Mathematical modelling of fluid flow processes in the fracture-porous reservoir

Abstract

Authors consider processes the filtration process in the reservoir. The model of the dual porosity of Warren and Root is usedto study the processes. The pores (matrix) are represented by rectangular parallelepipeds in this model, which have high porosity and low permeability. The low permeable pores are separated by a system of natural fracture that has high permeability and low porosity. Filtration of liquid in the formation is carried out through a system of fracture, and the matrix is a reservoir that continuously feeds the network of fracture. The redistribution of fluid between the matrix and fracture depends on the shape and size of the matrix blocks, the ratio of pore permeability and fracture system. The pressure distribution in the “system of fracture-matrix” system is described by the piezoconductivity equations. An analytical solution for the Warren and Rootmodel cannot be obtained in a general form, approximate solutions exist for special cases. The results of the computer simulation and the numerical solution of this problem is presented in this paper. The problem was approximated using an implicit difference scheme. The matrix sweep method was used for the calculation. Model pressure recovery curves were obtained. Analysis showed that the specific conductivity coefficient depends on the size of the matrix blocks and possible to evaluate the process of manifestation of the effect of dual porosity.