McKay, Donald. "Front matter" Multimedia Environmental Models ...

QWASI Multi-segment Equations
I(i) is total input (mol/h) to each reach from emissions, the atmosphere, and any
tributaries. It does not include advective inputs from other reaches.
DT(i) is the sum of D values for losses by reaction, burial, and volatilization plus all
advective losses from water, including net loss to sediment. The (i) refers to reach 1, 2,
3, or 4.
D(i,j) is water and particle flow between reaches i and j.
J(i) is a D value for the net output from each reach.
J(1) = DT(1)
J(2) = DT(2) – D(2,1) D(1,2)/J(1)
J(3) = DT(3) – D(3,2) D(2,3)/J(2)
J(4) = DT(4) – D(4,3) D(3,4)/J(3)
X(i) is the ratio of D values and is the fraction of the chemical in water and particle flow
that enters downstream reach (reach 1 is upstream of reaches 2, 3, and 4).
X(1) = D(1,2)/J(1)
X(2) = D(2,3)/J(2)
X(3) = D(3,4)/J(3)
Fraction of total input received by each reach, including upstream reaches.
Q(1) = I(1)
Q(2) = I(2) + I(1) X(1) = I(2) + Q(1) X(1)
Q(3) = I(3) + I(2) X(2) + I(1) X(1) X(2) = I(3) + Q(2) X(2)
Q(4) = I(4) + I(3) X(3) + I(2) X(2) X(3) + I(1) X(1) X(2) X(3) = I(4) + Q(3) X(3)
The solution for water fugacities fW(i) for each reach is as follows:
fW(4) = {Q(4) + [fW(5) D(5,4)]}/J(4)
fW(3) = {Q(3) + [fW(4) D(4,3)]}/J(3)
fW(2) = {Q(4) + [fW(3) D(3,2)]}/J(2)
fW(1) = {Q(4) + [fW(2) D(2,1)]}/J(1)
The sediment fugacities fS(i) can then be calculated from the steady-state equation in
Fig. 8.5.
fs(i) = fw(i)(DD(i) + DT(i))/(DB(i) + DS(i) + DR(i) + DT(i)) with D values specific to each
segment.
Figure 8.8 Steady-state mass balance equations for a series of four QWASI models with
flows in both directions.
X, is a ratio of D values, namely the ratio of the box-to-box advective transfer D
value and the total loss D value from the source. The denominators, J, contain terms
for losses from each box, again modified by fractions undergoing box-to-box transfer.
Inspection of the equations reveals the significance of each term. When the
connections are more complex with branching, the equations must be modified
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