collector systems are chain-and-flight systems made of plastic material (sludge scrapers on a pulley system) and traveling bridges with moving scraper arms. The typical lengths of rectangular basins are in the range of 20–50 m. In a circular sedimentation basin, the water is typically fed to the center and then flows into the direction of the outer wall, where an overflow weir is located from which the clarified water is removed. The flow velocity decreases with increasing distance from the center and the particles are able to settle. The sludge is collected at the deepest point of the sloped basin bottom. In most cases, circular basins are also equipped with a traveling bridge that moves a sludge scraper over the bottom of the basin to support the sludge collection. The diameters of circular sedimentation basins are often in the range of 20–40 m. To improve the sedimentation efficiency, lamella clarifiers can be introduced into the upper part of rectangular or circular sedimentation basins. Lamella clarifiers consist of inclined parallel plates (distance about 5–10 cm) that are arranged at an angle of about 60°. They decrease the distance a particle has to travel until it reaches a solid surface. Often, they act in a countercurrent flow regime, where the water flows from the bottom to the top of the plate stack in the opposite direction to the settling par-

80 | 4 Sedimentation and filtration

Inlet

Outlet

Traveling bridge collector system Sludge

Inlet

Outlet

Chain-and-flight collector system (a)

Sludge

Outlet

Inlet (b)

Sludge discharge

Fig. 4.5: Rectangular (a) and circular (b) sedimentation basins.

ticles. However, arrangements with cocurrent flow and cross-flow are also possible. Sedimentation basins with inclined parallel plates are often used as a separation step after coagulation and flocculation processes (Chapter 6). Since basins need to be taken out of operation for maintenance purposes after certain time intervals, at least two basins are necessary. If large volumes of water are to be treated, more basins may be necessary, because the basins cannot be made arbitrarily large.

4.2.3 Design considerations The general criterion for a complete sedimentation is that the hydraulic residence time in the basin is higher than the time needed for sedimentation. From this general condition, requirements for the basin dimensions can be derived.

4.2 Sedimentation |

81

.

V vh hB

vs

wB lB

Fig. 4.6: Idealized particle trajectory in the settling zone of a rectangular sedimentation basin.

For rectangular basins, the transport of a considered particle is influenced by the settling velocity, v s , and the horizontal flow velocity, v h (Figure 4.6). The horizontal velocity, v h , is given by the volumetric flow rate, V,̇ divided by the cross-sectional area of the basin in the flow direction, A: vh =

V̇ V̇ = A wB hB

(4.10)

where w B and h B are the width and the height of the basin, respectively. The horizontal velocity is related to the hydraulic residence time, t r , by: tr =

lB wB hB lB VB = = vh V̇ V̇

(4.11)

where l B and V B are the length and the volume of the basin, respectively. Defining the critical settling velocity, v s,c , as that settling velocity which allows a complete sedimentation within the residence time, t r , in a basin with the dimensions l B , w B , and h B , we get: V̇ V̇ h B h B V̇ h B V̇ v s,c = = = = = (4.12) tr VB wB hB lB wB lB AB where A B is the basin surface area (A B = w B l B ). Note that h B is here assumed to be the ̇ B is referred to as the surface loading rate or maximum settling distance. The ratio V/A overflow rate. It is the most important design parameter. Given that all the data needed for calculating the settling velocity are known, the required basin area for a complete sedimentation can be found from Equation (4.12). Overflow rates are typically in the range of 0.5–2.5 m/h where the higher values are valid for coagulation/flocculation flocs. The detailed dimensions of the rectangular basins can be found from recommendations based on practical experiences. The length to width ratio should be > 4–5, the length to height ratio > 15. The design of circular basins is more complex, because the horizontal velocity changes depending on the distance from the center of the basin (Figure 4.7). The horizontal velocity, v h , is given by: vh =

V̇ V̇ = A 2 π r hB

(4.13)

82 | 4 Sedimentation and filtration rB

vh hB

vs

Fig. 4.7: Idealized particle trajectory in the settling zone of a circular sedimentation basin.

where r is the radial distance from the water inlet at the center of the basin and A is the (variable) cross-sectional area in the flow direction, given by the product of circumference and basin height. Here, it is assumed that the height of the outer wall of the basin, h B , is the (constant) height that is available as the settling zone. For a given time t, the vertical distance covered by the particle is given by dh = v s t, and the horizontal distance is given by dr = v h t. Rearranging for t, equating both expressions, and introducing Equation (4.13) gives: t=

dh dr 2 π r h B dr = = vs vh V̇

(4.14)

Integration of Equation (4.14) leads to the general relationship: t=

π r2 h B h = vs V̇

(4.15)

For the residence time, t r , which is related to the critical settling velocity, v s,c , we find: tr =

π r2B h B hB = v s,c V̇

(4.16)

where r B is the radius of the basin. The settling velocity is then given by: v s,c =

V̇ V̇ = 2 π rB AB

(4.17)

where A B (= π r2B ) is the surface area of the circular sedimentation basin. Obviously, the same relationship between the critical settling velocity and the overflow rate is valid as for a rectangular sedimentation basin (Equation (4.12)). Accordingly, the overflow rate and the required basin surface area for a complete sedimentation can be calculated in the same way. The respective radius can be found from Equation (4.17).

4.3 Filtration

| 83

As can be derived from Equations (4.12) and (4.17), the overflow rate as a relevant design parameter for both basin types is independent of the basin depth. In principle, the basins could be designed as very shallow basins. However, in practice, a minimum depth is necessary for the deposited sludge and the sludge collection system. Therefore, practical basin depths are typically between 2 and 5 m. Finally, it has to be noted that all equations given in this section are derived for idealized conditions and allow only a rough estimate of the sedimentation process under practical conditions.

4.3 Filtration 4.3.1 Filtration processes: classification and basic principles The term filtration refers to the separation of particles from a fluid by passage through a porous medium. Generally, filtration processes can be subdivided into two classes, surface filtration and depth filtration (Figure 4.8). Depth filtration is also referred to as deep filtration or deep bed filtration.

Surface filtration

Depth filtration

Fig. 4.8: Schematic representation of surface filtration and depth filtration.

In surface filtration, a thin layer of porous material is used as filter material, for instance a metal sieve or a membrane. In principle, only particles larger than the pore width of the filter material are removed during surface filtration. If the deposited particles form a layer (filter cake) on the surface, the filtration effect is enhanced and smaller particles are also retained. This special type of filtration is referred to as cake

84 | 4 Sedimentation and filtration

filtration. However, if the filter cake becomes too thick, the flow rate is strongly reduced. In depth filtration, a bed of granular material is applied as a filter medium. The particles accumulate in the pore volume of the bed due to collision and adherence mechanisms. In the filter bed, particles are also accumulated that are much smaller than the pore volume between the grains of the filter medium. The relevant filtration mechanisms are described in Section 4.3.2. A general overview of the different types of filtration processes used in drinking water treatment is shown in Figure 4.9. Since membrane processes are treated in a separate chapter (Chapter 5), surface filtration is not further considered here and the discussion in the following sections is restricted to depth filtration.

Filtraon

Depth filtraon

Slow sand filtraon

Surface filtraon

Rapid filtraon

Monomedia filter bed

Pressure filter

Microsieving

Membrane filtraon

Dual-media filter bed

Open filter

Fig. 4.9: Types of filtration processes used in drinking water treatment.

Depth filtration can be carried out as slow sand filtration or as rapid filtration. The main difference consists in the flow velocity. Whereas the flow velocity in slow sand filtration is typically in the range of 0.05–0.3 m/h, the filter velocity in rapid filters is between 5 and 15 m/h. Slow sand filtration is carried out in large filter basins with run times up to six months. Sand with particle sizes in the range from 0.1–0.5 mm is used as granular filter material. Slow sand filters act as gravity filters. That means, the water flow is induced by a water head over the filter bed. During the long filter run time and due to the availability of nutrients, microorganisms can accumulate together with the particles on the surface of the filter bed. Particles and microorganisms form a biologically active layer, the so-called schmutzdecke. In this layer, organic matter is degraded, which is a positive side effect, in particu-

4.3 Filtration

| 85

lar with respect to the reduction of NOM (natural organic matter) as a disinfection byproduct precursor (Chapter 1, Section 1.2.3). On the other hand, the formation of the schmutzdecke leads to clogging and reduction of the water flow rate. Moreover, with increasing height of the schmutzdecke, the surface filtration effect (straining) becomes more relevant in comparison to deep filtration. If the head loss reaches the available head of the filter, the upper layer (some centimeters) of the bed including the schmutzdecke has to be removed by scraping. If the loss of material reaches a certain extent, fresh sand must be added to restore the initial bed height. Figure 4.10 shows a scheme of a slow sand filter. Head space

Overflow Supernatant water

Influent

Schmutzdecke Filter sand Supporting gravel Underdrainage Filtrate

Fig. 4.10: Scheme of a slow sand filter.

Rapid filters are the most frequently used filter type in drinking water treatment. Due to the much higher filter velocity, the space requirements are markedly lower than for slow sand filters. Rapid filters can be designed as open gravity filters (typically as rectangular concrete basins) or as closed pressure filters (typically as steel vessels, but also as rectangular concrete basins). Rapid filters can be operated with a single filter material (monomedia filters) or with combinations of two different filter materials (dualmedia filters) that are arranged as separate layers in a layered filter bed. In dual-media filters with a downstream flow regime, the upper filter bed layer typically consists of a coarse material of lower density and the lower filter bed layer consists of a finer material of higher density. In this case, the upper layer has the higher capacity and protects the lower layer from early exhaustion of capacity. The density differences between the different materials prevent a strong intermixing during filter backwashing. Quartz sand is the most common filter material in monomedia filters. In dualmedia filters, often anthracite (density: 1.4–1.8 g/cm3 ) is used as the upper filter layer, whereas quartz sand (density: 2.65 g/cm3 ) is used as the lower filter layer. Figure 4.11 shows a dual-media pressure filter in the filtration and backwashing mode. The run time of rapid filters is dictated by the particle concentration in the effluent and by the head loss. The filter run has to be stopped if the breakthrough concentration

86 | 4 Sedimentation and filtration

Exhaust air

Anthracite Sand

Air Influent

Filtrate

Filtration

Backwash water

Backwash water + sludge

Backwashing

Fig. 4.11: Scheme of a dual-media pressure filter in the filtration and backwashing mode.

of the particles reaches the allowed value or if the head loss reaches the maximum value. After that, the filter has to be regenerated by backwashing to restore the filter bed capacity. More information about typical filter design data can be found in Section 4.3.4.

4.3.2 Filtration mechanisms The separation of particles in depth filters is based on different mechanisms. Which mechanism dominates depends on the particle size and density. If the particles are larger than the void spaces between the filter grains, the particles are removed by straining. Straining causes the formation of a filter cake on the surface of the filter bed. In slow sand filtration, the formation of the so-called schmutzdecke is accepted to a certain extent, because accumulation of microorganisms in this layer contributes to the biodegradation of organic substances. On the other hand, the accumulation of material at the surface increases the head loss and therefore this layer has to be removed from time to time. In rapid filters, cake formation is unwanted because of the strong increase of the head loss and the insufficient utilization of the filter bed. Rapid filters are designed in such a manner that straining is minimized and depth filtration is encouraged. If necessary, sedimentation is applied as a pretreatment step prior to rapid filtration. Depth filtration is based on different transport and attraction mechanisms. Transport to the surface of the filter grains can occur by three major mechanisms: diffusion, sedimentation, and interception (Figure 4.12). After the particles have been transported to the surface, an attachment can take place, caused by weak molecular

4.3 Filtration

|

87

Diffusion Sedimentation

Interception

Fig. 4.12: Mechanisms of particle transport to a filter grain.

attraction forces, such as van der Waals forces. Small particles (< 1 μm) are mainly transported by diffusion, independent of the streamlines. Larger particles with a significant density difference to water can leave the streamlines and are transported under the influence of gravitational forces by sedimentation. Large particles (> 1 μm) that follow the fluid streamlines can attach to the grain surface if their radius is equal to or lower than the distance of the streamline from the surface. This mechanism is supported by the fact that the streamlines between adjacent filter grains are strongly compressed, with the consequence that the distance to the grain surfaces becomes lower.

4.3.3 Depth filtration theory In the literature, numerous models are available that can be used to describe the filter performance. In principle, these models can be subdivided into microscopic models, which are based on a detailed description of transport and attachment to a single filter grain, and phenomenological models that describe the process in a more general form using empirical equations and parameters together with fundamental relationships. Both types of models are suitable to demonstrate the effects of different process factors on the filtration process. However, the complexity of the filtration process does not allow a realistic prediction on a rigorous theoretical basis. Therefore, pilot studies are indispensable in most practical cases. The phenomenological models are helpful tools for evaluating data from pilot studies. In this section, a selection of basic equations is presented that allows a better understanding of the filtration process and the major impact factors. As an example of a microscopic model, the simple model of Yao et al. (1971) will be shown here. It is based on the transport and attachment efficiency caused by a single filter grain, also referred to as collector. The overall efficiency, γ O , is defined as the product of the transport efficiency, γ T , and the attachment efficiency, γ A : γO = γT γA

(4.18)

88 | 4 Sedimentation and filtration

with γT =

number of particles contacting the collector number of particles approaching the collector

(4.19)

γA =

number of particles adhering to the collector number of particles contacting the collector

(4.20)

and

The total transport efficiency is the sum of the efficiencies of the transport mechanisms diffusion, sedimentation, and interception (Section 4.3.2), γ D , γ S , and γ I , respectively: γT = γD + γS + γI

(4.21)

The transport efficiency of diffusion is determined by the Peclet number, which includes the diffusion coefficient in the liquid phase, D L , the superficial filter velocity, ̇ R ), and v F (= volumetric flow rate divided by the cross-sectional area of the filter, V/A the diameter of the collector (filter grain), d C : γ D = 4 Pe−2/3 Pe =

vF dC DL

(4.22) (4.23)

By expressing the diffusion coefficient, D L , by means of the Stokes–Einstein equation: kB T 3 π η dP

(4.24)

3 π η dP vF dC kB T

(4.25)

DL = we can also write: Pe =

where k B is the Boltzmann constant (1.381×10−23 J/K = 1.381×10−23 kg⋅m2 /(s2 ⋅K)), T is the absolute temperature, d P is the particle diameter, and η is the dynamic viscosity. The transport efficiency of sedimentation, γ S , is given by the ratio of the settling velocity, v s , and the superficial filter velocity, v F . The sedimentation velocity for laminar flow can be found from Stokes’s law (Equation (4.7)): γS =

(ρ P − ρ F ) d2P g vs = vF 18 η v F

(4.26)

where g is the gravitational acceleration (9.81 m/s2 ), ρ P is the particle density, ρ F is the fluid density (here the water density), d P is the particle diameter, and η is the dynamic viscosity. Finally, the efficiency of interception, γ I , is given by: γI =

3 dP 2 ( ) 2 dC

(4.27)

4.3 Filtration

| 89

Fig. 4.13: Total transport efficiency as a function of the particle diameter, calculated for the following conditions: v F = 10 m/h, d C = 1 mm, T = 288.15 K (15 °C), η = 1.138 × 10−3 kg/(m ⋅ s), ρ P = 1100 kg/m3 .

Figure 4.13 shows the total transport efficiency as a function of the particle diameter for typical process conditions and the contributions of the single mechanisms. Whereas the relevance of diffusion decreases with increasing particle size, the contributions of sedimentation and interception increase with increasing particle size. A minimum of the total transport efficiency exists near to the particle diameter of 1 μm. This is in accordance with experimental observations that particles in this size range are hard to remove by filtration. The absolute values of the transport efficiency are relatively low, but it has to be taken into account that these values are valid for a single filter grain, whereas a filter bed contains thousands of collectors. Consequently, the efficiency of particle removal increases markedly in a deep filter. Since it was observed that the transport efficiency calculated from Equations (4.22), (4.26), and (4.27) is often lower than the efficiency found in experiments, some extended semiempirical equations for the transport efficiency have been developed in the past. Some of them contain not only transport parameters but also parameters of the attachment mechanisms, for instance the Hamaker constant as a characteristic parameter of the van der Waals forces. Accordingly, these equations provide γ O rather than only γ T . Combining the mass flow to one single filter grain, the number of filter grains in a differential element of depth, and the material balance equation for this differential element, the following time-invariant filter equation can be derived: ρ∗ −3 (1 − ε B ) γ T γ A h ] ∗ = exp [ ρ0 2 dC

(4.28)

90 | 4 Sedimentation and filtration

Fig. 4.14: Removal efficiency as a function of the bed height calculated for two different particle diameters (collector diameters: 1 mm and 2 mm).

where ρ ∗ is the particle concentration (expressed as mass concentration), ρ ∗0 is the initial particle concentration, ε B is the filter bed porosity, and h is the filter bed height. Given that the filter bed height, h, is proportional to the time, t, with the filter velocity as the proportionality factor, Equation (4.28) can be considered a kind of first-order rate law (Chapter 2, Section 2.4). The transport efficiency, γ T , can be calculated by the abovementioned equations, whereas γ A is often set to 1 for the sake of simplification. The described model is a so-called clean bed model, because it does not consider the change of the transport conditions over the run time due to the accumulation of particles in the filter bed. Although it cannot exactly predict the filter process, it is useful to demonstrate the influence of different parameters on the filter performance, such as bed height, particle diameter, collector diameter, and filter velocity. Figures 4.14 and 4.15 show exemplarily the influence of the bed height, the particle diameter, and the collector diameter on the initial filter performance as calculated by Equation (4.28). The filter performance is expressed by the removal efficiency: Removal effciency (%) = 100 (1 − ρ∗/ρ ∗0 )

(4.29)

The curves were calculated with the same data set as used for the diagram shown in Figure 4.13. As can be seen from Figure 4.14, the removal efficiency increases with increasing bed height and decreasing collector diameter. Figure 4.15 reveals that the minimum of the total transport efficiency at about 1 μm shown in Figure 4.13 is reflected in a minimum of the removal efficiency at the same particle size.

4.3 Filtration

| 91

Fig. 4.15: Removal efficiency as a function of the particle diameter calculated for two different collector diameters (bed height: 2 m).

A frequently applied phenomenological model is based on the kinetic approach of Iwasaki (1937). It describes the overall filtration process with a first-order rate law: ∂ρ ∗ = −λ F ρ ∗ ∂z

(4.30)

where ρ ∗ is the particle concentration (expressed as mass concentration) in the liquid phase, z is the depth in the filter, and λ F is the filtration coefficient. Given that the filtration coefficient is constant at the beginning of the process (λ F = λ F,0 = constant), Equation (4.30) can be integrated to give: ρ∗ = exp(−λ F,0 z) ρ ∗0

(4.31)

Obviously, Equation (4.31) has the same mathematical form as Equation (4.28). Comparing these equations, we can derive that the empirical parameter λ F,0 includes all parameters that affect the transport and attachment mechanisms. An equation for the concentration of the accumulated particles (deposited particle mass/bed volume) can be found by considering the differential mass balance equation for the filter bed (Equation (2.128) in Chapter 2, Section 2.6.4): vF

∂ρ ∗ ∂ (ε B ρ ∗ ) ∂σ + + =0 ∂z ∂t ∂t

(4.32)

where ε B is the porosity of the filter bed and σ is the volume-related concentration of the particles accumulated on the filter grains. Neglecting the accumulation in the pore volume (second term on the left-hand side), we get: ∂σ ∂ρ ∗ = −v F ∂t ∂z

(4.33)

92 | 4 Sedimentation and filtration With Equation (4.30) and λ F = λ F,0 , we find: ∂σ = v F λ F,0 ρ ∗ ∂t

(4.34)

In the real filtration process, λ F changes with the filter run time as a result of the accumulation of particles in the bed. Therefore, a time-dependent parameter has to be introduced instead of the constant λ F,0 . The time-dependent filtration coefficient, λ F , can be expressed as the product of the initial filtration coefficient, λ F,0 , and a correction factor, f λ , which depends on the filter run time or filter loading: λ = λ F,0 f λ

(4.35)

In the filtration literature, different approaches to describe the correction factor are available. Alternatively, the factor f λ can be determined in pilot-plant experiments. Besides the changes in concentration and deposition, the head loss (pressure difference) is a further parameter that changes with the run time of the filter. As a first approximation, it can be assumed that the head loss increases linearly with the time as a result of the particle accumulation: ∆p t = ∆p t=0 + k p σ t

(4.36)

where ∆p t is the head loss at time t, ∆p t=0 is the initial head loss, k p is a constant, and σ t is the deposit at time t. The constant k p has to be determined from experiments and σ t can be calculated from the integral material balance of the filter: σ t V B = (ρ ∗0 − ρ ∗e ) V̇ t

(4.37)

where V B is the bed volume, ρ ∗0 is the initial particle concentration, and ρ ∗e is the eḟ R and V B = A R h, we get: fluent particle concentration. With v F = V/A σt =

(ρ ∗0 − ρ ∗e ) v F t h

(4.38)

4.3.4 Practical aspects The most important design parameters of depth filters are the filter velocity, the filter bed height, the bed density, and the filter run time. Important filter medium parameters are the size, the density, and the uniformity. The filter velocity (superficial filter velocity) is defined by: vF =

V̇ AR

(4.39)

where V̇ is the volumetric flow rate and A R is the cross-sectional area of the filter bed. It has to be noted that v F is not the real velocity in the filter bed, because only the

4.3 Filtration

|

93

void space between the filter grains (interstitial space) is available for water flow. The effective (interstitial) filter velocity, u F , is therefore given by: uF =

V̇ vF = AR εB εB

(4.40)

where ε B is the bed porosity. The bed porosity is given by: εB =

Vvoid V B − Vmedium Vmedium ρB = =1− =1− VB VB VB ρP

(4.41)

where V B is the bed volume (V B = A R h), Vmedium is the total volume of the filter medium (volume of all filter grains), ρ B is the bed density (total mass of the filter medium/bed volume), ρ P is the particle density, and h is the bed height. As we have seen in Section 4.3.3, the grain size is an important property of the filter medium that determines the filter efficiency. However, it is not easy to give exact data for the grain size, because the typical filter media (sand, anthracite, or other materials) are of nonspherical shape and show a more or less wide grain size distribution. For modeling purposes, often a mean grain diameter is used and the grains are assumed to be spherical. To characterize the grain size distribution, the uniformity coefficient can be used. It is based on a sieve analysis where the diameters are determined at which 10% and 60% of the media by weight are smaller. From these diameters, the uniformity coefficient, UC, can be calculated by: UC =

d60 d10

(4.42)

where d60 is the sixtieth percentile media grain size diameter and d10 is the tenth percentile media grain size diameter. Typical values are given in Table 4.2. The particle concentration in the effluent of a rapid filter and the head loss show a characteristic progress over the run time (Figure 4.16). In the first phase, referred to as ripening, the filter still has not reached its full performance and the concentration shows a peak. After that, the concentration remains relatively low over a long period of time due to an efficient filtration. If the capacity of the filter is exhausted, particle breakthrough occurs. The head loss increases linearly during the run time, starting from an initial value (Equation (4.36)). Accordingly, the maximum run time of rapid filters is dictated by two factors: the particle concentration in the effluent and the head loss. The filter run has to be stopped if the breakthrough concentration reaches the allowed value or if the head loss reaches the maximum value. Rapid filters should be designed in such a manner that both situations occur at nearly the same time. Rapid filters are regenerated by backwashing with filtrate. During backwashing, the filter bed expands (Figure 4.11). This expansion has to be considered in the filter design. Typical expansion rates are between 25% and 40%, depending on the filter medium. In dual-media filters, the density difference of the filter materials should be large to ensure that the intermixing during backwashing is minimized. The time required for backwashing is relatively short, typically < 30 min. Backwashing with water is often combined with an air scouring to enhance the removal of the particles. In

94 | 4 Sedimentation and filtration

Fig. 4.16: Particle concentration and head loss as a function of the filter run time. Tab. 4.2: Typical process and filter material data for slow sand filtration and rapid filtration. Parameter

Slow sand filter

Rapid filter

Filter velocity (m/h) Bed height (m) Head (m) Filter area (m2 ) Filter run time Mean media size (mm) Media uniformity coefficient Media particle density (g/cm3 )

0.05–0.3 1–1.5 0.5–1.5 Up to 10 000 1–6 months 0.1–0.5 150 g/mol. Since in NF or RO applications the focus is mainly on the rehttps://doi.org/10.1515/9783110551556-005

98 | 5 Membrane separation processes

Reverse osmosis

 p = 5-100 bar

Nanofiltration

Ultrafiltration

Microfiltration

 p = 3-20 bar

 p = 0.1-2 bar

 p = 0.1-2 bar

Univalent ions Polyvalent ions Dissolved organics

Colloids and viruses Particles (inorganic material, algae, bacteria)

Fig. 5.1: Efficiency of the membrane separation processes with respect to the removal of different types of water constituents.

moval of dissolved species, particles are typically removed by a pretreatment step to avoid the blocking of the dense membranes by particulate matter. In RO/NF processes, relatively high transmembrane pressures (in comparison to MF/UF) have to be applied, because the osmotic pressure caused by the dissolved species has to be overcome. As will be shown later, the osmotic pressure depends on the concentration of the dissolved species. Due to the higher concentration level in seawater in comparison to freshwater, the transmembrane pressure needed for desalination of seawater is much higher than the transmembrane pressure needed for the treatment of freshwater. Figure 5.1 gives a schematic comparison of the membrane processes with respect to the removal of the different types of water constituents and Figure 5.2 shows the separation limits of the membrane processes with respect to the size of the retained species. It has to be noted that the limits are not strict and given here only for orientation. In comparison to conventional filtration (Chapter 4, Section 4.3), which can only remove particles with sizes larger than about 1 μm, membrane processes distinctively extend the separation limits to smaller sizes. Figure 5.1 also gives the typical transmembrane pressure ranges for the different membrane processes. It has to be noted that, strictly speaking, only MF and UF are filtration processes if we define filtration as a process that is based on straining or size exclusion. NF and RO are separation processes that are mainly based on a diffusion mechanism and should be referred to as membrane separation processes. The more general term membrane separation can also be used for MF and UF. Nevertheless, in practice, the term mem-

5.1 Introduction

| 99

Reverse osmosis

Nanofiltration

Ultrafiltration

Microfiltration

0.1 nm

1 nm

10 nm

100 nm

1 µm

10 µm

Particle size Fig. 5.2: Separation limits of the membrane processes.

brane filtration is often used for the membrane processes independent of the specific separation mechanisms. Table 5.1 compares some of the most important process characteristics of the membrane processes MF/UF and NF/RO. More details are presented in the following sections. Tab. 5.1: Comparison between the membrane processes microfiltration/ultrafiltration and nanofiltration/reverse osmosis. Adapted from Crittenden et al. (2012). Process characteristic

Microfiltration/Ultrafiltration

Nanofiltration/Reverse osmosis

Objectives

Particle removal, microorganism removal

Target contaminants Most common membrane structure Most common membrane configuration Dominant exclusion mechanism Typical transmembrane pressure Typical recovery

Particles Homogeneous (MF) or integral-asymmetric (UF) Hollow fiber

Desalination, NOM removal, specific contaminant removal, softening Dissolved species Asymmetric composite Spiral-wound

Straining

Different diffusivity

0.1–2 bar

3–100 bar

> 95%

50–90%

100 | 5 Membrane separation processes

Tab. 5.1: (continued) Process characteristic

Microfiltration/Ultrafiltration

Nanofiltration/Reverse osmosis

Typical ranges of permeate flux Influenced by osmotic pressure Influenced by concentration polarization Most common flow pattern Backwashing Competing conventional processes

50–120 L/(m2 ⋅ h) No No

10–40 L/(m2 ⋅ h) Yes Yes

Dead-end Yes Granular filtration

Tangential (cross-flow) No Adsorption, ion exchange, precipitative softening

5.2 General aspects 5.2.1 Operational modes With respect to the flow regime, there are two common types of filtration/separation: dead-end filtration and cross-flow filtration (Figure 5.3). In dead-end filtration, the total fluid volume passes through the membrane. That means that the permeate (filtrate) volume equals the feed volume (given that the particle volume can be neglected). Particles that are too large to pass through the membrane accumulate on the membrane Dead-end filtration

Cross-flow filtration

Feed

Feed

Permeate

Retentate

Permeate

Cover layer thickness Permeate flux

Permeate flux Time

Cover layer thickness Time

Fig. 5.3: Membrane operation modes: dead-end and cross-flow filtration.

5.2 General aspects | 101

surface, which results in the formation of a cover layer that decreases the permeate flow over the time. Therefore, the cover layer (filter cake) has to be removed by periodic backwashing. Dead-end filtration is typically applied in microfiltration and ultrafiltration processes. During the run time of a dead-end filtration, no retentate (concentrate) occurs. However, a concentrated suspension is generated during backwashing. In cross-flow filtration, the fluid flows parallel to the membrane surface. Since a fraction of the water passes the membrane, the concentration on the feed side increases in the flow direction and a retentate (concentrate) leaves the cross-flow module. The volume of the retentate equals the difference between the feed volume and the permeate volume. Due to the tangential water flow, most of the deposited particles are washed away. Accordingly, filter cake formation is limited but not fully avoided. Therefore, cleaning of the membrane surface after a certain run time is also necessary in this type of flow regime. Cross-flow filtration is the typical operation mode in nanofiltration and reverse osmosis, whereas dead-end filtration is not suitable for the dense membranes used in NF or RO.

5.2.2 Basic process parameters The water volume that is passed through the membrane is typically expressed as volumetric water flux, J w , which is the volumetric flow rate, V,̇ normalized to the membrane surface area, A M : V̇ V = (5.1) Jw = AM AM t where V is the volume passed through the membrane and t is the time. The SI unit of J w is m3 /(m2 ⋅ s). For practical purposes, however, often L/(m2 ⋅ h) is used as the unit. The value of J w in a given system strongly depends on the flow resistances, which are determined by the membrane material and the deposits on the membrane surface. The volumetric water flux, J w , is typically in the range of 50–120 L/(m2 ⋅ h) for porous membranes (MF, UF) and in the range of 10–40 L/(m2 ⋅ h) for dense membranes. Since the effort for a membrane process strongly depends on the transmembrane pressure that is necessary for the water transport through the membrane, it is reasonable to normalize the flux by the transmembrane pressure, ∆p. The resulting parameter P (L/(m2 ⋅ h ⋅ bar)) is referred to as the permeability: P=

Jw ∆p

(5.2)

Typical ∆p ranges for the different membrane processes are given in Figure 5.1. It has to be noted that an alternative unit for the permeability can be found by using the unit kg/(m ⋅ s2 ) for the pressure difference. Together with the flux in m/s, we get the unit m2 ⋅ s/kg for P. The permeability, determined with pure water (without suspended solids and dissolved substances), is referred to as membrane permeability, P m . It depends on the dy-

102 | 5 Membrane separation processes namic viscosity of water, η (in kg/(m ⋅ s)), and the membrane resistance, R m (in 1/m): Pm =

1 η Rm

(5.3)

Since the viscosity and, particularly for NF and RO membranes R m , depends on the temperature, the membrane permeability is strongly influenced by the water temperature. P m is therefore typically given for a reference temperature and has to be calculated for other temperatures using the temperature dependence of η and a membrane specific correction factor for R m . In practice, it is not only the membrane resistance, R m , that is relevant for the permeability but also further resistances, resulting from the formation of a covering layer, from pore blocking, and (in the case of NF and RO) from the transmembrane osmotic pressure. These resistances have to be added to R m in Equation (5.3). The fraction of material removed from the water is expressed by a parameter that is referred to as the rejection, R: cP (5.4) R =1− cF where c P is the concentration in the permeate and c F is the concentration in the feed water. R can be calculated for specific compounds as well as for collective parameters. Instead of the molar concentrations (suitable for dissolved substances) mass concentrations can also be used in Equation (5.4) (suitable for dissolved substances as well as particles). As can be derived from Equation (5.4), the theoretically possible range of R goes from 0 (no rejection) to 1 (complete rejection). In cross-flow separation, the feed water with a given concentration, c F , is split into the retentate and the permeate, with a higher concentration, c R , in the retentate and a lower concentration, c P , in the permeate. The concentration increase over the membrane module can be expressed by the concentration factor, C F : CF =

cR cF

(5.5)

The (theoretical) lower limit of C F is 1, which would mean that no water is passed through the membrane and the retentate concentration is the same as the feed concentration. Under practical conditions, C F is > 1. The concentration factor can also be expressed by means of mass concentrations instead of molar concentrations. The recovery, ϕ, is the ratio of the volumetric flow rates of the permeate, V̇ P , and the feed water, V̇ F : V̇ P (5.6) ϕ= V̇ F Under dead-end flow conditions, where all the water is passed through the membrane, the recovery is 1 (or 100% if expressed as percentage recovery) if only the filtration stage is considered. However, over the whole process cycle, including backwashing, there is a certain loss of water (permeate taken as backwash water) that reduces the

5.2 General aspects |

103

overall recovery. Nevertheless, the overall recovery in dead-end filtration processes (MF, UF) under practical conditions is relatively high and typically > 0.9 (or > 90%). Under cross-flow conditions, the permeate flow is always lower than the feed water flow, because a fraction of the water leaves the membrane system as retentate. With respect to a maximum recovery, the fraction of the retentate should be as low as possible. However, in this case, the concentration factor becomes very high. This can lead to serious technical problems (e.g., scaling), which will be discussed later. Therefore, the recovery cannot be maximized and an optimum between recovery and concentration factor has to be found. If it is assumed that no dissolved species are transported through the membrane, a simple relationship between concentration factor and recovery can be derived: 1 CF = (5.7) 1−ϕ Figure 5.4 gives a graphical representation of this relationship.

Fig. 5.4: Relationship between the concentration factor and the recovery for cross-flow membrane systems (assumption: no transport of dissolved species through the membrane).

As shown in Figure 5.2, the separation efficiency of the different membrane processes depends on the size of the particles or dissolved species to be removed. For dissolved or colloidal species, the molecular weight is more accessible than the molecule size. Therefore, the separation efficiency is often given as molecular weight cutoff (MWCO). The molecular weight cutoff is that molecular weight that corresponds to a rejection of 0.9. All molecules larger than the MWCO are retained by greater than 90%.

104 | 5 Membrane separation processes

5.2.3 Fouling and scaling During the run time of membrane devices, substances are deposited on the membrane surface. This unwanted accumulation can be subdivided into fouling and scaling. Fouling means the accumulation of inorganic or organic particles or colloids. It can be further subdivided into inorganic and organic fouling. Biofouling is a specific form of organic fouling caused by biological material. Scaling is the precipitation of dissolved ions as solid salts on the surface after exceeding the respective solubility products (Chapter 2, Section 2.3.4). Since microfiltration and ultrafiltration do not reject dissolved ions, precipitation does not occur and salts do not accumulate on the feed side. Scaling is therefore not relevant for MF/UF. By contrast, scaling is a serious problem in NF/RO because these membranes reject ions with the result that the ion concentrations on the feed side increase (concentration polarization) and solubility products can be exceeded. This is particularly relevant if the water contains higher concentrations of ions that are able to form weakly soluble salts (e.g., calcium carbonate or calcium sulfate). To avoid scaling, acids or specific antiscalants can be added to the feed water. More details on concentration polarization and scaling are presented in Section 5.4.3. Fouling can occur on MF/UF as well as on NF/RO membranes. In MF/UF systems, periodic backwash can slow down but not completely avoid the formation of a fouling layer. Therefore, a more intensive cleaning with chemicals is necessary at certain time intervals. More details about backwash cycles and the role of the transmembrane pressure as a control parameter are given in Section 5.3.2. The chemical cleaning is typically carried out in situ. That means that the membrane module remains within the membrane unit during the cleaning. This type of cleaning is therefore also referred to as clean in place (CIP). During the cleaning process, a cleaning solution is circulated through the membrane elements. High velocities and elevated temperatures enhance the cleaning process. Rinsing with water is necessary after the chemical cleaning before the membrane units can be put in operation again. In NF/RO units, backwashing is not possible. However, since these units are operated in a cross-flow regime, shear forces caused by the flowing water impede the formation of the fouling layer. Additionally, a pretreatment of the water (particle removal) is typically applied to reduce fouling on the dense nanofiltration and reverse osmosis membranes. Nevertheless, chemical CIP is also necessary in NF/RO systems but at relatively long time intervals (between three and 12 months). Chemicals that are applied for CIP are in particular sodium hydroxide to remove organics, surfactants to remove organics and inert particles, and oxidants and disinfectants to remove organics and biofilms. Oxidants and disinfectants are not suited for polyamide membranes, which are typically used in NF/RO units, because the oxidizing chemicals destroy the membrane material.

5.3 Microfiltration and ultrafiltration

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5.3 Microfiltration and ultrafiltration 5.3.1 Membrane materials In microfiltration (MF) and ultrafiltration (UF), porous membranes are used to remove particulate matter (inorganic or organic particles, bacteria, viruses). The separation mechanism is based on size exclusion (straining) and is comparable with that of the conventional surface filtration. The main difference between microfiltration and ultrafiltration consists of the pore size of the membranes and, as a consequence, in the different removal efficiency for viruses. In contrast to MF membranes, the smaller pore size of UF membranes allows removal of small viruses in addition to turbidity and bacteria. MF/UF membranes can be produced from organic or inorganic materials. Commonly used organic membranes are made of polyvinylidene difluoride (PVDF), polysulfone (PS), and polyethersulfone (PES). Polypropylene (PP) and cellulose acetate (CA) membranes, frequently used in the past, have lost importance. Inorganic ceramic membranes (e.g., made of aluminum oxide, titanium oxide, zirconium oxide, or silicon carbide) have gained popularity, in particular due to their mechanical and chemical stability. The structure of MF membranes is typically homogeneous. Such membranes are also referred to as symmetric or isotropic membranes. UF membranes are typically asymmetric. That means that they consist of a thin active layer with narrow pores and a support layer with larger pores. In the case of UF membranes, which typically consist of a single polymer, the asymmetric structure is a result of a specific production process. Such asymmetric membranes that consist of a single material are also referred to as integral-asymmetric membranes.

5.3.2 Membrane modules and membrane operation The membranes used in MF/UF are typically applied in the form of capillaries (diameter: 0.5 to 5 mm) or hollow fibers (diameter: < 0.5 mm), which are arranged in tubular modules. Figure 5.5 shows such a module, which can be operated in a dead-end or a cross-flow mode. Since MF/UF membrane processes are typically applied to raw waters with relatively low particle concentrations, the most common operation mode is dead-end filtration. Although a dead-end flow operation requires frequent backwashing, it is often preferred due to the lower pumping costs in comparison to cross-flow operation. Besides, cross-flow operations also do not work without any cleaning, because irreversible deposits have to be removed from time to time. However, operating MF/UF in a cross-flow regime may be feasible for raw waters with higher turbidity. Each membrane module contains a very large number of capillaries or hollow fibers. The modules themselves are typically arranged in racks where they are oper-

106 | 5 Membrane separation processes

Capillaries or hollow fibers

Retentate*

Feed

*only if operated under cross-flow conditions Permeate

Fig. 5.5: Schematic representation of a capillary or hollow fiber module. Feed

Outside-in mode

Permeate

Capillary

Inside-out mode Feed

Permeate

Fig. 5.6: Inside-out and outside-in operation of capillary membrane modules.

ated in parallel connection. In this way, the required total membrane surface area for the treatment of a given water flow rate can be provided. Capillary and hollow fiber membranes can be operated in inside-out mode (crossflow or dead-end flow) or outside-in mode (dead-end flow). The principles are shown in Figure 5.6. The volumetric water flux, J w , during the operation of MF/UF membranes depends on the transmembrane pressure, the membrane material and structure, and the composition and thickness of the covering layer. It can be described in a general form by: J w = k w ∆p (5.8) where k w is the mass transfer coefficient for the water flux, also referred to as the membrane constant. The mass transfer coefficient, k w , depends not only on the membrane

5.3 Microfiltration and ultrafiltration

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107

characteristics but also on the cover layer (foulant layer) that is formed at the membrane surface and in the pores during the membrane run time. Because the foulant layer is not constant over the time, k w also changes during the filtration run time (Figure 5.3). The mass transfer coefficient k w can be expressed as the reciprocal of the product of the total membrane resistance, R t , and the dynamic water viscosity (Section 5.2.2): kw =

1 η Rt

(5.9)

R t summarizes the intrinsic (membrane) resistance, R m , and the (time depending) resistance of the foulant layer, R f : Rt = Rm + Rf

(5.10)

Whereas R m is practically constant over the run time, R f increases with increasing thickness of the foulant layer. Accordingly, R t increases and k w decreases over the run time. Consequently, the permeate flux decreases over the membrane run time due to the material deposition on the membrane surface. Therefore, the transmembrane pressure has to be increased in order to compensate for the decreasing permeate flux and to keep the recovery constant. During backwashing, a part of the accumulated material is removed and the necessary transmembrane pressure decreases again. However, periodic backwashing cannot completely remove the accumulated material with the consequence that the transmembrane pressure shows an increasing tendency over the filtration cycles. If the maximum allowed transmembrane pressure is reached, a chemical cleaning of the membrane surface is necessary. This characteristic development of the transmembrane pressure over the membrane run time is shown in Figure 5.7.

Fig. 5.7: Transmembrane pressure as a function of membrane filtration run time.

108 | 5 Membrane separation processes

5.3.3 Combination of microfiltration/ultrafiltration with other treatment techniques In practice, two groups of combinations of MF or UF with other treatment techniques can be found. The first group comprises combinations with upstream treatment steps in which MF/UF substitutes the conventional filtration. The second group comprises combinations where MF or UF is used as pretreatment to improve the performance of a subsequent treatment step. As discussed in the previous sections, MF and UF are only able to remove particulate matter. If MF or UF are combined with an upstream treatment technique that transforms dissolved water constituents into particles (by precipitation) or binds dissolved species onto particles (by adsorption), the spectrum of removable substances can be extended to dissolved water constituents. Examples for such process combinations are the precipitation of calcium and magnesium ions (hardness), the oxidation and precipitation of iron(II) and manganese(II) ions, and the adsorption of dissolved organic substances onto powdered activated carbon. In all these cases, MF or UF substitutes the gravity filtration that is conventionally used for particle separation in these processes (Chapters 9, 10, and 12). Coagulation/flocculation with sedimentation (Chapter 6) can be used as a pretreatment step to enhance MF/UF membrane filtration performance by reducing the particle concentration in the water to be treated. This leads to an extension of the filtration run time until backwashing and to reduced fouling. MF or UF as a pretreatment step is frequently applied prior to nanofiltration or reverse osmosis to reduce the membrane fouling on the dense NF/RO membranes.

5.4 Nanofiltration and reverse osmosis 5.4.1 Osmosis and osmotic pressure Osmosis refers to the flow of solvent molecules to a solution through a semipermeable membrane that stops the flow of solute only (Figure 5.8). As a result, the pressure on the solution side increases, in Figure 5.8 illustrated as hydrostatic pressure. The flow can be stopped by applying a counter pressure. The pressure that is needed to stop the flow is referred to as the osmotic pressure. If an external pressure higher than the osmotic pressure acts on the solution side, a solvent flow out of the solution is initiated. This reversed process is referred to as reverse osmosis (RO). Since water can pass through the membrane whereas solutes are retained, reverse osmosis can be used to remove dissolved species. Practical applications are seawater or brackish water desalination and the removal of organic and inorganic species from freshwater. Nanofiltration (NF) is based on the same principle and can be considered a specific form of reverse osmosis. Since nanofiltration membranes are not as dense as reverse osmosis membranes, small molecules and ions can pass the membrane. Nanofil-

5.4 Nanofiltration and reverse osmosis

| 109

p Reverse osmosis

Water

Fig. 5.8: Osmosis and osmotic pressure.

tration can be used, for instance, for softening (removal of the bivalent ions Ca2+ and Mg2+ ). The osmotic pressure, π, depends on the molar concentration of the solutes. For single solutes, the osmotic pressure is given by the van’t Hoff equation: π = cRT

(5.11)

where R is the gas constant (R = 8.3145 J/(mol ⋅ K) = 0.083145 bar ⋅ L/(mol ⋅ K)) and T is the absolute temperature. For multicomponent systems, such as raw waters for drinking water production, it has to be summed over the concentrations of all dissolved species: π = ∑ ci R T (5.12) i

The given equations for calculating the osmotic pressure are strictly valid only for ideal solutions. The deviations found for real solutions are typically expressed by the osmotic coefficient, φ, that relates the (measured) osmotic pressure of a real solution to the osmotic pressure of an ideal solution, which can be calculated by Equation (5.11) or (5.12): π real (5.13) φ= πideal The osmotic coefficient, φ, depends on the concentrations of the solutes and on the temperature of the solution. The osmotic coefficients show larger deviations from 1

110 | 5 Membrane separation processes

(ideal solution) only at higher concentrations. For seawater (salinity 35 g/kg), for instance, the osmotic coefficient within the relevant temperature range is between 0.90 (0 °C) and 0.91 (30 °C). For dilute solutions, such as freshwater, φ approaches 1 and the deviations from the state of an ideal solution can be neglected.

5.4.2 Mass transfer According to Figure 5.8, the osmotic pressure is the pressure that has to be overcome if dissolved species are to be removed by reverse osmosis. However, it has to be considered that the rejection of the solutes in practical processes is typically < 1. Accordingly, the permeate is not pure water but still contains a certain concentration of solutes and therefore also exhibits an osmotic pressure. Therefore, in the general case, not only the osmotic pressure on the feed side but the difference between the osmotic pressure on the feed side and the osmotic pressure on the permeate side is relevant for the water flux through the membrane. This difference is referred to as the transmembrane osmotic pressure: ∆π = π(feed) − π(permeate) (5.14) The water flux, J w , typically reported as L/(m2 ⋅ h), is then given by: J w = k w (∆p − ∆π)

(5.15)

where ∆p − ∆π is the driving force of the mass transfer and k w is the mass transfer coefficient for the water flux (also referred to as the membrane constant). In the ideal case, reverse osmosis (RO) membranes are impermeable to dissolved species. Accordingly, the osmotic pressure on the permeate side should be zero. Under real conditions, however, there is a certain slip of small ions and the concentration and the resulting osmotic pressure on the permeate side is not absolutely zero, but very small when compared with the feed side. In nanofiltration (NF) systems, the situation is slightly different. Here, the membrane material is not as dense as in the case of reverse osmosis and more dissolved ions, particularly small univalent ions, are able to pass through the membrane. Accordingly, there is a significant concentration on the permeate side and also a respective osmotic pressure. That has the consequence that for a given water composition, ∆π is smaller in comparison to RO and a lower transmembrane pressure is needed to get the same driving force. Additionally, the higher permeability of NF membranes (higher values of k w ) allows higher fluxes at the same driving force or requires a lower driving force for the same flux. NF is therefore also referred to as the low-pressure variant of RO (low-pressure reverse osmosis, LPRO). Sometimes also the term low-energy reverse osmosis (LERO) is used due to the direct relationship between pressure and energy demand. The diffusive flux of dissolved salts, J s , through NF or RO membranes can be described in a simplified manner by using the concentration difference over the mem-

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| 111

brane as the driving force. Since NF or RO membranes are typically operated in a crossflow regime, the concentration on the feed side increases along the membrane surface from the initial feed concentration to the concentrate (retentate) concentration (Figure 5.3). For simplification, an average concentration is used to express the driving force. Accordingly, the mass transfer equation reads: J s = k s (cFC − c P )

(5.16)

where cFC is the average of the concentrations in the feed water and in the concentrate, c P is the concentration in the permeate, and k s is the mass transfer coefficient for the salt flux. The salt flux is typically given as mol/(m2 ⋅ s).

5.4.3 Concentration polarization and scaling During the operation of NF or RO membrane systems, dissolved ions, which do not pass through the membrane, are enriched at the feed side near to the surface of the membrane. This effect, which strongly influences the membrane performance, is referred to as concentration polarization. In Figure 5.9, the concentration polarization is schematically shown for cross-flow conditions. Here, J w is the water flux, and J s is the (comparatively lower) salt flux through the membrane. Due to the higher water flux in comparison to the salt flux, the concentration near to the membrane surface increases, which leads to a characteristic concentration gradient in the vicinity of the membrane surface. In a small layer, the concentration increases from the bulk concentration, c b , to the concentration at the membrane surface, c m . Although the concentration gradient induces a diffusive transport of ions away from the membrane surface, the concentration increase dominates the overall effect. cm Membrane

c (x) cb

Js Jw Water flow

x Fig. 5.9: Concentration polarization.

cP

112 | 5 Membrane separation processes

The consequences for the mass transfer of water and solutes can be derived from Equations (5.15) and (5.16), respectively. If the salt concentration on the feed side increases, the osmotic pressure increases as well. As a result, the transmembrane osmotic pressure, ∆π, increases and, given that the transmembrane pressure ∆p is constant, the water flux decreases. Furthermore, the increase of the mean salt concentration on the feed side, cFC , leads to an increase of the salt flux. Consequently, the concentration polarization reduces both the recovery and the rejection. If the ion concentration in the feed water increases to such an extent that the solubility products of weakly soluble salts are exceeded, these salts precipitate on the membrane surface. This effect is referred to as scaling. Scaling reduces the water flux through the membrane and, consequently, the recovery. In general, precipitation can be expected when the ion concentration is already high in the feed water and when the solubility product of the respective salt is low. Ca2+ ions play a particular role in scaling, because they not only belong to the major ions in all freshwaters but also form a number of weakly soluble salts with other frequently occurring ions. Calcium-containing precipitation products are in particular calcium sulfate (CaSO4 ), calcium carbonate (CaCO3 ), calcium fluoride (CaF2 ), and calcium hydrogenphosphate (CaHPO4 ). Precipitation of other weakly soluble alkaline earth sulfates (e.g., BaSO4 , SrSO4 ) is also possible, particularly in sulfate-rich waters. As shown in Chapter 2 (Section 2.3.4), the solubility product of an arbitrary salt Cm An(s) , consisting of a cation C and an anion A, is given by: ∗ Ksp = a m (Cn+ ) a n (Am− ) = γ m (Cn+ ) c m (Cn+ ) γ n (Am− ) c n (Am− )

(5.17)

where a is the equilibrium activity (the product of the molar equilibrium concentration, c, and the activity coefficient, γ). ∗ (the solubility exponent) is used to express Often, the negative logarithm of Ksp the solubility product: ∗ ∗ pKsp = − log Ksp (5.18) As can be derived from Equations (5.17) and (5.18), the solubility of a salt is lower the ∗ . Table 5.2 lists some solubility exponents for hardly soluble higher the value of pKsp salts that are relevant for scaling. Tab. 5.2: Solubility exponents of some salts that are relevant for scaling. Salt

∗ pK sp (25 °C)

CaCO3 CaSO4 CaF2 CaHPO4 BaSO4 SrSO4

8.5 4.3 10.5 6.7 9.9 6.5

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| 113

Precipitation takes place if the product of the actual activities or concentrations (the so-called ion activity product, IAP), calculated in analogy to Equation (5.17), ex∗ , which refers to the equilibrium activities. This conceeds the solubility product Ksp dition is often expressed by the saturation index, SI, which must be greater than zero for precipitation to occur (SI > 0, supersaturated solution): SI = log

a m (Cn+ ) a n (Am− ) IAP ∗ = log ∗ Ksp Ksp

(5.19)

In principle, there are two measures to avoid scaling: i) prevention of precipitation by addition of chemicals and ii) reduction of the concentration increase by limiting the recovery to keep the saturation index for the problematic salts lower than zero (undersaturated solution). To prevent precipitation, specific chemicals can be added to the water. One option is to add hydrochloric acid or to introduce carbon dioxide in order to transform carbonate to hydrogencarbonate according to: + − CO2− 3 + H 󴀕󴀬 HCO3

CO2− 3

+ CO2 + H2 O 󴀕󴀬

2 HCO−3

(5.20) (5.21)

This measure reduces the carbonate concentration and therefore the risk of calcium carbonate precipitation but has no impact on the sulfate scaling. Alternatively, antiscalants can be used. Antiscalants are chemicals that keep ions in solution or disturb the crystal growth during precipitation. Frequently used antiscalants are phosphonates, polyphosphates, and polyacrylates. According to the relationship between recovery and concentration factor (Equation (5.7), Figure 5.4), a reduction of the recovery decreases the concentration factor and helps to avoid scaling. On the other hand, with respect to the process efficiency, the recovery should be as high as possible. However, the more the recovery approaches 100%, the stronger the increase in the concentration factor. Therefore, a compromise has to be found under consideration of the initial concentration levels of the critical ions in the water. Frequently, both measures to avoid scaling are used in parallel. In this case, the process has to be optimized for a given water composition with respect to recovery and to the effects and costs of the added chemicals.

