Page 669 - The Toxicology of Fishes

Exposure Assessment and Modeling in the Aquatic Environment 649

TABLE 14.1
D Values Used to Describe the Equilibria and Kinetic Processes in the Mass Balance Model: Equations
Used to Calculate These D Values, Process Rate Expressions Df (mol/hr), and Actual D Values for
Anthracene and Pyrene Shown in the Illustrations
D Value Process Rate
Process Symbol (mol/Pa hr) (mol/hr) Anthracene Pyrene
Sediment burial D B G B C S D B f S 3.2 59.5
Sediment transformation D S V S C S k S D S f S 57.0 330
Sediment resuspension D R G R C S D R f S 3.12 58.7
Sediment to water diffusion D T k T A S C S /K SW D T f S 101 435
Water to sediment diffusion D T k T A S C W D T f W 101 435
Sediment deposition D D G D C P D D f W 41.9 787
Water transformation D W V W C W k W D W f W 4840 7060
Volatilization D V k V A W C W D V f W 348 389
Absorption D V k V A W C A /K AW D V f A 348 389
Water outflow D J G J C W D J f W 1580 6800
Suspended particle outflow D Y G Y C P D Y f W 22.4 422
Rain dissolution D M G M C A /K AW D M f A 24.2 104
Wet particle deposition D C G C C Q D C f A 23.8 157
Dry particle deposition D Q G Q C Q D Q f A 8.9 58.8
Water inflow D I G I C I D I f I 1580 6800.8
Suspended particle outflow D X G X C X D X f I 108 2020

This equation is conceptually identical to that for money in a bank. The change in the balance over a
month (the inventory change in $/month) equals the difference between the rate of deposits or inputs
and the rate of withdrawals or outputs, also expressed in $/month. Mathematically, this is expressed by
a differential mass balance equation for water and sediments. The fugacity versions are more concise
than the concentration versions and are given in Equation 14.2 and Equation 14.3 to illustrate the concept.
dV Z W W f ) dt = E W + ( D I + D X) + ( D V + D Q + D C + D M)
(
I f
A f
W
+ ( D D T) − f W( D V + D W + D J + D Y + D D + D T) (14.2)
S f D R +
dV Z S S f ) dt = W f ( D D + D T) − ( D R + D T + D D + D B) (14.3)
S (
S f
Each of the Df terms represents the rate of a specific process (mol/hr or g/hr) by which the chemical
enters, leaves, or changes location in the system. The groups (VZf) are the total amount (mol or g) in
the compartment. Values of each D must be established from environmental conditions and chemical
properties. We make no attempt here to explain all such terms in detail; the aim is merely to convey
that this is one approach by which a process mass balance can be established for a two-compartment
system.
At steady state, which can be achieved after a long time with constant inputs, the water and sediment
concentrations and fugacities become constant, the derivatives on the left become zero, and the two
resulting algebraic equations can be solved to give the prevailing steady-state fugacities or concentrations:

f I D +
f A D +
E W + ( D X) + ( D Q + D C + D M)
f W = I V
D (
D V + D W + D J + D Y + D D + D T)( D S + D B) ( D R + D T + D S + D B) (14.4)
f W( D D + D T)
f S =
D R + D T + D S + D B
D
The differential equations can, if desired, be solved analytically or numerically, yielding equations that
describe how the concentrations change with time (i.e., the dynamic situation).