Membrane distillation model based on heat exchanger theory and configuration comparison

Improving the energy efficiency of membrane distillation (MD) is essential for its widespread adoption for renewable energy driven desalination systems. Here, an energy efficiency framework for membrane distillation modules is developed based on heat exchanger theory, and with this an accurate but vastly simplified numerical model for MD efficiency and flux is derived. This heat exchanger analogy shows that membrane distillation systems may be characterized using non-dimensional parameters from counter-flow heat exchanger (HX) theory such as effectiveness (ε) and number of transfer units (NTU). Along with the commonly used MD thermal efficiency (η), “MD effectiveness” ε should be used to understand the energy efficiency (measured as gained output ratio, GOR) and water vapor flux of single stage membrane distillation systems. GOR increases linearly with η (due to decreasing conduction losses), but increases more rapidly with an increase in ε (better heat recovery). Using the proposed theoretical framework, the performance of different single stage MD configurations is compared for seawater desalination. The gap between the membrane and the condensing surface constitutes the major resistance in both air gap (AGMD) and permeate gap (PGMD) systems (75% of the total in AGMD and 50% in PGMD). Reducing the gap resistance by increasing gap conductance (conductive gap MD (CGMD)), leads to an increase in ε through an increase in NTU, and only a small decrease in η, resulting in about two times higher overall GOR. GOR of direct contact MD (DCMD) is limited by the size of the external heat exchanger, and can be as high as that of CGMD only if the heat exchanger area is about 7 times larger than the membrane. While MD membrane design should focus on increasing the membrane's permeability and reducing its conductance to achieve higher η, module design for seawater desalination should focus on increasing ε by reducing the major resistance to heat transfer. A simplified model to predict system GOR and water vapor flux of PGMD, CGMD and DCMD, without employing finite difference discretization, is presented. Computationally, the simplified HX model is several orders of magnitude faster than full numerical models and the results from the simplified model are within 11% of the results from more detailed simulations over a wide range of operating conditions.