A porous media CFD model for the simulation of hemodialysis in hollow fiber membrane modules

A computational model was developed to predict the performance of hollow fiber membrane hemodialyzers. Blood and dialysate were modelled as fluids flowing through two interpenetrating porous media. Concerning hydrodynamics, experimental Darcy permeabilities measured for commercial hemodialyzers were used for both compartments. Concerning mass transfer, both diffusion and ultrafiltration were simulated. On the blood side theoretical Sherwood numbers for parallel flow in pipes were adopted. On the dialysate side Sherwood numbers were derived from CFD predictions for regular hexagonal fiber bundles. Solute concentrations on the two sides were alternatively computed in an iterative way and were coupled by sink/source terms describing mass transfer. Unlike previous models, the present one is fully predictive, in that it does not use an empirically adjusted global mass transfer coefficient but requires only basic membrane properties (diffusive and hydraulic permeabilities and reflection coefficient). A further novelty is the inclusion of oncotic pressure effects. The model predicts 3-D flow and solute concentration fields and overall performance parameters such as clearance as functions of geometry, flow rates, solute species and membrane properties. In particular, two commercial hemodialyzer configurations were simulated; the predicted clearances of urea and B12 vitamin were found to agree well with experimental measurements.