Publisher Summary Most of the hydrogen is produced industrially by the steam reforming of hydrocarbons or alcohols (e.g., for fuel-cell applications). The process gas stream coming from the steam reformer is composed by H2, CO, CO2, H2O, and small amounts of unconverted reactants (CH4). The CO concentration of the gas leaving the reformer must be reduced up to a specified level, with two main goals: (1) to increase the H2 production rate and (2) to purify the process stream. To these ends, the water–gas shift reaction (WGSR) is widely used. An attractive alternative to increase the CO conversion is the membrane reactor (MR). The main idea of this design is the selective permeation of reaction products (e.g., H2) to shift the equilibrium toward products and, consequently, increase the conversion, or reduce the amount of catalyst for a desired conversion level. In this chapter, the performance of the MR for the WGSR is simulated and compared with that of a fixed-bed reactor (CR) for isothermal and adiabatic operations. The analysis is further extended to a MR under nonisothermal, nonadiabatic conditions.