Theoretical analysis of convective flow profiels in a hollow-fiber membrane bioreactor

Although a number of recent experimental and theoretical investigations have demonstrated that radial convection can have dramatic effects on the overall performance of hollow-fiber membrane bioreactors, available theoretical analyses are unable to accurately describe the detailed convective recirculation (or Starling) flow which occurs in these devices. We have developed analytical expressions for the radial and axial velocities and pressure profiles in the hollow-fiber bioreactor, operated in either the closed-shell (recycle) or open-shell (ultrafiltration) mode, by solving the coupled momentum and continuity equations in the fiber lumen, matrix, and surrounding shell. The local velocity profiles were then used to evaluate the flow streamlines and extent of recirculation as a function of operating conditions and geometry. Calculations were also performed to determine the residence time distribution in the membrane bioreactor. For closed-shell operation, the residence time distribution in the hollow-fiber devices is bimodal; the first peak is associated with the fluid that remains in the fiber lumen throughout its passage down the fiber, while the second peak is associated with the fluid that crosses the membrane and enters the shell. Our calculations clearly demonstrate the complex dependence of the flow on membrane properties, hollow-fiber module geometry, and operating conditions. These results have important implications for the design and analysis of hollow-fiber membrane bioreactors with immobilized enzymes or cells.