New semi-analytical method for numerical simulation of fluid and heat flow in fractured reservoirs

Permeability and flow in many petroleum, gas, and geothermal reservoirs are dominated by fractures. Despite major advances in recent years, mathematical modeling of fluid and heat flow infractured reservoirs remains a difficult problem. Porous medium approximations have been shown to be inadequate for many flow processes in fractured systems, while double-or multiple-porosity techniques may involve excessive amounts of numerical work or large discretization errors. We have developed a new method for modeling fluid and heat flow in fractured reservoirs which is an extension of a technique developed by Vinsome and Westerveld (1980), for calculating heat exchange between permeable layers and impermeable semi-finite confining beds during thermally enhanced oil recovery. Our methods combines a finite-difference description of global flow in the fractures with an analytical representation of interporosity flow by means of trial functions for fluid pressures and temperatures in the matrix blocks. The trial functions contain adjustable parameters which are calculated for each time step in a fully coupled way based on matrix block shapes and dimensions, utilizing simple mass and energy conservation principles. We have incorporated the semi-analytical technique into our general purpose multiphase simulator MULKOM. The method was verified by comparison with exact analytical solutions for fluid and heat exchange with individual matrix blocks. Applications were made to geothermal well test and production-injection problems with interporosity fluid and heat flow. The calculations show excellent agreement with numerical simulations using the method of ″multiple interacting continua″ (MINC), with no noticeable increase in computing work compared to porous medium calculations.