Multiscale finite volume method for finite-volume-based simulation of poroelasticity

Sokolova, Irina; Bastisya, Muhammad Gusti; Hajibeygi, Hadi

doi:10.1016/j.jcp.2018.11.039

Cited by 58 publications

(26 citation statements)

References 43 publications

(58 reference statements)

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“…In the FVM, the basic mathematical idea is to convert volume integrals in a partial differential equation that contains a divergence to surface integrals, using the divergence theorem (Sokolova et al, 2019). Fluxes at the surfaces of each Finite Volume will be derived afterward.…”

Section: Finite Volume Methods (Fvm) and Two-pointmentioning

confidence: 99%

Investigation of the Effect of the Discontinuity Direction on Fluid Flow in Porous Rock Masses on a Large-Scale Using Hybrid FVM-DFN and Streamline Simulation

Namdari

Baghbanan

Hashemolhosseini³

2021

MGPB

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Understanding the fluid behaviour in rock masses is of great importance in various rock mass-related engineering projects, such as seepage in tunnels, geothermal reservoirs, and hazardous waste disposal. Different approaches have been implemented to study the flow pattern in fractured porous rock masses. Laboratory experiments can provide good information regarding this issue, but high expenses aside, they are time-consuming and suffer the lack of ability to study field scale mediums. Numerical methods are beneficial in simulating such mediums with the Discrete Fracture Network (DFN) method in terms of costs and time as they offer sufficient flexibility and creativity. In this paper, a Matlab code was extended to study the flow regime in a Dual Permeability Media (DPM) with two point sources in the right and left side of the model as an injector and a producer well, respectively. A high permeability discontinuity with different angles was embedded in a very low-permeability limestone matrix. Pressure equations were solved implicitly with a two-point flux approximation scheme of the Finite Volume Method (FVM). Streamlines were traced in the medium and used to analyse the model’s hydraulic behaviour with the aid of Time Of Flight (TOF) for each point. The results show that the FVM-DFN hybrid method can be used as a fast method for fluid flow in DPM with the aid of streamline simulation to study the fluid flow in a large model with discontinuity.

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Section: Finite Volume Methods (Fvm) and Two-pointmentioning

confidence: 99%

Investigation of the Effect of the Discontinuity Direction on Fluid Flow in Porous Rock Masses on a Large-Scale Using Hybrid FVM-DFN and Streamline Simulation

Namdari

Baghbanan

Hashemolhosseini³

2021

MGPB

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“…Note that the inertial terms are not included as for their minimal impacts. Through the theory of the linear elasticity, only the elastic part of the total strain is proportional to the stress field, i.e., here, C is the 4th rank elasticity or stiffness tensor 56 . For 2D isotropic homogeneous discrete elements, one can express it through the Lame’s constants and as where is the Dirac delta.…”

Section: Governing Equationsmentioning

confidence: 99%

Geomechanical simulation of energy storage in salt formations

Kumar

Makhmutov

Spiers

et al. 2021

Sci Rep

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A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/Salt_Cavern.

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“…The Biot's equations can be solved by analytical solutions for simple cases [8,9]. In complex cases, the finite difference approximation [10,11], finite volume discretization [12,13], or more commonly finite element methods such as the mixed formulation or discontinuous/enriched Galerkin, [14][15][16][17][18][19][20][21], can be used. These numerical methods, however, require significant computational resources, and the accuracy of the solution depends heavily on the quality of the generated mesh.…”

Section: Introductionmentioning

confidence: 99%

Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations

2020

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This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.

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Multiscale finite volume method for finite-volume-based simulation of poroelasticity

Cited by 58 publications

References 43 publications

Investigation of the Effect of the Discontinuity Direction on Fluid Flow in Porous Rock Masses on a Large-Scale Using Hybrid FVM-DFN and Streamline Simulation

Investigation of the Effect of the Discontinuity Direction on Fluid Flow in Porous Rock Masses on a Large-Scale Using Hybrid FVM-DFN and Streamline Simulation

Geomechanical simulation of energy storage in salt formations

Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations

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