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.

There are 4 million organic chemicals (IUPAC).
1000 new organic chemicals are synthesized each year.
A fraction of these is toxic or carcinogenic, and the vast majority of them break
down in the environment.

If organics 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.

Organic chemistry is the chemistry of compounds of carbon. Organic chemicals are
obtained from material produced originally by living organisms (petroleum, coal,
and plant residues) or they are synthesized from other organic compounds or
inorganics (carbonates or cyanides).
7.1 NOMENCLATURE

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.
Figure 7.1
Some common classes
of organic compounds
(left) and examples
(right). R and R`
indicate different alkyl
group.

In the environment, alkanes  alcohol.
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.
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.
Figure 7.2
Examples of cyclic organic
compounds (including
alicyclic, aromatic, and
heterocyclic compounds).

Drinking water standards. Organic chemicals for which maximum allowable drinking
water standards have been established are shown in Figure 7.3.
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.
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 - 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
intracellular 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 CO2 and H2O are referred to as
"mineralization." In the broadest sense, "biotransformation" refers to any
microbially 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" - the utilization of organic chemicals at
low concentrations in the presence of one or more primary substrates that are used
as carbon and energy sources.
"Co-metabolism" - 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 wide variety of pesticides. Dehalogenation,
dealkylation, hydrolysis, oxidation, reduction, ring cleavage, and condensation
reactions are all known to occur either metabolically or via co-metabolism (see
Table 7.1). In co-metabolism, the microbe does not even derive carbon or net
energy from the degradation; rather, the pesticide is “caught up” in the overall
metabolic reactions as a detoxification or other enzymatic reaction.

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) below. The reaction rate expression is
then
(1)
where C is the toxic organic concentration in solution and kb is the pseudo-first-order
biotransformation rate constant.
 Table 7.2 is a summary of pseudo-first-order and second-order rate constants kb 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
(2)
Where kb = 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 concentration yield/ organic concentration utilized
KM = Michaelis half saturation constant, M L-3.
Typical cell concentrations in surface waters would be 106 – 107 cells mL-1 and less in
groundwater
Table 7.2
Selected Biotransformation
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 (KM ≈ 0.1-10
mg L-1). Therefore the equation becomes
(3a)
where kb` = μ/YKM.

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 CT is the total whole water chemical concentration, C is the dissolved phase
concentration and Cp is the particulate adsorbed concentration.

If the substrate concentration C is very large such that C >> KM , then the
microorganisms are growing exponentially, and the rate expression in equation (2)
reduces to
(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 for
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 CO2 off-gas and synthesis into biomass. These
experiments are called heterotrophic uptake experiments.

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
H2O2, hydroxyl radicals ·OH, singlet oxygen O2, 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.

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 (∼1 × 10-9 M in sunlit natural waters) react rapidly with
phenols and amines in natural waters to form acids and aromatic radicals:

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 O2 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, H2O2, metal salts, and azo
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.
H2O2 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 k3 is the overall reaction
rate constant which is a function of rf, the rate of peroxide formation. 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 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 O2(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 (CH2O
such as glucose C6H12O6) 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, H2S 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 kAB is directly proportional to the
one-electron reduction potential of the redox couple.
(11)
where H2X is the reductant.
 Schwarzenbach et al. have shown that, in the case of juglone, it is not the diprotic
dihydroquinone H2JUG that is the reactant with nitroaromatics, but rather the
anions HJUG- and JUG2-. Reductants in natural waters include quinone, juglone
(oak tree exudate), lawsone, and Fe-porphyrins. Nitroreduction 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 (H2S, Fe2+, and CH4) to determine if the reaction is favored
thermodynamically (Table 7.5). In the absence of bacteria, the reaction may be slow.
Table 7.5
Redox Half-Reactions
Pertinent in Wastewater,
Groundwater, and
Sediment Reactions
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:
- it loses its "extra" energy through energy emission, that is, fluorescence or
phosphorescence;
- 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 kp is the rate constant for
photolysis. Photo1ysis rate constants can be measured in the yield with sunlight or
under laboratory conditions.
 The first-order rate constant, kp can be estimated directly:
(13)
where kp = photolysis rate constant, s-1
J = 6.02 × 1020 = conversion constant
φ = quantum yield
Iλ = sunlight intensity at wavelength λ, photons cm-2 s-1
ελ = 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 light 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-2 nm-1 by multiplying by the wavelength (nm) and 3.03 ×
1039.
 The intensity of light varies over the depth of the water column and may be related
by
(15)
where Iz is the intensity at depth z, I0 is the intensity at the surface, and Ke 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 k2 is the indirect photolysis rate constant, X is the concentration of the nontarget
intermediary, and kp 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 H2O2 produces ·OH, but this pathway is relatively unimportant
because H2O2 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 H2O2 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 acid 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 ka and kb, several nonneutral 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).
(18)
where kh = kb [OH-] + ka [H+] + kn and kh is the pseudo-first-order hydrolysis rate
constant, T-1; kb is the base-catalyzed rate constant, molarity-1 T-1; ka is the acidcatalyzed rate, polarity-1 T-1 ; and kn is the neutral rate constant, T-1.
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 ratio of the fugacity of the chemical
(escaping tendency from air and water).
(19)
where pg is the partial pressure of the chemical of interest in the gas phase
Csl is its saturation solubility.

