Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Numerical Simulation of Fluid Flow in 2-D Naturally Fractured Reservoirs Tensors Using the Embedded Discrete Fracture Model and the Projection-Based Embedded Discrete Fracture Model Approaches with the Multi-Point Flux Approximation with a Diamond Stencil
Submission Author:
André Demski de Oliveira , PE , Brazil
Co-Authors:
André Demski de Oliveira, Twany Correia, Túlio de Moura Cavalcante, Paulo Roberto Maciel Lyra, DARLAN KARLO ELISIÁRIO DE CARVALHO
Presenter: André Demski de Oliveira
doi://10.26678/ABCM.COBEM2021.COB2021-0809
Abstract
Naturally Fractured Reservoirs (NFR) are part of the main sources of water and energy worldwide. However, due to their geological complexity and the high contrast of permeability, it is difficult to obtain accurate forecasts and estimates of their production behavior. The study of fluid flow through NFR has advanced strongly over the last years. Despite of that, the numerical modeling and simulation of such reservoirs, involving fractures of different scales is still a great challenge from a mathematical and numerical point of views. In this context, the Hierarchical Fracture Model has proved to be a powerful tool to reduce computational costs and improve accuracy. This approach consists in dividing the fractures into similar groups that receive different treatments, in order to improve accuracy, optimize and reduce computational costs. In this context, usually, longer fractures are modeled explicitly as major fluid conduits or barriers which are explicitly discretized using equidimensional strategies, or by means of Lower Dimensional Discrete Fracture models and Hybrid Dimensional approaches. An interesting alternative is the use of the Embedded Discrete Fracture Model (EDFM). In this model, each fracture plane is embedded within the cells of the computational mesh of the matrix rock, being discretized through the cell surfaces. By discretizing fractures as small, interconnected segments and adding them to the computational domain, the EDFM is able to combine features of continuous models and discrete matrix-fracture models. Therefore, EDFM was developed as a technique that directly incorporates fractures in a conventional structured mesh, bypassing the extra computational cost of using unstructured meshes and remaining compatible with the complex fracture geometries, such as non-planar fractures and fractures with variable aperture. However, previous works show that classic EDFM does not work properly for fractures that behave as barriers, i.e., with permeability lower than the rock matrix, but a variant of this model, called projection-based Embedded Discrete Fracture Model (pEDFM) can effectively deal with impermeable flow barriers. This is achieved through the projections of the fractures on the faces of the matrix control volumes, which provides the introduction of additional connections. In this context, we implement the EDFM and the pEDFM with a Multipoint Flux Approximation method with Diamond stencil (MPFA-D), which is very flexible and robust being capable of handling highly heterogeneous and anisotropic media using general polygonal meshes to solve the pressure equation. To validate our formulation, we have solved some representative problems found in literature obtaining promising results.
Keywords
Embedded Discrete Fracture Model, Multipoint Flux Approximation, Projection-Based Embedded Discrete Fracture Model, Numerical simulation, Naturally Fractured Reservoirs
