Abstract
Capillary dominated flow or imbibition—whether spontaneous or forced—is an important physical phenomena in understanding the behavior of naturally fractured water-driven reservoirs (NFR’s). When the water flows through the fractures, it imbibes into the matrix and pushes the oil out of the pores due to the difference in the capillary pressure. In this paper, we focus on modeling and quantifying the oil recovered from NFR’s through the imbibition processes using a novel fully implicit mimetic finite difference (MFD) approach coupled with discrete fracture/discrete matrix (DFDM) technique. The investigation is carried out in the light of different wetting states of the porous media (i.e., varying capillary pressure curves) and a full tensor representation of the permeability. The produced results proved the MFD to be robust in preserving the physics of the problem, and accurately mapping the flow path in the investigated domains. The wetting state of the rock affects greatly the oil recovery factors along with the orientation of the fractures and the principal direction of the permeability tensor. We can conclude that our novel MFD method can handle the fluid flow problems in discrete-fractured reservoirs. Future works will be focused on the extension of MFD method to more complex multi-physics simulations.
Highlights
Fractured reservoirs (NFR’s) have been an important research topic in the field of multiphase flow in porous media due to the complex nature of the multi-phase flow in the fracture–matrix system
The following conclusions can be drawn from this work: (1) The comparison between the numerical and the analytical solutions for spontaneous imbibition processes in a closed system with different wetting rock states showed a great match as the oil and water phases mobilize to achieve equilibrium in the system
If the principal direction of the permeability tensor is aligned with the fracture orientation, water tends to flow in the fracture first missing oil spots in the matrix
Summary
Fractured reservoirs (NFR’s) have been an important research topic in the field of multiphase flow in porous media due to the complex nature of the multi-phase flow in the fracture–matrix system. In MHFE method, Lagrange multipliers are used to account for the physical properties at the interface This method has been tested for the effect of fractured media on the imbibition of water into the matrix in counter-current flow and proved to be accurate. If a simple and good grid is necessary for FVM and MHFE, this is not necessarily required for mimetic finite difference (MFD) method whose formulation resembles the mixed-hybrid formulation (Brezzi et al 2005, 2005; Brezzi and Fortin 2012; Brezzi et al 2006) To overcome these restrictions, mimetic finite difference (MFD) method was introduced to model highly unstructured polygons (Da Veiga et al 2009; Lipnikov et al 2014) based on numerical computation of the basis broadening its applicability.
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