Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Lie, Knut-Andreas; Møyner, Olav

doi:10.1017/9781009019781.008

Cited by 4 publications

(8 citation statements)

References 51 publications

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“…These methods were implemented inside the Matlab Reservoir Simulation Toolbox, MRST. 70 Within MRST, we generalized a dual-porosity module provided by Ashworth and Doster 71 to fit our multi-porous extension. Although our examples have illustration purposes only, they are selected in such a way to mimic a probable geological scenario.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The solutions of the partial differential equations were obtained using the integral finite difference method to solve the fluid flow problem (through porous media) and the virtual element method (VEM) to solve the solid mechanics problem. These methods were implemented inside the Matlab Reservoir Simulation Toolbox, MRST 70 . Within MRST, we generalized a dual‐porosity module provided by Ashworth and Doster 71 to fit our multi‐porous extension.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Adamus,

Healy,

Meredith

et al. 2024

Num Anal Meth Geomechanics

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We propose the generalization of the anisotropic poroelasticity theory. At a large scale, a medium is viewed as quasi‐static, which is the original assumption of Biot. At a smaller scale, we distinguish different sets of pores or fractures that are characterized by various fluid pressures, which is the original poroelastic extension of Aifantis. In consequence, both instantaneous and time‐dependent deformation lead to fluid content variations that are different in each set. We present the equations for such phenomena, where the anisotropic properties of both the solid matrix and pore sets are assumed. Novel poroelastic coefficients that relate solid and fluid phases in our extension are proposed, and their physical meaning is determined. To demonstrate the utility of our equations and emphasize the meaning of new coefficients, we perform numerical simulations of a triple‐porosity consolidation. These simulations reveal positive pore pressure transients in the drained behaviour of weakly connected pore sets, and these may result in the mechanical weakening of the material.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Adamus,

Healy,

Meredith

et al. 2024

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

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“…This work uses the Matlab Reservoir Simulation Toolbox (MRST) 18,19 to solve the mathematical model for twocomponent flow of CO 2 and CH 4 in idealized reservoirs.…”

Section: Reservoir Simulation Modelmentioning

confidence: 99%

“…MRST is an open-source software package for reservoir modeling and simulation written in Matlab and developed by SINTEF Digital in Norway, and the MRST module Compositional provides well-known solution strategies for compositional simulations. 19 Lie and Møyner 19 have previously benchmarked the compositional module of MRST against the commercial reservoir simulator Eclipse 300 20 as well as AD-GPRS (the Stanford University research simulator). 21 In section 2.2, we also present a comparison between MRST and the commercial reservoir simulator CMG-GEM.…”

Section: Reservoir Simulation Modelmentioning

confidence: 99%

“…The above set of equations are solved by an implicit numerical method, where equation-of-state methods based on thermodynamics determine the vapor and liquid compositions of the hydrocarbon system (i.e., flash calculations), as described in detail by Lie and Møyner. 19 The model requires the equation of state (EoS) as a constitutive relationship, typically described by a third degree algebraic equation for the phase compressibility factor with coefficients depending on pressure, temperature, and mole fractions for a given mixture. The Peng−Robinson EoS 23 and Lohrenz−Bray−Clark viscosity correlation for hydrocarbon mixtures 24 are used as default settings in MRST and are also employed in the simulations presented in this work.…”

Section: Reservoir Simulation Modelmentioning

confidence: 99%

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Prediction of Optimal Production Time during Underground CH₄ Storage with Cushion CO₂ Using Reservoir Simulations and Artificial Neural Networks

Helland,

Friis,

Assadi

et al. 2023

Energy Fuels

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Effective Characterization of Fractured Media With PEDL: A Deep Learning‐Based Data Assimilation Approach

Nan,

Zhang,

Xie

et al. 2024

Water Resources Research

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Geological formations with fractures are frequently encountered in various research fields. Accurately characterizing these fractured media is of paramount importance when it comes to tasks that demand precise predictions of liquid flow and solute transport within them. Since directly measuring fractured media poses inherent challenges, data assimilation (DA) techniques are typically employed to derive inverse estimates of media properties using observable state variables. Nonetheless, the considerable difficulties arising from the strong heterogeneity and non‐Gaussian nature of fractured media have diminished the effectiveness of existing DA methods. In this study, we formulate a novel DA approach known as parameter estimator with deep learning (PEDL) that harnesses the capabilities of DL to capture nonlinear relationships and extract non‐Gaussian features. To evaluate PEDL's performance, we conduct three case studies, comprising two numerical cases and one real‐world case. In these cases, we systematically compare PEDL with three widely used DA methods: ensemble smoother with multiple DA (ESMDA), iterative local updating ES (ILUES), and ES with DL‐based update (ESDL). Notably, in the problems characterized by highly non‐Gaussian features, ESMDA and ILUES produce significantly divergent results. Conversely, employing the DL‐based update, ESDL demonstrates improved performance. However, its estimation uncertainty remains high, potentially attributable to ESDL's updating mechanism. Comprehensive analyses confirm PEDL's validity and adaptability across various ensemble sizes and DL model architectures. Moreover, even in scenarios where structural difference exists between the accurate reference model and the simplified forecast model, PEDL adeptly identifies the primary characteristics of fracture networks.

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Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Cited by 4 publications

References 51 publications

Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Prediction of Optimal Production Time during Underground CH₄ Storage with Cushion CO₂ Using Reservoir Simulations and Artificial Neural Networks

Effective Characterization of Fractured Media With PEDL: A Deep Learning‐Based Data Assimilation Approach

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Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Cited by 4 publications

References 51 publications

Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Prediction of Optimal Production Time during Underground CH4 Storage with Cushion CO2 Using Reservoir Simulations and Artificial Neural Networks

Effective Characterization of Fractured Media With PEDL: A Deep Learning‐Based Data Assimilation Approach

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Prediction of Optimal Production Time during Underground CH₄ Storage with Cushion CO₂ Using Reservoir Simulations and Artificial Neural Networks