A Stochastic Model for Deep Bed Filtration and Well Impairment

Abstract

Injectivity decline during sea/produced water flooding is a wide spread phenomenon in offshore waterflood projects. The injectivity decreases due to solid and liquid particles that are present in the injected water. Capture of particles by porous rock results in permeability damage. In this work, a new pore level model for deep bed filtration of water with particles in porous media is developed. The model accounts for particles and pore size distribution, as well as size exclusion mechanism (a particle is captured by a smaller size pore). The system of equations derived consists of the continuity particle number equations and of the kinetics of particle entrapment and pore plugging. The particle velocity reduction and the particle accessibility, due to restriction for particles to move via large pores only, are incorporated in the model. An analytical solution of the pore level stochastic system is obtained for a medium with small pore size variation. It allows derivation of the averaged concentration equations which differs from the traditional ones. Finally, the modification of the classical deep bed filtration model that accounts for velocity reduction and particle accessibility effects is proposed.