The problem of fluid transport inside ceramic, porous, multi-channel microfiltration membranes has been studied experimentally and computationally. The transport of permeate in a seven (star-shaped) channel tubular membrane is modeled according to Darcy’s equation for flow in porous media; the resultant Laplace equation is solved numerically on the complex, multi-connected geometry of interest using the Boundary Integral Method (BIM). Based on this model, we propose an efficient and novel procedure for determining the effective permeability (K-m) of the membrane module by comparing computational results with on-line experimental measurements of permeate flux at various levels of Trans-Membrane Pressure (TMP). Besides determining K-m, the proposed approach can be used to identify alternative designs and operating conditions in membrane modules of arbitrary geometrical complexity.