2.2. Contaminant Fate and Transport Models (Water Quality Models)
2.2.3. Material Flux Processes
Material transport involves the transport of a chemical in bulk form from one phase to another phase. Deposition of particles to the bottom of a lake or river and the resuspension of particles from sediment into water column are two examples. The atmospheric depositions onto water or soil can also be listed among the material transport processes.
These processes are dependent on a velocity of the flow rate. With this information, a
this can be shown using the product of the flow rate and the fugacity of the medium from which the chemical is carried out and the fugacity capacity of the chemical in that medium. In this section, flow rate calculations explain all the material transport processes.
Atmospheric deposition consists of wet and dry deposition from the air. Wet deposition of a compound from the atmosphere occurs when that compound is scavenged from the atmosphere by rain, snow, or fog. The efficiency of wet deposition of a compound is directly related to its water solubility and vapor pressure. For wet deposition to occur, the compound should dissolve in rain water or snow and scavenged.
Rain dissolution can be calculated by simply multiplying the rain rate (given as
3 2
rain / area.
m m h) with the volume fraction of aerosols (very small particles in the air that hold the contaminant) with the area of air in contact with the compartment into which rain dissolution will occur as follows:
Rain dissolution
= A U v
w R Q , (2.10)where Aw [L2] is the surface area of water (in the case of the air-water interaction), UR
[L/T] is the rain rate, and vQ [L3/L3] is the volume fraction of aerosols.
Wet deposition incorporates the scavenging of the contaminant into the medium by rain or snow. The same simple approach used in rain dissolution can be used with the
incorporation of a scavenging ratio. In the case of the air-water interaction, the equation would be
Wet Deposition =A U Qvw R Q , (2.11)
where Aw [L2] is the surface area of water, UR [L/T] is the rain rate, Q is the scavenging ratio, and vQ [L3/L3] is the volume fraction of aerosols.
Dry particle deposition of particle-bound chemicals in a water body depends on the deposition layer, particle size, and macro and micrometeorology. In the simplest case, dry depositional flux can be described by the area of the compartment into which the deposition would occur, the dry deposition rate, and the volume fraction of a contaminant in the aerosol phase:
Dry Deposition =A U vw Q Q , (2.12)
where Aw [L2] is the surface area of water, UD [L/T] is the dry deposition rate, and vQ [L3/L3] is the volume fraction of aerosols. For the case of air-soil interactions, the same equations hold with the substitution of a soil surface area for a water surface area. Soil runoff describes the amount of contaminant transfer from soil to water via solid particles running off into the water from the soil. Average annual runoff rate of solids multiplied by the area of soil can be used for this transport mechanism. The use of
8 3 2
2.3 10x − m m h/ (0.0002m year/ )has been suggested by Mackay (2001) for the average runoff rate of solids from soil to water. The estimate is
solids runoff
soil runoff =A Us , (2.13)
where As [L2] is the soil surface area, Usolids runoff [L/T] is the solids runoff rate. Similar to soil runoff, water runoff, the contaminant transfer during the runoff of water from soil to water, can be estimated in a similar fashion using the average runoff rate. Mackay (2001) also suggests an average value for runoff rate of water from soil, which is3.9 10x −5m h/ (0.34m year/ ). The formula is
water runoff
water runoff = A U
s , (2.14)where As [L2] is the soil surface area, Usolids runoff [L/T] is the solids runoff rate.
Sediment deposition can be explained in terms of the fall velocity of particles onto which contaminant is sorbed. The velocity of a settling particle is given by the well-known equation of the fall velocity (Kiely, 1997):
4( )
3
s fall
D
V gd
C ρ ρ
ρ
= − , (2.15)
where g [L/T2] is the gravitational acceleration, d [L] is the effective particle diameter, and CD is the drag coefficient.
For laminar flow, the drag coefficient is equal to 24/Re, and Re is the Reynold’s number.
Thus, the equation for the fall velocity becomes Stoke’s Law for the velocity of a settling particle.
2
18
s fall
V gd ρ ρ
μ
⎛ − ⎞
= ⎜ ⎟
⎝ ⎠ , (2.16)
where µ [L2/T] is the kinematic viscosity of the water. Although the particle diameter is a variable, the average particle diameter can be used as the effective diameter of the particles. Hence, a constant average settling velocity can be described for the flow domain. When possible, sediment traps can be used to check the reliability of this equation.
The deposition onto the sediments is the result of the multiplication of this settling velocity and the area onto which the particles will fall.
2
Deposition .
18
s
fall sed sed
V A A gd ρ ρ
μ
⎛ − ⎞
= = ⎜ ⎟
⎝ ⎠. (2.17)
When the shear stress on the bottom of the water column exceeds a critical value, the resuspension of settled sediments occurs. The resuspension rate is directly proportional to excess shear stress on the surface of the sediments. Several different expressions, all complicated, have been used to describe the resuspension process. Thus, for the purpose of simplification, an average resuspension rate for the whole water body can be used to
resuspension of contaminants from a small lake as 1.1 10x −8m m h3/ 2 (0.0001m year/ ). Resuspension occurs over the entire area of the sediments, so the resuspension flux is estimated by multiplying the resuspension rate by the area from which the resuspension occurs:
Resuspension=Uresuspension.Ased . (2.18)
All the values calculated in this section can be multiplied with appropriate fugacity capacities and converted to transportation constants for each medium for a specific chemical. We can combine all of the above information and form a static steady state fugacity model and use the resulting single concentration value for each medium as the average concentration for an exposure assessment study. This model assumes that each compartment is well mixed and attains one single value for concentration and that all the parameters are defined in the model.