Abstract
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.
Highlights
Fractured reservoirs contain large percentage of the worldwide oil
Regions can be defined: (A) the time interval when the pressure drop has not yet reached the end of the matrix block and the dimensionless shape factor changes linearly versus time; (B) the pressure drop reaches the end of the matrix block, and pressure of no-flow limit within the matrix block is decreasing and the dimensionless shape factor curvature is reduced; (C) pressure of no-flow limit within the matrix block is equal to the fracture pressure and no fluid transitions occur between the matrix and the fracture
Taking into account the pressure-dependent permeability of the matrix, the pressure drop reaches the end of the matrix block with delay, and as shown in Figure 7, the dimensionless shape factor increases at the transient period, and after the arrival of the pressure drop to the end, the dimensionless shape factor between the matrix and the fracture is fixed
Summary
Fractured reservoirs contain large percentage of the worldwide oil. There are two different matrix and fracture systems with different physical characteristics inside such oil reserves. Abbasi et al (2018a) investigated the effect of block size distribution on the fluid flow and shape factor between the matrix and fracture by presenting an analytical model. In line with previous studies, fluid flow modeling in porous media based on dual porosity concept involve assumptions that distance them from real prevailing conditions in reservoirs Such assumptions include ignoring quadratic pressure gradient term, homogeneous porous media, and constant permeability during the reservoir life. In this paper, considering more realistic assumptions about the nature of the fractured reservoirs such as the heterogeneity of the matrix block, the quadratic gradient pressure in the equation of diffusion and the change of rock properties by changing the pressure, the analytical modeling of the fluid flow from the matrix to the fracture is discussed. In order to validate the results of the proposed analytical model, results of the new method are compared with the results of the commercial simulator
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