Flow of dispersed particles through porous media — Deep bed filtration

Transport of dispersed particles in liquids through porous beds is widely recognized to occur in many industrial processes. The process of particle deposition from a colloidal suspension flowing through a porous medium is usually called deep bed filtration. The goal of the process can be either filtration of the particles by the granular media or, on the contrary, avoiding the particle filtration. Physical and chemical forces between suspended particles and grains of the media (collectors), particle size, fluid velocity and grain size play vital roles in the removal of particles from a suspension. Particle deposition can change the pore morphology and consequently the porosity of the porous medium and the local pressure gradient. This can cause permeability decline and therefore, loss of productivity or injectivity of wells. This article presents a comprehensive review of the literature related to deep bed filtration theories. ent mathematical models for evaluating both initial and transient stage of particle removal have been proposed during last decades. Trajectory analysis or convective diffusion equations have been used in microscopic modeling or so-called fundamental modeling to compute initial removal efficiency. Although these could predict the filter performance under favorable conditions but they underestimate the removal efficiency under unfavorable conditions. Hence, semi-empirical equations were developed for predicting removal efficiency under unfavorable conditions. Macroscopic or phenomenological modeling has been used to predict transient stage removal efficiency of deep bed filtration process. Predicting filter performance by this method requires the knowledge of functionality of filter coefficient. Filter coefficient can be obtained by using search optimization technique along with effluent concentration history. A review on different mathematical models for evaluating both initial and transient stage of particle removal process is presented.