A Computational Workflow for Flow and Transport in Fractured Porous Media Based on a Hierarchical Nonlinear Discrete Fracture Modeling Approach

Wenjuan Zhang,Waleed Diab,Hadi Hajibeygi,Mohammed Al Kobaisi

doi:10.3390/en13246667

Abstract

Modeling flow and transport in fractured porous media has been a topic of intensive research for a number of energy- and environment-related industries. The presence of multiscale fractures makes it an extremely challenging task to resolve accurately and efficiently the flow dynamics at both the local and global scales. To tackle this challenge, we developed a computational workflow that adopts a two-level hierarchical strategy based on fracture length partitioning. This was achieved by specifying a partition length to split the discrete fracture network (DFN) into small-scale fractures and large-scale fractures. Flow-based numerical upscaling was then employed to homogenize the small-scale fractures and the porous matrix into an equivalent/effective single medium, whereas the large-scale fractures were modeled explicitly. As the effective medium properties can be fully tensorial, the developed hierarchical framework constructed the discrete systems for the explicit fracture–matrix sub-domains using the nonlinear two-point flux approximation (NTPFA) scheme. This led to a significant reduction of grid orientation effects, thus developing a robust, applicable, and field-relevant framework. To assess the efficacy of the proposed hierarchical workflow, several numerical simulations were carried out to systematically analyze the effects of the homogenized explicit cutoff length scale, as well as the fracture length and orientation distributions. The effect of different boundary conditions, namely, the constant pressure drop boundary condition and the linear pressure boundary condition, for the numerical upscaling on the accuracy of the workflow was investigated. The results show that when the partition length is much larger than the characteristic length of the grid block, and when the DFN has a predominant orientation that is often the case in practical simulations, the workflow employing linear pressure boundary conditions for numerical upscaling give closer results to the full-model reference solutions. Our findings shed new light on the development of meaningful computational frameworks for highly fractured, heterogeneous geological media where fractures are present at multiple scales.

Highlights

Modeling fluid flow and transport in fractured porous media on the field scale, both accurately and efficiently, has been a long-standing issue in a number of energy- and environment-related disciplines, such as production of oil and gas from naturally fractured reservoirs, extraction of geothermal energies, disposal of nuclear waste underground, sequestration of carbon dioxide in deep saline reservoirs, Energies 2020, 13, 6667; doi:10.3390/en13246667 www.mdpi.com/journal/energiesEnergies 2020, 13, 6667 just to name a few
The equivalent/effective medium models assume that fractures and the surrounding porous matrix are in equilibrium at all times
There is no obvious breakthrough curves depicted in Figure suggest that the flux solution of Ups-LPcurves is closer to the winner that performs significantly better than the other, the breakthrough depicted reference solution than that of Different realizations of the were generated using in Figure 21 suggest that the flux solution of Ups-linear pressure (LP) is closer to the reference solution than thatthe of same parameters andrealizations additional simulations were carried out on these

Summary

Introduction

Modeling fluid flow and transport in fractured porous media on the field scale, both accurately and efficiently, has been a long-standing issue in a number of energy- and environment-related disciplines, such as production of oil and gas from naturally fractured reservoirs, extraction of geothermal energies, disposal of nuclear waste underground, sequestration of carbon dioxide in deep saline reservoirs, Energies 2020, 13, 6667; doi:10.3390/en13246667 www.mdpi.com/journal/energiesEnergies 2020, 13, 6667 just to name a few. The models can be classified into the following three categories: equivalent/effective medium models, multi-continuum models and discrete fracture–matrix (DFM) models. The matrix and fracture properties are all lumped into single equivalent (effective) properties This single-medium model facilities efficient numerical simulations as conventional reservoir simulators can be used directly without many modifications. The multi-continuum models, notably the dual-continuum models such as dual-porosity/dual-permeability, conceptualize the whole system as two separate yet interacting continua This model was first proposed in [2] and was introduced to the petroleum industry by Warren and Root [3]. The multi-continuum models represent a significant step forward and have become the method of choice for many years They are most applicable for densely fractured reservoirs and are inadequate for capturing the dominant effects of large highly conductive fractures. Non-neighboring connections (NNCs) are introduced to connect the fracture control volumes to the porous matrix

Objectives

Methods

Results

Conclusion