Modelling the simultaneous heat and mass transfer of direct contact membrane distillation in hollow fibre modules

This paper presents a new procedure for modelling the simultaneous heat and mass transfer in direct contact membrane distillation (DCMD) in a hollow fibre configuration. Iterative calculations in classic dimensionless analysis were applied to develop semi-empirical models, employing the analogy between heat and mass transfer. The procedure incorporated the significant effect of the membrane module's geometry: length and tortuosity of fibres in the bundle and fibres’ size. Additionally, the new procedure showed the influence of the exponent β of Prandtl and Schmidt numbers on the validity of the models to simultaneously describe heat and mass transfer in the DCMD process. Current results agreed well with other analyses in the literature. The value close to 0.33 of β, as conventionally used, could be applied for heat transfer and minimal mass transfer. In other more intensive mass transfer cases, it was found that the values of β could go up to 0.55. The new models demonstrated a linear relationship between heat and mass fluxes and their respective driving forces, namely conductive heat flux against temperature gradient and mass flux against water vapour pressure difference across the membrane. Finally these semi-empirical models were applied to evaluate the performance of various hollow fibre modules of different length and types.