Modeling colmatation of a porous medium during the injection of water with impurity particles

In the process of oil production, the reservoir pressure gradually decreases with time and, to maintain it, water injection, also known as waterflooding, is applied. The formation water composition typically contains various impurities, minerals and metals. They settle on the pore matrix, decrease the porosity of the bottomhole zone and slow down the advance of the water-oil displacement front. This negatively affects the productivity of the well and reduces oil production. Therefore, the study of these processes is a relevant task. The natural process of pore blocking is called colmatation. The purpose of this work is to evaluate the influence of reservoir and fluid parameters on the distribution of porosity, permeability and impurity concentration as a result of the colmatation phenomenon. To solve the problem, we use a system of equations of continuum mechanics that includes the mass balance equations for particles in suspension and carrier fluid, Darcy's law for water filtration into the reservoir, the Kozeny-Karman formula for the relationship between the initial porosity and permeability, and an equation describing the kinetics of particle settling on the porous matrix. A solution to the system of equations is found using an explicit finite-difference scheme. The distribution of impurity concentration in the reservoir is obtained. It is shown for the first time that a decrease in the coefficient of colmatation leads to a decrease in the rate of colmatation and the emergence of a stabilized zone near the displacement front. It has been established that although the coefficient of colmatation is a small parameter, it has a significant effect on the waterflooding nature. Analysis of the sensitivity of the water-oil displacement characteristics to the reservoir and fluid parameters shows that the velocity of the displacement front and the coordinate of this front increase with an increase in permeability and pressure at the bottomhole of an injection well and decrease with an increase in viscosity in accordance with Darcy's law.