7. TOXIC ORGANIC 7. TOXIC ORGANIC CHEMICALSCHEMICALS

If we live as if it matters and it doesn't master, it doesn't matter. If we live as if it matters and it doesn't master, it doesn't matter. If we live as if it doesn't matter, and it matters, then it matters. If we live as if it doesn't matter, and it matters, then it matters.

- - The Precautionary PrincipleThe Precautionary Principle, International Conference on an, International Conference on anAgenda of Science for Environment and Development IntoAgenda of Science for Environment and Development Into

the 21 st Century, Vienna, Austria (1991)the 21 st Century, Vienna, Austria (1991)

There are 4 million organic chemicals with names given by the InternaThere are 4 million organic chemicals with names given by the International Union of Pure and Applied Chemistry (IUPAC). Approximately tional Union of Pure and Applied Chemistry (IUPAC). Approximately 1000 new organic chemicals are synthesized and used commercially ea1000 new organic chemicals are synthesized and used commercially each year. Only a fraction of these prove to be toxic or carcinogenic, and ch year. Only a fraction of these prove to be toxic or carcinogenic, and the vast majority of them break down in the environment. the vast majority of them break down in the environment.

If they do not, if they are persistent as wel1 as toxic, we may need to usIf they do not, if they are persistent as wel1 as toxic, we may need to use mathematical models to determine if they pose an unreasonable risk e mathematical models to determine if they pose an unreasonable risk to humans or the environment. We estimate their fate and transport in to humans or the environment. We estimate their fate and transport in the environment, their exposure concentration to humans and wildlife, the environment, their exposure concentration to humans and wildlife, and perform waste load allocations to meet water quality standards.and perform waste load allocations to meet water quality standards.

Organic chemistry is the chemistry of compounds of Organic chemistry is the chemistry of compounds of carboncarbon. Organic c. Organic chemicals are obtained from material produced originally by living orghemicals are obtained from material produced originally by living organisms (such as petroleum, coal, and plant residues) or they are syntheanisms (such as petroleum, coal, and plant residues) or they are synthesized from other organic compounds or inorganics (e.g., carbonates or sized from other organic compounds or inorganics (e.g., carbonates or cyanides). cyanides).

7.1 NOMENCLATURE7.1 NOMENCLATURE

There are many different ways to name organic compounds including common There are many different ways to name organic compounds including common names, lUPAC names, and trade names. Figure 7.1 shows some classes of organinames, lUPAC names, and trade names. Figure 7.1 shows some classes of organic compounds that are widely used. The left-hand side of the figure gives some gec compounds that are widely used. The left-hand side of the figure gives some general classes of compounds and the right-hand side is a specific example of each. neral classes of compounds and the right-hand side is a specific example of each.

In the environment, alkanes are slowly oxidized to form an alcohol, beginning a In the environment, alkanes are slowly oxidized to form an alcohol, beginning a chain of reactions.chain of reactions.These reactions are usually microbially mediated (enzymes catalyze the reactionThese reactions are usually microbially mediated (enzymes catalyze the reactions), but other abiotic processes such as photolysis, hydrolysis, chemical oxidation s), but other abiotic processes such as photolysis, hydrolysis, chemical oxidation or reduction may also be important. or reduction may also be important.

Microbial "infallibility" would state that all organic chemicals that are synthesizMicrobial "infallibility" would state that all organic chemicals that are synthesized can be mineralized all the way to carbon dioxide and water as shown above. ed can be mineralized all the way to carbon dioxide and water as shown above. But many synthetic compounds have not been shown to degrade in the environmBut many synthetic compounds have not been shown to degrade in the environment, or they might degrade extremely slowly, or only under special conditions.ent, or they might degrade extremely slowly, or only under special conditions.

Figure 7.1

Some common classes of organic compounds (left) and examples (right). R and R` indicate different alkyl group.

Microbes are not infallible, although given the proper conditions, enough time, aMicrobes are not infallible, although given the proper conditions, enough time, and in concert with other physical and chemical reactions, they can often help to nd in concert with other physical and chemical reactions, they can often help to break down most organic chemicals. On the other hand, microbes and plants cabreak down most organic chemicals. On the other hand, microbes and plants can sometimes synthesize chemicals in nature that are quite toxic and rather slow n sometimes synthesize chemicals in nature that are quite toxic and rather slow to degrade.to degrade.

Chlorinated organic chemicals are not purely man-made (xenobiotics), but now Chlorinated organic chemicals are not purely man-made (xenobiotics), but now we know that some chlorinated organic chemicals are synthesized by plants and we know that some chlorinated organic chemicals are synthesized by plants and quite common in nature.quite common in nature.

To oxidize benzene to carbon dioxide and water requires that the very stable beTo oxidize benzene to carbon dioxide and water requires that the very stable benzene ring must be cleaved. Under anaerobic conditions this can be a difficult tanzene ring must be cleaved. Under anaerobic conditions this can be a difficult task.sk.

There are many toxic organic chemicals that cause problems in the environment There are many toxic organic chemicals that cause problems in the environment and comprise various "priority pollutant" lists. One of the most important lists iand comprise various "priority pollutant" lists. One of the most important lists is that for drinking water standards. Organic chemicals for which maximum allos that for drinking water standards. Organic chemicals for which maximum allowable drinking water standards have been established are shown in Figure 7.3. wable drinking water standards have been established are shown in Figure 7.3.

Figure 7.2Figure 7.2Examples of cyclic Examples of cyclic organic compounds organic compounds (including alicyclic, (including alicyclic, aromatic, and heteraromatic, and heterocyclic compounds).ocyclic compounds).

Figure 7.3Figure 7.3(a) Volatile organic comp(a) Volatile organic comp

ounds that have maxiounds that have maximum contaminant levmum contaminant level (MCL) drinking wael (MCL) drinking water standards.ter standards.

(b) Some synthetic organi(b) Some synthetic organic chemicals for which c chemicals for which maximum contaminanmaximum contaminant levels (MCLs) have bt levels (MCLs) have been established.een established.

Figure 7.3Figure 7.3(continued).(continued).

The types of reactions: biological transformations, chemical hydrolysis, oxidaThe types of reactions: biological transformations, chemical hydrolysis, oxidation/reduction, photodegradation, volatilization. sorption, and bioconcentratition/reduction, photodegradation, volatilization. sorption, and bioconcentration are among the important reactions that organic chemicals undergo in naton are among the important reactions that organic chemicals undergo in natural waters.ural waters.

7.2.1 Biological Transformations7.2.1 Biological Transformations

Biological transformations refer to the microbially mediated transformation Biological transformations refer to the microbially mediated transformation of organic chemicals, often the predominant decay pathway in natural waterof organic chemicals, often the predominant decay pathway in natural waters. It may occur under aerobic or anaerobic conditions, by bacteria, algae, or fs. It may occur under aerobic or anaerobic conditions, by bacteria, algae, or fungi, and by an array of mechanisms (dealkylation, ring cleavage, dehalogenungi, and by an array of mechanisms (dealkylation, ring cleavage, dehalogenation, etc.). It can be an intracellular or extracellunar enzyme transformation.ation, etc.). It can be an intracellular or extracellunar enzyme transformation.

The term "biodegradation" is used synonymously with "biotransformation," The term "biodegradation" is used synonymously with "biotransformation," but some researchers reserve "biodegradation" only for oxidation reactions tbut some researchers reserve "biodegradation" only for oxidation reactions that break down the chemical. Reactions that go all the way to COhat break down the chemical. Reactions that go all the way to CO22 and H and H22O aO are referred to as "mineralization." In the broadest sense, "biotransformatiore referred to as "mineralization." In the broadest sense, "biotransformation" refers to any microbially mediated reaction that changes the organic chemn" refers to any microbially mediated reaction that changes the organic chemical. ical.

7.2 ORGANICS REACTIONS

The term "secondary substrate utilization" refers to the utilization of The term "secondary substrate utilization" refers to the utilization of organic chemicals at low concentrations (less than the concentration reorganic chemicals at low concentrations (less than the concentration required for growth) in the presence of one or more primary substrates tquired for growth) in the presence of one or more primary substrates that are used as carbon and energy sources. "Co-metabolism" refers to hat are used as carbon and energy sources. "Co-metabolism" refers to the transformation of a substrate that cannot be used as a sole carbon the transformation of a substrate that cannot be used as a sole carbon or energy source but can be degraded in the presence of other substrator energy source but can be degraded in the presence of other substrates. es.

Many toxic organic reactions in natural waters are microbially mediatMany toxic organic reactions in natural waters are microbially mediated with both bacteria and fungi degrading a wade variety of pesticides. ed with both bacteria and fungi degrading a wade variety of pesticides. Dehalogenation, dealkylation, hydrolysis, oxidation, reduction, tong clDehalogenation, dealkylation, hydrolysis, oxidation, reduction, tong cleavage, and condensation reactions are all known to occur either metaeavage, and condensation reactions are all known to occur either metabolically or via co-metabolism (see Table 7.1). bolically or via co-metabolism (see Table 7.1).

Several bacterial genera are known that are capable of utilizing certaiSeveral bacterial genera are known that are capable of utilizing certain organics as the sole carbon, energy, or nitrogen source. n organics as the sole carbon, energy, or nitrogen source. PseudomonasPseudomonas (with 2,4-D and paraquat), (with 2,4-D and paraquat), NocardiaNocardia (with dalapon and propanil), and (with dalapon and propanil), and AspergillusAspergillus species (with trifluralin and picloram) are poignant exampl species (with trifluralin and picloram) are poignant examples.es.

Table 7.1 Biological Transformations Common in the Aquatic/Terrestrial Environment

It is convenient when possible to express rate expressions for organic transfIt is convenient when possible to express rate expressions for organic transformations as pseudo-first-order-reactions, such as equation (1) below. The ormations as pseudo-first-order-reactions, such as equation (1) below. The reaction rate expression is thenreaction rate expression is then

(1)(1)

where where CC is the toxic organic concentration in solution and is the toxic organic concentration in solution and kkbb is the pseudo-f is the pseudo-first-order biotransformation rate constant. irst-order biotransformation rate constant. Table 7.2 is a summary of pseudo-first-order and second-order rate constaTable 7.2 is a summary of pseudo-first-order and second-order rate constants nts kkbb for the disappearance of toxic organics from natural waters and grou for the disappearance of toxic organics from natural waters and groundwater via biotransformation.ndwater via biotransformation.The actual microbial biotransformation rate follows the Monod or MichaelThe actual microbial biotransformation rate follows the Monod or Michaelis-Menton enzyme kinetics expression, whereis-Menton enzyme kinetics expression, where

(2)(2)

Where: Where: kkbb = pseudo-first-order biological transformation rate constant,T = pseudo-first-order biological transformation rate constant,T -1-1; ; μμ = = maximum growth rate, Tmaximum growth rate, T-1-1; ; XX = viable microbial biomass concentratio = viable microbial biomass concentration, M Ln, M L-3-3; ; YY = cell yield, microbial cell conc yield/ organic conc utilized; = cell yield, microbial cell conc yield/ organic conc utilized; KKMM = Michaelis half saturation constant, M L= Michaelis half saturation constant, M L -3-3..

Table 7.2 Selected Biotransfor-mation Rate Constants.

Under typical environmental conditions, the concentration of dissolved organics (Under typical environmental conditions, the concentration of dissolved organics (CC < < 10 10 μμg Lg L-1-1) is less than that of the Michaelis half-saturation constant () is less than that of the Michaelis half-saturation constant (KKM M ≈ 0.1-10 ≈ 0.1-10 mg Lmg L--

11). Therefore the equation becomes). Therefore the equation becomes

(3a)(3a)

where kwhere kbb`̀ = = μμ/Y/YKKMM. This is essentially second-order biotransformation kinetics. It is fir. This is essentially second-order biotransformation kinetics. It is fir

st order in bacteria biomass (st order in bacteria biomass (XX) and first order in chemical concentration () and first order in chemical concentration (CC). ). Sometimes organic chemicals that are adsorbed to suspended particulate matter are bSometimes organic chemicals that are adsorbed to suspended particulate matter are biodegraded in addition to soluble chemical. Equation (3a) must be rewritten in terms iodegraded in addition to soluble chemical. Equation (3a) must be rewritten in terms of both dissolved and adsorbed chemical concentrationsof both dissolved and adsorbed chemical concentrations

(3b)(3b)

where where CCTT is the total whole water chemical concentration, is the total whole water chemical concentration, CC is the dissolved phase con is the dissolved phase concentration. and centration. and CCpp is the particulate adsorbed concentration. is the particulate adsorbed concentration.If the substrate concentration If the substrate concentration CC is very large such that is very large such that CC >> >> KKMM (not likely in natural (not likely in natural waters), then the microorganisms are growing exponentially, and the rate expression iwaters), then the microorganisms are growing exponentially, and the rate expression in equation (2) reduces ton equation (2) reduces to

(4)(4)

which is a zero-order rate expression in which is a zero-order rate expression in CC and first-order in and first-order in XX..

Biotransformation experiments are conducted by batch, column, and cBiotransformation experiments are conducted by batch, column, and chemostat experimental methods. Other fate pathways (photolysis, hydhemostat experimental methods. Other fate pathways (photolysis, hydrolysis, volatilization) must be accounted for in order to correctly evalrolysis, volatilization) must be accounted for in order to correctly evaluate the effects of biodegradation.uate the effects of biodegradation.

It is incumbent on the fate modeler to understand the range of breakdIt is incumbent on the fate modeler to understand the range of breakdown products (metabolites) in biological transformation reactions. Metown products (metabolites) in biological transformation reactions. Metabolites can be as toxic (or more toxic) than the parent compound. abolites can be as toxic (or more toxic) than the parent compound.

Following all the metabolites and pathways in the biological degradatiFollowing all the metabolites and pathways in the biological degradation of organic chemicals can be complicated. Polychlorinated biphenyls on of organic chemicals can be complicated. Polychlorinated biphenyls (PCBs) are mixtures of many isomers - the total number of different or(PCBs) are mixtures of many isomers - the total number of different organic chemicals is 209 congeners. ganic chemicals is 209 congeners.

Figure 7.3b shows the structures, where Figure 7.3b shows the structures, where xx and and yy represent the combina represent the combinations of chlorine atoms (one to five) at different positions on the biphentions of chlorine atoms (one to five) at different positions on the biphenyl rings. Each congener has distinct properties that result in a different yl rings. Each congener has distinct properties that result in a different reactivity than the others. Both the reactivity than the others. Both the raterate of the biological transformatio of the biological transformation and the n and the pathwaypathway can be different far each of the congeners. can be different far each of the congeners.

There are several basic types of biodegradation experiments. Natural wThere are several basic types of biodegradation experiments. Natural water samples from lakes or rivers can have organic toxicant added to thater samples from lakes or rivers can have organic toxicant added to them in batch experiments. Disappearance of toxicant is monitored.em in batch experiments. Disappearance of toxicant is monitored.

Organic xenobiotic chemicals can be added to a water-sediment sample Organic xenobiotic chemicals can be added to a water-sediment sample to simulate to simulate in situin situ conditions, or a contaminated sediment sample alone conditions, or a contaminated sediment sample alone may be used with or without a spiked addition. Primary sewage, activatmay be used with or without a spiked addition. Primary sewage, activated sludge, or digester sludge may be used as a seed to test degradability ed sludge, or digester sludge may be used as a seed to test degradability and measure xenobiotic disappearance. and measure xenobiotic disappearance.

