This paper describes a computational study of a proposed recuperative catalytic converter intended for the catalytic combustion of lean methane streams. The design is based on the principle of alternating layers of washcoated monolith channels through which the fluid passes in counter-current flow. Heat transfer occurs continuously across the boundary separating the layers, thus the exiting hot gas exchanges energy with the incoming cold gas. Monoliths composed of cordierite and silicon carbide are compared, each of which had 12% by volume washcoat applied. The effects of layer thickness, monolith length and space time are compared. It is found that the monolith comprised of higher thermal conductivity material is more effective in enhancing the temperature in the reactor. Conversion of methane entering the reactor at relatively low temperatures can be oxidised with some added thermal energy. (C) 2012 Elsevier B.V. All rights reserved.