5.4.4 Membrane materials For nanofiltration and reverse osmosis, dense membranes are used. These membranes have no distinct pores; the relevant transport mechanism is diffusion. Membranes used in NF and RO are typically asymmetric composite membranes consisting of a porous support layer (e.g., made of polysulfone or polyethersulfone) and a very thin

114 | 5 Membrane separation processes

(≈ 50 nm) active layer. The support layer provides mechanical stability to the membranes, whereas the small active layer thickness reduces the mass transfer resistance and enables a high water flux. This active layer (dense membrane material) is polymerized directly on the support layer and consists in most cases of polyamides (PA). In comparison to asymmetric cellulose acetate (CA) membranes, more frequently used in the past, PA membranes are chemically and physically more stable. In particular, they are more stable against biodegradation and hydrolysis and also stable in a wide pH range. However, due to their surface characteristics they are susceptible to biological and particulate fouling. Oxidants (e.g., ozone, free chlorine) can deteriorate the membrane material and should not be added prior to the NF or RO application. The membrane material used in nanofiltration is less dense than that in reverse osmosis and additionally in most cases also slightly charged (Section 5.1), which supports the rejection of bivalent ions. Accordingly, the key difference between nanofiltration and reverse osmosis is that the latter retains univalent ions, whereas nanofiltration allows them to pass and retains practically only bivalent ions. Charged nanofiltration membranes are therefore especially suitable for softening (removal of Ca2+ and Mg2+ ).

5.4.5 Membrane modules and operation In nanofiltration and reverse osmosis systems, typically spiral-wound membrane elements are used (Figure 5.10). In these elements, membrane sheets together with spacer material are rolled up around a central permeate collecting tube. The permeate spacer or permeate carrier is sandwiched by two membrane sheets. Woven polyester fabric is the most common permeate spacer material. Three edges of the sandwich are glued to form an envelope; the fourth edge is connected with the central permeate collecting tube. Feed spacers, typically nets of polypropylene, are arranged between the membrane envelopes to provide an open channel for the feed water flow. The specific structure of the feed spacers promotes mixing of the water flow and enhances the washing off of salts and other rejected substances from the membrane surface. The thickness of the feed spacers is in the range of 0.5–2 mm. Spiral-wound membranes are cross-flow devices. The feed water flows through the membrane element in the axial direction, while the permeate flows in the radial direction towards the permeate collection tube. The spiral-wound elements are arranged in series connection in pressure vessels mounted on special skids. Typically, a number of pressure vessels are operated in parallel. This arrangement is referred to as a membrane stage. Within a stage, the flow velocity on the retentate (concentrate) side decreases due to the water flux through the membrane with the consequence that the mass transfer decreases and the concentration polarization increases. Therefore, often two-stage facilities are used, where the number of parallel pressure vessels in the second stage is reduced to compensate for the decreasing volumetric flow rate of the retentate of the first stage, which is the

5.4 Nanofiltration and reverse osmosis

Perforated permeate collection tube

|

115

Feed water

Permeate

Membranes Concentrate Permeate carrier Outer wrap

Feed water and concentrate spacers

Fig. 5.10: Spiral-wound membrane element.

feed of the second stage (Figure 5.11). Such a cascade arrangement avoids suboptimal velocity conditions and increases the overall recovery. More than two stages are also possible, but not as common as two-stage facilities.

Membrane stage 1

Concentrate 2nd stage

Concentrate 1st stage

Membrane stage 2

Permeate 1st stage

Permeate 2nd stage

Feed water

Permeate

Fig. 5.11: Two-stage RO membrane facility.

Due to the structure of dense membranes, backwashing is not possible. Therefore, an efficient pretreatment of the feed water is required to minimize fouling and scaling. Particles can be removed by granular filtration or by microfiltration/ultrafiltration prior to the NF/RO separation. To avoid scaling, the measures discussed in Section 5.4.3 can be applied. As already discussed in Section 5.1, RO membranes are able to reject all ions including univalent ions, whereas in nanofiltration only the larger ions (in particular the

116 | 5 Membrane separation processes

bivalent ions) are rejected. Except for this difference, dense membranes are not very selective. This should be kept in mind if NF/RO should be used to remove organics. In this case a parallel desalination and softening always occurs. Depending on the raw water quality and the treatment objective, a substream treatment can be a feasible option. The treated substream is then blended with untreated water to reach the targeted concentration level. Application of NF/RO separation typically requires a posttreatment of the permeate. Since small gaseous molecules are not removed by the membranes, dissolved carbon dioxide can pass through the membrane. On the other hand, Ca2+ and, in particular in RO also hydrogencarbonate, are rejected, which causes a strong disturbance of the calco–carbonic equilibrium (for details of the calco–carbonic equilibrium see Chapter 8). This effect is additionally reinforced if CO2 or other acids are added in order to control scaling (Section 5.4.3). Low pH values and high CO2 concentrations make the water corrosive. Therefore, the permeate has to be treated by one of the deacidification processes described in Chapter 8. In many cases, mechanical deacidification (stripping of CO2 ) is sufficient. Otherwise, chemical deacidification with alkaline substances can be additionally applied. Under certain circumstances, it can also be necessary to slightly increase the hardness in the permeate. Possible methods are described in Chapter 9 (Section 9.4).

6 Coagulation and flocculation 6.1 Introduction and treatment objectives Raw waters used for drinking water production often contain colloids with particle sizes between 1 nm and 1 μm and small suspended solids with particle sizes in the lower μm range. This is particularly true for surface water. Such small particles are difficult to remove by conventional sand filtration or by sedimentation. This problem will be exemplarily demonstrated here for sedimentation. The influence of the particle size on the filtration efficiency was already discussed in Chapter 4 (Section 4.3). Assuming laminar flow, the terminal settling velocity, v s , of a solid particle can be calculated by Stokes’s law: vs =

(ρ P − ρ F ) d2P g 18 η

(6.1)

where ρ P is the particle density, ρ F is the fluid density (here water density), d P is the particle diameter, η is the dynamic viscosity, and g is the gravitational acceleration (9.81 m/s2 ). Table 6.1 lists settling velocities and related settling times for a sedimentation height of 1 m, calculated for different particle densities and sizes. It can be derived from the results of the theoretical calculations that very long times are needed for sedimentation of very small particles. Additionally, at smaller particle sizes (< 0.1 μm), the Brownian motion becomes relevant with the consequence that the settling velocity becomes even slower and tends towards zero. Tab. 6.1: Settling velocities and settling times for particles of different sizes and densities calculated from Stokes’s law. The calculation was carried out by assuming a water temperature of 20 °C (density: 1 g/cm3 , dynamic viscosity: 1 × 10−3 kg/(m ⋅ s)). Particle density (g/cm3 )

Particle diameter (μm)

Settling velocity (m/h)

Settling time for 1 m (h)

1.5

10 1 0.1 0.01 10 1 0.1 0.01

9.81 × 10−2 9.81 × 10−4 9.81 × 10−6 9.81 × 10−8 2.94 × 10−1 2.94 × 10−3 2.94 × 10−5 2.94 × 10−7

1.02 × 101 1.02 × 103 1.02 × 105 1.02 × 107 3.40 × 100 3.40 × 102 3.40 × 104 3.40 × 106

2.5

https://doi.org/10.1515/9783110551556-006

118 | 6 Coagulation and flocculation

To overcome the problems in separation of small particles from natural waters, it is necessary to bring the small particles into contact and allow them to form larger aggregates that are easier to remove. This objective can be reached by applying coagulation and flocculation processes. The term coagulation refers to the destabilization of colloidal solutions and particle suspensions under formation of small aggregates (microflocs), whereas the term flocculation refers to the formation of larger aggregates (macroflocs) that can be removed from the water by filtration or sedimentation. As a result of coagulation/flocculation, a water is produced that is practically free of colloids and turbidity. During coagulation/flocculation not only are inorganic particles removed but under appropriate conditions also the NOM (natural organic matter) concentration is reduced, in particular the concentration of the high molecular NOM fraction. The removal of colloidal and finely dispersed solids is based on different mechanisms that typically act in parallel. Table 6.2 gives a brief overview; details are discussed in the following sections. Tab. 6.2: Mechanisms of particle aggregation. Mechanism

Principle

Nonspecific coagulation

Destabilization of the colloidal solution by electrolyte addition, compression of the electric double layer of the particles Destabilization of the colloidal solution by neutralization of the surface charge by adsorption of counterions Aggregation of destabilized particles and precipitation products formed from the coagulants, formation of larger particles (macroflocs), supported by addition of polyelectrolytes (flocculants), formation of polymer bridges between the particles, network formation Entrapping of particles in the precipitates formed by the coagulants

Specific coagulation Flocculation

Sweep coagulation

6.2 Coagulation 6.2.1 Stability of colloidal solutions For better understanding of the coagulation processes, the stability of the colloidal solution has to be considered in more detail. From thermodynamic considerations, in particular from the consideration of the change of the free energy (Gibbs energy), dG, it can be derived that the aggregation of neutral (uncharged) particles should be a spontaneously proceeding process. The thermodynamic condition for a spontaneously proceeding process is that the free energy (Gibbs energy) decreases as a result of the process (dG < 0). For systems with small particles, where the particle surface

6.2 Coagulation |

119

becomes relevant (systems with large surface to volume ratio), the change of the free energy (Gibbs energy), dG, is given by: dG = −S dT + V dp + σ dA

(6.2)

where S is the entropy, T is the absolute temperature, V is the volume, p is the pressure, σ is the surface tension, and A is the surface area, which is larger the smaller the particles are. Under the assumption of an isothermal and isobaric process it can be derived from Equation (6.2) that dG becomes negative if dA is negative: dG = σ dA

at

dT = 0 , dp = 0

(6.3)

Therefore, a spontaneous decrease of the surface area or, in other words, a spontaneous particle aggregation could be expected. However, in contrast to that expectation, colloidal solutions are often stable over long periods of time. The reason for the deviant behavior is that the colloids or small suspended particles in aqueous systems carry charges with the consequence that repulsion forces between the like-charged particles exist, which are not considered in Equation (6.2). Thus, the stability of colloidal solutions is a result of the preponderance of the electrostatic repulsion forces over the van der Waals attraction forces. The surface charge of colloids and small suspended particles originates from different sources. Aluminosilicates (e.g., clay minerals) contain cations, which compensate for the negative charges of the silicate crystal structure, resulting from the isomorphic substitution of silicon by aluminum. In aqueous systems, these cations are released and negatively charged particles are left. These structural charges are permanent charges. Oxides and hydroxides but also clay minerals carry surface OH groups that in aqueous systems can undergo deprotonation or protonation depending on the pH of the water. Protonation of the surface OH groups leads to positive charges, whereas deprotonation gives negative charges: ≡SOH + H+ 󴀕󴀬 ≡SOH+2 −

(6.4) +

≡SOH 󴀕󴀬 ≡SO + H

(6.5)

The symbol ≡SOH stands here for a surface OH group. The reaction equations show the influence of the pH on the formation of charges. Such pH-dependent charges are variable charges. Deprotonation or protonation are also possible for specific functional groups of the organic material (e.g., deprotonation of the acidic –OH and –COOH groups of humic substances). A further origin of surface charges is the sorption of ions, in particular the formation of surface complexes. Here, the surface OH groups are replaced by ions with different charge, for instance: − − ≡SOH + SO2− 4 󴀕󴀬 ≡SSO4 + OH

(6.6)

120 | 6 Coagulation and flocculation

In most cases, the particles occurring in natural aqueous systems are negatively charged. Between the like-charged particles, repulsive forces exist that depend on the charge and the distance between the particles. If we consider two particles with the charges Q1 and Q2 , we can derive from Coulomb’s law that the repulsive force, F C , is proportional to the charges and indirectly proportional to the square of the distance, L, between the charges: Q1 Q2 FC ∝ (6.7) L2 For reasons of electroneutrality, the negative charges at the solid surfaces are compensated by counterions in the solution. As a result, an electric double layer is formed around each particle. The formation of this electric double layer makes the situation with respect to the repulsion forces more complex in comparison to the simple case described by Coulomb’s law. For the further discussion on the stability of colloidal solutions, it is necessary to take at first a closer look at the electric double layer, in particular at the course of the repulsion potential within the electric double layer. The repulsion potential, E R , has its highest value directly at the surface and decreases with increasing distance from the surface due to the shielding of the negative surface charge by the increasing number of counterions. Figure 6.1 shows the repulsion potential as a function of the distance from the particle surface and the structure of the electric double layer. Repulsion potential ER,0 ER,C

Zeta potential

ER  ER ,0e DL x

ER,DL

Distance from the

Charged surface



particle surface, x

Shear plane Diffuse layer

Compact layer

Electroneutrality

Double layer

Fig. 6.1: Repulsion potential as a function of the distance from the particle surface and structure of the electric double layer (adapted from Weber and DiGiano, 1996).

6.2 Coagulation |

121

The layer in the direct vicinity of the surface consists of counterions only. Accordingly, the decrease of the repulsion potential is highest in this layer. This compact layer is also referred to as the Stern layer. In the next layer, the concentration of the counterions decreases and the concentration of the coions increases. This layer is referred to as the diffuse layer or Guy–Chapman layer. If the distance from the surface is great enough, the concentrations of co- and counterions converge and electrical neutrality is established. The zeta potential (ζ ), also shown in Figure 6.1, is of practical relevance and will be discussed in more detail in Section 6.2.2. The repulsion potential, E R , as a function of the distance can be expressed in a simplified manner by: E R = E R,0 e−κDL x (6.8) where E R,0 is the surface potential, x is the distance from the surface, and 1/κ DL is the Debye length, a parameter that describes how far an electrostatic effect of a charge carrier persists. According to Equation (6.8), the Debye length corresponds to that distance x where the repulsion potential equals E R,0 /e (x = 1/κ DL ). The Debye length can also be interpreted as the (formal) thickness of the double layer. Within the electric double layer, the net positive electric charge in the fluid compensates for the net negative surface charge. Accordingly, the complete system is electrically neutral. As already mentioned, the stability of colloidal solutions is determined by the interplay of attractive and repulsive forces, where the attractive forces are van der Waals

ER Repulsion potential Energy barrier

Resulting interaction potential, ER - EA

x

Attraction potential

EA Fig. 6.2: Interaction potential and energy barrier in the vicinity of the particle surface.

122 | 6 Coagulation and flocculation

forces and the repulsive forces are electrostatic forces. Both types of forces show a different dependence on the distance. In the intermediate distance range, the repulsive forces dominate and the interaction potential, which is the difference between the repulsion and the attraction potential, shows a maximum (Figure 6.2). This maximum represents the energy barrier that has to be overcome by the kinetic energy of the particles to allow them to aggregate. Accordingly, at a given kinetic energy, the aggregation is easier the lower the energy barrier is. Possible measures that can be used to decrease the energy barrier and to destabilize the system are described in Section 6.2.3.

6.2.2 The zeta potential as a characteristic parameter of the electric double layer To characterize the potential in the double layer, the so-called zeta potential (ζ potential) can be used. The zeta potential is that potential that corresponds to the transport velocity of the charged particles in an electric field. It has to be noted that the zeta potential is identical neither to the potential at the surface nor to the potential at the Stern layer, because it is not only the pure colloids nor the colloids with strongly bound counterions that are transported in the electric field. In practice, also a certain portion of the counterions of the diffuse layer stay attached to the moving particles. The zeta potential therefore represents a potential at a shear plane within the diffuse layer. Accordingly, it is lower than the surface potential and the potential of the compact layer (Figure 6.1). In contrast to the other potentials that are difficult to determine, the zeta potential can be easily determined with special, commercially available devices. That makes it an important parameter that is frequently used to control coagulation processes. To determine the zeta potential, the electrophoretic mobility of the particles, u, is measured experimentally by an optical method. The electrophoretic mobility is the velocity of the charged particles, v, in an electric field with the field strength, E, where E is given by the ratio of voltage, U, and electrode distance, L (E = U/L): u=

v vL = E U

(6.9)

The zeta potential, ζ , can be calculated from the electrophoretic mobility, u, by using the Smoluchowski equation: η ζ =u (6.10) ε0 ε r where η is the dynamic viscosity of the solution, ε0 is the permittivity of the vacuum (approximately 8.854 × 10−12 F/m = 8.854 × 10−12 C/(V ⋅ m)), and ε r is the relative permittivity (dielectric constant). The electrophoretic mobility is typically given in (μm/s)/(V/cm). In basic SI units, 1 (μm/s)/(V/cm) equals 1 × 10−8 (m/s)/(V/m). For water at 25 °C (η = 0.89 × 10−3 kg/(m ⋅ s), ε r = 78.46), the following relationship

6.2 Coagulation | 123

between the electrophoretic mobility and the zeta potential holds: m m 0.89 × 10−3 kg Vm 1 −12 s V ms 8.854 × 10 A s 78.46 kg m2 = 0.0128 = 0.0128 V A s3 μm/s u=1 ⇒ ζ = 12.8 mV V/cm

ζ = 1 × 10−8

(6.11) (6.12)

Note that the following equivalence relationships for the units are used in Equation (6.11): 1 C = 1 A ⋅ s and 1 V = 1 J/C = 1 kg ⋅ m2 /(A ⋅ s3 ). The decrease of the zeta potential during a coagulation process is an indicator for the decrease of both the repulsion potential and the energy barrier. Therefore, the zeta potential can be used to assess the coagulation efficiency.

6.2.3 Destabilization of colloidal solutions by coagulation processes The extension of the electric double layer depends on the ionic strength of the solution. The ionic strength, I, is defined by: I = 0.5 ∑ c i z2i

(6.13)

i

where c i is the molar concentration and z i is the charge of the ion i (Chapter 2, Section 2.2). It follows from the theory of the electric double layer that the double layer thickness (1/κ DL ) is inversely proportional to the square root of the ionic strength: 1 1 ∝ κ DL √I

(6.14)

The higher the ionic strength in the solution, the shorter the distance from the surface to that point where an equal distribution of the oppositely charged ions is reached. That means that increasing the concentration or the charge of the ions in the solution compresses the double layer. Accordingly, the local gradient of the electrostatic repulsion potential becomes steeper. Given that the attraction potential remains unchanged, a faster decrease of the repulsion potential decreases the energy barrier, the maximum of the interaction potential (Figure 6.3). By reducing the energy barrier, the particles can aggregate more easily. Therefore, salt addition is a possible way to destabilize colloidal solutions. The higher the concentration and the higher the charge of the added ions, the more pronounced the destabilization effect. Since this destabilization effect depends only on the charge and the concentration of the added ions and not on their specific chemical nature, it is referred to as nonspecific coagulation. However, it has to be stated that nonspecific coagulation alone is not an appropriate measure to destabilize colloidal solutions in drinking water treatment, because it requires relatively high salt concentrations that are unwanted in drinking water.

124 | 6 Coagulation and flocculation

ER

ER Low ion concentration

High ion concentration

ER - EA ER - EA x

EA

x

EA

Fig. 6.3: Decrease of the energy barrier by increasing the ion concentration in the solution (nonspecific coagulation).

Besides nonspecific coagulation also specific coagulation can lead to a destabilization of colloidal solutions. Specific coagulation is based on the neutralization of the surface charge by adsorption of highly charged counterions with high affinity to the colloid particles. Specific coagulation is therefore also referred to as coagulation by charge neutralization. The decrease of the surface charge by adsorption of counterions results in a shift of the repulsion potential curve to lower values, which decreases the energy barrier. The principle is schematically shown in Figure 6.4. In water treatment, in particular Al3+ and Fe3+ salt solutions are used as coagulants. These metal ions form aqua complexes in water ([Al(H2 O)6 ]3+ , [Fe(H2 O)6 ]3+ ), which further undergo pH-dependent hydrolysis reactions leading to hydroxo complexes. Besides mononuclear also highly charged polynuclear complexes are formed during the hydrolysis reactions. At low and medium pH values, positively charged complexes predominate (Section 6.2.4). These coagulants act in different ways. Due to the high charges of the hydrolysis products these species cause a compression of the electric double layer, at least to a certain extent. On the other hand, the colloids and small suspended particles in raw water typically carry negative charges, and the positively charged hydroxo complexes of Al3+ and Fe3+ are able to act as specific coagulants. It is therefore not possible to exactly distinguish between both coagulation mechanisms if aluminum and iron salts are applied as coagulants. It can be assumed that in practice specific and nonspecific coagulation act in parallel. In the case of organic particles with negatively charged functional groups (e.g., anionic groups of humic or fulvic acids), the surface charge can also be reduced by

6.2 Coagulation | 125

ER

ER Decrease of the surface potential

ER - EA ER - EA x

EA

x

EA

Fig. 6.4: Decrease of the energy barrier by partial neutralization of the surface charge (specific coagulation).

decreasing the pH (protonation of the anionic groups). This effect is utilized in the so-called enhanced coagulation (Section 6.2.4).

6.2.4 Coagulants The conventional coagulants used in drinking water treatment are aluminum and iron salts, such as aluminum sulfate (Al2 (SO4 )3 ⋅ 18 H2 O), aluminum chloride (AlCl3 ⋅ 6 H2 O), ferric sulfate (Fe2 (SO4 )3 ⋅ 9 H2 O), ferrous sulfate (FeSO4 ⋅ 7 H2 O), ferric chloride (FeCl3 ⋅6 H2 O), and ferric chloride sulfate (FeClSO4 ). If ferrous sulfate is dissolved in water, the primarily formed Fe2+ ions are rapidly oxidized to Fe3+ by dissolved oxygen. As already mentioned in Section 6.2.3, the Al3+ and Fe3+ ions originating from the dissolution of the aluminum and iron salts form aqua complexes ([Al(H2 O)6 ]3+ , [Fe(H2 O)6 ]3+ ) that further undergo transformation to different hydroxo complexes of which in particular the highly charged polynuclear complexes are best suited to inducing coagulation. If we take an aluminum salt as an example, the first step of the hydroxo complex formation can be formulated as follows: [Al(H2 O)6 ]3+ 󴀕󴀬 [Al(H2 O)5 OH]2+ + H+

(6.15)

This type of reaction is also referred to as hydrolysis (decomposition reaction with water as reactant). The reaction shown in Equation (6.15) is often written in a simplified manner, without considering the water molecules in the complexes, as: Al3+ + H2 O 󴀕󴀬 AlOH2+ + H+

(6.16)

126 | 6 Coagulation and flocculation

Tab. 6.3: Formation of aluminum hydroxo complexes. Mononuclear complexes AlOH2+ Al(OH)+2 Al(OH)03 Al(OH)3(s) Al(OH)−4

Al3+ + H2 O 󴀕󴀬 AlOH2+ + H+ Al3+ + 2 H2 O 󴀕󴀬 Al(OH)+2 + 2 H+ Al3+ + 3 H2 O 󴀕󴀬 Al(OH)03 + 3 H+ Al(OH)03 󴀕󴀬 Al(OH)3(s) Al3+ + 4 H2 O 󴀕󴀬 Al(OH)−4 + 4 H+

Polynuclear complexes Al2 (OH)4+ 2 Al3 (OH)5+ 4 Al4 (OH)6+ 6 Al6 (OH)3+ 15 Al8 (OH)4+ 20 Al13 O4 (OH)7+ 24

+ 2 Al3+ + 2 H2 O 󴀕󴀬 Al2 (OH)4+ 2 + 2H 5+ 3+ 3 Al + 4 H2 O 󴀕󴀬 Al3 (OH)4 + 4 H+ + 4 Al3+ + 6 H2 O 󴀕󴀬 Al4 (OH)6+ 6 + 6H 6 Al3+ + 15 H2 O 󴀕󴀬 Al6 (OH)3+ + 15 H+ 15 8 Al3+ + 20 H2 O 󴀕󴀬 Al8 (OH)4+ + 20 H+ 20 7+ 3+ 13 Al + 28 H2 O 󴀕󴀬 Al13 O4 (OH)24 + 32 H+

Tab. 6.4: Formation of iron(III) hydroxo complexes. Mononuclear complexes FeOH2+ Fe(OH)+2 Fe(OH)03 Fe(OH)3(s) Fe(OH)−4

Fe3+ + H2 O 󴀕󴀬 FeOH2+ + H+ Fe3+ + 2 H2 O 󴀕󴀬 Fe(OH)+2 + 2 H+ Fe3+ + 3 H2 O 󴀕󴀬 Fe(OH)03 + 3 H+ Fe(OH)03 󴀕󴀬 Fe(OH)3(s) Fe3+ + 4 H2 O 󴀕󴀬 Fe(OH)−4 + 4 H+

Polynuclear complexes Fe2 (OH)4+ 2 Fe2 (OH)3+ 3 Fe3 (OH)6+ 3 Fe3 (OH)5+ 4

2 Fe3+ + 2 H2 O 󴀕󴀬 Fe2 (OH)4+ 2 2 Fe3+ + 3 H2 O 󴀕󴀬 Fe2 (OH)3+ 3 3 Fe3+ + 3 H2 O 󴀕󴀬 Fe3 (OH)6+ 3 3 Fe3+ + 4 H2 O 󴀕󴀬 Fe3 (OH)5+ 4

+ 2 H+ + 3 H+ + 3 H+ + 4 H+

In subsequent reactions, further mononuclear and polynuclear hydroxo complexes can be formed. Comparable reactions sequences are also found for [Fe(H2 O)6 ]3+ . Tables 6.3 and 6.4 list the simplified reaction equations for the formation of mononuclear and polynuclear hydroxo complexes of aluminum and iron. Whereas verified information about the formation of the mononuclear complexes exists (including the complex stability constants), knowledge about the occurrence of different polynuclear species is still insufficient. The tables list some examples of polynuclear complexes that are frequently reported in the literature. It has to be noted that the species Al(OH)3(s) and Fe(OH)3(s) listed in the table are the solid hydroxides that are formed during the sequence of the hydrolysis reactions. They are in equilibrium with the dissolved neutral complexes of the same composition, Al(OH)03 and Fe(OH)03 .

6.2 Coagulation | 127

As can be derived from Tables 6.3 and 6.4, the complex formation is connected with a release of protons, which may influence the pH of the water. To what extent the pH is influenced in practice depends on several factors, in particular the number of protons released, the initial pH of the water, and the content of buffer substances that are able to bind the released protons (e.g., hydrogencarbonate). Conversely, the pH determines the speciation of the complex species (Section 6.4.2). Due to the different influence factors, the hydrolysis proceeds more or less uncontrolled and the resulting mixture of hydroxo complex species may be different depending on the water characteristics and the coagulant dosage. If such high amounts of aluminum or iron coagulants are added to the water that the solubility product of the respective hydroxides Al(OH)3(s) or Fe(OH)3(s) is distinctly exceeded, the hydroxides rapidly precipitate. During settling, the primarily formed amorphous hydroxides of aluminum and iron are able to entrap colloids, small suspended particles, and even some dissolved species. This mechanism is referred to as sweep coagulation. The precipitation takes place in a medium pH range (Section 6.4.2). At higher pH values, the solubility of the hydroxides increases again due to the formation of the negatively charged hydroxo complexes Al(OH)−4 or Fe(OH)−4 . At this point, it is necessary to take a look at the role of hydrogencarbonate (bicarbonate) as the most important buffer substance in natural waters. Generally, buffer systems are specific acid/base systems that are able to keep the pH nearly constant by binding introduced protons or hydroxide ions. Hydrogencarbonate is able to bind protons as well as hydroxide ions under formation of CO2 and CO2− 3 , respectively. Buffering against the protons, which are released during the hydrolysis of aluminum and iron(III) salts, is based on the reaction: H+ + HCO−3 󴀕󴀬 CO2 + H2 O

(6.17)

In particular, at higher coagulant dosages and weakly buffered waters, this buffer reaction can lead to a total consumption of the available hydrogencarbonate and subsequently to a strong decrease of the pH to values out of the optimum range (Section 6.4.2). To overcome this problem, the coagulant dosage must be limited, or basic substances must be added. However, sometimes it is desirable to reduce the pH to a certain extent in order to neutralize the negatively charged components of the natural organic matter (in particular anionic species of humic or fulvic acids) and to allow them to take part in the floc formation. Higher amounts of NOM in the water are unwanted because NOM is a precursor for the formation of disinfection byproducts (Chapter 14). This specific form of coagulation with focus on NOM reduction is referred to as enhanced coagulation. For enhanced coagulation, the optimum pH that is necessary to fulfill the two different requirements (removal of NOM and removal of turbidity) has to be found by experiments. As an alternative to the simple aluminum and iron salts, prehydrolyzed coagulants have been developed, which are efficient over a wide range of pH and require lower

128 | 6 Coagulation and flocculation

dosages. Prehydrolyzed aluminum-based coagulants are polymeric substances with the general formula {Aln (OH)m Cl3n−m }x , where x is the number of the monomeric units. Frequently used coagulants of this type are aluminum chlorohydrate (ACH) with n = 2 and m = 5 and polyaluminum chloride (PACl) with n = 2 and m = 3. These coagulants are easily soluble in water and form highly charged cations such as [Al3 (OH)4 ]5+ , [Al8 (OH)20 ]4+ , and [Al13 O4 (OH)24 ]7+ . Since the OH− ligands of the complexes are already present in the coagulants, they must not be formed from water by the hydrolysis reactions shown above. Therefore, the release of protons and the consumption of hydrogencarbonate are lower if prehydrolyzed coagulants are used instead of the simple sulfates or chlorides. This can be demonstrated by a comparison of the overall reaction equations for the formation of the hydroxide, which is typically the final step of the hydrolysis reactions: Al2 (SO4 )3 ⋅ 18 H2 O 󴀕󴀬 2 Al(OH)3(s) + 6 H+ + 3 SO2− 4 + 12 H2 O +

−

Al2 (OH)3 Cl3 + 3 H2 O 󴀕󴀬 2 Al(OH)3(s) + 3 H + 3 Cl +

−

Al2 (OH)5 Cl + H2 O 󴀕󴀬 2 Al(OH)3(s) + H + Cl

(6.18) (6.19) (6.20)

If we compare the proton release on an equimolar basis with respect to Al, we can derive from the reaction equations that the most protons are released if aluminum sulfate is used and the fewest if aluminum chlorohydrate (ACH) is used. Polyaluminum chloride (PACl) takes an intermediate position, but its proton release is only the half of the proton release from aluminum sulfate. Prehydrolyzed iron(III) coagulants are also available. The most important product is polyferric sulfate (PFS) with the general formula {Fe2 (OH)n (SO4 )3−n/2 }x . In aqueous solutions, highly charged complexes are formed, such as [Fe2 (OH)3 ]3+ , [Fe3 (OH)4 ]5+ , and [Fe3 (OH)3 ]6+ . Due to the smaller pH decrease, the application of prehydrolyzed coagulants is particularly advantageous for weakly buffered waters.

6.3 Flocculation 6.3.1 Principle In principle, coagulation alone is able to destabilize colloidal solutions and suspensions of finely dispersed particles with the result that aggregates are formed. However, theses primary aggregates (microflocs) are relatively small and not easy to remove from the water. Therefore, a second process step is necessary, in which the destabilized particles further aggregate into larger particles (macroflocs) that can be removed by sedimentation and/or filtration. This second step is referred to as flocculation. In contrast to coagulation, flocculation proceeds under different hydrodynamic conditions and with other reaction times.

6.3 Flocculation | 129

In the coagulation stage, the coagulants have to be introduced into the water in such a way that the chemicals are very quickly and intensively distributed in the water by rapid mixing. The destabilization occurs very fast. The required reaction time is on the order of seconds. The further aggregation in the flocculation stage requires collisions between the microflocs. These collisions can be induced by Brownian motion or creating relative motions of the particles by means of stirring or by a specific hydrodynamic reactor design. Here, it has to be ensured that the introduced stirrer energy or the turbulences in the reactor are not too high, because otherwise the formed macroflocs are destroyed again. The typical hydraulic residence times in the flocculation reactors are between 10 and 45 min. To support the flocculation, water soluble polymers (polyelectrolytes) can be used as flocculant aids (or flocculants). These polymers adsorb onto the surfaces of the destabilized particles and form bridges between them. Figure 6.5 shows the principle of bridging. Colloid

Flocculant

Colloid

Bridging

Fig. 6.5: Bridging mechanism.

It has to be noted that the term flocculation can be used different manners. In a broader sense, flocculation means the aggregation of destabilized particles with or without flocculant aids. In a narrower sense, the term flocculation is used to describe the formation of macroflocs through bridging and network formation by flocculant aids (water-soluble polymers).

6.3.2 Flocculants The polymers that should be used as flocculants must be water-soluble and nontoxic. The most frequently used flocculants are nonionic polyacrylamide and anionic acrylamide/acrylate copolymers (Figure 6.6). Both molecular groups, the acrylamide group and the acrylate group, are polar and able to adsorb onto mineral surfaces. The polarity is necessary to make the polymers water-soluble, whereas the adsorption property is a precondition for bridging and macrofloc formation. It is assumed that the acryl-

130 | 6 Coagulation and flocculation

Acrylamide group CH2

CH

Acrylate group CH2

CH

C NH2

O

(a)

C O

O

Hydrolysis of the acrylamide group CH2

CH

(b)

O

CH2 + H2O

C NH2

CH + NH4+

C O

O

Fig. 6.6: Molecular groups in polyacrylamide and acrylamide/acrylate copolymers (a) and acrylamide hydrolysis (b).

amide group is the most relevant group for the adsorption, whereas the primary function of the negatively charged acrylate group is to extend the polymer chains by electrostatic repulsion, which enhances the range of influence and improves the bridging. It has to be noted that polyacrylamide always contains a certain fraction of acrylate, because the acrylamide group undergo a hydrolysis under formation of an acrylate group. Instead of synthetic polymers, natural polymers can also be used as flocculant aids. Examples are starch, chitosan (from chitin shells), and sodium alginate (from brown algae). It has to be noted that the application of special flocculants is not absolutely necessary, because after the application of the coagulants the surface potential is strongly reduced and the aggregation becomes possible under the condition that the particles are able to collide. Furthermore, the hydroxo complexes (in particular the polynuclear hydroxo complexes) can also form bridges between the destabilized particles. Nevertheless, a flocculant aid is often used in practice to make the floc formation more efficient.

6.3.3 Kinetic aspects As already mentioned, particle growth requires a previous particle collision. Small particles (< 0.1 μm) undergo Brownian motion that leads to particle-particle collisions. This primary aggregation mechanism is referred to as microscale flocculation or perikinetic flocculation. During this primary phase of aggregation, particles with sizes up to about 1 μm are formed. The rate of microscale flocculation depends on the kinetic energy of the particles, the collision efficiency, and the viscosity of the aque-

6.3 Flocculation | 131

ous system. The aggregation in the perikinetic phase of the flocculation process, expressed by the decrease of the particle number with time, follows a second-order rate law (Chapter 2, Section 2.4). Under the simplifying assumption of a monodisperse system, the following rate equation holds: −

4 kB T 2 dN = αP N = k2 N 2 dt 3η

(6.21)

where N is the number concentration of particles (number of particles per unit of volume, 1/m3 ), α P is the collision efficiency factor of the perikinetic flocculation (attachments per collision, dimensionless, range from 0 to 1), k B is the Boltzmann constant (1.38 × 10−23 J/K = 1.38 × 10−23 kg ⋅ m2 /(s2 ⋅ K)), T is the absolute temperature (K), η is the dynamic viscosity of water (kg/(m ⋅ s)), and k2 is the second-order rate constant (m3 /s). In the second stage of flocculation, collisions caused by velocity gradients lead to further growth of the particles (particle sizes > 1 μm). Velocity gradients can be induced by gently stirring the water. This flocculation mechanism is referred to as macroscale flocculation or orthokinetic flocculation. The rate of orthokinetic flocculation depends on the velocity gradient, the volume fraction of the particles in the water, and the collision efficiency. This process step follows a first-order rate law (Chapter 2, Section 2.4). For monodisperse systems, the respective rate law reads: −

dN 4 = α O ϕ G N = k1 N dt π

(6.22)

where α O is the collision efficiency factor of the orthokinetic stage (dimensionless, range from 0 to 1), ϕ is the floc volume per unit of solution volume (dimensionless), G is the root mean square (RMS) velocity gradient (1/s), and k 1 is the first-order rate constant (1/s). The total particle volume, V P , per unit of solution volume, V L , can be expressed by: N π d3P VP ϕ= = (6.23) VL 6 where N is the particle number per unit of volume (1/m3 ) and d P is the particle diameter. Note that ϕ is a constant quantity, because the decrease of N during the process is compensated by an equivalent increase of d3P . The RMS velocity gradient, G (1/s), for uniform shear flow (laminar flow conditions) is given by: G=√

P η VR

(6.24)

where P is the power input by mixing (W = kg ⋅ m2 /s3 ), η is the dynamic viscosity (kg/(m ⋅ s)), and V R is the reactor volume (m3 ). Equation (6.24) is known as the Camp–

132 | 6 Coagulation and flocculation

Stein equation. For turbulent flow conditions, as occurs in many flocculation units, G has to be multiplied with an empirical correction factor. When compared with microscale flocculation, macroscale flocculation is the slower process and determines the overall rate. Flocculation reactors are therefore designed with respect to the orthokinetic flocculation. Although criticized for its simplification, the RMS velocity gradient and its relationship to the power input is widely used as a characteristic parameter for the design of flocculation basins. Often also the Camp number, Ca, which is the product of the RMS velocity gradient, G, and the hydraulic residence time, t r , is used as a characteristic process parameter: Ca = G t r

(6.25)

Typical values for flocculation basins are G = 5–100 s−1 and t r = 10–30 min, depending on the flocculator type. The RMS velocity gradient can also be used to characterize the rapid mixing and coagulation basin. Here, the velocity gradients are much higher (up to 1 000 s−1 and even higher), whereas the residence times are shorter (< 5 min). More details about coagulation/flocculation facilities will be given in Section 6.5.

6.4 Important influence factors and process conditions 6.4.1 General aspects The removal of colloids and small suspended solids is a very complex process, influenced by a number of factors, such as concentration and surface properties of the particles, chemical properties of the coagulants and flocculants and their reactions in water, coagulant and flocculant concentration, composition of the water to be treated, water temperature, and others. It is therefore not possible to design such a process on a theoretical basis alone. Instead, the optimum process conditions have to be found by laboratory-scale or pilot-scale experiments with the water to be treated. In so-called jar tests in the laboratory, the optimum coagulant and flocculant dosages as well as the most suitable pH value can be found for the respective water sample. A jar test apparatus consists of a number of stirred beakers, where series of experiments with varying influence factors can be carried out in parallel under identical hydrodynamic conditions (Figure 6.7). The parameters that are typically used to assess the process efficiency are the relative removal of the turbidity (measured

6.4 Important influence factors and process conditions

|

133

Fig. 6.7: Jar test apparatus.

as NTU) and/or the relative removal of the natural organic matter (measured as dissolved organic carbon, DOC, or UV absorbance at 254 nm), the residual coagulant and flocculant concentrations, and the sludge volume. Additionally, the filterability of the treated water can be tested. To find the optimum hydrodynamic conditions, pilot-scale experiments are necessary. Although an exact prediction of the coagulation/flocculation efficiency is not possible, useful recommendations can be derived from theoretical basics and practical experiences. A brief overview will be given in the following sections.

6.4.2 pH value The pH value is the most important parameter that influences the coagulation process. In particular, it determines the hydrolysis of the metal cations, the solubility of the hydroxides, and the resulting total metal concentration in equilibrium with the hydroxide (residual concentration after precipitation). For an efficient coagulation process, the pH should be in a range where positively charged hydroxo complexes are formed, which are able to destabilize the colloids and small suspended particles, and where the total solubility of the hydroxides is low enough to ensure a low residual coagulant concentration in the treated water. The diagrams in Figures 6.8 and 6.9 show the concentrations of the mononuclear hydroxo complexes of aluminum and iron in equilibrium with the respective solid hydroxides and the resulting total solubility of the aluminum and iron species. In both cases, a solubility minimum exists in the medium pH range. If compared with aluminum hydroxide, the solubility minimum of iron is lower and slightly shifted to higher pH values. Relevant concentrations of polynuclear hydroxo complexes, not shown in the diagrams, can be expected in the pH range left from the solubility minimum.

134 | 6 Coagulation and flocculation

Fig. 6.8: Solubility diagram of Al(OH)3 . The diagram shows the concentrations of mononuclear aluminum species in equilibrium with the solid hydroxide as a function of pH. The red curve depicts the solubility curve, i.e., the total concentration of all aluminum species. In the concentration range above this curve, the solution is supersaturated and precipitation of aluminum hydroxide can be expected.

Fig. 6.9: Solubility diagram of Fe(OH)3 . The diagram shows the concentrations of mononuclear iron(III) species in equilibrium with the solid hydroxide as a function of pH. The red curve depicts the solubility curve, i.e., the total concentration of all iron(III) species. In the concentration range above this curve, the solution is supersaturated and precipitation of iron(III) hydroxide can be expected.

6.4 Important influence factors and process conditions

|

135

Generally, the pH range around the minimum solubility is best suited for an effective coagulation with low residual concentrations of the coagulant. Therefore, in most practical applications, the pH values ranges from 6–8.

6.4.3 Temperature The temperature influences in particular the particle motion mechanisms in the aqueous phase (diffusion, convection), which determine the collision probability. Since the motion of particles becomes slower with decreasing temperature, the rate of the floc formation decreases with decreasing temperature. Given that the temperature is not an arbitrary parameter in drinking water treatment, the design of a coagulation/ flocculation process should be based on the worst case (i.e., the lowest expected water temperature).

6.4.4 Type and dosage of coagulants and flocculant aids Due to the complex character of the coagulation/flocculation process, it is not possible to give generally valid recommendations concerning the type and the concentration of the coagulants and flocculant aids. The best suitable type of coagulant or flocculant aid and the optimum dosages for each type of water has to be determined in jar test experiments. Therefore, only some general experiences can be reported here. For most applications, aluminum as well as iron coagulants can be used. According to the diagrams given in Figures 6.8 and 6.9, the solubility of iron hydroxide is much lower than that of aluminum hydroxide over a wide pH range. Accordingly, the residual iron concentrations after the flocculation/precipitation are low. Iron coagulants can therefore be used also at relatively high pH values (pH > 7.5). During the application of both types of coagulants, protons are released as a result of the hydrolysis reactions. This can be a problem if weakly buffered waters have to be treated. Here, it is often necessary to add bases to compensate for the proton release during the hydrolysis. Alternatively, prehydrolyzed coagulants can be used. The advantage of the prehydrolyzed coagulants over the conventional aluminum and iron salts consists of the lower proton release (Section 6.2.4). From several studies, it can be further derived that under optimum conditions the required dosage of prehydrolyzed coagulants (calculated on the basis of the metal) may be lower for the same coagulation effect when compared with the conventional salts.

136 | 6 Coagulation and flocculation

Tab. 6.5: Coagulant dosages for different water types and related floc separation processes (according to Jekel, 2017). Case

Water characteristics

Coagulant dosage

Suitable particle separation process

1

Low turbidity, low DOC

< 0.5 mg/L Al, < 1 mg/L Fe

Direct rapid filtration

2

Low turbidity, high DOC

0.3–0.6 mg Al/mg DOC, 0.6–1.2 mg Fe/mg DOC

Direct filtration or sedimentation

3

Moderate turbidity, low DOC

1–5 mg/L Al, 2–10 mg/L Fe

Sedimentation

4

High turbidity, high DOC

See case 2 or 3, whichever value is higher

Sedimentation and filtration

Generally, the required coagulant dosages strongly depend on the water quality parameters, the primary goal of the coagulation/flocculation process (turbidity removal, NOM removal, or both), and the subsequent separation process. Table 6.5 gives a rough orientation. The most widely used flocculant aids are synthetic polymers on a polyamide basis. Whether a polymeric flocculant aid is necessary or not and which is the optimum concentration has to be determined in experiments. The dosages applied in drinking water treatment are typically not very high (< 0.5 mg/L). In many cases, national regulations concerning the allowed residual concentration in the treated water exist.

6.4.5 Preozonation Ozone has been reported to improve the coagulation/flocculation process. This effect is referred to as microflocculation. The cause of the microflocculation effect is not yet known. It can be considered assured that ozonation changes the structure of the organic matter. This might have consequences for the interactions between the organic molecules but also between organic molecules and metal ions (coagulants, Ca2+ ) and thus directly or indirectly influences the coagulation/flocculation. It was observed that in the case of preozonation, the coagulant dosage could be reduced by 20 to 50% in comparison to coagulation without preozonation. Furthermore, it was found that the extent of the effect depends on the concentrations of NOM and Ca2+ in the water and is more pronounced at lower NOM concentrations.

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| 137

6.5 Coagulation/flocculation systems If type and optimum concentrations of coagulant and flocculant have been selected, for instance on the basis of jar tests, the optimum process conditions have to be found. In particular, the following design issues have to be considered: i) dosage and efficient distribution of the chemicals, ii) mixing intensity and time for flocculation, and iii) separation of the formed flocs. For chemical dosage and particle destabilization often flash mixing with rapid mixers is applied. The rapid mix tanks are equipped with especially designed impellers. The duration of mixing is a crucial factor. If the duration is too short, the chemicals will not be sufficiently distributed in the water. If the duration is too long, the newly formed aggregates will be damaged by the shear forces. Alternatively, the chemicals can simply be introduced into tubes or channels, where the turbulence is increased by baffles (principle of a static mixer). For the flocculation stage, different types of reactors are in use, which will be described later in this section. The separation of the formed flocs is typically carried out by sedimentation, filtration, or combinations of both. Filtration and sedimentation are discussed in detail in Chapter 4. Figure 6.10 shows the process schemes of some typical variants of the coagulation/flocculation process. The conventional and widespread variant consists of four stages: rapid mixing/coagulation, flocculation, sedimentation, and sand/gravel filtration. Under favorable conditions, the filtration stage can be omitted. For waters with low turbidity or low DOC, a direct filtration without sedimentation after the flocculation stage is possible. For low turbidity, the contact filtration may also be suitable. The contact filtration (or in situ filtration) is a specific process version that dispenses with the flocculation and sedimentation stages. Here, the destabilized colloidal solution is directly fed to a sand/gravel filter where the flocculation and separation takes place. In the conventional process, coagulation, flocculation, and sedimentation are carried out in separate basins (tanks). Figure 6.11 shows such a process scheme together with typical hydraulic residence times. The water is at first fed into the rapid mix/coagulation basin where the chemicals are added. After particle destabilization, the water is fed into the flocculation basin, which is also designed as a mixed reactor but with a larger volume and a lower stirrer velocity in comparison to the coagulation reactor. The slow mixing creates a velocity gradient that is necessary for particle collision (Section 6.3) but avoids damage of the formed flocs. Typically, vertical shaft turbines or horizontal paddle wheels are used in the flocculation basin. The floc separation is carried out by sedimentation. If necessary, an additional filtration stage can be introduced into the treatment process.

138 | 6 Coagulation and flocculation

Rapid mix/ Coagulation

Flocculation

Sedimentation

Rapid mix/ Coagulation

Flocculation

Sedimentation

Rapid mix/ Coagulation

Flocculation

Filtration

Rapid mix/ Coagulation

Filtration

Filtration

Fig. 6.10: Process schemes for different coagulation/flocculation systems. Chemicals

Influent

Effluent

Sludge

Residence time:

Rapid mix

Flocculation basin

Sedimentation basin

2…5 min

10…45 min

90…180 min

Fig. 6.11: Conventional coagulation/flocculation/sedimentation process. Coagulant

Flocculant

Effluent

Influent

Sludge

Fig. 6.12: Multichamber coagulation/flocculation/sedimentation reactor.

6.5 Coagulation/flocculation systems | 139

Influent from rapid mixer

Top view

Effluent to settling basin

Fig. 6.13: Hydraulic flocculator with horizontal baffles. Influent from rapid mixer

Side view

Effluent to settling basin

Fig. 6.14: Hydraulic flocculator with vertical baffles.

As an alternative to the separate basins in the conventional coagulation/flocculation process, compact reactors with different chambers can be used (multichamber reactors, Figure 6.12). Here, the chambers take over the functions of the conventional basins. In the given example, the sedimentation chamber is equipped with an additional lamella clarifier in the upper part to improve the floc separation. Instead of the mechanical flocculation in stirred reactors, flocculation can also be carried out as hydraulic flocculation. In this case, the water with the destabilized particles flows through a reactor with baffles that induce multiple flow reversals. In this way, the required velocity gradient is created but with a low turbulence that does not damage the flocs. Horizontal as well as vertical baffled hydraulic flocculators are in use (Figures 6.13 and 6.14). The hydraulic flocculators are simple but effective. They do not contain any moving parts and are easy to maintain. However, they are not very flexible. Hydraulic flocculation is an option in cases where a simple low-cost solution is wanted. In recent decades, different types of compact reactors have been developed, which integrate all three steps (mix/coagulation, flocculation, sedimentation). Here, the different processes take place in different compartments of the reactor (Figures 6.15 and

140 | 6 Coagulation and flocculation

Effluent

Sludge Influent

Fig. 6.15: Flocculation clarifier.

Effluent

Influent Sludge

Sludge

Fig. 6.16: Recirculated solids contact clarifier.

6.16). Whereas Figure 6.15 shows the simple form of a flocculation clarifier with compartments for rapid mixing, floc growth, and sedimentation, the reactor shown in Figure 6.16 contains a turbine that acts in such a way that a portion of the formed flocs undergo an internal recirculation. This leads to an increase of the overall process rate and consequently to a reduction of the required residence time, because – according to Equations (6.21) and (6.22) – the aggregation rate depends on the particle concentration. In comparison to the conventional coagulation/flocculation systems, these compact reactors allow for space reduction but are much more difficult to control. In particular, it is easier to optimize different reactors or reactor chambers than a singlestage reactor that has to meet the requirements of the different process steps.

7 Gas–liquid exchange 7.1 Introduction The term gas–liquid exchange covers all water treatment processes or stages of treatment processes where a gas compound is transferred from the gas phase to the water, which is in contact with the gas phase, or where a dissolved gas or a volatile substance is transferred from the aqueous phase to the adjacent gas phase. The direction of the mass transfer depends on the concentrations in the phases in relation to the respective equilibrium state. Accordingly, gas–liquid exchange processes can be subdivided into two classes: absorption and desorption processes (Figure 7.1).

Gas phase Absorption

Desorption Gas-liquid interface Aqueous phase

Fig. 7.1: Schematic representation of absorption and desorption.