Radiolabeled organic chemicals can be used to estimate metabolic degrRadiolabeled organic chemicals can be used to estimate metabolic degradation (mineralization) by measuring COadation (mineralization) by measuring CO22 off-gas and synthesis into bi off-gas and synthesis into biomass. These experiments are called heterotrophic uptake experiments.omass. These experiments are called heterotrophic uptake experiments.

The organic chemical may be added in minute concentrations to simulaThe organic chemical may be added in minute concentrations to simulate exposure in natural conditions, or it may be the sole carbon source to te exposure in natural conditions, or it may be the sole carbon source to the culture to determine whether transformation reactions are possible.the culture to determine whether transformation reactions are possible.

Biodegradation is affected by numerous factors that influence Biodegradation is affected by numerous factors that influence biological growth:biological growth:

Temperature:Temperature: effects on biodegradation of toxics are similar to those on effects on biodegradation of toxics are similar to those on biochemical oxygen demand (BOD) using an Arrhenius-type biochemical oxygen demand (BOD) using an Arrhenius-type relationship.relationship.

Nutrients:Nutrients: are necessary for growth and often limit growth rate. Other are necessary for growth and often limit growth rate. Other organic compounds may serve as a primary substrate so that the organic compounds may serve as a primary substrate so that the chemical of interest is utilized via co-metabolism or as a secondary chemical of interest is utilized via co-metabolism or as a secondary substrate.substrate.

Acclimation:Acclimation: is necessary for expressing repressed (induced) enzymes or is necessary for expressing repressed (induced) enzymes or fostering those organisms that can degrade the toxicant through fostering those organisms that can degrade the toxicant through gradual exposure to the toxicant over time. A shock load of toxicant gradual exposure to the toxicant over time. A shock load of toxicant may kill a culture that would otherwise adapt if gradually exposed.may kill a culture that would otherwise adapt if gradually exposed.

Population density or biomass concentration:Population density or biomass concentration: organisms must be organisms must be present in large enough numbers to significantly degrade the toxicant present in large enough numbers to significantly degrade the toxicant (a lag often occurs if the organisms are too few).(a lag often occurs if the organisms are too few).

7.2.2 Chemical Oxidation7.2.2 Chemical Oxidation

Chemical oxidation takes place in the presence of dissolved oxygen in natuChemical oxidation takes place in the presence of dissolved oxygen in natural waters. Oxygen is reduced and the organic chemical is oxidized, but the ral waters. Oxygen is reduced and the organic chemical is oxidized, but the reaction can be slow. Alternatively, chemical oxidation can be triggered by reaction can be slow. Alternatively, chemical oxidation can be triggered by photochemical transients that may have considerable oxidizing power but lphotochemical transients that may have considerable oxidizing power but low concentrations. ow concentrations.

Oxidants such as peroxyl radicals ROO·, alkoxy radicals RO·, hydrogen pOxidants such as peroxyl radicals ROO·, alkoxy radicals RO·, hydrogen peroxide Heroxide H22OO22, hydrokyl radicals ·OH, singlet oxygen O, hydrokyl radicals ·OH, singlet oxygen O22, and solvated elect, and solvated electrons are produced in low concentrations and react quickly in natural waterons are produced in low concentrations and react quickly in natural waters. Because of their large oxidizing power, they may react with a variety of rs. Because of their large oxidizing power, they may react with a variety of trace organics in solution, but each transient reacts rather specifically with trace organics in solution, but each transient reacts rather specifically with certain trace organic moieties. certain trace organic moieties.

It is better to determine the relevant oxidant chemistry and to measure the It is better to determine the relevant oxidant chemistry and to measure the oxidant concentration when possible. Since the transient chemical oxidants oxidant concentration when possible. Since the transient chemical oxidants are often generated photochemically, light-absorbing chromophores, such are often generated photochemically, light-absorbing chromophores, such as humic and fulvic acids and algal pigments, and sunlight intensity will inas humic and fulvic acids and algal pigments, and sunlight intensity will influence oxidation rates.fluence oxidation rates.

Alkyl peroxyl radicals ( 1 × 10∼Alkyl peroxyl radicals ( 1 × 10∼ -9-9 M in sunlit natural waters) react rapidly M in sunlit natural waters) react rapidly with phenols and amines in natural waters to form acids and aromatic radwith phenols and amines in natural waters to form acids and aromatic radicals:icals:

Singlet oxygen reacts specifically with olefins:Singlet oxygen reacts specifically with olefins:

Singlet oxygen concentrations in sunlit natural waters are on the order of Singlet oxygen concentrations in sunlit natural waters are on the order of 11×10×10-12 -12 M. All of these oxidation reactions may be assumed to be second-orM. All of these oxidation reactions may be assumed to be second-order reactions:der reactions:

(5)(5)

where where CC is the organic concentration and Ox is the oxidant concentration. is the organic concentration and Ox is the oxidant concentration. Table 7.3: the second-order rate constants for chemical oxidation of selectTable 7.3: the second-order rate constants for chemical oxidation of selected priority organic chemicals with singlet oxygen and alkyl peroxyl radicaed priority organic chemicals with singlet oxygen and alkyl peroxyl radicals.ls.

Table 7.3 Table 7.3 Second-Order Reaction Rate Constants for Chemical OSecond-Order Reaction Rate Constants for Chemical Oxidation: Summary Table of Oxidation Data with Singlet Oxygen xidation: Summary Table of Oxidation Data with Singlet Oxygen

OO22 and Alkyl Peroxyl Radicals ROO and Alkyl Peroxyl Radicals ROO∙∙

Free radical oxidation requires a chain or series of reactions involving Free radical oxidation requires a chain or series of reactions involving an initiation step, propagation, and subsequent termination. We will an initiation step, propagation, and subsequent termination. We will illustrate the free radical reaction using the alkyl peroxyl radical ROOillustrate the free radical reaction using the alkyl peroxyl radical ROO· as an example.· as an example.

The chemical is represented as an arbitrary organic, RH. A-B is the initThe chemical is represented as an arbitrary organic, RH. A-B is the initiator, which is any free radical source including peroxides, Hiator, which is any free radical source including peroxides, H22OO22, metal , metal salts, and auto compounds. Investigators have utilized a commercially asalts, and auto compounds. Investigators have utilized a commercially available azo initiator to estimate the reactivity of pesticides to ROO· in vailable azo initiator to estimate the reactivity of pesticides to ROO· in natural waters. natural waters.

If no initiators are available in the water, then reaction (c) represents thIf no initiators are available in the water, then reaction (c) represents the probable oxidation pathway, a slow reaction with dissolved oxygen. Oe probable oxidation pathway, a slow reaction with dissolved oxygen. Otherwise steps (a) and (b) lead to peroxide formation, step (d). Once the therwise steps (a) and (b) lead to peroxide formation, step (d). Once the highly reactive peroxide radical is formed, it continues to react with the highly reactive peroxide radical is formed, it continues to react with the organic chemical, RH, and regenerates another free radical, R', as giveorganic chemical, RH, and regenerates another free radical, R', as given in reaction (e). n in reaction (e).

This step may be repeated thousands of times for every photon of light This step may be repeated thousands of times for every photon of light absorbed. Chance collisions between free radicals can terminate the reaabsorbed. Chance collisions between free radicals can terminate the reaction, reactions (f), (g), and (h). At the low pollutant concentrations fouction, reactions (f), (g), and (h). At the low pollutant concentrations found in natural waters, reaction (f) is the most likely termination step. Hynd in natural waters, reaction (f) is the most likely termination step. Hydrogen peroxide may also be formed, especially when natural dissolved drogen peroxide may also be formed, especially when natural dissolved organic matter (DOC) and humates are present. Horganic matter (DOC) and humates are present. H22OO22 is a powerful oxi is a powerful oxidant in natural waters.dant in natural waters.

If the initiation step is rapid, then the rate-limiting step is the rate of If the initiation step is rapid, then the rate-limiting step is the rate of oxidation of the organic in reaction (e):oxidation of the organic in reaction (e):

(6)(6)

Provided that reaction (d) is more raped than reaction (e), the rate of Provided that reaction (d) is more raped than reaction (e), the rate of peroxide formation isperoxide formation is

(7)(7)

and assuming steady state, the rate of radical be equal to the rate of and assuming steady state, the rate of radical be equal to the rate of termination:termination:

(8), (9)(8), (9)

Substituting equation (9) into equation (6), we find the final reaction rate Substituting equation (9) into equation (6), we find the final reaction rate for the oxidation of the organic chemical isfor the oxidation of the organic chemical is

(10)(10)

The rate of reaction is a pseudo-first-order reaction, where The rate of reaction is a pseudo-first-order reaction, where kk33 is the overal is the overall reaction rate constant which is a function of l reaction rate constant which is a function of rrff, the rate of peroxide forma, the rate of peroxide formation. If the rate of peroxide formation is relatively constant (as expected in tion. If the rate of peroxide formation is relatively constant (as expected in natural waters), then the free radical oxidation of the toxic organic can be natural waters), then the free radical oxidation of the toxic organic can be computed as a pseudo-first-order reaction.computed as a pseudo-first-order reaction.

First-order oxidations of pesticides and organic chemicals have been reporFirst-order oxidations of pesticides and organic chemicals have been reported in natural waters. However, these oxidations are often microbially meted in natural waters. However, these oxidations are often microbially mediated. Strictly chemical free radical oxidation of toxic organics in natural diated. Strictly chemical free radical oxidation of toxic organics in natural waters remains important for a few classes of compounds. Free radical oxiwaters remains important for a few classes of compounds. Free radical oxidation is often a part of the photolytic cycle of reactions in natural waters dation is often a part of the photolytic cycle of reactions in natural waters and atmospheric waters.and atmospheric waters.

Oxidations of organic chemicals by OOxidations of organic chemicals by O2(aq)2(aq) is generally slow, but it can be m is generally slow, but it can be mediated by microorganisms. Cytochrome P450 monooxygenase is a well-stediated by microorganisms. Cytochrome P450 monooxygenase is a well-studied enzyme with an iron porphyrin active site. Methanotrophs and otheudied enzyme with an iron porphyrin active site. Methanotrophs and other organisms can use this pathway to oxidize organics in natural waters, a tr organisms can use this pathway to oxidize organics in natural waters, a type of biological transformation.ype of biological transformation.

7.2.3 Redox Reactions7.2.3 Redox Reactions

Electron acceptors such as oxygen, nitrate, and sulfate can be reduced in Electron acceptors such as oxygen, nitrate, and sulfate can be reduced in natural waters while oxidizing trace organic contaminants. Oxidation reacnatural waters while oxidizing trace organic contaminants. Oxidation reactions of toxic organic chemicals are especially important in sediments and tions of toxic organic chemicals are especially important in sediments and groundwater, where conditions may be anoxic or anaerobic. The general sgroundwater, where conditions may be anoxic or anaerobic. The general scheme for utilization of electron acceptors in natural waters fort lows thercheme for utilization of electron acceptors in natural waters fort lows thermodynamics (Table 7.4).modynamics (Table 7.4).

The sequence of electron acceptors is approximately:The sequence of electron acceptors is approximately:

The organic chemical in Table 7.4 is represented as a simple carbohydrate The organic chemical in Table 7.4 is represented as a simple carbohydrate (CH(CH22O such as glucose CO such as glucose C66HH1212OO66) but other organics may be important red) but other organics may be important reductants in natural waters and groundwaters.uctants in natural waters and groundwaters.

Strict chemical reduction reactions that do not involve a biological catalyst (aStrict chemical reduction reactions that do not involve a biological catalyst (abiotic reactions) are common in groundwater but less important in natural wabiotic reactions) are common in groundwater but less important in natural waters and sediments, where a great complement of enzymes are available for reters and sediments, where a great complement of enzymes are available for redox transformations. In groundwater, Hdox transformations. In groundwater, H22S is a common reductant. It can reduS is a common reductant. It can reduce nitrobenzene to aniline in homogeneous reactions.ce nitrobenzene to aniline in homogeneous reactions.

Table 7.4 Redox Reactions in a Closed Oxidant System at 25ºC and pH 7.0 and Their Free Energies of Reaction.

Likewise, humic substances and their decay products (natural organic mLikewise, humic substances and their decay products (natural organic matter, NOM) are good reductants in homogeneous systems. atter, NOM) are good reductants in homogeneous systems. Figure 7.4 is a structure-activity relationship demonstrating that, in homFigure 7.4 is a structure-activity relationship demonstrating that, in homogeneous solution, the second-order kinetic rate constant ogeneous solution, the second-order kinetic rate constant kkABAB is directly p is directly proportional to the one-electron reduction potential of the redox couple.roportional to the one-electron reduction potential of the redox couple.

(11)(11)

where Hwhere H22X is the reductant. X is the reductant. Schwarzenbach et al. have shown that, in the case of juglone, it is not the Schwarzenbach et al. have shown that, in the case of juglone, it is not the diprotic dihydroquinone Hdiprotic dihydroquinone H22JUG that is the reactant with nitroaromaticJUG that is the reactant with nitroaromatics, but rather the anions HJUGs, but rather the anions HJUG-- and JUG and JUG2-2-. Reductants in natural waters . Reductants in natural waters include quinone, juglone (oak tree exudate), lawsone, and Fe-porphyrininclude quinone, juglone (oak tree exudate), lawsone, and Fe-porphyrins. s. The reduction of nitroaromatic compounds in natural waters and soil wThe reduction of nitroaromatic compounds in natural waters and soil water may be viewed as an electron transfer system that is mediated by Nater may be viewed as an electron transfer system that is mediated by NOM or its constituents. OM or its constituents.

Figure 7.4

Liner free-energy relationship between second-order rate constant and the one electron potential for reduction of substituted nitrobenzenes with natural organic matter (Juglone). From Schwarzenbach, et al..

Natural organic matter contains electron transfer mediators such as quinones, hydroquinones, and Fe-porphyrNatural organic matter contains electron transfer mediators such as quinones, hydroquinones, and Fe-porphyrin-like substances.in-like substances.

These mediators are reactants that are regenerated in the process by the bulk reductant, which is in excess.These mediators are reactants that are regenerated in the process by the bulk reductant, which is in excess.

One can add half-reactions of xenobiotic organic oxidations with standard reductants in sediments and groundOne can add half-reactions of xenobiotic organic oxidations with standard reductants in sediments and groundwater (Hwater (H22S, FeS, Fe2+2+, and CH, and CH44) to determine if the reaction is favored thermodynamically (Table 7.5). In the absenc) to determine if the reaction is favored thermodynamically (Table 7.5). In the absence of bacteria, the reaction may be slow. e of bacteria, the reaction may be slow.

Table 7.5

Redox Half-Reactions Pertinent in Wastewater, Groundwater, and Sediment Reactions

Table 7.5 (continued)

7.2.4 Photochemical Transformation Reactions7.2.4 Photochemical Transformation Reactions

Direct photolysis, a light-initiated transformation reaction, is a Direct photolysis, a light-initiated transformation reaction, is a function of the incident energy on the molecule and the quantum yield function of the incident energy on the molecule and the quantum yield of the chemical.of the chemical.

