Size Exclusion Mechanism, Suspension Flow through Porous Medium

Hooman Fallah,Afrouz Fallah,Mohammad Afkhami,Abazar Rahmani,Ali Ahmadi

doi:10.4236/ijmnta.2012.14017

Hooman Fallah, Afrouz Fallah + Show 3 more

Open Access

https://doi.org/10.4236/ijmnta.2012.14017

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Abstract

A lot of investigations have been done in order to understand the mechanisms of the transport of particulate suspension flow through porous medium. In general, Deep Bed Filtration studies have been conducted to analyse the mechanism involved in the processes of capturing and retaining particles occurs throughout the entire depth of the filter and not just on the filter surface. In this study, the deep bed filtration mechanism and the several mechanisms for the capture of suspended particles are explained then the size exclusion mechanism has been focused (particle capture from the suspension by the rock by the size exclusion). The effects of particle flux reduction and pore space inaccessibility due to selective flow of different size particles will be included in the model for deep bed filtration. The equations for particle and pore size distributions have been derived. The model proposed is a generalization of stochastic Sharma-Yortsos equations. Analytical solution for low concentration is obtained for any particle and pore size distributions. As we will see, the averaged macro scale solutions significantly differ from the classical deep bed filtration model.

Highlights

The following model predicts that the particle breakthrough happens after injection of one pore volume
A lot of investigations have been done in order to understand the mechanisms of the transport of particulate suspension flow through porous medium
In the case of constant filtration coefficient, the particle penetration depth equals 1, but here, as we focused on the size exclusion capture, the phenomenological model (1) does not account for particle size distributions

Summary

Introduction

The following model predicts that the particle breakthrough happens after injection of one pore volume. Several attempts to correlate the formation damage with sizes of particles and pores were unsuccessful [2] (A model for average concentrations is not general enough or may be size exclusion mechanisms never dominate). In the case of a porous medium with the uniform pores size distribution, this assumption results in independent deep bed filtration of different particle size populations. As we will see, if we consider size exclusion mechanism, either smaller particles than the pore or larger particles, do not perform deep bed filtration. Analytical solution will shows for a small pore size variation medium, only the intermediate size particles perform deep bed filtration. In this case, the population velocity is particle size-dependent. The averaged equations for deep bed filtration of intermediates size particles differ from the classical deep bed filtration

Deep Bed Filtration

Advective Velocity

Derive the Equations

Filtration in a Single Pore Size Medium

Highlighted Assumptions

Conclusions