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>

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.

Direct Simulation Based Model-Predictive Control of Flow Maldistribution in Parallel Microchannels

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Mathieu Martin ◽  
Chris Patton ◽  
John Schmitt ◽  
Sourabh V. Apte
Keyword(s):  
Fluid Flow ◽  
Model Predictive Control ◽  
Numerical Simulations ◽  
Active Control ◽  
Predictive Control ◽  
Nonlinear Flow ◽  
Flow Simulations ◽  
Flow Through ◽  
Parallel Microchannels ◽  
Flow Maldistribution

Flow maldistribution, resulting from bubbles or other particulate matter, can lead to drastic performance degradation in devices that employ parallel microchannels for heat transfer. In this work, direct numerical simulations of fluid flow through a prescribed parallel microchannel geometry are performed and coupled with active control of actuated microvalves to effectively identify and reduce flow maldistribution. Accurate simulation of fluid flow through a set of three parallel microchannels is achieved utilizing a fictitious-domain representation of immersed objects such as microvalves and artificially introduced bubbles. Flow simulations are validated against experimental results obtained for flow through a single high-aspect ratio microchannel, flow around an oscillating cylinder, and flow with a bubble rising in an inclined channel. Results of these simulations compare very well to those obtained experimentally, and validate the use of the solver for the parallel microchannel configuration of this study. System identification techniques are employed on numerical simulations of fluid flow through the geometry to produce a lower dimensional model that captures the essential dynamics of the full nonlinear flow, in terms of a relationship between valve angles and the exit flow rate for each channel. A model-predictive controller is developed, which employs this reduced order model to identify flow maldistribution from exit flow velocities and to prescribe actuation of channel valves to effectively redistribute the flow. Flow simulations with active control are subsequently conducted with artificially introduced bubbles. The model-predictive control methodology is shown to adequately reduce flow maldistribution by quickly varying channel valves to remove bubbles and to equalize flow rates in each channel.

scholarly journals Validation Strategy of Reduced-Order Two-Fluid Flow Models Based on a Hierarchy of Direct Numerical Simulations

2020 ◽  
Vol 105 (4) ◽  
pp. 1381-1411
Author(s):  
Pierre Cordesse ◽  
Alberto Remigi ◽  
Benjamin Duret ◽  
Angelo Murrone ◽  
Thibaut Ménard ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Reduced Order ◽  
Flow Models ◽  
Two Fluid ◽  
Validation Strategy

scholarly journals Modelling of Coupled Hydro-Thermo-Chemical Fluid Flow through Rock Fracture Networks and Its Applications

Geosciences ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 153
Author(s):  
Chaoshui Xu ◽  
Shaoqun Dong ◽  
Hang Wang ◽  
Zhihe Wang ◽  
Feng Xiong ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Rock Mass ◽  
Rock Fracture ◽  
Fractured Reservoirs ◽  
Experimental Studies ◽  
Heat Extraction ◽  
Rock Masses ◽  
Fracture Networks ◽  
Fracture Intersection ◽  
Flow Through

Most rock masses contain natural fractures. In many engineering applications, a detailed understanding of the characteristics of fluid flow through a fractured rock mass is critically important for design, performance analysis, and uncertainty/risk assessment. In this context, rock fractures and fracture networks play a decisive role in conducting fluid through the rock mass as the permeability of fractures is in general orders of magnitudes greater than that of intact rock matrices, particularly in hard rock settings. This paper reviews the modelling methods developed over the past four decades for the generation of representative fracture networks in rock masses. It then reviews some of the authors’ recent developments in numerical modelling and experimental studies of linear and non-linear fluid flow through fractures and fracture networks, including challenging issues such as fracture wall roughness, aperture variations, flow tortuosity, fracture intersection geometry, fracture connectivity, and inertia effects at high Reynolds numbers. Finally, it provides a brief review of two applications of methods developed by the authors: the Habanero coupled hydro-thermal heat extraction model for fractured reservoirs and the Kapunda in-situ recovery of copper minerals from fractures, which is based on a coupled hydro-chemical model.

Non-Newtonian Response of EHL Film Temperature

2007 ◽  
Author(s):  
M. Kaneta ◽  
H. Nishikawa ◽  
S. Okabayashi ◽  
J. Wang ◽  
P. Yang
Keyword(s):  
Fluid Flow ◽  
Numerical Simulations ◽  
Newtonian Fluid ◽  
Contact Region ◽  
Optical Interferometry ◽  
Experimental Results ◽  
Moving Surface ◽  
Oil Film ◽  
Flow Models ◽  
Parallel Direction

The temperature and thickness of oil film in point EHL contacts between a rough stationary surface and a smooth moving surface are measured with infrared and optical interferometry techniques. The ridges and furrows of the roughness are aligned with the parallel direction to that of lubricant entrainment. The experimental results are compared with numerical simulations based on Eyring and Newtonian fluid flow models. Under certain conditions, the average film temperature across the oil film near the central contact region is higher at the furrow position than at the ridge position. It is revealed that this phenomenon is caused by shear thinning behavior of lubricant.

Sign in / Sign up

Export Citation Format

Share Document