Model of colmatage-suffosion filtration of disperse systems in a porous medium

Abstract

532.546A model of colmatage-suffosion filtration of disperse systems in a porous medium is analyzed numerically based on a new kinetic equation for saturation of the pore space with settled particles.Modeling of the phenomena of precipitation of particles from a disperse medium in its filtration in a porous medium and clogging of the pores with these particles (colmatage of the pores) and unclogging of the pores under the action of different forces (suffosion) is of great importance for various technological processes. Some mathematical models of colmatage-suffosion filtration of disperse systems in porous media are given in [ 1,2]. These models' drawbacks were discussed in [3,4]. In the latter works, based on a balance equation for the concentration of particles suspended in the filtered liquid, new kinetic equations of active porosity [5,6], and a generalized Darcy law a model of colmatage-suffosion filtration that is devoid of the mentioned drawbacks of the models of [ 1, 2] is proposed and studied. At the same time it is noteworthy that in [2] a balance equation is written in a more general form than in [3,4], where the change in the saturation of the pore space with the settled particles and the "free" liquid not connected with the settled mass, the change in the volume concentration of the suspended solid substance in the moving mixture, etc. are taken into account separately. In [7] instead of a kinetic equation for the change in the active porosity [5,6] it is proposed that a kinetic equation for the saturation of the pore space with settled particles in the loose body where allowance is made not only for colmatage and suffosion effects but also for sedimentation precipitation of the particles be used. In [8] a model of colmatage-suffosion filtration of multicomponent systems is proposed and issues of correct formulation of the problem and the existence of invariant and self-similar solutions are discussed. In [9], based on the model of [3,4], the joint influence of the effects of convective diffusion, colmatage, and suffosion on the concentration of particles in the flow, the active-porosity profiles, the filtration rate, and other filtration characteristics was investigated, and the range of qualitative agreement between the obtained theoretical results and the experimental data given in [2] was determined. Just as in [3,4], a material-balance equation for particles suspended in a liquid is used as the balance equation in [8,9]. In this work a model based on the balance equation of [2], the kinetic equation of [7], and a generalized Darcy law is investigated. In light of the foregoing the proposed model takes into account in a more general form the filling of the pore volume with the filtered liquid, the settled particles, and the "free" liquid not connected with the settled mass and takes into consideration at the same time the effects of colmatage, suffosion, sedimentation precipitation of the particles, etc. After the formulation of the model a specific problem is considered whose numerical solution ...

Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

“…In accordance with [42], the process of particle deposition and release depends on the pressure gradient, and the greater module of pressure gradient the smaller probability of the deposition of the particles and greater the probability of the release of the particles from pores. In accordance with [42,45], the kinetic Equation (7) characterising the deposition and release of solid particles in the active zone of the porous medium is written as…”

A Deep Bed Filtration Model of Two-Component Suspension in Dual-Zone Porous Medium

“…where K (m) is filtration coefficient, |∇p| is the modulus of pressure gradient, k 0 = const. We generalized the kinetic equation of the process of attachment and detachment of particles in the active zone for a two-component suspension reflecting the dynamic factors [18,37] as follows…”

“…where K is a sufficiently large number for which c (i) j K = 0 approximately. After simple transformations, the schemes (18) and (19) take the form…”

“…In empirical (phenomenological) models [7,[16][17][18][19], the process of filtering a suspension in a porous medium is described using equations of continuum mechanics, which are supplemented by empirical relations. In classical deep bed filtration models system of partial differential equations describing the process consists of mass balance equation end kinetic equation of deposition [16,17].…”

“…In reversible deposition [18][19][20][21][22][23][24][25][26], both attachment and detachment of suspended particles may occur in parallel and kinetic equation has the form…”