Advancing Graph‐Based Algorithms for Predicting Flow and Transport in Fractured Rock

Abstract

Discrete fracture network (DFN) models are a powerful alternative to continuum models for subsurface flow and transport simulations because they explicitly include fracture geometry and network topology, thereby allowing for better characterization of the latter's influence on flow and transport through fractured media. Recent advances in high performance computing have opened the door for flow and transport simulations in large explicit three‐dimensional DFN, but this increase in model fidelity and system size comes at a huge computational cost because of the large number of mesh elements required to represent thousands of fractures (with sizes that can range several orders of magnitude, from millimeter to kilometer). In most subsurface applications, fracture characteristics are only known statistically and numerous realizations are needed to bound uncertainty in flow and transport in the system, thereby exacerbating the computational burden. Graphs provide a simple and elegant way to characterize, query, and interrogate fracture network connectivity. We propose a DFN model reduction framework where various graph representations are used in conjunction with high‐fidelity DFN simulations to increase computational efficiency while retaining accuracy of key quantities of interest. The appropriate choice of a graph representation, namely, which attributes of the DFN are to be represented as nodes and which ones as edges connecting those nodes, depends on the relevant scientific questions. We demonstrate that the proposed DFN model reduction framework provides an efficient means for DFN modeling through both system reduction of the DFN using graph‐based properties and combining DFN and graph‐based flow and transport simulations.

Stress‐Induced Anomalous Transport in Natural Fracture Networks

“…DFN models represent fractures as discrete entities and enable the study of the effects of fracture geometrical properties on fluid flow and transport explicitly. Fluid flow and transport in DFNs have been the subjects of many investigations over the past decades, and recent advances in computational power have enabled more detailed flow and transport studies in complex three-dimensional (3-D) DFNs with multiscale heterogeneity (Benedetto et al, 2016;Hyman & Jiménez-Martínez, 2018;Hyman et al, 2019;Makedonska et al, 2015;Maillot et al, 2016;Viswanathan et al, 2018).…”

Graph-based flow modeling approach adapted to multiscale discrete-fracture-network models

“…Therefore, mixed analytical-numerical techniques have been developed, such as using the boundary element method to deduce pipe conductances [23], or using the Image theory to account for impermeable fracture borders on the flow [25]. More recently, graphs have been used as a complement to DFN flow and transport simulations [26]. They have been successfully used to identify the DFN backbone, i.e., fractures participating to shortest travel times or carrying the major flows [27][28][29][30][31].…”

Accessing Preferential Foam Flow Paths in 2D Micromodel Using a Graph-Based 2-Parameter Model

“…Modelling porous media with graph models has been recently given new life. Graph-based models have been used to find least resistance paths and predict breakthrough points successfully in heterogeneous porous media (Rizzo and Barros 2017).Graph models have also found use in discrete fracture modelling to rapidly characterize, query, and interrogate fracture network connectivity (Viswanathan et al 2018) The path-proposing is done via an algorithm that makes use of a graph representation of the porous network. Nodes of the graph represent the pores, while the graph edge weights represent throats.…”