Size-Exclusion Colloidal Transport in Porous Media--Stochastic Modeling and Experimental Study

Abstract

Suspension, colloidal, and emulsion flow in rocks with particle size-exclusion may have a strong effect on the reservoir and on the well behavior during fines migration and production, drillingfluid invasion into oil-or gas-bearing formations, or injection of seawater or produced water. The stochastic microscale equations for size-exclusion colloidal transport in porous media (PM) are derived. The proposed model includes the following new features: It accounts for the accessible flux in the expression for capture rate, it accounts for the increase of inlet concentration caused by the injected particles entering only the accessible area, and it accounts for the dilution of effluent accessible flux in the overall flux of the produced suspension. Two sets of laboratory tests on short-term injection of monosized suspensions have been carried out in engineered PM. The treatment of the laboratory data for short-term continuous-suspension injection shows good agreement with the modeling results. The proposed model shows a better fit to the experimental data than the previous population-balance model for suspension transport in PM, which validates the proposed modified model. Microscale Modeling for Particle Straining The stochastic modeling of suspension flow in PM, accounting for straining particle capture, is established in this section. The medium is represented by the model of triangular parallel capillaries alternated with mixing chambers. The analytical model for lowretention filtration is derived, and the steady-state solution is obtained.

Calculation of the filtration of polydisperse suspension with a small rate

“…Mathematical methods used to construct the asymptotics can be generalized to the case of variable porosity and permeability, depending on the concentration of retained particles [18].…”

Filtration model of the unsteady suspension flow in a porous medium

“…The mathematical model of the particle transport and retention in a filter is based on the mechanical and geometric interaction of particles with a porous medium [4][5][6]. A homogeneous porous medium with pores having the same cross section throughout its entire length is considered.…”

Modeling of Fine Migration in a Porous Medium

“…When constructing the particle diffusion models the influence of fluid viscosity and electrical interaction of the particles with the channel walls are neglected. It is assumed that the solid particles pass freely through the large pores and get stuck in the throat of small pores which are smaller than the particle diameter [4,5]. The retained particles cannot be driven out by the fluid flow or other particles.…”