A modified Ergun equation for modeling dialysate flow in a hollow fiber hemodialyzer

Presenter: Ruhit Sinha, Engineering Mechanics

Authors: R. Sinha, A. Staples

Abstract: Efficient mass transfer in hollow-fiber hemodialyzers depends critically on dialysate flow outside the fibers, yet modeling this shell-side flow remains a long-standing challenge. Conventional single-fiber models are efficient but fail to capture module-scale behavior, while porous-media approaches rely on uncertain parameters such as Darcy’s permeability (κ), typically estimated from empirical correlations or the Ergun equation. Here, we develop a three-dimensional computational fluid dynamics model resolving the full shell-side flow field and validate it against experimental data from nine modules. The simulations yield realistic Kozeny constants—7–8.5 for longitudinal and 15–20 for transverse flow—consistent with experiments and contrasting with single-fiber predictions. Extending the analysis to eighteen modules, we derive a modified Ergun equation with a revised Blake–Kozeny constant (A′) based on hydraulic diameter rather than outer fiber diameter. The conventional assumption A = 150 overpredicts pressure gradients by up to 35%, whereas A′ follows a polynomial relation with packing density, offering a computationally efficient and generalizable framework for modeling transport in densely packed membrane systems.