Evaluation of the relevant mass and heat transfer phenomena in a packed bed membrane reactor for the direct conversion of CO2 to dimethyl ether

•Heat and mass transfer phenomena in a packed bed membrane reactor for DME synthesis.•Thiele modulus-efficiency correlation to account for pore diffusion effects.•Sherwood-type correlation for the concentration polarization of carbon membranes.•2D heterogeneous reactor model for the CO2 hydrogenation to dimethyl ether.•Membrane reactor optimization based on relevant mass transfer phenomena.