Henry's constant can be "dimensionless" [mg/L (in air)/mg/L (in water)] or it has
units of atm m3 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 KL 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 first term on the right-hand side of the equation as a liquidfilm 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, rg, or the liquid phase resistance, rl, 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
transfer.
 In terms of a differential equation, the overall gas transfer:
(31)
where Csat = pg/H, A is the interfacial surface area, and V is the volume of the liquid.

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 kli 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/Kδ
predominates.
(34), (35)
where CD 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 Dl is the diffusivity of the chemical in water and MW is the molecular weight,
and
(38)
where Dg is the diffusivity of the chemical in air.
 The mass transfer rate constant, kli, can then be related to the oxygen reaeration
rate, ka, by a ratio of the diffusivity of the chemical to that of oxygen in water:
(39)
where DO2 is 2.4 × 10-5 cm2 s-1 at 20 ºC.

The reaeration rate, ka, can be calculated from any of the formulas available. In
addition, the overall gas-film transfer rate may be calculated from
(40)
where vg 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 s-1 kgi 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 Sw is solubility (mol L-1), MP is the melting point (ºC), and Kow is the
estimated octanol/water partition coefficient.
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 Kow 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 environmental
conditions as:
(42)
(43)
Where U10 is the 10-m wind velocity (m s-1), ScL and ScG are the dimensionless liquid
and gas Schmidt numbers.
 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 KL 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:
- physical adsorption due to van der Waals forces;
- chemisorption due to a chemical bonding or surface coordination reaction;
- 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, Kow, is related to the solubility of a chemical
in water.
Tables 7.9 and 7.11 provide log Kow values for a number of organic chemicals of
environmental interest.
Table 7.11
Octanol/Water Partition
Coefficients of Selected
Organics, 298 K

The laboratory procedure for measuring Kow 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 ratio of octanol and water is set at the estimated
Kow.
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. Kow 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 Kow 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 ºC.

For organics that are solid in their pure state at 25 ºC,
(45)
where MP is the melting point of the pollutant (ºC) and △Sf is the entropy of fusion of
the pollutant (cal mol-1 deg-1).


The octanol/water partition coefficient is dimensionless, but it derives from the
partitioning that occurs in the extraction between the chemical in octanol and 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 (Koc).

Karickhoff et al. and Schwarzenbach and Westall have published useful empirical
equations for predicting Koc as a function of Kow
(46)
(47)

Once an estimate of Koc is obtained, the calculation of a sediment/water partition
coefficient suitable for natural waters is straightforward because the
(48)
where foc is the decimal fraction of organic carbon present in the particulate matter
(mass/mass).
 Figure 7.7 is a schematic of how Kp, Koc, and Kow are interrelated. Figure 7.7 is the
Langmuir adsorption isotherm for sorption of one chemical on particulate matter.
Figure 7.7
Relationship between the
sediment/water partition
coefficient Kp, the organic
carbon partition coefficient
Koc, and the octanol/water
partition coefficient Kow.
Plot (a) and (b) are for only
one chemical and (c) is for
many chemicals.

Kp 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 sorptiondesorption:
(50), (51)
where C is the concentration of dissolved toxicant, Cp is the concentration of particulate
toxicant, Cpc is the maximum adsorptive concentration of the solids, and k1 and k2
are the adsorption and desorption rate constants, respectively.