Absorption is the uptake of a gas in the aqueous phase. Absorption is typically used in water treatment to introduce a gas into the water to initiate a subsequent chemical reaction. A typical example for absorption is the enrichment of water with oxygen from the air (aeration) in order to support oxidation processes such as the oxidation of iron(II) and manganese(II) ions. Other frequently used absorption processes are the introduction of ozone into the water to oxidize organic material, the introduction of chlorine to disinfect the water, and the enrichment of water with carbon dioxide to increase the hardness of very soft waters by means of a reaction of CO2 with calcium hydroxide or calcium carbonate. Desorption processes are applied to remove unwanted dissolved gases (e.g., dihydrogen sulfide, methane, excess amounts of carbon dioxide) or volatile substances (e.g., volatile organic compounds, VOCs) from the water. These processes are also referred to as degassing or stripping. Here, the mass transfer occurs from the aqueous phase to a stripping gas. Due to economic reasons, air is typically used as the stripping gas. The use of air has the further advantage that the water is enriched with oxygen from the air. Table 7.1 summarizes the most important absorption and desorption processes used in drinking water treatment. https://doi.org/10.1515/9783110551556-007

142 | 7 Gas–liquid exchange

Tab. 7.1: Absorption and desorption processes used in drinking water treatment. Process type

Substance to be introduced (absorption) or removed (desorption)

Objective

Additional information

Absorption

Oxygen, O2 (air)

Oxidation of Fe2+ and Mn2+

Chapter 10: Deironing and demanganization

Ozone, O3

Oxidation of organic substances, disinfection

Chapter 13: Oxidation; Chapter 14: Disinfection

Chlorine, Cl2

Disinfection

Chapter 14: Disinfection

Carbon dioxide, CO2

Increase of hardness, pH control

Chapter 9: Softening and dealkalization

Carbon dioxide, CO2

Removal of CO2 , pH control, corrosion control, establishment of the calco–carbonic equilibrium

Chapter 8: Deacidification

Dihydrogen sulfide, H2 S

Odor control

–

Gaseous or volatile organics (e.g., methane, haloforms)

Removal of unwanted and harmful organic substances, taste and odor control

–

Desorption

In this chapter, only the general basics of gas–liquid exchange are explained. For details of specific applications, the respective chapters, listed in Table 7.1, should be consulted.

7.2 Theoretical basics 7.2.1 Gas–water partitioning The gas to liquid or liquid to gas mass transfer is driven by concentration differences and ends in an equilibrium state given by Henry’s law. Henry’s law describes the partitioning of a gas or volatile substance between the gas and the liquid phase. According to this law, a linear relationship exists between the concentration of a gaseous (or volatile) compound in the liquid phase and its concentration (or partial pressure) in the gas phase (Chapter 2, Section 2.3.2). Typically, Henry’s law is written in the form: caq = H p

(7.1)

7.2 Theoretical basics

| 143

where caq is the molar concentration of the dissolved gas in the aqueous phase, H is the Henry constant (equilibrium constant), and p is the partial pressure of the gas. The unit of H in this writing of Henry’s law is mol/(L ⋅ bar). If Henry’s law is written in the form of Equation (7.1), a high value of the Henry constant indicates a high solubility of the gas. As with other equilibrium constants, the Henry constant depends on the temperature. Generally, the solubility of gases increases with decreasing temperature. Alternatively, Henry’s law can be formulated in an inverse form: p = Hinv caq

(7.2)

where Hinv is the inverse of the equilibrium constant H (Hinv = 1/H). In contrast to H, a high value of Hinv indicates a high volatility. It has to be noted that both versions of writing Henry’s law can be found in the literature and often the same abbreviation H (without qualifier) is used, which may cause confusion. It is therefore important to notice the unit when Henry constants are taken from the literature or from databases. Another point that has to keep in mind when using Henry constants concerns the fact that a number of modified formulations of Henry’s law can be found in the literature where other concentration measures are used to describe the composition of the gas and/or the aqueous phase. For absorption/desorption modeling purposes, the formulation using molar (or mass) concentrations for both phases is particularly relevant. The partial pressure of a gas in a gas mixture, p, is related to its molar concentration in the gas phase, c g , by the following expression, which can be derived from the state equation of an ideal gas: p=

ng R T = cg R T Vg

(7.3)

where n g is the substance amount (number of moles) in the gas phase, V g is the volume of the gas phase, R is the universal gas constant (0.083145 bar L/(mol ⋅ K)), and T is the absolute temperature. Accordingly, Equation (7.1) can also be written in the form: caq = H R T c g = K c c g (7.4) where K c is a dimensionless distribution constant that is related to H by: Kc = H R T

(7.5)

With the molecular weight, M, of the dissolved gas we can further write: Kc =

caq caq M ρ ∗aq = ∗ = cg cg M ρg

(7.6)

Accordingly, the value of K c is not only valid for the ratio of the molar concentrations, c, but also for the ratio of the mass concentrations, ρ ∗ . It has to be noted that the inverse form of Equation (7.6) can also be found in the literature.

144 | 7 Gas–liquid exchange

Tab. 7.2: Selected Henry and distribution constants according to Equations (7.1) and (7.6) (Sander, 2018). Gas

O2 O3 Cl2 CO2 CH4 H2 S

H (mol/(L bar))

K c (–)

10 °C

25 °C

10 °C

25 °C

0.0018 0.0166 0.1380 0.0521 0.0019 0.1505

0.0013 0.0110 0.0950 0.0340 0.0014 0.1000

0.042 0.391 3.249 1.227 0.045 3.543

0.032 0.273 2.355 0.843 0.035 2.479

Table 7.2 lists selected equilibrium constants for gases with relevance for drinking water treatment. In order to calculate the partitioning of a gas or vapor between the gas phase and the aqueous phase in a closed system (e.g., in a reactor), Henry’s law has to be combined with the material balance equation for a closed system. In this case, it is reasonable to use the same concentration unit for both phases, for instance the molar concentration or the mass concentration, together with the distribution constant given by Equation (7.6). The material balance equation for a substance distributed between the gas and the aqueous phase in a closed system reads: mtotal = m g + maq = ρ ∗g V g + ρ ∗aq Vaq

(7.7)

where mtotal is the total mass of the considered gas or vapor in the closed system, m g and maq are the masses in the gas phase and in the aqueous phase, respectively, V g and Vaq are the volumes of the gas and the aqueous phase, respectively, and ρ ∗g and ρ ∗aq are the respective mass concentrations. If we factor out the mass concentration in the gas phase and consider Equation (7.6), we receive: mtotal = ρ ∗g (V g +

ρ ∗aq ρ ∗g

Vaq ) = ρ ∗g (V g + K c Vaq )

(7.8)

After rearranging Equation (7.8), the gas phase concentration, ρ ∗g , in the state of equilibrium is found to be: mtotal ρ ∗g = (7.9) (V g + K c Vaq ) and the equilibrium concentration in the aqueous phase is given by: ρ ∗aq = K c ρ ∗g

(7.10)

7.2 Theoretical basics

|

145

Alternatively, ρ ∗aq can be calculated by factoring out ρ ∗aq in Equation (7.7): ρ ∗aq =

mtotal Vg ( + Vaq ) Kc

(7.11)

The gas phase concentration, ρ ∗g , is then given by: ρ ∗g =

ρ ∗aq Kc

(7.12)

An equation that relates the equilibrium concentration in the aqueous phase to the gas–water volume ratio can be derived by factoring out Vaq on the right-hand side of Equation (7.11): mtotal (7.13) ρ ∗aq = 1 Vg Vaq ( + 1) K c Vaq If we assume that in the case of a desorption process the total mass of the gas is initially dissolved in the aqueous phase (mtotal /Vaq = ρ ∗aq,0 ), the relative residual concentration in the aqueous phase can be expressed as a function of the gas–water volume ratio by: ρ ∗aq 1 = (7.14) ∗ 1 Vg ρ aq,0 1+ K c Vaq If the volume ratio is replaced by the ratio of the volumetric flow rates, V̇ g /V̇ aq , Equation (7.14) can also be applied to describe the equilibrium state in a continuous flow reactor. Figure 7.2 shows the relative residual concentration in the aqueous phase as a function of the gas–water volume ratio calculated from Equation (7.14). As can be seen from the diagram, desorption is more efficient the higher the gas–water volume ratio

Fig. 7.2: Influence of the gas–water volume ratio on the efficiency of a desorption process.

146 | 7 Gas–liquid exchange

and the lower the distribution constant are. However, it can be also derived from the diagram that above a certain volume ratio, the efficiency gain only grows slowly. For the case of gas to water transfer (absorption), it can be assumed that the total mass of the gas to be transferred is initially concentrated in the gas phase (mtotal /V g = ρ ∗g,0 ). From Equation (7.9), an expression can be derived that describes the relative residual concentration in the gas phase as a function of the water-gas volume ratio (or ratio of the respective volumetric flow rates): ρ ∗g ρ ∗g,0

=

1 1 + Kc

Vaq Vg

(7.15)

In contrast to desorption, the absorption is the more efficient the grater the water-gas ratio and the greater K c is (Figure 7.3). As with desorption, the efficiency only increases strongly up to a certain volume ratio.

Fig. 7.3: Influence of the water-gas volume ratio on the efficiency of an absorption process.

Analogous equations for the desorption and absorption efficiency can be derived for molar concentrations if the material balance (Equation (7.7)) is written for the substance amounts, n, instead of the masses, m.

7.2.2 Mass transfer The mass transfer from the donor phase (aqueous phase in the case of desorption, gas phase in the case of absorption) to the receiving phase can be described by the twofilm theory (Figure 7.4). Herein, the interface is considered a sharp boundary, where

7.2 Theoretical basics

Donor phase

| 147

Receiving phase Interface

c1

c1*

c2* c2

Boundary layer

Boundary layer

Fig. 7.4: Concentration profiles in the vicinity of the interface between the donor phase and the receiving phase during absorption or desorption processes.

equilibrium between the concentrations in both phases exists. All mass transfer resistances are assumed to be concentrated in laminar films on both sides of the interface. Due to the mass transfer resistances, concentration gradients exist across the laminar films. These gradients act as driving forces for the mass transfer and are assumed to be linear. The general mass transfer equation (Chapter 2, Section 2.5) reads: ṅ = k m aVR ∆c V R

(7.16)

where ṅ is the mass flow (mol/s), aVR is the area available for mass transfer related to the reactor volume (m2 /m3 ), k m is the mass transfer coefficient (m/s), and ∆c is the concentration difference (driving force), here the difference between the concentration in the bulk phase and the concentration at the interface (mol/m3 ). According to the two-film model, this mass transfer equation has to be applied to both phases. For the donor phase (here phase 1), we can write: ṅ 1 = k m,1 aVR (c1 − c∗1 ) V R

(7.17)

The respective equation for the receiving phase reads: ṅ 2 = k m,2 aVR (c∗2 − c2 ) V R

(7.18)

The concentrations at the interface, c∗1 and c∗2 , are related by the equilibrium relationship (Equation (7.6)). As a result of the mass transfer, the concentration in the donor phase decreases and the concentration in the receiving phase increases with time. Accordingly, the concentration differences (the driving forces of the mass transfer) in both phases decrease with time and vanish, when the equilibrium state is reached in

148 | 7 Gas–liquid exchange

the whole system, which means that in both phases the respective equilibrium concentrations not only occur at the interface but also in the bulk phase. Due to the continuity of the mass transfer, ṅ 1 must be equal to ṅ 2 . For the mass transfer from the liquid to the gas phase (desorption), the complete mass transfer equation reads: ṅ aq = ṅ g = k aq aVR (caq − c∗aq ) V R = k g aVR (c∗g − c g ) V R

(7.19)

Here, the subscripts aq and g stand for the aqueous and the gas phase, respectively. The formulation of the driving forces takes into account the fact that during the ongoing desorption process the concentration in the liquid phase is higher, whereas the concentration in the gas phase is lower than the respective equilibrium value. For the gas to liquid transfer (absorption), the mass transfer equation reads: ṅ g = ṅ aq = k g aVR (c g − c∗g ) V R = k aq aVR (c∗aq − caq ) V R

(7.20)

Both equations have the same mathematical form and differ only in the sign of the concentration differences and the related direction of mass transfer. For convenience, the following discussion will be restricted to the case of desorption only. The respective expressions for absorption can be easily found in an analogous manner. To further simplify the mass transfer equation, it can be assumed that the mass transfer resistance is concentrated only on one side of the interface, for desorption typically on the side of the liquid (Figure 7.5). A possible influence of the mass transfer resistance in the gas phase is considered by introducing an overall mass transfer coefficient. Donor phase (liquid phase)

Receiving phase (gas phase) Interface

caq

* caq

cg* = cg

Boundary layer

Fig. 7.5: Concentration profile in the vicinity of the interface during desorption under the assumption that the mass transfer resistance is concentrated on the liquid side.

7.2 Theoretical basics

|

149

Under this assumption, Equation (7.19) simplifies to: ṅ g = ṅ aq = k̂ aq aVR (caq − c∗aq ) V R

(7.21)

where k̂ aq is the overall mass transfer coefficient for the liquid film, which is related to the mass transfer coefficients k aq and k g by: 1 1 Kc = + ̂k aq k aq k g

(7.22)

Note that the mass transfer coefficients are reciprocals of the mass transfer resistances. Accordingly, Equation (7.22) describes the addition of the transport resistances in both phases to an overall resistance. Due to the fact that the overall mass transfer coefficient is thought to be on the liquid side, K c has to be additionally introduced into the resistance term of the gas side. Since it is assumed in this simplified approach that no concentration gradient exists on the gas side (c∗g = c g ), the liquid-phase equilibrium concentration at the interface is given by: c∗aq = K c c∗g = K c c g

(7.23)

The molar flow, ṅ aq , out of the liquid phase can be expressed by the change of the concentration in the aqueous phase with time according to: ṅ aq = V R

dcaq = k̂ aq aVR (caq − c∗aq ) V R dt

(7.24)

Finally, we get the mass transfer equation in a form that can be used for reactor design purposes: dcaq = k̂ aq aVR (caq − c∗aq ) (7.25) dt In the next section, the derivation of reactor design equations will be shown for a counterflow packed column as an example.

7.2.3 Design equations for counterflow packed columns Counterflow (or countercurrent flow) packed columns are frequently used for absorption or desorption processes in water treatment. Appropriate design equations can be derived by combining the material balance equation for the counterflow packed column with a mass transfer equation. As an example, we will use Equation (7.25) to describe the mass transfer during desorption in a column with the cross-sectional Area A R . Given that the change of the concentration in a control volume dV with the differential length dz (dV = A R dz) is caused by the mass transfer out of the liquid phase, we can write using Equation (7.25) (Chapter 2, Section 2.6.3): vz

dcaq dcaq = = k̂ aq aVR (caq − c∗aq ) dz dt

(7.26)

150 | 7 Gas–liquid exchange

where z is the axial position along the column and v z is the superficial flow velocity in the z direction, which is given by: vz =

V̇ aq AR

(7.27)

Separation of the variables and integration over the column height (z = h) gives: z=h

∫ dz = 0

h=

caq,in

dcaq ∫ caq − c∗aq k̂ aq aVR c aq,out vz

caq,in

dcaq ∫ ̂k aq aVR caq − c∗aq caq,out vz

(7.28)

(7.29)

where caq,in and caq,out are concentrations at the inlet and the outlet of the column, respectively. Note that for desorption holds: caq,in > caq,out . Equation (7.29) is the basic equation of the so-called NTU-HTU model, where NTU stands for the number of transfer units and HTU stands for the height of a transfer unit. HTU is given by the first term on the right-hand side of Equation (7.29) and NTU is given by the second term. The product of HTU and NTU gives the height of the column that is necessary to reach a given residual concentration in the aqueous phase: h = HTU ⋅ NTU with: HTU =

vz k̂ aq aVR

and:

caq,in

NTU =

∫ caq,out

=

V̇ aq A R k̂ aq aVR

dcaq caq − c∗aq

(7.30)

(7.31)

(7.32)

Generally, the NTU is a measure of the difficulty of the gas–liquid exchange. The less favorable the transfer process, the higher the required number of transfer units, NTU, is. The HTU is an indicator for the efficiency of the equipment, because it is determined by the mass transfer coefficient and the surface area available for mass transfer. The lower the value of HTU the more efficient the process. It has to be noted that there is only a minor influence of the flow velocity, because the mass transfer coefficient increases with increasing flow velocity. Consequently, both the numerator and the denominator in Equation (7.31) increase with increasing v z . The height of a transfer unit, HTU, can be calculated if the volumetric mass transfer coefficient (k̂ aq aVR ) is known. The volumetric mass transfer coefficient can be found either from empirical correlations or from experiments. To determine the number of transfer units, NTU, the integral in Equation (7.32) has to be solved. Before a solution is presented, at first a graphical representation of the problem will be shown.

7.2 Theoretical basics

caq,in

| 151

cg,out

P1

Vaq Vg

P2 caq,out

cg,in

Fig. 7.6: Schematic representation of the desorption process in a countercurrent flow column.

In Figure 7.6, a general scheme of a column operated under countercurrent flow conditions is depicted. The point P1 represents the water inlet and the gas outlet, whereas the point P2 represents the water outlet and the gas inlet. The material balance equation over the whole desorption column reads: V̇ aq (caq,in − caq,out ) = V̇ g (c g,out − c g,in )

(7.33)

Given that the balance equation must be valid for each point in the column where c g > c g,in and caq > caq,out , we can also write: V̇ aq (c g − c g,in ) = (caq − caq,out ) V̇ g

(7.34)

Equation (7.34) is the equation of the operating line of the desorption process. The operating line together with the equilibrium line, given by Henry’s law, is shown in Figure 7.7. This type of diagram is known as McCabe–Thiele diagram. It can be used

Equilibrium line Gas-phase concentration

NTU P1

cg,out

Operating line

cg,in

P2

caq,out

caq,in

Liquid-phase concentration

Fig. 7.7: McCabe–Thiele diagram for a desorption process (with c g,in = 0).

152 | 7 Gas–liquid exchange

to find the number of transfer units by drawing steps between the operating line and the equilibrium line. Note that in Figure 7.7 it is assumed that the gas phase is initially free of the substance to be stripped (c g,in = 0). To find an analytical solution to the NTU integral, it is reasonable to introduce a stripping factor, which is defined as the ratio of the slopes of the equilibrium line (1/K c ) and the operating line (V̇ aq / V̇ g ): S=

V̇ g 1/K c = ̇ ̇ ̇ Vaq / V g Vaq K c

(7.35)

The mathematical form of the analytical solution to the NTU integral depends on the initial gas phase concentration, c g,in , of the gas to be stripped. For the case that the stripping gas already contains a certain concentration of the gas to be stripped from the aqueous phase (c g,in > 0), for instance when CO2 is stripped with air, the following general solution holds: NTU =

caq,in − c∗aq,out S 1 S−1 ]} ln { + ( )[ S−1 S S caq,out − c∗aq,out

(7.36)

Given that the outlet of the liquid phase is the inlet of the gas phase (Figure 7.6) and the equilibrium liquid-phase concentration can be expressed by the distribution constant and the bulk gas phase concentration (Equation (7.23)), Equation (7.36) can also be written in the form: NTU =

caq,in − K c c g,in S 1 S−1 ]} ln { + ( )[ S−1 S S caq,out − K c c g,in

(7.37)

If the gas to be stripped does not occur in the stripping gas (c g,in = 0), the solution simplifies to: S 1 S − 1 caq,in NTU = ] (7.38) ln [ + ( ) S−1 S S caq,out Although demonstrated here for desorption, the HTU-NTU model can also be applied in an analogous manner for absorption, which will be briefly shown below. For absorption, typically a gas side overall mass transfer coefficient is used: 1 1 1 = + ̂k g k g K c k aq

(7.39)

The respective equations for the HTU and the NTU read: HTU = and:

V̇ g A R k̂ g aVR c g,in

NTU = ∫ c g,out

dc g c g − c∗g

(7.40)

(7.41)

7.3 Reactors for gas–liquid exchange | 153

The general solution to the NTU integral is: NTU =

c g,in − c∗g,out A 1 A−1 ]} ln { + ( )[ A−1 A A c g,out − c∗g,out

(7.42)

where A is the absorption factor defined by: A=

V̇ aq K c V̇ g

(7.43)

Given that the mass transfer resistance is here assumed to be on the gas side only, caq,in equals c∗aq,in and the gas phase equilibrium concentration at the gas outlet is related to the bulk liquid-phase concentration by: c∗g,out =

caq,in Kc

(7.44)

7.3 Reactors for gas–liquid exchange As can be derived from the theoretical considerations in the previous section, the efficiency of a gas–liquid exchange process depends on the distribution equilibrium (Henry’s law), the volumetric flow rate ratio, and the mass transfer rate. The mass transfer rate itself depends on the driving force, the mass transfer coefficient, which is a reciprocal measure of the transport resistance, and the interface area available for mass transfer. With respect to the mass transfer rate, sufficient contact times (to compensate for slow mass transfer and low driving forces) and large interface areas are required. In practice, for both absorption and desorption, different types of reactors (or contactors) are in use that more or less fulfill these requirements. Table 7.3 gives an overview of the most relevant reactor types. It has to be noted that in the case of aeration the boundary between absorption and desorption is fluent. In particular, if air is used as a stripping gas and the water has an oxygen deficit, then absorption of oxygen occurs in parallel to desorption of the unwanted water constituents. For such multipurpose aeration, bubble diffusers and cascade aerators can be used alongside the typical desorption reactors. Tab. 7.3: Reactors for absorption and desorption. Absorption

Desorption

Bubble diffusers Cascade aerators Venturi-type injectors Static mixers

Spray columns Corrugated plates columns Packed columns Sieve tray columns

154 | 7 Gas–liquid exchange

Bubble diffusers are reactors with gas inlets made of porous materials (mostly ceramic) that are located at the reactor bottom. The gas is introduced through the pores and form fine bubbles. The mass transfer from the gas phase to the liquid phase can be improved by creating plug flow and by increasing the contact time. Therefore, multichamber contactors are often used with alternating countercurrent and cocurrent flow. In cascade aerators, the water flows as a thin film over a series of steps, where water-air mixing occurs in the splash zones (waterfall effect). Venturi-type injectors utilize the Venturi effect, which means the reduction of the fluid pressure resulting from the increased flow velocity through a constricted section of a tube. The induced partial vacuum initiates the gas suction. The gas is dispersed in the water as tiny bubbles allowing a fast mass transfer. Static mixers are tubes that contain inbuilt mixing elements, such as crossing bars or crossing corrugated plates. Bubble diffusers, Venturi-type injectors, and static mixers are often used for ozonation. Schematic representations are therefore presented in Chapter 13. Venturitype injectors are also applied in water chlorination. Spray columns can be used for aeration and air stripping. The water is sprayed through nozzles and forms small droplets (Figure 7.8a). The contact between the stripping gas and water in a column can be improved by inbuilt corrugated plates (Figure 7.8b) or by introducing a packed bed consisting of inert elements, for instance Pall rings, Raschig rings, Intalox saddles, or Berl saddles (Figure 7.8c). These special packings were developed to reach a compromise between a high fluid flow and a high interfacial area between the gas and the liquid. In sieve tray columns, the water flows horizontally over a series of perforated trays (Figure 7.8d). The columns shown in Figure 7.8 are typically operated in a countercurrent flow regime. Spray columns and corrugated plates columns are sometimes also operated in a cocurrent flow regime. In this case, water and air are both introduced at the top of the column. The air is sucked in by the water flow (water jet pump principle) and an air blower is no longer necessary. That saves energy, but the unfavorable progress of the driving forces during the process leads to a lower efficiency in comparison to countercurrent flow conditions.

7.3 Reactors for gas–liquid exchange | 155

Waste gas

Waste gas

Spray nozzles

Spray nozzles Water

Water

Corrugated plates Countercurrent flow

Air

Air

Influent

Influent

Air

Air Pump

Pump

Air blower

Air blower

Treated water

Treated water

(a)

(b) Waste gas Waste gas

Spray nozzles

Spray nozzles

Water

Water

Perforated plates (trays)

Air

Packed bed (rings, saddles)

Influent Air

Air

Influent Air

Pump

Pump

Air blower

Air blower Treated water

Treated water

(c)

(d)

Fig. 7.8: Reactors used for desorption (air stripping): (a) spray column; (b) corrugated plates column; (c) packed-bed column; (d) sieve tray column.

8 Deacidification 8.1 Introduction and treatment objective Raw water, in particular groundwater, often contains high concentrations of dissolved carbon dioxide, CO2(aq) . Although dissolved carbon dioxide is transformed into carbonic acid (H2 CO3 ) only to a very small extent, the combination CO2 +H2 O behaves like the true carbonic acid and is therefore also referred to as carbonic acid. Since dissolved carbon dioxide is corrosive against metal and cement materials, high concentrations of carbon dioxide are unwanted in drinking water. However, the dissolved gas carbon dioxide is not an isolated water constituent but a component of a complex reaction system. As an acid it undergoes dissociation and it can also react with solid calcium carbonate. The respective equilibrium of this reaction system is referred to as the calco– carbonic equilibrium. The calco–carbonic equilibrium relates the CO2 concentration in the water to the dissolution or precipitation of calcium carbonate, CaCO3 . According to this equilibrium, a certain CO2 concentration in the water is necessary to keep calcium carbonate (mineral name: calcite) in solution (as Ca2+ and HCO−3 ). If more CO2 than this equilibrium concentration is removed from the water, calcium carbonate precipitates, which can lead to unwanted encrustations and blockages in tubes and reactors. The treatment objective is therefore not to remove the total CO2 but only the excess CO2 concentration, which is higher than that in the state of the calco–carbonic equilibrium, or in other words, the objective is to establish the calco–carbonic equilibrium in raw waters with CO2 excess. The specific treatment processes that can be used in drinking water treatment to reach this goal are referred to as deacidification processes. Since high concentrations of dissolved CO2 (carbonic acid) are accompanied with low pH values, deacidification also means an increase of the pH. Before discussing the different treatment options (Section 8.3), it is necessary to recapitulate the basics of the calco–carbonic equilibrium, its graphical representation, and the assessment method (Section 8.2). Basics of acid/base and precipitation/ dissolution equilibria that are necessary to understand the calco–carbonic equilibrium are given in Chapter 2 (Section 2.3.3 and 2.3.4). More detailed information about this fundamental equilibrium in aqueous systems can be found in special hydrochemistry textbooks (e.g., Worch, 2015).

8.2 The calco–carbonic equilibrium 8.2.1 Basics The calco–carbonic equilibrium (also referred to as the lime/carbonic acid equilibrium) is one of the fundamental reaction equilibria in the hydrosphere. It links the https://doi.org/10.1515/9783110551556-008

158 | 8 Deacidification

carbonic acid system with the precipitation/dissolution of calcium carbonate (calcite). The calcium and hydrogencarbonate (bicarbonate) ions, Ca2+ and HCO−3 , present in all natural waters in relatively high concentrations, as well as the dissolved gas carbon dioxide (also referred to as carbonic acid) are involved in this system. Through the dissociation of the carbonic acid, also a direct link exists to the pH of the water. The overall reaction equation of the calco–carbonic equilibrium reads: CaCO3(s) + CO2(aq) + H2 O 󴀕󴀬 Ca2+ + 2 HCO−3

(8.1)

The reaction from left to right describes the dissolution of calcite, whereas the reverse reaction from right to left describes the precipitation of calcite. When going into more detail, we can see that this complex reaction is composed of three elementary reactions, which are the first and the second dissociation step of the carbonic acid as well as the precipitation/dissolution equilibrium of calcite: CO2(aq) + H2 O 󴀕󴀬 H+ + HCO−3 HCO−3

󴀕󴀬

CaCO3(s) 󴀕󴀬

+

H + CO2− 3 Ca2+ + CO2− 3

(8.2) (8.3) (8.4)

The elementary reaction equilibria are characterized by their respective equilibrium constants, which are the acidity constants, K ∗a1 and K ∗a2 , and the solubility product, ∗ . The respective laws of mass action read: Ksp K ∗a1 = K ∗a2 =

a(H+ ) a(HCO−3 ) a(H+ ) γ(HCO−3 ) c(HCO−3 ) = a(CO2 ) c(CO2 ) a(H+ ) a(CO2− 3 ) a(HCO−3 )

=

2− a(H+ ) γ(CO2− 3 ) c(CO3 )

γ(HCO−3 ) c(HCO−3 )

∗ 2+ 2+ 2− 2− = a(Ca2+ ) a(CO2− Ksp 3 ) = γ(Ca ) c(Ca ) γ(CO3 ) c(CO3 )

(8.5) (8.6) (8.7)

For practical applications, the laws of mass action have to be written with measurable concentrations and activity coefficients instead of activities (right-hand side of the Equations (8.5)–(8.7)). There are two exceptions: i) the proton activity is directly measurable by a pH meter and must therefore not be substituted, and ii) in contrast to the ions, the behavior of the neutral CO2 can be considered as ideal (no interactions with the other solutes) with the consequence that a(CO2 ) equals c(CO2 ). Selected val∗ at different temperatures are listed in Table 8.1 (Section 8.2.2). ues of K ∗a1 , K ∗a2 , and Ksp Writing the second reaction equation (Equation (8.3)) in the reverse direction and adding all three reaction equations gives the overall reaction equation (Equation (8.1)). It has to be noted that, due to the complexity of the system, there is no single equilibrium state but an infinite number of possible equilibrium states, each of them characterized by a specific combination of the following parameters: c(CO2 ), 2+ c(HCO−3 ), c(CO2− 3 ), c(Ca ), and pH. The different situations that may occur in aqueous systems can be depicted by means of Equation (8.1).

8.2 The calco–carbonic equilibrium | 159

If the considered water is in the state of calco–carbonic equilibrium, calcium carbonate will neither be dissolved nor precipitated. The CO2(aq) concentration has exactly that value that is necessary to keep the calcium and hydrogencarbonate ions in solution. If the water contains a lower concentration of CO2 in comparison to the equilibrium state, calcium and hydrogencarbonate ions form solid calcium carbonate that precipitates until the equilibrium state is reached (reaction from right to left). Waters with CO2 deficits are therefore referred to as calcite-precipitating waters. Since the establishment of a new equilibrium state proceeds spontaneously by calcite precipitation, no specific technical measures are necessary. CO2 deficits can be found, for instance, in lakes with a high photosynthetic activity of submerged aquatic plants and phytoplankton, because CO2 is consumed during photosynthesis. The establishment of a new equilibrium state by formation of CO2 and simultaneous precipitation of CaCO3 can be observed in calcium-rich lakes as turbidity caused by fine white carbonate particles. This effect is also known as biogenic decalcification. If the water contains a higher concentration of CO2 than in the state of equilibrium, calcium carbonate will be dissolved under consumption of CO2 and formation of Ca2+ and HCO−3 (reaction from left to right) until the equilibrium state is reached. Waters with excess concentrations of CO2 are referred to as calcite-dissolving waters. Higher concentrations of CO2 are often found in groundwater as a result of biological degradation processes in the overlying soil layer. The CO2 produced by degradation of organic material is dissolved and transported with the seepage water to the groundwater level. The establishment of a new equilibrium state (related to the higher CO2 concentration) by dissolution of carbonate is only possible if solid calcium carbonate is available in the subsurface and the contact time of the water with the carbonate is long enough to allow the dissolution of the required amount of carbonate. If these conditions are not fulfilled, the water remains in a nonequilibrium state with an excess concentration of CO2 . High CO2 concentrations are problematic in view of drinking water treatment and distribution. Since dissolved carbon dioxide behaves like an acid (‘carbonic acid’, Equation (8.2)), high CO2 concentrations are correlated with low pH values. This combination of high CO2 concentrations and low pH values promotes metal corrosion. Furthermore, CO2 is also corrosive against cement materials because it facilitates the dissolution of carbonates. Such waters have to be treated with specific methods to remove the excess concentration of CO2 . As already mentioned in Section 8.1, the treatment objective is to reach the state of the calco–carbonic equilibrium. A stronger removal of CO2 makes no sense, because it would lead to unwanted calcium carbonate precipitation. It has to be noted that, besides the three reactions shown above, also other reactions (in particular the formation of ion pairs consisting of the cations Ca2+ and Mg2+ and different anions) have a certain impact on the calco–carbonic equilibrium. However, for our further discussion it is sufficient to consider the three basic reactions only.

160 | 8 Deacidification

The calco–carbonic equilibrium can be best depicted by means of the Tillmans curve as will be shown in the following section.

8.2.2 Tillmans curve and Langelier equation The Tillmans curve and the Langelier equation are important tools for dealing with the calco–carbonic equilibrium with respect to deacidification processes. The Tillmans curve allows a graphical representation of the calco–carbonic equilibrium and the effects of different treatment processes, whereas the Langelier equation provides the basis for the assessment of the calcite saturation state. As already mentioned before, each equilibrium state in the calco–carbonic sys2+ tem is characterized by five variables: c(CO2 ), c(HCO−3 ), c(CO2− 3 ), c(Ca ), and pH. However, according to the overall reaction equation (Equation (8.1)), only three variables are necessary to describe the equilibrium uniquely. These variables are the carbonic acid concentration, the hydrogencarbonate concentration, and the calcium concentration. If these concentrations are fixed, the pH is given by the ratio of c(CO2 ) and c(HCO−3 ) and the related acidity constant (Equation (8.5)), whereas the carbonate concentration is given by the solubility product and the calcium concentration (Equation (8.7)). If we further set the calcium concentration to a fixed value, then the calco–carbonic equilibrium can be represented in a two-dimensional diagram as a curve c(CO2 ) = f(c(HCO−3 ) with c(Ca2+ ) as the curve parameter. In practice, the curve parameter is typically given as the deviation from the stoichiometric ratio between hydrogencarbonate and calcium in the form c(HCO−3 ) − 2 c(Ca2+ ). This difference has the value 0 if both species occur in the exact stoichiometric ratio given by Equation (8.1): c(HCO−3 ) = 2 c(Ca2+ ). The reason for deviations from the stoichiometric ratio of Ca2+ and HCO−3 , which are typically found in natural waters, is that Ca2+ as well as HCO−3 are introduced into the water not only by dissolution of calcium carbonate but also from other sources, independently from each other. The following equation for the equilibrium curve can be derived by combining the laws of mass action for the elementary reactions given in Equations (8.5)–(8.7): c(CO2 ) =

KT 2 c (HCO−3 ) c(Ca2+ ) fT

(8.8)

where K T is an overall equilibrium constant and f T is an overall activity coefficient. This equation was first described by Josef Tillmans and is therefore referred to as the Tillmans equation and the corresponding graph is called the Tillmans curve. According to the derivation of the Tillmans equation, K T can be found from the acidity constants of the carbonic acid, K ∗a1 and K ∗a2 , and the solubility product of cal∗ : cium carbonate, Ksp K∗ (8.9) K T = ∗ a2 ∗ K a1 Ksp

8.2 The calco–carbonic equilibrium | 161

In the same way, the activity coefficients of all ions in the three laws of mass action can be summarized in the overall coefficient f T . Given that the activity coefficient of an ion with the charge z, γz , is related to the activity coefficient of a univalent ion, γ1 , by: 2 γ z = γ1z (8.10) and considering the activity coefficients in the single laws of mass action, the summarized activity coefficient, f T , can be calculated from the activity coefficient of a univalent ion, γ1 , by: γ3 1 (8.11) fT = 1 8 = 6 γ1 γ1 γ1 The activity coefficient for a univalent ion, γ1 , can be found from the ionic strength, I, for instance by using the Güntelberg equation: log γ1 = −0.5

√I 1 + 1.4√I

(8.12)

It should be pointed out here that the ionic strength has to be introduced into Equation (8.12) in the unit mol/L instead of the unit mmol/L that is often used in raw water analyses. Selected values of K T and f T in the relevant ranges of temperature and ionic strength are given in Tables 8.1 and 8.2. Figure 8.1 shows Tillmans curves for three different values of the curve parameter, c(HCO−3 ) − 2 c(Ca2+ ), calculated for ϑ = 10 °C and I = 10 mmol/L. In the area above the equilibrium curves, we find all water compositions (with respect to CO2 and HCO−3 ) where the CO2 concentration is higher than that in the state of equilibrium

Fig. 8.1: Tillmans curves for different concentration differences c(HCO−3 ) − 2 c(Ca2+ ), calculated for ϑ = 10 °C and I = 10 mmol/L.

162 | 8 Deacidification

(calcite-dissolving waters). Waters with compositions that fall in the area below the equilibrium curves contain lower CO2 concentrations in comparison to the equilibrium state (calcite-precipitating waters). The lines in the sketch are lines of constant pH. They represent water compositions with equal pH and can be found from the law of mass action of the first dissociation step of carbonic acid (Equation (8.5)). The lines of constant pH intersect the respective equilibrium curve at different points. Accordingly, each equilibrium state is characterized by its own specific pH, referred to as the equilibrium pH (or pH of calcite saturation). The equilibrium pH can be calculated by combining the law of mass action for the second dissociation step of carbonic acid with the solubility product (Equations (8.6) and (8.7)): a(H+ ) = KLa fLa c(HCO−3 ) c(Ca2+ ) pHeq = − log KLa − log fLa −

(8.13)

log c(HCO−3 )

− log c(Ca ) 2+

(8.14)

Equation (8.14) is known as the Langelier equation, sometimes also referred to as the ∗ ) is the Langelier constant and f Langelier–Strohecker equation. KLa (= K ∗a2 /Ksp La is the summarized activity coefficient of the Langelier equation, which is given by: fLa =

γ81 γ31

= γ51

log fLa = 5 log γ1

(8.15)

Selected values of KLa and fLa in the relevant ranges of temperature and ionic strength are given in Tables 8.1 and 8.2. Tab. 8.1: Constants of the calco–carbonic equilibrium at different temperatures. Temperature (°C)

∗ log K sp

∗ log K a1

∗ log K a2

log K T

log K La

5 10 15 20 25

−8.387 −8.406 −8.428 −8.453 −8.481

−6.515 −6.465 −6.422 −6.386 −6.356

−10.555 −10.488 −10.429 −10.376 −10.329

4.347 4.383 4.421 4.463 4.508

−2.168 −2.082 −2.001 −1.923 −1.848

Tab. 8.2: Activities coefficients γ1 , f T , and fLa at different ionic strengths. Ionic strength, I (mmol/L)

Activity coefficient of a univalent ion, γ1

Overall activity coefficient in the Tillmans equation, f T

Overall activity coefficient in the Langelier equation, f La

2.5 5.0 7.5 10.0 12,5 15.0 17.5 20.0

0.9476 0.9286 0.9149 0.9039 0.8947 0.8866 0.8794 0.8729

1.3810 1.5596 1.7050 1.8330 1.9499 2.0589 2.1620 2.2602

0.7641 0.6905 0.6411 0.6035 0.5732 0.5478 0.5260 0.5068

8.3 Deacidification processes

| 163

The difference between the measured pH and the calculated equilibrium pH is referred to as the saturation index SI: SI = pHmeas − pHeq

(8.16)

The saturation index can be used to assess the saturation state of a water with respect to the calco–carbonic equilibrium. A negative SI (measured pH lower than equilibrium pH) indicates a calcite-dissolving water, whereas a positive SI (measured pH higher than equilibrium pH) indicates a calcite-precipitating water. If SI = 0, the water is in the state of calco–carbonic equilibrium (i.e., saturated with calcite). If the saturation index is negative, deacidification must be considered. The decision for deacidification depends on the magnitude of the deviation from the equilibrium state and the concrete limit value. Limits can be defined for SI, but also for the amount of calcite that water is allowed to dissolve. The calcite dissolution capacity of a water can be determined by an iterative calculation on the basis of Equation (8.1) (computational simulation of the dissolution of increasing amounts of calcite). After each iteration step, which changes the concentrations of calcium and hydrogencarbonate as well as the activity coefficient, fLa , the deviation from the equilibrium is to be checked again by means of SI. The iterations can be stopped when SI equals 0.

8.3 Deacidification processes 8.3.1 Treatment options In principle, the removal of dissolved carbon dioxide can be carried out in two different ways. The simplest method is to strip the dissolved CO2 by means of a stripping gas. This process is referred to as mechanical or physical deacidification. For economic reasons, air is typically used as the stripping gas. However, atmospheric air contains CO2 and the transfer of CO2 from the aqueous phase to the air is limited by Henry’s law. According to Henry’s law, the CO2 concentration in the air is in equilibrium with a certain concentration of CO2 in the aqueous phase. This equilibrium concentration is the lowest CO2 concentration that can be reached by stripping with air (Section 8.3.2). Alternatively, dissolved CO2 can be removed by a chemical transformation. In particular, carbonates and hydroxides are able to transform CO2 into hydrogencarbonate. These processes are known as chemical deacidification (Section 8.3.3).

8.3.2 Mechanical deacidification Mechanical deacidification means the stripping of the dissolved gas carbon dioxide by means of air as a stripping gas. The introduction of air into the water is also referred to as aeration (Chapter 7). Figure 8.2 shows the operating line for the stripping process and the related changes in water composition by means of the Tillmans dia-

164 | 8 Deacidification

Fig. 8.2: Mechanical deacidification: operating lines for different hydrogencarbonate concentrations. Whether the equilibrium state can be reached (a) or not (b) depends on the hydrogencarbonate concentration. Equilibrium curve calculated for ϑ = 10 °C, I = 10 mmol/L, c(HCO−3 ) = 2 c(Ca2+ ).

gram. The decrease of the CO2 concentration during mechanical deacidification is accompanied by an increase of the pH value. The concentrations of other inorganic carbon species (hydrogencarbonate, carbonate) are unaffected by the mechanical deacidification process. The lowest CO2 concentration that can be reached by aeration is the equilibrium concentration related to the CO2 concentration in the air. This minimum molar concentration can be calculated by Henry’s law (Chapter 2, Section 2.3.2): c(CO2 ) = H(CO2 ) p(CO2 )

(8.17)

For an assumed temperature of 10 °C, the Henry constant of carbon dioxide is 52.1 mol/(m3 ⋅ bar). With the CO2 partial pressure in air of about 0.0004 bar (corresponding to ≈ 400 ppm CO2 in the air and 1 bar total pressure), we get: c(CO2 ) = 52.1 mol/(m3 ⋅ bar) ⋅ 0.0004 bar = 0.021 mol/m3 = 0.021 mmol/L (8.18) The corresponding mass concentration can be found with the molecular weight of CO2 (M = 44.01 g/mol): ρ ∗ (CO2 ) = c ⋅ M = 0.021 mmol/L ⋅ 44.01 mg/mmol = 0.924 mg/L

(8.19)

Particularly in raw waters with low concentrations of hydrogencarbonate, this minimum concentration is higher than the equilibrium concentration of CO2 in the calco– carbonic equilibrium (Figure 8.2, case b). In such cases, the mechanical deacidification has to be combined with an additional chemical deacidification to reach the

8.3 Deacidification processes

| 165

calco–carbonic equilibrium. It has to be noted that the given minimum concentration is a theoretical value. In the practical process, the attainable minimum concentration is slightly higher. The efficiency of the mechanical deacidification strongly depends on the rate of the mass transfer from the liquid phase to the gas phase and the duration of the contact of both phases (Chapter 7, Section 7.2.2). Large interface areas and long contact times promote the mass transfer. Reactors for mechanical deacidification are therefore designed in such a manner that the air is finely dispersed in the aqueous phase (e.g., by sieve plates). Often inbuilt components are also used in the reactors to increase the time and the intensity of the contact between the liquid and the gas phase. In principle, all reactor types that allow a fast mass transfer from the aqueous phase to the gas phase can be used in mechanical deacidification, from simple diffusers and spray columns to packed-bed columns (Chapter 7, Section 7.3). Figure 8.3 shows

Waste air

Influent

Inlet air

Air blower (a)

Effluent

Influent Perforated plate Inlet air

Waste air

Corrugated plates

Effluent

(b) Fig. 8.3: Reactors used for mechanical deacidification: sparger plate aerator (a) and corrugated plate aerator (b).

166 | 8 Deacidification

two specific reactor types that are frequently used for mechanical deacidification: a sparger plate aerator and a corrugated plate aerator.

8.3.3 Chemical deacidification The general principle of chemical deacidification consists of the transformation of dissolved CO2 into hydrogencarbonate, HCO−3 . This transformation can be carried out in two different ways: by adding solutions of bases (Ca(OH)2 or NaOH) or by filtration over solid carbonates (CaCO3 or CaCO3 ⋅ MgO). In the first case, the OH− ions of the bases react with CO2 to form HCO−3 : CO2 + OH− 󴀕󴀬 HCO−3

(8.20)

The complete reaction equations read: 2 CO2 + Ca2+ + 2 OH− 󴀕󴀬 Ca2+ + 2 HCO−3 +

−

+

CO2 + Na + OH 󴀕󴀬 Na +

HCO−3

(8.21) (8.22)

where bold characters indicate the added chemicals. Since the production of clear solutions of the weakly soluble calcium hydroxide (the so-called limewater) is more expensive, Ca(OH)2 is typically used as milk of lime, a suspension that still contains undissolved particles besides Ca2+ and OH− ions. The resulting turbidity in the treated water has to be removed by filtration after the treatment. The application of Ca(OH)2 leads to an increase of the water hardness, in particular of the carbonate hardness. The water quality parameter hardness comprises the concentrations of the alkaline earth ions Ca2+ and Mg2+ . The carbonate hardness is that fraction of the hardness that is equivalent to the hydrogencarbonate and carbonate ion concentration. For more details about water hardness see also Chapter 9. It follows from the stoichiometry of Equation (8.21) that the removal of 1 mmol/L (= 44.01 mg/L) CO2 leads to a carbonate hardness increase of 0.5 mmol/L. In the case of the application of a NaOH solution there is no formation of turbidity (due to the much better solubility of the solid NaOH) and no increase of hardness (no introduction of alkaline earth ions), but the introduction of higher concentrations of Na+ may be problematic due to the risk of exceeding the limit value for drinking water that is set in many national regulations (e.g., in Germany it is 200 mg/L Na+ ). In both cases, the reaction is relatively fast. However, if the dosage of the bases is not very exact, there is a risk of overalkalization. That means that more CO2 than necessary is removed and the water becomes calcite-precipitating with a pH higher than the equilibrium pH. In the worst case, if all the CO2 is consumed, the pH increases strongly due to the OH− excess and a large amount of calcite precipitates.

8.3 Deacidification processes

| 167

During the filtration over calcium carbonate (CaCO3 ) or half-burnt dolomite (CaCO3 ⋅ MgO), the following reactions take place: CO2 + H2 O + CaCO3(s) 󴀕󴀬 Ca2+ + 2 HCO−3 3 CO2 + 2 H2 O + CaCO3 ⋅MgO(s) 󴀕󴀬 Ca

2+

+ Mg

2+

+ 4 HCO−3

(8.23) (8.24)

Calcium carbonate is obtained from different mineral deposits as finely crystalline or porous material. Half-burnt dolomite (half-calcined dolomite) is produced from the mineral dolomite, CaCO3 ⋅ MgCO3 , by a thermal treatment at temperatures where only the MgCO3 component of the double salt is split into MgO and CO2 and the CaCO3 component remains unchanged. In principle, the untreated dolomite could also be used for chemical deacidification, but half-burnt dolomite requires shorter reaction times and is therefore preferred. The reaction of CO2 with CaCO3 (Equation (8.23)) is exactly the same as the overall reaction of the calco–carbonic equilibrium (Equation (8.1)). That means that if the contact time is long enough, the excess concentration of CO2 is completely removed and the deacidification process stops exactly at the equilibrium state. Unfortunately, the reaction times are relatively long and therefore long contact times (large filters) are needed. A faster reaction is possible by using synthetic calcium carbonate instead of the natural material. However, this synthetic carbonate contains residual amounts of calcium oxide (CaO) from the production process that behaves, in contact with water, like a base: CaO + H2 O 󴀕󴀬 Ca2+ + 2 OH− (8.25) Therefore, there is also a certain risk of overalkalization, particularly in the first period of the reactor run time. The risk of overalkalization also exists for half-burnt dolomite, CaCO3 ⋅ MgO, where the magnesium oxide component reacts with water under formation of OH− : (8.26) MgO + H2 O 󴀕󴀬 Mg2+ + 2 OH− Both filter materials (calcium carbonate and half-burnt dolomite) increase the carbonate hardness of the water, but the effect varies in strength for the different materials. The theoretical total hardness increase (calculated from the stoichiometry of the reactions) for an assumed CO2 removal of 1 mmol/L (= 44.01 mg/L) is 1 mmol/L in the case of CaCO3 and 0.67 mmol/L in the case of CaCO3 ⋅ MgO. In this regard, halfburnt dolomite has an advantage over calcium carbonate. In both cases, however, the hardness increase is higher than that caused by Ca(OH)2 for the same CO2 removal (0.5 mmol/L). In all chemical deacidification processes, the decrease of the concentration of CO2 is related to an equivalent increase of the HCO−3 concentration. However, the concentration ratio ∆c(CO2 )/∆c(HCO−3 ) is different if we compare both solid filter materials with the bases NaOH and Ca(OH)2 (which show equal effects). Accordingly,

168 | 8 Deacidification

Fig. 8.4: Operating lines of the chemical deacidification processes. Equilibrium curve calculated for ϑ = 10 °C, I = 10 mmol/L, c(HCO−3 ) = 2 c(Ca2+ ).

the operating lines in the Tillmans diagram have different slopes (Figure 8.4) and the strength of the pH change is also different. For the same initial water composition, the pH increase is strongest in the case of the bases NaOH and Ca(OH)2 , followed by half-burnt dolomite and calcium carbonate, whereas the hydrogencarbonate concentration increase is the highest for CaCO3 , followed by half-burnt dolomite and the bases NaOH and Ca(OH)2 . It has to be noted that the pH increase in all cases of chemical deacidification is lower than during mechanical deacidification (vertical operating line, Figure 8.2). Some characteristic hydrochemical data of the chemical deacidification processes are summarized in Table 8.3. Tab. 8.3: Ratio of the molar concentration changes of CO2 and HCO−3 (slopes of the operating lines), hardness increase, and consumption of chemicals for the different types of chemical deacidification (calculated from the reaction equations). Chemicals used for deacidification

∆c(CO2 ) ∆c(HCO−3 )

Theoretical hardness increase (in mmol/L) at a CO2 removal of 1 mmol/L (44.01 mg/L)

Theoretical consumption of chemicals (in kg) for removal of 1 kg CO2

Ca(OH)2 NaOH CaCO3(s) CaCO3 ⋅ MgO(s)

−1 −1 −0.5 −0.75

0.5 0 1.0 0.67

0.842 0.909 2.274 1.063

8.3 Deacidification processes |

169

8.3.4 Practical aspects Besides economic aspects (e.g., energy consumption, chemical demand, technical effort), the raw water composition is a crucial factor that has to be taken into account when choosing the appropriate treatment process for a given water. In comparison to chemical deacidification, mechanical deacidification has the advantage that it needs no chemicals and the interference with the water composition is not as strong (only pH increase, no introduction of additional ions, no increase of the hydrogencarbonate concentration and the carbonate hardness). Therefore, mechanical deacidification is often preferred. Due to the limitation of the CO2 removal discussed in Section 8.3.2, mechanical deacidification is particularly suitable for waters with high hydrogencarbonate concentrations. In the case of HCO−3 concentrations higher than about 2 mmol/L, the equilibrium state can be safely reached with mechanical deacidification alone. However, if the hydrogencarbonate concentration in the water is very high, then the CO2 concentration in the equilibrium state, which is the end concentration of the deacidification process, is also relatively high (Figure 8.1). Therefore, it may be reasonable to moderately reduce the hydrogencarbonate concentration by an upstream dealkalization process (Chapter 9) before applying mechanical deacidification in order to prevent corrosion. The acceptable CO2 concentration in the water depends on the pipe material that is used for the drinking water distribution. It is recommended that the CO2 concentration should be lower than 1 mmol/L if copper pipes are used and lower than 0.5 mmol/L if hot zinc dipped iron pipes are used. At very low hydrogencarbonate concentrations (< 1 mmol/L HCO−3 ), the calco– carbonic equilibrium cannot be reached, because the CO2 concentration in the calco– carbonic equilibrium is lower than that in the gas–liquid equilibrium, which is determined by the CO2 partial pressure in the stripping air (Figure 8.2, case b). In this case, chemical deacidification has to be used alone or in combination with mechanical deacidification. In particular, if the raw water contains high concentrations of CO2 , it is reasonable to apply mechanical deacidification as a first step followed by chemical deacidification. However, since waters with low hydrogencarbonate concentrations have a low buffer capacity, the application of bases in the chemical deacidification step is problematic due to the high risk of overalkalization. Therefore, carbonate materials are better suited in this case. As an alternative, a partial chemical deacidification with CaCO3 , CaCO3 ⋅ MgO, or Ca(OH)2 can be applied as the first step, followed by mechanical deacidification. This is a particularly appropriate treatment option for soft and weakly buffered raw waters where a moderate increase of the hardness and the buffer capacity (hydrogencarbonate concentration) can be accepted or is even wanted. In this first step, the hydrogencarbonate concentration is increased to such an extent that it reaches a concentration

170 | 8 Deacidification

Fig. 8.5: Operating lines of a two-stage deacidification process. First stage (a): partial deacidification by filtration over CaCO3 connected with an increase of the hydrogencarbonate concentration. Second stage (b): mechanical deacidification. Equilibrium curve calculated for ϑ = 10 °C, I = 10 mmol/L, c(HCO−3 ) − 2 c(Ca2+ ) = 2 mmol/L. Dashed line: Single-stage mechanical deacidification.

range where the subsequent mechanical deacidification is suitable to reach the calco– carbonic equilibrium. The principle of this two-stage process is shown in Figure 8.5. In a range where the hydrogencarbonate concentration is between about 1 and 2 mmol/L HCO−3 , whether the calco–carbonic equilibrium can be reached by mechanical deacidification or not depends on the hydrogencarbonate concentration and the specific course of the equilibrium curve for the given water. The higher the value of the curve parameter c(HCO−3 ) − 2 c(Ca2+ ), the lower the CO2 equilibrium concentrations at a given HCO−3 concentration (Figure 8.1). However, the difference between the minimum CO2 concentration that can be reached by mechanical deacidification and the equilibrium concentration is not very high in this range of the calco–carbonic equilibrium. The approach to the equilibrium is mostly close enough to fulfill the requirements given by the drinking water limit values. Therefore, an additional chemical treatment step besides the mechanical deacidification is often omitted in this HCO−3 concentration range.

