A model to evaluate and predict performance of hollow fiber membrane contactor modules is presented for the extraction of compounds with interfacial chemical reactions. The model is based on the film theory approach combined with facilitation factors. Mass transfer coefficients are calculated using published correlations and chemical reaction effects are accounted for by calculated facilitation factors. The shell side flow maldistribution due to random packing of fibers in the module bundle is estimated using Voronoi tessellations and the friction factor-Re. The computer simulation of random packing is accomplished using random sequential addition. The model is correlated with experimental data on the extraction of uranyl nitrate from an acidic aqueous medium into TBP/DIPB extractant. The model correlates experimental data very well for this system. By accounting for the non-linearity of the interfacial effects in this way the rigorous solution of a system of coupled non-linear PDEs may be avoided, but the model can still provide accurate predictive design and analysis information for the system.