When light strikes the pollutant molecule, the energy content of the When light strikes the pollutant molecule, the energy content of the molecule is increased and the molecule reaches an excited electron molecule is increased and the molecule reaches an excited electron state. This excited state is unstable and the molecule reaches a normal state. This excited state is unstable and the molecule reaches a normal (lower) energy level by one of two paths: (lower) energy level by one of two paths: - (1) it loses its "extra" energy through energy emission, that is, - (1) it loses its "extra" energy through energy emission, that is, fluorescence or phosphorescence; fluorescence or phosphorescence; - (2) it is converted to a different molecule through the new electron - (2) it is converted to a different molecule through the new electron distribution that existed in the excited state. Usually the organic distribution that existed in the excited state. Usually the organic chemical is oxidized.chemical is oxidized.

Photolysis may be direct or indirect. Indirect photolysis occurs when Photolysis may be direct or indirect. Indirect photolysis occurs when an intermediary molecule becomes energized, which then reacts with an intermediary molecule becomes energized, which then reacts with the chemical of interest.the chemical of interest.

The basic equation for direct photolysis is of the form:The basic equation for direct photolysis is of the form:

(12)(12)

Where Where CC is the concentration of organic chemical, and is the concentration of organic chemical, and kkpp is the rate constant for ph is the rate constant for photolysis. Photo1ysis rate constants can be measured in the yield with sunlight or unotolysis. Photo1ysis rate constants can be measured in the yield with sunlight or under laboratory conditions. der laboratory conditions. The first-order rate constant, The first-order rate constant, kkpp can be estimated directly: can be estimated directly:

(13)(13)

where where kkpp = photolysis rate constant, s = photolysis rate constant, s-1-1

JJ = 6.02 × 10 = 6.02 × 1020 20 = conversion constant= conversion constant φφ = quantum yield = quantum yield IIλλ = sunlight intensity at wavelength = sunlight intensity at wavelength λλ, photons cm, photons cm-2-2 s s-1-1

εελλ = molar absorbtivity or molar extinction coefficient at wavelength = molar absorbtivity or molar extinction coefficient at wavelength λλ,, molaritymolarity-1-1 cm cm-1-1.. The near-surface photolysis rate constants, quantum yields, and wavelengths at whiThe near-surface photolysis rate constants, quantum yields, and wavelengths at which they were measured are presented in Table 7.6. Photolysis will not be an importach they were measured are presented in Table 7.6. Photolysis will not be an important fate process unless sunlight is absorbed in the visible or near-ultraviolet wavelennt fate process unless sunlight is absorbed in the visible or near-ultraviolet wavelength ranges (above 290 nm) by either the organic chemical or its sensitizing agent.gth ranges (above 290 nm) by either the organic chemical or its sensitizing agent.

The quantum yield is defined byThe quantum yield is defined by

(14)(14)

An einstein is the unit of fight on a molar basis (a quantum or photon is the An einstein is the unit of fight on a molar basis (a quantum or photon is the unit of light on a molecular basis). The quantum yield may be thought of as unit of light on a molecular basis). The quantum yield may be thought of as the efficiency of photoreaction. Incoming radiation is measured in units of ethe efficiency of photoreaction. Incoming radiation is measured in units of energy per unit area per time (e g., cal cmnergy per unit area per time (e g., cal cm -2-2 s s-1-1). The incident light in units of e). The incident light in units of einsteins cminsteins cm-2-2 s s-1 -1 nmnm-1-1 can be converted to watts cm can be converted to watts cm-2-2 nm nm-1-1 by multiplying by th by multiplying by the wavelength (nm) and 3.03 × 10e wavelength (nm) and 3.03 × 103939..The intensity of light varies over the depth of the water column and may be The intensity of light varies over the depth of the water column and may be related by related by

(15)(15)

wherewhere I Izz is the intensity at depth z, I is the intensity at depth z, I00 is the intensity at the surface, and is the intensity at the surface, and KKee is is an extinction coefficient for light disappearance. an extinction coefficient for light disappearance. Light disappearance is caused by the scattering of light by reflection off partLight disappearance is caused by the scattering of light by reflection off particulate matter, and absorption by any molecule. Absorbed energy can be coiculate matter, and absorption by any molecule. Absorbed energy can be converted to heat or can cause photolysis. Light disappearance is a function of nverted to heat or can cause photolysis. Light disappearance is a function of wavelength and water quality (e.g., color, suspended solids, dissolved organiwavelength and water quality (e.g., color, suspended solids, dissolved organic carbon).c carbon).

Indirect or sensitized photolysis occurs when a nontarget molecule is traIndirect or sensitized photolysis occurs when a nontarget molecule is transformed directly by light, which, in turn, transmits its energy to the polnsformed directly by light, which, in turn, transmits its energy to the pollutant molecule. Changes in the molecule then occur as a result of the inclutant molecule. Changes in the molecule then occur as a result of the increased energy content.reased energy content.

The kinetic equation for indirect photolysis is The kinetic equation for indirect photolysis is

(16)(16)

where where kk22 is the indirect photolysis rate constant, X is the concentration of is the indirect photolysis rate constant, X is the concentration of the nontarget intermediary, and the nontarget intermediary, and kkpp is the overall pseudo-first-order rate is the overall pseudo-first-order rate constant for sensitized photolysis. constant for sensitized photolysis. The important role of inducing agents (e.g., algae exudates and nitrate) The important role of inducing agents (e.g., algae exudates and nitrate) has been demonstrated. has been demonstrated.

Inorganics, especially iron, play an important role in the photochemical Inorganics, especially iron, play an important role in the photochemical cycle in natural waters. Hydrogen peroxide, a common transient oxidancycle in natural waters. Hydrogen peroxide, a common transient oxidant, is a natural source of hydroxyl radicals in rivers, oceans, and atmospht, is a natural source of hydroxyl radicals in rivers, oceans, and atmospheric water droplets. eric water droplets.

Direct photolysis of HDirect photolysis of H22OO22 produces ·OH, but this pathway is relatively unim produces ·OH, but this pathway is relatively unimportant because Hportant because H22OO22 does not absorb visible light very strongly. The import does not absorb visible light very strongly. The important source of ·OH involves hydrogen peroxide and iron (II) in a photo-Fentoant source of ·OH involves hydrogen peroxide and iron (II) in a photo-Fenton reaction.n reaction.

Hydroxyl radicals are a highly reactive and important transient oxidant of a Hydroxyl radicals are a highly reactive and important transient oxidant of a wide range of organic xenobiotics in solution. They can be generated by direwide range of organic xenobiotics in solution. They can be generated by direct photolysis of nitrate and nitrite in natural waters, or they can be generatect photolysis of nitrate and nitrite in natural waters, or they can be generated from Hd from H22OO22 in the reaction shown above. Nitrobenzene, anisole, and several in the reaction shown above. Nitrobenzene, anisole, and several pesticides have been shown to be oxidized by hydroxyl radicals in natural wpesticides have been shown to be oxidized by hydroxyl radicals in natural waters. aters.

7.2.5 Chemical Hydrolysis7.2.5 Chemical Hydrolysis Chemical hydrolysis is that fate pathway by which an organic chemical reacts Chemical hydrolysis is that fate pathway by which an organic chemical reacts with water. Particularly, a nucleophile (hydroxide, water, or hydronium ions), with water. Particularly, a nucleophile (hydroxide, water, or hydronium ions), N, displaces a leaving group, X, as shown.N, displaces a leaving group, X, as shown.

Hydrolysis does not include acid-base, hydration, addition, or elimination reacHydrolysis does not include acid-base, hydration, addition, or elimination reactions. The hydrolysis reaction consists of the cleaving of a molecular bond and tions. The hydrolysis reaction consists of the cleaving of a molecular bond and the formation of a new bond with components of the water molecule (Hthe formation of a new bond with components of the water molecule (H++, OH, OH--). ). It is often a strong function of pH (see Figure 7.5).It is often a strong function of pH (see Figure 7.5).

Three examples of a hydrolysis reaction are presented below.Three examples of a hydrolysis reaction are presented below.

Types of compounds that are generally susceptible to hydrolysis are:Types of compounds that are generally susceptible to hydrolysis are:- Alkyl halides- Alkyl halides- Amides- Amides- Amines- Amines- Carbamates- Carbamates- Carboxylic acid esters- Carboxylic acid esters- Epoxides- Epoxides- Nitriles- Nitriles- Phosphonic acrid esters- Phosphonic acrid esters- Phosphoric acid esters- Phosphoric acid esters- Sulfonic acid esters- Sulfonic acid esters- Sulfuric acid esters- Sulfuric acid esters

The kinetic expression for hydrolysis isThe kinetic expression for hydrolysis is

A summary of these data is presented in Table 7.7.A summary of these data is presented in Table 7.7.

Hydrolysis experiments usually involve fixing the pH at some target value, eHydrolysis experiments usually involve fixing the pH at some target value, eliminating other fate processes, and measuring toxicant disappearance over liminating other fate processes, and measuring toxicant disappearance over time. A sterile sample in a glass tube, filled to avoid a gas space, and kept in time. A sterile sample in a glass tube, filled to avoid a gas space, and kept in the dark eliminates the other fate pathways. In order to evaluate the dark eliminates the other fate pathways. In order to evaluate kkaa and and kkbb, s, several non-neutral pH experiments must be conducted as depicted in Figure everal non-neutral pH experiments must be conducted as depicted in Figure 7.5.7.5.

Often, the hydrolysis reaction rate expression in equation (17) is simplified tOften, the hydrolysis reaction rate expression in equation (17) is simplified to a pseudo-first-order reaction rate expression at a given pH and temperatuo a pseudo-first-order reaction rate expression at a given pH and temperature (Table 7.7, 298 K and pH 7).re (Table 7.7, 298 K and pH 7).

(18)(18)

where where kkhh = = kkbb [OH [OH--] + ] + kkaa [H [H++] + ] + kknn and and kkhh is the pseudo-first-order hydrolysis is the pseudo-first-order hydrolysis rate constant, Trate constant, T-1-1; ; kkbb is the base-catalyzed rate constant, molarity is the base-catalyzed rate constant, molarity-1-1 T T-1-1; ; kkaa is t is the acid-catalyzed rate, polarityhe acid-catalyzed rate, polarity-1-1 T T-1-1 ; and ; and kknn is the neutral rate constant, T is the neutral rate constant, T-1-1..

Table 7.7Table 7.7

Selected Chemical Selected Chemical Hydrolysis Rate Hydrolysis Rate Constants, at 298 Constants, at 298 K and pH 7.K and pH 7.

Figure 7.5Figure 7.5

Effect of pH Effect of pH on hydrolysis on hydrolysis rate rate constants.constants.

7.2.6 Volatilization/Gas Transfer7.2.6 Volatilization/Gas Transfer

The transfer of pollutants from water to air or from air to water is an The transfer of pollutants from water to air or from air to water is an important fate process to consider when modeling organic chemicals. important fate process to consider when modeling organic chemicals. Volatilization is a transfer process; it does not result in the breakdown Volatilization is a transfer process; it does not result in the breakdown of a substance, only its movement from the liquid to gas phase, or vice of a substance, only its movement from the liquid to gas phase, or vice versa. versa. Gas transfer of pollutants is analogous to the reaeration of oxygen in Gas transfer of pollutants is analogous to the reaeration of oxygen in surface waters and will be related to known oxygen transfer rates. The surface waters and will be related to known oxygen transfer rates. The rate of volatilization is related to the site of the molecule (as measured rate of volatilization is related to the site of the molecule (as measured by the molecular weight).by the molecular weight).

Gas transfer models are often based on two-film theory (figure 7.6). Gas transfer models are often based on two-film theory (figure 7.6). Two-film theory was derived by Lewis and Whitman in 1923. Mass Two-film theory was derived by Lewis and Whitman in 1923. Mass transfer is governed by molecular diffusion through a stagnant liquid transfer is governed by molecular diffusion through a stagnant liquid and gas film. Mass moves from areas of high concentration to areas of and gas film. Mass moves from areas of high concentration to areas of low concentration. Transfer can be limited at the gas film or the liquid low concentration. Transfer can be limited at the gas film or the liquid film. film. Oxygen, for example, is controlled by the liquid-film resistance. Oxygen, for example, is controlled by the liquid-film resistance. Nitrogen gas, although approximately four times more abundant in Nitrogen gas, although approximately four times more abundant in the atmosphere than oxygen, has a greater liquid-film resistance than the atmosphere than oxygen, has a greater liquid-film resistance than oxygenoxygen..

Volatilization, as described by two-film theory, is a function of Henry`s constaVolatilization, as described by two-film theory, is a function of Henry`s constant, the gas-film resistance, and the liquid-film resistance. The film resistance dnt, the gas-film resistance, and the liquid-film resistance. The film resistance depends on diffusion and mixing. Henry's constant, epends on diffusion and mixing. Henry's constant, HH, is a ratio of a chemical's , is a ratio of a chemical's vapor pressure to its solubility. It is a thermodynamic radio of the fugacity of tvapor pressure to its solubility. It is a thermodynamic radio of the fugacity of the chemical (escaping tendency from air and water).he chemical (escaping tendency from air and water).

(19)(19)

where where ppgg is the partial pressure of the chemical of interest in the gas phase, and is the partial pressure of the chemical of interest in the gas phase, and CCslsl is its saturation solubility. is its saturation solubility. Henry's constant can be "dimensionless" [mg/L (in air)/mg/L (in water)] or it Henry's constant can be "dimensionless" [mg/L (in air)/mg/L (in water)] or it has units of atm mhas units of atm m33 mol mol-1-1..

Figure 7.6

Two-film theory of gas-liquid interchange.

The value of The value of HH can be used to develop simplifying assumptions for modeling volati can be used to develop simplifying assumptions for modeling volatilization. If either the liquid-film or the gas-film controls - that is, one resistance is lization. If either the liquid-film or the gas-film controls - that is, one resistance is much greater than the other - the lesser resistance can be neglected. much greater than the other - the lesser resistance can be neglected. The flux of contaminants across the boundary can be modeled by Fick's first law oThe flux of contaminants across the boundary can be modeled by Fick's first law of diffusion at equilibrium,f diffusion at equilibrium,

(20)(20)

where where D D is the molecular diffusion coefficient and is the molecular diffusion coefficient and dC/dxdC/dx is the concentration gradi is the concentration gradient in either the gas or liquid phase. ent in either the gas or liquid phase. If we consider the molecular diffusion to occur through a thin stagnant film, the mIf we consider the molecular diffusion to occur through a thin stagnant film, the mass flux is thenass flux is then

(21)(21)

where k = where k = DD//ΔΔzz in which in which ΔΔzz is the film thickness and k is the mass transfer coeffici is the film thickness and k is the mass transfer coefficient with units of LTent with units of LT-1-1. . At steady state, the flux through both films of Figure 7.6 must be equal:At steady state, the flux through both films of Figure 7.6 must be equal:

(22)(22)

If Henry's law applies exactly at the interface, we can express the If Henry's law applies exactly at the interface, we can express the concentrations in terms of bulk phase concentrations, which are measurable by concentrations in terms of bulk phase concentrations, which are measurable by substitution below:substitution below:

(23)(23)

(24)(24)

(25)(25)

By rearranging equation (25), we can solve for By rearranging equation (25), we can solve for NN in terms of bulk phase in terms of bulk phase concentration, mass transfer coefficients for each phase, and Henry's constant:concentration, mass transfer coefficients for each phase, and Henry's constant:

(26)(26)

where where KKLL is the overall mass transfer coefficient derived for expression of the is the overall mass transfer coefficient derived for expression of the gas transfer in terms of a liquid phase concentration.gas transfer in terms of a liquid phase concentration.

