Transcript Document
7. TOXIC ORGANIC CHEMICALS
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.
- The Precautionary Principle, International Conference on an Agenda of Science for Environment and Development Into the 21 st Century, Vienna, Austria (1991)
There are 4 million organic chemicals with names given by the International Union of Pure and Applied Chemistry (IUPAC). Approximately 1000 new organic chemicals are synthesized and used commercially each year. Only a fraction of these prove to be toxic or carcinogenic, and 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 use mathematical models to determine if they pose an unreasonable risk to humans or the environment. We estimate their fate and transport in the environment, their exposure concentration to humans and wildlife, and perform waste load allocations to meet water quality standards.
Organic chemistry is the chemistry of compounds of carbon. Organic chemicals are obtained from material produced originally by living organisms (such as petroleum, coal, and plant residues) or they are synthesized from other organic compounds or inorganics (e.g., carbonates or cyanides). Organic chemists are concerned with the synthesis of new organic chemicals to make new products; but environmental scientists are concerned with the degradation of these chemicals in the environment. We want them to be below toxicity thresholds and to be nonpersistent.
7.1 NOMENCLATURE
There are many different ways to name organic compounds including common names, 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 general 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 chain of reactions.
These reactions are usually microbially mediated (enzymes catalyze the reactions), but other abiotic processes such as photolysis, hydrolysis, chemical oxidation or reduction may also be important.
Microbial "infallibility" would state that all organic chemicals that are synthesized 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 environment, 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, and 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 can sometimes synthesize chemicals in nature that are quite toxic and rather slow to degrade.
Chlorinated organic chemicals are not purely man-made (xenobiotics), but now we know that some chlorinated organic chemicals are synthesized by plants and quite common in nature.
Figure 7.2 shows some examples of cyclic organic chemicals that are sometimes difficult to degrade in the environment.
To 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 task.
There are many toxic organic chemicals that cause problems in the environment and comprise various "priority pollutant" lists. One of the most important lists is that for drinking water standards. Organic chemlicals for which maximum allowable drinking water standards have been established are shown in Figure 7.3.
Figure 7.2
Examples of cyclic organic compounds (including alicyclic, aromatic, and heterocyclic compounds).
Figure 7.3
(a) Volatile organic compounds that have maximum contaminant level (MCL) drinking water standards.
(b) Some synthetic organic chemicals for which maximum contaminant levels (MCLs) have been established.
Figure 7.3
(continued).
7.2 ORGANICS REACTIONS
The types of reactions: biological transformations, chemical hydrolysis, oxidation/reduction, photodegradation, volatilization. sorption, and bioconcentration are among the important reactions that organic chemicals undergo in natural waters.
7.2.1 Biological Transformations
Biological transformations refer to the microbially mediated transformation of organic chemicals, often the predominant decay pathway in natural waters. It may occur under aerobic or anaerobic conditions, by bacteria, algae, or fungi, and by an array of mechanisms (dealkylation, ring cleavage, dehalogenation, etc.). It can be an intracel lunar or extracellunar enzyme transformation.
The term "biodegradation" is used synonymously with "biotransformation," but some researchers reserve "biodegradation" only for oxidation reactions that break down the chemical. Reactions that go all the way to CO 2 and H 2 O are referred to as "mineralization." In the broadest sense, "biotransformation" refers to any mlcrobially mediated reaction that changes the organic chemical. It does not have to be an oxidation reaction, nor does it have to yield carbon or energy for microbial growth or maintenance.
The term "secondary substrate utilization" refers to the utilization of organic chemicals at low concentrations (less than the concentration required for growth) in the presence of one or more primary substrates that are used as carbon and energy sources. "Co-metabolism" refers to 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 substrates.
Many toxic organic reactions in natural waters are microbially mediated with both bacteria and fungi degrading a wade variety of pesticides. Dehalogenation, dealkylation, hydrolysis, oxidation, reduction, tong cleavage, and condensation reactions are all known to occur either metabolically or via co-metabolism (see Table 7.1).
Several bacterial genera are known that are capable of utilizing certain organics as the sole carbon, energy, or nitrogen source. Pseudomonas (with 2,4-D and paraquat), Nocardia (with dalapon and propanil), and Aspergillus species (with trifluralin and picloram) are poignant examples.
Table 7.1 Biological Transformations Common in the Aquatic/Terrestrial Environment
It is convenient when possible to express rate expressions for organic transformations as pseudo-first-order-reactions, such as equation (1) belolw. The reaction rate expression is then (1)
where C is the toxic organic concentration in solution and k
b
pseudo-first-order biotransformation rate constant. is the Table 7.2 is a summary of pseudo-first-order and second-order rate constants k
b
for the disappearance of toxic organics from natural waters and groundwater via biotransformation.
The actual microbial biotransformation rate follows the Monod or Michaelis-Menton enzyme kinetics expression, where (2)
Where: k
b
= pseudo-first-order biological transformation rate constant,T 1 ; μ = maximum growth rate, T -1 ; X = viable microbial biomass concentration, M L -3 ; Y = cell yield, microbial cell conc yield/ organic conc utilized; K
M
= Michaelis half saturation constant, M L -3 .
Table 7.2 Selected Biotransfor mation Rate Constants.
Under typical environmental conditions, the concentration of dissolved organics (C < 10 μg L -1 ) is less than that of the Michaelis half-saturation constant (K
M
≈ 0.1-10 mg L -1 ). Therefore the equation becomes (3a)
where k b ` = μ/YK
M
concentration (C). . This is essentially second-order biotransformation kinetics. It is first order in bacteria biomass (X) and first order in chemical Sometimes organic chemicals that are adsorbed to suspended particulate matter are biodegraded in addition to soluble chemical. Equation (3a) must be rewritten in terms of both dissolved and adsorbed chemical concentrations (3b)
where C
T
is the total whole water chemical concentration, C is the dissolved phase concentration. and C
p
is the particulate adsorbed concentration.
If the substrate concentration C is very large such that C >> K natural waters), then the microorganisms are growing exponentially, and the rate expression in equation (2) reduces to
M
(not likely in (4)
which is a zero-order rate expression in C and first-order in X.
Biotransformation experiments are conducted by batch, column, and chemostat experimental methods. Other fate pathways (photolysis, hydrolysis, volatilization) must be accounted for in order to correctly evaluate the effects of biodegradation.
It is incumbent on the fate modeler to understand the range of breakdown products (metabolites) in biological transformation reactions. Metabolites can be as toxic (or more toxic) than the parent compound.
Following all the metabolites and pathways in the biological degradation of organic chemicals can be complicated. Polychlorinated biphenyls (PCBs) are mixtures of many isomers - the total number of different organic chemicals is 209 congeners.
Figure 7.3b shows the structures, where x and y represent the combinations of chlorine atoms (one to five) at different positions on the biphenyl rings. Each congener has distinct properties that result in a different reactivity than the others. Both the rate of the biological transformation and the pathway can be different far each of the congeners.
There are several basic types of biodegradation experiments. Natural water samples from lakes or rivers can have organic toxicant added to them in batch experiments. Disappearance of toxicant is monitored.
Organic xenobiotic chemicals can be added to a water-sediment sample to simulate in situ conditions, or a contaminated sediment sample alone may be used with or without a spiked addition. Primary sewage, activated sludge, or digester sludge may be used as a seed to test degradability and measure xenobiotic disappearance.
