Several investigators have studied formation damage due to invasion of solid suspensions and some modeling approaches have also been reported in the literature, most notably the application of effective medium theory and percolation theory in two and three-dimensional capillary networks. This paper presents a new model, which is based on mass balance transfer function of particles flowing through the porous media. The linear forms of the model are described as well as the radial forms. 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 is solved by MATLAB program (Version 5.3.2) and SIMULINK software. The results of the simulation run agree reasonably well with the experimental damage data obtained in laboratory.
The phenomenon of solid particle invasion and occupation of the porous medium is a subject that is encountered in reservoir engineering applications. Numerous investigators study the process of solid particle invasion in a porous medium, related to deep bed filtration. The literature abounds with a number of theoretical studies and different approaches at mathematical modeling of permeability alteration due to solid particle invasion and capturing a porous medium. A mathematical model is obviously necessary for theoretical explanation of the phenomenon of solid particle invasion into a porous medium. An attempt to describe the phenomenon of formation damage caused by solid particle invasion and capturing a porous medium and the subsequent permeability alteration, is one of the reasons to develop a new mathematical model in this study.
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