Design for cascade of crossflow direct contact membrane distillation

The use of crossflow direct contact membrane distillation (XF-DCMD) modules allows lower velocities and volumetric flows on the brine side while still maintaining good heat-transfer coefficients. The key to using these modules in energy-efficient processes requires that the heat be recovered from the hot distillate exit stream with close temperatures of approach. This is best accomplished in a cascade of crossflow modules arranged in a manner approaching the behavior of countercurrent DCMD modules. A short-cut design method is presented to determine the number of such identical modules needed to extract maximum heat recovery between an inlet and exit brine temperature. This method is dependent on two observations: (1) existence of a unique relationship between brine temperature drop across a stage (ΔT_stage) and the temperature of closest approach between brine and distillate streams at the top of the stage (Δ_Tend), which defines an operating line; (2) Δ_Tend remains relatively constant from stage to stage. As in other thermal processes, there is a tradeoff between energy efficiency and area (here, membrane area). The optimum will be a function of the relative costs of energy and membrane area. For brine entrance and exit temperatures of 95°C and 32-38°C, respectively, and a specific stage area of 2.9 m ²/(mt/h), the optimum number of stages moves from six to two as the price of energy decreases from $4 US/mt steam equivalent to $0.73 US/mt steam equivalent.