Material balance expressions recycle reactors

Biomass recycle as sketched in Figure 30.4D is frequently used in fermentors as a way of increasing the biomass productivity. The increased biomass productivity obtained with a recycle fermentor is a function of the recycle ratio, r, and the cell concentration factor, C = XJX, achieved in the concentrator. Equations expressing the recycle system behavior are derived from material balances around the reactor. For the cell biomass balance at steady state ... 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

---