scholarly journals Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

Solid Earth ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 2235-2254
Author(s):  
Maximilian O. Kottwitz ◽  
Anton A. Popov ◽  
Steffen Abe ◽  
Boris J. P. Kaus
Keyword(s):  
Fluid Flow ◽  
Cell Size ◽  
Fracture Network ◽  
Fracture Networks ◽  
Flow Localization ◽  
Computational Costs ◽  
Pipe Model ◽  
Hydraulic Aperture ◽  
Discrete Fracture ◽  
Equivalent Continuum

Abstract. Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the possibility of including matrix properties, choosing the right cell size to discretize the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process we term intersection flow localization (IFL). We propose a new method to generate ECMs that includes this effect with a directional pipe flow parameterization: the fracture-and-pipe model. Our approach is compared against an ECM method that does not take IFL into account by performing ECM-based upscaling with a massively parallelized Darcy flow solver capable of representing permeability anisotropy for individual grid cells. While IFL results in an increase in permeability at the local scale of the ECM cell (fracture scale), its effects on network-scale flow are minor. We investigated the effects of IFL for test cases with orthogonal fracture formations for various scales, fracture lengths, hydraulic apertures, and fracture densities. Only for global fracture porosities above 30 % does IFL start to increase the systems permeability. For lower fracture densities, the effects of IFL are smeared out in the upscaling process. However, we noticed a strong dependency of ECM-based upscaling on its grid resolution. Resolution tests suggests that, as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECMs are applicable to upscale flow in fracture networks.

scholarly journals Equivalent continuum-based upscaling of flow in discrete fracture networks: The fracture-and-pipe model

2021 ◽  
Author(s):  
Maximilian O. Kottwitz ◽  
Anton A. Popov ◽  
Steffen Abe ◽  
Boris J. P. Kaus
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Fractured Rock ◽  
Fracture Network ◽  
Fracture Networks ◽  
Computational Costs ◽  
Pipe Model ◽  
Discrete Fracture ◽  
Fractured Rock Masses ◽  
Equivalent Continuum

Abstract. Predicting effective permeabilities of fractured rock masses is a key component of reservoir modelling. This is often realized with the discrete fracture network (DFN) method, where single-phase incompressible fluid flow is modelled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in significant computational costs. Equivalent continuum models (ECM) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While this has the advantage of lower computational costs and the possibility to include matrix properties, choosing the right cell size for discretizing the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes-flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process termed intersection flow localization (IFL). We propose a new method to generate ECM's that includes this effect with a directional pipe flow parametrization: the fracture-and-pipe model. Our approach is tested by conducting resolution tests with a massively parallelized Darcy-flow solver, capable of representing the full permeability anisotropy for individual grid cells. The results suggest that as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECM's are applicable to upscale flow in fracture networks, which reduces computational expenses for numerical permeability predictions of fractured rock masses. Furthermore, incorporating the off-diagonal terms of the individual permeability tensors into numerical simulations results in an improved representation of anisotropy in ECM's that was previously reserved for the DFN method.

Linking direct and continuum fluid flow models for fractured media: The intersection problem

2020 ◽  
Author(s):  
Maximilian O. Kottwitz ◽  
Anton A. Popov ◽  
Steffen Abe ◽  
Boris J. P. Kaus
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Rock Masses ◽  
Fracture Networks ◽  
Direct Flow ◽  
Flow Models ◽  
Flow Simulations ◽  
Hydraulic Aperture ◽  
Continuum Flow ◽  
Equivalent Continuum

<p>Finding an adequate bridge between direct and continuum modeling approaches has been the fundamental issue of upscaling fluid flow in rock masses. Typically, numerical simulations of direct fluid flow (e.g. Stokes or Lattice-Boltzmann) in fractured or porous media serve as small-scale building blocks for larger-scale continuum flow simulations (e.g. Darcy). For fractured rock masses, the discrete-fracture-network (DFN) modeling approach is often used as an initial step to upscale flow properties by parameterizing the permeability of each fracture with its hydraulic aperture and solving steady-state flow equations within the fracture system. However, numerical simulations of Stokes flow in small fracture networks (FN) indicate that, depending on the orientation of the applied pressure gradient, fluid flow tends to localize at places where fractures intersect. This effect causes discrepancies between direct and equivalent continuum flow modeling approaches, which ought to be taken into account when modeling flow at the network scale.</p><p>In this study, we compare direct flow simulations of small fracture networks to their continuum representation obtained with several techniques in order to find an upscaling approach that takes these intersection effects into account. Direct flow simulations are conducted by solving the Stokes equations in 3D using our open-source finite-difference software LaMEM. Continuum flow simulations are realized with a newly developed parallel finite-element code, which solves fully anisotropic 3D Darcy flow with specific permeability tensors for each voxel. The direct flow simulations serve as benchmarks to optimize the continuum flow models by comparing resulting permeabilities. We tested two different schemes to generate the equivalent continuum representation: </p><p>(1) Fully resolved isotropic permeability discretizations (fracture permeability is obtained from a refined cubic law) where voxel sizes are a fraction of the minimal hydraulic aperture of the FN or</p><p>(2) coarse anisotropic permeability discretizations (permeability tensors are rotated according to fracture orientation) with voxel sizes larger than the minimal hydraulic aperture of the FN.</p><p>We then assess different scenarios to incorporate the intersection effects by adding, averaging and/or multiplying the permeabilities of the intersecting fractures within intersection voxels. Preliminary results for scheme 1 suggest that a simple addition of both intersecting fracture permeabilities delivers the best fit to the results of the direct flow simulations, if the voxel size is about 68% of the minimal hydraulic aperture. Scheme 2 systematically underestimates the direct flow permeabilities by about 26%.</p>

