Disclosed are reactors and reaction processes for contacting hydrocarbon reactant in the presence of oxygen stored and released within a thermal mass region of the reactor, and catalytically converting at least a portion of alkane, e.g., methane, in the hydrocarbon reactant to produce a reaction mixture comprising a C5+ composition. Oxygen storage and release for carrying out the catalytic conversion is achieved by including an oxygen storage material in a thermal mass region of the reactor. Flow-through reactors can be used to carry out oxygen storage and the hydrocarbon conversion reactions. Reverse-flow reactors are examples of flow-through reactors, which can be used to carry out oxygen storage and the hydrocarbon conversion reactions.