9 Softening and dealkalization 9.1 Introduction and treatment objectives The term softening covers all treatment processes that are applied to reduce the hardness of water. The hardness of water is a quality parameter that is used to describe the content of alkaline earth ions in the water, in particular the content of calcium and magnesium ions, with calcium ions having typically a higher concentration in comparison to magnesium ions. Problems caused by hardness are, for instance, a higher consumption of detergents (washings agents), precipitation of calcium carbonate (scaling) on heating installations in household appliances and technical facilities, problems in preparing specific meals (legumes, for instance, remain hard during cooking), influence on the taste of tea and coffee, and also specific corrosion effects. On the other hand, for health reasons and to ensure a good taste of the tap water, treated water should have a certain content of minerals. The objective of softening processes is therefore not the total removal of calcium and magnesium but the reduction of hardness to bring hard or very hard water to the range of moderately hard water. More details about the classification of hardness with respect to the alkaline earth ion concentration are given in Section 9.2. From the practical point of view it is reasonable to differentiate between carbonate and noncarbonate hardness. Carbonate hardness comprises that part of hardness that is equivalent to the hydrogencarbonate (bicarbonate) and carbonate concentrations, whereas the noncarbonate hardness is that part of hardness that is equivalent to the concentrations of the other anions. The carbonate hardness is much more problematic than the noncarbonate hardness because the carbonate hardness is responsible for the scaling (precipitation of calcium carbonate) on heating installations, which occurs when the water is heated. Scaling reduces the heat transfer (the deposit has a much lower thermal conductivity than the metal of the heater) and can lead, in the worst case, to the destruction of the heater caused by heat accumulation. Neglecting the very low carbonate concentration in the medium pH range (see carbonic acid speciation in Chapter 1, Figure 1.4), the precipitation of calcium carbonate can be described by the following reaction equation: Ca2+ + 2 HCO−3 󴀕󴀬 CaCO3(s) ↓ + H2 O + CO2

(9.1)

During heating, the dissolved gas CO2 is removed from the aqueous phase and the equilibrium is shifted to the right and calcium together with the equivalent amount of hydrogencarbonate form CaCO3 that precipitates. Carbonate hardness is therefore also referred to as temporary hardness, whereas the noncarbonate hardness, which is not subject to any changes during heating, is referred to as permanent hardness. It has to be noted that magnesium ions are also able to form a carbonate, but magnesium carbonate is much more soluble than calcium carbonate. Furthermore, the https://doi.org/10.1515/9783110551556-009

172 | 9 Softening and dealkalization

magnesium ions occur in natural waters typically in distinctly lower concentrations in comparison to the calcium ions. Therefore, the calcium based hardness receives special attention in practice. Due to the problems resulting from scaling, the focus in drinking water treatment, but also in process and service water treatment, is often mainly on the reduction of the carbonate hardness. That means that hydrogencarbonate has to be removed from the water. Processes that serve the purpose of removing carbonate hardness are also referred to as dealkalization processes. Most dealkalization processes reduce the carbonate hardness as well as the total hardness, but there are also treatment techniques available that only shift the ratio of carbonate to noncarbonate hardness at a constant level of the total hardness. Another aspect is that high concentrations of hydrogencarbonate are accompanied by high carbon dioxide concentrations and low pH values if the water is calcitedissolving or in the state of the calco–carbonic equilibrium (see Tillmans diagram, Figure 8.1). For that reason it may be reasonable to decrease the hydrogencarbonate concentration before applying a deacidification process (Section 8.3.4). That results in lower CO2 concentrations and higher pH values in the treated water and helps to prevent corrosion. Since the raw waters used for drinking water production are often too hard, softening and dealkalization are widely used treatment processes. However, it has to be noted that in some cases the hardness of water can also be too low in comparison to the target range of medium hardness. In these cases, it may be necessary to increase the water hardness to bring the water into the medium hardness range. This is particularly true for very soft waters from reservoirs or when the hardness should be adapted to that of water from another source prior to mixing. The following sections focus on softening; the special case of water hardening is considered separately in Section 9.4.

9.2 Hardness of water: definitions and units The total hardness (TH) is generally defined as the sum of the concentrations of calcium and magnesium ions. According to the international system of units (SI), the unit of hardness is mmol/L. Besides the molar concentration, also other traditional units are used in the practice of water treatment. These units are typically defined with CaO or CaCO3 as a reference substance (Table 9.1). Conversions can be carried out by stoichiometric calculations. If the concentrations are given as mass concentrations, the magnesium mass concentration has to be converted formally into a calcium concentration under consideration of the ratio of the molecular weights M(Ca) : M(Mg) = 40.08 g/mol : 24.305 g/mol = 1.649.

9.2 Hardness of water: definitions and units

| 173

Tab. 9.1: Units of water hardness. Unit

Definition/reference

1 mmol/L Ca2+ equals

1 mg/L Ca2+ equals

mmol/L (conform to SI)

mmol/L Ca2+ and Mg2+

1 mmol/L Ca2+

0.025 mmol/L Ca2+

mg/L (or ppm)

mg/L CaCO3

100.1 mg/L CaCO3

2.5 mg/L CaCO3

°dH (German degree)

10 mg/L CaO

5.608 °dH

0.14 °dH

°Clark (Clark degree, English degree)

1 grain/imperial gallon (= 14.254 mg/L) CaCO3

7.023 °Clark

0.175 °Clark

°f (French degree)

10 mg/L CaCO3

10.01 °f

0.25 °f

For instance, from the equivalence factor Ca/Mg and the conversion factor given in Table 9.1, the following equation for conversion of mass concentrations (ρ ∗ ) of Ca2+ and Mg2+ into hardness in mg/L CaCO3 can be derived: Hardness[mg/L CaCO3 ] = 2.5ρ ∗ (Ca2+ )[mg/L] + 4.12ρ ∗ (Mg2+ )[mg/L]

(9.2)

The definition of hardness ranges is slightly different in different countries. According to European regulations, three ranges of hardness are defined on the basis of molar concentrations: soft, moderately hard, and hard. By contrast, in the USA and other countries four ranges are defined on the basis of the unit mg/L CaCO3 : soft, moderately soft, hard, and very hard. The conversion of the different units shows that the ranges are not identical. The respective concentration ranges for both classification systems are given in Table 9.2. Tab. 9.2: Definitions of hardness ranges. Hardness range

USA mg/L CaCO3

Soft Moderately hard Hard Very hard ∗

0–60 61–120 121–180 > 180

Europe ∗

mmol/L

mmol/L ∗

mg/L CaCO3

0–0.6 0.61–1.2 1.21–1.8 > 1.8

< 1.5 1.5–2.5 > 2.5 –

< 150.2 150.2–250.3 > 250.3 –

Basis of definition

As already mentioned in Section 9.1, it is often reasonable to differentiate between carbonate and noncarbonate hardness. The definitions are based on equivalence relationships and can be demonstrated by ion balances as shown in Figure 9.1, where the bars stand for the equivalent concentrations (equivalent concentration = molar concentration × absolute value of ion charge, Chapter 2, Section 2.2). In most cases, water contains carbonate hardness (CH) and noncarbonate hardness (NCH). That means that a part of the total hardness (TH) is equivalent to the hy-

174 | 9 Softening and dealkalization Case A: TH = CH + NCH Ca2+ + Mg2+

Case B: TH = CH, NCH = 0 Na+ + K+ + …

Ca2+ + Mg2+

Total hardness Carbonate hardness

Total hardness Carbonate hardness

Noncarbonate hardness

HCO3- + CO32-

Na+ + K+ + …

SO42- + Cl- + NO3- + …

SO42- + Cl- + NO3+…

HCO3- + CO32-

(a)

(b)

Fig. 9.1: Definition of carbonate and noncarbonate hardness for different water compositions. The bars represent the equivalent concentrations of the major cations and anions. Case A: The equivalent concentrations of calcium and magnesium are higher than those of hydrogencarbonate and carbonate, and the total hardness consists of carbonate and noncarbonate hardness. Case B: The equivalent concentrations of calcium and magnesium are lower than those of hydrogencarbonate and carbonate, and the total hardness consists of carbonate hardness only.

drogencarbonate and carbonate ion concentration, whereas another part is equivalent to the other anions, such as chloride or sulfate (case A in Figure 9.1): TH = CH + NCH c(Ca

2+

+ Mg )TH = c(Ca 2+

2+

(9.3)

+ Mg )CH + c(Ca 2+

2+

+ Mg )NCH 2+

(9.4)

The carbonate hardness can be calculated on the basis of its definition by means of the respective equivalence relationship: − 2 c(Ca2+ + Mg2+ )CH = c (HCO−3 ) + 2 c (CO2− 3 ) ≈ c (HCO3 )

(9.5)

Since in the medium pH range, which is relevant for drinking water treatment, the carbonate concentration is much lower than the hydrogencarbonate concentration (Chapter 1, Figure 1.4), c(CO2− 3 ) can be neglected in the calculation. Rearranging Equation (9.5) gives: 1 CH = c(Ca2+ + Mg2+ )CH ≈ c (HCO−3 ) (9.6) 2 Accordingly, the carbonate hardness can be simply calculated from the hydrogencarbonate concentration. However, it has to be noted that Equations (9.5) and (9.6) give feasible results only if the equivalent concentration of hydrogencarbonate (and carbonate) is lower than or exactly equal to the sum of the equivalent concentrations of calcium and magnesiumions in the water, because the carbonate hardness can be at maximum as high as the total hardness but not higher. Case B in Figure 9.1 shows the less common situation where the equivalent concentration of hydrogencarbonate (and carbonate) is higher than the sum of the equivalent concentrations of calcium and magnesium ions. In this case, the total amount of calcium and magnesium is equivalent to only a part of the hydrogencarbonate/carbonate.

9.3 Softening and dealkalization processes

| 175

The excess of hydrogencarbonate/carbonate ions is here equivalent to other cations. In this case, noncarbonate hardness does not exist and the total hardness equals the carbonate hardness (TH = CH). Here, a formal application of Equation (9.6) would lead to a carbonate hardness that is higher than the total hardness, which is impossible. In this case, the calculation result has to be rejected and carbonate hardness has to be set equal to the total hardness.

9.3 Softening and dealkalization processes 9.3.1 Overview There are different treatment techniques that can be used to remove the total hardness and/or the carbonate hardness. Table 9.3 gives an overview of the available treatment processes and their effects with regard to softening and dealkalization. Tab. 9.3: Softening and dealkalization processes. Treatment process Precipitation With Ca(OH)2 With NaOH With Na2 CO3 With Na3 PO4

Softening Dealkalization (removal of Ca2+ and Mg2+ ) (removal of HCO−3 ) × × × ×

× ×

Acid addition HCl or H2 SO4

×

Ion exchange Ca2+ /Na+ exchange × Ca2+ /H+ exchange × CARIX process ×

× ×

Membrane processes Nanofiltration × Reverse osmosis ×

×

Precipitation with Ca(OH)2 (sometimes also in combination with NaOH) is widely used for softening/dealkalization in central drinking water treatment plants. Ion exchange processes, particularly if they are able to remove total and carbonate hardness, may be a reasonable alternative. In particular, the CARIX process is an interesting option in cases where not only hardness but also other ions (e.g., sulfate) have be removed. The same is true for reverse osmosis, which is able to remove all ions (demineralization). It can be used to treat a substream that is later blended with untreated water

176 | 9 Softening and dealkalization

(split-stream treatment or split treatment). In this way it reduces not only the hardness but also the content of other ions. Another option is to use nanofiltration, the low-pressure version of reverse osmosis. Nanofiltration membranes preferentially reject bivalent ions. The application of membrane processes for drinking water treatment has gained in importance in recent years (Chapter 5). Due to its uncomplicated operation, Ca2+ /Na+ ion exchange is especially used in decentralized softening, for instance in household appliances such as dishwashers or in special water filters. The precipitation processes with sodium carbonate or sodium phosphate were used in the past in special cases where process water or service water with very low hardness was needed. In the meantime, these processes have often been replaced by other techniques, in particular by ion exchange or membrane processes. Sometimes, it may be reasonable to remove only the carbonate hardness but not to reduce the total hardness, for instance when the total hardness is not too high but consists nearly totally of carbonate hardness. Here, the change of the ratio of carbonate and noncarbonate hardness by acid addition could be an option.

9.3.2 Precipitation processes The precipitation with limewater or milk of lime (Ca(OH)2 ) as a precipitation agent is the most frequently applied softening/dealkalization process. This process, also referred to as lime softening or lime dealkalization, is based on the following reactions: Ca2+ + 2 HCO−3 + Ca2+ + 2 OH− 󴀕󴀬 2 CaCO3(s) ↓ + 2 H2 O 2+

Mg

+

2 HCO−3

+ 2 Ca

2+

CO2(aq) + Ca

2+

(9.7)

−

(9.8)

−

(9.9)

+ 4 OH 󴀕󴀬 2 CaCO3(s) ↓ + Mg(OH)2(s) ↓ + 2 H2 O + 2 OH 󴀕󴀬 CaCO3(s) ↓ + H2 O

To differentiate between the original water constituents and the ions that come from the added precipitation agent, the latter are indicated by bold characters. The general principle of the calcium removal consists of the transformation of the water constituents carbon dioxide (CO2(aq) ) and hydrogencarbonate (HCO−3 ) by hy2+ droxide ions (OH− ) into carbonate (CO2− 3 ), which precipitates with calcium ions (Ca ) as solid calcium carbonate (CaCO3(s) ) when the solubility product is exceeded. The transformation occurs according to: CO2(aq) + 2 OH− 󴀕󴀬 CO2− 3 + H2 O HCO−3

−

+ OH 󴀕󴀬

CO2− 3

+ H2 O

(9.10) (9.11)

In the case of magnesium ions, the hydroxide is primarily formed instead of the carbonate. This different behavior of magnesium in comparison to calcium can be explained by the solubility products of the respective hydroxides and carbonates (Ta∗ , or the ble 9.4). Note that the solubility is higher the higher the solubility product, Ksp

9.3 Softening and dealkalization processes

| 177

∗ , of the carbonates and hydroxides of calcium and magnesium Tab. 9.4: Solubility exponents, pKsp at 25 °C. ∗ Compound pK sp

CaCO3 Ca(OH)2 MgCO3 Mg(OH)2

8.46 5.30 5.17 11.30

∗ (Chapter 2, Section 2.3.4). In the case of calcium, lower the solubility exponent, pKsp ∗ is higher) than the solubility product of the carbonate is lower (accordingly the pKsp that of the hydroxide, whereas the solubility products of magnesium carbonate and hydroxide show the inverse order. Since the precipitation process with Ca(OH)2 removes not only the hardnesscausing ions Ca2+ and Mg2+ but also the equivalent amount of hydrogencarbonate, it has to be classified as a combined softening and dealkalization process. The dosage of Ca(OH)2 that is necessary for the precipitation process depends on the treatment goal. In many cases, there is no need to remove Mg2+ and the required Ca(OH)2 dose can be derived from the demand for Ca2+ precipitation according to Equations (9.7) and (9.9) and considering the amount that is necessary to raise the pH to an optimum range for precipitation (pH ≈ 10). If Mg2+ should also be removed, a higher lime milk amount has to be applied, which is connected with a stronger pH increase. This process is also referred to as excess lime treatment. High concentrations of phosphate (> 1 mg/L PO3− 4 ) in the raw water affect the crystallization of calcium carbonate adversely due to precipitation of Ca3 (PO)4 that blocks the crystal surface of the carbonate and hinders further crystal growth. After the precipitation process, the precipitates have to be removed. Sedimentation alone is typically not sufficient. Therefore, an additional filtration step has to be used to remove the residual turbidity (Chapter 4). Coagulation/flocculation agents can be added to support the separation process (Chapter 6). The formation of larger amounts of magnesium hydroxide has a negative impact on the efficiency of the separation processes due to the gelatinous consistency of the Mg(OH)2 precipitate. Generally, high concentrations of magnesium in the raw water and/or high pH values promote the precipitation of Mg(OH)2 . A specific aspect in this context is the ratio of Ca2+ and HCO−3 in the water to be treated. According to Equation (9.7), the stoichiometric ratio of the pristine ions that take part in the precipitation process, c(Ca2+ ) : c(HCO−3 ), is 1 : 2. That means that per mmol HCO−3 that should be removed at least 0.5 mmol Ca2+ must be available in the water; the respective condition is therefore 2 c(Ca2+ ) ≥ ∆c(HCO−3 ). If this condition is not fulfilled, the calcium deficit will be compensated by calcium from the precipitation agent leaving an excess concentration of OH− that increases the pH strongly and promotes the formation of Mg(OH)2 .

178 | 9 Softening and dealkalization

Instead of lime milk, a sodium hydroxide (NaOH) solution can also be used as a precipitation agent. In this case, the respective reactions are: Ca2+ + HCO−3 + Na+ + OH− 󴀕󴀬 CaCO3(s) ↓ + Na+ + H2 O 2+

Mg Ca

2+

+

−

+

−

+ 2 Na + 2 OH 󴀕󴀬 Mg(OH)2(s) ↓ + 2 Na +

+

+ CO2(aq) + 2 Na + 2 OH 󴀕󴀬 CaCO3(s) ↓ + 2 Na + H2 O

(9.12) (9.13) (9.14)

The main difference in comparison to the application of Ca(OH)2 is that there is a lower reduction of hydrogencarbonate at the same Ca2+ removal rate. This can be derived from a comparison of Equations (9.7) and (9.12). The stoichiometric ratios of the removed ions, c(Ca2+ ) : c(HCO−3 ), according to Equations (9.7) and (9.12) are 1 : 2 and 1 : 1, respectively. Generally, both precipitation agents can also be used as a mixture allowing a high flexibility of the process with respect to the ratio of softening and dealkalization effects. In contrast to lime milk, sodium hydroxide solutions contain no undissolved particles that may pass the process without taking part in the reaction and require removal from the water together with the precipitation product. On the other hand, sodium ions are introduced into the water (Equations (9.12)–(9.14)). This may be problematic in cases where higher amounts of hydrogencarbonate should be removed and the raw water already contains high Na+ concentrations. Independent of the specific precipitation agent, the application of the bases is connected with an increase of the pH. However, there is an upper limit value for drinking water (often 9.0 or 9.5, depending on national regulations) that must be met. The pH can be decreased after the precipitation process by introducing CO2 , which is referred to as recarbonation. Another option is to treat only a substream (extensive dealkalization) and to blend the treated substream with untreated water, which has a higher CO2 content and a lower pH. This split treatment has the additional advantage that the volume to be treated is lower and the reactors can be smaller. A positive side effect of the softening/dealkalization consists of the removal of reduced iron and manganese species (Fe2+ and Mn2+ ) due to the formation and precipitation of the respective carbonates. A further removal of iron and manganese can be reached by introducing air into the alkaline water after the precipitation in order to oxidize Fe2+ and Mn2+ to iron hydroxide and manganese dioxide. The high pH values favor the oxidation (Chapter 10). The solid oxidation products can then be removed together with the other precipitation products. Figure 9.2 shows a general scheme of the lime softening/dealkalization process. In the practice of drinking water treatment, two different technological variants of the lime dealkalization process are used, conventional dealkalization and rapid dealkalization (also referred to as pellet softening). The conventional dealkalization process consists of the steps mixing, precipitation/flocculation, sedimentation, and filtration (Figure 9.3). The first three steps can also be combined in a multichamber reactor. If necessary, aeration and recarbonation steps are arranged upstream of the final filtration to oxidize manganese and iron ions and to decrease the pH, respectively. This process places only low demands on the water quality with respect to turbidity

9.3 Softening and dealkalization processes |

Precipitation agent

179

Flocculant Air

CO2 Flocculant

Feed water

Particle separation

Precipitation

Treated water

Bypass (in the case of split treatment)

Fig. 9.2: General process scheme of the lime softening/dealkalization process. The dashed lines indicate optional variants. Rapid mixing

Precipitation/ flocculation

Sedimentation

Chemicals

Recarbonation Filtration CO2

Feed water

CaCO3 sludge Treated water

Fig. 9.3: Process scheme of the conventional lime dealkalization.

and contents of iron, manganese, and natural organic matter. Typically, coagulation/ flocculation agents are used together with the precipitation agent to improve the separation of the precipitates and simultaneously remove suspended solids and colloids (Chapter 6). Dealkalization with Ca(OH)2 or NaOH can also be carried out in fluidized-bed reactors (Figure 9.4). This process is often referred to as rapid dealkalization or pellet softening. The water to be treated and the precipitation agent are fed continuously into the lower part of the reactor. To support the crystallization in the fluidized bed, sand is added as seeding material. The calcium carbonate precipitates on the surface of the seeding material and on the growing carbonate crystals. Accordingly, the mass of the carbonate particles increases with time. If the mass of the particles is too high for keeping them in the fluidized bed, the particles settle and accumulate at the bottom of the reactor, from where they are discharged. To support the settling of the precipitation product and to prevent carbonate particles and seeding material from flushing out, the reactors often have a conical shape in the upper part, which reduces the water velocity and improves the separation of the particles from the water.

180 | 9 Softening and dealkalization

Effluent

Seeding grains Lime milk

Lime milk

Influent CaCO3 pellets

Fig. 9.4: Pellet softening (rapid dealkalization) in a fluidized-bed reactor.

For pellet softening, only relatively small reactors are necessary, and the precipitation product occurs as compact pellets with low water content. The obtained calcium carbonate pellets are easier to use for further purposes than the precipitation/ flocculation sludge produced by the sedimentation in conventional dealkalization. On the other hand, pellet softening is more sensitive to water constituents that disturb the crystallization process (turbidity, phosphate, high magnesium concentrations). Furthermore, the pH should not be too high in order to avoid the formation of gelatinous Mg(OH)2 . In this context, the abovementioned condition 2 c(Ca2+ ) ≥ ∆c(HCO−3 ) should be fulfilled for the water to be treated, because otherwise the pH increase is too strong. Since the separation of the crystals in the reactor is not always complete, an additional filtration step is needed in the rapid dealkalization process as well. Depending on the requirements, recarbonation and aeration can be additionally integrated into the process as in the case of conventional dealkalization. If not only the carbonate hardness but also the noncarbonate hardness should be removed, the lime dealkalization process (Equations (9.7)–(9.9)) can be complemented by using sodium carbonate as a second precipitation agent. Sodium carbonate is also referred to as soda ash and this process is therefore known as lime–soda ash softening. The additional precipitation reactions that remove the noncarbonate hardness can be demonstrated by using sulfate as an example for the equivalent anions of the noncarbonate hardness: + 2− + 2− Ca2+ + SO2− 4 + 2 Na + CO3 󴀕󴀬 CaCO3(s) ↓ + 2 Na + SO4 2+

Mg

+ SO2− 4

+ 2 Na

+

+ CO2− 3

+ Ca

2+

(9.15)

−

+ 2 OH 󴀕󴀬 Mg(OH) 2(s) ↓ + CaCO3(s) ↓ + 2 Na+ + SO2− 4

(9.16)

9.3 Softening and dealkalization processes | 181

As in the case of using NaOH as a precipitation agent, the sodium concentration in the treated water increases. For the sake of completeness, it should be noted here that a nearly complete removal of carbonate and noncarbonate hardness is possible by using sodium phosphate (Na3 PO4 ⋅ 12 H2 O) as a precipitation agent: + − 3 Ca2+ + 6 HCO−3 + 6 Na+ + 2 PO3− 4 󴀕󴀬 Ca3 (PO4 )2(s) ↓ + 6 Na + 6 HCO3

3 Mg + 6 HCO−3 3 Ca2+ + 3 SO2− 4 3 Mg2+ + 3 SO2− 4 2+

+ + +

+

6 Na + 2 PO3− 4 6 Na+ + 2 PO3− 4 6 Na+ + 2 PO3− 4

󴀕󴀬 󴀕󴀬 󴀕󴀬

+

Mg3 (PO4 )2(s) ↓ + 6 Na + 6 HCO−3 Ca3 (PO4 )2(s) ↓ + 6 Na+ + 3 SO2− 4 Mg3 (PO4 )2(s) ↓ + 6 Na+ + 3 SO2− 4

(9.17) (9.18) (9.19) (9.20)

Here, the first two equations show the removal of carbonate hardness, whereas the last two equations demonstrate the removal of noncarbonate hardness with sulfate as an example for the anions that are equivalent to noncarbonate hardness. ∗ = 32.5 and Since the solubility of Ca3 (PO4 )2 and Mg3 (PO4 )2 is much lower (pKsp 25, respectively) than those of the carbonates and hydroxides (Table 9.1), Ca2+ and Mg2+ can be removed by this process to a much higher extent than by the other precipitation processes. In the past, this softening process was therefore often used as a second stage after the lime-soda ash process for industrial purposes where very soft water is needed, for instance as boiler feed water in power plants. In the meantime, ion exchange processes have replaced this precipitation process in industrial applications. For drinking water treatment, this process has no relevance.

9.3.3 Acid addition The dosage of mineral acids may be reasonable when the total hardness is not too high and only the ratio of carbonate to noncarbonate hardness has to be changed. The basic principle of this dealkalization process consists of the transformation of HCO−3 into CO2 by the protons from the mineral acids according to: HCO−3 + H+ 󴀕󴀬 H2 O + CO2(aq)

(9.21)

The complete reaction equations for hydrochloric acid and sulfuric acid (written in bold characters) read: Ca2+ (Mg2+ ) + 2 HCO−3 + 2 H+ + 2 Cl− 󴀕󴀬 Ca2+ (Mg2+ ) + 2 Cl− + 2 H2 O + 2 CO2(aq) (9.22) 2+ 2+ 2− Ca2+ (Mg2+ ) + 2 HCO−3 + 2 H+ + SO2− 4 󴀕󴀬 Ca (Mg ) + SO4 + 2 H2 O + 2 CO2(aq) (9.23)

The total hardness remains unchanged; the hydrogencarbonate ions as the equivalent anions of the carbonate hardness are transformed into CO2 and replaced by the anions chloride or sulfate originating from the added acids. Accordingly, the carbonate hardness is reduced, whereas the noncarbonate hardness increases.

182 | 9 Softening and dealkalization

In this process, a very exact dosage is necessary to leave a certain residual concentration of hydrogencarbonate in the treated water. An overdose of acid would lead to the total consumption of HCO−3 with the consequence that the water would lose its most important buffer substance and the pH would strongly decrease. Furthermore, acid addition increases the CO2 content of the water, which makes the water more corrosive. Consequently, the CO2 excess concentration must be removed by deacidification (Chapter 8). Moreover, the concentrations of chloride and sulfate also increase. The transformation of 1 mmol/L HCO−3 by acid addition leads to an introduction of 35.5 mg/L chloride or 48 mg/L sulfate. Here, the respective limit values for chloride and sulfate in drinking water have to be considered. The increase of the Cl− or SO2− 4 concentrations may be particularly a problem in the case of high acid dosages and raw waters with high original chloride or sulfate content.

9.3.4 Ion exchange processes Since ion exchange is the subject of a separate chapter (Chapter 11), the basics of ion exchange are explained here only to that extent that is necessary to understand the softening and dealkalization processes. Ion exchangers (also referred to as ion exchange resins) are solid materials that consist of a polymeric matrix (copolymers, such as styrene/divinylbenzene or (meth)acrylic acid/divinylbenzene) with different functional groups. Depending on the chemical nature of the functional groups, ion exchangers can be distinguished into acidic, basic, and complex forming functional groups. For softening/ dealkalization, ion exchangers with acidic and basic functional groups are of particular relevance. The acidic and basic groups can be further subdivided into strongly and weakly acidic or basic groups, where the strength of the acidic and basic groups is defined in the same way as for free acids and bases, which means on the basis of the extent of deprotonation or protonation characterized by the acidity or basicity constant (Chapter 2, Section 2.3.3). In contact with water, strongly acidic groups are nearly totally deprotonated and strongly basic groups are nearly totally protonated and therefore both groups occur in ionic form over nearly the whole pH range. By contrast, the deprotonation of weakly acidic groups and the protonation of weakly basic groups in contact with water strongly depend on the pH. Ionic forms can be found therefore only in certain pH ranges (higher pH values in the case of weakly acidic ion exchangers, lower pH values in the case of weakly basic ion exchangers). Typical acidic groups are the strongly acidic sulfonic acid group (–SO3 H) and the weakly acidic carboxylic acid group (–COOH). Basic resins contain strongly basic quaternary amino groups (–NR3 OH) or weakly basic tertiary, secondary, or primary amino groups (–NR2 , NRH, –NH2 ). The symbol R stands here for organic groups such as the methyl group (–CH3 ) or other alkyl groups. Due to the formation of negative charges, the acidic resins are able to exchange cations and are therefore referred to as cation

9.3 Softening and dealkalization processes

| 183

exchangers. In contrast, the positively charged basic resins are able to exchange anions and are referred to as anion exchangers. A specific characteristic of the weakly acidic exchangers is that their deprotonation is promoted by the reaction with the water constituent hydrogencarbonate according to: R–COOH + HCO−3 󴀕󴀬 R–COO− + H2 O + CO2(aq) (9.24) Note that here and in the following paragraphs the resin constituents (organic matrix, R, and functional group) are written in bold letters. Generally, ion exchange processes can be carried out in batch, fixed-bed, or fluidized-bed reactors (Chapter 2, Section 2.6.4). In drinking water treatment, the fixed-bed reactor is the most common reactor type. Strongly acidic resins loaded with sodium ions can be used to remove the hardness-causing ions calcium and magnesium without any influence on the hydrogencarbonate concentration (softening without dealkalization). Since bivalent cations have a higher affinity to the exchanger than univalent ions and are therefore bound preferentially, calcium and magnesium ions are removed very efficiently by this ion exchange process. The respective reaction can be described as: R–SO−3 Na+ + (Ca2+ , Mg2+ ) 󴀕󴀬 R–SO−3 (Ca2+ , Mg2+ ) + Na+

(9.25)

It has to be noted that here and in the following text a simplified notation of the reaction equations is used. All relevant water constituents involved in the exchange reaction are written in brackets without considering their stoichiometric factors. As can be seen from Equation (9.25), the carbonic acid system (CO2 , HCO−3 , CO2− 3 ) is not influenced by this process. However, due to the removal of calcium, the water becomes more undersaturated with respect to calcium carbonate or – in other words – more calcite-dissolving. The reason for that is that the relevant equilibrium curve of the calco–carbonic equilibrium is shifted to the right due to the lower Ca2+ concentration (Chapter 8, Section 8.2.2). Furthermore, the exchange process leads to an increase of the sodium concentration in the treated water. According to the equivalence condition, 2 mmol Na+ (46 mg) are released from the resin per mmol Ca2+ or Mg2+ that is bound. The regeneration of the loaded resin can be carried out with a sodium chloride solution. A highly concentrated regeneration solution has to be applied to displace the stronger bound bivalent ions from the functional groups. Nevertheless, the regeneration is typically not complete, which reduces the initial exchange capacity. For softening with dealkalization, weakly acidic resins are suitable. This process can be written in a simplified manner as: R–COOH + (Ca2+ , Mg2+ , HCO−3 ) 󴀕󴀬 R–COO− (Ca2+ , Mg2+ ) + CO2(aq) + H2 O

(9.26)

Due to the reaction of hydrogencarbonate ions with the protons of the functional group of the resin (Equation (9.24)), negatively charged binding sites are formed where

184 | 9 Softening and dealkalization

cations can be bound. As with the strongly acidic exchangers, the bivalent cations (Ca2+ , Mg2+ ) have a higher affinity to the exchanger than the univalent ions and are bound preferentially. It has to be noted that in the case of weakly acidic resins, the reaction with hydrogencarbonate is a precondition for the formation of negative binding sites, because the intrinsic dissociation of the –COOH group at medium pH values is very low. That means that the exchange capacity is limited by the available hydrogencarbonate concentration. Accordingly, at maximum the carbonate hardness can be removed. As a consequence of the transformation of hydrogencarbonate, the process leads to an increase of the CO2 concentration and a decrease of the pH in the treated water. Therefore, the application of this process requires a subsequent removal of the formed CO2 (e.g., by mechanical deacidification, Chapter 8), which simultaneously increases the pH of the water. The regeneration can be carried out by strong or weak acids. Due to the strong affinity of the weak functional group to protons, neither excess amounts nor high concentrations of the regeneration acid are necessary. If the hydrogencarbonate concentration in the raw water exceeds the sum of the equivalent concentrations of Ca2+ and Mg2+ (case B in Figure 9.1), more negative sites are formed by the reaction of the functional groups with hydrogencarbonate than necessary for the removal of Ca2+ and Mg2+ . In this special case, univalent ions (Na+ , K+ ) are also removed. Since the removal of univalent ions is normally not necessary in drinking water treatment, this process is not appropriate for such types of water. For drinking water treatment, a specific process, referred to as the CARIX process, was developed. This process is based on a combined application of a weakly acidic and a strongly basic resin, the latter initially loaded with HCO−3 . Both resins are applied in a single filter in the form of a mixed bed. The name of the process refers to the regeneration of the resins with dissolved CO2 (CARIX = carbonic acid regenerated ion exchanger). The CARIX process allows not only a softening and dealkalization but also a partial demineralization. This process can be represented in a very simplified form by: R–COO− (Ca2+ )

R–COOH + (Ca2+ , HCO−3 , SO2− 4 ) 󴀕󴀬 R–NR+3 HCO−3

+ CO2(aq) + H2 O

(9.27)

R–NR+3 (SO2− 4 )

Here, Ca2+ stands as an example for the hardness-causing ions, HCO−3 stands for the alkalinity, and SO2− 4 stands for the other anions in the water. During the process, sulfate displaces hydrogencarbonate from the strongly basic resin (partial demineralization). The hydrogencarbonate released from the basic resin reacts with the protons of the weakly carboxylic acid group of the acidic resin to form negative binding sites, where the bivalent ions can be bound (softening). Typically, the capacity of the cation exchanger in the CARIX process is greater than that of the anion exchanger, which allows a simultaneous binding of both released and pristine hydrogencarbonate. In to-

9.3 Softening and dealkalization processes

| 185

tal, calcium and magnesium ions as well as hydrogencarbonate and other anions are removed during this process (softening/dealkalization with partial demineralization). The resin mixed bed is regenerated with carbon dioxide. Carbon dioxide dissociates in water into protons and hydrogencarbonate. The protons regenerate the acidic resin and the hydrogencarbonate regenerates the basic resin. However, the regeneration efficiency of carbon dioxide is limited. Therefore, the exchange on both resins remains incomplete. This incomplete exchange makes the CARIX process particularly appropriate for drinking water treatment, where only a partial softening, dealkalization, and demineralization is necessary. Due to the incomplete exchange, it is typically not necessary to blend the treated water with untreated water.

9.3.5 Membrane processes In the last decades, a number of pressure-driven membrane processes have been developed that are suitable for different treatment objectives. Detailed information on membrane processes in drinking water treatment is given in Chapter 5. The discussion here is therefore restricted to the special application for softening. In contrast to the membrane processes microfiltration and ultrafiltration that only allow removal of particulate matter and larger molecules, the membrane processes nanofiltration (NF) and reverse osmosis (RO) are well suited to removing ions from water and therefore also to removing the hardness-causing ions Ca2+ and Mg2+ . The membranes used in reverse osmosis are dense membranes (membranes with no detectable pores) and the separation principle is based on diffusion. The membranes used in nanofiltration have typically the character of dense membranes as well, but they are less dense than the reverse osmosis membranes. Due to the higher permeability of nanofiltration membranes lower pressures are necessary. Nanofiltration is therefore also referred to as low-pressure reverse osmosis (LPRO). As indicated by the name, reverse osmosis is the inversion of the spontaneous osmosis process. Whereas osmosis refers to the flow of the solvent water through a semipermeable membrane into a solution, reverse osmosis refers to the water flow out of a solution. The inversion of the water flow can be reached by applying an external pressure that overcomes the osmotic pressure of the water to be treated. The osmotic pressure that has to be overcome is directly proportional to the total molar concentration of all solutes in the water (Chapter 5, Section 5.4). The water flux, J w , through RO and NF membranes is given by: J w = k w (∆p − ∆π)

(9.28)

where k w is the mass transfer coefficient (membrane constant), ∆p is the transmembrane pressure (pressure difference between the feed side and the permeate side of the

186 | 9 Softening and dealkalization

membrane), and ∆π is the transmembrane osmotic pressure (osmotic pressure difference between the feed side and the permeate side of the membrane). Reverse osmosis can be used to produce pure water from an aqueous solution. In the ideal case, reverse osmosis removes all dissolved inorganic and organic water constituents. In practice, however, there is also a certain solute flux through the membrane. Nevertheless, the reverse osmosis is very efficient in removing dissolved water constituents, particularly ions, including the very small univalent ions (rejection of univalent ions > 90%). Reverse osmosis is widely used in desalination of seawater with transmembrane pressures of 60 to 80 bars. In freshwater treatment, the transmembrane pressures are in the range of 6 to 12 bars due to the lower salt contents resulting in lower osmotic pressures that have to be overcome. Since the objective in drinking water treatment is not to produce completely deionized water, only substreams are treated and subsequently blended with untreated water. RO is typically applied when, besides softening, further targets should be achieved (e.g., removal of harmful organics, removal of Na+ , Cl− , and other ions). If the main target is softening rather than desalination, the application of nanofiltration is an appropriate option. The applied transmembrane pressure is markedly lower than in RO (3–5 bar). The NF membranes are less dense and often carry charges on the surface. That makes them well suited for the selective removal of the larger bivalent ions Ca2+ and Mg2+ (Chapter 5, Section 5.1). As with reverse osmosis, nanofiltration is typically applied to substreams that are subsequently blended with untreated water. In both membrane processes, the feed water must be free of turbidity to avoid a blockage of the membrane surface. Therefore, an appropriate pretreatment (coagulation/flocculation, filtration, membrane filtration) is necessary. Furthermore, to avoid scaling (particularly precipitation of calcium carbonate) at the membrane surface, a mineral acid, carbon dioxide, or specific antiscalants have to be added to the feed stream. Alternatively, the permeate yield can be reduced to prevent too high ion concentrations on the feed/retentate side of the membrane (Chapter 5, Section 5.4.3). As an unavoidable byproduct of the membrane processes NF and RO that are operated under cross-flow conditions (Chapter 5, Section 5.2.1), a concentrate stream occurs that amounts to about 10 to 25% of the treated substream. The need for concentrate disposal is a drawback of membrane softening. Furthermore, membrane treatment has a strong effect on the calco–carbonic equilibrium. Whereas the ions involved in the calco–carbonic equilibrium are removed, the content of the dissolved gas CO2 is nearly unaffected. As a result, the water becomes calcite-dissolving. Therefore, a posttreatment of the blended water is necessary to establish (or reestablish) the calco–carbonic equilibrium, for instance by aeration (stripping of CO2 , Chapter 8). Figure 9.5 shows the general process scheme of a membrane softening process.

9.4 Special case: hardening of water

Pump

| 187

Deacidification

Membrane unit Concentrate

Waste air

Feed water Blended water

Permeate

Air

Bypass (untreated water)

Treated water

Fig. 9.5: Scheme of a membrane softening process.

9.4 Special case: hardening of water As already mentioned in Section 9.1, the hardness of drinking water should be in the medium range. Hard raw waters have to be treated by softening or dealkalization to reach this medium range as demonstrated in the previous sections. By contrast, for very soft waters it can be necessary to increase the water hardness to reach this range. A typical application is the treatment of very soft reservoir water. A hardness increase may be also necessary in cases where waters from different sources should be blended and different hardness levels have to be balanced. Hardness increase can be carried out by introducing CO2 into the water followed by one of the chemical deacidification processes with calcium (or calcium and magnesium) containing chemicals described in detail in Chapter 8 (Section 8.3.3). As a result of the reaction of the introduced CO2 with lime water, calcium carbonate, or halfburnt dolomite, the hardness-causing ions Ca2+ (and Mg2+ in the case of half-burnt dolomite) and equivalent amounts of hydrogencarbonate are introduced into the water. Accordingly, the carbonate hardness increases. The respective reaction equations are: 2 CO2 + Ca2+ + 2 OH− 󴀕󴀬 Ca2+ + 2 HCO−3 CO2 + H2 O + CaCO3(s) 󴀕󴀬

Ca + 2 HCO−3 2+ 2+

3 CO2 + 2 H2 O + CaCO3 ⋅ MgO(s) 󴀕󴀬 Ca

(9.29)

2+

+ Mg

+

(9.30) 4 HCO−3

(9.31)

The extent of the hardness increase in relation to the CO2 consumption for the different processes was already discussed in Chapter 8 (Table 8.3). The introduction of CO2 can be carried out by one of the techniques described for gas absorption in Chapter 7.

10 Deironing and demanganization 10.1 Introduction and treatment objectives Iron and manganese can occur in natural waters in different forms. The speciation of iron and manganese in water is strongly influenced by the pH and the redox intensity (or redox potential). Whereas the pH characterizes the acidic or basic character of a considered aqueous system, the redox intensity, pe, characterizes its redox state. High values of pe indicate oxidizing conditions, whereas low values indicate reducing conditions. Instead of the dimensionless redox intensity, which is defined as the negative logarithm of the electron activity (analog to the pH as the negative logarithm of the proton activity), the measurable parameter redox potential, E H (in mV), can also be used to characterize the redox state (Chapter 2, Section 2.3.5). The relationship between the redox intensity and the activities (or simplifying for dilute solutions, the concentrations) of the species involved in a redox half-reaction is given by: 1 Πa i ν i (Ox) pe = pe0 + log (10.1) ne Πa i ν i (Red) where pe0 is the standard redox intensity, n e is the number of electrons that are exchanged in the reaction, Πa i ν i (Ox) and Πa i ν i (Red) are the products of the activities on the oxidant side and the reductant side of the half-reaction, respectively, and the exponents ν i are the respective stoichiometric factors. The standard redox intensity, pe0 , is related to the equilibrium constant of the half-reaction by: pe0 =

1 log K ∗ ne

(10.2)

Note that Equation (10.1) is derived from the law of mass action for a redox halfreaction and, according to the rules for formulating laws of mass action in aqueous systems, water and solids are not considered in the equation (Chapter 2, Section 2.3.5). The speciation of iron and manganese in the medium pH range is dominated by the redox couples Fe2+ /Fe(OH)3(s) and Mn2+ /MnO2(s) . Applying Equation (10.1) to these redox couples, we find: Fe(OH)3(s) + 3 H+ + e− 󴀕󴀬 Fe2+ + 3 H2 O pe = pe0 + log

c3 (H+ ) c(Fe2+ )

(10.3) (10.4)

and: MnO2(s) + 4 H+ + 2 e− 󴀕󴀬 Mn2+ + 2 H2 O pe = pe0 + https://doi.org/10.1515/9783110551556-010

c4 (H+ )

1 log 2 c(Mn2+ )

(10.5) (10.6)

190 | 10 Deironing and demanganization The standard redox intensities, pe0 , for the redox couples Fe2+ /Fe(OH)3(s) and Mn2+ / MnO2(s) at 25 °C are 16.3 and 20.8, respectively. Equations (10.4) and (10.6) define the specific Fe2+ and Mn2+ concentrations that can be expected at a given pe and pH. In the case of iron and manganese, besides Fe2+ , Fe(OH)3 , Mn2+ , and MnO2 , some further species can occur for which the respective pe and pH functions have to be formulated in an analogous manner. From all these equations, the predominance area diagrams (also referred to as pe–pH diagrams or Pourbaix diagrams) shown in Figures 10.1 and 10.2 can be derived. It has to be noted that the boundary lines in the diagrams are not strict boundaries, but lines that only separate the areas where the considered species are predominant. More details about the drawing of Pourbaix diagrams can be found in hydrochemistry textbooks (e.g., Worch, 2015). It can be derived from the diagrams that iron and manganese occur in dissolved form only under reducing conditions, whereas under oxidizing conditions (at least in the medium pH range) solid compounds predominate, in particular iron(III) hydroxide (Fe(OH)3 ) and manganese dioxide (MnO2 ). Under strongly reducing conditions, where sulfur occurs as dihydrogen sulfide (H2 S) or its dissociation products (HS− , S2− ), solid ∗ of FeS and MnS at sulfides are formed, which show a very low solubility. The pKsp 25 °C are 18.1 and 13.5, respectively, which are relatively high values. Note that a high ∗ indicates a low solubility (Chapter 2, Section 2.3.4). According to the value of pKsp dissociation equilibria of H2 S (H2 S 󴀕󴀬 H+ + HS− and HS− 󴀕󴀬 H+ + S2− ), the sulfides are preferentially formed at higher pH values. Iron and manganese carbonates are also formed at higher pH values, because the equilibrium between hydrogencarbonate and carbonate is shifted to carbonate at higher pH values (for carbonic acid speciation, see ∗ values of iron carbonate and manganese carbonate Figure 1.4 in Chapter 1). The pKsp at 25 °C are 10.5 and 10.7, respectively.

Fig. 10.1: pe–pH diagram of iron. The diagram is calculated for 25 °C and the following total element concentrations: c(C) = 1 ⋅ 10−3 mol/L, c(Fe) = 1 ⋅ 10−5 mol/L, c(S) = 1 ⋅ 10−4 mol/L.The red lines are the boundaries of the stability area of liquid water.

10.1 Introduction and treatment objectives |

191

Fig. 10.2: pe–pH diagram of manganese. The diagram is calculated for 25 °C and the following total element concentrations: c(C) = 1 ⋅ 10−3 mol/L, c(Fe) = 1 ⋅ 10−5 mol/L, c(S) = 1 ⋅ 10−4 mol/L. The red lines are the boundaries of the stability area of liquid water.

According to the previous discussion, iron and manganese in dissolved forms (as Fe2+ and Mn2+ ) can often be found in such groundwaters where reducing conditions exist. In particular at lower pH values, the concentrations are often in the medium mg/L range, in extreme cases also in the higher mg/L range. At higher pH values, the solubility is increasingly limited by carbonate formation and the concentrations are only in the lower mg/L range. As a rule, the concentration of manganese in groundwater is lower than the iron concentration. Dissolved iron and manganese can also be found in surface waters, especially in eutrophic lakes or reservoirs (lakes or reservoirs with high biomass production) during stagnation periods. In particular during the summer stagnation, a high oxygen demand for the degradation of dead biomass together with the interrupted replenishment of dissolved oxygen from the upper layer of the water body (epilimnion) leads to reducing conditions in the deeper layers (hypolimnion) with the consequence that iron and manganese can be released from the sediment. In polytrophic lakes (lakes with even higher biomass production), the oxidants O2 and NO−3 are totally consumed by degradation processes during the stagnation period with the consequence that sulfate is reduced to sulfide. In this case, Mn2+ and Fe2+ are fixed by formation of hardly soluble sulfides, which leads to only low concentrations of Mn2+ and Fe2+ in the liquid phase. From a health point of view, the typically occurring iron and manganese concentrations are not problematic. At higher concentrations, Fe2+ and Mn2+ can give the water a metallic taste. However, the need to remove dissolved iron and manganese from the water results mainly from the fact that both ions form intensely brown colored suspended particles (iron hydroxide and manganese dioxide as well as inter-

192 | 10 Deironing and demanganization

mediates with different water contents) if they are oxidized. The color of the water ranges from reddish brown to brownish black depending on the contents of iron and manganese hydroxides or hydrated oxides that are formed by oxidation. In particular, iron easily forms oxidation products when the water comes in contact with air and the redox intensity increases. In contrast, the manganese oxidation is comparatively slower. The precipitating oxidation products can lead to problems during drinking water distribution due to the blockage of pipes and armatures. Furthermore, colored and particle-containing water is not accepted by consumers due to aesthetic reasons. A further negative effect is that water contaminated with iron and manganese often contains iron and manganese bacteria that form a brown colored slime together with the oxidation products, for instance in toilet tanks or faucets. Moreover, colored and particle-containing water is also not suitable for many industrial and other commercial purposes. If the eutrophic lakes or reservoirs are used as drinking water resources, the seasonal iron and manganese problem can be solved by drawing the water from another (higher) horizon, where oxidizing conditions prevail. In contrast, groundwater under reducing conditions that permanently contains dissolved iron and manganese has to be treated before it can be used as drinking water. The treatment processes that are applied to remove dissolved iron and manganese (Fe2+ , Mn2+ ) are referred to as deironing and demanganization processes. Deironing is sometimes also called deferrization (derived from ferrum, the Latin name for iron). Typical limit values for drinking water set in national regulations are 0.2 or 0.3 mg/L for iron and 0.05 mg/L for manganese. The recommended guide values for the dissolved iron and manganese species after treatment are lower; typical values are < 0.02 mg/L for iron and < 0.01 mg/L for manganese.

