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

Air (subscript 1)
E 1 + G A1C B1 + f 2D 21 + f 3D 31 = f 1(D 12 + D 13 + D R1 + D A1) = f 1D T1
Water (subscript 2)
E 2 + G A2C B2 + f 1D 12 + f 3D 32 + f 4D 42 = f 2(D 21 + D 24 + D R2 + D A2) = f 2D T2
Soil (subscript 3)
Sediment (subscript 4)
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E 3 + f 1D 13 = f 3(D 31 + D 32 + D R3) = f 3D T3
E 4 + f 2D 24 = f 4(D 42 + D R4 + D A4) = f 4D T4
In each case, E i is the emission rate (mol/h), G A is the advective inflow rate (m 3 /h),
C Bi is the advective inflow concentration (mol/m 3 ), D Ri is the reaction rate D value,
and D Ai is the advection rate D value. D Ti is the sum of all loss D values from
medium i. Sediment burial and air-to-stratospheric transfer can be included as an
advection process or as a pseudo reaction.
These four equations contain four unknowns (the fugacities), thus solution is
possible. After some algebra, it can be shown that
where
and
f 2 = (I 2 + J 1J 4/J 3 + I 3D 32/D T3 + I 4D 42/D T4)/(D T2 – J 2J 4/J 3 – D 24·D 42/D T4)
f 1 = (J 1 + f 2J 2)/J 3
f 3 = (I 3 + f 1D 13)/D T3
f 4 = (I 4 + f 2D 24)/D T4
J 1 = I 1/D T1 + I 3D 31/(D T3D T1)
J 2 = D 21/D T1
J 3 = 1 – D 31D 13/(D T1D T3)
J 4 = D 12 + D 32D 13/D T3
I i = E i + G AiC Bi
i.e., the total of emission and advection inputs into each medium.