(27)(27)

We may think of the thirst term on the right-hand side of the equation as a liquid-We may think of the thirst term on the right-hand side of the equation as a liquid-film resistance and the second term as a gas phase resistance using an electrical refilm resistance and the second term as a gas phase resistance using an electrical resistance analogy. sistance analogy. We can compare the two resistances to determine if theWe can compare the two resistances to determine if the

(28)(28)

gas phase resistance, gas phase resistance, rrgg, or the liquid phase resistance, , or the liquid phase resistance, rrll, predominates., predominates.Equivalently, we could choose to write the overall mass transfer in terms of the bEquivalently, we could choose to write the overall mass transfer in terms of the buck gas phase concentration.uck gas phase concentration.

(29), (30)(29), (30)

If the gas is soluble, then If the gas is soluble, then HH is small and the gas-film resistance controls mass tran is small and the gas-film resistance controls mass transfer. sfer. In terms of a differential equation, the overall gas transfer: In terms of a differential equation, the overall gas transfer:

(31)(31)

where where CCsatsat = = ppgg//HH, A is the interfacial surface area, and , A is the interfacial surface area, and VV is the volume of the liqui is the volume of the liquid.d.

In streams, In streams, A/VA/V is the reciprocal depth of the water and the equation can be ex is the reciprocal depth of the water and the equation can be expressed aspressed as

(32)(32)

where where ZZ is the mean depth and is the mean depth and kkli li is termed the volatilization rate constant (Tis termed the volatilization rate constant (T-1-1).).Equations (31) and (32) apply for either gas absorption or gas stripping from tEquations (31) and (32) apply for either gas absorption or gas stripping from the water body. It is a reversible process.he water body. It is a reversible process.The mass transfer coefficients are dependent on the hydrodynamic characterisThe mass transfer coefficients are dependent on the hydrodynamic characteristics of the air-water interface and flow regime. For flowing water, we may writtics of the air-water interface and flow regime. For flowing water, we may write e

(33)(33)

where where uu is the mean stream velocity and is the mean stream velocity and ZZ is the mean depth. is the mean depth. For smooth flow (no ripples or waves) and wind speed less than 5 msFor smooth flow (no ripples or waves) and wind speed less than 5 ms-1-1, , 1/K1/Kδδ pre predominates.dominates.

(34), (35)(34), (35)

where where CCDD is the dimensionless drag coefficient, is the dimensionless drag coefficient, WW is the wind speed, and is the wind speed, and vv is th is the kinematic viscosity. e kinematic viscosity.

The transfer term for aerodynamically rough flow with wave is The transfer term for aerodynamically rough flow with wave is

(36)(36)

where where dd is the diameter or amplitude of the waves, is the diameter or amplitude of the waves, uu** is the surface shear velocit is the surface shear velocity and y and αα i is a constant dependent on the physics of the wave properties.s a constant dependent on the physics of the wave properties.The diffusion coefficients in water and air have been related to molecular weightThe diffusion coefficients in water and air have been related to molecular weight

(37)(37)

where where DDll is the diffusivity of the chemical in water and MW is the molecular wei is the diffusivity of the chemical in water and MW is the molecular weight, andght, and

(38)(38)

where where DDgg is the diffusivity of the chemical in air. is the diffusivity of the chemical in air. The mass transfer rate constant, The mass transfer rate constant, kklili, can then be related to the oxygen reaeratio, can then be related to the oxygen reaeration rate, n rate, kkaa, by a ratio of the diffusivity of the chemical to that of oxygen in water:, by a ratio of the diffusivity of the chemical to that of oxygen in water:

(39)(39)

where where DDO2O2 is 2.4 × 10 is 2.4 × 10-5-5 cm cm22 s s-1-1 at 20 at 20 ººC. C.

The reaeration rate, The reaeration rate, kkaa, can be calculated from any of the formulas availab, can be calculated from any of the formulas available. In addition, the overall gas-film transfer rate may be calculated from le. In addition, the overall gas-film transfer rate may be calculated from

(40)(40)

Where Where vvgg is the kinematic viscosity of all (a function of temperature) as pre is the kinematic viscosity of all (a function of temperature) as presented in Table 7.8, Z is the water depth, and W is the wind speed in m ssented in Table 7.8, Z is the water depth, and W is the wind speed in m s -1-1 kkgi gi has units of Thas units of T-1-1..

Solubility, vapor pressure, and Henry's constant data are presented in TabSolubility, vapor pressure, and Henry's constant data are presented in Table 7.9.le 7.9.Dimensionless Henry's constant refer to a concentration ratio of mg/L air Dimensionless Henry's constant refer to a concentration ratio of mg/L air per mg/L in the water phase.per mg/L in the water phase. Yalkowsky measured the solubility of 26 halogenated benzenes at 25 Yalkowsky measured the solubility of 26 halogenated benzenes at 25 ººC anC and developed the following relationship:d developed the following relationship:

(41)(41)

Where Where SSww is solubility (mol L is solubility (mol L-1-1), MP is the melting point (), MP is the melting point (ººC), and C), and KKowow is th is the estimated octanol/water partition coefficient.e estimated octanol/water partition coefficient.

Table 7.8 Table 7.8 Kinematic Viscosity of AirKinematic Viscosity of Air

Table 7.9 Table 7.9 Summary Table of Volatilization Data at 20 Summary Table of Volatilization Data at 20 ºCºC

Table 7.9 Table 7.9 (continued)(continued)

Lyman et al. compiled solubility data on 78 organic compounds and presented estiLyman et al. compiled solubility data on 78 organic compounds and presented estimation methods based on mation methods based on KKowow for different classes of compounds. They also includ for different classes of compounds. They also included a method based on the molecular structure. ed a method based on the molecular structure.

Mackay measured Henry's constant for 22 organic chemicals as part of a study of Mackay measured Henry's constant for 22 organic chemicals as part of a study of volatilization characteristics.volatilization characteristics.Transfer coefficients for the gas and liquid phases were correlated for correlated fTransfer coefficients for the gas and liquid phases were correlated for correlated for environmental conditions as:or environmental conditions as:

(42)(42)

(43)(43)

Where UWhere U1010 is the 10-m wind velocity (m s is the 10-m wind velocity (m s-1-1), Sc), ScLL and Sc and ScGG are the dimensionless liqu are the dimensionless liquid and gas Schmidt numbers.id and gas Schmidt numbers.Volatile compounds such as those shown in Figure 7.3a are easily removed from wVolatile compounds such as those shown in Figure 7.3a are easily removed from water and wastewater by purging with air or by passing them through an air strippater and wastewater by purging with air or by passing them through an air stripping tower. In natural waters, they are removed by stripping from the atmosphere. ing tower. In natural waters, they are removed by stripping from the atmosphere. The overall mass transfer coefficient The overall mass transfer coefficient KKLL can be related to that of oxygen (Table 7.1 can be related to that of oxygen (Table 7.10) because so much information exists for oxygen transfer in natural waters.0) because so much information exists for oxygen transfer in natural waters.

Table 7.10 Table 7.10 Estimated Henry`s Constant and Mass Transfer CoefficiEstimated Henry`s Constant and Mass Transfer Coefficients for Selected Organics at 20 ents for Selected Organics at 20 ººCC

7.2.7 Sorption Reaction7.2.7 Sorption Reaction Soluble organics in natural waters can sorb onto particulate suspended matSoluble organics in natural waters can sorb onto particulate suspended material or bed sediments. The mechanism and the processes by which this occerial or bed sediments. The mechanism and the processes by which this occurs include: urs include: - (1) physical adsorption due to van der Waals forces; - (1) physical adsorption due to van der Waals forces; - (2) chemisorption due to a chemical bonding or surface coordination react- (2) chemisorption due to a chemical bonding or surface coordination reaction;ion;- (3) partitioning of the organic chemical into the organic carbon phase of t- (3) partitioning of the organic chemical into the organic carbon phase of the particulates. he particulates.

Physical adsorption is purely a surface electrostatic phenomenon. PartitioniPhysical adsorption is purely a surface electrostatic phenomenon. Partitioning refers to the dissolution of hydrophobic organic chemicals into the organng refers to the dissolution of hydrophobic organic chemicals into the organic phase of the particulate matter; it is an ic phase of the particulate matter; it is an ababsorption phenomenon rather thsorption phenomenon rather than a surface reaction, and it may occur slowly over time scales of minutes to an a surface reaction, and it may occur slowly over time scales of minutes to days. days.

Adsorption isotherms refer to the equilibrium relationship of sorption betwAdsorption isotherms refer to the equilibrium relationship of sorption between organics and particulates at constant temperature. The chemical is disseen organics and particulates at constant temperature. The chemical is dissolved in water in the presence of various concentrations of suspended solids. olved in water in the presence of various concentrations of suspended solids.

The sorption of toxicants to suspended particulates and bed sediments is a sThe sorption of toxicants to suspended particulates and bed sediments is a significant transfer mechanism. Partitioning of a chemical between particulaignificant transfer mechanism. Partitioning of a chemical between particulate matter and the dissolved phase is not a transformation pathway; it only rte matter and the dissolved phase is not a transformation pathway; it only relates the concentration of dissolved and sorbed states of the chemical.elates the concentration of dissolved and sorbed states of the chemical.The octanol/water partition coefficient, The octanol/water partition coefficient, KKowow, is related to the solubility of a c, is related to the solubility of a chemical in water. hemical in water. Tables 7.9 and 7.11 provide log Tables 7.9 and 7.11 provide log KKowow values for a number of organic chemical values for a number of organic chemicals of environmental interest. s of environmental interest.

Table 7.11

Ocranol/Water Partition Coefficients of Selected Organics, 298 K

The laboratory procedure for measuring The laboratory procedure for measuring KKow ow is given by Lyman.is given by Lyman.- 1. Chemical is added to a mixture of pure octanol (a nonpolar solvent) a- 1. Chemical is added to a mixture of pure octanol (a nonpolar solvent) and - pure water (a polar solvent). The volume radio of octanol and water ind - pure water (a polar solvent). The volume radio of octanol and water is set at the estimated s set at the estimated KKowow..- 2. Mixture is agitated until equilibrium is reached.- 2. Mixture is agitated until equilibrium is reached.- 3. Mixture is centrifuged to separate the two phases. The phases are ana- 3. Mixture is centrifuged to separate the two phases. The phases are analyzed for the chemical.lyzed for the chemical.- 4. - 4. KKowow is the ratio of the chemical concentration in the octanol phase to c is the ratio of the chemical concentration in the octanol phase to chemical concentration in the water phase, and has no units. The logarithm hemical concentration in the water phase, and has no units. The logarithm of of KKowow has been measured from -3 to +7. has been measured from -3 to +7.

If the octanol/water partition coefficient cannot be reliably measured or is If the octanol/water partition coefficient cannot be reliably measured or is not available in databases, it can be estimated from solubility and moleculnot available in databases, it can be estimated from solubility and molecular weight information,ar weight information,

(44)(44)

where MW is the molecular weight of the pollutant (g molwhere MW is the molecular weight of the pollutant (g mol-1-1) and ) and SS is in un is in units of ppm for organics that are liquid in their pure state at 25 its of ppm for organics that are liquid in their pure state at 25 ººC.C.

For organics that are solid in their pure state at 25 For organics that are solid in their pure state at 25 ººC,C,

(45)(45)

where MP is the melting point of the pollutant (where MP is the melting point of the pollutant (ººC) and △C) and △SSff is the entropy of f is the entropy of fusion of the pollutant (cal molusion of the pollutant (cal mol-1-1 deg deg-1-1).).

The octanol/water partition coefficient is dimensionless, but it derives from thThe octanol/water partition coefficient is dimensionless, but it derives from the partitioning that occurs in the extraction between the chemical in octanol an e partitioning that occurs in the extraction between the chemical in octanol an water.water.

Octanol was chosen as a reference because it is a model solvent with some proOctanol was chosen as a reference because it is a model solvent with some properties that make it similar to organic matter and lipids in nature.perties that make it similar to organic matter and lipids in nature.For a wide variety of organic chemicals, the octanol water partition coefficient For a wide variety of organic chemicals, the octanol water partition coefficient is a good estimator of the organic carbon normalized partition coefficient (is a good estimator of the organic carbon normalized partition coefficient (KKococ).).

Karickhoff et al. and Schwarzenbach and Westall have published useful empiriKarickhoff et al. and Schwarzenbach and Westall have published useful empirical equations for predicting cal equations for predicting KKococ as a function of as a function of KKowow

(46)(46)

(47)(47)

Once an estimate of Once an estimate of KKococ is obtained, the calculation of a sediment/water partitio is obtained, the calculation of a sediment/water partition coefficient suitable for natural waters is straightforward because then coefficient suitable for natural waters is straightforward because the

(48)(48)

where where ffococ is the decimal fraction of organic carbon present in the particulate m is the decimal fraction of organic carbon present in the particulate matter (mass/mass). atter (mass/mass).

Figure 7.7 is a schematic of how Figure 7.7 is a schematic of how KKpp, , KKococ,, and and KKowow are interrelated. Figure 7.7a is are interrelated. Figure 7.7a is the Langmuir adsorption isotherm for sorption of one chemical on particulate the Langmuir adsorption isotherm for sorption of one chemical on particulate matter. Figure 7.7b shows but matter. Figure 7.7b shows but KKpp is directly proportional to is directly proportional to ffococ. There is a . There is a yy-inte-intercept in Figure 7.7b if other mechanisms in addition to absorption partitioning rcept in Figure 7.7b if other mechanisms in addition to absorption partitioning are important. Figure 7.7c results, indicating the direct linear relationship on a are important. Figure 7.7c results, indicating the direct linear relationship on a log-log plot between log-log plot between KKococ, and , and KKowow..

Figure 7.7Figure 7.7Relationship between the seRelationship between the sediment/water partition coefdiment/water partition coefficient ficient KKpp, the organic carb, the organic carbon partition coefficient on partition coefficient KKococ, , and the octanol/water partiand the octanol/water partition coefficient tion coefficient KKowow..Plot (a) and (b) are for only Plot (a) and (b) are for only one chemical and (c) is for one chemical and (c) is for many chemicals.many chemicals.

KKpp is a measure of the actual partitioning in natural waters. is a measure of the actual partitioning in natural waters.

The linear portion of the adsorption isotherm (Figure 7.7a) can be expressed The linear portion of the adsorption isotherm (Figure 7.7a) can be expressed by equation:by equation:

(49)(49)

The Langmuir isotherm in Figure 7.7a is derived from the kinetic eq`n for sorThe Langmuir isotherm in Figure 7.7a is derived from the kinetic eq`n for sorption-desorption:ption-desorption:

(50), (51)(50), (51)

where where C C is the concentration of dissolved toxicant, is the concentration of dissolved toxicant, CCpp is the concentration of p is the concentration of particulate toxicant, articulate toxicant, CCpcpc is the maximum adsorptive concentration of the solids, is the maximum adsorptive concentration of the solids, and and kk1 1 and and kk22 are the adsorption and desorption rate constants, respectively. are the adsorption and desorption rate constants, respectively.