10.2 Basics of deironing and demanganization 10.2.1 General considerations and thermodynamic aspects As shown in the previous section, iron and manganese can occur in dissolved or solid form, depending on pe and pH. In oxic surface waters, iron and manganese occur mainly in oxidized, particulate form. These particles are removed together with other suspended solids during the common particle separation processes. In contrast, in water with low redox potential (e.g., groundwater), iron and manganese occur in dissolved form as Fe2+ and Mn2+ , respectively. To remove these ions, specific treatment processes, referred to as deironing and demanganization, have to be applied. The general principle of deironing and demanganization consists of the oxidation of the reduced ions and separation of the solid oxidation products. For economic reasons, mainly oxygen from the air is used as the oxidant. The oxidant is introduced into the water by aeration (Chapter 7). Aeration has a number of positive side effects, for

10.2 Basics of deironing and demanganization | 193

instance stripping of dissolved gases that may occur under reducing conditions (e.g., CO2 , H2 S, CH4 ) or oxidation of ions, such as HS− or NH+4 . In specific cases, also pure oxygen, ozone, or other chemicals (e.g., potassium permanganate or hydrogen peroxide) are used as oxidants, for instance if the oxidation of the iron and manganese ions is hampered by strong complex formation with humic substances or if the deironing and demanganization should be combined with other treatment objectives (e.g., oxidation of organic water constituents). The minimum redox intensity that is necessary to decrease the iron concentration to the guide value of 0.02 mg/L Fe2+ (3.58 ⋅ 10−7 mol/L) can be derived from Equation (10.4) and amounts to pe = 1.75 (E H = 103 mV) at pH = 7 and 25 °C. For Mn2+ with a guide value of 0.01 mg/L (1.82 ⋅ 10−7 mol/L), we find the minimum redox intensity from Equation (10.6) to be pe = 10.17 at pH = 7 and 25 °C (E H = 600 mV). To prove whether a given oxidant is able to increase the redox intensity to the required values, the redox intensity of the half-reaction of the oxidant has to be considered. In the case of oxygen as the oxidant, the half-reaction reads: O2 + 4 H+ + 4 e− 󴀕󴀬 2 H2 O

(10.7)

and the respective redox intensity equation for a water that is saturated with oxygen from the air is: 1 pe = pe0 + lg [p(O2 ) c4 (H+ )] (10.8) 4 with pe0 = 20.75 at 25 °C. For the partial pressure of oxygen in air (p(O2 ) = 0.209 bar) and a pH of 7, we find pe = 13.58 (E H = 801 mV), which is higher than the redox intensities needed to reach the guide values for Fe2+ and Mn2+ . That means that the conversion to the target extent is thermodynamically possible. The overall reactions that take place during deironing and demanganization with oxygen from air as the oxidant can be described in a simplified manner by: 4 Fe2+ + O2 + 10 H2 O 󴀕󴀬 4 Fe(OH)3(s) ↓ + 8 H+ 2+

2 Mn

+

+ O2 + 2 H2 O 󴀕󴀬 2 MnO2(s) ↓ + 4 H

(10.9) (10.10)

It has to be noted that the actual reactions are much more complex than shown in Equations (10.9) and (10.10). During oxidation, a number of intermediates (hydrated oxides with different water contents) occur. In the case of Mn2+ oxidation, autocatalytic reactions at the surface of MnO2 also play an important role. Furthermore, a certain fraction of Mn2+ may be only adsorbed onto MnO2 and not further oxidized. As can be derived from Equations (10.9) and (10.10), the oxidation is accompanied by the formation of protons. As long as enough hydrogencarbonate (bicarbonate) is available in the water, the protons are bound to the hydrogencarbonate under formation of CO2 (buffer effect): HCO−3 + H+ 󴀕󴀬 H2 O + CO2

(10.11)

194 | 10 Deironing and demanganization

Otherwise, bases (e.g., NaOH) have to be added to avoid a strong decrease of the pH. Low pH values are unwanted because they disturb the precipitation of Fe(OH)3 due to the formation of hydroxo complexes combined with a solubility increase (Figure 6.9 in Chapter 6). Moreover, the reaction rate is also a function of pH and decreases with decreasing pH (Section 10.2.2). The theoretical oxygen consumption for the oxidation of 1 mg Fe2+ is 0.14 mg O2 and the respective consumption for the oxidation of 1 mg Mn2+ is 0.29 mg O2 . However, the real oxygen consumption is much higher, because during the increase of the redox potential in the water also other oxidation processes take place, as can be derived from the redox sequence shown in Figure 10.3. In particular, the oxidation of HS− and NH+4 are important oxygen-consuming side reactions. Ammonium ions frequently occur in groundwaters even under moderately reducing conditions, whereas hydrogensulfide dominates over sulfate only under strongly reducing conditions. The oxidation reactions can be written as: + HS− + 2 O2 󴀕󴀬 SO2− 4 +H

NH+4

+ 2 O2 󴀕󴀬

NO−3

(10.12) +

+ 2 H + H2 O

(10.13)

The oxygen consumption per mg HS− and NH+4 is 1.93 mg and 3.56 mg, respectively. As in the oxidation of Fe2+ and Mn2+ , protons are formed during the reactions. As can be derived from the redox sequence, the oxidation of iron and manganese is thermodynamically possible if the redox potential is sufficiently high. Whereas the oxidation of Fe2+ proceeds easily even at moderate redox potentials, the oxidation of Mn2+ requires higher redox potentials. At first the iron and then the ammonium

Fig. 10.3: Redox sequence in aqueous systems. The boundary lines are calculated for ϑ = 25 °C, c(Fe) = 1 × 10−6 mol/L, and c(Mn) = 1 × 10−6 mol/L.

10.2 Basics of deironing and demanganization | 195

ions have to be oxidized before the manganese ions can be oxidized. However, the thermodynamics of the redox reactions is only one factor that determines the process. The other relevant factor is the reaction kinetics of the oxidation. Under unfavorable conditions, the reaction rate of the redox processes can be very slow, so that no measurable conversion can be observed, even if the thermodynamics allow the reaction. However, an appropriate catalyst can accelerate the process. Bacteria are also able to mediate the redox processes. Catalytic and biological effects are especially relevant for manganese oxidation. In the following section, the basics of the different mechanisms will be presented. The consequences for the practical process design will be discussed separately in Section 10.3.

10.2.2 Oxidation mechanisms and kinetic aspects According to Stumm and Morgan (1996), the kinetics of the homogeneous abiotic oxidation of iron can be written as: dc(Fe2+ ) c(Fe2+ ) c(O2 ) =k dt c2 (H+ )

(10.14)

dc(Fe2+ ) = k 󸀠 c(Fe2+ ) c2 (OH− ) p(O2 ) dt

(10.15)

− or: − with:

k󸀠 =

k H(O2 ) K 2w

(10.16)

where k and k󸀠 are the respective rate constants, H is the Henry constant (H(O2 ) = c(O2 )/p(O2 )), p(O2 ) is the partial pressure of oxygen, and K w is the dissociation constant of water (K w = c(H+ ) c(OH− )). According to Equations (10.14) and (10.15), the reaction rate increases with increasing oxygen concentration (or increasing partial pressure), increasing iron(II) concentration, and increasing pH. In particular the pH has a strong influence. For instance, if the pH is increased by 1 unit (= increase of c(OH− ) by a factor of 10), the reaction rate increases by the factor of 100. The oxidation of Mn2+ in homogenous solutions is extremely slow at low and medium pH values. Only from pH values greater than 8 does the half-life decrease to values in the range of some hours. However, if the Mn2+ is in contact with the oxidation product, the reaction is accelerated by an autocatalytic process. In this case, the Mn2+ is adsorbed on the surface of the oxidation product MnO2 where it can be oxidized in a surface reaction. According to Faust and Aly (1998), this autocatalytic

196 | 10 Deironing and demanganization

mechanism can be described in a simplified manner by: O2

Mn2+ → MnO2(s)

(slow)

(10.17)

Mn2+ + MnO2 → Mn2+ ⋅ MnO2(s)

(fast)

(10.18)

(slow)

(10.19)

O2

Mn2+ ⋅ MnO2(s) → 2 MnO2(s)

Whereas the reaction kinetics of the homogeneous oxidation of Mn2+ can be described analogously to Equations (10.14) and (10.15), the kinetics of the autocatalytic process is more complex and requires consideration of the homogeneous and the heterogeneous parts of the reaction. The different rates of adsorption and oxidation lead to the effect that within a limited contact time, a fraction of Mn2+ remains adsorbed according to Equation (10.18) but will not be further oxidized. It could also be shown that MnO2 catalyzes not only the Mn2+ oxidation but also the oxidation of Fe2+ . Under certain conditions, the oxidation processes are supported by iron and manganese bacteria (e.g., Gallionella ferruginea, Pseudomonas manganoxidans, and others) that form biofilms in the filters that are used for particle separation in the deironing and demanganization process. The bacteria are able either to gain energy from the oxidation of the reduced species (e.g., Gallionella) or to form extracellular polymeric substances that interact with the metal ions. The metabolic activities are not fully understood in all cases, but the effects are catalytic in nature and may accelerate the oxidation of Fe2+ and Mn2+ . In comparison to chemical oxidation, the biologically catalyzed oxidation of iron(II) starts already at relatively low redox potentials and at pH values between 6 and 7. The addition of only a small amount of oxygen is sufficient to raise the redox potential into the required range. At higher oxygen contents, on the other hand, the chemical oxidation of iron is relatively fast. Under these conditions, the contribution of the biological oxidation is of secondary relevance. Under the practical conditions of drinking water treatment, iron oxidation is mainly a chemical oxidation. Accordingly, the deironing process in a filter with fresh filter material requires only a very short running-in phase. The chemical oxidation of manganese is more difficult. Higher redox potentials and, particularly for chemical oxidation, very high pH values are necessary. Here, biologically mediated oxidation strongly improves the total transformation process. However, the growth rate of the manganese bacteria is very slow. Therefore, biological manganese removal in a fresh filter starts only after a relatively long running-in phase (up to three months). In summary, it has to be stated that the oxidation of Fe2+ and Mn2+ is a very complex process, where different mechanisms are involved, in particular chemical oxidation in the homogeneous phase, and adsorption and autocatalysis on oxidic surfaces, as well as biologically mediated oxidation processes. Typically, these mechanisms act

10.3 Practical aspects |

197

in parallel. Which mechanism dominates the overall oxidation process depends on the chemical nature of the reduced species, the process design, and the process conditions.

10.3 Practical aspects As already mentioned before, deironing and demanganization processes are frequently used in groundwater treatment. In most cases, the oxidation of the reduced ions Fe2+ and Mn2+ is carried out with atmospheric oxygen as the oxidant. Other, more expensive oxidants (pure oxygen, ozone, potassium permanganate, hydrogen peroxide) are only used if oxidation with air is impaired by a problematic water composition, for instance when iron and manganese ions are strongly bound to humic substances. Accordingly, the typical deironing/demanganization process consists of aeration followed by filtration. If necessary, the process is coupled with a deacidification (Chapter 8). The introduction of air can be carried out by open aeration with waterfall aerators (e.g., spray aerators, cascade aerators, cone aerators) or by pressure aeration (direct injection into the pipeline, closed spray reactors supplied with compressed air). In the first case, the introduction of air is accompanied by the stripping of dissolved gases, such as CO2 , CH4 , and H2 S. For gas–liquid exchange see also Chapter 7. The central element of the deironing/demanganization process is the filter that retains the oxidation products. The solids accumulated in the filter bed provide the catalytic active surfaces for the further oxidation and also act as carriers for the biofilms formed by iron and manganese bacteria. The most commonly used filter materials are quartz sand or gravel. If a simultaneous deacidification is wanted, also half-burnt dolomite or calcium carbonate can be used (Chapter 8, Section 8.3.3). In this case, the pH is increased, which has a positive effect on the oxidation kinetics (Section 10.2.2). Due to the deposition of oxidation products, the filter resistance increases over the filter run time. Therefore, the oxidation products, deposited on the filter material, have to be removed through backwashing from time to time. During backwashing, water is pumped backwards through the filter. Optionally, compressed air can be introduced prior to the backwash water in order to expand the filter bed and to break up the compacted layers of oxidation products. Water free of disinfectants has to be used for backwashing to avoid killing of the bacteria in the biofilm. For filtration see also Chapter 4, Section 4.3. The formation of the biofilm on fresh or backwashed filter material requires a certain running-in time. In particular, the running-in time for biological manganese removal is very long (one to three months). This time can be shortened if a certain amount of used filter material (seeding material) is added to the fresh filter material. Another option is to start the filter run with chemically dominated oxidation with

198 | 10 Deironing and demanganization

potassium permanganate according to: 2 MnO−4 + 3 Mn2+ + 2 H2 O 󴀕󴀬 5 MnO2(s) + 4 H+

(10.20)

With increasing run time, the dosage of permanganate can be reduced and the dominant process mechanism switches from chemical oxidation to biological/ catalytic oxidation. Here, it has to be taken into account that in a single-stage process the iron is also oxidized by permanganate, although filter conditioning is not mandatory for the deironing process. Iron oxidation proceeds according to: MnO−4 + 3 Fe2+ + 7 H2 O 󴀕󴀬 MnO2(s) + 3 Fe(OH)3(s) + 5 H+

(10.21)

In a two-stage process with separate deironing and demanganization, the filter conditioning can be restricted to the second stage (demanganization filter). The process design depends on the chemical composition of the water to be treated, in particular on the content of iron and manganese but also on the content of other constituents relevant for the treatment process. Waters with very low redox potentials are characterized by lower concentrations of iron and manganese and occurrence of dihydrogen sulfide and methane (Section 10.1). Such waters can be treated by open aeration with subsequent filtration. A single-stage monomedia filter is typically sufficient. The open aeration allows the stripping of the dissolved gases dihydrogen sulfide and methane and also of dissolved CO2 . Figure 10.4 shows a typical process scheme of single-stage deironing/demanganization of groundwater.

Sedimentation basin Clear water Cascade aerator -CO2 Filter sludge +O2 Treated water Monomedia gravity filter

Clear water basin

Extraction well Backwash water

Fig. 10.4: Process scheme of single-stage deironing/demanganization with open cascade aeration. The dashed lines show the flow regime during backwashing.

10.3 Practical aspects | 199

Influent

Deironing

Nitrificaon

Demanganizaon

Effluent

Fig. 10.5: Zone formation in a monomedia filter according to the redox sequence.

In monomedia filters, a distinct formation of zones according to the redox sequence can be found. This zone formation is schematically shown in Figure 10.5. Higher concentrations of iron and manganese are typically found in waters under moderately reduced conditions (Section 10.1). In principle, raw waters with higher iron and manganese concentrations can also be treated in a single-stage monomedia filtration process. Alternatively, a dual-media filter (e.g., sand, anthracite) or a two-stage filtration with two monomedia filters may be suitable. A two-stage filtration may be in particular necessary when the manganese concentration is very high. This technique allows separation of the iron and the manganese oxidation and permits adjustment of the process conditions according to the different requirements (e.g., different filter run times, intermediate CO2 removal to increase the pH for the subsequent demanganization, filter conditioning only for the second filter). The scheme of a two-stage process is shown in Figure 10.6. A general approach for the process design is based on the maximum filter velocity as the essential design parameter. The maximum filter velocity is that filter velocity that still allows a complete conversion of the considered reduced species within the filter. The reaction time, t R , needed for a complete conversion is determined by the reaction rate and has to be derived from the rate equation. This is the crucial point of this model approach. We will come back to this point later. The condition for a complete conversion within the filter is that the residence time, t r , within the filter is greater than the required reaction time: tr ≥ tR

(10.22)

200 | 10 Deironing and demanganization

Spray aeration tanks Air Clear water basin

Treated water

Extraction well

Closed rapid filters Deironing Demanganization

Fig. 10.6: Two-stage deironing/demanganization process with intermediate aeration (backwashing not shown).

The residence time, t r , is related to the superficial filter velocity, v F , and the filter height, h F : hF hF εB tr = = (10.23) uF vF where u F is the interstitial filter velocity and ε B is the filter bed porosity. If the required reaction time is known, the maximum filter velocity that just allows a complete conversion in a filter with the given height, h F , can be found from Equations (10.22) and (10.23). Alternatively, the required filter height for a given filter velocity can be calculated. The superficial filter velocity is also related to the volumetric flow rate, V,̇ and the cross-sectional area of the filter, A R : vF =

V̇ AR

(10.24)

Equation (10.24) can be used to find the filter area that is needed to treat a given volumetric flow rate at the maximum filter velocity. As already mentioned, the knowledge of the required reaction time is the crucial point of this model approach. Due to the complexity of the oxidation processes and the various hydrochemical impacts that have to be considered, there is a variety of uncertainties regarding the appropriate kinetic models and the exact rate constants. In the literature, some empirical equations are available that relate the required re-

10.3 Practical aspects | 201

action time or the maximum filter velocity to some important process parameters, for instance metal ion and oxygen concentration, filter grain size, water temperature, and pH. However, the validity of these empirical equations is often subject to limitations with regard to the value ranges of the parameters. In practice, the filter type (monomedia, dual-media), arrangement (single-stage, two-stage), material, and design are therefore often selected on the basis of experiences with raw waters of comparable composition or on the basis of pilot-plant experiments with the water to be treated.

11 Ion exchange 11.1 Types and applications of ion exchange resins Ion exchangers, also referred to as ion exchange resins or ion exchange polymers, are solid polymeric materials (resins) that contain specific functional groups that are able to bind dissolved ions from the water. In return, the originally bound ions are released from the functional groups. A simplified scheme of such an ion exchange process is shown in Figure 11.1. Polymeric Funconal matrix group

Ions type A

Ions type B

Fig. 11.1: Simplified scheme of the ion exchange process.

In the original state, the functional groups can be either ionic (carrying permanent positive or negative charges in the relevant pH range) or neutral. In the first case, the functional groups are loaded with a specific sort of (weakly bound) counterions that can be exchanged with (stronger bound) ions from the water. Neutral groups (weakly acidic or basic groups) must be first transformed into their ionic forms before they can uptake ions from the aqueous phase. The ionization is possible either by deprotonation (in the case of neutral acidic groups) or by protonation (in the case of neutral basic groups). The strength of ionization depends on the pH and the respective acidity or basicity constants of the functional groups. Accordingly, resins with weakly acidic or weakly basic groups carry charges only in specific pH ranges and work only in these pH ranges. The solid matrix consists of cross-linked copolymers such as styrene/divinylbenzene, acrylic acid/divinylbenzene or methacrylic acid/divinylbenzene. These copolymers form three-dimensional networks where divinylbenzene acts as the cross-linking https://doi.org/10.1515/9783110551556-011

204 | 11 Ion exchange

component. Depending on the polymerization conditions, the resulting matrix can have either a gel or a macroporous structure. The conventional gel-type resins are polymerized without any additional ingredients and have a microporous (microreticular) structure. Macroporous (macroreticular) resins can be produced by adding a porogen (inert liquid or solid) to the organic phase prior to the polymerization. After the polymerization, the porogen is extracted, leaving a discrete pore system inside the resin beads. Thus, macroporous resins not only have a gel porosity (microporosity) but additionally a system of macropores whose size and surface area can be predetermined by the added ingredients. Macroporous resins have larger pores and a higher thermal, chemical, and mechanical resistance in comparison to gel resins. On the other hand, gel resins have typically higher capacities. Gel-type resins have only a very low porosity in the dry state, but they can uptake high amounts of water. In contact with water, hydration takes place that allows ions to diffuse through the resin. During the exchange reactions, microreticular resins can exhibit significant swelling or shrinking effects due to differences between the hydrated radii of the ions that are exchanged. In contrast, the pore structure of macroporous resins is more stable. Shrinking or swelling is not so strongly pronounced. Macroporous resins maintain their porosity even in nonaqueous solutions. For water treatment, mainly gel resins are used, but in some cases also special macroporous resins are applied. With respect to the chemical nature of the functional groups, resins can be differentiated between acidic, basic, and complex-forming ion exchangers. The acidic and basic ion exchangers make up the majority of the ion exchanger materials. They can be further subdivided into weakly and strongly acidic or basic exchangers. The difference between weakly and strongly acidic or basic functional groups consists of the different acidity or basicity constants and the related degree of deprotonation or protonation, dependent on pH (for basics of acid/base equilibria see also Chapter 2, Section 2.3.3). Strong acidic functional groups (pK ∗a < 1) are deprotonated (negatively charged) and strong basic groups (pK ∗b < 1, pK ∗a > 13) are protonated (positively charged) over nearly the whole range of pH. In the case of weakly acidic and basic groups, the transition between the ionic and neutral state occurs in the medium pH range. That means that weakly acidic groups are predominantly negatively charged only at relatively high pH values (pH > pK ∗a ), whereas weakly basic groups are predominantly positively charged only at low pH values (pH < pK ∗a ). Note that in the case of basic groups, the pK ∗a is the pK ∗a of the protonated form, which is related to the corresponding pK ∗b by pK ∗a + pK ∗b = pK ∗w , where pK ∗w is the dissociation constant of water. Acidic ion exchangers in the deprotonated (anionic) form are able to exchange cations. In contrast, basic ion exchangers in the protonated (cationic) form are able to exchange anions. Acidic ion exchangers are therefore also referred to as cation exchangers, whereas basic ion exchangers are also referred to as anion exchangers. Accordingly, there are four types of acidic and basic ion exchangers: strong acid (equivalent term: strongly acidic) cation exchangers (SAC exchangers), weak acid (equivalent

11.1 Types and applications of ion exchange resins

| 205

term: weakly acidic) cation exchangers (WAC exchangers), strong base (equivalent term: strongly basic) anion exchangers (SBA exchangers), and weak base (equivalent term: weakly basic) anion exchangers (WBA exchangers). In SAC exchange resins, sulfonic acid groups (–SO3 H) are incorporated as strongly acidic functional groups. They are introduced into the styrene/divinyl matrix by sulfonation of styrenic aromatic rings. In contact with water, the dissociation equilibrium: R–SO3 H 󴀕󴀬 R–SO−3 + H+ (11.1) is widely shifted to the right-hand side. The pK ∗a values of such resins are lower than 1, which means that the functional group is totally dissociated in the relevant medium pH range. It has to be noted that here and in the following sections R stands for the organic matrix or arbitrary organic constituents of the functional group and bold characters indicate the solid resin phase. Weakly acidic ion exchangers contain carboxylic acid groups (–COOH) as functional groups. Carboxylic acid groups are introduced by using acrylic acid or methacrylic acid – which already contain the carboxylic acid group – instead of styrene as a component in the copolymerization. The pK ∗a values are in the range of 4–6 depending on the specific exchanger type. The dissociation: R–COOH 󴀕󴀬 R–COO− + H+

(11.2)

is therefore strongly influenced by the pH of the water. For instance, for a resin with a pK ∗a of 6, at pH = 6 only 50% of the functional groups occur in the ionic form. To get a higher fraction of the ionic form, pH values higher than 6 are required. However, there is an additional reaction that supports the formation of the charged form of the functional group. In the presence of hydrogencarbonate (bicarbonate), which is a major constituent of all natural waters, the dissociation equilibrium is shifted to the right by a side reaction of the protons with hydrogencarbonate: R–COOH 󴀕󴀬 R–COO− + H+

(11.3)

H+ + HCO−3 󴀕󴀬 CO2(aq) + H2 O

(11.4)

R–COOH + HCO−3 󴀕󴀬 R–COO− + CO2(aq) + H2 O

(11.5)

Strong base ion exchange resins contain quaternary alkylammonium groups with the general formula –NR+3 . The simplest form is –N(CH3 )+3 . Another frequently used functional group is –N(CH3 )2 C2 H4 OH+ . Resins with the first group are also known as strong base ion exchange resins type 1, whereas the second type is referred to as strong base ion exchange resins type 2. The type 1 resins are stronger basic and have the higher chemical stability in comparison to the type 2 resins. On the other hand, the regeneration efficiency of type 2 resins is greater than that of type 1 resins. In the strong base ion exchange material, the positive charges are compensated by anions such as OH− . In contact with water, the functional groups are ionized according

206 | 11 Ion exchange

to: R–NR3 OH + H+ 󴀕󴀬 R–NR+3 + H2 O

(11.6)

Since the pK ∗b values of the alkylammonium groups are lower than 1 (corresponding pK ∗a > 13), the equilibrium is widely on the right-hand side and the groups occur in the relevant pH range only in ionized form. Tertiary, secondary, and primary amino groups (–NR2 , –NHR, –NH2 ) are neutral groups with a weakly basic character. According to the relatively low pK ∗a values of the protonated forms between 4 and 9 (corresponding to pK ∗b values of 10 to 5), they will be protonated in water to a higher extent only in the acidic pH range: R–NH2 + H+ 󴀕󴀬 R–NH+3

(11.7)

Basic resins can be produced on the basis of polystyrenic as well as polyacrylic matrices. The introduction of the basic groups into a polystyrenic matrix can be achieved by chloromethylation of aromatic rings and subsequent amination (transformation of the chloromethyl group into an amino group). Depending on the chemicals used for the amination step, strong base as well as weak base resins can be produced. For instance, the application of trimethylamine leads to strongly basic groups, whereas the application of dimethylamine leads to weakly basic groups. Due to the synthesis process, the functional groups are initially in the chloride form but can then be transformed into the OH− form (strong base resin) or neutral form (weak base resin) with sodium hydroxide solution. The amination of a polyacrylic matrix is possible via acid amide formation with an amine, which initially leads to a weak base resin, from which, in a further reaction step, also a strong base resin can be produced. Table 11.1 gives a summarizing overview of the different groups of acidic and basic ion exchange materials. In water treatment, acidic and basic ion exchangers can be used for different purposes, in particular for softening, dealkalization, demineralization, nitrate removal, and removal of heavy metals. Macroporous anion exchange resins can also be used to remove dissolved organic matter. Tab. 11.1: Types of acidic and basic ion exchange resins. Type of ion Functional group exchange resin

Deprotonation/protonation in water

pK a∗ Ions that can be bound

Strongly acidic Sulfonic acid group

R–SO3 H → R–SO−3 + H+

13 Anions

Weakly basic

Tertiary, secondary, and primary amino groups

R–NR2 (–NRH, –NH2 ) + H+ 󴀕󴀬 R–NR2 H+ (–NRH+2 , –NH+3 )

4–6 Cations 4–9 Anions

11.2 Selectivity of ion exchange resins

| 207

For the removal of heavy metal cations, a specific type of ion exchange resins was developed, the complex-forming ion exchange resins, also referred to as chelateforming ion exchange resins. In contrast to the acidic and basic exchangers, the bonding mechanism of this type is based on the complex formation, in particular the formation of chelate complexes. Chelate complexes are complexes with ligands that are able to form more than one bond to the central ion (polydentate ligands). The functional groups of these ion exchange resins are such polydentate ligands. Their chemical structure is comparable to those that are also found in conventional synthetic complexing agents. The iminodiacetate group, –N(CH2 COO− )2 , is such a functional group. Since the complex formation with heavy metal cations is much stronger than that with alkaline earth ions, such resins are particularly suitable for selective removal of heavy metal cations from natural waters.

11.2 Selectivity of ion exchange resins The ion exchange process can be expressed in a general form by the following reaction equation: z B Az A + z A Bz B 󴀕󴀬 z A Bz B + z B Az A (11.8) where the bold characters indicate the ions bound to the resin. z A and z B are the ion charges and the corresponding stoichiometric factors. The respective law of mass action for the ion exchange process reads: z

KAB =

cAB cBz A

z

(

cBA cAz B

)

(11.9)

resin

The selectivity coefficient KAB (conditional equilibrium constant) describes how selectively the ion B is bound to the resin in comparison to the reference ion A. Generally, the selectivity depends on the strength of the interactions between the ion and the functional group and is therefore influenced by all factors that have an impact on these interactions. The selectivity of the uptake of an ion by strong acid and strong base exchange resins depends particularly on the charge and the radius of the hydrated ion. As a general rule, the selectivity for bivalent ions is higher than that for univalent ions. Within a series of ions with the same charge, the ion with the smaller radius (in the hydrated state) is bound preferentially. At least for the major ions, the selectivity sequences found for the weakly acidic and weakly basic resins are equal to those of the strongly acidic and strongly basic resins. The only difference between the selectivity sequences for weak and strong groups consists of the fact that the weak acid and weak base exchanger resins have the highest selectivity for protons and hydroxide ions, respectively, according to the weak character of the acidic and basic functional groups. Typical selectivity sequences for acidic and basic resins are listed in Table 11.2.

208 | 11 Ion exchange

Tab. 11.2: Selectivity sequences for acidic and basic ion exchangers. Resin Type

Selectivity sequence

Strong acid cation (SAC) exchange resin Weak acid cation (WAC) exchange resin Strong base anion (SBA) exchange resin Weak base anion (WBA) exchange resin

Ca2+ > Mg2+ > K+ > Na+ > H+ H+ ≫ Ca2+ > Mg2+ > K+ > Na+ − − − − SO2− 4 > NO3 > Cl > HCO3 > OH − − OH− ≫ SO2− > NO > Cl 4 3

In the case of complex-forming ion exchange resins, the selectivity depends on the relative strength of the complex formation. Generally, the chelate complex formation with heavy metal ions (d element ions) is much stronger than that with alkaline earth ions. This is the same effect as can be found for free chelate-forming agents such as nitrilotriacetic acid (NTA) or ethylenediaminetetraacetic acid (EDTA). Therefore, heavy metal ions can be selectively removed from water even if their concentration is much lower than that of the major water constituents Ca2+ and Mg2+ .

11.3 Hydrochemical effects of ion exchange processes If ion exchange processes are applied in water treatment, the hydrochemical state of the water is strongly affected. This is particularly true for the acidic and basic exchangers as can be shown by the following examples. If strong acid cation or strong base anion exchange resins are applied in the H+ form or OH− form, respectively, the exchange of these ions with other ions from the water results in a strong shift of the pH. As mentioned in Section 11.1, weakly acidic functional groups in cation exchangers react with hydrogencarbonate from the water (Equation (11.5)) under formation of carbon dioxide. That means that this reaction results in a change of the carbonic acid species distribution. In the case of weak base anion exchange resins, the necessary protonation of the neutral amino groups leads to a consumption of protons and to an increase of the pH. In the case of softening by ion exchange, the removal of Ca2+ results in a change of the calcite saturation state. All these changes in the hydrochemical state resulting from the application of ion exchange resins can be depicted by means of the Tillmans diagram, the graphical representation of the calco–carbonic equilibrium. The Tillmans diagram was already used to demonstrate the course of deacidification processes (Chapter 8). However, the changes in the hydrochemical state as a result of the application of ion exchangers are often much stronger than in the case of deacidification processes. It is therefore necessary to extend the Tillmans diagram in order to capture also extreme hydrochemical states. In the extended Tillmans diagram, the more general function m = f(−p) replaces the function c(CO2 ) = f(c(HCO−3 )) that is used in the conventional diagram. Here, m is the m alkalinity (total alkalinity) and p is the phenolphthalein alkalinity,

11.3 Hydrochemical effects of ion exchange processes |

209

defined by: − + m = c(HCO−3 ) + 2 c(CO2− 3 ) + c(OH ) − c(H )

p=

c(CO2− 3 )

−

(11.10)

+

− c(CO2 ) + c(OH ) − c(H )

(11.11)

Accordingly, the total concentration of the dissolved inorganic carbon species, c(DIC), can be expressed by m and p: c(DIC) = c(CO2 ) + c (HCO−3 ) + c (CO2− 3 )= m−p

(11.12)

Note that the negative p value (−p) is also referred to as phenolphthalein acidity. Depending on the considered pH range, some of the concentrations in Equations (11.10)– (11.12) can be neglected (see also the carbonic acid speciation shown in Figure 1.4, Chapter 1). The resulting approximations are listed in Table 11.3. Tab. 11.3: Approximate m and p values in different ranges of the pH value. pH range

Negligible concentrations

Low pH Medium pH High pH

− c(HCO−3 ), c(CO2− 3 ), c(OH ) 2− + − c(H ), c(CO3 ), c(OH ) c(H+ ), c(CO2 ), c(HCO−3 )

m≈

p≈ +

c(DIC) ≈ +

−c(H ) −c(CO2 ) − c(H ) c(CO2 ) c(HCO−3 ) −c(CO2 ) c(HCO−3 ) + c(CO2 ) 2− 2− − − 2c(CO2− 3 ) + c(OH ) c(CO3 ) + c(OH ) c(CO3 )

Introducing the parameters ϕ and ∆ under consideration of the respective laws of mass action: ϕ=

c(HCO−3 ) 2 c(CO2− 3 ) + = f(HCO−3 ) + 2 f(CO2− 3 ) c(DIC) c(DIC) 1 f(HCO−3 ) = c(H+ ) K a2 +1+ [ ] K a1 c(H+ ) 1 f(CO2− 3 )= 2 + c (H ) c(H+ ) [ + + 1] K a1 K a2 K a2 Kw − c(H+ ) ∆ = c(OH− ) − c(H+ ) = c(H+ )

(11.13) (11.14)

(11.15)

(11.16)

leads to the general balance equation: m = c(DIC) ϕ + ∆

(11.17)

In Equations (11.14) and (11.15), K a1 and K a2 are the conditional acidity constants of the first and second dissociation step of the carbonic acid (Chapter 8, Section 8.2). K w in Equation (11.16) is the conditional dissociation constant of water (K w = c(H+ ) c(OH− )). To consider the link to the precipitation/dissolution equilibrium of calcium carbonate,

210 | 11 Ion exchange

the stoichiometric deviation (SD) between m (including the carbonate and hydrogencarbonate concentration) and c(Ca2+ ) has to be introduced. With: SD = m − 2 c(Ca2+ )

(11.18)

c(DIC) ϕ + ∆ − SD − 2 c(Ca2+ ) = 0

(11.19)

we get the balance equation:

In the extended Tillmans diagram, SD is used as a generalized parameter of the equilibrium curves. In the medium pH range, SD becomes c(HCO−3 )−2 c(Ca2+ ), which is the curve parameter used in the conventional Tillmans diagram (Chapter 8, Section 8.2.2). Considering Equation (11.15) and the conditional solubility product of calcium carbonate (Ksp = c(Ca2+ ) c(CO2− 3 )), we can derive the following quadratic equation: c2 (DIC) ϕ + (∆ − SD) c(DIC) − 2 Ksp [

c2 (H+ ) c(H+ ) + + 1] = 0 K a1 K a2 K a2

(11.20)

Combining Equations (11.12) and (11.17) gives: p=

ϕ−1 ∆ m+ ϕ ϕ

(11.21)

Since both ϕ and ∆ are functions of pH, Equation (11.21) represents the linear relationship between p and m at constant pH. Equation (11.20) can be solved for given values of pH and SD to find the respective DIC concentration in the state of the calco–carbonic equilibrium. The required values of ϕ and ∆ are available from the definition equations (Equations (11.13) and (11.16)) and the corresponding m and p values can be found from Equations (11.12) and (11.17). Repeating the calculation with other pH values gives the data needed to draw the equilibrium curve for a constant SD in the generalized form −p = f(m). The lines of constant pH can be derived from Equation (11.21) and the definition equations for ϕ and ∆. Figure 11.2 shows an extended Tillmans diagram. In the upper right quadrant, the pH is in the medium range and therefore −p equals c(CO2 ) and m equals c(HCO−3 ) as shown in Table 11.3. This quadrant is therefore identical with the conventional Tillmans diagram shown in Chapter 8, Section 8.2.2 (Figure 8.1). The upper left and the lower right quadrants show the situation at very low and very high pH values, respectively. Furthermore, it follows from Equation (11.12) that hydrochemical states with m < p are not possible, because otherwise we would get negative DIC concentrations. Therefore, all possible water compositions must be located in the diagram above the line m = p. The inserted arrows in Figure 11.2 show the directions in which the composition can change if the pH and the carbonic acid species concentrations vary as a result of ion exchange processes. The specific effects in different applications are shown in the respective sections. Note that all Tillmans curves shown in this chapter were calculated for 10 °C and an ionic strength of 10 mmol/L.

11.4 Practical applications of ion exchange resins

|

211

Fig. 11.2: Extended Tillmans diagram. The inserted arrows indicate possible changes in the water composition as a result of ion exchange processes.

11.4 Practical applications of ion exchange resins 11.4.1 General considerations Ion exchange is one of the most appropriate technologies for the removal of dissolved inorganic ions. The possibility to regenerate the resin after the exhaustion of the uptake capacity is an important advantage of this technology. On the other hand, in most ion exchange processes the regeneration leads to the formation of highly concentrated salt solutions, which requires an appropriate waste disposal. The demand for regeneration chemicals and the need to dispose of regeneration wastes results in relatively high operation costs. However, the application of membrane processes as an alternative method for ion removal also leads to concentrated solutions and is faced with further problems such as scaling and fouling. In principle, ion exchange can be carried out in batch, fixed-bed, and fluidizedbed reactors. In most cases, fixed-bed reactors are used. During the loading of the ion exchange resin with the target ion, a mass transfer zone (MTZ) is formed that travels through the reactor. The length of the mass transfer zone depends on the kinetics of the uptake process. If the MTZ reaches the end of the fixed bed, the outlet concentration of the target ion increases until the total exchange capacity is exhausted and the outlet concentration equals the inlet concentration (Figure 11.3). It has to be noted that the process characteristics of fixed-bed ion exchange is comparable to that of fixed-bed adsorption. Therefore, Chapter 12 should be consulted for additional details on MTZ traveling and breakthrough curve (BTC) development.

212 | 11 Ion exchange

c0

c0

c0

c0

c0

c0

c

c

c0

MTZ

c

c

c

c

c Saturation time

1 Real BTC

c/c0 Real breakthrough time

Time

Ideal BTC tb

tbid

Ideal breakthrough time Fig. 11.3: Traveling of the mass transfer zone and development of the breakthrough curve (BTC) for a single ion.

If the capacity of the resin is exhausted, the process has to be stopped and the exchanger material has to be regenerated. During the regeneration, the original loading form is restored. The regenerant solution is typically fed into the reactor from the opposite direction (countercurrent regeneration, Figure 11.4). To ensure a continuous treatment process, multiple reactor systems have to be used. The knowledge of the breakthrough behavior is the basis for the reactor design. A simplifying approach can be derived by assuming a very fast uptake (instantaneous establishment of the equilibrium). In this case, the length of the MTZ reduces to zero and the real S-shaped breakthrough curve is transformed into a concentration step (ideal breakthrough curve, Figure 11.3). The related ideal breakthrough time, tid b , can be calculated on the basis of a material balance only: tid b =

q0 mie q0 V R ρ B + tr = + tr ̇ c0 V c0 V̇

(11.22)

where q0 is the ion exchanger capacity in equilibrium with c0 , mie is the ion exchanger mass, c0 is the inlet concentration, V̇ is the volumetric flow rate, t r is the residence time, V R is the ion exchanger bed volume, and ρ B is the bed density.

11.4 Practical applications of ion exchange resins

| 213

Raw water

Resin bed

Wastewater

Regenerant solution, backwash water

Treated water

Fig. 11.4: Simplified scheme of a fixed-bed ion exchange process in the loading (left) and regeneration (right) phase.

More sophisticated breakthrough curve models consider the mass transfer processes and are able to predict real S-shaped breakthrough curves. These model approaches are comparable to the models used for adsorption processes (Chapter 12). If more than one single ion is able to bind to the exchanger, the ions compete for the available binding sites. In a fixed-bed reactor, each ion forms its individual mass transfer zone that travels with its specific velocity through the resin bed. The velocities of the mass transfer zones of the different ions depend on their bond strength. The higher the affinity of a considered ion to the exchanger, the slower the travel velocity of its mass transfer zone. The differences in the MTZ travel velocities of the ions lead to displacement effects. If we consider a two-component system as an example, we can observe the following situation: the less preferred ion travels faster through the ion exchanger bed and is bound in a considered layer without any competition at first. Later, if the slower traveling (preferred bound) ion reaches the same bed layer, the first ion is partially displaced by the second ion according to the different bond strengths. This displacement effect leads to a characteristic breakthrough behavior with a concentration overshoot, as shown in Figure 11.5. Modeling of such breakthrough curves is rather complicated and will not be further considered here. The capacity of ion exchangers is commonly given as ion equivalents that can be bound, either related to the mass or to the bed volume of the exchanger material. Typically, the manufacturers give the capacities related to the bed volume and for a given loading form, for instance H+ or Na+ form for cation exchangers and free base form or Cl− form for anion exchangers. Typical values of the total capacity of cation exchangers are 2 equivalents/L for strong acid ion exchange resins and 4 equivalents/L for weak acid ion exchange resins. The total capacities of strong base and weak base ion

214 | 11 Ion exchange

Fig. 11.5: Breakthrough behavior of a two-component system.

exchange resins are in the range of 1 to 1.5 equivalents/L. In particular when considering the process design, the usable capacity (operating capacity) is more important than the total capacity (equilibrium capacity). The maximum operating capacity is the capacity that can be exploited until the breakthrough occurs (breakthrough capacity). The operating capacity depends on the mass transfer rate, which is particularly determined by the concentration and the type of the ions to be removed, the temperature, the porosity and particle size of the resin beads, the filter velocity, and the contact time in the exchanger bed (= bed height divided by the interstitial flow velocity). The faster the mass transfer is the smaller the mass transfer zone and the higher the percentage of the operating capacity related to the equilibrium capacity. Furthermore, it has to be taken into account that an incomplete regeneration further decreases the operating capacity in the subsequent loading cycles. This additional factor is particularly relevant for strongly acidic and strongly basic exchangers that are difficult to regenerate.

11.4.2 Softening and dealkalization Softening and dealkalization are processes that are frequently used in drinking water treatment. Besides other techniques, ion exchange processes can be used to remove calcium and magnesium (softening) as well as hydrogencarbonate (dealkalization) from the water. For more details about softening and dealkalization (definitions, other treatment technologies) see Chapter 9. Strong acid cation (SAC) exchange resins originally loaded with sodium ions are able to remove the hardness-causing ions calcium and magnesium from water without any effect on the hydrogencarbonate concentration (softening without dealkalization). Because of the preferential binding of bivalent ions, calcium and magnesium

11.4 Practical applications of ion exchange resins

| 215

ions are removed very efficiently by this ion exchange process. The reaction can be described as: R–SO−3 Na+ + (Ca2+ , Mg2+ ) 󴀕󴀬 R–SO−3 (Ca2+ , Mg2+ ) + Na+

(11.23)

Here and in the following text, a simplified writing of the reaction equations is used, where all relevant water constituents involved in the exchange reaction are written in brackets without considering their stoichiometric factors. The carbonic acid system (CO2 , HCO−3 , CO2− 3 ) is not influenced by this process. However, due to the removal of calcium, the water becomes more undersaturated with respect to calcium carbonate or – in other words – more calcite-dissolving. The reason for that is that the affiliated equilibrium curve of the calco–carbonic equilibrium is shifted to the right due to the reduced Ca2+ concentration (Figure 11.6). Note that m – 2c(Ca2+ ) is the curve parameter of the Tillmans curve (Section 11.3). Furthermore, the sodium concentration in the treated water increases. According to the equivalence condition, 2 mmol Na+ (46 mg) are released from the resin per mmol Ca2+ (or Mg2+ ) that is bound.

Fig. 11.6: Change of the calcite saturation state during softening with a strong acid cation (SAC) exchange resin in the Na+ form. R = raw water, P = product water.

The regeneration of the loaded resin is carried out with a sodium chloride solution. To displace the strongly bound alkaline earth ions from the resin a relatively high concentration of the regenerant solution (about 10 %) is necessary. Nevertheless, the regeneration is often incomplete. If softening should be coupled with dealkalization, the application of weak acid cation (WAC) exchange resins is an appropriate option. This process can be written in

216 | 11 Ion exchange

a simplified manner as: R–COOH + (Ca2+ , Mg2+ , HCO−3 ) 󴀕󴀬 R–COO− (Ca2+ , Mg2+ ) + CO2 + H2 O

(11.24)

Due to the reaction of the hydrogencarbonate ions with the protons of the functional group of the resin (Equation (11.5)), negatively charged binding sites are formed where cations can be bound. According to the selectivity sequence given in Section 11.2, the bivalent cations (Ca2+ , Mg2+ ) have a higher affinity to the exchanger than the univalent ions and are bound preferentially. The reaction with hydrogencarbonate is the precondition for the formation of negative sites on the weakly acidic resin, because the intrinsic dissociation of the functional groups at medium pH values is very low. Accordingly, at maximum the carbonate hardness (part of the calcium and magnesium concentration that is equivalent to hydrogencarbonate) can be removed. If all hydrogencarbonate is transformed into CO2 , no more negative binding sites are formed. As a consequence of the transformation of hydrogencarbonate to carbon dioxide, the pH decreases. The process stops at pH ≈ 4.2, where the hydrogencarbonate is nearly totally transformed into CO2 and the carboxylic acid groups show no intrinsic dissociation. The application of this process requires subsequent removal of the formed CO2 , which simultaneously increases the pH again (deacidification, Chapter 8). The regeneration can be carried out by strong or weak acids. Due to the strong affinity of the weakly acidic functional group to protons, excess amounts and high concentrations of the acids are not necessary. If the hydrogencarbonate concentration in the raw water exceeds the sum of the equivalent concentrations of Ca2+ and Mg2+ (see for instance case B in Figure 9.1, Chapter 9), more negative sites are formed by the reaction of the functional groups with hydrogencarbonate than necessary for the removal of Ca2+ and Mg2+ . In this special case, also univalent ions (Na+ , K+ ) are removed. Since removal of univalent ions is normally not necessary in drinking water treatment, this ion exchange process is not appropriate for such types of water. Since a complete removal of calcium, magnesium, and hydrogencarbonate is not wanted in drinking water treatment, an incomplete treatment or a split-stream treatment followed by blending of treated with untreated water are used in practice. Figure 11.7 shows exemplarily the change of the chemical state of the water as a result of softening/dealkalization with a weak acid cation exchange resin. If carbonate and noncarbonate hardness are to be removed, a two-stage process can be used. In the first stage, a weak acid cation exchanger is applied, which removes the carbonate hardness, whereas in the second stage a strong acid cation exchanger removes more Ca2+ and Mg2+ ions. Process schemes of softening with a strong acid cation exchanger in Na+ form and softening/dealkalization with a combination of a weak acid cation exchanger in H+ form and a strong acid cation exchanger in Na+ form are shown in Figure 11.8. Especially for the requirements of drinking water treatment, the CARIX process was developed. The CARIX process allows not only softening and dealkalization but

11.4 Practical applications of ion exchange resins

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Fig. 11.7: Change of the chemical state of the water during softening/dealkalization with a weak acid cation (WAC) exchange resin under the assumption of a complete transformation of hydrogencarbonate (m → 0). R = raw water, P = product water.

Strong acid cation (SAC) exchanger

Weak acid cation (WAC) exchanger

Strong acid cation (SAC) exchanger

Aerator CO2

R-SO3Na

R-COOH

R-SO3Na

Air

Softening Ca2+ , Mg2+ , Na+

(a)

Partial softening & dealkalization Ca2+ , Mg2+ , HCO3- CO2

(b)

Softening

Degassing

Ca2+ , Mg2+ , Na+

CO2

Fig. 11.8: Process schemes of softening and dealkalization by ion exchange: (a) softening with a strong acid cation exchanger in Na+ form; (b) softening and dealkalization with a combination of a weak acid cation exchanger in H+ form and a strong acid cation exchanger in Na+ form.

218 | 11 Ion exchange

also a partial demineralization. It is based on the combined application of a weakly acidic and a strongly basic resin, the latter initially loaded with HCO−3 . Both resins are applied in a single filter in the form of a mixed bed. The name of the process refers to the regeneration of the resins with dissolved CO2 (CARIX = carbonic acid regenerated ion exchanger). This process can be represented in a very simplified manner by: R–COO− (Ca2+ )

R–COOH + (Ca2+ , HCO−3 , SO2− 4 ) 󴀕󴀬 R–NR+3

HCO−3

+ CO2(aq) + H2 O R–NR+3

(11.25)

(SO2− 4 )

Here, Ca2+ stands as an example for the hardness-causing ions, HCO−3 stands for the alkalinity, and SO2− 4 stands as an example for the other anions in the water. The single processes, which in practice proceed in parallel, can be described as follows. First, sulfate displaces hydrogencarbonate from the strong base anion exchange resin. Then, the released hydrogencarbonate reacts with the protons of the weakly acidic carboxyl group of the cation exchange resin to form negative binding sites (Equation (11.5)), where the bivalent ions can be bound. Typically, the capacity of the cation exchanger in the CARIX process is greater than that of the anion exchanger, which allows the protons of the cation exchanger to react not only with the hydrogencarbonate released from the anion exchanger but also with the pristine hydrogencarbonate. The resin mixed bed is regenerated by carbon dioxide. Carbon dioxide dissociates in water into protons and hydrogencarbonate ions. The protons regenerate the acidic resin and the hydrogencarbonate ions regenerate the basic resin. Since the regeneration efficiency of carbon dioxide is limited, the exchange on both resins remains incomplete. This incomplete exchange makes the CARIX process particularly appropriate for drinking water treatment, where only partial softening, partial dealkalization and partial demineralization are necessary. Due to the incomplete exchange, there is typically no need to blend the treated water with untreated raw water. However, a removal of CO2 (deacidification, Chapter 8) is necessary to increase the pH and bring the water into the state of calco–carbonic equilibrium. The change of the chemical state of the water during the CARIX process is shown in Figure 11.9. For reasons of clarity, operating lines for the single reaction steps are shown in the diagram, although in practice the processes run in parallel. Operating lines 1 and 3 show the transformation of hydrogencarbonate (pristine and released from the SBA exchanger) to CO2 by the protons from the WAC exchanger (decrease of m and increase of −p). Operating line 2 demonstrates the displacement of hydrogencarbonate from the SBA exchanger by other anions, in particular sulfate (increase of m at constant −p). It has to be noted that the real operating lines are slightly shorter than the hypothetical operating lines due to the incomplete exchange processes. Table 11.4 summarizes the different variants of softening and dealkalization.

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Fig. 11.9: Hypothetical (dashed lines) and practical (full lines) change of the chemical state of the water during the CARIX process. R = raw water, P = product water, P∗ = hypothetical product water. Tab. 11.4: Softening and dealkalization by ion exchange resins. Variant Cation exchange Anion exchange resin Features resin 1

Strongly acidic

–

Softening, removal of Ca2+ and Mg2+

2

Weakly acidic

–

Softening with dealkalization, removal of carbonate hardness (Ca2+ /Mg2+ and equivalent amounts of HCO−3 )

3

Weakly acidic and strongly acidic

–

Two-stage ion exchange, combination of variants 1 and 2, removal of carbonate and noncarbonate hardness

4

Weakly acidic

Strongly basic

Mixed-bed ion exchange, softening, dealkalization, partial demineralization

11.4.3 Demineralization Demineralization (deionization, desalination) with ion exchangers can be carried out in different ways. In all cases, a cation exchanger has to be combined with an anion exchanger. Possible variants are listed in Table 11.5. The variants 1 and 2 with complete demineralization are frequently used to produce pure water for industrial purposes. In drinking water treatment, where a complete demineralization is not wanted, the salt concentration can be reduced by a split-stream treatment with blending of the treated water with untreated water or by variant 3.

