Most previous studies of air- and liquid-gap membrane distillation (AGMD and LGMD) processes using a composite membrane have been focused on an experimental approach. In this paper, rigorous theoretical investigations of the AGMD and LGMD processes were performed with a flat sheet type module using a composite membrane comprised of a polytetrafluoroethylene (PTFE) active layer and a polypropylene (PP) support layer. The model predictions were verified by comparing with measured data, where good agreement between the prediction results and experimental data was obtained. It was observed that as the gap size increased the AGMD permeate flux decreased exponentially with increased diffusion resistance. On the other hand, the LGMD permeate flux decreased exponentially and then increased asymptotically after attaining a minimum at a certain liquid-gap size (5-7 mm). This phenomenon was due to the onset and enhancement of a natural convection, resulting in an improvement in heat and mass transfer in the liquid gap.