Page 668 - The Toxicology of Fishes

648 The Toxicology of Fishes

Atmospheric
Deposition

Point Source Wet Dry.
Discharge Rain Dep. Dep. Absorption

Volatilization Advective Outflow
water + particles
Inflow
water + particles

Water Reaction

Deposition

W–S Diffusion

S–W Diffusion

Resuspension Active Sediment
Burial Buried Sediment Sediment Reaction

FIGURE 14.1 Input and output processes that are quantified by the Quantitative Water Air Sediment Interaction (QWASI)
model.

take a variety of forms; for example, a rate of outflow in units of g/hr can be expressed as the product
3
of a water flow rate (m /hr) and a concentration (g/m ). A reaction rate can be expressed as the product
3
of a volume (m ), concentration (g/m ), and rate constant (hr ), the latter being 0.693/half-life (hr). A
3
3
–1
volatilization rate can be the product of an area (m ), concentration (g/m ), and mass transfer coefficient
3
2
or velocity (m/hr). The resulting mass balance equations become quite lengthy, and extreme care must
be taken to ensure that units are consistent. The model is likely to be applied to a variety of toxicants
that differ in properties. The expressions must allow the user to input these various properties while
ensuring that the equations remain valid; that is, the model should be robust enough to accept these
inputs and treat them correctly.
An alternative and ultimately equivalent approach is to use the concept of fugacity as a surrogate
for concentration, as described by Mackay (2001). The concentration (C) (mol/m ) is expressed as a
3
product of fugacity f (Pa) and a Z value (mol/Pa m ). Fugacity can be regarded as partial pressure, or
3
escaping tendency, of a substance. The Z value is specific to the substance and the medium in which
it resides and can be viewed as a kind of solubility. Z values are deduced from equilibrium partition
coefficients. A partition coefficient K between two phases 1 and 2, such as air and water, can be
12
shown to be Z /Z . Usually, Z is first defined for air, then the values for other phases such as water,
1
2
sediment, and fish are deduced. All process rates (mol/hr) are expressed as the product of a fugacity
(f) (Pa) and a D value (mol/Pa hr). Fugacity-based and concentration-based equations are essentially
identical, but the fugacity equations are more compact. D values are best thought of as rate constants
for the process expressed in terms of fugacity. Applying the list of D values in Table 14.1 to the diagram
in Figure 14.1 and defining fugacities for the chemical in air (f ), inflow water (f ), water column (f ),
W
I
A
and sediment (f ), we can write the fundamental mass balance equations for water and sediment
S
compartments in the form:
−
inventory change (mol/hr) = input rate (mol/hrr) output rate (mol/hr) (14.1)