Solving design equations for a hollow fiber bioreactor with arbitrary kinetics

An approach for solving the hollow fiber bioreactor design equations is presented. The original set of differential mass balance equations is cast into an equivalent system of integral equations by generating the appropriate Green’s functions. Mathematical features common to all hollow fiber bioreactors (HFBRs) operating with laminar flow are imbedded in the corresponding Green’s functions on the lumen side, and thus separated from specific aspects arising from mass transport through the permeable wall. On the spongy matrix side, the appropriate Green’s functions are expressed in terms of the mass transfer properties without involving any chemical kinetic parameters; this avoids repetitive computational effort when treating different reaction kinetics. The derived integral equations are numerically solved on an appropriately transformed coordinate system. The numerical method is well suited for problems where steep gradients of concentration cause an inaccurate numerical integration and low rates of convergence if the equations are solved with a uniform rectangular grid on the original coordinate system. The effectiveness of the proposed approach for the simulation of HFBRs with power-law, Michaelis–Menten and zero-order kinetics is demonstrated. The method is readily extendible to treat problems with chemical kinetics described by any arbitrary functional form.