Properties of a pair of fracture networks produced by triaxial deformation experiments: insights on fluid flow using discrete fracture network models

2016 ◽  
Vol 25 (3) ◽  
pp. 813-827 ◽  
Author(s):  
Ghislain Trullenque ◽  
Rishi Parashar ◽  
Clément Delcourt ◽  
Lucille Collet ◽  
Pauline Villard ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Network Models ◽  
Fracture Network ◽  
Discrete Fracture Network ◽  
Fracture Networks ◽  
Triaxial Deformation ◽  
Discrete Fracture

Comparison of discrete fracture network and equivalent continuum simulations of fluid flow through two-dimensional fracture networks for the DECOVALEX–2011 project

2012 ◽  
Vol 76 (8) ◽  
pp. 3179-3190 ◽  
Author(s):  
C. T. O. Leung ◽  
A. R. Hoch ◽  
R. W. Zimmerman
Keyword(s):  
Fluid Flow ◽  
Fracture Network ◽  
Two Dimensional ◽  
Field Scale ◽  
Continuum Approach ◽  
Discrete Fracture ◽  
Grid Block ◽  
Flow Through ◽  
Equivalent Continuum ◽  
Equivalent Continuum Approach

AbstractFluid flow through a two-dimensional fracture network has been simulated using a discrete fracture model. The computed field-scale permeabilities were then compared to those obtained using an equivalent continuum approach in which the permeability of each grid block is first obtained by performing fine-scale simulations of flow through the fracture network within that region. In the equivalent continuum simulations, different grid-sizes were used, corresponding to N by N grids with N = 10, 40, 100 and 400. The field-scale permeabilities found from the equivalent continuum simulations were generally within 10% of the values found from the discrete fracture simulations. The discrepancies between the two approaches seemed to be randomly related to the grid size, as no convergence was observed as N increased. An interesting finding was that the equivalent continuum approach gave accurate results in cases where the grid block size was clearly smaller than the 'representative elementary volume'.

scholarly journals Erratum: Properties of a pair of fracture networks produced by triaxial deformation experiments: insights on fluid flow using discrete fracture network models

2017 ◽  
Vol 25 (3) ◽  
pp. 895-895
Author(s):  
Ghislain Trullenque ◽  
Rishi Parashar ◽  
Clément Delcourt ◽  
Lucille Collet ◽  
Pauline Villard ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Network Models ◽  
Fracture Network ◽  
Discrete Fracture Network ◽  
Fracture Networks ◽  
Triaxial Deformation ◽  
Discrete Fracture

scholarly journals Hybrid Analytical and Numerical Approach for Modeling Fluid Flow in Simplified Three-Dimensional Fracture Networks

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
D. Roubinet ◽  
S. Demirel ◽  
E. B. Voytek ◽  
X. Wang ◽  
J. Irving
Keyword(s):  
Fluid Flow ◽  
Three Dimensional ◽  
Fracture Network ◽  
Numerical Approach ◽  
Fracture Networks ◽  
Surrounding Matrix ◽  
Mesh Free ◽  
Fracture Scale ◽  
The Impact ◽  
Numerical Approaches

Modeling fluid flow in three-dimensional fracture networks is required in a wide variety of applications related to fractured rocks. Numerical approaches developed for this purpose rely on either simplified representations of the physics of the considered problem using mesh-free methods at the fracture scale or complex meshing of the studied systems resulting in considerable computational costs. Here, we derive an alternative approach that does not rely on a full meshing of the fracture network yet maintains an accurate representation of the modeled physical processes. This is done by considering simplified fracture networks in which the fractures are represented as rectangles that are divided into rectangular subfractures such that the fracture intersections are defined on the borders of these subfractures. Two-dimensional analytical solutions for the Darcy-scale flow problem are utilized at the subfracture scale and coupled at the fracture-network scale through discretization nodes located on the subfracture borders. We investigate the impact of parameters related to the location and number of the discretization nodes on the results obtained, and we compare our results with those calculated using reference solutions, which are an analytical solution for simple configurations and a standard finite-element modeling approach for complex configurations. This work represents a first step towards the development of 3D hybrid analytical and numerical approaches where the impact of the surrounding matrix will be eventually considered.

scholarly journals Water Intrusion Characterization in Naturally Fractured Gas Reservoir Based on Spatial DFN Connectivity Analysis

