Water-gas-shift (WGS) membrane reactor is a promising approach to purify hydrogen produced by hydrocarbon or biomass reforming to fuel cell grade (<10 ppm CO). CO2-selective polymer membranes suitable for the above operation can potentially be fabricated into spiral wound modules with catalyst packed on the feed side and sweep gas flowing on the permeate side. This paper presents a detailed model based on both mass and enthalpy balances as well as pressure drop to study this intricate reactive separation system. The kinetics of the WGS reaction was incorporated using a published rate expression for the commercial CuO/ZnO/Al2O3 catalyst. The resulting 1-D (cocurrent or countercurrent flow of feed and sweep streams) or 2-D (crossflow) system of differential equations was solved using COMSOL Multiphysics. The model was validated by comparing the predicted CO results with previously published experimental data for a lab-scale flat rectangular membrane reactor. The effects of the type of flow mode on concentration and temperature profiles within the membrane reactor were predicted. Also, a sensitivity study was carried out to quantify the effects of operating parameters like feed pressure, sweep to feed flow rate ratio, and steam/CO ratio on membrane area and hydrogen recovery. Results show that although the countercurrent flow mode is the most efficient in terms of CO reduction, the crossflow mode might provide a better trade-off between CO reduction and heat management. For the countercurrent mode, it was also shown that it is important to enhance both the CO2 permeance as well as the catalyst activity to reduce the membrane reactor size.