The boundary between simple and complex descriptions of membrane reactors: The transition between 1-D and 2-D analysis

Studies of the steam reforming of methane were carried out at high temperature (773–923 K) and pressure (0.1–2.0 MPa (1–20 atm)) using a commercial Ni/MgAl2O4 catalyst in a reactor equipped with a tubular hydrogen-selective silica–alumina membrane. The membrane was prepared using a chemical vapor deposition (CVD) method which gave a H2 permeance of 1.6 × 10−7 mol m−2 s−1 Pa−1 with a H2/CH4 selectivity of 710 at 923 K. Operation as a membrane reactor gave improved methane conversions and hydrogen yields compared to use as a packed-bed reactor at all temperatures and pressures. One-dimensional (1-D) and two-dimensional (2-D) models without adjustable parameters were developed to describe the performance of the two reactors. The 2-D model gave a slightly better fit to the membrane reactor results than the 1-D model, which predicted higher conversion at high pressure than observed experimentally. This was because the 2-D model correctly accounted for decreased permeant concentrations in the vicinity of the membrane (concentration polarization) which reduce the driving force for permeation and give lower conversions. A general criterion, denoted as the Order-Hierarchy Criterion, is developed for predicting when a 2-D model should be applied instead of a 1-D model for describing reactor performance. The 2-D description is necessary when both deviations from plug-flow behavior occur and when the rate of permeation > the rate of reaction, calculated at entrance conditions.