220 | 11 Ion exchange

Tab. 11.5: Demineralization by ion exchange processes. Variant Cation exchange Anion exchange resin resin

Features

1

Strongly acidic

Strongly basic

Complete demineralization, removal of CO2

2

Strongly acidic

Weakly basic

Complete demineralization, no removal of CO2

3

Weakly acidic

Strongly basic (weakly basic)

Partial demineralization

A widely used variant of demineralization is based on the combination of a strong acid cation exchanger in the H+ form and a strong base anion exchanger in the OH− form in a two-stage process. In the first stage, the protons originally bound to the cation exchanger are exchanged by other cations: − − − R–SO−3 H+ + (Ca2+ , Mg2+ , Na+ , SO2− 4 , Cl , NO3 , HCO3 ) 󴀕󴀬 − − R–SO−3 (Ca2+ , Mg2+ , Na+ ) + (H+ , SO2− 4 , Cl , NO3 , CO2(aq) )

(11.26)

The released protons transform hydrogencarbonate to carbon dioxide: HCO−3 + H+ 󴀕󴀬 CO2(aq) + H2 O

(11.27)

The effluent is a strongly acidic solution (mixture of mineral acids). As long as no CO2 is degassed, c(DIC) remains constant. The operating line in the Tillmans diagram has the slope -1 and ends at a negative m value (note that m ≈ −c(H+ ) at low pH, Table 11.3). In the second stage, the acidic effluent of the first exchanger is fed into the strong base anion exchange resin column, where the OH− ions of the exchanger are replaced by the anions from the acidic solution: − − R–N(CH3 )+3 OH− + (H+ , SO2− 4 , NO3 , Cl , CO2(aq) ) 󴀕󴀬 − − − R–N(CH3 )+3 (SO2− 4 , NO3 , Cl , HCO3 ) + H2 O

(11.28)

The released OH− ions transform CO2(aq) back to HCO−3 that is also bound to the anion exchanger: CO2(aq) + OH− 󴀕󴀬 HCO−3 (11.29) The hydroxide ions released from the anion exchanger neutralize the protons released from the cation exchanger. Accordingly, the only product of the process is water. The neutralization increases the m value from the negative range to 0. Simultaneously, the removal of CO2 decreases the −p alkalinity to 0. Since the formed hydrogencarbonate is bound to the anion exchanger, the m value does not further increase. Accordingly, the process ends in the origin of the Tillmans diagram with p = 0 and m = 0 (Figure 11.10), which is the state of pure water. The amount of OH− needed to transform CO2 and therefore also the required amount of the strong base anion exchanger can be reduced by an intermediate degassing of CO2 .

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Fig. 11.10: Change of the chemical state of water during demineralization by ion exchange. R = raw water, P1 and P2 = product waters of the different process variants.

The regeneration of the cation exchange resin is carried out with acids (HCl, H2 SO4 ). If H2 SO4 is used, attention has to be paid to the possible precipitation of CaSO4 . The strong base anion exchange resin is regenerated with NaOH. Due to the low affinity of the resins for H+ and OH− , concentrated regenerant solutions of high purity have to be used. Instead of the strong base anion exchanger also a weak base anion exchanger can be used together with the strong acid cation exchanger. The first stage is the same as given above (Equation (11.26)). The ion exchange process on the anion exchanger can be described by: − − R–NR2 + (H+ , SO2− 4 , Cl , NO3 , CO2(aq) ) 󴀕󴀬 − − R–NR2 H+ (SO2− 4 , NO3 , Cl ) + CO2(aq)

(11.30)

The protons of the acidic effluent of the cation exchanger protonate the weakly basic groups of the anion exchanger allowing them to bind the anions from the cation exchanger effluent. In contrast to the application of the strong base anion exchanger, a transformation of CO2 according to Equation (11.29) does not occur. Therefore, the carbon dioxide is not removed in this process. The process ends at m = 0 and −p > 0 (Figure 11.10). If necessary, the carbon dioxide has to be removed subsequently by stripping or other deacidification processes (Chapter 8). The regeneration of the weak base exchange resin can be carried out with alkaline solutions, such as NaOH or aqueous solutions of NH3 . Due to the weakly basic character of the functional groups, they are easy to deprotonate and the regenerant solution does not need to be highly concentrated or extremely pure.

222 | 11 Ion exchange

A third variant consists of an application of a weak acid cation exchanger as the first stage instead of a strong acid exchanger resin: − − − R–COOH + (Ca2+ , Mg2+ , Na+ , SO2− 4 , Cl , NO3 , HCO3 ) 󴀕󴀬 − − R–COO− (Ca2+ , Mg2+ ) + (Na+ , SO2− 4 , Cl , NO3 , CO2(aq) )

Strong acid cation (SAC) exchanger

Aerator

(11.31)

Strong base anion (SBA) exchanger

CO2

R-SO3H

R-NR3OH

Air Demineralization with intermediate degassing Ca2+↓, Mg2+ ↓, Na+ ↓ K+ ↓, HCO3- ↓ CO2↑, H+↑ (a) Strong acid cation (SAC) exchanger

CO2↓

Weak base anion (WBA) exchanger

-

SO42 ↓, Cl-↓, NO3-↓, HCO3-↓

Aerator

CO2

R-SO3H

R-NR2

Air Demineralization Ca2+↓, Mg2+↓, Na+↓ K+↓, HCO3-↓ CO2↑, H+↑

SO42-↓, Cl-↓, NO3-↓

Degassing CO2↓

(b) Fig. 11.11: Process schemes of demineralization processes: (a) demineralization with a strong acid and a strong base ion exchange resin and intermediate degassing of CO2 ; (b) demineralization with a strong acid and a weak base ion exchange resin and subsequent degassing of CO2 .

11.4 Practical applications of ion exchange resins

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223

Due to the reaction of the protons of the weakly acidic groups with the hydrogencarbonate of the water, negative binding sites are formed that are able to bind the cations. It follows from this mechanism that a complete demineralization would only be possible if the equivalent concentration of the hydrogencarbonate ions equals the sum of the equivalent concentrations of all cations. Only under this condition will enough negative binding sites for all cations be formed. Since this condition is not fulfilled in practice, only a partial demineralization is possible. However, this may be a sufficient result, in particular in drinking water treatment. Sometimes, a combination with a strong acid cation exchanger may be appropriate. The regeneration of the weak acid cation exchanger is very easy due to the high affinity of the weakly acidic carboxylic acid groups to protons. The concentration and purity of the regenerant acids must not be very high. Furthermore, not only strong but also weak acids can be used for regeneration. As a second stage, a strong base anion exchange resin can be applied. Since the pH of the cation exchange resin effluent is relatively low (Figure 11.10), a weak base anion exchanger can also be used if its pK ∗a is higher than the pH (dominance of the protonated forms of the functional groups). The regeneration of the anion exchange resins can be done as described above. Figure 11.11 shows two common technological variants of the demineralization process.

11.4.4 Removal of nitrate Strong base anion exchangers in the Cl− form are able to remove unwanted anions such as sulfate and nitrate. Sulfate and nitrate have a higher affinity to the exchanger than chloride and are therefore preferentially bound (Table 11.2). Although the selectivity for chloride is higher than that for hydrogencarbonate, small amounts of HCO−3 can also be bound. The respective reaction equation reads: − − + 2− − − − R–N(CH3 )+3 Cl− + (SO2− 4 , NO3 , HCO3 ) 󴀕󴀬 R–N(CH3 )3 (SO4 , NO3 , HCO3 ) + Cl (11.32)

In this process, the different anions compete for the positive binding sites of the functional groups, which results in a complex process characterized by different mass transfer zones in the resin bed. The mass transfer zones of the different ions travel through the exchanger bed with velocities that are determined by the bond strength of the ions (Section 11.4.1). The stronger the ion is bound to the resin, the slower is the traveling velocity of its mass transfer zone. During the travel through the resin bed, the stronger bound (slower traveling) ions displace the weaker bound ions. The displacement effects lead to concentration overshoots for the weaker bound ions. As a result, the effluent shows a high variability in composition (Figure 11.12). In raw waters used for drinking water production, typically the nitrate concentration is more problematic than the concentration of sulfate due to the health impli-

224 | 11 Ion exchange

Fig. 11.12: Breakthrough curves of the anions sulfate, nitrate, and hydrogencarbonate as can be found for a conventional strong base anion exchanger.

cations of nitrate and its transformation product nitrite (Section 1.2.5). Therefore, the selective removal of nitrate is the main objective in most cases. However, according to the selectivity sequence (Table 11.2), the bivalent ion sulfate is preferentially bound to the anion exchanger. To solve this problem, specific nitrate-selective ion exchange resins were developed. These resins contain modified functional groups with larger alkyl groups (ethyl or butyl groups) instead of the methyl groups in the conventional type 1 strong base anion exchangers. The larger alkyl groups make it more difficult for sulfate ions to attach to the resin (steric hindrance) and allow for binding of higher amounts of the smaller nitrate ions. The regeneration of the loaded strong base anion exchanger can be carried out by a sodium chloride solution (typical concentration: 4–8%). Due to the low affinity of the resin to chloride, excess amounts in comparison to the stoichiometric quantity are necessary.

11.4.5 Removal of humic substances The removal of humic substances by ion exchangers is an adsorption process rather than a pure ion exchange process. Strongly or weakly basic anion exchange resins, in particular macroporous resins, are able to adsorb humic and fulvic acids. This specific application of ion exchange is of minor relevance for drinking water treatment since alternative technologies for the removal of natural organic matter are available. However, this process is frequently used in the treatment of boiler feed water for power plants.

11.4 Practical applications of ion exchange resins

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225

11.4.6 Removal of heavy metals Heavy metal cations can be efficiently removed from water by using chelate-forming ion exchangers. As already mentioned in Section 11.1, these ion exchangers contain iminodiacetate groups, –N(CH2 COO− )2 , which are able to form chelate complexes with cations. In drinking water treatment, the chelate-forming ion exchange resins are applied in the Ca2+ form. Due to the higher affinity of the chelate-forming functional groups to heavy metal ions (d element ions), the Ca2+ ions can be easily replaced by the heavy metal ions. The respective reaction equation for the uptake of a bivalent heavy metal cation, Me2+ , is: R–N(CH2 COO− )2 Ca2+ + Me2+ 󴀕󴀬 R–N(CH2 COO− )2 Me2+ + Ca2+

(11.33)

The strong complex formation with heavy metal ions requires two-stage regeneration. At first, the anionic functional groups are transformed into their neutral forms by means of a strong acid (e.g., HCl) according to: R–N(CH2 COO− )2 Me2+ + 2 H+ + 2 Cl− 󴀕󴀬 R–N(CH2 COOH)2 + Me2+ + 2 Cl−

(11.34)

In the second stage, in the absence of competing heavy metal ions, the calcium form is reestablished by adding a calcium hydroxide solution: R–N(CH2 COOH)2 + Ca2+ + 2 OH− 󴀕󴀬 R–N(CH2 COO− )2 Ca2+ + 2 H2 O

(11.35)

Alternatively, weak base anion exchangers can be used to remove heavy metal cations. Here, the Lewis base property of the amino groups is utilized. Lewis bases have lone electron pairs and are able to interact with reaction partners that are able to accept electrons (Lewis acids). The Lewis base property of the amino group results from the existence of a lone electron pair at the nitrogen atom. In contrast to alkaline and alkaline earth ions, the Lewis acid property of heavy metal ions is much more pronounced. Accordingly, they can be bound to amino groups with high selectivity. To maintain electroneutrality in the aqueous phase, an equivalent number of anions (e.g., of sulfate) are bound to the exchanger. The reaction can be described as follows: 2+ 2− R–NR2 + Me2+ + SO2− 4 󴀕󴀬 R–NR2 (Me , SO4 )

(11.36)

The regeneration is carried out in a two-stage process by using sulfuric acid and sodium hydroxide to transform the functional groups back to the free base form. Due to the formation of the protonated form within the first stage, the functional groups lose their Lewis base property and the bound heavy metal ions are released, whereas the remaining sulfate ions are transformed to hydrogensulfate ions that are bound to the protonated (positively charged) functional groups: + 2− + − 2+ R–NR2 (Me2+ , SO2− + SO2− 4 4 ) + 2 H + SO4 󴀕󴀬 R–NR2 H HSO4 + Me

(11.37)

In the second stage, the protonated functional groups are transformed into the neutral form by the base NaOH and the hydrogensulfate anions are released as sulfate: R–NR2 H+ HSO−4 + 2 Na+ + 2 OH− 󴀕󴀬 R–NR2 + 2 H2 O + 2 Na+ + SO2− 4

(11.38)

12 Adsorption 12.1 Introduction Adsorption of solutes onto solid surfaces (Figure 12.1) is frequently used in drinking water treatment to remove unwanted dissolved compounds. Porous materials with large inner surfaces (high number of adsorption sites) are used as adsorbents. The most important adsorbent for water treatment is activated carbon. Activated carbon is able to remove organic micropollutants (mainly from anthropogenic sources) as well as natural organic matter (NOM) from the water. NOM is unwanted in water, in particular due to its capability to form halogenated disinfection byproducts (e.g., trihalomethanes) during water disinfection with chlorine (Chapter 14). Since NOM (measured as dissolved organic carbon, DOC) is present in all raw waters and often not totally removed by upstream processes, it competes with the organic micropollutants for the available adsorption sites on the activated carbon. This competition effect is often relatively strong, not least because of the different concentration levels of DOC and micropollutants. The typical DOC concentrations in raw waters are in the lower mg/L range, whereas the concentrations of organic micropollutants are typically in the ng/L or μg/L range. Desorption Liquid phase

Surface

Adsorbate Adsorption

Solid phase

Adsorbed phase Adsorbent

Fig. 12.1: Basic terms of adsorption.

Activated carbon is applied either as powdered activated carbon (PAC) or as granular activated carbon (GAC). The particle sizes of powdered activated carbons are in the medium micrometer range, whereas the GAC particles have diameters in the lower millimeter range. Depending on the particle size, different reactor types are in use: batch reactors or flow-through reactors for PAC suspensions and fixed-bed adsorbers for GAC. The application of PAC requires an additional treatment step (sand filtration, membrane filtration) to remove the loaded activated carbon particles from the water. Since the fine PAC particles are difficult to reactivate, PAC is typically used as a one-way adsorbent and has to be disposed of by incineration or in landfill sites after application.

https://doi.org/10.1515/9783110551556-012

228 | 12 Adsorption

The adsorption in fixed-bed adsorbers filled with GAC is a semicontinuous process. If the adsorption capacity of the GAC is exhausted, the carbon has to be removed from the fixed-bed adsorber and replaced by fresh or reactivated activated carbon. To allow a continuous water treatment, multiple adsorber systems are necessary. The reactivation of GAC can be carried out by a thermal process under conditions similar to those in GAC production by gas activation (Section 12.2.1). Both technical variants (PAC and GAC adsorption) have advantages and disadvantages that will be discussed in more detail in Section 12.4.3. Although activated carbon is the most widely used adsorbent in water treatment, other adsorbents may be more suitable for specific applications. In particular, if ionic species (e.g., arsenate) are to be removed, oxidic adsorbents with pH-dependent surface charges (e.g., granular ferric hydroxide, aluminum oxide) are better suited as adsorbents than activated carbon, which is not very efficient in the removal of ions. Because of the lower relevance of ion adsorption in water treatment, the following discussion will be restricted to activated carbon adsorption.

12.2 Activated carbons 12.2.1 Production Activated carbons are highly porous adsorbents. They can be produced from different carbon-containing raw materials and by different activation processes. The most common raw materials are wood, wood charcoal, peat, lignite and lignite coke, hard coal and coke, bituminous coal, and petrol coke, as well as residual materials such as coconut shells, sawdust, or plastic residuals. For organic raw materials like wood, sawdust, peat, or coconut shells, a preliminary carbonization process is necessary to transform the original cellulose structures into a carbonaceous material. This can be done by means of dehydrating chemicals. The dehydration is typically carried out at elevated temperatures under pyrolytic conditions and leads to destruction of the cellulose structures with the result that the carbon skeleton is left. This process, also referred to as chemical activation, combines carbonization and activation (pore formation) processes. Typical dehydrating chemicals are zinc chloride and phosphoric acid. Remaining residuals of the chemicals in the final product may be critical in view of the application in drinking water treatment. Most of the activated carbons used in drinking water treatment are therefore produced by an alternative process termed gas activation. In gas activation, carbonized materials such as coals or cokes are used as raw materials. These carbon-rich materials already have a minor porosity. For activation, the raw material is brought in contact with an activation gas (steam, carbon dioxide, air) at elevated temperatures (800–1 000 °C). During activation, the activation gas reacts

12.2 Activated carbons

| 229

with the solid carbon material to form gaseous products (CO, CO2 ). In this manner closed pores are opened and existing pores are enlarged. Activated carbons show a broad variety of internal surface areas ranging from some hundreds m2 /g to more than a thousand m2 /g depending on the raw material and the activation process used. Activated carbons for water treatment should not have pores that are too fine so that larger molecules are also allowed to enter the pore system and to adsorb onto the adsorption sites on the inner surface. Internal surface areas of activated carbons applied for water treatment are typically in the range of 800–1 000 m2 /g. As a result of the activation process, different oxygen-containing functional groups exist at the carbon surface (e.g., carboxyl groups, carboxylic anhydrides, lactone and lactole groups, phenolic hydroxyl groups, pyron-type groups).

12.2.2 Adsorption properties Activated carbons are able to adsorb many organic substances, mainly by weak intermolecular interactions (van der Waals forces), in particular by London dispersion forces. These attraction forces may be superimposed by π–π interactions in the case of aromatic adsorbates (interactions between the π electron systems of the aromatic compounds and the π system of the activated carbons, which consist of irregularly oriented graphite microcrystallites). To a lesser extent, also electrostatic interactions between charged surface oxide groups and ionic adsorbates are possible. Some general trends in activated carbon adsorption are given below: – The adsorption increases with increasing internal surface (increasing micropore volume) of the adsorbent. – The adsorption increases with increasing molecule size of the adsorbates as long as no size exclusion hinders the adsorbate molecules from entering the pore system. – The adsorption decreases with increasing temperature because (physical) adsorption is an exothermic process. – The adsorbability of organic substances increases with decreasing polarity (solubility, hydrophilicity) of the adsorbate. – Aromatic compounds are better adsorbed than aliphatic compounds of comparable size. – Organic ions (e.g., phenolates or protonated amines) are not adsorbed as strongly as the corresponding neutral compounds (pH dependence of the adsorption of weak acids and bases). – In multicomponent systems, competitive adsorption takes place, resulting in a decreased adsorption of a considered compound in comparison with its singlesolute adsorption. – Inorganic ions (e.g., metal ions) can be adsorbed only to a lesser extent by interactions with the functional groups of the adsorbent surface.

230 | 12 Adsorption

12.3 Theoretical basics of the adsorption process 12.3.1 Adsorption equilibrium Adsorption equilibrium data of single adsorbates are typically reported as adsorption isotherms: qeq = f(ceq ) T = constant (12.1) where qeq is the adsorbed amount in the state of equilibrium (equilibrium adsorbent loading), ceq is the equilibrium concentration, and T is the temperature. The equilibrium data can be determined by using the bottle-point method and applying the material balance equation for a batch system: qeq =

VL (c0 − ceq ) mA

(12.2)

In this experimental method, each bottle is filled with the adsorbate solution of known volume, V L , and known initial concentration, c0 . After adding a defined adsorbent mass, m A , the solution is shaken or stirred until the state of equilibrium is reached (c = ceq = constant). To find different points of the isotherm, different initial concentrations have to be applied or different adsorbent masses have to be added to the bottles. The time required to reach the equilibrium state is typically between some hours and some weeks depending on the type and the particle size of the activated carbon. Generally, the larger the particle size is, the longer the required equilibration time is. For further application, the set of experimental isotherm data (qeq , ceq ) is typically described by an appropriate isotherm equation. The most frequently used isotherm equation for single-solute aqueous-phase adsorption onto activated carbon is the Freundlich isotherm: n qeq = K F ceq (12.3) where K F and n are the isotherm parameters. This equation is applied as an equilibrium relationship in most kinetic and breakthrough curve models (Sections 12.3.2 and 12.3.3). Moreover, the Freundlich isotherm is often used in prediction models for multisolute adsorption. The Freundlich isotherm can be linearized by transforming the equation into the logarithmic form: log qeq = log K F + n log ceq

(12.4)

The lower the n value, the more concave (with respect to the concentration axis) the isotherm shape. Freundlich isotherms with n < 1, showing relatively high adsorbent loadings at low concentrations, are referred to as favorable isotherms. As an example, linearized Freundlich isotherms of some selected adsorbates are shown in Figure 12.2. If a solution contains more than one adsorbable solute, the adsorbates compete for the available adsorption sites on the adsorbent surface. In this case, the adsorbed

12.3 Theoretical basics of the adsorption process

| 231

Fig. 12.2: Isotherms of selected adsorbates (activated carbon F300).

amount of a considered component depends not only on the concentration of this component but also on the concentrations of all other components. Since it is not possible to experimentally determine all dependences in such a complex system, it is necessary to resort to a prediction tool that allows precalculation of the competitive adsorption on the basis of easily accessible single-solute adsorption data. At present, the ideal adsorbed solution theory (IAST) is the most commonly used method to describe and predict multisolute adsorption. The IAST is a model that is derived from basic thermodynamic equations, in particular from the equations for the chemical potentials of the adsorbates in the liquid phase and in the two-dimensional adsorbed phase, and from the Gibbs fundamental equation (Myers & Praunitz, 1965; Radke & Prausnitz, 1972). The resulting set of equations has to be solved by an appropriate numerical method. The necessary input data for IAST predictions are the concentrations and the isotherm parameters of all components in the multisolute system. Given that the single-solute isotherms of the mixture components can be described by the Freundlich isotherm, the adsorbed amounts at given concentrations of the mixture components can be calculated by means of the following equations that are derived from the IAST: N

N

∑ zi = ∑ i=1

i=1

ci φ n i 1/n i ( ) K F,i

N

qtotal

zi = [∑ ] φ ni i=1

q i = z i qtotal

=1

(12.5)

−1

(12.6) (12.7)

232 | 12 Adsorption

where c i and q i are the concentration and adsorbed amount of the component i, n i and K i are the parameters of the single-solute isotherms of the component i, qtotal is the total adsorbed amount, and z i is the mole fraction of the component i in the adsorbed phase. φ is the spreading pressure term that is derived from the Gibbs fundamental equation. Despite its physical meaning, for practical applications it can simply be considered a calculation quantity. If that spreading pressure term is found that fulfils Equation (12.5), then the mole fractions z i are also fixed (see left-hand side of the equation). With φ and z i , the total adsorbed amount, qtotal , can be calculated from Equation (12.6). Finally, the partial adsorbent loadings of all components can be found from Equation (12.7). If activated carbon adsorption is applied in drinking water treatment, not only organic micropollutants are adsorbed but also natural organic matter (NOM), which occurs in all raw waters used for drinking water production. NOM (measured as dissolved organic carbon, DOC) is a multicomponent mixture with unknown composition and neither the concentrations nor the isotherm parameters of the NOM constituents are known. Therefore, the IAST cannot be applied in its original form to describe the NOM adsorption. To overcome this problem, a fictive component approach (so-called adsorption analysis) was developed. The basic principle of adsorption analysis consists of a formal transformation of the unknown multicomponent system NOM into a defined mixture of a limited number of fictive components. Each fictive component of this mixture system stands for a DOC fraction with a characteristic adsorbability (e.g., nonadsorbable, weakly adsorbable, strongly adsorbable). The fictive components (typically three to five) are defined by assigning characteristic Freundlich isotherm parameters. On the basis of a measured DOC isotherm (total mixture isotherm) and the fixed Freundlich isotherm parameters, an IAST based search routine is applied to find the concentration distribution of the fictive components that best describe the measured isotherm data. The concentrations found by this method and the related Freundlich isotherm parameters characterize the adsorption behavior of the NOM fractions and can be used for further modeling purposes (e.g., reactor design). Figure 12.3 shows the results of an adsorption analysis for a river water as an example. In this example, three fictive components are defined with Freundlich coefficients of 0 (mg/g)/(mg/L)n , 15 (mg/g)/(mg/L)n , and 50 (mg/g)/(mg/L)n . The Freundlich exponent, n, is assumed to be 0.2 for both adsorbable fractions. The adsorbable NOM fractions are strong competitors for the micropollutants (Figure 12.4). The simplest approach to describing the competitive adsorption of NOM and micropollutants would be to add the micropollutant (given that its concentration and isotherm parameters are known) as a further component to the NOM system (characterized by the adsorption analysis) and to apply the IAST to the combined NOMmicropollutant system. This approach, however, fails in many cases for different reasons (e.g., nonideal behavior, different accessibility to the micropores, pore blockage by NOM fractions, need to use mass concentrations for the DOC instead of the molar concentrations as required by the thermodynamic IAST). To overcome these problems,

12.3 Theoretical basics of the adsorption process

| 233

Fig. 12.3: Adsorption analysis of a river water with a total DOC concentration of 4.9 mg/L. The Freundlich coefficients are given in (mg/g)/(mg/L)n .

Fig. 12.4: Atrazine adsorption from pure water (single-solute adsorption) and adsorption in the presence of NOM (5.2 mg/L DOC). Competitive adsorption modeled by means of the tracer model (Worch, 2012).

specific model approaches, such as the tracer model (TRM) and the equivalent background compound model (EBCM) were developed. Both models are based on the IAST and require the measurement of a micropollutant isotherm in the presence of NOM. The tracer model uses the adsorption analysis to characterize the NOM background and compensates the deviations of the experimental

234 | 12 Adsorption

data from the IAST prediction by a correction of the micropollutant isotherm parameters. The modified isotherm parameters can be found from the micropollutant mixture isotherm by a fitting procedure. The equivalent background model (EBCM) defines only one competing compound (the equivalent background compound) that represents the NOM. The parameters of the equivalent background compound can be determined from the micropollutant mixture isotherm by an IAST based fitting procedure. Details of the complex multisolute adsorption modeling approaches can be found in respective monographs (e.g., Worch, 2012).

12.3.2 Adsorption kinetics Adsorption equilibria at the internal surface of porous adsorbents are not established instantaneously, because the mass transfer from the solution to the adsorption sites within the adsorbent particles is constrained by mass transfer resistances. The rate of adsorption is usually limited by the diffusion through a hydrodynamic boundary layer at the outer particle surface (external film diffusion) and the diffusion within the porous adsorbent particles (intraparticle diffusion). Since film diffusion and intraparticle diffusion act in series, the slower process determines the total adsorption rate. The mass transfer parameters, together with the equilibrium data, are essential input data for the determination of the required contact times in slurry adsorbers as well as for fixed-bed adsorber modeling. A fundamental difference between film and intraparticle diffusion consists of the dependence on the hydrodynamic conditions, in particular on the stirrer velocity in slurry reactors or on the flow velocity in fixed-bed adsorbers. An increase in the stirrer or flow velocity increases the rate of film diffusion due to the reduction of the boundary layer thickness. In contrast, the intraparticle diffusion is independent of the stirrer or flow velocity. The particle radius influences the film diffusion as well as the intraparticle diffusion due to the change of the total surface area available for mass transfer and the change of the diffusion path length. Generally, the diffusion processes become faster with decreasing particle size. For spherical particles, the rate of the film diffusion is given by: dq 3 kF (c − c s ) = dt rP ρP

(12.8)

where q is the mean adsorbent loading, c is the concentration in the bulk phase, c s is the equilibrium concentration at the external surface of the adsorbent particle, k F is the film mass transfer coefficient (m/s), r P is the particle radius, and ρ P is the particle density. In general, the mass transfer within the adsorbent particles takes place in parallel by pore diffusion (diffusion within the pore liquid) and surface diffusion (diffusion in the adsorbed state along the pore walls), but the portions of the different diffusion

12.3 Theoretical basics of the adsorption process

Solid-phase film

| 235

Boundary layer (film)

Adsorbent particle rP

Bulk solution

qs

q,c

c

q cs

rP r

Fig. 12.5: Concentration and adsorbent loading profiles according to the LDF model.

processes are difficult to separate. Therefore, often only a single intraparticle diffusion mechanism is assumed to be predominant and considered in the kinetic model. For most aqueous-phase adsorption processes on porous adsorbents, the intraparticle diffusion can be successfully described by a surface diffusion approach (homogeneous surface diffusion model, HSDM). The HSDM can be further simplified by using a linear driving force (LDF) equation to describe the internal diffusion within the pore system instead of the exact Fick’s law that is used in the HSDM. Using the LDF approach, the intraparticle mass transfer can be described by: dq = k ∗S (q s − q) dt

(12.9)

where q s is the adsorbent loading at the external adsorbent surface in equilibrium with c s and q is the mean adsorbent loading. k ∗S is the volumetric intraparticle mass transfer coefficient. It already includes the area available for the mass transfer and has the unit 1/s. With this simplifying approach for the intraparticle diffusion, the complete kinetic model obtains the character of a two-film model with one boundary film on the solution side and another that is assumed to be located in the solid particle. Figure 12.5 shows the respective concentration and adsorbent loading profiles according to the LDF model. To describe the adsorption kinetics mathematically, the kinetic equations have to be coupled with the equilibrium relationship (single-solute isotherm or multisolute prediction model, e.g., IAST) and the respective material balance equation for the re-

236 | 12 Adsorption

actor. In the case of multisolute adsorption, kinetic equations for all components have to be formulated.

12.3.3 Adsorption dynamics in fixed-bed adsorbers Adsorption in a fixed-bed adsorber is a time- and distance-dependent process. During the adsorption process, each adsorbent particle in the bed accumulates adsorbate from the percolating solution as long as the state of equilibrium is reached. This equilibration process proceeds successively, layer by layer, from the column inlet to the column outlet. However, due to the slow adsorption kinetics, there is no sharp boundary between loaded and unloaded adsorbent layers. Instead, the equilibration takes place in a more or less broad zone of the adsorbent bed, referred to as the mass transfer zone (MTZ). Accordingly, at a given time, a distinction can be made between three different zones within the adsorbent bed. In the first zone between the adsorber inlet and the MTZ, the adsorbent is already loaded with the adsorbate to the adsorbed amount, q0 , which is in equilibrium with the inlet concentration, c0 . The available adsorption capacity in this zone is exhausted, and no more mass transfer from the liquid phase to the adsorbent particles takes place. Therefore, the concentration in the liquid phase is constant and equals c0 . In the second zone (the MTZ), the mass transfer from the liquid phase to the solid phase takes place. Due to the mass transfer from the liquid to the solid phase, the concentration in this zone decreases from c = c0 to c = 0 and the adsorbed amount increases from q = 0 to q = q0 (c0 ). The shape and length of the mass transfer zone depend on the adsorption rate and the shape of the equilibrium curve. The adsorbent in the third zone is still free of adsorbate. The fluid-phase concentration in this zone is c = 0. During the adsorption process, the MTZ travels through the adsorber with a velocity that is much slower than the water velocity. The stronger the adsorption of the adsorbate, the greater the difference between the MTZ velocity and the water velocity. As long as the MTZ has not reached the adsorber outlet, the outlet concentration is c = 0. The adsorbate occurs in the adsorber outlet for the first time when the mass transfer zone reaches the end of the adsorbent bed. This time is referred to as the breakthrough time. After the breakthrough time, the concentration in the adsorber outlet increases due to the progress of adsorption in the MTZ and the related decrease of the remaining adsorbent capacity. If the entire MTZ has left the adsorber, the outlet concentration equals c0 . At this point, all adsorbent particles in the adsorbent bed are saturated to the equilibrium adsorbent loading and no more adsorbate uptake takes place. The corresponding time is referred to as the saturation time. The concentration versus time curve, which is measurable at the adsorber outlet, is referred to as the breakthrough curve (BTC). The BTC is a mirror of the mass transfer zone and is therefore affected by the same factors as the MTZ, in particular adsorp-

12.3 Theoretical basics of the adsorption process

c0

c0

c0

c0

c

c

c

c

c0

c0

c

c

| 237

c0

MTZ

c Saturation time

1 Real BTC

c/c0 Real breakthrough time

Time

Ideal BTC tb

tbid

Ideal breakthrough time

Fig. 12.6: Traveling of the mass transfer zone (MTZ) through the adsorber and development of the breakthrough curve (BTC).

tion rate and shape of the equilibrium curve. The position of the BTC on the time axis depends on the traveling velocity of the MTZ, which in turn depends on the flow velocity and the strength of adsorption. For a given flow velocity it holds that the more adsorbable the solute is, the later the breakthrough occurs. The relation between the traveling of the MTZ and the development of the BTC is schematically shown in Figure 12.6. The spread of the MTZ is mainly determined by the mass transfer resistances. In the limiting case of infinitely fast mass transfer processes, the length of the MTZ reduces to zero and the sigmoid BTC becomes a concentration step. This concentration step is referred to as ideal BTC, and the time after the concentration step occurs is termed the ideal breakthrough time. Each real BTC can be approximated by a related ideal BTC that intersects the real BTC at its barycenter. Fixed-bed adsorption possesses two important advantages in comparison to adsorption in batch reactors. While in batch reactors the mass transfer driving force, and therefore also the adsorption rate, decreases during the process due to the decreasing concentrationinthereactor, theadsorbentinthefixed-bed adsorber isalwaysincontact with water having the inlet concentration, c0 , which results in a high driving force over the whole process. Furthermore, in a batch reactor, very low residual concentrations can only be achieved if very high adsorbent doses are applied. In contrast, in a fixedbed adsorber, the adsorbate will be totally removed until the breakthrough occurs.

238 | 12 Adsorption

Fig. 12.7: Breakthrough curves of a two-component system.

In the case of a multisolute adsorbate system, individual MTZs for all components occur, which travel with different velocities through the adsorbent bed, according to the different adsorption strengths of the components. As a result, displacement processes take place. Figure 12.7 shows the breakthrough behavior of a two-component system as an example. Since the MTZ of the weaker adsorbable component 1 travels faster through the adsorber, it always reaches the layer of fresh adsorbent as the first component and is therefore adsorbed in this layer as a single solute without any competition. Later, when the stronger adsorbable component 2 reaches the same layer, a new (bisolute) equilibrium state is established. This is connected with a partial displacement of the previously adsorbed component 1. As a result of this displacement process, the concentration of component 1 in the region between both MTZs is higher than its initial concentration and the related BTC shows a concentration overshoot. In multisolute systems, the MTZs are often not so strictly separated as in the example shown in Figure 12.7. Instead, an overlapping of the multiple MTZs can be observed. Figure 12.8 shows individual and total breakthrough curves of a three-component adsorbate mixture with overlapping mass transfer zones as an example. NOM breakthrough curves look similar to the curve shown in Figure 12.8b with the exception that the curve typically starts with a concentration higher than zero due to the existence of a nonadsorbable fraction that breaks through instantaneously (see the results of the adsorption analysis shown in Figure 12.3). For single-solute adsorption, the ideal breakthrough time,tid b , can be simply calculated from an integral material balance equation for the fixed-bed adsorber. The comparatively short residence time of water, t r , can be neglected in the balance equation, and the ideal breakthrough time is given by: tid b =

q0 m A q0 m A + tr ≈ c0 V̇ c0 V̇

(12.10)

12.3 Theoretical basics of the adsorption process

|

239

Fig. 12.8: Breakthrough curves of a three-component system with overlapping mass transfer zones: (a) individual BTCs, (b) total (summary) breakthrough curve.

where m A is the adsorbent mass in the adsorber, V̇ is the volumetric flow rate, c0 is the inlet concentration, and q0 is the amount adsorbed in equilibrium with c0 . The calculation of the breakthrough times of the components of a multicomponent system is more complicated and requires the combination of material balance equations of all components in all zones with a multicomponent adsorption equilibrium model, such as the IAST. A suitable model that can be used to calculate ideal breakthrough times for multisolute systems is the equilibrium column model (ECM). To calculate real breakthrough curves for single-solute or multisolute systems, the adsorption kinetics also has to be considered. In general, a complete BTC model consists of three constituents: i) the differential material balance equation for the fixedbed adsorber, ii) the equilibrium relationship, and iii) a set of equations describing the external and internal mass transfer. The differential material balance equation for a fixed-bed adsorber reads (Chapter 2, Section 2.6.4): ∂c ∂c ∂q vF + εB + ρB =0 (12.11) ∂z ∂t ∂t For single-solute adsorption, the isotherm equation (e.g., Freundlich isotherm) can be used as the equilibrium relationship, whereas for the more relevant competitive adsorption, the IAST has to be introduced into the breakthrough curve model. For NOM adsorption, an adsorption analysis must be carried out prior to the application of the breakthrough curve model to determine the input data of the fictive components. In the case of competitive adsorption of NOM and micropollutants, the necessary input data can be estimated by using the adsorption analysis in combination with the tracer model (Section 12.3.1). The mass transfer can be described by Equations (12.8) and (12.9). The intraparticle mass transfer coefficients have to be determined by experiments. Film mass transfer coefficients can be estimated from empirical correlations on the basis of process and substance parameters.

240 | 12 Adsorption

12.4 Practical aspects of activated carbon adsorption 12.4.1 Application of powdered activated carbon in slurry reactors Due to its small particle size, powdered activated carbon (PAC) is typically applied in slurry reactors. The PAC is added to the water in the form of a suspension with typical doses in the range of 5–50 g/m3 . In principle, slurry adsorbers can be operated either discontinuously as batch adsorbers or continuously as continuous flow slurry adsorbers. In practice, the continuous process is favored. If coagulation/flocculation is part of the treatment train, the activated carbon suspension can also be added directly to the coagulation/flocculation tanks. Under ideal conditions, the adsorbent in batch adsorbers is in contact with the adsorbate solution until the equilibrium is reached. Batch adsorber design for singlesolute adsorption is therefore very simple and requires only combining the material balance equation with the isotherm. The material balance equation for the batch reactor reads: VL qeq = (c0 − ceq ) (12.12) mA In the case of single-solute adsorption, the equilibrium loading, qeq , has to be replaced by the respective isotherm equation (e.g., Freundlich isotherm, Equation (12.3)). The resulting equation has to be solved to find the adsorbent dosage needed to reach a specified residual adsorbate concentration, ceq . The simple batch adsorber modeling approach can also be used for flow-through adsorbers if the contact time is long enough to reach the equilibrium state. The only change that has to be made is to replace the dose m A /V L in Equation (12.12) by the respective flow rate ratio, ṁ A / V:̇ mA ṁ A m A t = = ̇ t V VL V L

(12.13)

However, for shorter contact times, where the adsorption equilibrium is not established, the adsorption kinetics has to be considered in the process modeling. Alternatively, short term isotherms, with the same contact time as in the practical process, can be used as a basis for the process modeling. Typical contact times in practice are between 30 and 60 minutes. The diagram in Figure 12.9 demonstrates the relationship between the adsorbent dose and the adsorbate removal efficiency by means of the operating line of the batch process. The equation of the operating line can be derived from the general material balance equation for the batch process: q=

VL VL VL (c0 − c) = c0 − c mA mA mA

(12.14)

where q and c are the current adsorbent loading and concentration, respectively (0 ≤ q ≤ qeq ; c0 ≥ c ≥ ceq ).

12.4 Practical aspects of activated carbon adsorption

| 241

Fig. 12.9: Operating lines for single-solute single-stage adsorption.

The slope of the operating line is given by −V L /m A . The diagram shows that with increasing adsorbent dose the residual concentration decreases. Concurrently, the equilibrium adsorbent loading decreases. It can also be seen that a residual concentration of ceq = 0 cannot be reached in practice, because this would require that the slope of the operating line becomes zero, which means that the adsorbent mass must be infinitely large (ceq → 0, −V L /m A → 0, m A → ∞). Nevertheless, for strongly adsorbable substances with favorable isotherms, very low residual concentrations (often under the limit of detection) can be achieved with an acceptable adsorbent dose. In the case of multisolute adsorption, material balance equations for all components have to be combined with a competitive adsorption model (e.g., IAST). The combination of the IAST with the general form of the material balance equation: qi =

VL (c0,i − c i ) mA

(12.15)

gives the following set of equations: N

N

∑ zi = ∑ i=1

i=1

c0,i =1 mA φ n i 1/n i qtotal + ( ) VL Ki

(12.16)

N

c0,i 1 1 ⋅ = 1/n i φ n q m φ n i total A i i=1 qtotal + ( ) VL Ki ∑

(12.17)

The simultaneous solution of Equations (12.16) and (12.17) by means of a numerical method gives the total adsorbed amount, qtotal , and the spreading pressure term, φ,

242 | 12 Adsorption for given initial concentrations, c0,i and a given adsorbent dose, m A /V L . Since the mole fractions, z i , are also fixed according to the left-hand side of Equation (12.16), the partial adsorbent loadings can be calculated by multiplying the total adsorbed amount, qtotal , with the mole fraction, z i (Equation (12.7)). The equilibrium concentrations can be finally found from Equation (12.15). This modeling approach can be applied to both known and unknown mixtures. The latter must first be characterized by the adsorption analysis (Section 12.3.1). For systems consisting of a micropollutant and background NOM, the removal efficiency ceq /c0 for the micropollutant at a given DOC concentration and a given adsorbent dose cannot be easily predicted as already discussed in Section 12.3.1. However, it could be shown that the removal efficiency for a micropollutant in the presence of a given NOM concentration is independent of its initial concentration. Thus, the removal function ceq /c0 = f(m A /V L ) for the micropollutant has to be determined experimentally only once for a considered system with a given DOC concentration.

12.4.2 Application of granular activated carbon in fixed-bed adsorbers Fixed-bed adsorbers for drinking water treatment are constructed in an analogous manner to sand filters used for turbidity removal. The adsorbers can be designed as closed pressure filters or as open gravity filters with circular or rectangular cross section. The filters are typically made of corrosion resistant steel (stainless steel or steel coated with polymers) or concrete. The adsorbent in a fixed-bed adsorber is located on a perforated bottom, and the water usually streams downward through the adsorbent bed. Often, a small layer (5 to 10 cm) of sand (1 to 2 mm in diameter) is located between the activated carbon and the bottom. This helps to remove carbon fines. Since the pressure loss increases with time due to the accumulation of particles in the sand layer, backwashing is necessary in certain time intervals. This backwashing has to be done very carefully to avoid too strongly mixing the sand and the activated carbon. For raw waters with high turbidity, it is recommended that a sand filtration be applied before feeding the water to the GAC adsorber. For the combination of sand filtration and GAC adsorbers, separate filters for each step as well as dual-media filters are in use. Figure 12.10 shows two types of fixed-bed adsorbers frequently used in water treatment. The following specific parameters are used to characterize the operating conditions in fixed-bed adsorbers (Chapter 2, Section 2.6.4): – Filter velocity, v F (related to the empty cross-sectional area of the reactor, A R ): vF = where V̇ is the volumetric flow rate.

V̇ AR

(12.18)

12.4 Practical aspects of activated carbon adsorption

| 243

Influent

Backwash Effluent

Influent Effluent

(a)

(b)

Fig. 12.10: Typical fixed-bed adsorbers used in water treatment: (a) rectangular gravity concrete filter and (b) pressure GAC filter made of corrosion resistant steel.

–

–

Effective (i.e., interstitial) velocity, u F (related to the cross-sectional area available for the water flow, A R ε B ): V̇ vF = (12.19) uF = AR εB εB where ε B is the bed porosity. Empty bed contact time, EBCT (related to the filter velocity, v F ): EBCT =

–

h AR VR h = = vF V̇ V̇

(12.20)

where h is the adsorbent bed height and V R is the volume of the adsorbent bed in the reactor. Effective residence time, t r (related to the effective velocity, u F ): tr =

h h AR εB VR εB = = = EBCT ε B uF V̇ V̇

(12.21)

The water throughput is often given as bed volumes treated, BV (water volume fed to the adsorber divided by the volume of the adsorbent bed): BV =

VFeed V̇ t t = = VR V R EBCT

(12.22)

In Table 12.1, typical values of the main operating parameters are listed. The typical lifetime of such GAC adsorbers is between 100 and 600 days; the bed volumes treated (BV) within this operating time ranges from 2 000 to 20 000.

244 | 12 Adsorption

Tab. 12.1: Typical operating conditions of GAC adsorbers. Parameter

Symbol Unit Typical values

Bed height Cross-sectional area Filter velocity Empty bed contact time Effective contact time Particle diameter Bed volume Bed porosity

h AR vF EBCT tr dP VR εB

m m2 m/h min min mm m3 –

2–4 5–30 5–20 5–30 2–10 0.5–4 10–50 0.35–0.45

A fixed-bed adsorber can be designed on the basis of an appropriate breakthrough curve model (Section 12.3.3). Another option is to study the breakthrough behavior in a small lab-scale column and subsequently to apply a scale-up method. The rapid small-scale column test (RSSCT) is frequently used for such purposes (Crittenden et al., 1991). In this case, in contrast to predictive mathematical models, extensive isotherm or kinetic studies are not required to obtain a full-scale performance prediction. The fixed-bed adsorption process in a single adsorber is a semicontinuous process. Until the breakthrough, the water can be continuously treated, but when the breakthrough occurs, the process has to be stopped and the loaded activated carbon has to be reactivated. This is contrary to practical requirements in water treatment plants, where a continuous treatment process is indispensable. To overcome this problem and to reduce the capacity loss, which results from the need to stop the process at the first adsorbate breakthrough, multiple adsorber systems are typically applied in practice. In principle, there are two different ways to connect single fixed-bed adsorbers to a multiple adsorber system: series connection and parallel connection. The principle of series connection is demonstrated in Figure 12.11. As an example, a multiple adsorber system consisting of four adsorbers is shown at two different operation times. Only three adsorbers are in operation whereas one is out of operation in order to regenerate the adsorbent. In the given scheme, the time t1 shows a point of time where adsorber 1 is out of operation and the mass transfer zone is located between adsorbers 3 and 4. Since the mass transfer zone has already left adsorber 2, the adsorbent in this adsorber is fully saturated to the equilibrium. Therefore, adsorber 2 will be the next to go out of operation. Time t2 represents a later time. In the meantime, the regenerated adsorber 1 has been put in stream again. The mass transfer zone has traveled forward and is now located between adsorbers 4 and 1. The adsorbent in adsorber 3 is fully saturated. Next, adsorber 3 will be put out of operation, and so on. In an ideal case, all adsorbers can be operated until the equilibrium loading is reached for the entire adsorbent bed (saturation time, maximum utilization of the adsorbent capacity). However, if the mass transfer zone is very long and the number of adsor-

12.4 Practical aspects of activated carbon adsorption

1

2

3

|

245

4

t1

R

R

t2

Fig. 12.11: Fixed-bed adsorbers in series connection. R = adsorber out of operation for adsorbent reactivation, dark gray = adsorbent loaded to equilibrium, light gray = mass transfer zone, white = adsorbent free of adsorbate.

bers is limited, or if there is more than one MTZ as in mixture adsorbate systems, this maximum utilization might not be completely reached. Nevertheless, the adsorbent capacity is significantly better exploited than in a single adsorber. On the other hand, the cross-sectional area available for water flow-through is that of a single adsorber, independent of the number of adsorbers in operation. Therefore, such a series connection is not very flexible with respect to the water throughput. For a given linear filter velocity, this cross-sectional area limits the volumetric flow rate that can be treated (Equation (12.18)). In multiple adsorber systems with parallel connection, the total water stream to be treated is split into substreams, which are fed into a number of parallel operating adsorbers. The scheme in Figure 12.12 shows the location of the mass transfer zones and the degrees of saturation at two different operation times. The different adsorbers are put in operation at different start times. Consequently, at a given time, the traveled distances of the MTZs are different in the different adsorbers, and therefore the breakthrough times are also different. The effluents of the different adsorbers with different concentrations are blended to give a total effluent stream. Due to the different adsorber lifetimes, the blending of the effluents leads to low concentrations in the total effluent stream even if the effluent concentration of the adsorber that was first started is relatively high. If the blended effluent concentration becomes too high, the first loaded adsorber is put out of operation for adsorbent reactivation and another adsorber with reactivated adsorbent is put in operation. The time-shifted operation and the blending of the effluents allows operation of all adsorbers in the multiple system for longer than in the case of a single-adsorber system. Therefore, the adsorbent capacity is also

246 | 12 Adsorption

1

2

3

R

4

t1

R

t2

Fig. 12.12: Fixed-bed adsorbers in parallel connection. R = adsorber out of operation for adsorbent reactivation, dark gray = adsorbent loaded to equilibrium, light gray = mass transfer zone, white = adsorbent free of adsorbate.

better exploited than in a single adsorber. Although the effluent concentration in this type of multiple adsorber systems is not zero, the concentration can be minimized and the treatment goal can be met by choosing an appropriate number of adsorbers and an optimum operating time regime. The main advantage of the parallel connection is that the total cross-sectional area increases with increasing number of adsorbers. This type of multiple adsorber system is therefore very flexible and can be adapted to different requirements regarding the water volume to be treated. It is in particular suitable for the treatment of large amounts of water.

12.4.3 Fixed-bed versus batch adsorber As shown in the previous sections, activated carbon can be used in two different forms: as PAC in batch or flow-through slurry reactors or as GAC in fixed-bed adsorbers (adsorption filters). Both technical options exhibit advantages as well as disadvantages. PAC suspensions are easy to dose and are therefore ideally suited for temporary application. Due to the small particle size, the adsorption rate is very fast. Displacement processes due to competitive adsorption are less pronounced in comparison to fixed-bed adsorption. A concentration increase over the initial concentration is therefore not observed. Disadvantages of the PAC application in slurry reactors are in particular the particle discharge from the reactor that requires an additional separation step, the remaining residual concentration, and the missing regenerability of PAC.

12.4 Practical aspects of activated carbon adsorption

| 247

Fig. 12.13: Equilibrium adsorbent loadings achievable in a fixed-bed adsorber (adsorption filter) and in a batch adsorber for the same initial concentration of the adsorbate.

Fixed-bed adsorbers assure low outlet concentrations (zero in the ideal case) until the breakthrough of the adsorbate. Particle discharge does not need to be suspected. GAC can be reactivated and therefore repeatedly applied. The slower adsorption kinetics, leading to flat breakthrough curves, as well as possible concentration overshoots due to displacement processes are the main disadvantages of GAC application in fixedbed adsorbers. An important difference between batch reactors and fixed-bed adsorbers consists of the different exploitation of the adsorbent capacity for the same initial adsorbate concentration. The adsorption process in a batch reactor proceeds along the operating line whose slope is given by the reciprocal of the adsorbent dose (Figure 12.13). Consequently, the residual concentration is lower than the initial concentration, c0 , and the adsorption capacity that can be utilized in the batch process is the adsorbent loading in equilibrium with the residual concentration, ceq . In the case of fixed-bed adsorption, the adsorbate solution is fed continuously to the adsorber and the adsorbent loading in the saturated zone behind the mass transfer zone is in equilibrium with the inlet concentration, c0 . Accordingly, the adsorbent loading is higher in this case than in the case of a batch process. Figure 12.13 demonstrates the advantage of the fixedbed adsorption with respect to the exploitation of the adsorbent capacity. However, it has to be noted that the equilibrium loading, qeq (c0 ), for the fixed-bed adsorption is the maximum loading, which can only be reached if the process is operated until saturation (e.g., when using adsorbers in series connection). If the fixed-bed adsorption process has to be stopped at an earlier time (e.g., when using a single adsorber or adsorbers in parallel connection), the adsorbed amount is slightly lower than in the saturation state and the capacity gain in comparison to the batch process is lower.

248 | 12 Adsorption

12.4.4 Biologically active carbon filters If fixed-bed adsorbers are exposed to raw waters that contain microorganisms, then accumulation and growth of these microorganisms can take place on the surface of the adsorbent particles. Activated carbon with its rough surface and its adsorption properties is a favored medium for accumulation of microorganisms. Under these conditions, the GAC filter acts not only as an adsorber but also as a bioreactor, in which biodegradation of NOM fractions and micropollutants contributes to the overall removal of organics. The effect of biodegradation is reflected in the shape of the breakthrough curve. Figure 12.14 shows a typical NOM breakthrough curve of a biologically active GAC adsorber in comparison with a NOM breakthrough curve of an adsorber without biological activity. The main difference in comparison to pure adsorption is that the NOM breakthrough curve of a biologically active adsorber does not end at the inlet concentration level but at a lower steady-state concentration. The lower steady-state concentration of the BTC is the result of the mass loss due to the degradation of NOM fractions. The level of the steady-state concentration depends on the content of degradable NOM fractions, the degradation rates, and the empty bed contact time. A total degradation within the given contact time cannot be expected, because NOM always contains certain amounts of persistent and slowly degradable components.

