Calculation of colloids filtration in a porous medium

Abstract

Construction of underground storage facilities for hazardous radioactive waste requires soil grouting to prevent the penetration of groundwater. Modern technologies of grouting use a liquid-type colloidal silica grout which is injected in a porous soil and forms a protective waterproof layer after solidification. Colloids filtration in a porous medium is an important problem of underground hydromechanics.The purpose of the study is the numerical solution of the filtration problem of suspensions and colloids in a porous medium. A fluid with fine particles is injected into an empty porous medium. Suspended particles are transported by the fluid flow in a porous medium and partially get stuck in the pores. Calculation of the suspended and retained particles concentrations, depending on time and coordinate, is the theoretical basis of the soil grouting technology.The one-dimensional problem of deep bed filtration with suspended solid particles in a porous medium for variable porosity and permeability is solved by modified finite difference methods. The use of standard methods for solving the problem is impossible because of the solution discontinuity on the mobile boundary of two-phases. To calculate the global solution near the line of discontinuity and away from it, the counter-current scheme, the Lax-Wendroff scheme and the Total Variation Diminishing finite difference scheme are used. To eliminate the effects of dissipation and dispersion in the TVD-scheme various functions-delimiters are used.The result of this work is the numerical solution of the nonlinear filtration problem in a porous medium with size-exclusion mechanism of particles retention. The curvilinear two-phase boundary is calculated. A comparison of obtained numerical solutions using different methods of constructing difference schemes is provided. The graphs of suspended particles concentrations are constructed in dependence on time and coordinates.The comparison of the numerical solutions obtained by different finite-difference methods makes it possible to choose the best way for solving the filtration problem. The counter-current scheme strongly smoothes out the solution on the line of fracture. Using a non-monotonic Lax-Wendroff scheme, a solution with unnatural oscillations near the two-phase boundary is obtained. To calculate the filtration problem, TVD-schemes are the most acceptable. The best result is obtained when using the TVD-scheme with the function-delimiter min2.