A multicontinuum approach for the problem of filtration of oily water systems across thin flat membranes: I. The framework

A multicontinuum model is built to estimate the permeate flux of an oily water system across a thin flat membrane in cross filtration methodology is demonstrated. Several continua are constructed to represent droplet and pore-size distribution of both the dispersed oil phase and the porous membrane, respectively. The possible permeation of the oil phase has been divided into three criteria. In the first criterion, oil droplets of a given size range may permeate through a given size range of the porous membrane, in the second criterion, oil droplets of another size range may be rejected through another pore size range, and in the third criterion, oil droplets may break apart leaving a tail inside the pore space, which will eventually permeate, and the rest will sweep off due to shear stress. These protocols identify the methodology of the proposed multicontinuum approach, which is introduced in this first part. (c) 2017 American Institute of Chemical Engineers AIChE J, 63: 4604-4615, 2017