At steady-state, eq`n (51) reduces to a Langmuir isotherm in which the amAt steady-state, eq`n (51) reduces to a Langmuir isotherm in which the amount adsorbed is linear at low dissolved toxicant concentrations but graduount adsorbed is linear at low dissolved toxicant concentrations but gradually becomes saturated at the maximum value (ally becomes saturated at the maximum value (rrcc) at high dissolved concen) at high dissolved concentrations.trations.

(52)(52)

Generally, the adsorption capacity of sediments is inversely related to partGenerally, the adsorption capacity of sediments is inversely related to particle size: clays > silts > sands. Sorption of organic chemicals is also a functiicle size: clays > silts > sands. Sorption of organic chemicals is also a function of the organic content of the sediment, as measured by on of the organic content of the sediment, as measured by KKococ, and silts are , and silts are most likely to have the highest organic content.most likely to have the highest organic content.Sometimes a Freundlich isotherm is inferred from empirical data. The funSometimes a Freundlich isotherm is inferred from empirical data. The function is of the formction is of the form

(53)(53)

where where nn is usually greater than 1. In dilute solutions, when is usually greater than 1. In dilute solutions, when nn approaches 1, approaches 1, the Freundlich coefficient, the Freundlich coefficient, KK, is equal to the partition coefficient, , is equal to the partition coefficient, KKpp..

The partition coefficient is derived from simplification of the kinetic eq`ns The partition coefficient is derived from simplification of the kinetic eq`ns (50) and (51) if (50) and (51) if rrc c >> >> r r (the linear portion of the Langmuir isotherm). In this (the linear portion of the Langmuir isotherm). In this case, we may writecase, we may write

(54a), (54b)(54a), (54b)

Where Where kkf f is the adsorption rate constant and is the adsorption rate constant and kkrr is the desorption rate consta is the desorption rate constant.nt.The total concentration of toxicant:The total concentration of toxicant:

(55)(55)

Where Where ffdd and and ffpp are the dissolved and particulate fractions, respectively: are the dissolved and particulate fractions, respectively:

and the ratio of the reaction rate constants is related byand the ratio of the reaction rate constants is related by(58)(58)

Where the Where the ∞ subscripts indicate chemical equilibrium.∞ subscripts indicate chemical equilibrium.

(56), (57)

From kinetics experiments where dissolved and particulate concentrations From kinetics experiments where dissolved and particulate concentrations are monitored over time, the ratio of steady-state concentrations can be reare monitored over time, the ratio of steady-state concentrations can be read from the graph (Figure 7.8).ad from the graph (Figure 7.8).

Sorption reactions usually reach chemical equilibrium quickly, and the kinSorption reactions usually reach chemical equilibrium quickly, and the kinetic relationships can often be assumed to be at steady-state. This is sometietic relationships can often be assumed to be at steady-state. This is sometimes referred to as the "local equilibrium" assumption, when the kinetics omes referred to as the "local equilibrium" assumption, when the kinetics of adsorption and desorption are rapid relative to other kinetic and transpof adsorption and desorption are rapid relative to other kinetic and transport processes in the system.rt processes in the system.

O'Conner and Connolly first reported that, for organics and metals alike, tO'Conner and Connolly first reported that, for organics and metals alike, the sediment/water partition coefficient he sediment/water partition coefficient KKpp declines as sediment (solids) con declines as sediment (solids) concentrations increase. It is a consistent phenomenon in natural waters that icentrations increase. It is a consistent phenomenon in natural waters that is particularly important for hydrophobic organic chemicals. For example, s particularly important for hydrophobic organic chemicals. For example, the the KKpp for a chemical in sediments is much lower than that observed in the for a chemical in sediments is much lower than that observed in the water column. Most researchers attribute this fact to artifacts in the way twater column. Most researchers attribute this fact to artifacts in the way that one attempts to measure hat one attempts to measure KKpp, including complexation of a chemical by c, including complexation of a chemical by colloids and dissolved organic carbon that pass a membrane filter.olloids and dissolved organic carbon that pass a membrane filter.

Figure 7.8 Figure 7.8

Kinetic sorption Kinetic sorption experiment in a experiment in a batch reactorbatch reactor

7.2.8 Bioconcentration and Bioaccumulation7.2.8 Bioconcentration and Bioaccumulation

Bioconcentration of toxicants is defined as the direct uptake of aqueous toxBioconcentration of toxicants is defined as the direct uptake of aqueous toxicant through the gills and epithelial tissues of aquatic organisms. This fate icant through the gills and epithelial tissues of aquatic organisms. This fate process is of interest because it helps to predict human exposure to the toxiprocess is of interest because it helps to predict human exposure to the toxicant in food items, particularly fish.cant in food items, particularly fish.

Bioconcentration is part of the greater picture of bioaccumulation and bioBioconcentration is part of the greater picture of bioaccumulation and biomagnification that includes food chain effects. Bioaccumulation refers to umagnification that includes food chain effects. Bioaccumulation refers to uptake of the toxicant by the fish from a number of different sources includiptake of the toxicant by the fish from a number of different sources including bioconcentration from the water and biouptake from various food itemng bioconcentration from the water and biouptake from various food items (prey) or sediment ingestion. Biomagnification refers to the process whers (prey) or sediment ingestion. Biomagnification refers to the process whereby bioaccumulation increases with each step on the trophic ladder.eby bioaccumulation increases with each step on the trophic ladder.

The terms bioconcentration, bioaccumulation, and biomagnification are soThe terms bioconcentration, bioaccumulation, and biomagnification are sometimes mistakenly used interchangeably. It is useful to accept the followimetimes mistakenly used interchangeably. It is useful to accept the following definitions for the sake of discussion.ng definitions for the sake of discussion.

Bioconcentration: the uptake of toxic organics through the gill membrane Bioconcentration: the uptake of toxic organics through the gill membrane and epithelial tissue from the dissolved phase.and epithelial tissue from the dissolved phase.

Bioaccumulation: the total biouptake of toxic organics by the organism froBioaccumulation: the total biouptake of toxic organics by the organism from food items (benthos, fish prey, sediment ingestion, etc.) as well as via mam food items (benthos, fish prey, sediment ingestion, etc.) as well as via mass transport of dissolved organics through the gill and epithelium.ss transport of dissolved organics through the gill and epithelium.

Biomagnification: that circumstance where bioaccumulation causes an incBiomagnification: that circumstance where bioaccumulation causes an increase in total body burden as one proceeds up the trophic ladder from prirease in total body burden as one proceeds up the trophic ladder from primary producer to top carnivore.mary producer to top carnivore.

Bioconcentration experiments measure the net bioconcentration effect afteBioconcentration experiments measure the net bioconcentration effect after r x x days, having reached equilibrium conditions, by measuring the toxicant days, having reached equilibrium conditions, by measuring the toxicant concentration in the test organism. The BCF (bioconcentration factor) is tconcentration in the test organism. The BCF (bioconcentration factor) is the ratio of the concentration in the organism to the concentration in the whe ratio of the concentration in the organism to the concentration in the water.ater.

The BCF derives from a kinetic expression relating the water toxicant concentThe BCF derives from a kinetic expression relating the water toxicant concentration and organism mass:ration and organism mass:

(59)(59)

where where ee = efficiency of toxic absorption at the gill = efficiency of toxic absorption at the gill kk11 = (L filtered/kg organism per day) = (L filtered/kg organism per day)

kk22 = depuration rate constant including excretion and clearance of = depuration rate constant including excretion and clearance of metabolites, day metabolites, day-1-1

CC = dissolved toxicant, = dissolved toxicant, μμg Lg L-1-1

BB = organism biomass, kg L = organism biomass, kg L-1-1

FF = organism toxicant residue (whole body), = organism toxicant residue (whole body), μμg kgg kg-1-1

Steady-state solution isSteady-state solution is

(60)(60)

where BCF has units of (where BCF has units of (μμg/kg)/(g/kg)/(μμg/L). g/L). Bioconcentration is analogous to sorption of hydrophobic organics. Organic chBioconcentration is analogous to sorption of hydrophobic organics. Organic chemicals tend to partition into the fatty tissue of fish and other aquatic organisemicals tend to partition into the fatty tissue of fish and other aquatic organisms, and BCF is analogous to the sediment/water partition coefficient, ms, and BCF is analogous to the sediment/water partition coefficient, KKpp. . Bioconcentration also can be measured in algae and higher plants, where uptaBioconcentration also can be measured in algae and higher plants, where uptake occurs by adsorption to the cell surfaces or sorption into the tissues.ke occurs by adsorption to the cell surfaces or sorption into the tissues.

An empirical relationship for bioconcentration (BCF-An empirical relationship for bioconcentration (BCF-KKowow) in bluegill sunfis) in bluegill sunfish in 28 days exposure for 84 organic priority pollutants wash in 28 days exposure for 84 organic priority pollutants was

(61)(61)

and for rainbow trout with ten chlorobenzenes it wasand for rainbow trout with ten chlorobenzenes it was(62)(62)

for low-level exposures typical of natural waters. Fathead minnow, bluegilfor low-level exposures typical of natural waters. Fathead minnow, bluegill, rainbow trout, brook trout, and mosquito fish are the species most frequl, rainbow trout, brook trout, and mosquito fish are the species most frequently involved in bioconcentration tests.ently involved in bioconcentration tests.

Bioconcentration experiments, Bioconcentration experiments, per seper se, do not measure the metabolism or d, do not measure the metabolism or detoxification of the chemical. Chemicals can be metabolized to more or less etoxification of the chemical. Chemicals can be metabolized to more or less toxic products that may have different depuration characteristics. The biotoxic products that may have different depuration characteristics. The bioconcentration experiment only measures the final body burden at equilibriconcentration experiment only measures the final body burden at equilibrium (although interim data that were used to determine when equilibrium um (although interim data that were used to determine when equilibrium was reached may be available). was reached may be available).

The fact that a chemical bioaccumulates at all is an indication that it resistThe fact that a chemical bioaccumulates at all is an indication that it resists biodegradation and is somewhat "biologically hard" or "nonlabile."s biodegradation and is somewhat "biologically hard" or "nonlabile."

The kinetics of bioaccumulation are shown schematically in Figure 7.9.The kinetics of bioaccumulation are shown schematically in Figure 7.9.

Fish can lose unmetabolized toxics via biliary excretion or "desorption" thFish can lose unmetabolized toxics via biliary excretion or "desorption" through the gill. On the other hand, toxic organics can undergo biotransforrough the gill. On the other hand, toxic organics can undergo biotransformations and be eliminated as metabolic products. mations and be eliminated as metabolic products.

The rate constant, The rate constant, kk22, includes total depuration (both excretion of unmetab, includes total depuration (both excretion of unmetabolized toxics, olized toxics, kk22

`̀,, and elimination of metabolites, and elimination of metabolites, kk22````)).. Only a fraction of thi Only a fraction of this elimination is returned to the water column as dissolved parent compouns elimination is returned to the water column as dissolved parent compound, designated as d, designated as kk22

`̀ in Figure 7.9. in Figure 7.9.

Hydrophobic organics tend to accumulate in fatty tissue of animals. LipidnHydrophobic organics tend to accumulate in fatty tissue of animals. Lipidnormalized bioconcentration factors both in the laboratory and in the field ormalized bioconcentration factors both in the laboratory and in the field have been correlated successfully with the hydrophobicity of toxic organics have been correlated successfully with the hydrophobicity of toxic organics as measured by the octanol/water partition coefficient, as measured by the octanol/water partition coefficient, KKowow (Table 7.12). (Table 7.12).

Biomagnification occurs in lake trout for PCBs in the Great Lakes due to tBiomagnification occurs in lake trout for PCBs in the Great Lakes due to the contribution of alewife and small fish to the diet of these top carnivores.he contribution of alewife and small fish to the diet of these top carnivores.

Figure 7.9 Figure 7.9 Bioaccumulation kinetics for hydrophobic Bioaccumulation kinetics for hydrophobic organic chemicals in fishorganic chemicals in fish

Table 7.12Table 7.12

Bioconcentration FBioconcentration Factor (BCF) for Selactor (BCF) for Selected Organic Cheected Organic Chemicals in Fish (Unimicals in Fish (Units: ts: μμg/kg fish- g/kg fish- μμg L g L waterwater))

7.2.9 Comparison of Pathway7.2.9 Comparison of Pathway Most of the transformations discussed in Section 7.2 are expressed as secondMost of the transformations discussed in Section 7.2 are expressed as second-order reactions. It is difficult to compare the magnitudes of these reactions--order reactions. It is difficult to compare the magnitudes of these reactions-the rate constants all have different units. Each of the transformations can bthe rate constants all have different units. Each of the transformations can be written as pseudo-first-order reactions assuming that the second concentrae written as pseudo-first-order reactions assuming that the second concentration in the reaction rate expression can be assumed to be relatively constant. tion in the reaction rate expression can be assumed to be relatively constant.

The overall reaction rate:The overall reaction rate:

(63)(63)

where where CC = dissolved organic concentration, ML = dissolved organic concentration, ML-3-3

tt = time, T = time, T kkbb = biotransformation rate constant, T = biotransformation rate constant, T-1-1

kkoo = oxidation rate constant, T = oxidation rate constant, T-1-1

kkrr = reduction rate constant, T = reduction rate constant, T-1-1

kkpp = photolysis rate constant, T = photolysis rate constant, T-1-1

kkhh = hydrolysis rate constant, T = hydrolysis rate constant, T-1-1

kkvv = volatilization rate constant, T = volatilization rate constant, T-1-1

Equation (63) includes an assumption that the atmosphere has a neg1igible Equation (63) includes an assumption that the atmosphere has a neg1igible concentration (partial pressure) of the organic, so only volatilization occurs concentration (partial pressure) of the organic, so only volatilization occurs (stripping out of the water body).(stripping out of the water body).For first-order reactions in a batch reactor in a batch reactor without transport, the For first-order reactions in a batch reactor in a batch reactor without transport, the reaction rate:reaction rate:

(64)(64)

Solving for the concentration as a function of time: Solving for the concentration as a function of time:

(65), (66)(65), (66)

Taking the natural logarithm of both sides of equation (66) and solving for time Taking the natural logarithm of both sides of equation (66) and solving for time (half-life) yields the well-known relationship below:(half-life) yields the well-known relationship below:

(67)(67)

where where tt1/21/2 = overall half-life of the chemical due to all transformation reactions = overall half-life of the chemical due to all transformation reactions

= the sum of all the pseudo-first-order reaction rate constants= the sum of all the pseudo-first-order reaction rate constants

Individual half-lives may be compared to determine which reaction predominates Individual half-lives may be compared to determine which reaction predominates (gives the shortest half-life). (gives the shortest half-life).

n

iik

1

7.3 ORGANIC CHEMICALS IN LAKES7.3 ORGANIC CHEMICALS IN LAKES 7.3.1 Completely Mixed Systems7.3.1 Completely Mixed Systems

As an approximation, lakes can be represented as ideal completely mixed flow througAs an approximation, lakes can be represented as ideal completely mixed flow through reactors (CMF systems) or a network of CMF compartments. h reactors (CMF systems) or a network of CMF compartments. A mass balance system of equations:A mass balance system of equations:

Figure 7.10: a schematic of the various reactions in the lake water column and sedimeFigure 7.10: a schematic of the various reactions in the lake water column and sediment. nt. An assumption of local equilibrium may be used to relate the particulate adsorbed coAn assumption of local equilibrium may be used to relate the particulate adsorbed concentration to the dissolved concentration through the partition coefficient ncentration to the dissolved concentration through the partition coefficient KKpp..

