Note that from Eqs. (7.17) and (7.18), R « VMCM(t)/VDCD(0) for t > tLAG. The substitution of the apparent partition coefficient with the retention ratio allows us to state the mole balance at time t (provided t > tLAG) in a much simplified form:

Given this relationship between CA(t) and CD(t), where retention is factored in, we can proceed to convert Eq. (7.3) into Eq. (7.5), where a is the same as before, and b now needs to be multiplied by the partition-related factor, 1 - R. The so-modified ordinary differential, Eq. (7.5), is solved by standard methods, using integration limits from tLAG to t (not 0 to t), and the desired effective permeability derived as

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