Display omitted •CO2 hydrogenation to dimethyl ether (DME) via a membrane reactor.•Development of a phenomenological membrane reactor model for DME synthesis.•Sweep gas fed in cocurrent mode to promote water and heat removal.•Effect of the membrane properties on the reactor performance.•High sweep gas flow rates promote the removal of water, enhancing DME synthesis. The direct hydrogenation of CO2 to dimethyl ether (DME) is a promising technology for CO2 valorisation. In this work, a 1D phenomenological reactor model is developed to evaluate and optimize the performance of a membrane reactor for this conversion, otherwise limited by thermodynamic equilibrium and temperature gradients. The co-current circulation of a sweep gas stream through the permeation zone promotes both water and heat removal from the reaction zone, thus increasing overall DME yield (from 44% to 64%). The membrane properties in terms of water permeability (i.e., 4·10−7 mol·Pa−1m−2s−1) and selectivity (i.e., 50 towards H2, 30 towards CO2 and CO, 10 towards methanol), for optimal reactor performance have been determined considering, for the first time, non-ideal separation and non-isothermal operation. Thus, this work sheds light into suitable membrane materials for this applications. Then, the non-isothermal performance of the membrane reactor was analysed as a function of the process parameters (i.e., the sweep gas to feed flow ratio, the gradient of total pressure across the membrane, the inlet temperature to the reaction and permeation zone and the feed composition). Owing to its ability to remove 96% of the water produced in this reaction, the proposed membrane reactor outperforms a conventional packed bed for the same application (i.e., with 36% and 46% improvement in CO2 conversion and DME yield, respectively). The results of this work demonstrate the potential of the membrane reactor to make the CO2 conversion to DME a feasible process.