Role of Dispersion in Injectivity Impairment: Mathematical and Laboratory Study

Abstract

Severe injectivity decline during the injection of sea/produced water is a serious problem in offshore waterfloodings. The permeability impairment occurs due to capture of particles from injected water by the rock. The reliable modelling-based prediction of this decline is important for the injected-water-treatment design, for injected water management (injection of sea- or produced water, their combinations, water filtering etc.). Particle transport in porous media is determined by advective flow of carrier water and by hydrodynamic dispersion in micro-heterogeneous media. Thus, the particle flux is the sum of advective and dispersive fluxes. Transport of particles in porous media is described by an advection-diffusion equation and by a kinetic equation of particle capture. Conventional models for deep bed filtration take into account hydrodynamic particle dispersion in the mass balance equation but do not consider the effect of dispersive flux on retention kinetics. In the present study, a model for deep bed filtration taking into account particle hydrodynamic dispersion in both the mass balance and retention kinetics equations is proposed. Analytical solutions are obtained for flows in infinite and semi-infinite reservoirs and in finite porous columns. The physical interpretation for the steady-state flows described by the proposed and the traditional models favours the former. Comparative matching of experimental data on particle transport in porous columns by the two models is performed for two sets of laboratory data.