Radiolabeled organic chemicals can be used to estimate metabolic degradation (mineralization) by measuring CO into biomass. These experiments are called heterotrophic uptake experiments.
2 off-gas and synthesis
The organic chemical may be added in minute concentrations to simulate exposure in natural conditions, or it may be the sole carbon source to the culture to determine whether transformation reactions are possible.
Biodegradation is affected by numerous factors that influence biological growth:
Temperature: effects on biodegradation of toxics are similar to those on biochemical oxygen demand (BOD) using an Arrhenius-type relationship.
Nutrients: are necessary for growth and often limit growth rate. Other organic compounds may serve as a primary substrate so that the chemical of interest is utilized via co-metabolism or as a secondary substrate.
Acclimation: is necessary for expressing repressed ( induced) enzymes or fostering those organisms that can degrade the toxicant through gradual exposure to the toxicant over time. A shock load of toxicant may kill a culture that would otherwise adapt if gradually exposed.
Population density or biomass concentration: organisms must be present in large enough numbers to significantly degrade the toxicant (a lag often occurs if the organisms are too few).
7.2.2 Chemical Oxidation
Chemical oxidation takes place in the presence of dissolved oxygen in natural waters. Oxygen is reduced and the organic chemical is oxidized, but the reaction can be slow. Alternatively, chemical oxidation can be triggered by photochemical transients that may have considerable oxidizing power but low concentrations.
Oxidants such as peroxyl radicals ROO·, alkoxy radicals RO·. hydrogen peroxide H 2 O 2 , hydrokyl radicals ·OH, singlet oxygen O 2 , and solvated electrons are produced in low concentrations and react quickly in natural waters. Because of their large oxidizing power, they may react with a variety of trace organics in solution, but each transient reacts rather specifically with certain trace organic moieties. Thus it is not useful to consider a general second-order rate constant for all oxidants in a given water body.
It is better to determine the relevant oxidant chemistry and to measure the oxidant concentration when possible. Since the transient chemical oxidants are often generated photochemically, light-absorbing chromophores, such as humic and fulvic acids and algal pigments, and sunlight intensity will influence oxidation rates.
Alkyl peroxyl radicals ( aromatic radicals:
∼
1
×
10 -9 M in sunlit natural waters) react rapidly with phenols and amines in natural waters to form acids and
Singlet oxygen reacts specifically with olefins:
Singlet oxygen concentrations in sunlit natural waters are on the order of 1
×
10 -12 M. All of these oxidation reactions may be assumed to be second-order reactions: (5)
where C is the organic concentration and Ox is the oxidant concentration. Table 7.3: the second-order rate constants for chemical oxidation of selected priority organic chemicals with singlet oxygen and alkyl peroxyl radicals.
Table 7.3 Second-Order Reaction Rate Constants for Chemical Oxidation: Summary Table of Oxidation Data with Singlet Oxygen O 2 and Alkyl Peroxyl Radicals ROO∙
Free radical oxidation requires a chain or series of reactions Involving an initiation step, propagation, and subsequent termination. We will illustrate the free radical reaction using the alkyl peroxyl radical ROO· as an example.
The chemical is represented as an arbitrary organic, RH. A-B is the initiator, which is any free radical source including peroxides, H 2 O 2 , metal salts, and auto compounds. Investigators have utilized a commercially available azo initiator to estimate the reactivity of pesticides to ROO· in natural waters.
If no initiators are available in the water, then reaction (c) represents the probable oxidation pathway, a slow reaction with dissolved oxygen. Otherwise steps (a) and (b) lead to peroxide formation, step (d). Once the highly reactive peroxide radical is formed, it continues to react with the organic chemical, RH, and regenerates another free radical, R', as given in reaction (e).
This step may be repeated thousands of times for every photon of light absorbed. Chance collisions between free radicals can terminate the reaction, reactions (f), (g), and (h). At the low pollutant concentrations found in natural waters, reaction (f) is the most likely termination step. Hydrogen peroxide may also be formed, especially when natural dissolved organic matter (DOC) and humates are present. H 2 O 2 is a powerful oxidant in natural waters.
If the initiation step is rapid, then the rate-limiting step is the rate of oxidation of the organic in reaction (e): (6)
Provided that reaction (d) is more raped than reaction (e), the rate of peroxide formation is (7)
and assuming steady state, the rate of radical be equal to the rate of termination: (8), (9)
Substituting equation (9) into equation (6), we find the final reaction rate for the oxidation of the organic chemical is (10)
The rate of reaction is a pseudo-first-order reaction, where k
3
is the overall reaction rate constant which is a function of r
f
, the rate of peroxide formation. If the rate of peroxide formation is relatively constant (as expected in natural waters), then the free radical oxidation o( the toxic organic can be computed as a pseudo-first-order reaction.
First-order oxidations of pesticides and organic chemicals have been reported in natural waters. However, these oxidations are often microbially mediated. Strictly chemical free radical oxidation of toxic organics in natural waters remains important for a few classes of compounds. Free radical oxidation is often a part of the photolytic cycle of reactions in natural waters and atmospheric waters.
Oxidations of organic chemicals by O 2(aq) is generally slow, but it can be mediated by microorganisms. Cytochrome P450 monooxygenase is a well-studied enzyme with an iron porphyrin active site. Methanotrophs and other organisms can use this pathway to oxidize organics in natural waters, a type of biological transformation.
7.2.3 Redox Reactions
Electron acceptors such as oxygen, nitrate, and sulfate can be reduced in natural waters while oxidizing trace organic contaminants. Oxidation reactions of toxic organic chemicals are especially important in sediments and groundwater, where conditions may be anoxic or anaerobic. The general scheme for utilization of electron acceptors in natural waters fort lows thermodynamics (Table 7.4).
The sequence of electron acceptors is approximately:
The organic chemical in Table 7.4 is represented as a simple carbohydrate (CH 2 O such as glucose C 6 H 12 O 6 ) but other organics may be important reductants in natural waters and groundwaters.
Strict chemical reduction reactions that do not involve a biological catalyst (abiotic reactions) are common in groundwater but less important in natural waters and sediments, where a great complement of enzymes are available for redox transformations. In groundwater, H 2 S is a common reductant. It can reduce 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 matter, NOM) are good reductants in homogeneous systems. Figure 7.4 is a structure-activity relationship demonstrating that, in homogeneous solution, the second-order kinetic rate constant k
AB
directly proportional to the one-eleciron reduction potential of the is redox couple.
(11)
where H 2 X Is the reductant. Schwarzenbach et al. have shown that, in the case of juglone, it is not the diprotic dihydroquinone H 2 JUG that is the reactant with nitroaromatics, but rather the anions HJUG and JUG 2 . Reductants in natural waters include quinone. juglone (oak tree exudate), lawsone, and Fe-porphyrins. Nitroreductlon is a two-electron, two-proton transfer reaction.
The reduction of nitroaromatic compounds in natural waters and soil water may be viewed as an electron transfer system that is mediated by NOM 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-porphyrin-like substances.
