In recent years many research results, both theoretical and experimental, have been published to improve the accuracy of dual porosity modeling. Most of these studies dealt with the accuracy of matrix-fracture transfer flow (MFTF) calculations (so-called transfer functions). Some studies concentrated on creating empirical transfer functions through single matrix block modeling, while others incorporated MFTF calculations in dual porosity model by using some type of sub-gridding or averaging technique. However, flow in fractures and its effects on MFTF have not been fully studied in the literature.
In this paper, we first compare methods for MFTF calculations under static fracture conditions, followed by results of numerically modeling fluid flow in matrix blocks with adjoining fractures undergoing dynamic conditions. The system studied is an oil-saturated matrix block surrounded by fractures in which water is injected to generate dynamic flow conditions. Hence, there are two dynamic flow systems. One is counter-current imbibition inside the matrix block, and the other is two-phase flow in the fractures.
Results show that MFTF can be characterized by three flow regimes. The first is before water breakthrough at the producing end of the fracture, during which little imbibition occurs inside of the matrix block depending on injection rates. The second is transient flow inside the matrix block. During this flow period the most injected water is imbibed into the block. The last flow regime occurs when flow in both systems approaches a pseudo-steady type behavior. Dimensional analysis shows that two parameters can be used to characterize these flow regimes. One is a global time scale ratio and the other is a storativity ratio. The use of proper boundary conditions imposed on both systems plays a vital role in accurately modeling MFTF. Results show that the usual assumption of phase saturation continuity between matrix block and fracture in a conventional dual porosity model generates erroneous results, especially breakthrough time at producers. Our approach is also successfully used to model published experimental data without any adjustment to measured rock and fluid data.