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 (rc) 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 Koc, 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, Kp.

The partition coefficient is derived from simplification of the kinetic eq`ns (50) and
(51) if rc >> r (the linear portion of the Langmuir isotherm). In this case, we may
write
(54a), (54b)
Where kf is the adsorption rate constant and kr is the desorption rate constant.
 The total concentration of toxicant:
(55)
Where fd and fp 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 Kp 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 Kp 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 Kp, 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 concentration and
organism mass:
(59)
where e = efficiency of toxic absorption at the gill
k1 = (L filtered/kg organism per day)
k2 = 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, Kp.
 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-Kow) 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, k2, includes total depuration (both excretion of unmetabolized
toxics, k2`, and elimination of metabolites, k2``). Only a fraction of this elimination
is returned to the water column as dissolved parent compound, designated as k2` in
Figure 7.9.

Hydrophobic organics tend to accumulate in fatty tissue of animals. Lipid
normalized 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, Kow (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 carnivores.
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 fishμg 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
kb = biotransformation rate constant, T-1
ko = oxidation rate constant, T-1
kr = reduction rate constant, T-1
kp = photolysis rate constant, T-1
kh = hydrolysis rate constant, T-1
kv = volatilization rate constant, T-1

Equation (63) includes an assumption that the atmosphere has a neg1igible
concentration (partial pressure) of the organic, so only volatilization occurs
(stripping out of the water body).
 For first-order reactions 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 t1/2 = overall half-life of the chemical due to all transformation reactions
n
 k = the sum of all the pseudo-first-order reaction rate constants
i 1

i
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 Kp.
(68)
where Kp = 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
Cp = particulate adsorbed concentration, µg L-1
CT = 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 Kp.
(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 CT 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 C2
and adsorbed sediment Cp2, may also be different due to the dependence of Kp2, on
solids concentration. Generally, Kp2 < Kp1, 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 effects, 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 Cprecip is the precipitation concentration, Cg 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 vd is the deposition velocity (LT-1), Cg is the gas phase concentration (ML-3) and Jd
is the areal mass flux due to dry deposition (ML-2T-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, vd
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 – CT, and C - but the
assumption of local equilibrium allows us to write the equation entirely in terms of
total (whole water, unfiltered) concentration.
(73)
where CT = total concentration = C + Cp, ML-3
V = volume of the lake, L3
t = time, T
Q = flowrate in and out, L3T-1
fp = particulate fraction of total chemical concentration, dimensionless
= Cp/ CT = KpM /(1 + KpM)
fd = dissolved fraction of total chemical concentration, dimensionless
= C/ CT = 1 /(1 + KpM)
C = dissolved chemical concentration, ML-3
Cp = particulate chemical concentration, ML-3
ks = sedimentation rate constant,T-1
ki = 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 CTo = 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
(78)

By inspection, one can prove that equations (75) and (78) are equal when
(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
compartmentalization 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 of chemical
degradation, these can be slow processes
taking years to decades.
Figure 7.13
Schematic of lake recovery from a
persistent hydrophobic pollutant

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 7.14
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 eastern
Iowa. It drains approximately 3084 square miles (7978 km2) 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 sedimentation since it was created in
1958.

At conservation pool (680 ft above mean sea level, msl), the reservoir has a
capacity of 38,000 acre-ft (4.79× 107 m3), a surface area of 4900 acres (1.98×
107m2), 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 × 107
m3).

The total pesticide concentration is the sum of the particulate plus the dissolved
concentrations, with instantaneous sorptive equilibrium assumed
(80)
where fd = C/ CT = 1/(1 + KpM) = fraction of dissolved pesticide
fp = Cp/ CT = KpM/(1 + KpM) = fraction of particulate pesticide
W(t) = time-variable loading of pesticide, M/T
CT = total concentration in the water column, ML-3
k
= sum
of the pseudo-first-order degradation rate constants
τ = mean hydraulic detention time
V = reservoir volume, L3
ks = sedimentation rate constant, T-1

The fish residue equation is
(81)
where k1 = pesticide uptake rate by fish, T-1
kd = depuration rate constant, T-1
F = whole-body fish residue level, M/M wet weight
B = fish biomass concentration, M/L3 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)
(83)
where CTo = initial total pesticide concentration in lake, ML-3
CTin,o = initial total pesticide inflow concentration, ML-3
ω = rate of exponentially declining inflow concentration,T-1

