In this paper, we formulate a mathematical model of a two-phase flow near wells with hydraulic fracturing, based on the dimensional and similarity analysis and under the assumption of a ...quasi-stationary distribution of saturation in the fractures. The reliability of the model is assessed on the basis of test cases in three-dimensional and simplified one-dimensional formulations. The model makes it possible to avoid building a numerical solution of the problem of saturation transfer inside the fractures, which fundamentally simplifies and speeds up the construction of a whole numerical solution of the two-phase flow problem in the fracture drainage area of an oil reservoir.
A simplified mathematical model of two-phase multicomponent flow in the reservoir— multistage hydraulic fractures—horizontal well system is proposed. The formulation of transport problems in the well ...and in hydraulic fractures is simplified based on the dimensional analysis and similarity theory. The possibility of transition to a quasi-steady-state problem of distribution of the mixture components in high-permeability hydraulic fractures is shown. The dimension of the problem in reservoir is reduced by decomposing the problem into a set of problems in independent fixed stream tubes. For numerical solution of the problem, the resulting reduction in computer time reaches two orders of magnitude and can be further reduced by using parallel computing. Accelerating the solution of the direct problem is fundamentally necessary for the possibility of solving the inverse problem of identifying the porosity and permeability properties of fractures from the results of interpretation of tracer studies.
The general formulation of a two-phase multicomponent filtration model which describes all stages of indicator studies of multi-stage fracturing on horizontal wells is given. The equations of the ...model are presented in a dimensionless form with normalization to the characteristic scales. The statements of the direct problem and the inverse problem of interpreting the results of tracer studies are presented. Simplification of model based on the analysis of the characteristic scales and sizes of the similarity criteria that determine the solution of the problem is shown. Simplification includes transition to quasistationary equations for the average values of saturation and concentration of tracers in fractures and in the wellbore and decomposition of three-dimensional problems for pressure, saturation and tracer concentrations in the reservoir into a set of one-dimensional problems near fracture faces. The presented simplification of the model is intended for a reduction of numerical simulation computational costs, which makes it possible to construct a solution of the inverse problem for interpreting tracer studies based on a multivariate solution of direct problems.
The article presents a three-dimensional mathematical model for two-phase fluid flow near a multistage hydraulically fractured horizontal well (MSHFHW). The flow in the reservoir and in the fractures ...is simulated separately, and the flow rate is governed by Darcy's law. Finite volume method is used for spatial approximation. The obtained systems of linear equations for pressure in the reservoir and in the fractures are solved simultaneously, which allows us to avoid using iterative process for solution adjustment both in the fractures and the reservoir. Saturation is calculated by the implicit adaptive scheme AIM.
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