On modeling incipient crystallization of sparingly soluble salts in frontal membrane filtration

Modeling incipient crystallization ("scaling") in desalination membrane modules is a very difficult task due to several complications arising from the interplay of physico-chemical solution conditions (leading to supersaturation) with the flow field and related transport processes, including solid phase generation phenomena and membrane surface geometrical changes caused by the developing discrete particles. Although eventually all these aspects must be included in a comprehensive process model, it is fruitful to isolate and tackle them separately, thereby improving our understanding and developing techniques which will facilitate the ensuing synthesis of an integrated modeling framework. The focus in this work is on solid phase generation phenomena accounting for the membrane surface geometrical changes. A mean field model is developed that includes bulk and surface particle nucleation and growth processes. The relative importance of the two types of processes is analyzed. It is shown that, if thick concentration boundary layers exist around surface particles, the mean field theory--although not strictly valid--can be approximately used to estimate the transport coefficients, in conjunction with a unit cell problem for transport processes around a single surface particle. The unit cell problem is formulated and typical results for the flow and concentration field therein are presented as well as the corresponding mass transfer coefficients.