Three-dimensional trajectory analysis and network simulation of deep bed filtration

Abstract

A three-dimensional simulator of deep bed filtration in granular porous media is developed. The void space of the porous medium is modeled as a network of unit cells of the constricted-tube type with mouth and constriction diameters distributed according to prescribed size distributions. The rate of deposition in each cell is determined using the particle trajectory analysis which requires determination of the flow field in the unit cell and of all the forces and torques acting on the particle. The overall rate of deposition, expressed in terms of the filter coefficient, is determined through a detailed numerical procedure that involves simultaneous solution of the local deposition rate equations, the mass balance equation at the nodes of the network, and the equations of perfect mixing of outgoing streams at pore intersections (nodes). Numerical results agree with the experimental observation that deposition in oblique flow channels contributes substantially to the overall rate of deposition. It is found that substitution of even a few relatively large unit cells (weak collectors) into a network of otherwise uniformly sized unit cells increases the flow rate of lateral streams and leads to higher filter coefficients thanks to high impacted fractions in transverse pores.