Exact solution to non-linear filtration in heterogeneous porous media

• Published in: International journal of non-linear mechanics 2023-04, Vol.150, p.104363, Article 104363
• Main Authors: Kuzmina, L.I., Osipov, Y.V.
• Format: Article
• Language: English
• Subjects: Deep bed filtration; Exact solution; Finite filtration time; Heterogeneous porous media; Non-linear filtration function
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2023.104363

Many technological processes of chemical and environmental engineering are associated with the filtration of fine particles in porous media, specifically in heterogeneous reservoirs. A one-dimensional model of deep bed filtration of suspensions and colloids in a heterogeneous porous medium is derived. The model includes the mass balance equation with variable porosity for the concentrations of suspended and retained particles and the deposit growth equation with the non-linear filtration function depending on the retained concentration and on the spatial coordinate. Using the method of characteristics, a formula for the curvilinear concentration front is obtained. The problem is reduced to one nonlinear equation in partial derivatives of the first order. An exact solution is obtained for the hyperbolic heterogeneity, and a Riemann invariant providing a relation between the solutions on the characteristics, is found. The properties of the solutions are studied. The cases of infinite and finite filtration time are considered. •Non-linear filtration model in a heterogeneous porous medium.•An explicit formula for the curvilinear concentration front.•Local exact solutions at the front and at the inlet of the porous medium.•Exact solution and Riemann invariant for the hyperbolic filtration function.•Finite filtration time for a nonsmooth filtration function.