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 groundwater (H bacteria, the reaction may be slow. 2 S, Fe 2+ , and CH 4 ) to determine if the reaction is favored thermodynamically (Table 7.5). In the absence of
Table 7.5
Redox Half-Reactions Pertinent in Wastewater, Groundwater, and Sediment Reactions
Table 7.5 (continued)
7.2.4 Photochemical Transformation Reactions
Direct photolysis, a light-initiated transformation reaction, is a function of the incident energy on the molecule and the quantum yield of the chemical.
When light strikes the pollutant molecule, the energy content of the molecule is increased and the molecule reaches an excited electron state. This excited state is unstable and the molecule reaches a normal (lower) energy level by one of two paths: - (1) it loses its "extra" energy through energy emission, that is, fluorescence or phosphorescence; - (2) it is converted to a different molecule through the new electron distribution that existed in the excited state. Usually the organic chemical is oxidized.
Photolysis may be direct or indirect. Indirect photolysis occurs when an intermediary molecule becomes energized, which then reacts with the chemical of interest.
The basic equation for direct photolysis is of the form: (12)
Where C is the concentration of organic chemical, and k for photolysis. Photo1ysis rate constants can be measured in the yield with sunlight or under laboratory conditions.
p
is the rate constant The first-order rate constant, k
p
can be estimated directly: (13)
where k
p
= uhotolvsls rate constant s-1 J = 6.02
×
10 20 = conversion constant φ = quantum yield I λ ε λ = sunlight intensity at waveBength L, photons cm-B s- 1 = molar absorbtivity or molar extinction coefficient at wavelength λ, molarity -1 cm -1 .
The 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 important 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.
The quantum yield is defined by (14)
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 the efficiency of photoreaction. Incoming radiation is measured in units of energy per unit area per time (e g., cal cm -2 s -1 ). The incident light in units of einsteins cm -2 s -1 nm -1 can be converted to watts cm multiplying by the wavelength (nm) and 3.03
×
10 39 .
-2 nm -1 by The intensity of light varies over the depth of the water column and may be related by (15)
where I
z
is the intensity at depth z, I 0 is the intensity at the surface, and K
e
is an extinction coefficient for light disappearance. Light disappearance is caused by the scattering of light by reflection off particulate matter, and absorption by any molecule. Absorbed energy can be converted to heat or can cause photolysis. Light disappearance is a function of wavelength and water quality (e.g., color, suspended solids, dissolved organic carbon).
Indirect or sensitized photolysis occurs when a nontarget molecule is transformed directly by light, which, in turn, transmits its energy to the pollutant molecule. Changes in the molecule then occur as a result of the increased energy content.
The kinetic equation for indirect photolysis is (16)
where k
2
is the indirect photolysis rate constant, X is the concentration of the nontarget intermediary, and k
p
is the overall pseudo-first-order rate constant for sensitized photolysis. The important role of inducing agents (e.g., algae exudates and nitrate) has been demonstrated.
Inorganics, especially iron, play an important role in the photochemical cycle in natural waters. Hydrogen peroxide, a common transient oxidant, is a natural source of hydroxyl radicals in rivers, oceans, and atmospheric water droplets.
Direct photolysis of H 2 O 2 produces ·OH, but this pathway is relatively unimportant because H 2 O 2 does not absorb visible light very strongly. The important source of ·OH involves hydrogen peroxide and iron (II) in a photo-Fenton reaction.
Hydroxyl radicals are a highly reactive and important transient oxidant of a wide range of organic xenobiotics in solution. They can be generated by direct photolysis of nitrate and nitrite in natural waters, or they can be generated from H 2 O 2 in the reaction shown above. Nitrobenzene, anisole, and several pesticides have been shown to be oxidized by hydroxyl radicals in natural waters.
7.2.5 Chemical Hydrolysis
Chemical hydrolysis is that fate pathway by which an organic chemical reacts with water. Particularly, a nucleophile (hydroxide, water, or hydronium ions), N, displaces a leaving group, X, as shown.
Hydrolysis does not include acid-base, hydration, addition, or elimination reactions. The hydrolysis reaction consists of the cleaving of a molecular bond and the formation of a new bond with components of the water molecule (H + , OH ). It is often a strong function of pH (see Figure 7.5).
Three examples of a hydrolysis reaction are presented below.
Types of compounds that are generally susceptible to hydrolysis are: - Alkyl halides - Amides - Amines - Carbamates - Carboxylic acid esters - Epoxides - Nitriles - Phosphonic acrid esters - Phosphoric acid esters - Sulfonic acid esters - Sulfuric acid esters
The kinetic expression for hydrolysis is
A summary of these data is presented in Table 7.7.
Hydrolysis experiments usually involve fixing the pH at some target value, eliminating 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 the dark eliminates the other fate pathways. In order to evaluate k
a
and k
b
, several non-neutral pH experiments must be conducted as depicted in Figure 7.5.
Often, the hydrolysis reaction rate expression in equation (17) is simplified to a pseudo-first-order reaction rate expression at a given pH and temperature (Table 7.7, 298 K and pH 7).
where k
h
= k
b
[OH ] + k
a
[H + ] + k
n
hydrolysis rate constant, T -1 ; k
b
and k
h
is the pseudo-first-order is the base-catalyzed rate constant, molariry -1 T -1 ; k
a
is the acid-catalyzed rate, polarity -1 T -1 ; and k
n
is the neutral rate constant, T -1 .
(18)
Table 7.7
Selected Chemical Hydrolysis Rate Constants, at 298 K and pH 7.
Figure 7.5
Effect of pH on hydrolysis rate constants.
7.2.6 Volatilization/Gas Transfer
The transfer of pollutants from water to air or from air to water is an important fate process to consider when modeling organic chemicals. 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 versa. Gas transfer of pollutants is analogous to the reaeration of oxygen in 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 by the molecular weight).
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 transfer is governed by molecular diffusion through a stagnant liquid 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 film. Oxygen, for example, is controlled by the liquid-film resistance. Nitrogen gas, although approximately four times more abundant in the atmosphere than oxygen, has a greater liquid-film resistance than oxygen
.
Volatilization, 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 depends on diffusion and mixing. Henry's constant, H, is a ratio of a chemical's vapor pressure to its solubility. It is a thermodynamic radio of the fugacity of the chemical (escaping tendency from air and water).
(19)
where p
g C sl
is the partial pressure of the chemical of interest in the gas phase, and is its saturation solubility. Henry's constant can be "dimensionless" [mg/L (in air)/mg/L (in water)] or it has units of atm m 3 mol -1 .
Figure 7.6
Two-film theory of gas-liquid interchange.
The value of H 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 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 of diffusion at equilibrium, (20)
where D is the molecular diffusion coefficient and dC/dx is the concentration gradient in either the gas or liquid phase. If we consider the molecular diffusion to occur through a thin stagnant film, the mass flux is then (21)
where k = D/Δz in which Δz is the film thickness and k is the mass transfer coefficient with units of LT -1 . At steady state, the flux through both films of Figure 7.6 must be equal: (22)
If Henry's law applies exactly at the interface, we can express the concentrations in terms of bulk phase concentrations, which are measurable by substitution below: (23) (24) (25)
By rearranging equation (25), we can solve for N in terms of bulk phase concentration, mass transfer coefficients for each phase, and Henry's constant: (26)
where K
L
is the overall mass transfer coefficient derived for expression of the gas transfer in terms of a liquid phase concentration.
