| Abstract | Freshwater is a limited resource, which has driven the development of new purification and water-reuse technologies. One promising technology for water treatment is membrane distillation (MD). One of the main problems of MD, and of many desalination technologies, is membrane fouling, which reduces the performance of the membrane. This work presents a mathematical model that aims to predict distillate fluxes in direct-contact MD when fouling occurs as salts are deposited onto the membrane surface, forming an inorganic fouling layer. The mathematical model uses a heat- and mass-transfer formulation for prediction of the distillate flux under steady state conditions, and it is combined with the cake-filtration theory to represent the distillate fluxes after the onset of membrane fouling. Model results agree well with experimental observation of distillate fluxes, both before (~12–14 kg m−2 h−1) and after the onset of membrane fouling, with root-mean-square errors smaller than 1.4 kg m−2 h−1 in all the experiments. These results suggest that the cake-filtration theory can be used to represent water flux decline in MD membranes prone to inorganic fouling. From our experiments and from the modelling exercise, we found that the onset of membrane failure was relatively constant; the precipitation reaction constant is conditioned by the physicochemical interaction between the feed solution and the membrane; and the rate of flux decline after membrane fouling depends on flow conditions as well as on the precipitation compound. However, the proposed model has limitations that must be addressed in future investigations to validate it under a wider range of operating conditions, for membranes composed by other materials and with different feed solutions to address organic, biological, and/or colloidal fouling, which typically occur under real conditions. |