Fig. 12.14: NOM breakthrough behavior in the case of adsorption with and without biodegradation (schematic).

12.4 Practical aspects of activated carbon adsorption |

249

Degradable micropollutants are also removed in biologically active carbon filters. In contrast to NOM, the steady-state effluent concentration of micropollutants can even be zero provided that the degradation rate is fast enough. Nondegradable micropollutants may be indirectly affected by the biological processes, because the removal of NOM fractions by biodegradation can lead to a weaker competition for the adsorption sites and consequently to a stronger adsorption of the nondegradable micropollutants. Under conventional conditions, the effect of biological NOM reduction is not strongly pronounced, because NOM in its original form contains mainly larger molecules, which are not, or only slowly, degradable. However, the NOM degradation can be enhanced by preozonation. Ozonation prior to adsorption breaks down the NOM molecules, which makes them more assimilable and microbially oxidizable. As a consequence, the biomass concentration within the adsorbent bed increases and the NOM is degraded to a higher degree. Therefore, a lower steady-state concentration at the adsorber outlet can be expected. The combination of ozonation and GAC application is referred to as the biological activated carbon process or biologically enhanced activated carbon process. Since ozonation not only increases the biodegradability of NOM but also decreases its adsorbability because of the formation of small polar molecules (Section 12.2.2), only low ozone doses are applied in practice (typically < 1 mg O3 /mg DOC).

13 Oxidation processes 13.1 Introduction Oxidation processes are widely used to transform or remove dissolved inorganic or organic water constituents. Generally, the processes are differentiated between specific and nonspecific oxidation. Specific oxidation processes are used to transform specific inorganic water constituents, such as Fe2+ , Mn2+ , or H2 S into the respective oxidized species. The oxidation of Fe2+ and Mn2+ with oxygen from the air and the subsequent removal of the oxidized forms Fe(OH)3(s) and MnO2(s) (deironing and demanganization) is discussed in detail in Chapter 10. H2 S, which gives the water a bad taste and odor, can be oxidized by air or other oxidants to sulfate, which can be accepted in drinking water up to relatively high concentrations. In contrast, the target substances of nonspecific oxidation processes are not specific individual substances but the entirety of the organic water constituents. The objective of nonspecific oxidation is to improve the water quality and to increase the efficiency of subsequent treatment processes by a full or partial oxidation of natural and anthropogenic organic water constituents. This chapter only deals with these nonspecific oxidation processes. It has to be noted that oxidation processes can also be used to disinfect the water. This application is discussed in a separate chapter (Chapter 14). The conventional oxidant that is used to oxidize organic water constituents is ozone. Ozone reacts with organics either directly or indirectly after forming reactive radicals, such as hydroxyl radicals (∙ OH). Reactive radicals are chemical species with unpaired valence electrons (denoted by a dot beside the symbol of the respective atom). These species show a very high reactivity and act as very efficient oxidants. They are not only formed during the application of ozone but can also be produced in a targeted manner by specific methods. These special oxidation processes that are based on reactive radicals as oxidants are referred to as advanced oxidation processes (AOPs). Besides ∙ OH radicals also other reactive oxygen species (ROS) are formed in advanced oxidation processes. Table 13.1 lists the most important oxygen species that are able to act as oxidants together with their respective half-reactions and the related standard redox intensities, pe0 , and standard redox potentials, E0H . As a rule, the higher the pe0 and E0H , the stronger the oxidation power. However, it has to be taken into account that all given half-reactions are pH-dependent. For practical purposes, it is therefore reasonable to compare standard redox intensities or potentials for a defined pH. This can be done by using the following general relationship that can be derived from the laws of mass action of the redox half-reactions: pe0 (pH) = pe0 −

https://doi.org/10.1515/9783110551556-013

np pH ne

(13.1)

252 | 13 Oxidation processes

Tab. 13.1: Oxygen based oxidants. All standard redox intensities and standard redox potentials are given for 25 °C. Oxidant

Formula Half-reaction

pe0

E H0 (V) pe0 at E H0 (V) at pH = 7 pH = 7

Hydroxyl radical Atomic oxygen Ozone Hydrogen peroxide Superoxide radical Hydroperoxyl radical Oxygen

∙ OH

48.5 41.0 35.3 30.2 29.7 28.0 20.8

2.86 2.42 2.08 1.78 1.75 1.65 1.23

O O3 H2 O2 O∙− 2 HO∙2 O2

∙ OH

+ H+ + e− 󴀕󴀬 H2 O O + 2 H+ + 2 e− 󴀕󴀬 H2 O O3(g) + 2 H+ + 2 e− 󴀕󴀬 O2(g) + H2 O H2 O2 + 2 H+ + 2 e− 󴀕󴀬 2 H2 O + − O∙− 2 + 4 H + 3 e 󴀕󴀬 2 H2 O HO∙2 + 3 H+ + 3 e− 󴀕󴀬 2 H2 O O2(g) + 4 H+ + 4 e− 󴀕󴀬 2 H2 O

41.5 34.0 28.3 23.2 20.4 21.0 13.8

2.45 2.01 1.67 1.37 1.20 1.24 0.81

where pe0 (pH) is the standard redox intensity at a given pH, n p is the number of protons in the half-reaction, and n e is the number of electrons in the half-reaction. As an example, Table 13.1 shows the respective data for pH = 7 in addition to the generally valid parameters pe0 and E0H . The definitions of the redox potential and the redox intensity as well as the relationship between both parameters are given in Chapter 2, Section 2.3.5, together with other basics of redox reactions. In the following sections, the conventional ozonation and the advanced oxidation processes (AOPs) will be discussed separately.

13.2 Ozonation 13.2.1 Oxidation mechanisms Ozonation is the most common nonspecific oxidation process in drinking water treatment. It uses ozone, O3 , and ozone derived ∙ OH radicals as oxidants and is applied in order to transform or mineralize organic water constituents. In particular, it is applied to remove color and taste and odor compounds, to eliminate trace synthetic organic compounds, to mineralize or transform dissolved natural organic matter (NOM), and sometimes also to assist the coagulation/flocculation process (microflocculation, Chapter 6, Section 6.4.5). During ozonation, NOM is often not fully mineralized to inorganic compounds, in particular CO2 and H2 O, but only transformed into smaller, more polar organic compounds. However, this is not a drawback, because the transformation of NOM has positive effects on other treatment processes. The organic transformation products are more biodegradable (due to their higher polarity) and also more suitable for entering the pore system of activated carbons (due to their smaller size), even if polar compounds are less well adsorbed than nonpolar ones (Chapter 12, Section 12.2.2). In this way, ozonation can support subsequent adsorption as well as bi-

13.2 Ozonation

| 253

ological treatment steps (biological adsorption, slow sand filtration). Anthropogenic micropollutants are also not always fully mineralized, but only transformed into other organic compounds. Here, attention has to be paid to such transformation products that may be more harmful than the parent compounds. The direct oxidation by ozone leads in a first step to the introduction of polar oxygen-containing groups into the organic molecules. This is a very selective reaction and can be observed in particular for unsaturated and aromatic compounds. By contrast, the indirect oxidation based on ∙ OH radicals, which have a higher redox potential than ozone, is nonselective and can lead, in the best case, to a complete oxidation of the organic substances (mineralization). The formation of ∙ OH radicals is favored at higher pH values (pH > 5). However, carbonate and hydrogencarbonate ions as well as humic substances act as radical scavengers and limit the efficiency of the radical-based oxidation. The formation of radicals from ozone is a very complex process. The reaction mechanism starts with the formation of HO−2 , which is the anion of the Brønsted acid hydrogen peroxide (H2 O2 󴀕󴀬 H+ + HO−2 ): O3 + OH− → HO−2 + O2

(13.2)

The hydroperoxide anion reacts with further ozone in a complex series of reactions to form ∙ OH radicals. In the literature, different possible mechanisms are discussed. As an example, the mechanism proposed by Merenyi et al. (2010) will be shown here in a condensed form. In a first step, hydroperoxyl (HO∙2 ) and ozonide (O∙− 3 ) radicals are formed: HO−2 + O3 → HO−5 → HO∙2 + O∙− 3

(13.3)

In a competing reaction, the intermediate HO−5 can decompose to O2 and OH− . The hydroperoxyl radical is an acid (pK ∗a = 4.9) that dissociates at higher pH values under formation of a superoxide radical according to: HO∙2 → H+ + O∙− 2

(13.4)

The formed superoxide radical, O∙− 2 , can react with ozone in an electron transfer reac: tion to the ozonide radical, O∙− 3 ∙− O∙− 2 + O3 → O3 + O2

(13.5)

Finally, the ozonide radicals formed in reactions 13.3 and 13.5 are transformed into hydroxyl radicals in two steps with the oxide radical anion, O∙− , as an intermediate: ∙− O∙− 3 → O + O2 ∙−

O

∙

(13.6) −

+ H2 O → OH + OH

(13.7)

It has to be noted that the formed radicals can be consumed by the abovementioned radical scavengers but also by ozone itself, which limits the overall radical yield.

254 | 13 Oxidation processes

13.2.2 Ozone generation and introduction Ozone is typically produced onsite in specific high voltage ozone generators. The generation is based on the corona discharge principle. Ozone can be generated either from pure oxygen or from air. The advantage of using air as a starting gas is the lower costs. However, when using air as a starting gas, nitrogen oxides are formed from the nitrogen of the air and the achievable ozone concentrations in the gas phase are lower than in the case of using pure oxygen. The typical ozone concentrations in the gas phase are 10–50 mg/L if the ozone is produced from air and 60–160 mg/L if it is produced from pure oxygen. The corresponding liquid-phase concentrations of ozone in the state of equilibrium are available from Henry’s law (Chapter 2, Section 2.3.2): caq = H p

(13.8)

where caq is the ozone concentration in the aqueous phase, H is the Henry constant of ozone, and p is the ozone partial pressure. According to the ideal gas law, the partial pressure p can be expressed by the molar concentration in the gas phase, c g : p=

ng R T = cg R T Vg

(13.9)

where n g is the substance amount (number of moles) in the gas phase, V g is the volume of the gas phase, R is the gas constant (0.083145 bar ⋅ L/(mol ⋅ K)), and T is the absolute temperature. Introducing Equation (13.9) into Equation (13.8) gives: caq = H R T c g = K c c g

(13.10)

where K c (= H R T) is the (dimensionless) distribution constant. If we multiply the left-hand side and the right-hand side of Equation (13.10) with the molecular weight of ozone, we can introduce the respective mass concentrations, ρ ∗ . The value of the distribution constant K c remains unchanged: ρ ∗aq = K c ρ ∗g

(13.11)

Table 13.2 lists Henry constants, distribution constants, and the solubility of ozone for different temperatures and gas phase concentrations. It has to be noted that the given solubility data are theoretical equilibrium data. They represent the maximal achiev-

13.2 Ozonation

|

255

Tab. 13.2: Henry constants, distribution constants, and solubility data of ozone. Temperature (°C)

5 10 15 20 25

H (mol/(L ⋅ bar))

0.0196 0.0168 0.0145 0.0126 0.0110

K c (–)

0.453 0.396 0.347 0.307 0.273

Solubility (in mg/L) at a gas phase concentration of 10 mg/L

50 mg/L

100 mg/L

4.53 3.96 3.47 3.07 2.73

22.65 19.80 17.35 15.35 13.65

45.3 39.6 34.7 30.7 27.3

able concentrations under the given conditions. The concentrations achievable under practical conditions may be lower, depending on the water composition and the mass transfer rate. To introduce the generated ozone into the water to be treated, mostly bubble diffusers, Venturi-type injectors, or static mixers are used (Figure 13.1). Bubble diffusers are reactors with gas inlets made of porous materials (mostly ceramic) at the reactor bottom. The gas is introduced through the pores and forms fine bubbles. Often multichamber contactors are used with alternating countercurrent and cocurrent flow in order to improve the mass transfer from the gas phase to the liquid phase by creating plug flow and increasing the contact time. Venturi-type injectors utilize the Venturi effect, which means the reduction of the fluid pressure resulting from an increased flow velocity through a constricted section of a tube. The induced partial vacuum initiates the ozone suction. The ozone gas is dispersed in the water as tiny bubbles allowing a fast mass transfer. Static mixers are tubes that contain inbuilt mixing elements, such as crossing bars or crossing corrugated plates. Injectors and static mixers can also be applied in combination (injector followed by a static mixer). Another variant is to introduce the ozone by an injector into a side stream that is pumped to a higher pressure. The higher pressure increases the available vacuum. The ozone-containing side stream is then combined with the main stream by means of a static mixer that increases the turbulence and improves the mixing (Figure 13.2). The ozone dosage applied in drinking water treatment is often chosen based on the DOC content of the water. The typical ozone dosage used in practice is in the range of 1–2 mg ozone per mg DOC. As already discussed in Section 13.1, ozonation of NOM leads to smaller and more polar transformation products, which improves the biodegradability and the accessibility to adsorbent pores. Furthermore, ozonation supports coagulation/flocculation.

256 | 13 Oxidation processes

Inlet

Outlet

Ozone

(a) Water inflow

(b)

Gas/water mixture

Gas suction

Gas Gas/water mixture Water

(c)

Mixing elements, e.g. crossing bars or crossing corrugated plates

Fig. 13.1: Ozone introduction into the water: (a) bubble diffuser, (b) Venturi-type injector, (c) static mixer.

13.2 Ozonation

| 257

Ozone

Injector Pump

Influent

Static mixer

Effluent

Fig. 13.2: Side stream ozone injection system.

Therefore, if ozonation is applied, the ozone is typically introduced into the water directly before the treatment steps slow sand filtration, adsorption, or coagulation/ flocculation.

13.2.3 Oxidation byproducts A problem that has to be taken into account when ozonation is applied in drinking water treatment consists of the formation of unwanted oxidation byproducts. If these substances are not removed by the subsequent treatment steps, they can negatively affect the drinking water quality. To minimize the formation of oxidation byproducts, a maximum allowed ozone dosage is often set by respective legal regulations. Ozonation of NOM introduces oxygen-containing functional groups into the organic molecules, which leads to the formation of aldehydes, ketones, and carboxylic acids. The products of NOM ozonation are often easily biodegradable and cause only a minor risk when the ozonation is followed by a biological treatment. If synthetic organic micropollutants are present in the raw water, a broad variety of transformation products can be formed and attention has to be paid to potentially harmful byproducts. A further problem consists of the formation of bromate and brominated organic compounds. The reason for the formation of these compounds is that natural waters used as raw waters for drinking water production typically contain low concentrations of bromide, Br− . Bromide reacts in complex reaction mechanisms with ozone to form bromate, BrO−3 , which is suspected to be carcinogenic, and in a competitive reaction also to harmful brominated organic compounds.

258 | 13 Oxidation processes The oxidation of bromide (Br− , oxidation number, ON: −1) to bromate (ON: +5) proceeds stepwise with hypobromite/hypobromous acid (BrO− /HBrO, ON: +1) and bromite (BrO−2 , ON: +3) as intermediates, either with ozone as the only oxidant (direct oxidation) or with ozone and ozone derived ∙ OH radicals as oxidants (combination of direct and indirect oxidation). Figure 13.2 shows possible reaction pathways as proposed by Song et al. (1997). The disproportionation of the radical BrO∙ (occurring in the direct-indirect and in the indirect-direct pathway) leads to the nonradical species BrO−2 and BrO− : 2 BrO∙ + H2 O 󴀕󴀬 BrO− + BrO−2 + 2 H+ (13.12) The formation of brominated organic compounds starts with the direct oxidation of bromide to hypobromite, which is in equilibrium with the hypobromous acid, HBrO. The pK ∗a of 8.6 indicates that in most practical cases (pH < 8.6) the neutral acid is the dominant species. HBrO reacts with natural organic matter to form brominated organic compounds, such as bromoform or brominated acetic acids. The reaction mechanism is as follows: Br− + O3 → BrO− + O2

(13.13)

+

H + BrO 󴀕󴀬 HBrO

(13.14)

HBrO + NOM → TOBr

(13.15)

−

The abbreviation TOBr in Equation (13.15) stands for the collective parameter total organic bromine, which includes all brominated organic compounds.

HOBr/BrO OH

BrO Disproportionation -

BrO2 O3 -

BrO3 direct-indirect

O3

O3

Br OH

BrO O3 -

Br

BrO2

O3 BrO Disproportionation

O3 -

BrO3 direct

-

BrO2 O3 -

BrO3

indirect-direct

Fig. 13.3: Possible reaction pathways of bromate formation during ozonation of water, adapted from Song et al. (1997).

13.3 Advanced oxidation processes |

BrO3-

O3 Br -

O3 BrO

259

-

H+

NOM

TOBr, e.g. CHBr3

HOBr NH3

NH2Br, NHBr2

Fig. 13.4: Formation of oxidation byproducts during ozonation of bromide-containing water.

Both the formation of bromate (except by the indirect-direct pathway shown in Figure 13.3) and the formation of organobromine compounds start with the oxidation of bromide to hypobromite. The next steps have the character of competitive reactions as shown in a simplified manner in Figure 13.4. Which direction is the preferred one depends on the NOM concentration and the pH of the considered water. A higher NOM concentration diminishes the BrO−3 formation and enhances the formation of organobromine compounds. The pH influences the competing reactions in a different manner. The formation of bromate is enhanced by higher pH values due to the favored formation of ∙ OH. In contrast, lower pH values enhance the formation of the undissociated hypobromous acid (Equation (13.14)) and accordingly the subsequent reaction of HBrO with NOM (Equation (13.15)). A further competing reaction is possible if ammonia, NH3 , is present in the ozonated water. In this case, bromamines (NH2 Br, NHBr2 ) can be formed by a reaction of NH3 with HBrO. However, the bromamines are not very stable and are subject to decomposition reactions.

13.3 Advanced oxidation processes 13.3.1 Definition and classification Advanced oxidation processes (AOPs) are oxidation processes that are based on reactive radicals acting as oxidants. The most important reactive radical is the hydroxyl radical ∙ OH, which has a much higher standard redox potential than conventional oxidants but also than other radicals (Table 13.1). To produce reactive radicals, different methods can be used: – mixing of the conventional oxidants ozone and hydrogen peroxide – combining of UV irradiation and oxidants – catalytic processes – photocatalytic processes. Although ozonation is also partly based on the action of radicals, it is usually not counted among the AOPs but referred to as a conventional oxidation process.

260 | 13 Oxidation processes

The efficiency of all AOPs is strongly influenced by the water composition, in particular by the concentration of radical scavengers (e.g., hydrogencarbonate, carbonate, humic substances). In contrast to ozonation, the advanced oxidation processes are rarely used in drinking water treatment up to now. In particular, economic reasons (e.g., energy consumption, demand for chemicals or specific catalysts) or technical problems (e.g., separation of catalysts from the treated water) have prevented a wider use of these advance oxidation processes so far. Therefore, only a brief description of the general principles will be presented in the following sections.

13.3.2 Mixing of O3 and H2 O2 : the peroxone process The peroxone process uses a mixture of the conventional oxidants ozone, O3 , and hydrogen peroxide, H2 O2 . As already shown in Section 13.2.1, hydroxyl radicals are already produced by the spontaneous decomposition of ozone. An additional introduction of hydrogen peroxide into the water increases the formation of hydroxyl radicals. As in the case of the ∙ OH formation from ozone (Equation (13.2)), the reaction mechanism starts with the formation of the hydrogen peroxide anion: H2 O2 + OH− 󴀕󴀬 HO−2 + H2 O

(13.16)

The further reactions are the same as described in Section 13.2.1 (Equations (13.3)– (13.7)), which can be summarized as: HO−2 + 2 O3 + H2 O → 3 O2 + 2 ∙ OH + OH−

(13.17)

The overall reaction equation describing the formation of ∙ OH radicals from hydrogen peroxide in the presence of ozone is then: H2 O2 + 2 O3 → 3 O2 + 2 ∙ OH

(13.18)

In addition to the oxidation with hydroxyl radicals formed by the decomposition of ozone and by the mechanism described above, direct oxidation with ozone takes also place in the peroxone process. However, compared to the application of ozone alone, the ratio of direct and indirect (radical) oxidation is strongly shifted to the hydroxyl radical oxidation.

13.3.3 H2 O2 and UV irradiation In this AOP, the water is fed into a UV reactor after adding hydrogen peroxide. Under UV irradiation with wave lengths λ < 280 nm (UV-C), H2 O2 is subject to a photodissociation that leads to ∙ OH radicals: H2 O2 + h ν → 2 ∙ OH

(13.19)

13.3 Advanced oxidation processes |

261

In this equation, the product h ν (Planck constant, h, times wave frequency, ν) symbolizes the input of radiation energy. The photodissociation initiates a chain reaction, the so-called Haber–Weiss mechanism. The propagation cycle includes the reactions: ∙

OH + H2 O2 → H2 O + HO∙2

HO∙2

(13.20) ∙

+ H2 O2 → O2 + H2 O + OH

(13.21)

radical HO∙2

Here, the hydroperoxyl occurs as an intermediate. The possible termination reactions of the radical chain are recombination reactions between two hydroxyl radicals, two hydroperoxyl radicals, or a hydroxyl and a hydroperoxyl radical: ∙

OH + ∙ OH → H2 O2

HO∙2 ∙

OH

+ HO∙2 + HO∙2

(13.22)

→ H2 O2 + O2

(13.23)

→ H2 O + O2

(13.24)

13.3.4 O3 and UV irradiation As in the case of the H2 O2 /UV process, the reaction mechanism starts with a photodissociation: O3 + h ν → O2 + O (13.25) Since ozone absorbs UV light at 254 nm, low-pressure UV (LPUV) lamps are used that emit UV light of this wavelength. The atomic oxygen produced by the photodissociation of ozone reacts with water under formation of hydrogen peroxide: O + H2 O → H2 O2

(13.26)

The resulting mixture of ozone and hydrogen peroxide produces hydroxyl radicals in the same manner as in the peroxone process, according to the overall equation: 2 O3 + H2 O2 → 2 ∙ OH + 3 O2

(13.27)

Besides the mechanism shown above, other reactions can also contribute to the overall oxidation process. Under the influence of UV, the intermediate hydrogen peroxide can produce ∙ OH radicals by photodissociation according to Equation (13.19) (Section 13.3.3), but the efficiency is relatively low when LPUV lamps are used. Furthermore, molecular ozone and direct photolysis of organic compounds may also contribute to the overall oxidation effect.

13.3.5 Photocatalysis The photocatalytic oxidation process uses semiconductors as catalysts. To understand the oxidation mechanism at the surface of a semiconductor, at first some basics of the electronic band structure of solid materials have to be recapitulated in brief.

262 | 13 Oxidation processes

Energy Conduction band

Band gap

Conduction band Band gap

Conduction band

(a)

Valence band

Valence band

Valence band

Conductor

Semiconductor

Insulator

Energy Conduction band -

-

- + - - + Valence band

+ -

UV

(b) Fig. 13.5: Band theory of solids. (a) Energy bands in conductors, semiconductors, and insulators. (b) Electron excitation in semiconductors by UV light.

Due to the overlapping of a large number of atom orbitals in a solid crystal structure, the discrete energy levels of the orbitals are split into quasicontinuous energy bands. Two bands are formed by the orbital overlapping: the valence band with a lower energy, which contains the valence electrons, and the conduction band with a higher energy. A precondition for electrical conduction is the availability of electrons in the conduction band. In contrast to conductors (metals) where the valence band and the conduction band overlap and the conduction band is partially occupied by electrons, the energy bands in insulators and semiconductors are separated by an energy gap, the band gap. In the case of semiconductors, the band gap between the valence band and the conduction band is relatively small (Figure 13.5a). Therefore, it is possible to overcome the gap and to bring electrons from the valence band to the conduction band by means of an energy input (electron excitation). As a result of the electron excitation, positive holes are left in the valence band. The introduction of energy in photocatalytic oxidation with semiconductors is carried out by UV irradiation (Figure 13.5b).

13.3 Advanced oxidation processes

Semiconductor h+

e-

h+

e-

| 263

Water

O2

O2 -

H2O

OH

Fig. 13.6: The principle of photocatalysis.

The process starts with raising electrons from the valence band of the semiconductor (SC) to the conduction band: SC + h ν → SC(h+ + e− )

(13.28)

where h+ indicates the positive hole that is left in the valence band after raising an electron to the conduction band and e− indicates the electron that is raised to the conduction band. The subsequent reactions at the interface between the semiconductor and the aqueous solution are schematically shown in Figure 13.6. The mobile electrons in the conduction band can be transferred in a surface reaction to the oxygen dissolved in water, followed by different consecutive radical reactions: e− + O2 → O∙− 2 − O∙− 2 +e + O∙− 2 +H

→ 󴀕󴀬

O2− 2 HO∙2

(13.29) (13.30) (13.31)

The reactive radical ∙ OH is formed by an electron transfer from the water molecule to the positive hole in the valence band: h+ + H2 O → ∙ OH + H+

(13.32)

h+ + OH− → ∙ OH

(13.33)

or The excitation of electrons requires a sufficient energy. The energy demand depends on the semiconductor material and the widths of its band gap. The currently available semiconductors, in particular the most frequently used titanium dioxide

264 | 13 Oxidation processes

(TiO2 ), require energy that can only be provided by UV radiation. Since the UV fraction in the sunlight is relatively small, a photocatalysis with sunlight is not very efficient. On the other hand, the alternative application of UV lamps increases the process costs. Another problem results from the fact that the photocatalysis is a surface reaction, which requires large surface areas of the catalyst material. Nanoparticles provide large surface areas but they are heavily to separate from the water after the oxidation.

13.3.6 Fenton reaction The Fenton reaction is a homogeneous catalytic reaction that uses the so-called Fenton’s reagent consisting of iron(II) ions, Fe2+ , and hydrogen peroxide, H2 O2 . Fe2+ is oxidized to Fe3+ by H2 O2 under formation of a hydroxyl radical: Fe2+ + H2 O2 → Fe3+ + ∙ OH + OH−

(13.34)

Fe3+ is then reduced back to Fe2+ by hydrogen peroxide. In this reaction, a hydroperoxyl radical is formed, which can also react with Fe3+ : Fe3+ + H2 O2 → Fe2+ + HO∙2 + H+ 3+

Fe

+ HO∙2

(13.35)

+

→ Fe

+ H + O2

2+

(13.36)

Iron is not consumed in this process; it only acts as a catalyst. A modification of the conventional Fenton process, the so-called photo-Fenton process, uses UV radiation to increase the ∙ OH formation by additional reactions: H2 O2 + h ν → ∙ OH + ∙ OH 3+

Fe

+ H2 O + h ν → Fe

2+

∙

+ OH + H

(13.37) +

(13.38)

A problem with the Fenton process consists of the low solubility of iron(III) hydroxide, Fe(OH)3 (Figure 6.9 in Chapter 6). To prevent Fe(OH)3 precipitation (loss of catalyst), the Fenton process has to be carried out at low pH values (pH < 5) or complexing agents have to be added to the water to keep the iron ions in solution. Both measures are not well suited for drinking water treatment.

13.3 Advanced oxidation processes

| 265

13.3.7 The EE/O concept As shown in the previous sections, some of the AOPs are based on UV irradiation. To characterize the performance of such electric energy driven processes and to compare the different processes, often the figure of merit EE/O (electric energy per order, also abbreviated as EEO ) is used. The parameter EE/O is defined as that energy that is necessary to decrease the concentration of a pollutant or a collective parameter (DOC, TOC) by one order of magnitude (90%) in one cubic meter polluted water (Bolton, 2001). It can also be used to characterize the performance of UV disinfection (Chapter 14). For a flow-through system, the EE/O value (in kWh/m3 ) can be calculated by: EE/O =

P cin ) V̇ log ( cout

(13.39)

where P is the electric power in kW, V̇ is the volumetric flow rate in m3 /h, cin is the influent concentration, and cout is the effluent concentration. The respective equation for batch systems reads: Pt (13.40) EE/O = cin V L log ( ) cout where V L is the volume of water treated in the time, t.

14 Disinfection 14.1 Introduction To ensure the hygienic quality of the treated drinking water, a final disinfection is frequently necessary. This is especially true if surface water is used as raw water. By contrast, groundwater is often of such high quality that disinfection can be dispensed with. Due to the variety of microorganisms that may occur in water, the hygienic quality of water is typically characterized by the determination of selected indicator organisms. These indicator organisms are not necessarily pathogens but their occurrence indicates possible hygienic problems. Typical indicator organisms or organism groups are Escherichia coli (E. coli), Pseudomonas aeruginosa, Clostridium perfringens, Coliform bacteria, and Enterococci (Chapter 1, Section 1.2.3). Accordingly, the efficiency of disinfection is characterized by the reduction of the concentration of these indicator organisms (Section 14.2). Disinfection can be carried out by chemicals but also by UV irradiation. The selection of a suitable disinfection method must be adjusted to local requirements. Important selection criteria for the disinfection method are the raw water quality, the costs, the formation of unwanted byproducts, and the existence and duration of a depot effect (long lasting disinfection effect of disinfectant residuals in the distribution system). Most frequently, strongly oxidizing chemicals (chlorine, chlorine dioxide, ozone), which are able to destroy the cells (in particular the cell walls and the enzymes in the cells), are added to the water. In particular, chlorine is widely used as a disinfectant (Section 14.3). In water, dissolved chlorine (Cl2 ) is transformed into hypochlorous acid (HClO, also written as HOCl) and hypochlorite (ClO− ), which are also oxidizing disinfectants. The mixture of these three disinfectant species is referred to as free chlorine. If ammonia is present in the water, chloramines, such as monochloramine (NH2 Cl), dichloramine (NHCl2 ), and trichloramine (NCl3 ) are formed, which are referred to as combined chlorine. Combined chlorine has also a disinfecting effect (Section 14.4). Chlorine dioxide (ClO2 ) is an alternative to chlorine and has some advantages with respect to the formation of halogenated disinfection byproducts (Section 14.5). It is often used together with chlorine, particularly if it is produced from chlorine. The strong oxidant ozone (O3 ) is – in principle – also suitable for disinfection (Section 14.6). However, due to its high reactivity it is not very stable. Therefore, it has – in contrast to free chlorine and chlorine dioxide – no depot effect that impedes bacterial aftergrowth within the water distribution system. It is therefore rather used as an oxidant in upstream stages of the treatment train (Chapter 13, Section 13.2) than as a disinfectant. Table 14.1 shows the standard redox intensities and standard redox potentials of the oxidants used as chemical disinfectants. However, it has to be noted that the https://doi.org/10.1515/9783110551556-014

268 | 14 Disinfection

Tab. 14.1: Redox intensities and redox potentials of the common chemical disinfectants. Oxidant/Disinfectant Formula Half-reaction Ozone Hypochlorous acid Chlorine Chlorine dioxide

O3 HClO Cl2 ClO2

Hypochlorite

ClO−

O3(aq) + 2 H+ + 2 e− 󴀕󴀬 O2(aq) + H2 O HClO + H+ + 2 e− 󴀕󴀬 Cl− + H2 O Cl2(aq) + 2 e− 󴀕󴀬 2 Cl− ClO2(aq) + e− 󴀕󴀬 ClO−2 ClO2(aq) + 2 H2 O + 5 e− 󴀕󴀬 Cl− + 4 OH− ClO− + H2 O + 2 e− 󴀕󴀬 Cl− + 2 OH−

pe0

E H0 (V)

34.6 25,3 23.6 17.6 14.1 15.1

2.04 1.49 1.39 1.04 0.83 0.89

standard redox intensity alone does not allow the drawing of conclusions about the strength of the disinfecting effects. Other factors such as the ability to penetrate cell walls and the pH of the water also have an impact on the disinfection efficacy. As an alternative to chemical disinfection, UV irradiation and membrane processes can be used to disinfect drinking water. The inactivation of microorganisms by UV light (Section 14.7) is based on damage of the deoxyribonucleic acid (DNA). Out of the different membrane processes used in water treatment, in particular ultrafiltration is a suitable option for disinfection purposes. In this chapter, only the chemical disinfection and the infection by UV irradiation are considered. Membrane disinfection is discussed in Chapter 5 together with other membrane processes.

14.2 Disinfection efficiency The disinfection efficiency is typically tested with selected microorganisms (biodosimetry) and expressed as log reduction. The log reduction, LR, is defined as the logarithm of the ratio of the number concentrations of organisms before and after the treatment, N0 and N, respectively: LR = log

N0 = log N0 − log N N

(14.1)

The percentage reduction, PR, is given by: PR = (1 −

N ) 100% N0

(14.2)

Accordingly, the relationship between log reduction and percentage reduction is: PR = (1 − 10−LR ) 100%

(14.3)

The relationship between log reduction and percentage reduction is demonstrated for some examples in Table 14.2.

14.2 Disinfection efficiency | 269

Tab. 14.2: Relationship between log reduction and percentage reduction. Log reduction Percentage reduction 1 2 3 4 5

90% 99% 99.9% 99.99% 99.999%

The disinfection rate for specific microorganisms can be described by a simple pseudo-first-order rate law (Chick–Watson model): ln

N N = 2.303 log = −k CW c n t N0 N0

(14.4)

where k CW is the disinfection rate constant (L/(mg ⋅ min)), c is the disinfectant concentration (mg/L), n is a constant, and t is the contact time (min). A first-order rate law results under the condition that k CW , c, and n are constant. Typically, it is further assumed that the concentration and the time are of equal relevance for the disinfection rate. Then n can be set to 1 and Equation (14.4) becomes: ln

N N = 2.303 log = −k CW c t N0 N0

(14.5)

This model is widely used due to its simple structure. For specific cases (e.g., accelerating rate, decelerating rate, lag phase), however, more complex models have to be applied. Figure 14.1 shows schematically different forms of semilog plots of disinfection data that can be found in practice.

Fig. 14.1: Different shapes of semilog plots of disinfection data. The red line corresponds to the Chick–Watson model.

270 | 14 Disinfection

Tab. 14.3: Efficiency of different disinfection methods (adapted from Crittenden et al., 2012). Disinfectant

Bacteria Viruses Protozoa Endospores

Chlorine Combined chlorine Chlorine dioxide Ozone UV light

+++ ++ +++ +++ ++

+++ excellent ++ good

+++ + +++ +++ + + fair

+/− − ++ ++ +++

++/+/− − + +++ +

− poor

Equation (14.5) suggests that the specific level of disinfection (ratio N/N0 ) for the considered microorganisms under given conditions not only depends on the time (as in conventional first-order rate laws) but on the product ct. The product ct (also written as Ct according to the alternative use of the capital letter C for the concentration) is therefore a characteristic parameter that can be used to compare the relative effectiveness of different disinfectants or the resistance of different microorganisms against a given disinfectant. Furthermore, ct values can be used as basic data for the process design. Note that according to the usual practice in disinfection modeling, the symbol c (or C) is used here for the mass concentration. A comparable approach can be used for UV disinfection. In this case, the product ct, which has the meaning of a disinfectant dose, has to be substituted by the respective UV dose (radiant exposure), given by the product of the average UV irradiance (Table 14.5 in Section 14.7) and the time of exposure, E e t (Ws/m2 = J/m2 ). The efficiency of the available disinfection methods with respect to the inactivation of different microorganisms varies. Table 14.3 gives a qualitative assessment of the efficiency of different disinfection processes. More details, including problems and limitations, are discussed in the following sections.

14.3 Disinfection with chlorine Chlorine is widely used to disinfect water. Typically, the chlorine gas, stored in gas tanks or gas flasks, is introduced into a water substream by means of an injector (for the principle of an injector see also Chapter 13, Section 13.2.2) and the chlorine solution is then fed to the main stream of the water to be disinfected (Figure 14.2). In water, chlorine is subject to a redox disproportionation that leads to chloride, Cl− , and hypochlorous acid, HClO: ±0

−1

+1

Cl2 + H2 O 󴀕󴀬 H+ + Cl− + HClO

(14.6)

Hypochlorous acid is a weak acid (pK ∗a = 7.6 at 25 °C) that is in equilibrium with its anion hypochlorite, ClO− : HClO 󴀕󴀬 H+ + ClO− (14.7)

14.3 Disinfection with chlorine |

271

Chlorine

Injector Pump

Effluent

Influent

Static mixer

Contactor

Fig. 14.2: Introduction of chlorine into the water.

Fig. 14.3: Speciation of hypochlorous acid.

The pH-dependent acid-base speciation is shown in Figure 14.3. With decreasing temperature, the equilibrium is slightly shifted to the side of the undissociated hypochlorous acid. The mixture of dissolved chlorine, hypochlorous acid, and hypochlorite is referred to as free chlorine. However, it has to be noted that at pH values higher than 5, the chlorine residual in the mixture can be neglected and free chlorine is therefore mainly HClO and ClO− . The concentration of free chlorine is expressed as mg/L Cl2 . Since chlorine gas is toxic, its handling requires specific safety precautions. As an alternative, hypochlorite and hypochlorous acid can be produced by dissolving solid sodium hypochlorite: NaClO → Na+ + ClO− +

−

H + ClO 󴀕󴀬 HClO

(14.8) (14.9)

272 | 14 Disinfection

This is in particular an option for smaller waterworks that want to avoid the safety effort. In comparison to hypochlorite, hypochlorous acid is more reactive and, due to its neutral character, can more easily penetrate the cell walls of microorganisms. Therefore, it is a better disinfectant than hypochlorite. According to the equilibrium between HClO and ClO− shown in Figure 14.3, the fraction of HClO decreases with increasing pH. Accordingly, the disinfection efficiency decreases with increasing pH as well. The formation of free chlorine and its availability for disinfection is strongly influenced by various other water constituents. Chlorine as an oxidant can be consumed by the oxidation of reduced species, such as Fe2+ , Mn2+ , or H2 S/HS− . These compounds should be removed before the disinfection stage. When ammonia is present in the water, chloramines are formed: NH3 + HClO 󴀕󴀬 NH2 Cl + H2 O

(14.10)

NH2 Cl + HClO 󴀕󴀬 NHCl2 + H2 O

(14.11)

NHCl2 + HClO 󴀕󴀬 NCl3 + H2 O

(14.12)

The formation of chloramines is influenced by the pH of the water. Whereas at pH 8 monochloramine is the only product, at lower pH values also certain amounts of dichloramine are formed. In the typical pH range of drinking water, only traces of trichloramine are formed. The sum of the concentrations of monochloramine, dichloramine, and trichloramine is referred to as combined chlorine. The formation of combined chlorine and the availability of free chlorine residuals as a function of the chlorine to ammonia ratio in the water are depicted in Figure 14.4.

Fig. 14.4: Concentration of free and combined chlorine as a function of the chlorine to ammonia ratio.

14.3 Disinfection with chlorine

|

273

As long as the molar chlorine to ammonia ratio is lower than 1, the formation of chloramines consumes the free chlorine and the concentration of combined chlorine increases with increasing chlorine to ammonia ratio (zone 1 in Figure 14.4). Simultaneously, the concentration of the free ammonia decreases. At a molar chlorine to ammonia ratio of 1, all free ammonia is transformed into chloramines, in particular monochloramine. At higher chlorine concentrations, more dichloramine is formed but also degradation reactions become relevant, for instance: 2 NH2 Cl + HClO → N2 + 3 H+ + 3 Cl− + H2 O

(14.13)

In total, the concentrations of both free and combined chlorine decrease with increasing chlorine concentration (zone 2 in Figure 14.4) until a breakpoint is reached. From this point, the added chlorine is no longer consumed by side reactions and the free chlorine residual available for disinfection increases (zone 3 in Figure 14.4). For an effective disinfection with free chlorine, the chlorine dosages should be higher than the breakpoint (breakpoint chlorination). Since chloramines also show a disinfecting effect, the formation of combined chlorine can be applied as an alternative disinfection process (Chapter 14.4). The chlorine dosages applied in practice vary depending on national regulations. They are typically in the lower mg/L range (1–6 mg/L). To avoid bacterial aftergrowth in the water distribution system, the treated water should have a certain residual concentration of free chlorine, often also set by national regulations. A serious problem for the water chlorination consists of the formation of disinfection byproducts (DBPs). The reaction of free chlorine with natural organic matter leads to halogenated organic compounds: NOM + Free chlorine → Halogenated DBPs

(14.14)

The formation of chlorinated compounds results from the direct reaction of free chlorine with the organic matter. The formation of brominated compounds in addition to chlorinated compounds can be explained by the oxidation of bromide, which occurs in the raw water, by chlorine, which is a stronger oxidant than bromine: 2 Br− + Cl2 󴀕󴀬 Br2 + 2 Cl−

(14.15)

Like chlorine, bromine also undergoes a redox disproportionation that, in this case, leads to bromide and hypobromous acid, HBrO: Br2 + H2 O 󴀕󴀬 H+ + Br− + HBrO

(14.16)

The hypobromous acid is a weak acid (pK ∗a = 8.6 at 25 °C) that is in equilibrium with its anion hypobromite, BrO− : HBrO 󴀕󴀬 H+ + BrO−

(14.17)

274 | 14 Disinfection

Tab. 14.4: Selected disinfection byproducts formed during chlorination of drinking water. Trihalomethanes (THMs) Trichloromethane (chloroform) Bromodichloromethane Dibromochloromethane Tribromomethane (bromoform)

CHCl3 CHBrCl2 CHBr2 Cl CHBr3

Haloacetic acids (HAAs) Monochloroacetic acid Dichloroacetic acid Trichloroacetic acid Monobromoacetic acid Dibromoacetic acid

CH2 Cl–COOH CHCl2 –COOH CCl3 –COOH CH2 Br–COOH CHBr2 –COOH

As already discussed in Chapter 13 (Section 13.2.3), HBrO is able to brominate natural organic matter under formation of brominated organic compounds, here expressed as the collective parameter total organic bromine, TOBr: HBrO + NOM → TOBr

(14.18)

The major halogenated disinfection byproducts are trihalomethanes and haloacetic acids (Table 14.4). In addition, further compounds are formed, such as halogenated acetonitriles, halogenated ketones, and chlorophenols. In animal experiments, THMs were shown to cause cancer. Higher concentrations of haloacetic acids have negative effects on the nervous system and the liver. Therefore, the formation of halogenated DBPs has to be minimized. There are different options to reduce the health risk caused by DBPs: i) the precursor concentration can be reduced by an enhanced NOM removal, ii) the chlorine dosage can be optimized, considering the minimum dose required for the necessary disinfection effect, and iii) an alternative disinfectant or disinfection process can be used.

14.4 Disinfection with combined chlorine As shown in Section 14.3, chloramines are formed by the reaction of hydrochlorous acid, HClO, and ammonia, NH3 . The chloramines also have disinfecting effects and can be therefore used as disinfectants. In this specific process, both chlorine and small amounts of ammonia are added to the water, where they react to form chloramines. This disinfection process is also referred to as chloramination. In particular, monochloramine is the target compound of this reaction, because monochloramine is a good disinfectant that has – in contrast to the other chloramines – no negative impact on taste and odor of the treated water. To ensure the preferential formation of monochloramine, the molar stoichiometric ratio of chlorine and ammonia should be

14.5 Disinfection with chlorine dioxide

| 275

near to 1 as discussed in the previous section (Figure 14.4). At lower values of the ratio, free ammonia is left, which is a nutrient for microorganisms and can be microbially oxidized to nitrite and nitrate. If the ratio is higher, more dichloramine is formed and the decomposition reactions become relevant. In comparison to free chlorine, monochloramine is a weaker disinfectant. However, it is more stable in solution than free chlorine and therefore useful in all cases where long lasting disinfectants are needed (e.g., large distribution systems). Monochloramine forms significantly lower amounts of halogenated disinfection byproducts, such as THMs and HAAs. Its application can lead to the formation of N-nitrosodimethylamine (NDMA), which is toxic and suspected to be carcinogenic. However, the very low concentrations that are found in treated water are considered to be unproblematic. Disinfection by combined chlorine is especially common in the USA. Here, combined chlorine is mainly used for residual maintenance and in addition to a different primary disinfectant.

14.5 Disinfection with chlorine dioxide Chlorine dioxide, ClO2 , is an alternative disinfectant that can be used to partially or totally substitute chlorine. If chlorine dioxide is used, no trihalomethanes are formed. Furthermore, the formation of other halogenated compounds is strongly reduced. This is an important advantage over chlorine. On the other hand, inorganic byproducts (chlorite, chlorate) are formed and the application is more expensive. Therefore, chlorine dioxide is often used together with chlorine in order to minimize the required concentrations and the negative side effects of both chemicals. Chlorine dioxide is an unstable gas, which requires an onsite generation in the waterworks. To generate ClO2 , different processes can be used, in particular the chlorine/ chlorite process, the chlorite/acid process, and the chlorite/peroxodisulfate process. All methods are based on redox processes. In these processes, chlorite and peroxodisulfate are applied as aqueous solutions of the sodium salts. In the chlorine/chlorite process, chlorine reacts with a sodium chlorite (NaClO2 ) solution under formation of chlorine dioxide and chloride: ±0

+3

+4

−1

Cl2 + 2 ClO−2 󴀕󴀬 2 ClO2 + 2 Cl−

(14.19)

Chlorine can be introduced into the chlorite solution directly as a gas or indirectly as an aqueous chlorine solution. In the latter case, hypochlorous acid occurs as an intermediate (Equation (14.6)). The formed HClO reacts with chlorite according to: +1

+3

+4

−1

HClO + 2 ClO−2 󴀕󴀬 2 ClO2 + Cl− + OH−

(14.20)

276 | 14 Disinfection

Note that addition of Equations (14.6) and (14.20) results in the same overall reaction equation as given above (Equation (14.19)). To avoid the introduction of chlorite into the drinking water, an excess amount of chlorine has to be used. Consequently, this process leads to a mixture of the residual free chlorine and the formed chlorine dioxide. In principle, it is possible to set any ratio of chlorine and chlorine dioxide. In this way, the disinfection process can be optimized with respect to the formation of byproducts. The chlorite/acid process is based on a reaction between a sodium chlorite solution and hydrochloric acid: +3

−1

+4

−1

5 ClO−2 + 4 H+ + 4 Cl− 󴀕󴀬 4 ClO2 + 5 Cl− + 2 H2 O

(14.21)

In contrast to the chlorite/chlorine process, no toxic chlorine gas is needed and the only disinfectant in the produced solution is ClO2 . In the chlorite/peroxodisulfate process, chlorite is oxidized by peroxodisulfate: +3

+4

2− 2 ClO−2 + S2 O2− 8 󴀕󴀬 2 ClO2 + 2 SO4

(14.22)

In this reaction, peroxodisulfate (ON(O) : −14/8) is reduced to sulfate (ON(O) : −2). The application of chlorine dioxide leads to the formation of the inorganic disinfection byproducts chlorite, ClO−2 , and chlorate, ClO−3 . Since chlorine dioxide is a relatively strong oxidant (Table 14.1) is able to oxidize other water constituents. During the oxidation reactions, it will be reduced according to the sequence: +4

+3

−1

ClO2 → ClO−2 → Cl−

(14.23)

Here, chlorite occurs as an intermediate. Furthermore, chlorite and chlorate are formed as a result of the decomposition of the unstable chlorine dioxide according to the redox disproportionation: +4

+3

+5

2 ClO2 + 2 OH− 󴀕󴀬 ClO−2 + ClO−3 + H2 O

(14.24)

If chlorine dioxide is applied together with chlorine (e.g., if chlorine dioxide is produced by the chlorine/chlorite process), the free chlorine formed from chlorine can react with chlorite to form chlorate: +1

+3

+5

−1

ClO− + ClO−2 󴀕󴀬 ClO−3 + Cl−

(14.25)

Chlorite and chlorate were found to cause hemolytic anemia. It is therefore necessary to minimize the formation of these inorganic disinfection byproducts.

14.7 UV disinfection

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14.6 Disinfection with ozone Due to its high standard redox potential that allows an oxidative destruction of cells, ozone is in principle suitable as a disinfectant (Table 14.1). However, its high reactivity diminishes the depot effect, which is necessary to impede bacterial aftergrowth within the distribution system. Another drawback results from the fact that ozone oxidizes natural organic matter under formation of biologically degradable substances. Since these substances also facilitate the bacterial aftergrowth, disinfection with ozone should not be the last stage in the drinking water treatment. This restriction contradicts the rule that the disinfection step should be arranged at the end of the treatment train. Consequently, ozone is much more often used in drinking water treatment as an unspecific oxidant (with an additional disinfection effect) in upstream stages of the treatment train than as a specific disinfectant at the end of the treatment train. Ozonation leads to the formation of different groups of byproducts, in particular organic substances with oxygen-containing functional groups (aldehydes, ketones, carboxylic acids), bromate, and brominated organic compounds. The application of ozone as an oxidant, its generation and introduction into the water as well as the formation of oxidation byproducts are discussed in detail in Chapter 13 (Section 13.2).

14.7 UV disinfection Disinfection can also be carried out by using ultraviolet (UV) radiation. UV radiation in the wavelength range of 240–290 nm acts directly on the deoxyribonucleic acid (DNA) of bacteria or on the ribonucleic acid (RNA) of viruses. The high short-wavelength UV energy is absorbed by cellular DNA or RNA with the result that new bonds between adjacent nucleotides are formed. As a result of the dimerization of adjacent pyrimidine bases (in particular thymine–thymine dimerization in DNA and uracil–uracil dimerization in RNA), the organisms are no more able to reproduce and infect. In contrast to the application of chlorine and chlorine dioxide, which acts mainly against bacteria and viruses, UV radiation has also a disinfection effect on parasites, such as Giardia and Cryptosporidium, which may occur in particular in surface waters. If the irradiation is too weak, the cells can be reactivated by an enzymatic repair of the DNA or RNA. Therefore, the radiant exposure (for definition see Table 14.5) should be at least 400 J/m2 and has to be continuously controlled. To characterize the UV irradiation process and the UV lamps, specific parameters are used. Table 14.5 gives some general radiometry measures and SI units. For practical purposes, additional technical parameters are used to characterize the UV systems; the most important are given in Table 14.6.

278 | 14 Disinfection

Tab. 14.5: General radiometry units. Term

Alternative terms

Symbol

Definition

Radiant energy

–

Qe

Total energy delivered

Radiant flux

Radiant power

P e (or Φ e ) Radiant energy per unit time, output power

Irradiance

Fluence rate, dose E e rate, intensity ∗

Radiant exposure Fluence, exposure H e dose, dose

SI unit J (= Ws) W (= J/s)

Radiant flux received by a unit of surface area

W/m2

Radiant energy received by a unit of surface area or irradiance integrated over irradiation time

J/m2

∗

Although not in accordance with the SI definition, the term intensity is frequently used to describe the irradiance Tab. 14.6: Technical parameters used to characterize UV systems.