(27)
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 resistance analogy. We can compare the two resistances to determine if the (28)
gas phase resistance, r
g
, or the liquid phase resistance, r
l
, predominates.
Equivalently, we could choose to write the overall mass transfer in terms of the buck gas phase concentration.
(29), (30)
If the gas is soluble, then H is small and the gas-film resistance controls mass tractsfer. In terms of a differential equation, the overall gas transfer: (31)
where C
sat
liquid.
= p
g
/H, A is the interfacial surface area, and V is the volume of the
In streams, A/V is the reciprocal depth of the water and the equation can be expressed as (32)
where Z is the mean depth and k
li
is termed the volatilization rate constant (T -1 ).
Equations (31) and (32) apply for either gas absorption or gas stripping from the water body. It is a reversible process.
The mass transfer coefficients are dependent on the hydrodynamic characteristics of the air-water interface and flow regime. For flowing water, we may write (33)
where u is the mean stream velocity and Z is the mean depth. For smooth flow (no ripples or waves) and wind speed less than 5 ms -1 ,
1/K δ
predominates.
(34), (35)
where C
D
is the dimensionless drag coefficient, W is the wind speed, and v is the kinematic viscosity.
The transfer term for aerodynamically rough flow with wave is (36)
where d is the diameter or amplitude of the waves, u * is the surface shear velocity and α is a constant dependent on the physics of the wave properties.
The diffusion coefficients in water and air have been related to molecular weight (37)
where D
l
is the diffusivity of the chemical in water and MW is the molecular weight, and (38)
where D
g
is the diffusivity of the chemical in air. The mass transfer rate constant, k
li
, can then be related to the oxygen reaeration rate, k
a
, by a ratio of the diffusivity of the chemical to that of oxygen in water: (39)
where D
O2
is 2.4
×
10 -5 cm 2 s -1 at 20 ºC.
The reaeration rate, k from
a
, can be calculated from any of the formulas available. In addition, the overall gas-film transfer rate may be calculated (40)
Where v presented in Table 7.8, Z is the water depth, and W is the wind speed in m s -1
k gi g
is the kinematic viscosity of all (a function of temperature) as has units of T -1 .
Solubility, vapor pressure, and Henry's constant data are presented in Table 7.9.
Dimensionless Henry's constant refer to a concentration ratio of mg/L air per mg/L in the water phase.
Yalkowsky measured the solubility of 26 halogenated benzenes at 25 ºC and developed the following relationship: (41)
Where S
w
is solubility (mol L -1 ), MP is the melting point (ºC), and K
ow
the estimated octano1/water partition coefficient.
is
Table 7.8 Kinematic Viscosity of Air
Table 7.9 Summary Table of Volatilization Data at 20 ºC
Table 7.9 (continued)
Lyman et al. compiled solubility data on 78 organic compounds and presented estimation methods based on K
ow
for different classes of compounds. They also included a method based on the molecular structure.
Mackay measured Henry's constant for 22 organic chemicals as part of a study of volatilization characteristics.
Transfer coefficients for the gas and liquid phases were correlated for correlated for environmental conditions as: (42) (43)
Where U 10 is the 10-m wind velocity (m s -1 ), Sc L liquid and gas Schmidt numbers.
and Sc G are the dimensionless Volatile 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 stripping tower. In natural waters, they are removed by stripping from the atmosphere. The overall mass transfer coefficient K
L
can be related to that of oxygen (Table 7.10) because so much information exists for oxygen transfer in natural waters.
Table 7.10 Estimated Henry`s Constant and Mass Transfer Coefficients for Selected Organics at 20 ºC
7.2.7 Sorption Reaction
Soluble organics in natural waters can sorb onto particulate suspended material or bed sediments. The mechanism and the processes by which this occurs include: - (1) physical adsorption due to van der Waals forces; - (2) chemisorption due to a chemical bonding or surface coordination reaction; - (3) partitioning of the organic chemical into the organic carbon phase of the particulates. Physical adsorption is purely a surface electrostatic phenomenon. Partitioning refers to the dissolution of hydrophobic organic chemicals into the organic phase of the particulate matter; it is an absorption phenomenon rather than a surface reaction, and it may occur slowly over time scales of minutes to days.
Adsorption isotherms refer to the equilibrium relationship of sorption between organics and particulates at constant temperature. The chemical is dissolved in water in the presence of various concentrations of suspended solids. After an initial kinetic reaction, a dynamic equilibrium is established in which the rate of the forward reaction (sorption) is exactly equal to the rate of the reverse reaction (desorption).
The sorption of toxicants to suspended particulates and bed sediments is a significant transfer mechanism. Partitioning of a chemical between particulate matter and the dissolved phase is not a transformation pathway; it only relates the concentration of dissolved and sorbed states of the chemical.
The octanol/water partition coefficient, K
ow
, is related to the solubility of a chemical in water. Tables 7.9 and 7.11 provide log K
ow
environmental interest.
values for a number of organic chemicals of Table 7.11
Ocranol/Water Partition Coefficients of Selected Organics, 298 K
The laboratory procedure for measuring K
ow
is given by Lyman.
- 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 is set at the estimated K
ow
.
- 2. Mixture is agitated until equilibrium is reached.
- 3. Mixture is centrifuged to separate the two phases. The phases are analyzed for the chemical.
- 4. K
ow
is the ratio of the chemical concentration in the octanol phase to chemical concentration in the water phase, and has no units. The logarithm of K
ow
has been measured from -3 to +7.
If the octanol/water partition coefficient cannot be reliably measured or is not available in databases, it can be estimated from solubility and molecular weight information, (44)
where MW is the molecular weight of the pollutant (g mol -1 ) and S is in units of ppm for organics that are liquid in their pure state at 25 "C.
For organics that are solid in their pure state at 25 ºC, (45)
where MP is the melting point of the pollutant (ºC) and
△
S f
entropy of fusion of the pollutant (cal mol -1 deg -1 ).
is the
The octanol/water partition coefficient is dimensionless, but it derives from the partitioning that occurs in the extraction between the chemical in octanol an water.
Octanol 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.
For a wide variety of organic chemicals, the octanol water partition coefficient is a good estimator of the organic carbon normalized partition coefficient (K
oc
).
Karickhoff et al. and Schwarzenbach and Westal13o have published useful empirical equations for predicting K
oc
as a function of K
ow
(46) (47)
Once an estimate of K partition coefficient suitable for natural waters is straightforward because the
oc
is obtained, the calculation of a sediment/water (48)
where f
oc
is the decimal fraction of organic carbon present in the particulate matter (mass/mass). Figure 7.7 is a schematic of how K
p
, K
oc
, and K 7.7a is the Langmuir adsorption isotherm for sorption of one chemical on particulate matter. Figure 7.7b shows but K
p ow
are interrelated. Figure is directly proportional to f
oc
. There is a y-intercept 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 log-log plot between K
oc
, and K
ow
.
Figure 7.7
Relationship between the sediment/water partition coefficient K
p
, the organic carbon partition coefficient
K oc
, and the octanol/water partition coefficient K
ow
.
Plot (a) and (b) are for only one chemical and (c) is for many chemicals.
K p
is a measure of the actual partitioning in natural waters.
