A Novel Workflow to Model Permeability Impairment through Particle Movement and Deposition in Porous Media

Abstract

This article presents a practical transfer function type solution to a complex problem in which variations in a number of parameters can be taken into account. A new mathematical model, which is based on mass balance transfer function of particles movement/retention in porous media, has been derived. It is used to predict permeability reduction as a function of time. The linear forms as well as the radial forms of the model are described. Although the differential equations derived are similar to the general form of diffusion-convection equations, the marked difference is the suitability of the model, for being applied for variation of parameters, such as particle concentration in the fluid, injection rate, density of solid particles, against the depth and time of invasion. This transfer function has been solved, and the results of the simulation run agree reasonably well with the experimental damage data obtained in laboratory. Owing to its simplicity, this model is more practical to describe permeability reduction for the flow of suspended particles in porous media. 123 868 A. K. Dahaghi et al. K Permeability (m 2 ) L Length (m) M Model parameter (s −1 ) m Mass of suspension particle (kg) p Pressure (N/m 2 ) q Volumetric flow rate (m 3 /s) t Time (s)

Seepage Migration Process of Soluble Contaminants in Porous Medium considering Adsorption History

“…Leij et al [27] studied the migration law of pollutants during equilibrium adsorption, established a semi-infnite equation, and obtained the analytical solution of a unidirectional stable seepage feld through Laplace and Fourier transform. Dahaghi et al [28] deduced a new mathematical model of pollutant migration, which considers the complex migration process of particles. Rowe and Bookeret [29] proposed a two-dimensional fnite layer calculation method considering vertical and horizontal directions and obtained the migration law of layered soil under the condition of linear equilibrium adsorption.…”