CO2 hydrogenation to syngas via reverse water–gas shift (RWGS) is modeled in a membrane decorated microchannel reactor. Coated CuO/ZnO/Al2O3 catalyst exists in the reaction channel which is physically separated from the neighboring permeate channel by a layer of supported sodalite (SOD) membrane selective to H2O and H2 transport. Pure H2 is used as the sweep gas. Two–dimensional, steady state, isothermal operation of the reactor is quantified by the momentum and mass conservations in the entire flow domain, membrane material transfer and catalytic reaction. Upon its benchmarking with the literature–based experimental data, the reactor model is used to study the effects of inlet velocities and partitioning of the reactive mixture and sweep streams, reactor pressure, and molar inlet H2:CO2 ratio. At 523 K, 15 bar and H2:CO2 = 3, the per cent CO2 conversion exceeds the thermodynamic limit of 16.8% and can be maximized to 52% when the inlet velocity of the H2 + CO2 mixture is minimized. Decreased dosing of the reactive mixture, however, limits the molar amount of CO2 converted and reduces reactor capacity. Both metrics are positively correlated with reactor pressure and the inlet velocity of the sweep gas but remain insensitive to flow direction. Syngas composition (molar exit (H2 – CO2)/(CO + CO2) ratio) can be varied between 1.7 and 9.8. The proposed reactor can deliver ∼2.5 times higher volume and catalyst mass–based productivity and ∼33% higher CO2 conversion than an equivalently operated packed–bed membrane reactor.