The linear portion of the adsorption isotherm (Figure 7.7a) can be expressed by equation: (49)
The Langmuir isotherm in Figure 7.7a is derived from the kinetic eq`n for sorption-desorption: (50), (51)
where C is the concentration of dissolved toxicant, C
p
of particulate toxicant, C
pc
is the concentration is the maximum adsorptive concentration of the solids, and k respectively.
1
and k
2
are the adsorption and desorption rate constants,
At steady-state, eq`n (51) reduces to a Langmuir isotherm in which the amount adsorbed is linear at low dissolved toxicant concentrations but gradually becomes saturated at the maximum value (r
c
) at high dissolved concentrations.
(52)
Generally, the adsorption capacity of sediments is inversely related to particle size: clays > silts > sands. Sorption of organic chemicals is also a function of the organic content of the sediment, as measured by K
oc
, and silts are most likely to have the highest organic content.
Sometimes a Freundlich isotherm is inferred from empirical data. The function is of the form (53)
where n is usually greater than 1. In dilute solutions, when n approaches 1, the Freundlich coefficient, K, is equal to the partition coefficient, K
p
.
The partition coefficient is derived from simplification of the kinetic eq`ns (50) and (51) if r
c
>> r (the linear portion of the Langmuir isotherm). In this case, we may write (54a), (54b)
Where k
f
is the adsorption rate constant and k
r
constant.
is the desorption rate The total concentration of toxicant: (55)
Where f
d
and f
p
are the dissolved and particulate fractions, respectively: (56), (57)
and the ratio of the reaction rate constants is related by (58)
Where the ∞ subscripts indicate chemical equilibrium.
From kinetics experiments where dissolved and particulate concentrations are monitored over time, the ratio of steady-state concentrations can be read from the graph (Figure 7.8).
Sorption reactions usually reach chemical equilibrium quickly, and the kinetic relationships can often be assumed to be at steady-state. This is sometimes referred to as the "local equilibrium" assumption, when the kinetics of adsorption and desorption are rapid relative to other kinetic and transport processes in the system.
O'Conner and Connolly first reported that, for organics and metals alike, the sediment/water partition coefficient K
p
declines as sediment (solids) concentrations increase. It is a consistent phenomenon in natural waters that is particularly important for hydrophobic organic chemicals. For example, the K
p
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 that one attempts to measure K
p
, including complexation of a chemical by colloids and dissolved organic carbon that pass a membrane filter.
Figure 7.8 Kinetic sorption experiment in a batch reactor
7.2.8 Bioconcentration and Bioaccumulation
Bioconcentration of toxicants is defined as the direct uptake of aqueous toxicant through the gills and epithelial tissues of aquatic organisms. This fate process is of interest because it helps to predict human exposure to the toxicant in food items, particularly fish.
Bioconcentration is part of the greater picture of bioaccumulation and biomagnification that includes food chain effects. Bioaccumulation refers to uptake of the toxicant by the fish from a number of different sources including bioconcentration from the water and biouptake from various food items (prey) or sediment ingestion. Biomagnification refers to the process whereby bioaccumulation increases with each step on the trophic ladder.
The terms bioconcentration, bioaccumulation, and biomagnification are sometimes mistakenly used interchangeably. It is useful to accept the following definitions for the sake of discussion.
Bioconcentration: the uptake of toxic organics through the gill membrane and epithelial tissue from the dissolved phase.
Bioaccumulation: the total biouptake of toxic organics by the organism from food items (benthos, fish prey, sediment ingestion, etc.) as well as via mass transport of dissolved organics through the gill and epithelium.
Biomagnification: that circumstance where bioaccumulation causes an increase in total body burden as one proceeds up the trophic ladder from primary producer to top carnivore.
Bioconcentration experiments measure the net bioconcentration effect after x days, having reached equilibrium conditions, by measuring the toxicant concentration in the test organism. The BCF (bioconcentration factor) is the ratio of the concentration in the organism to the concentration in the water.
The BCF derives from a kinetic expression relating the water toxicant conceritration and organism mass: (59)
where e = efficiency of toxic absorption at the gill
k 1 k 2
= (L filtered/kg organism per day) = depuration rate constant including excretion and clearance of metabolites, day -1 C = dissolved toxicant, μg L -1 B = organism biomass, kg L -1 F = organism toxicant residue (whole body), μg kg -1
Steady-state solution is (60)
where BCF has units of (μg/kg)/(μg/L). Bioconcentration is analogous to sorption of hydrophobic organics. Organic chemicals tend to partition into the fatty tissue of fish and other aquatic organisms, and BCF is analogous to the sediment/water partition coefficient,
K p
. Bioconcentration also can be measured in algae and higher plants, where uptake occurs by adsorption to the cell surfaces or sorption into the tissues.
An empirical relationship for bioconcentration (BCF-K
ow
) in bluegill sunfish in 28 days exposure for 84 organic priority pollutants was (61)
and for rainbow trout with ten chlorobenzenes it was (62)
for low-level exposures typical of natural waters. Fathead minnow, bluegill, rainbow trout, brook trout, and mosquito fish are the species most frequently involved in bioconcentration tests.
Bioconcentration experiments, per se, do not measure the metabolism or detoxification of the chemical. Chemicals can be metabolized to more or less toxic products that may have different depuration characteristics. The bioconcentration experiment only measures the final body burden at equilibrium (although interim data that were used to determine when equilibrium was reached may be available). The fact that a chemical bioaccumulates at all is an indication that it resists biodegradation and is somewhat "biologically hard" or "nonlabile."
The kinetics of bioaccumulation are shown schematically in Figure 7.9.
Fish can lose unmetabolized toxics via biliary excretion or "desorption" through the gill. On the other hand, toxic organics can undergo biotransformations and be eliminated as metabolic products.
The rate constant, k
2
, includes total depuration (both excretion of unmetabolized toxics, k
2 `
, and elimination of metabolites, k parent compound, designated as k
2 `
in Figure 7.9.
2
``). Only a fraction of this elimination is returned to the water column as dissolved
Hydrophobic organics tend to accumulate in fatty tissue of animals. Lipidnormalized bioconcentration factors both in the laboratory and in the field have been correlated successfully with the hydrophobicity of toxic organics as measured by the octanol/water partition coefficient, K carnivores.
ow
(Table 7.12). Biomagnification 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
Figure 7.9 Bioaccumulation kinetics for hydrophobic organic chemicals in fish
Table 7.12
Bioconcentration Factor (BCF) for Selected Organic Chemicals in Fish (Units: μg/kg fish μg L water)
7.2.9 Comparison of Pathway
Most of the transformations discussed in Section 7.2 are expressed as second order reactions. It is difficult to compare the magnitudes of these reactions-the rate constants all have different units. Each of the transformations can be written as pseudo-first-order reactions assuming that the second concentration in the reaction rate expression can be assumed to be relatively constant.
The overall reaction rate: (63)
where C = dissolved organic concentration, ML -3 t = time, T
k b k o k r k p k h k v
= biotransformation rate constant, T = oxidation rate constant, T = photolysis rate constant, T -1 = reduction rate constant, T -1 = hydrolysis rate constant, T -1 -1 = volatilization rate constant, T -1 -1
Equation (63) includes an assumption that the atmosphere has a neg1igible concentration (partial pressure) of the organic, so only volatilizatlon occurs (stripping out of the water body).
