MATHEMATICAL MODEL OF TWO-PHASE FILTRATION IN A POROUS MEDIUM TAKEN INTO ACCOUNT OF ITS DEFORMATION
Keywords:
deformation, permeability, porosity, oil debet, oil saturation, reservoir pressureAbstract
The work considers the process of filtration of water and oil phases, taking into ac count the deformation of the porous medium, opened by a system of production wells. The wells are grouped in rows. We assume that oil and water are incompressible and constant pressure was established in the oil well. A quasi-one-dimensional mathematical model of the process is proposed. The model used Darcy’s law to determine the filtration velocity, cases where the change in porosity is linear and the change in permeability is linear with reservoir pressure, and also considered the laws of exponential dependence and the laws of porosity dependence. Liquid, oil and water flow rates, as well as oil fractions, are calculated for various laws of changes in formation permeability. Using the proposed model, the influence of medium deformation on hydrodynamic parameters was analyzed. The problem was solved numerically using the large particle method. Due to the nonlinearity of the model, linearization was used in its approximation. Based on the results obtained, the effect of deformation of a porous medium on reservoir pressure, porosity, permeability, oil saturation and oil production was studied. According to the results obtained, an increase in the compressibility of the medium leads to a sharp de crease in porosity and permeability in the bottomhole zone. This slows down the process of reducing reservoir pressure. As the compressibility of the medium increases, oil sat uration increases. At relatively low values of medium compressibility, its decrease first leads to a slight increase in oil production, and then to its sharp decrease, while at rel atively high values, production increases evenly. It has been established that the share of oil in produced fluids decreases with increasing compressibility of the medium. As the pressure at the bottomhole xone decreases, the permeability and porosity of the medium decreases, the oil saturation and the proportion of oil in the produced fluids increase.
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