Hollow-fiber dialysis modules, the most common devices in renal replacement therapy, contain thousands of hollow fibers packed into a cylindrical housing, where blood and dialysate are flowing in opposite directions upstream and downstream of the fibers’ walls made of membrane material, exchanging solutes and water. One of the design goals when optimizing hollow-fiber dialyzers is to maximize the effectively utilized membrane area for mass exchange while preventing inefficiencies like dead zones and reverse flow through the membrane.

Understanding how counter-current operation affects average velocity, pressure distribution, and permeate flux is therefore essential to optimize module performance. One of the challenges is to determine optimal operating conditions (flow rates, pressures) for hollow-fiber dialysis modules. In order to reduce the time-consuming and costly testing of prototypes, module designs and operating conditions are to be investigated with the aid of flow simulations. A major numerical challenge is the multiscale nature of the module: fiber diameters are on the order of micrometers, while the housing extends over several centimeters.

A direct numerical simulation, in which all geometric features of the fibers are resolved in the calculation grid, would require enormous amounts of memory and computing power. This is to be avoided by using suitable, effective models for the distribution of flow resistances in the hollow fiber module, whereby a distinction is made between the flow of blood (lumen side) and that of the dialysate (shell side).

We present examples, results and an outlook toward possible upscaling techniques that could enable an effective coupling between lumen and shell side and support more computationally feasible simulations in hollow fiber modules.