For first-order reactions in a batch reactor in a batch reactor without transport, the reaction rate: (64)
Solving for the concentration as a function of time: (65), (66)
Taking the natural logarithm of both sides of equation (66) and solving for time (half-life) yields the well-known relationship below: (67)
where t 1/2
i n
1
k i
= overall half-life of the chemical due to all transformation reactions = the sum of all the pseudo-first-order reaction rate constants
Individual half-lives may be compared to determine which reaction predominates (gives the shortest half-life).
7.3 ORGANIC CHEMICALS IN LAKES
7.3.1 Completely Mixed Systems
As an approximation, lakes can be represented as ideal completely mixed flow through reactors (CMF systems) or a network of CMF compartments. A mass balance system of equations:
Figure 7.10: a schematic of the various reactions in the lake water column and sediment. An assumption of local equilibrium may be used to relate the particulate adsorbed concentration to the dissolved concentration through the partition coefficient K
p .
(68a), (68b), (68c)
where K
p
= sediment/water partition coefficient, L kg -1 C = dissolved organic chemical concentration, µg L -1 r = mass sorbed, µg kg -1 M = suspended or bed solids concentration, kg L -1
C p
= particulate adsorbed concentration, µg L -1
C T
= total (dissolved plus particulate) concentration, µg L -1
Figure 7.10 Schematic of a fate model for organic chemicals in water and sediment
Sorptive equilibrium is usually a valid assumption in natural waters because the time scale for most sorption reactions (minutes to hours) is small compared to the time scale for reactions and transport (days to years). Figure 7.10 indicates a rapid local equilibrium assumption for bioconcentration. 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 bioconcentration factor (BCF) helps to simplify the equations, and it is another partitioning coefficient that we may use similar to K
p .
(69)
where BCF = bioconcentration factor, L kg -1 C = dissolved chemical concentration, µg L -1 F = residue concentration in whole fish, µg kg -1 The total concentration of chemical C
T
may be larger or smaller in the sediment than the overlying water depending on whether the water column or sediment was contaminated first. Partitioning of the chemical between the dissolved pore water C
2
and adsorbed sediment C
p2
, may also be different due to the dependence of K
p2
, on solids concentration. Generally,
K p2
< K
p1
, because the sediment has a much higher solids concentration.
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 e177c1s, can be assessed in this context.
Anthropogenic inputs may also enter the water body from the atmosphere via wet precipitation and dry deposition. The concentration in rainfall is related to the gas phase concentration and Henry's constant, so the deposition mass is equal to the volume of rainfall times the aqueous phase concentration (70)
Where C
precip
is the precipitation concentration, C
g
is the gas phase concentration, and H is Henry's constant with the appropriate units. The flux of contaminants due to dry deposition is related to the depositional velocity and the gaseous concentration (71)
where v
d
is the deposition velocity (LT (ML -3 ) and J
d
-1 ), C
g
is the gas phase concentration is the areal mass flux due to dry deposition (ML -2 T -1 ). Equation (71) is empirical. Both gases and aerosol particles may contribute to dry deposition but the gas phase concentration should be proportional in either case, v
d
serving as the empirical proportionality constant.
The mass balance equation for a lake with toxic organic chemical inputs can be written assuming complete mixing, steady flow conditions, instantaneous local sorption equilibrium, and no atmospheric deposition.
(72)
Equation (72) has three unknown dependent variables – C terms of total (whole water, unfiltered) concentration.
T
, and C - but the assumption of local equailibrium allows us to write the equation entirely in (73)
where C
T
= total concentration = C + C
p
, ML -3 V = volume of the lake, L 3 t = time, T Q = flowrate In and out, L 3 T -1
f p
= particulate fraction of total chemical concentration, dimensionless = C
p / C T = K p
M /(1 + K
p
M)
f d
= dissolved fraction of total chemical concentration, dimensionless = C/ C
T
= 1 /(1 + K
p
M) C = dissolved chemical concentration, ML -3
C k s k i p
= particulate chemical concentration, ML -3 = sedimentation rate constant,T -1 = sum of pseudo-first-order reaction rate constant [eq`n (63)], T -1
Equation (73) is an ordinary differential equation with constant coefficients. It is solvable by first-order methods such as the integration factor method. Dividing through by the constant volume and rearranging, we have (74)
The final solution is (75)
where C
To
= initial total input concentration, ML -3 α = integration factor τ = mean hydraulic detention time = V/Q, T We 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 initial conditions, and the second term is the asymptotic "hump" (the shape of a Langmuir isotherm), which builds to a steady-state concentration as t → ∞.
(76)
The steady-state concentration is directly proportional to the total concentration of organic inputs to the lake.
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 time required for the concentration in the lake to reach 95% of the value that it will ultimately achieve.
(77) or
By inspection, one can prove that equations (75) and (78) are equal when (78) (79)
Equation (79) gives the time to 95% of steady state. For the simplest case of a nonadsorbing dissolved chemical undergoing first-order reaction decay, α = k + 1/τ.
The greater is the flushing rate ( 1/τ) and the reaction rate constant, the less is time required to achieve steady state. Conservative substances (k = 0) take the longest time to reach steady state after a step function change in inputs.
7.3.2 Dieldrin Case Study in Coralville Reservoir, Iowa
The following case study is used to illustrate aspects of ecosystem recovery from a persistent hydrophobic organic pollutant. It also demonstrates the use of comparmentalization within a lake to simulate transport.
Figure 7.13: a schematic of water column, sediment, and fish concentrations following a period when large discharges of chemical were put into the system. Because the contaminant is hydrophobic and persistent, it remains in the system for a long time, accumulating in fish tissue and sediment. It disappears by washout (advection), burial into the deep sediment, and slow degradation reactions. Depending on the sediment dynamics of the system and the rate ofchemical degradation, these can be slow processes taking years to decades.
Figure 7.14: some persistent insecticides (e.g. chlorinated hydrocarbons) used in the Midwest. These chemicals were banned in the 1970s and early 1980s because of their persistence and propensity to bioaccumulate in fish and wildlife. Also shown are two replacement insecticides (ester compounds), which hydrolyze and break down in the environment. They are toxic but much less persistent.
Figure 7.13
Schematic of lake recovery from a persistent hydrophobic pollutant
Figure 7.14
Selected insecticides used in the past in the midwestern United States
Agricultural usage of pesticides in Iowa is widespread, particularly grass and broadleaf herbicides and row crop soil insecticides. One of the insecticides widely used for control of the corn rootworm and cutworm from 1960 to 1975 was the chlorinated hydrocarbon, aldrin.
Aldrin is microbially metabolized to its persistent epoxide, dieldrin. Dieldrin 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
×
10 -6 mm Hg at 25 ºC). It is known to bioaccumulate to levels as high as 1.6 mg/kg wet weight in edible tissue of Iowa catfish.
Coralville Reservoir is a mainstream impoundment of the Iowa River in easters Iowa. It drains approximately 3084 square miles (7978 km sedimentation since it was created in 1958. 2 ) of prime Iowa farmland and receives extensive agricultural runoff with 90% of its drainage basin in intensive agriculture. It is a variable-level, flood control and recreational reservoir, which has undergone considerable At conservation pool (680 ft above mean sea level, msl), the reservoir has a capacity of 38,000 acre-ft (4.79
×
10 7 m 3 ), a surface area of 4900 acres (1.98
×
10 7 m 2 ), 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 acre-ft (6.63
×
10 7 m 3 ).
