Abstract

Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different and complex boundary conditions. For the non-linear diffusion saturation equation we cannot apply Rayleigh-Ritz Finite Element Method (FEM). Traditionally, the way around it is to use Galerkin FEM or Mixed FEM formulation, iterative nature of those, makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms, decouple and solve analytically the dependent variables from saturation - the primary variable, this non-linear FEM problem reduces to a simple weighted integral weak form, which can be solved with Rayleigh-Ritz method. The advantage of this method is that it is non-iterative, which reduces computation time. We compared our numerical models with the analytical solution of this diffusion equation. We validated a Finite Difference Method (FDM) numerical model using X-Ray Tomography (CT) experimental data, and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example, using discrete fracture approach, was developed and its results compared with a commercial simulator.

Introduction

The quest to produce more oil has led various researchers to evaluate more complex reservoirs such as naturally fractured ones. The complexity of fluid flow in these types of reservoirs arises from the fact that there are two media, which can allow fluids to flow through them. This leads to the logical conclusion that there are two principal media of fluid flow. The first is through the porous medium called the matrix flow and the other is the flow through the fracture network. At the heart of this phenomenon lies the problem of interaction of these two flow media with each other. In naturally fractured reservoirs the matrix acts as a source where hydrocarbons are present whereas the fractures facilitate in fast recovery of these hydrocarbons. Hence it is important to study what makes the matrix produce more oil. Water is used as a means to efficiently displace oil. But fluid flow in porous media, which is determined primarily by capillary force, is relatively difficult phenomenon to quantify, as per Craig1, and there has been much research effort directed in this direction like that of Handy2, Garg et al.3, Babadagli and Ershaghi4, Li and Horne5, Akin and Kovscek6, Reis and Cil7, Zhou et al.8, to name a few. Also, depending on the geometry of the fracture, there may or may not be any capillary force in the fracture network. This force is responsible for imparting the spontaneity to fluid flow within naturally fractured reservoirs. Given the complexity of quantifying the spread of fractures, it is even difficult to ascertain the limits where the fracture flow acts as an independent flow entity instead of being a part of porous matrix.

Although very wide in its scope, fluid flow studies in fractured media, as we have narrowed it down, deals exclusively with the study of this spontaneous phenomenon that helps displace oil out of matrix.

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