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

Abstract

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. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4604–4615, 2017

A multicontinuum approach for the problem of filtration of oily‐water systems across thin flat membranes: II. Validation and examples

“…The parameters shown in Table are assumed constants throughout all numerical experiments. The dimensions of the feed channel are used to calculate the flux of the incoming feed given the CFV and is also required in the calculations of the critical velocity . In all the examples considered in this work, the output data of interest are the permeation flux across the different continua for both clean water and the oil, the total volume flow rate of the permeated water and oil phases, the critical entry pressure, and the critical velocities associated with all continua.…”

“…Several modeling approaches have been proposed to investigate the permeation mechanisms across the membrane . More details about these models can be found in the first part of this work . They may, generally, be categorized into three approaches according to the level of details they produce.…”

“…From models that generate integrated details about the filtration processes (e.g., Hermia models and Ho and Zydney model) to models which require comprehensive level of details like those involving computational fluid dynamics (CFD) . In our previous work, a new methodology has been introduced that not only estimates the permeation flux of the water but also the associated oil phase. This modeling methodology provides a macroscopic description that rests on the findings of the microfiltration studies .…”

“…Likewise, the critical velocity is the hydrodynamic bulk velocity in the feed channel at which pinned oil droplets dislodge the surface. While these CFD findings apply to single pinned oil droplet, the multicontinuum framework upscale this information to encounter the whole oily‐water membrane system . It should be noted that, while the multicontinuum framework has been developed based on the CFD findings on the behavior of individual oil droplets when they pin over pore openings, it can, generally, be extended to account for the cases in which oil droplets cluster and coalesce.…”

The critical pressure for microfiltration of oil-in-water emulsions using slotted-pore membranes

“…Common antifouling strategies include crossflow filtration, physical or chemical cleaning, surface wettability modification, stabilization by surfactants, and electrostatic repulsion [8][9][10][11][12][13]. More recently, a multicontinuum approach for estimation of the permeation capacity of thin flat membranes with a broad distribution of pore openings was formulated for oil-water emulsions with different droplet sizes and then validated using the experimental data [14,15].…”