The total pesticide concentration is the sum of the particulate plus the dissolved concentrations, with instantaneous sorptive equilibrium assumed (80)
where f
d = C/ C T
= 1/(1 + K
p
M) = fraction of dissolved pesticide
f p = C p / C T = K p
M/(1 + K
p
M) = fraction of particulate pesticide W(t) = time-variable loading of pesticide, M/T
C T
k
= total concentration in the water column, ML -3 = sum of the pseudo-first-order degradation rate constants τ = mean hydraulic detention time V = reservoir volume, L 3
k s
= sedimentation rate constant, T -1 The fish residue equation is (81)
where k
1 k d
= pesticide uptake rate by fish, T -1 = depuration rate constant, T -1 F = whole-body fish residue level, M/M wet weight B = fish biomass concentration, M/L 3 wet weight
Equations (80) and (81) may be solved analytically for constant coefficients and 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 exponential manner due to degradation by soil organisms or a ban on application. For an exponentially declining loading function at rate ω, the analytical solutions to equations (80) and (81) are (82)
where C
To
= initial total pesticide concentration in lake, ML -3
C Tin,o
= initial total pesticide inflow concentration, ML -3 ω = rate of exponentially declining inflow concentration,T -1 (83)
Figure 7.15 is a schematic diagram of hypothetical pond or lake configurations that are possible for this problem. Each box is assumed to be completely mixed with bulk exchange between water compartments. There is dispersion in Coralville Reservoir that seems to be simulated best by the eight-compartment model based on dye studies.
Figure 7.16: simulation of a two-compartment model (water and sediment) for dieldrin in Coralville Reservoir. Model parameters based on calibration are given on the figure. The rate of declining inputs was 0.164 yr -1 , sedimentation rate constant was 0.18 day -1 ; the rate of biodegradation of dieldrin in sediment was 0.005 day -1 ; and the bioconcentration factor (BCF) was 70,000.
Model results were within the range of field observations. Dieldrin residues in fish, sediment, and water were all declining at fishing of bigmouth buffalo fish.
∼
15% per year Approximately 50% of the pesticide load was exported from the reservoir, 40% underwent sedimentation, and 10% entered a huge biomass of bottom-feeding fish. The fishery was reopened in 1980 for commercial
A 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 pararrleters (Figure 7.17).
Figure 7.15
Compartmental configuration for a two-box pond model or an eight-box lake model
Figure 7.16
Result of model and field data for dieldrin in Coralville Reservoir water sediment and in fish.
Figure 7.17 Post-audit study of dieldrin model for Coralville Reservoir showing utility of the model for forecasting fish residue levels.
Multicompartment solutions of equations (80) and (81) must include interflows and bulk dispersion as well as an assumption regarding suspended solids and fish biomass distribution. For each constant-volume compartment, (84)
where V = compartment volume, m 3
C T
= total pesticide concentration of the compartment, µg L t = time, days -1
Q a Q b C a f d f p
= inflow of water from adjacent compartments, m = outflow of wafer to adjacent compartments, m 3 3 d d -1 -1 = total pesticide concentration in the adjacent compartment, µg L = fraction of the total pesticide in the dissolved phase = fraction of the total pesticide in the particulate phase
k da
= reaction rate constant for the dissolved phase, day -1
k pa
= reaction rate constant for the particulate phase, day -1
k s k sa
= settling rate constant of the compartment, day -1 = settling rate constant from the above compartment, day -1 E = bulk dispersion coefficient for adjacent compartments, m 2 d -1 -1 A = surface area between two adjacent compartments, m 2
V a
l = mixing length between midpoints of adjacent compartments, m = volume of above compartment, m 3
The general mass balance equation for the jth compartment can he reduced to a general matrix equation : (85)
where i = subscript denoting adjacent compartments j = subscript denoting the jth compartment
C j C i Q i,j Q j,i
= total pesticide concentration in the jth compartment, µg L -1 = total pesticide concentration in an adjacent compartment, µg L = flow into compartment i from j, m = flow from compartment i to j, m 3 d 3 -1 d -1
f d,j
= dissolved fraction of a pesticide in compartment j
f p,j
= particulate fraction ova pesticide in compartment j -1
k da
= sum of dissolved reaction rate constant, day -1
k pa
= sum of particulate reaction rate constant, day -1
k s,i
= settling rate constant for compartment i, day -1
k s,j
= settle ins rate constant from compartment j, day -1
E i,j
= bulk dispersion coefficient between adjacent compartments, m 2 d -1
A j
= surface area of compartment j, m 2
l i,j
= length between the midpoints of adjacent compartments, m
V j
= compartment volume, m 3
V i
= volume of adjacent compartment, m 3
Figure 7.18
Eight-compartment dieldrin model results for Coralville Reservoir, water compartments
Figure 7.19
Eight-compartment dieldrin model results for Coralville Reservoir, sediment compartments
7.4 ORGANIC CHEMICALS IN RIVERS AND ESTUARIES
Advection, dispersion, and reaction of chemicals may be simulated for large rivers 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 vertically, and it will be transported downstream by current velocity (advection) and longitudinal dispersion.
After an initial mixing period, a three-dimensional advection-dispersion equation with Taylor's analogy may be applied for steady flow conditions and a uniform channel.
(86) where C = chemical concentration, M L -3 t = time, T E = dispersion coefficients in the x-, y-, and z-directions, L 2 T -1
u i
= average velocities in the x-, y-, and z-directions, LT x = longitudinal distance, L -1 y = lateral (or transverse) distance, L z = vertical distance, L
The mass balance equation in the longitudinal downstream dimension becomes: (87)
At this point one must consider the role of the sediment/water partitioning and sediment transport because chemicals that are adsorbed to suspended solids or bed sediment have a different fate and toxic effect than dissolved chemicals.
Included for general applications should be kinetics of physical reactions (sedimentation, scour/resuspension, adsorption/desorption, and gas transfer), biological transformations (biological oxidation/reduction and co-metabolism), and chemical reactions (hydrolysis, oxidation, photolysis).
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 occur predominantly in the soluble phase (C under reducing conditions (λ` b ).
s
), although special transformation reactions may occur for chemical adsorped to the sediment
Because environmental conditions differ in the sediment (e.g., photolysis and volatilization are not expected to occur from the sediment), the overall pseudo first order rate constant (λ b ) is different in the bed sediment from that in the water column (λw).
Rate constants for adsorption and desorption also differ in the water column compared 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 concentration (S).
Figure 7.20 also includes sedimentation of suspended solids (S
w
) in the river water and scour/resuspension of bed sediment (S
b
) via the first-order rate constants k
s
and α, respectively
.
Mass 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 overlying water may occur during the recovery phase. In either case, an overall mass transfer coefficient may be assumed (k through a limiting rile thickness Δz.
L
) that gives the velocity at which dissolved chemical moves by molecular diffusion
Figure 7.20 Schematic of reactions in the river water column and sediment including adsorption (k
1 , k 3
), desorption (k
2 , k 4
), sedimentation (k
s
), scour and resuspension (α), and degradation (λ) for soluble chemical (C
s
), particulate adsorbed chemical (C
p
) and the concentration of solids in the water column (S
w
) and in the bed (S
b
). Mass transfer between the pore water of the bed and overlying water takes place via a mass transfer coefficient (k
L
).