Parameter

Unit

Remarks

Electric input power Arc length Power density Radiant power efficiency Radiant density Surface temperature

W cm W/cm % W/cm °C

– – Electric input power/arc length Radiant power/input power Radiant power/arc length –

According to the absorption maximum of the nucleic acids of about 260 nm, the wavelength range from about 240 to 290 nm is the most efficient for disinfection. The UV light suitable for disinfection can be generated by low-pressure or mediumpressure mercury UV lamps. Standard low-pressure (LP) mercury lamps work at relatively low temperatures (about 50 °C) with high radiant power efficiency (up to 40%). On the other hand, their power density is low (about 0.5 W/cm). LP lamps deliver a line spectrum with a maximum emission at a wavelength of 254 nm, which is near to the absorption maximum of the nucleic acids. The other relevant emission wavelength of 185 nm (VUV range) is filtered out by using doped quartz material for the lamp in order to avoid the formation of nitrate. Medium-pressure (MP) UV lamps work at higher temperatures (up to 900 °C) and deliver a quasicontinuous emission spectrum in the UV-C range from 200 to 280 nm, which can be used for disinfection. The main emission, however, lies in the UV-B and UV-A ranges (280–315 nm and 315–380 nm, respectively). Accordingly, the disinfection efficiency of MP lamps is lower than that of LP lamps. However, due to the wide emission spectrum, the disinfection effect is not restricted to the deterioration of the DNA or RNA but also includes attacks on other parts of the cells. The radiant power ef-

14.7 UV disinfection

| 279

ficiency of MP lamps is relatively low (< 15%), but this is compensated by a very high power density (> 100 W/cm). The MP lamps can be used to treat higher flow rates with a relatively low number of lamps. MP lamps are therefore often preferred in large waterworks. As an alternative, special low-pressure/high-output (LPHO) lamps were developed. Like the standard LP lamps, they deliver a monochromatic spectrum. They work at a higher temperature (about 90 °C) and allow higher power densities (2–3 W/cm) than the standard low-pressure UV lamps. LPHO lamps have a slightly lower radiant power efficiency (about 30%) than the standard LP lamps. Independent of the specific type of lamp, all lamps are encased in quartz sleeves for practical application. The quartz sleeves protect the lamps and provide a thermal barrier between the UV lamp and the water. UV reactors can contain one or more mercury lamps. Single-lamp UV radiators are suited for small volumetric flow rates. If larger volumes have to be treated, singlelamp reactors can be arranged in parallel connection or multilamp reactors can be used. Figure 14.5 shows a scheme of a multilamp UV radiator, in which the lamps are arranged parallel to the flow direction. Alternatively, the lamps can also be arranged perpendicular to the flow direction (Figure 14.6). In this case, the disinfecting area is not limited to the arc length (1.5–2 m). This arrangement is therefore often used for very large reactors.

Cross-section

Inlet

Electric connectors UV sensor Outlet Mercury lamps Fig. 14.5: Schematic representation of a multilamp UV radiator with lamps arranged in the flow direction.

The disinfection effect of UV radiators is typically tested with selected microorganisms and expressed as log reduction (Section 14.2). With a fluence of 400 J/m2 as recommended for drinking water disinfection, a 4-log reduction (99.99%) of most pathogens is possible.

280 | 14 Disinfection

Mercury lamps

Inlet

Outlet

(a)

Inlet

Outlet

(b) Fig. 14.6: Schematic representation of a multilamp UV radiator with lamps arranged perpendicular to the flow direction: (a) top view, (b) side view.

To compare different types of UV irradiation units and process conditions, the figure of merit EE/O (electric energy per order) can be used. For the definition of EE/O see Chapter 13 (Section 13.3.7). The most important factors that influence the process efficiency are the flow rate, the transmittance of the water as well as lamp aging and fouling. The flow rate determines the contact time, which is very important for the disinfection effect, because disinfection takes place only as long as the water is in the direct vicinity of the radiant. The transmittance of the water determines the distance up to which the radiation is effective. Lamp aging and fouling reduce the UV intensity. During the operation, the irradiation efficiency is controlled by UV sensors. The sensors are able to indicate disturbances in the disinfection process, such as decreasing radiant energy, fouling, or decreasing transmittance due to increasing turbidity. UV disinfection provides a number of advantages. It is a physical process that does not require chemicals and, accordingly, there is no need to generate, transport, or store chemicals. The taste and odor of the water is not influenced and there is no formation of disinfection byproducts. The main disadvantage is that there is no depot effect because no residual disinfectant (as in the case of chlorine) remains in the water. Together with the possible repair mechanisms for the nucleic acids, this can lead to a bacterial aftergrowth in the treated water.

Appendix: Glossary A Absorption Uptake of a gas in a liquid phase Acid After Brønsted’s acid/base theory, a substance that is able to donate protons (proton donor) Acid/base reaction After Brønsted’s acid/base theory, a reaction in which a proton is transferred from an acid to a base Activated carbon Highly porous carbonaceous material, produced in a specific thermal activation process, applied as → adsorbent in → adsorption processes Activity Concentration that acts in a reaction (effective concentration), different from measurable concentration Adsorbent Solid material that is able to collect solute molecules or ions from the liquid phase, typically a porous material with large (internal) surface (e.g., → activated carbon) Adsorption Accumulation of dissolved substances on the external and internal surface of a solid material (→ adsorbent) Advanced oxidation processes Oxidation processes in which reactive radicals act as strong oxidants Aeration Introduction of air into the water in order to oxidize or strip water constituents Aerobic In the presence of oxygen; requiring oxygen Alkaline earth metals Elements of the second group of the periodic table of elements; the alkaline earth ions Ca2+ and Mg2+ belong to the major cations in natural waters (→ hardness) Alkalinity Acid neutralizing capacity of a water, caused by hydrogencarbonate, carbonate, and hydroxide ions, also referred to as m alkalinity or m value Alluvial Deposited by rivers; alluvial deposits consist of gravel, sand, clay, silt, and organic matter Anaerobic In the absence of oxygen Anthropogenic Caused by humans Aquifer An underground water-bearing formation consisting of permeable material (permeable rocks, rock fractures, sand, gravel, silt) that is saturated with groundwater (→ saturated zone) Asymmetric membrane Membrane that consists of a thin active layer and a porous support layer, either of the same material (integral asymmetric membrane) or of different materials (composite membrane) Autocatalytic reaction Reaction in which the formed reaction product acts as catalyst (→ catalysis)

https://doi.org/10.1515/9783110551556-015

282 | Appendix: Glossary

B Backwash Removal of accumulated particles from a filter bed by reversing the water flow Bacterial aftergrowth Reproduction of bacteria in the water after disinfection (e.g., in the distribution system), also referred to as bacterial regrowth Base After Brønsted’s acid/base theory, a substance that is able to accept protons (proton acceptor) Biodegradation Degradation of organic material by microorganisms either in the presence of oxygen (aerobic degradation) or in the absence of oxygen (anaerobic degradation) Biofiltration Filtration through a material that carries a biofilm; combines the effects of filtration and biodegradation Biogenic decalcification Precipitation of calcium carbonate in lakes or reservoirs due to the consumption of carbon dioxide (disturbance of the calco–carbonic equilibrium) as a result of intensive photosynthesis Bivalent ion Ion with the charge +2 or −2, also referred to as divalent ion Breakthrough curve Characteristic temporal concentration course at the outlet of an adsorber or an ion exchanger column BTEX aromatics Group of monocyclic aromatic hydrocarbons, comprising benzene, toluene, ethylbenzene, and the three xylene isomers C Calcite-dissolving water Water that contains a higher CO2 concentration than in the calco–carbonic equilibrium and that is undersaturated with respect to calcite; the equilibrium state can be reached by calcite dissolution accompanied by CO2 consumption Calcite-precipitating water Water that contains a lower CO2 concentration than in the calco–carbonic equilibrium and that is supersaturated with respect to calcite; the equilibrium state can be reached by calcite precipitation accompanied by CO2 formation Calco–carbonic equilibrium Combined reaction equilibrium in aqueous systems that links the dissociation equilibria of dissolved carbon dioxide (‘carbonic acid’) with the precipitation/dissolution equilibrium of calcium carbonate (calcite) Carbonate hardness Fraction of the total → hardness that is equivalent to the hydrogencarbonate and carbonate concentration Catalysis Increasing the rate of a chemical reaction by addition of a substance (catalyst) that is not consumed during the reaction Chelate complex Complex (coordination complex) with ligands that are able to form multiple bonds to the central ion (→ complex) Chloramination A special → disinfection process that is based on chloramines that are produced in situ by hydrochlorous acid (transformation product of chlorine) and ammonia

Appendix: Glossary

| 283

Chlorination Introduction of chlorine into the water in order to disinfect it (→ disinfection) Clogging Accumulation of organic and inorganic particles and formation of a dense layer in the upper part of filters or at infiltration sites (riverbeds, infiltration basins); reduces the hydraulic conductivity Coagulation Destabilization of a colloidal solution by salt addition Colloids Finely dispersed particles within the size range from 1 nm to 1 μm Complex In chemistry, a compound consisting of a central ion, which is surrounded by so-called ligands (ions or molecules); also referred to as a coordination complex Concentration polarization Enrichment of ions on the feed side of a membrane due to the different flow rates of water and salts through the membrane; cause of scaling Contact filtration Dosing of coagulants/flocculants just before the water reaches the filter; also referred to as inline filtration Contaminant A substance that causes an impurity of the environment or a health risk, a pollutant Cross-flow filtration Filtration technique in membrane processes in which the feed water flows parallel to the membrane surface (also referred to as cross-flow separation) D Deacidification Removal of dissolved CO2 (‘carbonic acid’) Dead-end filtration Filtration technique in membrane processes in which the feed water flows perpendicular to the membrane surface Dealkalization Removal of carbonate hardness, removal of hydrogencarbonate Deferrization Another name for → deironing Deironing Removal of dissolved iron (Fe2+ ) Demanganization Removal of dissolved manganese (Mn2+ ) Demineralization Process that removes dissolved minerals from water; other terms are: deionization, desalination Denitrification Biochemical transformation of nitrate to nitrogen by microorganisms Depot effect Long-term effect; in water treatment a long lasting effect of a disinfectant and its sustained effectiveness in the distribution system Deprotonation Release of protons (by acids or acidic groups) Depth filtration Filtration mechanism in which particles accumulate in a granular filter bed Desorption 1. Transfer of a dissolved gas or volatile substance from the liquid phase to the gas phase 2. Transfer of an adsorbed substance back to the fluid phase Dimerization Chemical reaction that joins two molecular units (monomers); the resulting compound is referred to as dimer

284 | Appendix: Glossary

Diprotic acid Acid that can donate two protons Direct filtration Filtration directly after coagulation/flocculation, in contrast to the conventional treatment with the stages → coagulation/flocculation, → sedimentation, and → filtration with omission of the sedimentation stage Disinfection Inactivation or destruction of pathogenic microorganisms Dispersion In hydrology, the longitudinal and lateral spreading of a solute being transported through a porous medium resulting from the heterogeneous distribution of water flow velocities Disproportionation A reaction in which by transformation of identical reaction partners, different compounds are generated (2 A → B + C), often occurring in redox reactions (redox disproportionation) or in radical reactions (radical disproportionation) Drag coefficient Dimensionless quantity that describes the frictional resistance of settling particles E Electric double layer Specific arrangement of charges (surface charges, counterions, coions) around a solid particle in an aqueous system Electroneutrality The state of being electrically neutral; all aqueous systems must be electrically neutral, which requires that the number of positive ion equivalents must equal the number of negative ion equivalents Electrophoresis Motion of charged particles relative to a fluid (e.g., water) under the influence of an electric field Epilimnion Surface layer in a stratified lake (→ lake stratification) Equivalent (ion equivalent) Virtual fraction 1/z of an ion with the charge number z Eutrophic water body Water body rich in nutrients with an excessive growth of algae and low oxygen content (→ eutrophication) Eutrophication Excessive growth of algae and plants in water bodies due to the input of high amounts of nutrients; consequences are oxygen depletion due to high consumption for biomass degradation and change of the redox state from oxidizing to reducing conditions with several negative impacts on the water quality Extraction well Specific well, designed to withdraw groundwater or riverbank filtrate for drinking water production (also referred to as production well) F Filtration Solid-liquid separation by means of a solid filter material, which only the fluid can pass through Flocculation Aggregation of destabilized particles that improves their separability by filtration or sedimentation. In a broader sense, formation of macroflocs with or without flocculant aids (water soluble polymers); in a narrower sense, formation of macroflocs through bridging and network formation by flocculant aids

Appendix: Glossary

| 285

Fouling Accumulation of biotic or abiotic material on the surface or within the pores of a membrane G Gas–liquid exchange Transfer of a gas from the gas phase to the liquid phase (→ absorption) or of a gas or volatile substance from the liquid phase to the gas phase (→ desorption) Groundwater recharge Movement of water (e.g., rainwater, meltwater, surface water) downward to the groundwater; natural (through the water cycle) or artificial (intensified by artificial means) process H Half-life The time in which the initial concentration is reduced by half Hardness Water quality parameter, sum of the concentrations of the alkaline earth ions Ca2+ and Mg2+ ; can be further subdivided into → carbonate hardness and → noncarbonate hardness Heavy metals Different definitions in use; often defined as metals with a density > 5 g/cm3 (e.g., cadmium, chromium, copper, iron, lead, mercury, manganese, zinc); some of them essential in low concentrations and toxic at higher concentrations, some others nonessential and already toxic at low concentrations Hydrolysis Decomposition reaction with water as the reactant Hypolimnion Bottom layer of a stratified lake (→ lake stratification) I Infiltration Introduction of surface water (or treated wastewater) into the subsurface for groundwater recharge and near-natural water treatment Ion exchange Equivalent exchange of ions between an aqueous phase and functional groups of a solid material (→ ion exchanger) that is in contact with the aqueous phase Ion exchanger Polymeric material that carries functional groups that are able to bind ions (→ ion exchange); also referred to as ion exchange → resin Isotherm In general, a graph in thermodynamics that is valid for a constant temperature; here, an equilibrium curve of an (ad)sorption process ((ad)sorption isotherm) L Lake stratification Formation of different water layers in lakes in summer and winter due to the different temperatures and densities; result of the density anomaly of water (density maximum at 4 °C, lower densities at lower and higher temperatures)

286 | Appendix: Glossary

Law of mass action Fundamental law of the chemical equilibrium; relates the activities of the products to the activities of the starting substances, characterized by an equilibrium constant Le Chatelier’s principle Partial compensation of the disturbance of a system in the state of equilibrium (e.g., change of concentration, temperature, or pressure) by an opposite effect that minimizes the disturbing effect and leads to a new equilibrium state Ligand An ion or molecule that binds to a central metal ion to form a coordination complex; depending on the number of bonds that can be formed with the central ion, it can be differentiated between monodentate and polydentate ligands, where the latter are also referred to as chelate ligands M Mass transfer Mass transport from one location to another, for instance by diffusion Membrane Thin porous or dense material that acts as a separator and can be used in water treatment to remove particles or dissolved species from water Metalimnion The layer in a stratified lake that separates the → epilimnion from the → hypolimnion Methemoglobinemia Increased concentration of methemoglobin in the blood with negative impact on the oxygen transport; transformation of hemoglobin by nitrite (formed by reduction of nitrate) is one of the possible causes (secondary health effect of nitrate in drinking water) Microfiltration Membrane process that uses porous membranes; can be applied to remove particles Micropollutant Water pollutant that occurs in low concentrations, typically in the μg/L or ng/L range, also referred to as trace pollutant Mineralization Transformation of an organic substance into inorganic products, mainly carbon dioxide and water; if the organic compound contains heteroatoms other inorganic compounds are also formed, such as sulfate, nitrate, or chloride Molarity Molar concentration Monomer Molecule that can undergo polymerization and contributes constitutional units to the structure of a → polymer (macromolecule) Monoprotic acid Acids that can donate only one proton N Nanofiltration Membrane process that uses dense membranes; can be applied to remove dissolved water constituents Natural organic matter Totality of the particulate and dissolved organic water constituents of natural origin Nitrification Biochemical transformation of ammonia/ammonium to nitrite and nitrate by microorganisms

Appendix: Glossary

|

287

Noncarbonate hardness Fraction of the total → hardness that is equivalent to the concentrations of anions other than hydrogencarbonate and carbonate Nucleotide Building block (→ monomer unit) in ribonucleic acid and deoxyribonucleic acid consisting of three subunits: a nitrogenous base, a five-carbon sugar (ribose or deoxyribose), and a phosphate group O Osmosis Flow of water through a → semipermeable membrane from the side of pure water (or dilute solution) to the side of the concentrated solution Oxic Describes an environment in which oxygen is present Oxidant Substance that gains electrons (electron acceptor) and oxidizes the reaction partner (the → reductant) while it is being reduced; the oxidant and the related reductant form a redox couple Oxidation Loss of electrons, increase of the → oxidation state Oxidation state Hypothetical charge of an atom in a compound that results from a hypothetical cleavage of the bonds and assignment of the bonding electrons to the more electronegative partner; describes the degree of oxidation or reduction (loss or gain of electrons), indicated as Arabic numeral over the symbol of the atom or as Roman numeral in brackets behind the symbol of the atom; also referred to as oxidation number Ozonation Introduction of ozone into the water in order to oxidize water constituents P Partitioning Distribution of a substance between two different phases Permeability Ability of a natural or engineered material to transmit water Permeate In a membrane process, that fraction of water that passes through the membrane (also referred to as filtrate); sometimes the term permeate is especially used in the context of nanofiltration and reverse osmosis (dense membranes), whereas the term filtrate is used in the context of microfiltration and ultrafiltration (porous membranes) Persistence Resistance to degradation Phase In chemistry, a homogeneous region of material that is chemically uniform and physically distinct, separated from other phases by interfaces where the chemical and physical properties change significantly Photocatalysis Acceleration of a photoreaction by a catalyst (→ catalysis) Photodissociation Bond breaking caused by electromagnetic radiation (e.g., by → UV radiation) Photoreaction Reaction in which visible light or another form of electromagnetic radiation (e.g., → UV radiation) is involved or required Polyelectrolyte Polymer that contains electrolyte groups (i.e., functional groups that may be ionized in aqueous solution) in the monomer units

288 | Appendix: Glossary

Polymer Macromolecule composed of a large number of repeated subunits Polyprotic acid Acid with more than one proton Polytrophic water body Water body very rich in nutrients with an excessive growth of algae and very low oxygen content, higher level of → eutrophication in comparison to → eutrophic water bodies, also referred to as a hypertrophic water body Precipitation Formation of a solid product as a result of a reaction between dissolved substances (ions) Protonation Acceptance of protons by bases or basic groups R Rapid filtration Engineered depth filtration process with high filter velocity Reactant Compound that takes part in a chemical reaction Reaction kinetics Study and theoretical description of the rate of chemical reactions Reactivation Thermal process in which adsorbed substances are removed from the surface of activated carbons and in which the adsorption capacity is renewed Reactive radicals Chemical species with unpaired valence electrons that show a very high reactivity Recarbonation Introduction of CO2 into the water in order to lower the pH and to convert carbonate ions into hydrogencarbonate ions (often applied after lime softening) Receiving waters Bodies of water that receive wastewater discharges or surface runoff Redox intensity Negative decimal logarithm of the electron activity; master variable that determines the redox state of an aqueous system Redox potential Measurable potential that can be used to characterize the redox state in a considered water; parameter that can be used as an alternative to the → redox intensity Redox reaction Reaction in which electrons are transferred and the oxidation states of the reaction partners are changed; a coupled → reduction and → oxidation reaction Reductant Substance that loses electrons and reduces the reaction partner (the → oxidant) while it is being oxidized; the reductant and the related oxidant form a redox couple Reduction Gain of electrons, decrease of the oxidation state Resin In general, solid or highly viscous organic substance or substance mixture; here, synthetic polymeric ion exchange material (→ ion exchanger) Retentate In a membrane process, that fraction of water and water constituents that is rejected by the membrane (also referred to as concentrate) Reverse osmosis Membrane process that uses dense membranes; can be applied to remove dissolved substances, including small ions, from water; reversal of → osmosis

Appendix: Glossary

| 289

Riverbank filtration Subsurface water transport from a river to extraction wells due to a hydraulic gradient, associated with attenuation effects; can be applied as a pretreatment step in the drinking water production from surface water; more general term: bank filtration S Saturated zone Zone in the subsurface where the pore space (void volume) between the solid material is totally filled with water (→ aquifer) Scaling Precipitation of salts on surfaces, for instance on membrane surfaces or on heating installations Schmutzdecke Layer consisting of particles and microorganisms formed on the surface of a slow sand filter Sedimentation Settling of particles under the influence of the gravitational force Semipermeable membrane Membrane that is permeable to certain components of a solution and impermeable to others, for instance permeable to water and (in the ideal case) impermeable to solutes Slow sand filtration Filtration process carried out with a slow filter velocity in large basins filled with sand, in which the particles are mainly removed by straining at the surface and in which biodegradation of organic material takes place in the → schmutzdecke at the top of the filter bed Softening Removal of → hardness (Ca2+ and Mg2+ ) Sorption Accumulation of dissolved substances on a solid material, a more general term than → adsorption, as it includes all possible binding mechanisms on the surface or within the sorbent material Speciation In hydrochemistry, the concentration distribution of different species of the same element or the concentration distribution of coupled compounds (e.g., acids and conjugate bases) in an aqueous system, determined by the master variables pH and redox intensity Steady-state condition Constant mass flow through the reactor, no accumulation of mass over the time Stoichiometry Describes the proportions in which the substances participate in chemical reactions (reaction stoichiometry) or the quantitative composition of compounds (composition stoichiometry) Stripping Removal of unwanted dissolved gases or volatile substances from the water by means of a receiving gas (stripping gas) that flows through the water Surface filtration Filtration mechanism in which particles accumulate at the surface of thin filter materials Symmetric membrane Homogeneous membrane that consists of only one material T Thermocline Another name for → metalimnion Trace pollutant Another name for → micropollutant

290 | Appendix: Glossary

Transmembrane pressure Pressure difference between the feed side and the permeate side of a membrane Transmittance Effectiveness in transmitting radiant energy, for instance through a volume of water Turbidity Loss of clarity of the water as a result of light scattering by small particles; measure of cloudiness U Ultrafiltration Membrane process that uses porous membranes; can be applied to remove particles Univalent ion Ion with the charge +1 or −1, also referred to as a monovalent ion Unsaturated zone Layer in the subsurface between the land surface and the → water table, in which both water and air occur in the void volume between the solid particles, also referred to as → vadose zone Urban water cycle Cycle of water use, comprises the following main steps: extraction of water from the raw water source, drinking water treatment, water use, wastewater treatment, reintroduction of the treated wastewater into natural water bodies UV radiation Part of the electromagnetic spectrum with wavelengths ≤ 380 nm; can be subdivided into UV-A (315–380 nm), UV-B (280–315 nm), and UV-C (100–280 nm); UV radiation with wavelengths < 200 nm is referred to as VUV (vacuum ultraviolet) V Vadose zone Another name for → unsaturated zone van der Waals forces Weak intermolecular attraction forces, which include dispersion forces (between fluctuating dipoles, London forces), induction forces (between permanent and induced dipoles, Debye forces), and orientation forces (between permanent dipoles, Keesom forces) W Water table Top of the → saturated zone

Nomenclature Preliminary note: In the parameter list, general dimensions are given instead of special units. The dimensions for the basic physical quantities are indicated as follows: I electric current L length M mass N amount of substance (mol) T time Θ temperature Additionally, the following symbols for derived types of measures are used: E energy (L2 M T−2 ) F force (L M T−2 ) P pressure (M L−1 T−2 ) U voltage (L2 M I−1 T−3 )

English alphabet A

A a aVR BV Cd CF Ca CH c

area (L2 ) subscripts: B basin (surface area) M membrane p projected area (sphere) R reactor (cross-sectional area) absorption factor (dimensionless) activity (N L−3 ) total area available for mass transfer related to the reactor volume (L2 L−3 = L−1 ) bed volumes (dimensionless) drag coefficient (dimensionless) concentration factor (dimensionless) Camp number (dimensionless) carbonate hardness (N L−3 ) molar concentration (N L−3 ) subscripts: aq in the aqueous phase eq equilibrium F feed FC feed/concentrate average

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292 | Nomenclature

g gas phase in inlet l liquid phase out outlet P permeate R retentate S solid s solid-phase concentration s at the surface sat saturation (solubility) t at time t total total concentration 0 initial or inlet c∗ molar (equilibrium) concentration at the interface (N L−3 ) subscripts: aq aqueous phase g gas phase D dispersion coefficient (L2 T−1 ) superscript: ∗ retarded (= D/R d ) DL diffusion coefficient in the liquid (aqueous) phase (L2 T−1 ) d diameter (L) subscripts: C collector (filter grain) P particle E electric field strength (U L−1 ) Ee irradiance, fluence rate, dose rate (E L−2 T−1 = M T−3 ) EH redox potential (U) superscript: 0 standard ER repulsive potential (E) subscript: 0 at the surface (surface potential) EBCT empty bed contact time (T) EE/O electric energy per order; energy required to reduce the contaminant concentration in one cubic meter water by one order of magnitude (E L−3 ) e Euler number (2.71828 . . .) F combined parameter defined in Equations (3.15) and (3.18) (L T−1 ) F Faraday constant (96 485 C/mol, 96 485 As/mol) F force (F) subscripts: b buoyancy

Nomenclature |

F f

fLa fT fλ G G g H He Hinv HTU h

hν I IAP

J

K

K AB

293

C coulombic repulsion d frictional (drag) g gravity w weight mean fractional uptake (dimensionless) fraction (dimensionless) subscript: oc organic carbon summarized activity coefficient in the Langelier equation (dimensionless) summarized activity coefficient in the Tillmans equation (dimensionless) correction factor for the filtration coefficient, λ F (dimensionless) Gibbs free energy (E) or molar Gibbs free energy (E N−1 ) root mean square (RMS) velocity gradient (T−1 ) gravitational acceleration (9.81 m/s2 ) Henry constant (N L−3 P−1 ) radiant exposure, fluence, exposure dose (E L−2 = M T−2 ) Henry constant in the inverse form of Henry’s law (L3 P N−1 ) height of a transfer unit (L) height (L) subscripts: B basin F filter energy of a photon (Planck constant × frequency), used as symbol for irradiation in reaction equations (E) ionic strength (N L−3 ) ion activity product, defined in the same way as the solubility product but with actual activities instead of equilibrium activities (unit depends on the specific law of mass action) flux through membranes (M L−2 T−1 or N L−2 T−1 or L3 L−2 T−1 ) subscripts: s salt (M L−2 T−1 or N L−2 T−1 ) w water (L3 L−2 T−1 ) conditional equilibrium constant (unit depends on the specific law of mass action) subscripts: a acidity b basicity sp solubility product w water dissociation selectivity coefficient (equilibrium constant) of ion exchange reactions (dimensionless)

294 | Nomenclature

Kc K c,inv Kd KF KL KLa Koc Kow KT K∗

k

k

kB k CW kp k ∗s k̂

distribution constant (concentration ratio) related to Henry’s law (dimensionless) distribution constant (concentration ratio) related to the inverse form of Henry’s law (dimensionless) distribution constant in the linear sorption isotherm (L3 M−1 ) parameter of the Freundlich adsorption isotherm ((N M−1 )/(N L−3 )n or (M M−1 )/ (M L−3 )n ) parameter of the Langmuir adsorption isotherm (L3 N−1 or L3 M−1 ) Langelier constant (L3 N−1 ) organic carbon normalized sorption coefficient (L3 M−1 ) n-octanol-water partition coefficient (dimensionless) Tillmans constant (L6 N−2 ) thermodynamic equilibrium constant (unit depends on the specific law of mass action) subscripts: a acidity b basicity sp solubility product w water dissociation mass transfer coefficient (L T−1 or L P−1 T−1 , depending on the mass transfer equation) subscripts: aq aqueous phase F film diffusion g gas phase m general s solute w water flux through membranes rate constant (unit depends on the specific rate equation) subscripts: 1 first-order (T−1 ) 2 second-order (L3 N−1 T−1 or L3 T−1 ) Boltzmann constant (1.381 × 10−23 J/K) disinfection rate constant in the Chick–Watson model (L3n M−n T−1 or L3n N−n T−1 ) constant that describes the increase of head loss during filtration (L3 P M−1 ) modified (volumetric) intraparticle mass transfer coefficient (T−1 ) overall mass transfer coefficient (L T−1 ) subscripts: aq aqueous phase g gas phase

Nomenclature |

L LR l

M m m

ṁ

N N

NCH NTU n

n n ne nF np ṅ

P

295

distance, reactor length (L) logarithmic reduction (dimensionless) length (L) subscript: B basin molecular weight (M N−1 ) m alkalinity, total alkalinity (N L−3 ) mass (M) subscripts: A adsorbent aq in the aqueous phase g in the gas phase ie ion exchange resin S solid total total mass in the considered system mass flow rate (M T−1 ) subscripts: A adsorbent S solid molar flux (N L−2 T) number or number concentration, e.g., of particles or bacteria (dimensionless or objects/L3 ) subscript: 0 initial noncarbonate hardness (N L−3 ) number of transfer units (dimensionless) substance amount, number of moles (N) subscript: g in the gas phase exponent of the concentration in the Freundlich isotherm (dimensionless) exponent of the concentration in the Chick–Watson equation (dimensionless) number of electrons in a redox reaction (dimensionless) number of filters (dimensionless) number of protons in a redox reaction (dimensionless) molar flow rate (N T−1 ) subscripts: aq in the aqueous phase g in the gas phase permeability (L3 L−2 P−1 T−1 or L2 T M−1 ) subscript: m membrane

296 | Nomenclature

P Pe Pe PR p p pe

pH pK

pK ∗

pOH Q Q Qe q

qm q R R

power (M L2 T−3 or E T−1 ), electric power (U I or E T−1 ) radiant flux, radiant power (E T−1 ) Peclet number (dimensionless) percentage reduction (%) pressure (P) or partial pressure (P) phenolphthalein alkalinity (N L−3 ) redox intensity, negative decimal logarithm of the electron activity (dimensionless) superscript: 0 standard negative decimal logarithm of the proton activity (dimensionless) negative decimal logarithm of the conditional equilibrium constant (dimensionless) subscripts: a acidity b basicity sp solubility product w water dissociation negative decimal logarithm of the thermodynamic equilibrium constant (dimensionless) subscripts: a acidity b basicity sp solubility product w water dissociation negative decimal logarithm of the hydroxide ion activity (dimensionless) electric charge (I T) reaction quotient (same unit as the related equilibrium constant) radiant energy (E) (ad)sorbed amount, (ad)sorbent loading (N M−1 or M M−1 ) subscripts: eq equilibrium s at the surface total total 0 initial or in equilibrium with c0 maximum (ad)sorbent loading, parameter in the Langmuir isotherm (N M−1 or M M−1 ) mean adsorbent loading (N M−1 or M M−1 ) rejection (dimensionless) universal gas constant (8.3145 J/(mol ⋅ K), 8.3145 Pa ⋅ m3 /(mol ⋅ K), 0.083145 bar ⋅ L/(mol ⋅ K))

Nomenclature | 297

R

Rd Re r r r

S S SD SI T TH t

tid b U UC u uF V

V̇

resistance to flow in membrane processes (L−1 ) subscripts: f fouling layer m membrane t total retardation factor (dimensionless) Reynolds number (dimensionless) reaction rate (N L−3 T−1 ) radial distance (L) radius (L) subscripts: B basin P particle entropy (E Θ−1 ) or molar entropy (E N−1 Θ−1 ) stripping factor (dimensionless) stoichiometric deviation (calco–carbonic equilibrium), defined in Equation (11.18) (N L−3 ) saturation index (dimensionless) absolute temperature (Θ) total hardness (N L−3 ) time (T) subscripts: R reaction r residence, detention 0.5 half-life ideal breakthrough time (T) voltage (U) uniformity coefficient (dimensionless) electrophoretic mobility (L2 T−1 U−1 ) effective (interstitial) filter velocity (L T−1 ) volume (L3 ) subscripts: aq aqueous phase B basin or bed Feed feed volume g gas phase L liquid P particle R reactor volumetric flow rate (L3 T−1 ) subscripts: aq aqueous phase

298 | Nomenclature

v

w

x z z z

F feed G gas g gas phase L liquid P permeate velocity (L T−1 ) subscripts: c compound F filter velocity (superficial velocity, Darcy velocity) h horizontal s settling (sedimentation) s,c settling, critical w (pore) water z (superficial) velocity in z direction width (L) subscript: B basin distance from the surface (L) spatial variable in a reactor (L) ion charge number (dimensionless) adsorbed-phase mole fraction (dimensionless)

Greek alphabet α α

γ

γ

dispersivity (L) collision efficiency factor in particle aggregation (dimensionless) subscripts: O orthokinetic stage P perikinetic stage activity coefficient (dimensionless) subscripts: z ion with charge z 1 univalent ion 2 bivalent ion transport and attachment efficiency in filtration processes (dimensionless) subscripts: A attachment D diffusion I interception O overall

Nomenclature |

∆ ε

εr ε0 ζ η κ DL λ

λ λF

ν νi π

ρ

ρ∗

σ

299

S sedimentation T transport (total) concentration difference, defined in Equation (11.16) (N L−3 ) porosity (dimensionless) subscript: B bed or bulk relative permittivity, dielectric constant (dimensionless) permittivity of the vacuum (approx. 8.8542 × 10−12 F/m, 8.8542 × 10−12 C/ (V ⋅ m), 8.8542 × 10−12 C2 /(N ⋅ m2 )) zeta potential (U) dynamic viscosity (M L−1 T−1 ) reciprocal of the Debye length, reciprocal of the electric double layer thickness (L−1 ) degradation rate constant (T−1 ) superscript: ∗ retarded (= λ/R d ) wavelength (L) filtration coefficient (L−1 ) subscript: 0 initial kinematic viscosity (L2 T−1 ) stoichiometric coefficient of the component i in a reaction equation (dimensionless) osmotic pressure (P) subscripts: ideal ideal solution real real solution density (M L−3 ) subscripts: B bed F fluid P particle mass concentration (M L−3 ) subscripts: aq in the aqueous phase e effluent g in the gas phase 0 initial or inlet particle concentration in a filter bed (M L−3 ) subscript: t at time t

300 | Nomenclature

σ Φe φ φ ϕ ϕ ϕ

surface free energy, surface tension (F L−1 or M T−2 ) alternative symbol for radiant flux, P e (E T−1 ) osmotic coefficient (dimensionless) spreading pressure term in the ideal adsorbed solution theory (N M−1 ) recovery (dimensionless) particle–liquid volume ratio (dimensionless) equivalence factor (carbonic acid system), defined in Equation (11.13) (dimensionless)

Abbreviations ACH ADE AOP BTC BTEX BV CA CH CIP CMBR CMFR DBP DIC DNA DOC DOM EBCT EBCM ECM EDTA FBR GAC HAA HPC HSDM HTU IAP IAST LDF LERO LP LPHO LPRO MBE MF MP MWCO

Aluminum chlorohydrate Advection–dispersion equation Advanced oxidation process Breakthrough curve Benzene, toluene, ethylbenzene, xylenes Bed volumes (treated) Cellulose acetate Carbonate hardness Clean in place Completely mixed batch reactor Completely mixed flow reactor Disinfection byproduct Dissolved inorganic carbon Deoxyribonucleic acid Dissolved organic carbon Dissolved organic matter Empty bed contact time Equivalent background compound model Equilibrium column model Ethylenediaminetetraacetic acid Fixed-bed reactor Granular activated carbon Haloacetic acid Heterotrophic plate count Homogeneous surface diffusion model Height of a transfer unit Ion activity product Ideal adsorbed solution theory Linear driving force (model) Low-energy reverse osmosis (interchangeable with LPRO) Low-pressure (ultraviolet lamp) Low-pressure high-output (ultraviolet lamp) Low-pressure reverse osmosis Material balance equation Microfiltration Medium-pressure (ultraviolet lamp) Molecular weight cutoff

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302 | Abbreviations

MTZ NCH NDMA NF NOM NTA NTU ON PA PAC PACl PAH PES PFR PFS POC PP PS PVDF RNA RO ROS RSSCT SAC SBA SC SD SI SOC SOM TH THM TOC TOBr TRM TSS

Mass transfer zone Noncarbonate hardness N-nitrosodimethylamine Nanofiltration Natural organic matter Nitrilotriacetic acid 1. Nephelometric turbidity unit; 2. Number of transfer units Oxidation number, oxidation state Polyamide Powdered activated carbon Polyaluminum chloride Polycyclic aromatic hydrocarbon Polyethersulfone Plug flow reactor Polyferric sulfate Particulate organic carbon Polypropylene Polysulfone Polyvinylidene difluoride Ribonucleic acid Reverse osmosis Reactive oxygen species Rapid small-scale column test Strong acid cation exchanger (equivalent term: strongly acidic cation exchanger) Strong base anion exchanger (equivalent term: strongly basic anion exchanger) Semiconductor Stoichiometric deviation Système international (d’unités); international system of units Synthetic organic compound Solid organic matter, soil organic matter Total hardness Trihalomethane Total organic carbon Total organic bromine Tracer model Total suspended solids

Abbreviations

UF UV VOC WAC WBA WHO WWTP

| 303

Ultrafiltration Ultraviolet Volatile organic compound Weak acid cation exchanger (equivalent term: weakly acidic cation exchanger) Weak base anion exchanger (equivalent term: weakly basic anion exchanger) World Health Organization Wastewater treatment plant

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Index Absorption 17, 29, 38, 48, 141, 146, 152, 187, 277 – packed column 149 – reactors 153 Absorption factor 153 Acid/base equilibrium 30, 157, 204 Acid/base reactions 27 Acid/base theory – Brønsted 30 – Lewis 225 Acidity constant 31, 158 Activated carbon 15, 39, 58, 227 – chemical activation 228 – gas activation 228 – granular 19, 227, 242, 246 – powdered 19, 227, 240, 246 – production 228 – properties 229 – reactivation 228 Activity coefficient 26 Adsorbent 19, 39, 53, 227 – oxidic 228 Adsorber – batch adsorber 240, 246 – continuous flow slurry adsorber 240, 246 – fixed-bed adsorber 234, 242, 246 – slurry adsorber 234, 240 Adsorption 16, 18, 20, 21, 27, 38, 42, 51, 60, 227, 252 – biological 253 – breakthrough curve 236, 239 – competitive 232, 241 – dynamics 236 – equilibrium 230 – isotherm 230 – kinetics 234 – multisolute 231, 238, 241 Adsorption analysis 232, 242 Adsorption model – batch 240 – equilibrium column model 239 – homogeneous surface diffusion 235 – ideal adsorbed solution theory 231 – linear driving force 235 Advanced oxidation processes 19, 251, 259 Advection–dispersion equation 61, 63 https://doi.org/10.1515/9783110551556-019

Aeration 16, 17, 20, 42, 141, 163, 178, 186, 192, 197 Aerator 197 Aluminum – hydroxo complexes 126 – solubility diagram 133 Antiscalant 113 Artificial infiltration 58 Bacterial aftergrowth 267, 273, 277, 280 Bank filtration see Riverbank filtration Basicity constant 32 Biodegradation 19, 51, 57, 59, 60, 64, 68, 72, 248 – during riverbank filtration 60, 63, 72 – in activated carbon filters 248 – in slow sand filters 84 Biofiltration 16 Biofouling 104 Biologically active test filter 65 Breakthrough curve 53, 66, 212, 236 – fictive component approach 69 – NOM 68 Calcite-dissolving water 159, 163 Calcite-precipitating water 159, 163 Calco–carbonic equilibrium 10, 157, 164, 169, 170, 183, 186, 208 – elementary reactions 158 – overall reaction equation 158 – saturation index 163 Camp number 132 Carbon cycle 15 CARIX process 184, 216 Chick–Watson model 269 Chloramination 274 Chlorination 14, 42, 154, 273, 274 Chlorine/chlorite process 275 Chlorite/acid process 276 Chlorite/peroxodisulfate process 276 Clogging 71 Coagulant 124, 125 – dosage 135 – prehydrolyzed 127 Coagulation 16, 17, 58, 75, 108, 123, 252 – enhanced 125

308 | Index

– nonspecific 118, 123 – pH 133 – specific 118, 124 – sweep 118 – temperature 135 Colloid 117 Colloidal solution 9 – destabilization 123 – stability 118 Completely mixed batch reactor 46, 51 Completely mixed flow reactor 46, 47, 50, 52 Concentration – equivalent 26 – mass 25 – molar 25 Concentration polarization 104, 111 Contact filtration 137 Coulomb’s law 120 Cross-flow separation 100 Deacidification 16, 18, 19, 21, 29, 157, 197, 216 – chemical 163, 166, 169, 187 – mechanical 163, 169, 184, 186 Dead-end filtration 100 Dealkalization 16, 18, 75, 169, 172, 175, 206, 214 – by acid addition 176, 181 – by ion exchange 182–184, 214 – by precipitation 176 – conventional 178 – rapid 178 – with lime 176 – with sodium hydroxide 178 Deferrization see Deironing Degassing 141 Degradation rate constant 61, 65, 68, 70 Deionization see Demineralization Deironing 16, 18, 20, 23, 29, 59, 192, 197 – overall reaction 193 – principle 192 – process design 199 Demanganization 16, 18, 20, 23, 29, 59, 192, 197 – filter conditioning 198 – overall reaction 193 – principle 192 – process design 199 Demineralization 18, 206 – by ion exchange 219 – process schemes 223

Depot effect 19, 267, 277 Deprotonation 31 Desalination see Demineralization Desorption 16, 17, 29, 49, 141, 145 – operating line 151 – reactors 153 Direct filtration 75, 136 Disinfectants 267 Disinfection 16, 19–21, 29, 141, 267 – byproducts 14, 273, 276 – with chlorine 270 – with chlorine dioxide 275 – with combined chlorine 274 – with ozone 277 – with UV 277 Dispersion – hydrodynamic 62 – mechanical 62 Dispersivity 63 – prediction 71 Distribution constant 30, 143 Drag coefficient 55, 77 EBCT see Empty bed contact time EE/O 280 Electric double layer 120 Electron acceptor 35 Electron donor 35 Electrophoretic mobility 122 Empty bed contact time 55, 243, 244, 248 Epilimnion 5, 191 Equilibrium constant – conditional 28 – thermodynamic 27 Equivalent 26 Eutrophication 6, 191 Extraction well 72 Fenton reaction 264 Filter – dual-media 85 – monomedia 85 Filter performance 90 Filter velocity 54 – interstitial 93 – superficial 92 Filtration 16, 17, 20, 57, 59, 72, 75, 83, 137, 197 – cake filtration 84 – depth filtration 83, 86

Index | 309

– head loss 92 – mechanisms 86 – rapid filtration 84–86, 94 – slow sand filtration 84, 86, 94, 253 – surface filtration 83 Filtration coefficient 91, 92 Filtration model – microscopic 87 – phenomenological 91 Fixed-bed adsorber 19, 227, 234, 236, 242, 246, 248 Fixed-bed reactor 53, 183, 213 Flocculant 129 Flocculant aid 129, 130 – dosage 135 Flocculation 16, 17, 20, 58, 75, 108, 118, 128, 252 – macroscale 131 – microscale 130 – orthokinetic 131 – perikinetic 130 Flocculation basin 137 Flocculation clarifier 140 Flocculator – hydraulic 139 – multiple chamber 139 Flow velocity – effective 54 – interstitial 54 – superficial 54 Flux – mass 42 – solute 45, 110 – volumetric 44, 101, 106, 110 Fouling 104, 108, 114, 211, 280 Freundlich isotherm 39, 230 Gas–liquid exchange 17, 48, 59, 141 – reactors 49, 153 Gas–water partitioning 27, 29, 142 Geosorbent 39 Geosorption 39 Groundwater composition 4 Groundwater treatment 20 Güntelberg equation 27, 161 H2 O2 /UV 260 Haber–Weiss mechanism 261 Half-life 41

Hardening 172, 187 Hardness 13, 18, 108, 116, 141, 166, 169, 171, 187, 214 – carbonate 13, 166, 169, 171, 173 – definitions 172 – noncarbonate 171, 173 – total 167 – units 172 Heavy metal removal 206 – by ion exchange 225 Henry constant 29, 143 Henry isotherm 39 Henry’s law 29, 142, 153, 164, 254 Humic substances 4, 8, 12, 14, 193, 253 – removal by ion exchange 224 Hypolimnion 5, 191 Ideal adsorbed solution theory 231 Indicator organisms 7, 8, 267 Indicator pathogens 6 Infiltration 16, 17, 21, 39 Ion exchange 16, 18, 38, 42, 51 – breakthrough curve 211 – hydrochemical effects 208 – reactors 183 Ion exchange resin 203 – acidic 204, 206 – basic 204, 206 – capacity 213 – chelate-forming 207, 225 – macroporous matrix 204 – microporous matrix 204 – operating capacity 214 – selectivity 207 – total capacity 213 – usable capacity 214 Ion product of water 33 Ionic strength 26, 123 Iron – hydroxo complexes 126 – solubility diagram 133 – speciation 189 Iron oxidation – biological 196 – kinetics 195 Irradiance 278 Jar test 132 log Koc –log Kow correlations 70

310 | Index

Lake water treatment 21 Lamella clarifier 79 Langelier equation 160, 162 Langmuir isotherm 39 Law of mass action 27 Le Chatelier’s principle 34 Lime/carbonic acid equilibrium see Calco–carbonic equilibrium Limewater 20, 166, 176 Log reduction 268 Low-pressure reverse osmosis 185 Manganese – speciation 189 Manganese oxidation – autocatalytic 196 – biological 196 – kinetics 195 Mass transfer 42, 44, 46, 50, 51, 106, 110, 141, 146, 213, 255 – adsorption 234 – gas–liquid exchange 146 – ion exchange 213 – membrane process 106, 110 Mass transfer coefficient 43, 45, 106, 110, 111, 147, 150, 153, 234, 239 – film 234 – intraparticle 235 – overall 148 – salt flux 111 – water flux 106, 110 Mass transfer zone 53, 211, 236, 244 Material balance equation – batch adsorber 230 – bubble contactor 50 – completely mixed batch reactor 47, 51 – completely mixed flow reactor 47, 52 – fixed-bed adsorber 238 – fixed-bed reactor 54 – gas sparging in a CMFR 50 – gas–liquid exchange 144 – general 45 – packed-tower contactor 51 – plug flow reactor 48 McCabe–Thiele diagram 151 Mean residence time 47 Membrane – asymmetric 105, 113 – dense 97, 113

– integral-asymmetric 105 – porous 97 – spiral-wound 114 – symmetric 105 Membrane constant 106, 110 Membrane material 105 Membrane module 105 – capillary 105 – hollow fiber 105 Membrane processes 3, 17, 18, 76, 97, 176, 185, 268 – separation limits 99 Membrane resistance 102, 107 Metalimnion 5 Microbiological water quality 6 Microfiltration 16, 17, 76, 97, 105 Microorganisms 5, 6, 16, 19, 42, 59, 65, 84, 86, 248, 267, 268, 279 – size ranges 7 Micropollutants 4, 15, 227, 232, 248, 253 Microsieving 20 Milk of lime 166, 176 Molar flow rate 43 Molarity 25 Molecular weight cutoff 103 Multibarrier principle 15 Multiple adsorber systems – parallel connection 244 – series connection 244 Nanofiltration 16, 18, 97, 110, 176, 185 Natural organic matter 14, 18–20, 59, 85, 99, 118, 127, 133, 179, 224, 227, 232, 238, 242, 248, 252, 258, 273, 277 Nernst equation 37 Nitrate removal 206 – by ion exchange 223 Nitrogen cycle 10 n-octanol-water partition coefficient 70 NTU-HTU model 150 O3 /UV 261 Organic carbon – dissolved 14 – total 14 Osmosis 108 Osmotic pressure 45, 108, 185 – transmembrane 110 Overalkalization 166

Index | 311

Oxidant 35, 252 Oxidation 17, 19, 141, 251 – advanced 251, 259 – nonspecific 251 – photocatalytic 261 – specific 251 Oxidation byproducts 257 Ozonation 16, 19–21, 29, 42, 58, 251, 252, 257 Ozone – generation 254 – introduction 255 – solubility 255 Pellet softening 178, 179 pe–pH diagram see Pourbaix diagram Permeability 72, 101, 110 Peroxone process 260 pH adjustment 20 Photo-Fenton process 264 Plug flow reactor 46 Pore water velocity 67 Pourbaix diagram 190 – iron and manganese 190 Power density 278 Precipitation 8, 10, 27, 33, 34, 75 Precipitation/dissolution equilibrium 33, 157, 209 Predominance area diagram see Pourbaix diagram Preozonation 136, 249 Proton acceptor 31 Proton donor 31 Protonation 31 Protozoan parasites 7 Radiant energy 278 Radiant exposure 278 Radiant flux 278 Radiant power efficiency 278 Radical formation 253, 259–261, 264 Rapid mix/coagulation basin 137 Rate law 40 – first-order 40, 47, 48, 61, 63, 65, 90, 91, 131, 269 – pseudo-first-order 42, 65 – second-order 40, 41, 131 Reaction kinetics 25, 40, 46, 50, 195 Reaction quotient 28 Reaction rate 40, 194

Reaction time 47 Reactive oxygen species 251 Reactive radicals 16, 251, 259 Recarbonation 178 Recovery 102, 113 Redox couple 35 Redox intensity 5, 35, 36, 189, 193, 252 – standard 36, 189, 251, 252, 268 Redox potential 5, 18, 37, 59, 189, 192, 198, 252, 253 – standard 37, 251, 267, 277 Redox reaction 27, 195 – complete reaction 35, 38 – half-reaction 35, 189 Redox sequence 194 Reductant 35 Rejection 102 Reservoir water treatment 21 Retardation factor 62, 66 Reverse osmosis 16, 18, 97, 110, 175, 185 – low-energy 110 – low-pressure 110 River water composition 5 Riverbank filtrate 5 Riverbank filtrate treatment 22 Riverbank filtration 17, 21, 39, 51, 57, 71, 76 – attenuation processes 59 – transport modeling 60, 70 Scaling 13, 104, 112, 171, 186, 211 Schmutzdecke 84, 86, 94 Sedimentation 16, 17, 58, 75, 137 – overflow rate 81 – theory 76 Sedimentation basin 79, 81 Settling tank see Sedimentation basin Settling velocity 77, 78, 117 Softening 16, 18, 20, 75, 171, 175, 206, 214 – by ion exchange 175, 182, 183, 214 – by membrane processes 176, 185 – by precipitation 175, 176 – with lime 176 – with lime and soda ash 180 – with sodium hydroxide 178 – with sodium phosphate 181 Solubility – of gases 144 – of solids 34 Solubility exponent 34, 112

312 | Index

Solubility product 34, 104, 112, 127, 158 Sorbent 39 Sorption 38, 51, 57, 60, 63, 66, 68, 72 Sorption isotherm 60 Spring water composition 5 Standing water bodies – composition 5 – stagnation and circulation 5 Steady-state conditions 47 Stokes–Einstein equation 88 Stokes’s law 78, 88, 117 Stripping 17, 29, 42, 49, 141, 197 Stripping factor 152 Surface filtration 97 Thermocline 5 Tillmans curve 160, 210, 215 Tillmans diagram 164 – CARIX process 218 – demineralization 220 – extended 208 – softening/dealkalization by ion exchange 216 Tillmans equation 160 Total suspended solids 9 Trace pollutants 15 Transmembrane pressure 45, 97, 107

Treatment train 15, 19 Turbidity 9, 105, 118, 127, 136, 166, 177, 178, 180, 186, 242, 280 Two-film model 43, 51, 147, 235 Ultrafiltration 16, 17, 20, 76, 97, 105, 268 UV irradiation 268 UV lamps 278 van’t Hoff equation 109 Velocity gradient 131 Water constituents 4 – abiotic particulate matter 8 – inorganic 9, 13 – microorganisms 6 – organic 13 Water cycle – global 1 – natural 1 – urban 1, 3 Water resources – freshwater 4 – global 1 Zeta potential 121, 122