A process and apparatus for converting an alkane to an olefin. In one embodiment, the process involves oxidative coupling of an alkane, e.g., methane, with an oxidant, such as air, to produce an olefin having twice the number of carbon atoms as the alkane, e.g., ethylene. In another embodiment, the process involves oxidative dehydrogenation of an alkane, e.g., ethane, with an oxidant to form an olefin having the same number of carbon atoms as the alkane, e.g., ethylene. The process involves passing a flow of the oxidant from a first flow passage through a porous medium; diffusing a flow of the alkane from a second flow passage into the porous medium; and contacting the reactant alkane and the oxidant in the presence of a catalyst within the porous medium to produce the olefin.