To 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 contamination in the active sediment layer in terms of the particulate adsorbed concentration, C
p,b
: (88)
where r
b C p,b S b
= amount of chemical adsorbed per mass of dry sediment, µg kg = particulate adsorbed chemical concentration, µg L -1 = bed solids concentration, kg L -1 -1
The total concentration in the water column and in the bed sediment is the sum of the soluble and particulate adsorbed chemical, (89)
where C
T,w C s,w C p,w
= total concentration, µg L = soluble chemical concentration in the water column, µg L -1 = particulate adsorbed chemical concentration in the water column, µg L -1 -1
C T,b C s,b C p,b
= total bed concentration, µg L -1 = soluble chemical concentration in the bed sediment, µg L -1 = adsorbed chemical concentration in the bed sediment, µg L -1
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 liquid water volume. The final set of six equations is: (90) (91) (92) (93) (94) (95)
where C
s,w
= soluble chemical concentration in the water column, µg L -1 t = time, days A = cross-sectional area of the river, m 2 Q = volumetric flowrate of the river, m 3 d -1 x = longitudinal (downstream) distance, m E = longitudinal dispersion coefficients, m 2 d -1
k 1
, k
3
= adsorption rate constants, L kg -1 d -1
k 2
, k
4
= desorption rate constants, day -1
λ w , λ b
= overall pseudo-first-order rate constant of photolysis, volatilization, biological transformation, chemical hydrolysis, and oxidation reaction in the water (subscript w) and bed (subscript b), day -1
k L
= mass transfer coefficient between water column and pore water of bed sediment, m d -1
h = depth of water column, m
F x
(x, t) = distributed source of soluble chemical, µg L -1
C p,w
d -1 = particulate adsorbed chemical in the water column, µg L -1
k s
= sedimentation rate constant (v
w
/h, mean particle settling velocity divided by the mean depth), day -1 α = scour/resuspension rate constant, day -1
S b
= solids concentration in the bed, kg L -1
S w
= solids concentration in the water column, kg L γ = ratio of water depth (or volume) to depth of the active bed sediment layer (h/d) -1
F p
(x, t) = distributed source term for particulate adsorbed chemical to the water column, µg L -1 d -1 G(x, t) = distributed source term far suspended solids to the water column, kg L -1 d -1
C s,b
= soluble chemical concentration in the bad sediment, µg L r = amount of adsorbed chemical on sediment solids, µg kg -1 -1 (dry weight)
Equations (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 explicitly). If the kinetics of transformation reactions or the time of transport (advection, dispersion, scour/resuspension, and sedimentation) are relatively slow compared to the kinetics of sorption, then an assumption of instantaneous equilibrium may be utilized. Under these conditions, the sediment/water partition coefficients are simply the ratio of the adsorption rate constant to the desorption rate constant: (96)
where K
p,w
and K
p,b
are the partition coefficients (L kg -1 ) in the water column and bed, 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 K
p
on solids concentration.
Quite 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 zero (steady-state conditions, dS
b
/dt = 0). Thus the right-hand side of equation (95) may be rearranged and solved for α, the scour coefficient: (97) (98)
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 reduced 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 mass of bed sediment.
(99) (100)
where C
T
= C
s,w
+ C
p,w
= total concentration in the water column, µg L -1 ; and
F T
(x, t) is the distributed source for total chemical input, µg L -1 d -1 . In equation (99), C
T
is abbreviated, but identical to C
T,w
in equation (89). Equation (100) gives the change in sediment chemical concentration over time, so it is useful in predictions of recovery times for large rivers. (101)
The 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 concentration in water C
T,w
and in the bed C
T,b .
(102) (103)
The concentration of pore water in the bed has been defined on a total environmental volume in the sediment (µg L -1 total volume), not on a liquid water basis (µg L -1 H 2 O). One must divide the concentration C
s,b
by the porosity of the sediment (H example.
2 O volume/total volume) in order to obtain the pore water concentration that may be drained from a sediment core, for
Equations (99) and (100), coupled with the equilibrium relationships [equations (16), (17), (18)] provide a useful formulation for simulation of chemical spills, distributed source runoff, and point source problems under conditions of steady state for suspended solids and bed sediment with instantaneous sorption equilibrium.
To 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 splitting the equations into different physical processes. For each incremental time interval between t numerical scheme comprising three steps. At the first step the equation of chemical transport is solved:
j
and t
j+1
, we consider the (104)
At the second step we solve the diffusion equation: (105)
The third step solves the reaction rate equations for local transformations of chemicals, their interaction with the bottom sediments, and source influence. This representation of the chemical transport model simplifies its computation and allows for 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.
The third-step equations can be considered at each paint of the integration domain as a set of ordinary difference equations with the coefficients dependent on the spatial coordinates.
Example 7.3 Pesticide Degradation in a Irrigation Canal
Acrolein 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 steady-state model to calculate the acrolein concentration in the downstream receiving water below the treaded area of the Wahluke Branch Canal of the Columbia River Basin in Washington. Dosages required are typically 100 ppb acrolein.
k` v k` b
= 0.305 m d = 8.9 X = 10 8
×
10 cells L -9 -1 -1 L cells -1
U x
= 0.305 m s H = 0.91 m -1 d -1 Volatilization mass transfer coefficient Second-order biolysis rate constant Bacterial cells Mean velocity Mean depth
Calculate the overall pseudo-first-order reaction rate constant. Since acrolein is nearly totally soluble, the problem then becomes analogous to BOD degradation in a stream. The primary loss mechanism is apparently an initial hydration to β-hydroxypropionaldehyde and subsequent biotransformation. Assume plug-flow conditions and steady state.
Solution: For a plug-flow stream at steady state,
A linear regression equation was used for model calibration to obtain the parameter ∑k (Figure 7.21). The pseudo-first-order rate constant obtained by this method was 0.57 day -1 . 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 1.23 day -l , 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 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 day -1 , in close agreement to the measured rate constants.
Model Calibration
Figure 7.21 Acrolein in an irrigation canal (Wahluke Canal). Best fit of model to field data for Example 7.3
Measured Rate Constants Given:
Example 7.4 Rhine River Chemical Spill Model
A pulse input of pollutants, which were primarily organophosphate pesticides 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 estimated 7 metric tons of contaminants were washed into the Rhine by fire fighting runoff. A fish kill extended over 250 km following this spill. Subsequent monitoring of the pollutant plume by Swiss, German, French, and Dutch environmental agencies provided an excellent database for analyzing pollutant fate and transport.
Use 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 River. Field data for model calibration are given in Figure 7.22.
Solution: Equations (99) and (100) were solved with a split operator method under the steady flow assumption, time-variable concentrations.
The measured mass of material passing each of the four locations decreased with downstream distance (Figure 7.22). The sum of phosphoester pesticides was approximately 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). An overall pseudo thirst-order transformation rate constant of 0.20 day DDT. -1 was used 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 been hydrophobic, persistent, and trapped in the sediments, for example, Figure 7.22 shows the results of model calibration with little "tuning" of the parameters.
Figure 7.22 Result of field measured concentration at four locations and model results (thin solid lines) versus time in days of November 1986.