Steady-State Conversion in Terms of the Feed Concentration

5 Steady-State Conversion in Terms of the Feed Concentration of the Microorganisms 

Recall the expression X ss = (Csf — )/Csy for the steady-state conversion. Here we 

We multiply equation (4.30) by the denominator of the right-hand side and divide the resulting equation by CSf throughout to obtain 

Note that Xsss occurs twice in equation (4.33). But Xsss involves Cssa in its definition and Csss occurs three times in (4.33). Before we can solve for Xsss, we have to eliminate CSss in (4.33) by making use of the relation XSss = (Cs, - CSs, )/Csf in the equivalent form Csss = Css — Xsss Csr With this substitution, equation (4.33) becomes 

This is a quadratic equation in Xsss of the form + bXs3B + c = 0, or more 

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