Modeling of transient shape factor in fractured reservoirs considering the effect of heterogeneity, pressure-dependent properties and quadratic pressure gradient

Fractured reservoirs contain most of the oil in the world's reserves. The existence of two systems of matrix and fracture with completely different characteristics has caused the modeling of the mechanisms of fractured reservoirs to be more complex than conventional ones. Modeling of this type of reservoirs is possible using two methods of single and dual porosity model. Modeling via single porosity scheme is very time-consuming as it takes into account huge matrix blocks (low permeability and high porosity) and small fractures (high permeability and low porosity) alongside each other explicitly. The dual porosity model, however, attempts to solve this problem using the concept of shape factor, which is defined as the amount of fluid transferred from the matrix to the fracture. The shape factor coefficients expressed so far have been derived via simplifying assumptions which keep them away from real conditions prevailing in fractured reservoirs. In this paper, shape factor is calculated more realistically with consideration of the quadratic pressure gradient in the diffusivity equation, the heterogeneity of the matrix block and the change of the rock properties by pressure change. For these three cases, the analytical modeling of the flow of fluid from the matrix to the fracture system has been discussed and its results with previous models have been compared. In addition, the dependence of shape factor on the stated parameters was evaluated and in order to validate the results of the proposed analytical model, its results were compared with the results of a commercial simulator. Investigating the shape factor with the assumptions about the physics of the fractured reservoirs will improve our understanding of the fluid transfer between the matrix and the fracture, and this capability will allow numerical and commercial simulators to predict the behavior of fractured reservoirs more accurately.