Modelling the flux decline induced by gypsum scaling in direct contact membrane distillation

Scaling has been a major technical challenge in the membrane distillation (MD) process, hindering the broader application of MD processes. Despite the increasing number of studies on MD scaling, there are limited prediction tools to describe the scaling process and help make informed decisions about the experimental conditions to prevent scaling and its irreversible damage. In this paper, a semi-analytical model was developed based on the classical nucleation theory and crystal growth to model the membrane area reduction caused by the deposition of inorganic salt crystals on the membrane surface, which is equivalent to the decrease in permeate flux resulting from scaling. The model was developed using calcium sulphate, a model scalant. The model was validated and verified with available literature data, and it has been proved that the model has the capability to produce reasonable predictions on the onset of flux decline and the declining rate with respect to the experimental data with the coefficient of determination (R2) ranging from 0.74 to 0.96. The sensitivity analysis was applied on the model, which revealed that flux decline would happen earlier in the case of higher feed temperature, higher feed velocity, and higher initial feed concentration.