Model of oxygen transport limitations in hollow fiber bioreactors.

Axial and radial oxygen depletion are believed to be critical scale-limiting factors in the design of cell culture hollow fiber bioreactors. A mathematical analysis of oxygen depletion has been performed in order to develop effectiveness factor plots to aid in the scaling of hollow fiber bioreactors with cells immobilized in the shell-side. Considerations of the lumen mass transport resistances and the axial gradients were added to previous analyses of this immobilization geometry. An order of magnitude analysis was used to evaluate the impact of the shell-side convective fluxes on the oxygen transport. A modified Thiele modulus and a lumen and membrane resistance factor have been derived from the model. Use of these terms in the effectiveness factor plots results in a considerable simplification of the presentation and use of the model. Design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots. Model predictions of the oxygen limitations were compared to experimental measurements of the axial cell distributions in a severely oxygen limited hollow fiber bioreactor. Despite considerable uncertainty in our parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results.