(68a), (68b), (68c)(68a), (68b), (68c)

where where KKpp = sediment/water partition coefficient, L kg = sediment/water partition coefficient, L kg-1-1

CC = dissolved organic chemical concentration, = dissolved organic chemical concentration, µµg Lg L-1-1

rr = mass sorbed, = mass sorbed, µµg kgg kg-1-1

MM = suspended or bed solids concentration, kg L = suspended or bed solids concentration, kg L-1-1

CCp p = = particulate adsorbed concentration, particulate adsorbed concentration, µµg Lg L-1-1

CCTT = total (dissolved plus particulate) concentration, = total (dissolved plus particulate) concentration, µµg Lg L-1-1

Figure 7.10 Figure 7.10 Schematic of a fate Schematic of a fate model for organic model for organic chemicals in water and chemicals in water and sedimentsediment

Sorptive equilibrium is usually a valid assumption in natural waters because Sorptive equilibrium is usually a valid assumption in natural waters because the time scale for most sorption reactions (minutes to hours) is small comparthe time scale for most sorption reactions (minutes to hours) is small compared to the time scale for reactions and transport (days to years). ed to the time scale for reactions and transport (days to years). Figure 7.10 indicates a rapid local equilibrium assumption for bioconcentratiFigure 7.10 indicates a rapid local equilibrium assumption for bioconcentration. If uptake and depuration kinetics (hours to days) are fast relative to otheon. If uptake and depuration kinetics (hours to days) are fast relative to other reactions and time scales, this is a valid assumption. Use of the bioconcentrr reactions and time scales, this is a valid assumption. Use of the bioconcentration factor (BCF) helps to simplify the equations, and it is another partitioniation factor (BCF) helps to simplify the equations, and it is another partitioning coefficient that we may use similar to ng coefficient that we may use similar to KKpp..

(69)(69)

where BCF = bioconcentration factor, L kgwhere BCF = bioconcentration factor, L kg-1-1

C = dissolved chemical concentration, C = dissolved chemical concentration, µµg Lg L-1-1

F = residue concentration in whole fish, F = residue concentration in whole fish, µµg kgg kg-1-1 The total concentration of chemical The total concentration of chemical CCTT may be larger or smaller in the sedim may be larger or smaller in the sediment than the overlying water depending on whether the water column or sedient than the overlying water depending on whether the water column or sediment was contaminated first. Partitioning of the chemical between the dissolment was contaminated first. Partitioning of the chemical between the dissolved pore water ved pore water CC22 and adsorbed sediment and adsorbed sediment CCp2p2, may also be different due to th, may also be different due to the dependence of e dependence of KKp2p2, on solids concentration. Generally, , on solids concentration. Generally, KKp2p2 < < KKp1p1, because the , because the sediment has a much higher solids concentration. sediment has a much higher solids concentration.

A framework for a mass balance model for an organic chemical in a lake is A framework for a mass balance model for an organic chemical in a lake is given by Figure 7.10. Waste inputs, their fate and effects, can be assessed in given by Figure 7.10. Waste inputs, their fate and effects, can be assessed in this context.this context.Anthropogenic inputs may also enter the water body from the atmosphere Anthropogenic inputs may also enter the water body from the atmosphere via wet precipitation and dry deposition. The concentration in rainfall is revia wet precipitation and dry deposition. The concentration in rainfall is related to the gas phase concentration and Henry's constant, so the depositiolated to the gas phase concentration and Henry's constant, so the deposition mass is equal to the volume of rainfall times the aqueous phase concentran mass is equal to the volume of rainfall times the aqueous phase concentrationtion

(70) (70)

Where Where CCprecipprecip is the precipitation concentration, is the precipitation concentration, CCgg is the gas phase concent is the gas phase concentration, and ration, and HH is Henry's constant with the appropriate units. is Henry's constant with the appropriate units. The flux of contaminants due to dry deposition is related to the depositionaThe flux of contaminants due to dry deposition is related to the depositional velocity and the gaseous concentrationl velocity and the gaseous concentration

(71)(71)

where where vvdd is the deposition velocity (LT is the deposition velocity (LT-1-1), ), CCgg is the gas phase concentration is the gas phase concentration (ML(ML-3-3) and ) and JJdd is the areal mass flux due to dry deposition (ML is the areal mass flux due to dry deposition (ML-2-2TT-1-1). ). Equation (71) is empirical. Both gases and aerosol particles may contribute Equation (71) is empirical. Both gases and aerosol particles may contribute to dry deposition but the gas phase concentration should be proportional in to dry deposition but the gas phase concentration should be proportional in either case, either case, vvdd serving as the empirical proportionality constant. serving as the empirical proportionality constant.

The mass balance equation for a lake with toxic organic chemical inputs can be writThe mass balance equation for a lake with toxic organic chemical inputs can be written assuming complete mixing, steady flow conditions, instantaneous local sorption eten assuming complete mixing, steady flow conditions, instantaneous local sorption equilibrium, and no atmospheric deposition.quilibrium, and no atmospheric deposition.

(72)(72)

Equation (72) has three unknown dependent variables – Equation (72) has three unknown dependent variables – CCTT, and , and CC - but the assumpt - but the assumption of local equilibrium allows us to write the equation entirely in terms of total (whion of local equilibrium allows us to write the equation entirely in terms of total (whole water, unfiltered) concentration.ole water, unfiltered) concentration.

(73)(73)

where where CCTT = total concentration = = total concentration = CC + C + Cpp, ML, ML-3-3

VV = volume of the lake, L = volume of the lake, L33

tt = time, T = time, T QQ = flowrate In and out, L = flowrate In and out, L33TT-1-1

ffpp = particulate fraction of total chemical concentration, dimensionless = particulate fraction of total chemical concentration, dimensionless = = CCpp/ C/ CTT = K = KppMM /(1 + /(1 + KKppMM)) ffd d = dissolved fraction of total chemical concentration, dimensionless= dissolved fraction of total chemical concentration, dimensionless = = C/ CC/ CTT = 1 = 1 /(1 + /(1 + KKppMM) )

C C = dissolved chemical concentration, ML= dissolved chemical concentration, ML-3-3

CCpp = particulate chemical concentration, ML = particulate chemical concentration, ML-3-3

kkss = sedimentation rate constant,T = sedimentation rate constant,T-1-1

kkii = = sum of pseudo-first-order reaction rate constant [eq`n (63)], Tsum of pseudo-first-order reaction rate constant [eq`n (63)], T-1-1

Equation (73) is an ordinary differential equation with constant coefficients. Equation (73) is an ordinary differential equation with constant coefficients. It is solvable by first-order methods such as the integration factor method. DIt is solvable by first-order methods such as the integration factor method. Dividing through by the constant volume and rearranging, we haveividing through by the constant volume and rearranging, we have

(74)(74)

The final solution isThe final solution is

(75)(75)

where where CCToTo = initial total input concentration, ML = initial total input concentration, ML-3-3

αα = = integration factorintegration factor ττ = mean hydraulic detention time = = mean hydraulic detention time = VV//QQ, T, T

We see that the solution to a continuous Input of organic chemical to a lake iWe see that the solution to a continuous Input of organic chemical to a lake is composed of two terms in equation (75): the first term is the die-away of inis composed of two terms in equation (75): the first term is the die-away of initial conditions, and the second term is the asymptotic "hump" (the shape of a tial conditions, and the second term is the asymptotic "hump" (the shape of a Langmuir isotherm), which builds to a steady-state concentration as t Langmuir isotherm), which builds to a steady-state concentration as t → ∞.→ ∞.

(76) (76)

The steady-state concentration is directly proportional to the total concentraThe steady-state concentration is directly proportional to the total concentration of organic inputs to the lake.tion of organic inputs to the lake.

Because it takes an infinite amount of time (or the lake to reach steady state in Because it takes an infinite amount of time (or the lake to reach steady state in the strictest sense, we speak of time to 95% of steady state, that is, the length of the strictest sense, we speak of time to 95% of steady state, that is, the length of time required for the concentration in the lake to reach 95% of the value that itime required for the concentration in the lake to reach 95% of the value that it will ultimately achieve.t will ultimately achieve.

(77)(77)oror

(78)(78)

By inspection, one can prove that equations (75) and (78) are equal whenBy inspection, one can prove that equations (75) and (78) are equal when

(79)(79)

Equation (79) gives the time to 95% of steady state. For the simplest case of a nEquation (79) gives the time to 95% of steady state. For the simplest case of a nonadsorbing dissolved chemical undergoing first-order reaction decay, onadsorbing dissolved chemical undergoing first-order reaction decay, αα = = kk + 1/+ 1/ττ..

The greater is the flushing rate ( 1/The greater is the flushing rate ( 1/ττ) and the reaction rate constant, the less is ) and the reaction rate constant, the less is time required to achieve steady state. Conservative substances (time required to achieve steady state. Conservative substances (kk = 0) take the l = 0) take the longest time to reach steady state after a step function change in inputs.ongest time to reach steady state after a step function change in inputs.

7.3.2 Dieldrin Case Study in Coralville Reservoir, Iowa7.3.2 Dieldrin Case Study in Coralville Reservoir, IowaThe following case study is used to illustrate aspects of ecosystem recovery The following case study is used to illustrate aspects of ecosystem recovery from a persistent hydrophobic organic pollutant. It also demonstrates the from a persistent hydrophobic organic pollutant. It also demonstrates the use of compartmentalization within a lake to simulate transport.use of compartmentalization within a lake to simulate transport.

Figure 7.13: a schematic of water column, sediment, and fish concentratioFigure 7.13: a schematic of water column, sediment, and fish concentrations following a period when large discharges of chemical were put into the sns following a period when large discharges of chemical were put into the system. Because the contaminant is hydrophobic and persistent, it remains iystem. Because the contaminant is hydrophobic and persistent, it remains in the system for a long time, accumulating in fish tissue and sediment. It din the system for a long time, accumulating in fish tissue and sediment. It disappears by washout (advection), burial into the deep sediment, and slow dsappears by washout (advection), burial into the deep sediment, and slow degradation reactions. Depending on the sediment dynamics of the system aegradation reactions. Depending on the sediment dynamics of the system and the rate of chemical degradation, these can be slow processes taking yeand the rate of chemical degradation, these can be slow processes taking years to decades. rs to decades.

Figure 7.14: some persistent insecticides (e.g. chlorinated hydrocarbons) uFigure 7.14: some persistent insecticides (e.g. chlorinated hydrocarbons) used in the Midwest. These chemicals were banned in the 1970s and early 19sed in the Midwest. These chemicals were banned in the 1970s and early 1980s because of their persistence and propensity to bioaccumulate in fish an80s because of their persistence and propensity to bioaccumulate in fish and wildlife. Also shown are two replacement insecticides (ester compounds), d wildlife. Also shown are two replacement insecticides (ester compounds), which hydrolyze and break down in the environment. They are toxic but which hydrolyze and break down in the environment. They are toxic but much less persistent.much less persistent.

Figure 7.13Figure 7.13

Schematic of Schematic of lake recovery lake recovery from a from a persistent persistent hydrophobic hydrophobic pollutantpollutant

Figure 7.14Figure 7.14

Selected insectiSelected insecticides used in tcides used in the past in the he past in the midwestern Umidwestern United Statesnited States

Agricultural usage of pesticides in Iowa is widespread, particularly grass aAgricultural usage of pesticides in Iowa is widespread, particularly grass and broadleaf herbicides and row crop soil insecticides. One of the insecticind broadleaf herbicides and row crop soil insecticides. One of the insecticides widely used for control of the corn rootworm and cutworm from 1960 des widely used for control of the corn rootworm and cutworm from 1960 to 1975 was the chlorinated hydrocarbon, aldrin. to 1975 was the chlorinated hydrocarbon, aldrin.

Aldrin is microbially metabolized to its persistent epoxide, dieldrin. DieldrAldrin is microbially metabolized to its persistent epoxide, dieldrin. Dieldrin is itself an insecticide of certain toxicity and is also a hydrophobic substain is itself an insecticide of certain toxicity and is also a hydrophobic substance of limited solubility in water (0.25 ppm) and low vapor pressure (2.7 × nce of limited solubility in water (0.25 ppm) and low vapor pressure (2.7 × 1010-6-6 mm Hg at 25 mm Hg at 25 ººC). It is known to bioaccumulate to levels as high as 1.6 C). It is known to bioaccumulate to levels as high as 1.6 mg/kg wet weight in edible tissue of Iowa catfish.mg/kg wet weight in edible tissue of Iowa catfish.

Coralville Reservoir is a mainstream impoundment of the Iowa River in eaCoralville Reservoir is a mainstream impoundment of the Iowa River in easters Iowa. It drains approximately 3084 square miles (7978 kmsters Iowa. It drains approximately 3084 square miles (7978 km22) of prime ) of prime Iowa farmland and receives extensive agricultural runoff with 90% of its dIowa farmland and receives extensive agricultural runoff with 90% of its drainage basin in intensive agriculture. It is a variable-level, flood control arainage basin in intensive agriculture. It is a variable-level, flood control and recreational reservoir, which has undergone considerable sedimentationd recreational reservoir, which has undergone considerable sedimentation since it was created in 1958. n since it was created in 1958.

At conservation pool (680 ft above mean sea level, msl), the reservoir has a At conservation pool (680 ft above mean sea level, msl), the reservoir has a capacity of 38,000 acre-ft (4.79× 10capacity of 38,000 acre-ft (4.79× 1077 m m33), a surface area of 4900 acres (1.98), a surface area of 4900 acres (1.98× 10× 1077mm22), a mean depth of approximately 8 ft (2.44 m), and a mean detenti), a mean depth of approximately 8 ft (2.44 m), and a mean detention time of 14 days. In 1958, the capacity at conservation pool was 53,750 aon time of 14 days. In 1958, the capacity at conservation pool was 53,750 acre-ft (6.63 × 10cre-ft (6.63 × 1077 m m33).).

