Nowadays, in dry and rural areas, solar-powered membrane distillation (SPMD) technology is considered a feasible means for the production of pure water from brackish water. Prior to the design and construction of a SPMD pilot plant, there is a need to predict its performance theoretically by means of a computational simulation program. Unlike previous approaches followed by other investigators to develop a mathematical model that can describe the components of a SPMD pilot plant, the developed mathematical model in this study is based on the fact that the SPMD process by nature is unsteady. The performance of a proposed SPMD pilot plant is then obtained by means of a numerical solution of the model with the aid of a simulation computer program. The results reveal that the proposed SPMD pilot plant has some unique features, which differ from a similar MD process operated at steady-state conditions in a laboratory. The analysis of the system has shown that heat recovery via an external heat exchanger is not only possible, but even effective, and an economical way to intensify the SPMD process. The plant productivity can be improved by increasing the heat-exchanger capacity (KA), decreasing the flow rates of both feed and permeate or otherwise by increasing the effective surface area of the membrane. The achieved enhancements in the SPMD pilot plant productivity are directly related to an improved heat recovery rate in the heat exchanger. However, further analysis reported in this paper shows that the increase in KA and membrane area should be optimized for any planned capacity in the design of a SPMD pilot plant.