Intermediate product yield enhancement with a catalytic inorganic membrane—I. Analytical model for the case of isothermal and differential operation

A simple model is developed to examine the performance of a supported catalytic membrane within which occurs the consecutive-parallel reaction system given by A + B → R, with RATE = k1pA1ApBB, and A + R → P, with RATE = k2pA2ApRR. Closed-form solutions reveal that segregation of reactants A and B to opposite sides of the membrane is an effective strategy for increasing the desired product (R) point yield. However, increases in the component R yield come at the expense of the point catalyst utilization, due, in part, to depletion of reacting components B and R. The membrane performance is sensitive to the relative reaction orders with respect to component A for the special case in which the rates are zeroth-order with respect to B and R (B = R = 0). The segregation strategy is shown to be most beneficial if three requirements are met: (i) A1 < A2, (ii) k1, k2 sufficiently large and (iii) active layer sufficiently thin compared to support. Under favorable conditions [requirements (i)-(iii) met], component R is selectively produced near the active layer surface, and diffuses out of the membrane before further reaction to undesired product (P). The simulations indicate that the fractional increases in the R yield attained, as the degree of segregation is increased, exceed the fractional decreases in catalyst utilization. A secondary benefit of the membrane design is the confinement of reaction products in the bulk stream on the active layer side, thus reducing the downstream separation needs.