The total pesticide concentration is the sum of the particulate plus the dissolved concThe total pesticide concentration is the sum of the particulate plus the dissolved concentrations, with instantaneous sorptive equilibrium assumedentrations, with instantaneous sorptive equilibrium assumed

(80)(80)

where where ffd d = C/ C= C/ CTT = 1 = 1/(1 + /(1 + KKppMM) = fraction of dissolved pesticide) = fraction of dissolved pesticide ffp p = C= Cpp/ C/ CTT = K = KppMM/(1 + /(1 + KKppMM) = fraction of particulate pesticide) = fraction of particulate pesticide W(t) = time-variable loading of pesticide, M/TW(t) = time-variable loading of pesticide, M/T CCTT = total concentration in the water column, ML = total concentration in the water column, ML -3-3

= sum of the pseudo-first-order degradation rate constants= sum of the pseudo-first-order degradation rate constants ττ = mean hydraulic detention time = mean hydraulic detention time VV = reservoir volume, L = reservoir volume, L33

kkss = sedimentation rate constant, T = sedimentation rate constant, T-1-1

The fish residue equation isThe fish residue equation is

(81) (81)

where where kk11 = pesticide uptake rate by fish, T = pesticide uptake rate by fish, T-1-1

kkdd = depuration rate constant, T = depuration rate constant, T-1-1

FF = whole-body fish residue level, M/M wet weight = whole-body fish residue level, M/M wet weight BB = fish biomass concentration, M/L = fish biomass concentration, M/L33 wet weight wet weight

k

Equations (80) and (81) may be solved analytically for constant coefficients anEquations (80) and (81) may be solved analytically for constant coefficients and simple pesticide loading functions, W(t), or they may be integrated numericad simple pesticide loading functions, W(t), or they may be integrated numerically. In the case of a pesticide ban, the W(t) might typically decline in an exponelly. In the case of a pesticide ban, the W(t) might typically decline in an exponential manner due to degradation by soil organisms or a ban on application. ntial manner due to degradation by soil organisms or a ban on application. For an exponentially declining loading function at rate For an exponentially declining loading function at rate ωω, the analytical solutio, the analytical solutions to equations (80) and (81) arens to equations (80) and (81) are

(82)(82)

(83)(83)

where where CCToTo = initial total pesticide concentration in lake, ML = initial total pesticide concentration in lake, ML -3-3 CCTin,oTin,o = initial total pesticide inflow concentration, ML = initial total pesticide inflow concentration, ML-3-3

ωω = rate of exponentially declining inflow concentration,T = rate of exponentially declining inflow concentration,T -1-1

Figure 7.15 is a schematic diagram of hypothetical pond or lake configuratFigure 7.15 is a schematic diagram of hypothetical pond or lake configurations that are possible for this problem. Each box is assumed to be completeions that are possible for this problem. Each box is assumed to be completely mixed with bulk exchange between water compartments. There is disperly mixed with bulk exchange between water compartments. There is dispersion in Coralville Reservoir that seems to be simulated best by the eight-cosion in Coralville Reservoir that seems to be simulated best by the eight-compartment model based on dye studies. mpartment model based on dye studies.

Figure 7.16: simulation of a two-compartment model (water and sediment) Figure 7.16: simulation of a two-compartment model (water and sediment) for dieldrin in Coralville Reservoir. Model parameters based on calibratiofor dieldrin in Coralville Reservoir. Model parameters based on calibration are given on the figure. The rate of declining inputs was 0.164 yrn are given on the figure. The rate of declining inputs was 0.164 yr-1-1, sedim, sedimentation rate constant was 0.18 dayentation rate constant was 0.18 day-1-1; the rate of biodegradation of dieldrin ; the rate of biodegradation of dieldrin in sediment was 0.005 dayin sediment was 0.005 day-1-1; and the bioconcentration factor (BCF) was 70,; and the bioconcentration factor (BCF) was 70,000. 000.

Model results were within the range of field observations. Dieldrin residueModel results were within the range of field observations. Dieldrin residues in fish, sediment, and water were all declining at 15% per year Approxi∼s in fish, sediment, and water were all declining at 15% per year Approxi∼mately 50% of the pesticide load was exported from the reservoir, 40% unmately 50% of the pesticide load was exported from the reservoir, 40% underwent sedimentation, and 10% entered a huge biomass of bottom-feedinderwent sedimentation, and 10% entered a huge biomass of bottom-feeding fish. g fish.

A post-audit study in 1989 showed that the model was quite robust in its pA post-audit study in 1989 showed that the model was quite robust in its predictions to fish residue levels 10 years later with no adjustments to model redictions to fish residue levels 10 years later with no adjustments to model parameters (Figure 7.17).parameters (Figure 7.17).

Figure 7.15Figure 7.15

Compartmental Compartmental configuration for a configuration for a two-box pond model two-box pond model or an eight-box lake or an eight-box lake modelmodel

Figure 7.16Figure 7.16

Result of model and fieResult of model and field data for dieldrin in ld data for dieldrin in Coralville Reservoir wCoralville Reservoir water sediment and in fiater sediment and in fish.sh.

Figure 7.17 Figure 7.17 Post-audit study of dieldrin model for Coralville ResePost-audit study of dieldrin model for Coralville Reservoir showing utility of the model for forecasting fish residue levervoir showing utility of the model for forecasting fish residue leve

ls.ls.

Multicompartment solutions of equations (80) and (81) must include interflows and buMulticompartment solutions of equations (80) and (81) must include interflows and bulk dispersion as well as an assumption regarding suspended solids and fish biomass dislk dispersion as well as an assumption regarding suspended solids and fish biomass distribution. tribution. For each constant-volume compartment,For each constant-volume compartment,

(84)(84)

where where VV = compartment volume, m = compartment volume, m33

CCTT = total pesticide concentration of the compartment, = total pesticide concentration of the compartment, µµg Lg L-1-1

tt = time, days = time, days QQaa = inflow of water from adjacent compartments, m = inflow of water from adjacent compartments, m33 d d-1-1

QQbb = outflow of wafer to adjacent compartments, m = outflow of wafer to adjacent compartments, m33 d d-1 -1

CCaa = total pesticide concentration in the adjacent compartment, = total pesticide concentration in the adjacent compartment, µµg Lg L-1-1

ffdd = fraction of the total pesticide in the dissolved phase = fraction of the total pesticide in the dissolved phase ffpp = fraction of the total pesticide in the particulate phase = fraction of the total pesticide in the particulate phase kkdada = reaction rate constant for the dissolved phase, day = reaction rate constant for the dissolved phase, day -1-1

kkpapa = reaction rate constant for the particulate phase, day = reaction rate constant for the particulate phase, day -1-1

kkss = settling rate constant of the compartment, day = settling rate constant of the compartment, day-1-1

kksasa = settling rate constant from the above compartment, day = settling rate constant from the above compartment, day -1-1

EE = bulk dispersion coefficient for adjacent compartments, m = bulk dispersion coefficient for adjacent compartments, m22 d d-1-1 AA = surface area between two adjacent compartments, m = surface area between two adjacent compartments, m22

ll = mixing length between midpoints of adjacent compartments, m = mixing length between midpoints of adjacent compartments, m VVaa = volume of above compartment, m = volume of above compartment, m33

The general mass balance equation for the jth compartment can be reduced to a general mThe general mass balance equation for the jth compartment can be reduced to a general matrix equationatrix equation::

(85)(85)

where where ii = subscript denoting adjacent compartments = subscript denoting adjacent compartments jj = subscript denoting the jth compartment = subscript denoting the jth compartment CCjj = total pesticide concentration in the jth compartment, = total pesticide concentration in the jth compartment, µµg Lg L-1-1

CCii = total pesticide concentration in an adjacent compartment, = total pesticide concentration in an adjacent compartment, µµg Lg L-1-1

QQi,ji,j = flow into compartment = flow into compartment ii from from jj, m, m33 d d-1-1 QQj,ij,i = flow from compartment = flow from compartment jj to to ii, m, m33 d d-1-1 ffd,jd,j = dissolved fraction of a pesticide in compartment = dissolved fraction of a pesticide in compartment jj ffp,j p,j = particulate fraction ova pesticide in compartment = particulate fraction ova pesticide in compartment jj kkdada = sum of dissolved reaction rate constant, day = sum of dissolved reaction rate constant, day-1-1

kkpapa = sum of particulate reaction rate constant, day = sum of particulate reaction rate constant, day-1-1

kks,is,i = settling rate constant for compartment = settling rate constant for compartment ii, day, day-1-1

kks,js,j = settling rate constant from compartment = settling rate constant from compartment jj, day, day-1-1

EEi,ji,j = bulk dispersion coefficient between adjacent compartments, m = bulk dispersion coefficient between adjacent compartments, m2 2 dd-1-1

AAj j = surface area of compartment = surface area of compartment jj, m, m22

lli,ji,j = length between the midpoints of adjacent compartments, m= length between the midpoints of adjacent compartments, m VVjj = compartment volume, m= compartment volume, m33

VVii = volume of adjacent compartment, m = volume of adjacent compartment, m33

Figure 7.18Figure 7.18

Eight-compartment dEight-compartment dieldrin model results fieldrin model results for Coralville Reservoor Coralville Reservoir, water compartmenir, water compartmentsts

Figure 7.19Figure 7.19

Eight-compartment Eight-compartment dieldrin model resultdieldrin model results for Coralville Reses for Coralville Reservoir, sediment comrvoir, sediment compartmentspartments

7.4 ORGANIC CHEMICALS IN RIVERS AND 7.4 ORGANIC CHEMICALS IN RIVERS AND ESTUARIESESTUARIES

Advection, dispersion, and reaction of chemicals may be simulated for large Advection, dispersion, and reaction of chemicals may be simulated for large rivers in one, two, or three dimensions, depending on the application desirerivers in one, two, or three dimensions, depending on the application desired. A spill of chemical at the bank of a large river will be mixed laterally and d. A spill of chemical at the bank of a large river will be mixed laterally and vertically, and it will be transported downstream by current velocity (advectvertically, and it will be transported downstream by current velocity (advection) and longitudinal dispersion. ion) and longitudinal dispersion.

After an initial mixing period, a three-dimensional advection-dispersion equAfter an initial mixing period, a three-dimensional advection-dispersion equation with Taylor's analogy may be applied for steady flow conditions and a ation with Taylor's analogy may be applied for steady flow conditions and a uniform channel.uniform channel.

(86)(86)

where where CC = chemical concentration, M L = chemical concentration, M L-3-3

tt = time, T = time, T EE = dispersion coefficients in the = dispersion coefficients in the xx-, -, yy-, and -, and zz-directions, L-directions, L22TT-1-1

uuii = average velocities in the = average velocities in the xx-, -, yy-, and -, and zz-directions, LT-directions, LT-1-1

xx = longitudinal distance, L = longitudinal distance, L yy = lateral (or transverse) distance, L = lateral (or transverse) distance, L zz = vertical distance, L = vertical distance, L

The mass balance equation in the longitudinal downstream dimension bThe mass balance equation in the longitudinal downstream dimension becomes:ecomes:

(87)(87)

At this point one must consider the role of the sediment/water partitioniAt this point one must consider the role of the sediment/water partitioning and sediment transport because chemicals that are adsorbed to suspeng and sediment transport because chemicals that are adsorbed to suspended solids or bed sediment have a different fate and toxic effect than dinded solids or bed sediment have a different fate and toxic effect than dissolved chemicals. ssolved chemicals.

Included for general applications should be kinetics of physical reactionIncluded for general applications should be kinetics of physical reactions (sedimentation, scour/resuspension, adsorption/desorption, and gas tras (sedimentation, scour/resuspension, adsorption/desorption, and gas transfer), biological transformations (biological oxidation/reduction and consfer), biological transformations (biological oxidation/reduction and co-metabolism), and chemical reactions (hydrolysis, oxidation, photolysis).-metabolism), and chemical reactions (hydrolysis, oxidation, photolysis).

Figure 7.20 is a schematic of the reactions that occur in the water column and the Figure 7.20 is a schematic of the reactions that occur in the water column and the bed sediment. It is assumed that chemical and biological transformation reactions bed sediment. It is assumed that chemical and biological transformation reactions occur predominantly in the soluble phase (occur predominantly in the soluble phase (CCss), although special transformation re), although special transformation reactions may occur for chemical adsorped to the sediment under reducing conditioactions may occur for chemical adsorped to the sediment under reducing conditions (ns (λλ`̀bb). ).

Because environmental conditions differ in the sediment (e.g., photolysis and volatBecause environmental conditions differ in the sediment (e.g., photolysis and volatilization are not expected to occur from the sediment), the overall pseudo-first ordilization are not expected to occur from the sediment), the overall pseudo-first order rate constant (er rate constant (λλbb) is different in the bed sediment from that in the water column ) is different in the bed sediment from that in the water column ((λλww). ).

Rate constants for adsorption and desorption also differ in the water column comRate constants for adsorption and desorption also differ in the water column compared to the sediment because sorption processes and the sediment/water partitiopared to the sediment because sorption processes and the sediment/water partition coefficient, in particular, have been reported to be a strong function of the solids n coefficient, in particular, have been reported to be a strong function of the solids concentration (concentration (SS). ).

Figure 7.20 also includes sedimentation of suspended solids (Figure 7.20 also includes sedimentation of suspended solids (SSww) in the river water ) in the river water and scour/resuspension of bed sediment (and scour/resuspension of bed sediment (SSbb) via the first-order rate constants ) via the first-order rate constants kkss a and nd αα, respectively, respectively..

Mass transfer of contaminated river water to sediment pore water may occur in tMass transfer of contaminated river water to sediment pore water may occur in the initial stages of a chemical spill, or diffusion from contaminated sediment to ovhe initial stages of a chemical spill, or diffusion from contaminated sediment to overlying water may occur during the recovery phase.erlying water may occur during the recovery phase.

Figure 7.20 Schematic of reactions in the river water column and sediment including adsorption (k1, k3), desorption (k2, k4), sedimentation (ks), scour and resuspension (α), and degradation (λ) for soluble chemical (Cs), particulate adsorbed chemical (Cp) and the concentration of solids in the water column (Sw) and in the bed (Sb). Mass transfer between the pore water of the bed and overlying water takes place via a mass transfer coefficient (kL).

