Modeling the effects of capillary pressure with the presence of full tensor permeability and discrete fracture models using the mimetic finite difference method

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.

Performance analysis of linearization schemes for modelling multi-phase flow in porous media

“…It employs an unconditionally stable fully implicit method to guarantee robust solutions 28 , 29 . An in-depth discussion of the implementation of the OBL technique within an advanced parallel framework for reservoir simulation, using high-order discretization techniques, such as the Mixed Hybrid Finite Element Method (MHFEM) and Mimetic Finite Difference (MFD), can be found in the works of 30 – 34 ,among others, to which we direct the reader. In our computational framework, Newton’s method serves as the nonlinear solver 35 , 36 , a choice motivated by its robust performance in handling the nonlinearities inherent in the equations governing multi-phase flow in porous media 37 .…”

Relative Permeability-Dictated Huff-n-Puff Technique in Tight Reservoirs: Suitability and Limitation toward Field Implementation

“…21 An analytical solution of fractional-flow theory was also employed to describe the fluid flow characteristics toward the reservoir scale, with a study showing that the solution and model could yield accurate results in oil production performance. 22 Wei 23 investigated a scaling-up to reservoir-scale modeling on a potential of lowsalinity water huff-n-puff method, with key factors of injection timing, fluid volume, and a number of cycles found sensitive to the oil production. The authors also realized that the soaking time has no influence on the oil recovery, as found by Sun 20 and Lu, 24 implying that there is suitability of factors in designing the project.…”

“…Considering the reservoir properties, the porosity was found to be an inverse proportion to oil recovery, while the permeability was of the opposite . An analytical solution of fractional-flow theory was also employed to describe the fluid flow characteristics toward the reservoir scale, with a study showing that the solution and model could yield accurate results in oil production performance . Wei investigated a scaling-up to reservoir-scale modeling on a potential of low-salinity water huff-n-puff method, with key factors of injection timing, fluid volume, and a number of cycles found sensitive to the oil production.…”