Abstract
AbstractFiltering fluids with tiny particles in porous media occurs in many technological processes of environmental and civil engineering. To strengthen the foundation, a slurry is pumped into loose rock and, when hardened, strengthens it. Deep bed filtration is accompanied by the retention of particles. Various forces act on the particles and cause them to settle on the framework of the porous medium. The most common are the capture of particles in the inlets of narrow pores and attachment to the walls of wide pores. A model with two simultaneous particle capture mechanisms is considered. The problem is reduced to a standard model with an implicit aggregated filtration function. To simplify the calculations, it was previously proposed to use an approximate model with an explicit linear-constant filtration function. The linear-constant function has a break and does not optimally approximate the aggregated filtration function. The paper introduces a linear-fractional (hyperbolic) filtration function with a free parameter. The parameter is selected from the condition of the best approximation to the aggregated function. The system of equations in partial derivatives is integrated and reduced to a system of transcendental equations. It is shown that the solution to the model with a hyperbolic filtration function is closer to the true solution than the approximate solution with a linear-constant function. KeywordsFiltrationPorous mediumParticle captureMathematical modelAnalytical solution
Published Version
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