To write the proper mass balance equations for the concentration of chemical in thTo write the proper mass balance equations for the concentration of chemical in the dissolved and particulate-adsorbed phases, it is necessary to define the amount of e dissolved and particulate-adsorbed phases, it is necessary to define the amount of contamination in the active sediment layer in terms of the particulate adsorbed concontamination in the active sediment layer in terms of the particulate adsorbed concentration, centration, CCp,bp,b::

(88)(88)

where where rrbb = amount of chemical adsorbed per mass of dry sediment, = amount of chemical adsorbed per mass of dry sediment, µµg kgg kg-1-1

CCp,bp,b = particulate adsorbed chemical concentration, = particulate adsorbed chemical concentration, µµg Lg L-1-1

SSbb = bed solids concentration, kg L = bed solids concentration, kg L-1-1

The total concentration in the water column and in the bed sediment is the sum of tThe total concentration in the water column and in the bed sediment is the sum of the soluble and particulate adsorbed chemical,he soluble and particulate adsorbed chemical,

(89) (89)

where where CCT,wT,w = total concentration, = total concentration, µµg Lg L-1-1

CCs,ws,w = soluble chemical concentration in the water column, = soluble chemical concentration in the water column, µµg Lg L-1-1

CCp,wp,w = particulate adsorbed chemical concentration in the water column, = particulate adsorbed chemical concentration in the water column, µµg Lg L-1-1

CCT,bT,b = total bed concentration, = total bed concentration, µµg Lg L-1-1

CCs,bs,b = soluble chemical concentration in the bed sediment, = soluble chemical concentration in the bed sediment, µµg Lg L-1-1

CCp,bp,b = adsorbed chemical concentration in the bed sediment, = adsorbed chemical concentration in the bed sediment, µµg Lg L-1-1

All chemical concentrations in sediment and water refer to the mass per All chemical concentrations in sediment and water refer to the mass per unit of total environmental volume (in liters), rather than on a basis of unit of total environmental volume (in liters), rather than on a basis of liquid water volume. liquid water volume. The final set of six equations is:The final set of six equations is:

(90)

(91)

(92)

(93)

(94)

(95)

where where CCs,ws,w = soluble chemical concentration in the water column, = soluble chemical concentration in the water column, µµg Lg L-1-1

tt = time, days = time, days AA = cross-sectional area of the river, m = cross-sectional area of the river, m22

QQ = volumetric flowrate of the river, m = volumetric flowrate of the river, m33 d d-1-1

xx = longitudinal (downstream) distance, m = longitudinal (downstream) distance, m E E = longitudinal dispersion coefficients, m= longitudinal dispersion coefficients, m22 d d-1-1

kk11, , kk33 = adsorption rate constants, L kg = adsorption rate constants, L kg-1-1 d d-1-1

kk22, , kk44 = desorption rate constants, day = desorption rate constants, day-1-1

λλww, , λλbb = overall pseudo-first-order rate constant of photolysis, = overall pseudo-first-order rate constant of photolysis, volatilization, biological transformation, chemical hydrolysis, volatilization, biological transformation, chemical hydrolysis, and and oxidation reaction in the water (subscript oxidation reaction in the water (subscript ww) and bed ) and bed (subscript (subscript bb), ), dayday-1-1

kkLL = mass transfer coefficient between water column and pore water = mass transfer coefficient between water column and pore water of bed sediment, m d of bed sediment, m d-1-1

hh = depth of water column, m = depth of water column, m FFxx((x, tx, t) = distributed source of soluble chemical, ) = distributed source of soluble chemical, µµg Lg L-1-1 d d-1-1 CCp,wp,w = particulate adsorbed chemical in the water column, = particulate adsorbed chemical in the water column, µµg Lg L-1-1

kkss = sedimentation rate constant ( = sedimentation rate constant (vvww//hh, mean particle settling , mean particle settling velocity divided by the mean depth), day velocity divided by the mean depth), day-1-1

αα = scour/resuspension rate constant, day = scour/resuspension rate constant, day-1-1

SSbb = solids concentration in the bed, kg L = solids concentration in the bed, kg L-1-1

SSww = solids concentration in the water column, kg L = solids concentration in the water column, kg L-1-1

γγ = ratio of water depth (or volume) to depth of the active bed = ratio of water depth (or volume) to depth of the active bed sediment layer (sediment layer (h/dh/d))

FFpp((x, tx, t) = distributed source term for particulate adsorbed chemical to ) = distributed source term for particulate adsorbed chemical to the water column, the water column, µµg Lg L-1-1 d d-1-1

GG((x, tx, t) = distributed source term far suspended solids to the water ) = distributed source term far suspended solids to the water column, kg Lcolumn, kg L-1-1 d d-1-1

CCs,bs,b = soluble chemical concentration in the bad sediment, = soluble chemical concentration in the bad sediment, µµg Lg L-1 -1

rr = amount of adsorbed chemical on sediment solids, = amount of adsorbed chemical on sediment solids, µµg kgg kg-1-1 (dry (dry weight) weight)

Equations (90)-(95) are applicable for hydrophobic chemicals, which may take a lonEquations (90)-(95) are applicable for hydrophobic chemicals, which may take a long time to adsorb or desorb (the kinetics of adsorption and desorption are considered g time to adsorb or desorb (the kinetics of adsorption and desorption are considered explicitly). If the kinetics of transformation reactions or the time of transport (advecexplicitly). If the kinetics of transformation reactions or the time of transport (advection, dispersion, scour/resuspension, and sedimentation) are relatively slow comparetion, dispersion, scour/resuspension, and sedimentation) are relatively slow compared to the kinetics of sorption, then an assumption of instantaneous equilibrium may bd to the kinetics of sorption, then an assumption of instantaneous equilibrium may be utilized. Under these conditions, the sediment/water partition coefficients are simpe utilized. Under these conditions, the sediment/water partition coefficients are simply the ratio of the adsorption rate constant to the desorption rate constant:ly the ratio of the adsorption rate constant to the desorption rate constant:

(96)(96)

where where KKp,wp,w and and KKp,bp,b are the partition coefficients (L kg are the partition coefficients (L kg-1-1) in the water column and be) in the water column and bed, respectively. We allow the possibility of a different sediment-water partition coeffd, respectively. We allow the possibility of a different sediment-water partition coefficient for the bed sediment than for the water column due to the dependence of icient for the bed sediment than for the water column due to the dependence of KKpp o on solids concentration.n solids concentration.

Quite often the solids concentrations in a river and the bed are rather constant duriQuite often the solids concentrations in a river and the bed are rather constant during the period of interest. In this case, equation (95) may be assumed to be equal to zng the period of interest. In this case, equation (95) may be assumed to be equal to zero (steady-state conditions, ero (steady-state conditions, dSdSbb//dtdt = 0). = 0). Thus the right-hand side of equation (95) may be rearranged and solved for Thus the right-hand side of equation (95) may be rearranged and solved for αα, the s, the scour coefficient:cour coefficient:

(97)(97)

(98)(98)

Given the assumption of an instantaneous local equilibrium for sorption and a steady-state Given the assumption of an instantaneous local equilibrium for sorption and a steady-state solids concentration in the river water column, the set of six equations (90)-(95) can be redusolids concentration in the river water column, the set of six equations (90)-(95) can be reduced to a set of only two equations: one equation for the total concentration of chemical in thced to a set of only two equations: one equation for the total concentration of chemical in the water column of the river and one equation for the amount of adsorbed chemical per unit e water column of the river and one equation for the amount of adsorbed chemical per unit mass of bed sediment.mass of bed sediment.

(99)(99)

(100)(100)

where where CCTT = = CCs,ws,w + + CCp,wp,w = total concentration in the water column, = total concentration in the water column, µµg Lg L-1-1; and ; and FFTT((x, tx, t) is the di) is the distributed source for total chemical input, stributed source for total chemical input, µµg Lg L-1-1 d d-1-1. . In equation (99), In equation (99), CCTT is abbreviated, but identical to is abbreviated, but identical to CCT,wT,w in equation (89). in equation (89). Equation (100) gives the change in sediment chemical concentration over time, so it is usefuEquation (100) gives the change in sediment chemical concentration over time, so it is useful in predictions of recovery times for large rivers. l in predictions of recovery times for large rivers.

(101)(101)

The concentration of the chemical in the dissolved phase in the water columThe concentration of the chemical in the dissolved phase in the water column and sediment pore water can be calculated below in terms of the total concn and sediment pore water can be calculated below in terms of the total concentration in water entration in water CCT,wT,w and in the bed and in the bed CCT,bT,b..

(102)(102)

(103)(103)

The concentration of pore water in the bed has been defined on a total envirThe concentration of pore water in the bed has been defined on a total environmental volume in the sediment (onmental volume in the sediment (µµg Lg L-1-1 total volume), not on a liquid water total volume), not on a liquid water basis (basis (µµg Lg L-1-1 H H22O). One must divide the concentration O). One must divide the concentration CCs,bs,b by the porosity of by the porosity of the sediment (Hthe sediment (H22O volume/total volume) in order to obtain the pore water coO volume/total volume) in order to obtain the pore water concentration that may be drained from a sediment core, for example.ncentration that may be drained from a sediment core, for example.

Equations (99) and (100), coupled with the equilibrium relationships [equatiEquations (99) and (100), coupled with the equilibrium relationships [equations (16), (17), (18)] provide a useful formulation for simulation of chemical sons (16), (17), (18)] provide a useful formulation for simulation of chemical spills, distributed source runoff, and point source problems under conditions pills, distributed source runoff, and point source problems under conditions of steady state for suspended solids and bed sediment with instantaneous sorof steady state for suspended solids and bed sediment with instantaneous sorption equilibrium.ption equilibrium.

To solve numerically the set of equations (99) and (100), the model employs the scTo solve numerically the set of equations (99) and (100), the model employs the scheme proposed in Marchuk. The computational algorithm is based on a method of heme proposed in Marchuk. The computational algorithm is based on a method of splitting the equations into different physical processes. splitting the equations into different physical processes. For each incremental time interval between For each incremental time interval between ttjj and and ttj+1j+1, we consider the numerical s, we consider the numerical scheme comprising three steps. At the first step the equation of chemical transport cheme comprising three steps. At the first step the equation of chemical transport is solved:is solved:

(104)(104)

At the second step we solve the diffusion equation:At the second step we solve the diffusion equation:

(105)(105)

The third step solves the reaction rate equations for local transformations of chemThe third step solves the reaction rate equations for local transformations of chemicals, their interaction with the bottom sediments, and source influence. This repreicals, their interaction with the bottom sediments, and source influence. This representation of the chemical transport model simplifies its computation and allows fosentation of the chemical transport model simplifies its computation and allows for optimal solution algorithms at each step. The equations are treated as separate sr optimal solution algorithms at each step. The equations are treated as separate solutions at the first two steps and combined with each other at the third.olutions at the first two steps and combined with each other at the third.

The third-step equations can be considered at each point of the integration domaiThe third-step equations can be considered at each point of the integration domain as a set of ordinary difference equations with the coefficients dependent on the sn as a set of ordinary difference equations with the coefficients dependent on the spatial coordinates. patial coordinates.

Example 7.3 Pesticide Degradation in a Irrigation CanalExample 7.3 Pesticide Degradation in a Irrigation Canal

Acrolein is a toxic herbicide that is used for submersed weed control in irrigatiAcrolein is a toxic herbicide that is used for submersed weed control in irrigation canals. The data given below are from Bartley and Gangstad. Develop a steon canals. The data given below are from Bartley and Gangstad. Develop a steady-state model to calculate the acrolein concentration in the downstream receady-state model to calculate the acrolein concentration in the downstream receiving water below the treaded area of the Wahluke Branch Canal of the Columiving water below the treaded area of the Wahluke Branch Canal of the Columbia River Basin in Washington. Dosages required are typically 100 ppb acroleibia River Basin in Washington. Dosages required are typically 100 ppb acrolein.n.

k`k`vv = = 0.305 m d0.305 m d-1-1 Volatilization mass transfer coefficient Volatilization mass transfer coefficient k`k`bb = = 8.9 8.9 × 10× 10-9-9 L cells L cells-1-1 d d-1-1 Second-order biolysis rate constantSecond-order biolysis rate constantX = X = 101088 cells L cells L-1-1 Bacterial cellsBacterial cellsUUxx = = 0.305 m s0.305 m s-1-1 Mean velocityMean velocityH = H = 0.91 m0.91 m Mean depthMean depth

Calculate the overall pseudo-first-order reaction rate constant. Since acrolein iCalculate the overall pseudo-first-order reaction rate constant. Since acrolein is nearly totally soluble, the problem then becomes analogous to BOD degradats nearly totally soluble, the problem then becomes analogous to BOD degradation in a stream. The primary loss mechanism is apparently an initial hydration ion in a stream. The primary loss mechanism is apparently an initial hydration to to ββ-hydroxypropionaldehyde and subsequent biotransformation. Assume plug-hydroxypropionaldehyde and subsequent biotransformation. Assume plug-flow conditions and steady state.-flow conditions and steady state.

Solution:Solution: For a plug-flow stream at steady state, For a plug-flow stream at steady state,

A linear regression equation was used for model calibration to obtain the parameter A linear regression equation was used for model calibration to obtain the parameter ∑∑k k (Figure 7.21). The pseudo-first-order rate constant obtained by this method was 0.57 (Figure 7.21). The pseudo-first-order rate constant obtained by this method was 0.57 dayday-1-1. Then the pseudo-first-order rate constant was calculated from the measured rate . Then the pseudo-first-order rate constant was calculated from the measured rate constants given for volatilization and biodegradation. The result using this method was constants given for volatilization and biodegradation. The result using this method was 1.23 day1.23 day-l-l, about two times larger. The agreement between the two estimates is probably , about two times larger. The agreement between the two estimates is probably acceptable given large uncertainties in measuring rate constants. If the last two yield acceptable given large uncertainties in measuring rate constants. If the last two yield data points at km 48.3 and 64.4 are ignored, then the best fit regression line yields a data points at km 48.3 and 64.4 are ignored, then the best fit regression line yields a pseudo-thirst-order rate constant of 1.2 daypseudo-thirst-order rate constant of 1.2 day-1-1, in close agreement to the measured rate , in close agreement to the measured rate constants.constants.

Model CalibrationModel Calibration

Figure 7.21 Figure 7.21 Acrolein in an irrigation canal (Wahluke Canal). Acrolein in an irrigation canal (Wahluke Canal). Best fit of model to field data for Example 7.3Best fit of model to field data for Example 7.3

Measured Rate Constants Given:Measured Rate Constants Given:

A pulse input of pollutants, which were primarily organophosphate pesticides A pulse input of pollutants, which were primarily organophosphate pesticides and organic mercurial compounds, to the Reline River at Basel, Switzerland, and organic mercurial compounds, to the Reline River at Basel, Switzerland, was caused by a fire at a chemical warehouse on November 1, 1986. An estimawas caused by a fire at a chemical warehouse on November 1, 1986. An estimated 7 metric tons of contaminants were washed into the Rhine by fire-fighting ted 7 metric tons of contaminants were washed into the Rhine by fire-fighting runoff. A fish kill extended over 250 km following this spill. runoff. A fish kill extended over 250 km following this spill. Subsequent monitoring of the pollutant plume by Swiss, German, French, and Subsequent monitoring of the pollutant plume by Swiss, German, French, and Dutch environmental agencies provided an excellent database for analyzing pDutch environmental agencies provided an excellent database for analyzing pollutant fate and transport.ollutant fate and transport.Use the data given below and model equations (99) and (100) to estimate the fUse the data given below and model equations (99) and (100) to estimate the fate and transport of the sum of the phosphoester pesticides in the Rhine Riveate and transport of the sum of the phosphoester pesticides in the Rhine River. Field data for model calibration are given in Figure 7.22.r. Field data for model calibration are given in Figure 7.22.

Example 7.4 Rhine River Chemical SpillExample 7.4 Rhine River Chemical Spill Model Model

Solution:Solution: Equations (99) and (100) were solved with a split operator method un Equations (99) and (100) were solved with a split operator method under the steady flow assumption, time-variable concentrations.der the steady flow assumption, time-variable concentrations.The measured mass of material passing each of the four locations decreased witThe measured mass of material passing each of the four locations decreased with downstream distance (Figure 7.22). The sum of phosphoester pesticides was ah downstream distance (Figure 7.22). The sum of phosphoester pesticides was approximately 4700 kg at Maximiliansau (362 km), 3700 kg at Mainz (496 km), 3pproximately 4700 kg at Maximiliansau (362 km), 3700 kg at Mainz (496 km), 3200 kg at Bad Honnef (640 km), and 1400 kg at Lobith (865 km). 200 kg at Bad Honnef (640 km), and 1400 kg at Lobith (865 km). An overall pseudo thirst-order transformation rate constant of 0.20 dayAn overall pseudo thirst-order transformation rate constant of 0.20 day-1-1 was u was used in order to reproduce the estimated mass fluxes. Effects of the accident woused in order to reproduce the estimated mass fluxes. Effects of the accident would have occurred over a much longer duration if the pesticide chemicals had beld have occurred over a much longer duration if the pesticide chemicals had been hydrophobic, persistent, and trapped in the sediments, for example, DDT. en hydrophobic, persistent, and trapped in the sediments, for example, DDT. Figure 7.22 shows the results of model calibration with little "tuning" of the paFigure 7.22 shows the results of model calibration with little "tuning" of the parameters.rameters.

Figure 7.22 Result of field measured concentration at four locations and model results (thin solid lines) versus time in days of November 1986.