A New Approach for Mathematical Modeling of Formation Damage Due to Invasion of Solid Suspensions

Abstract

Abstract Formation damage due to invasion of solid suspensions has been studied by several investigators and some modelling 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 mathematical model, which is based on mass balance of particles flowing through the porous media. The linear as well as radial forms of the model are described. Although the differential equations derived take the general form of diffusion-convection equations, the marked difference is in terms of the suitability of the model to apply for variation of parameters such as particle concentration in the fluid, injection rate, density of solid particles, against the depth and time of invasion. The results of the simulation run agree reasonably well with the experimental damage data obtained on 80mm sandstone core plugs using a multi-port pressure-tapped core holder. The radial form of the model can be used to simulate formation damage in water injection wells whereas the linear model can simulate damage in filtration systems involving industrial water purification or oilfield water injection treatment.