Deep bed filtration model for cake filtration and erosion  

作　　者：L.I.KUZMINA Y.V.OSIPOV A.R.PESTEREV 

机构地区：[1]Department of Applied Mathematics,HSE University,Moscow 101000,Russia [2]Department of Computer Science and Applied Mathematics,Moscow State University of Civil Engineering,Moscow 129337,Russia

出　　处：《Applied Mathematics and Mechanics(English Edition)》2024年第2期355-372,共18页应用数学和力学（英文版）

摘　　要：Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

关 键 词：deep bed filtration cake filtration porous medium particle deposition and erosion analytical solution concentration front 

分 类 号：O368[理学—流体力学]