Energies ◽  
2020 ◽  
Vol 13 (16) ◽  
pp. 4235
Author(s):  
Pengyu Chen ◽  
Mauricio Fiallos-Torres ◽  
Yuzhong Xing ◽  
Wei Yu ◽  
Chunqiu Guo ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Water Flow ◽  
Fracture Network ◽  
Connectivity Analysis ◽  
Fracture Networks ◽  
Flow Paths ◽  
Water Intrusion ◽  
Discrete Fracture ◽  
Single Well ◽  
Water Flow Paths

In this study, the non-intrusive embedded discrete fracture model (EDFM) in combination with the Oda method are employed to characterize natural fracture networks fast and accurately, by identifying the dominant water flow paths through spatial connectivity analysis. The purpose of this study is to present a successful field case application in which a novel workflow integrates field data, discrete fracture network (DFN), and production analysis with spatial fracture connectivity analysis to characterize dominant flow paths for water intrusion in a field-scale numerical simulation. Initially, the water intrusion of single-well sector models was history matched. Then, resulting parameters of the single-well models were incorporated into the full field model, and the pressure and water breakthrough of all the producing wells were matched. Finally, forecast results were evaluated. Consequently, one of the findings is that wellbore connectivity to the fracture network has a considerable effect on characterizing the water intrusion in fractured gas reservoirs. Additionally, dominant water flow paths within the fracture network, easily modeled by EDFM as effective fracture zones, aid in understanding and predicting the water intrusion phenomena. Therefore, fracture clustering as shortest paths from the water contacts to the wellbore endorses the results of the numerical simulation. Finally, matching the breakthrough time depends on merging responses from multiple dominant water flow paths within the distributions of the fracture network. The conclusions of this investigation are crucial to field modeling and the decision-making process of well operation by anticipating water intrusion behavior through probable flow paths within the fracture networks.

scholarly journals A Novel Numerical Model for Fluid Flow in 3D Fractured Porous Media Based on an Equivalent Matrix-Fracture Network

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chi Yao ◽  
Chen He ◽  
Jianhua Yang ◽  
Qinghui Jiang ◽  
Jinsong Huang ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Hydraulic Conductivity ◽  
Fractured Rock ◽  
Fracture Network ◽  
Numerical Approach ◽  
Porous Matrix ◽  
Fractured Porous Media ◽  
Hydraulic Aperture ◽  
Matrix Fracture

An original 3D numerical approach for fluid flow in fractured porous media is proposed. The whole research domain is discretized by the Delaunay tetrahedron based on the concept of node saturation. Tetrahedral blocks are impermeable, and fluid only flows through the interconnected interfaces between blocks. Fractures and the porous matrix are replaced by the triangular interface network, which is the so-called equivalent matrix-fracture network (EMFN). In this way, the three-dimensional seepage problem becomes a two-dimensional problem. The finite element method is used to solve the steady-state flow problem. The big finding is that the ratio of the macroconductivity of the whole interface network to the local conductivity of an interface is linearly related to the cubic root of the number of nodes used for mesh generation. A formula is presented to describe this relationship. With this formula, we can make sure that the EMFN produces the same macroscopic hydraulic conductivity as the intact rock. The approach is applied in a series of numerical tests to demonstrate its efficiency. Effects of the hydraulic aperture of fracture and connectivity of the fracture network on the effective hydraulic conductivity of fractured rock masses are systematically investigated.

Modelling large-scale fractured reservoirs efficiently for geothermal energy and groundwater flow

2020 ◽  
Author(s):  
Simon Oldfield ◽  
Mikael Lüthje ◽  
Michael Welch ◽  
Florian Smit
Keyword(s):  
Fluid Flow ◽  
Geothermal Energy ◽  
Large Scale ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Persistent Problem ◽  
Fracture Evolution ◽  
Rapid Generation

<p>Large scale modelling of fractured reservoirs is a persistent problem in representing fluid flow in the subsurface. Considering a geothermal energy prospect beneath the Drenthe Aa area, we demonstrate application of a recently developed approach to efficiently predict fracture network geometry across an area of several square kilometres.</p><p>Using a strain based method to mechanically model fracture nucleation and propagation, we generate a discretely modelled fracture network consisting of individual failure planes, opening parallel and perpendicular to the orientation of maximum and minimum strain. Fracture orientation, length and interactions vary following expected trends, forming a connected fracture network featuring population statistics and size distributions comparable to outcrop examples.</p><p>Modelled fracture networks appear visually similar to natural fracture networks with spatial variation in fracture clustering and the dominance of major and minor fracture trends.</p><p>Using a network topology approach, we demonstrate that the predicted fracture network shares greater geometric similarity with natural networks. Considering fluid flow through the model, we demonstrate that hydraulic conductivity and flow anisotropy are strongly dependent on the geometric connection of fracture sets.</p><p>Modelling fracture evolution mechanically allows improved representation of geometric aspects of fracture networks to which fluid flow is particularly sensitive. This method enables rapid generation of discretely modelled fractures over large areas and extraction of suitable summary statistics for reservoir simulation. Visual similarity of the output models improves our ability to compare between our model and natural analogues to consider model validation.</p>

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