A benchmark study of the multiscale and homogenization methods for fully implicit multiphase flow simulations

Hajibeygi, Hadi; Olivares, Manuela Bastidas; HosseiniMehr, Mousa; Pop, Sorin; Wheeler, Mary F.

doi:10.1016/j.advwatres.2020.103674

Cited by 14 publications

(9 citation statements)

References 51 publications

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“…The flow problem for Eq. ( 1) with the parameterization (11)(12) is solved in two Scenarios: (1) homogeneous soil, with K sat = 2.77 • 10 −6 , θ res = 0.06, θ sat = 0.36, α = 10, q 0 = 2.77 • 10 −7 , q 1 = 2.50 • 10 −6 , which are representative for a sandy soil, and (2) non-homogeneous soil, with the same parameters as in Scenario (1), except the saturated hydraulic conductivity, which takes two constant values, K sat = 2.77 • 10 −6 for z < 1 and 500K sat for z ≥ 1 (modeling, for instance, a column filled with sand and gravel). To capture the transition from unsaturated to saturated regime, the pressure at the bottom boundary is fixed at ψ 0 = 0.5.…”

Section: Validation Of the One-dimensional Grw Flow Algorithmmentioning

confidence: 99%

“…The GRW computations are initialized by multiplying the initial condition by N = 10 24 particles. Since, as shown by (12), the hydraulic conductivity varies in time, the length of the time step determined by (5) for the maximum of K at every time iteration and by specifying a maximum r max = 0.8 of the parameter r i±1/2,k may vary in time (see Fig. 1).…”

Section: Validation Of the One-dimensional Grw Flow Algorithmmentioning

confidence: 99%

“…The accuracy and the robustness of the numerical schemes is the primary requirement for reliable and meaningful results of the current efforts to improve the understanding of the complexity and interdependence of the flow and transport processes in subsurface hydrology through numerical investigations. Numerical solvers for partial differential equations modeling individual or coupled processes are often used as basic elements in the formulation of the more complex problems of practical interest, such as parameter identification [14], hydraulic tomography [6], Monte Carlo approaches for systems with randomly distributed parameters [22], or upscaling for mutiphase flows in heterogeneous subsurface formations [12], among others.…”

Section: Introductionmentioning

confidence: 99%

“…Since the regions where degeneracy takes place depend on the evolution of the pressure ψ in time and space, they are not known a priori. To cope with the nonlinearity and degeneracy of the Richards' equation, different linearization methods are needed, such as the Newton scheme [28,12,16], which is second-order convergent but converges only locally (requires a starting point close enough to the solution) or the more robust but only first-order convergent Picard, modified Picard, or L schemes [30,23,21,26].…”

Section: Introductionmentioning

confidence: 99%

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Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

Suciu,

Illiano,

Prechtel

et al. 2020

Preprint

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In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic conductivity and recharge fields, processes at the field and regional scales. The numerical schemes are based on global random walk algorithms (GRW) which approximate the solution by moving large numbers of computational particles on regular lattices according to specific random walk rules. To cope with the nonlinearity and the degeneracy of the Richards equation and of the coupled system, we implemented the GRW algorithms by employing linearization techniques similar to the L-scheme developed in finite element/volume approaches. The resulting GRW L-schemes converge with the number of iterations and provide numerical solutions that are first-order accurate in time and second-order in space. A remarkable property of the flow and transport GRW solutions is that they are practically free of numerical diffusion. The GRW solutions are validated by comparisons with mixed finite element and finite volume solutions in one-and two-dimensional benchmark problems. They include Richards' equation fully coupled with the advection-diffusion-reaction equation and capture the transition from unsaturated to saturated flow regimes. For completeness, we also consider decoupled flow and transport model problems for saturated aquifers.

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Section: Validation Of the One-dimensional Grw Flow Algorithmmentioning

confidence: 99%

Section: Validation Of the One-dimensional Grw Flow Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

Suciu,

Illiano,

Prechtel

et al. 2020

Preprint

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show abstract

“…We highlight that the MSFV and ADM use a section of the fine-scale feature to construct the macro-scale solution without estimations of the macro-scale parameters. A preliminary study in parallel of the two approaches based on ADM and on numerical homogenization is contained in [4].…”

Section: Introductionmentioning

confidence: 99%

Adaptive numerical homogenization of non-linear diffusion problems

Bastidas¹,

Bringedal²,

Pop³

et al. 2019

Preprint

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We propose an efficient numerical strategy for solving non-linear diffusion problems defined in a porous medium with highly oscillatory characteristics. This scheme is based on the classical homogenization theory and uses a locally mass-conservative formulation at different scales. In addition, we discuss some properties of the proposed non-linear solvers and use an error indicator to perform a local mesh refinement. The main idea is to compute the effective parameters in such a way that the computational complexity is reduced but preserving the accuracy. We illustrate the behaviour of the homogenization scheme and of the non-linear solvers by performing two numerical tests. We consider both a quasi-periodic example and a problem involving strong heterogeneities in a non-periodic medium.

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Fluid flow and mass transport in fractured media with curved fractures and varying apertures: A 3D modeling approach

Wang

Yin

2023

Numerical Meth Engineering

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Fractured media have been extensively studied due to their significant impact on hydraulic properties of subsurface systems. However, accurately modeling and simulating flow and transport in complex 3D fractured media still remains a challenge. For this purpose, this work aims to develop a new 3D modeling approach and investigate flow and mass transport in fractured media. First, a modeling approach is presented for generating 3D complex structures and high quality finite element grids. This approach allows for the presence of a range of complex geometries, including curved fracture, multiple fractures and the coexistence of fracture‐inclusions. The resulting models and grids are of high quality, enabling accurate simulation and analysis of complex systems. Furthermore, stress‐dependent aperture and roughness are integrated in the computational scheme using Barton–Bandis law. The Galerkin finite element method is used for numerical discretization, then pressure and concentration are calculated in a unified formulation. Later, numerical tests are performed to analyze the role of 3D fractures in flow and mass transport. Simulation results show that fractures have a larger impact on pressure distribution and flow rate compared to inclusions. Fracture roughness increases the aperture then the effective conductivity is improved as well. Curved fractures may reduce flow rate more than planar fractures due to the tortuosity effect. The variation of equivalent permeability tensor is analyzed with varying orientation, roughness, and number of fractures. The impact of stress and fracture roughness causes a variation of fracture permeability and a high pressure gradient on the fracture‐matrix interface, resulting in different patterns of concentration evolution. Overall, this investigation provides insights into the role of 3D fractures in subsurface flow and transport, with implications for various applications.

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A benchmark study of the multiscale and homogenization methods for fully implicit multiphase flow simulations

Cited by 14 publications

References 51 publications

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

Adaptive numerical homogenization of non-linear diffusion problems

Fluid flow and mass transport in fractured media with curved fractures and varying apertures: A 3D modeling approach

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