A mathematical model for the design of membrane distillation (MD) processes applied to the water recovery from brines is developed in this study. The highly saline concentration inherent to this kind of system requires a robust thermodynamic method for water activity prediction and the consideration of temperature and concentration polarization effects for model accuracy. The MD model fitted reasonably well to experimental data and was further extended to incorporate balance and energy equations for a membrane distillation crystallization (MDC) process. A hierarchical design approach to be used alongside the model is suggested for MDC processes.

The main elementary processes were identified during simultaneous crystallization of NaCl and KCl from aqueous solutions by the batchwise evaporative method using NaCl seeds. In the early stages of the batch operation, when only NaCl crystallizes, the main elementary processes are molecular crystal growth, agglomeration, and secondary nucleation. When the eutonic condition is exceeded, a KCl primary nucleation event takes place in solution. Subsequently, part of the resulting KCl particles agglomerate with the NaCl particles. Besides, epitaxial growth of KCl upon NaCl crystals takes place. Consequently, the product is comprised of mixed composition polycrystalline particles and single crystals of each salt. The elementary phenomena just described were sensitive to crystallization conditions such as evaporation rate, seed size, and seed content, suggesting the possibility of controlling the morphological features of the particulate product as well as the chemical composition of its size fractions. Such knowledge is important in the context of wastewater treatment, where the particulate product should be suitable either for disposal as a residue or for further processing in easily separable size fractions for exploitation of valuable components.

-Crystallization in a Direct Contact Membrane Distillation (DCMD) process was studied both theoretically and experimentally. A mathematical model was proposed in order to predict the transmembrane flux in DCMD. The model fitted well experimental data for the system NaCl-H2O from undersaturated to supersaturated conditions in a specially designed crystallization setup at a bench scale. It was found that higher transmembrane fluxes induce higher temperature and concentration polarizations, as well as higher supersaturation in the vicinity of the solution-vapor interface. In this region, the supersaturation ratio largely exceeded the metastable limit for NaCl crystallization for the whole range of transmembrane fluxes of 0.37 to 1.54 kg/ (m 2 h), implying that heterogeneous primary nucleation occurred close to such interface either in solution or on the membrane surface. Solids formed in solution accounted for 14 to 36% of the total solids, whereas solid formed on the membrane surface (fouling) was responsible for 6 to 19%. The remaining solids deposited on other surfaces such as in pumps and pipe fittings. It was also discovered that, by increasing the supersaturation ratio, heterogeneous nucleation in solution increased and on the membrane surface decreased. Heterogeneous nuclei in solution grew in size both by a molecular mechanism and by agglomeration. Single crystals were cubic shaped with well-formed edges and dominant size of about 40 µm whereas agglomerates were about 240 µm in size. The approach developed here may be applied to understanding crystallization phenomena in Membrane Distillation Crystallization (MDC) processes of any scale.

A hierarchical design procedure for membrane distillation crystallization processes based on a rigorous mathematical model and presented in a previous article is extended to address important aspects of this technology not yet discussed. The possibility of pore blockage due to premature crystallization inside the membrane distillation module is analyzed, and additional design criteria based on solubility curve shapes and metastable zone limit widths are established. An alternative process configuration is proposed for the treatment of dilute feeds in order to take advantage of the higher transmembrane fluxes characteristic of low-concentration solutions.

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