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 eightcompartment model based on
dye studies.
Figure 7.15
Compartmental configuration
for a two-box pond model or
an eight-box lake model

Figure 7.16: simulation of a twocompartment 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.
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.
 Model results were within the
range of field observations.
Dieldrin residues in fish, sediment,
and water were all declining at
∼15% per year Approximately
50% of the pesticide load was
exported from the reservoir, 40%
underwent sedimentation, and 10%
entered a huge biomass of bottomfeeding fish. The fishery was
reopened in 1980 for commercial
fishing of bigmouth buffalo fish.
 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
parameters (Figure 7.17).

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, m3
CT = total pesticide concentration of the compartment, µg L-1
t = time, days
Qa = inflow of water from adjacent compartments, m3 d-1
Qb = outflow of wafer to adjacent compartments, m3 d-1
Ca = total pesticide concentration in the adjacent compartment, µg L-1
fd = fraction of the total pesticide in the dissolved phase
fp = fraction of the total pesticide in the particulate phase
kda = reaction rate constant for the dissolved phase, day-1
kpa = reaction rate constant for the particulate phase, day -1
ks = settling rate constant of the compartment, day-1
ksa = settling rate constant from the above compartment, day-1
E = bulk dispersion coefficient for adjacent compartments, m2 d-1
A = surface area between two adjacent compartments, m2
l = mixing length between midpoints of adjacent compartments, m
Va = volume of above compartment, m3

The general mass balance equation for the jth compartment can be reduced to a
general matrix equation:
(85)
where i = subscript denoting adjacent compartments
j = subscript denoting the jth compartment
Cj = total pesticide concentration in the jth compartment, µg L-1
Ci = total pesticide concentration in an adjacent compartment, µg L-1
Qi,j = flow into compartment i from j, m3 d-1
Qj,i = flow from compartment j to i, m3 d-1
fd,j = dissolved fraction of a pesticide in compartment j
fp,j = particulate fraction ova pesticide in compartment j
kda = sum of dissolved reaction rate constant, day-1
kpa = sum of particulate reaction rate constant, day-1
ks,i = settling rate constant for compartment i, day-1
ks,j = settling rate constant from compartment j, day-1
Ei,j = bulk dispersion coefficient between adjacent compartments, m2 d-1
Aj = surface area of compartment j, m2
li,j = length between the midpoints of adjacent compartments, m
Vj = compartment volume, m3
Vi = volume of adjacent compartment, m3
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, L2T-1
ui = average velocities in the x-, y-, and z-directions, LT-1
x = longitudinal distance, L
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 (Cs), although special transformation
reactions may occur for chemical adsorped to the sediment under reducing
conditions (λ`b).

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 (λb) 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 (Sw) in the river water
and scour/resuspension of bed sediment (Sb) via the first-order rate constants ks 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.
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 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, Cp,b:
(88)
where rb = amount of chemical adsorbed per mass of dry sediment, µg kg-1
Cp,b = particulate adsorbed chemical concentration, µg L-1
Sb = bed solids concentration, kg L-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 CT,w = total concentration, µg L-1
Cs,w = soluble chemical concentration in the water column, µg L-1
Cp,w = particulate adsorbed chemical concentration in the water column, µg L-1
CT,b = total bed concentration, µg L-1
Cs,b = soluble chemical concentration in the bed sediment, µg L-1
Cp,b = 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)

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 Kp,w and Kp,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
Kp 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, dSb/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 CT = Cs,w + Cp,w = total concentration in the water column, µg L-1
FT(x, t) is the distributed source for total chemical input, µg L-1 d-1.
 In equation (99), CT is abbreviated, but identical to CT,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 CT,w and in the bed CT,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
H2O). One must divide the concentration Cs,b by the porosity of the sediment (H2O
volume/total volume) in order to obtain the pore water concentration that may be
drained from a sediment core, for example.

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 tj and tj+1, we consider the numerical
scheme comprising three steps. At the first step the equation of chemical transport
is solved:
(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 point 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 steadystate 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 = 0.305 m d-1
k`b = 8.9 × 10-9 L cells-1 d-1
X = 108 cells L-1
Ux = 0.305 m s-1
H = 0.91 m

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 βhydroxypropionaldehyde 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-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, DDT.
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.