Internal mass transfer enhancement in flow-through catalytic membranes

Flow-through membrane reactors represent a strategy for process intensification, which benefits from the convective flow that is established due to a transmembrane pressure gradient. The interesting consequence from using these materials is the improved utilization of the catalyst dispersed in the membrane. We propose a theoretical analysis which quantifies the effectiveness factor (η) and the degree of conversion. More importantly, the regime of operation which maximizes the enhancement from convective effects is identified. It corresponds to conditions of not only high internal Peclet number (P), but also of comparable Thiele modulus (ϕ2). We find that these two parameters are related by a simple analytically derived expression: ϕ2C1:26 P. When this relationship holds, an upper limit to the enhancement in the effectiveness factor that can be observed is proportional to P. This result also provides an answer to the effectiveness–conversion trade-off in ‘dead-end’ operation, when both objectives are important. The analytical solutions enable the complete description of the system in Peclet–Thiele diagrams, where the different reaction-transport regimes are identified. Moreover, issues that become particularly relevant in membrane reactors are discussed: curvature, flow direction and the ratio between the concentration distributions at both surfaces. The simplified design rules obtained bridge the gap between materials synthesis (with permeability and thickness as tunable properties) and process design (enhancement of the internal transport and productivity)