Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable, heterogeneous porous media

Chaaban, Mohamad; Heider, Yousef; Markert, Bernd

doi:10.1016/j.ijheatfluidflow.2020.108566

Cited by 28 publications

(26 citation statements)

References 41 publications

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“…Proceeding with the same deformed granular assemblies (3D images extracted from the DEM RVE) as used for retention curve database generation in Section 3.2, LB single‐phase flow simulation is applied to generate the database of the pore‐fluid flow 89–97 . This database will then be used for the ANN‐based intrinsic permeability tensor estimation.…”

Section: Retention Behavior and Anisotropic Darcy Flow Representation In MLmentioning

confidence: 99%

An offline multi‐scale unsaturated poromechanics model enabled by self‐designed/self‐improved neural networks

Heider

Suh

Sun

2021

Num Anal Meth Geomechanics

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Supervised machine learning via artificial neural network (ANN) has gained significant popularity for many geomechanics applications that involves multi‐phase flow and poromechanics. For unsaturated poromechanics problems, the multi‐physics nature and the complexity of the hydraulic laws make it difficult to design the optimal setup, architecture, and hyper‐parameters of the deep neural networks. This paper presents a meta‐modeling approach that utilizes deep reinforcement learning (DRL) to automatically discover optimal neural network settings that maximize a pre‐defined performance metric for the machine learning constitutive laws. This meta‐modeling framework is cast as a Markov Decision Process (MDP) with well‐defined states (subsets of states representing the proposed neural network (NN) settings), actions, and rewards. Following the selection rules, the artificial intelligence (AI) agent, represented in DRL via NN, self‐learns from taking a sequence of actions and receiving feedback signals (rewards) within the selection environment. By utilizing the Monte Carlo Tree Search (MCTS) to update the policy/value networks, the AI agent replaces the human modeler to handle the otherwise time‐consuming trial‐and‐error process that leads to the optimized choices of setup from a high‐dimensional parametric space. This approach is applied to generate two key constitutive laws for the unsaturated poromechanics problems: (1) the path‐dependent retention curve with distinctive wetting and drying paths. (2) The flow in the micropores, governed by an anisotropic permeability tensor. Numerical experiments have shown that the resultant ML‐generated material models can be integrated into a finite element (FE) solver to solve initial‐boundary‐value problems as replacements of the hand‐craft constitutive laws.

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Section: Retention Behavior and Anisotropic Darcy Flow Representation In MLmentioning

confidence: 99%

An offline multi‐scale unsaturated poromechanics model enabled by self‐designed/self‐improved neural networks

Heider

Suh

Sun

2021

Num Anal Meth Geomechanics

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“…where K S 0S is the intrinsic permeability of the undeformed porous solid and j is a material parameter that governs the dependency of the permeability on the solid deformation. For more information regarding the permeability with anisotropic properties, the reader is referred to [24]. The term K S =l FR in Eq.…”

Section: Momentum Balance Of U Fmentioning

confidence: 99%

“…5.3, one has to distinguish between p L and p I , whereas p I À p L can explicitly be determined from Eq. (24). For this purpose, the definition of the net pore pressure p :¼ p F is exploited, which is equal to the weighted sum of the pore ice pressure p I and the pore water pressure p L [88].…”

Section: Ice-water Equilibrium In Poresmentioning

confidence: 99%

“…The macroscopic TPM [19,32,36,40,70,71], which extends the Theory of Mixtures (TM) [18,113] by the concept of volume fractions is used as a continuum-mechanical framework for the description of the deformable, heterogeneous porous solid. For a more detailed discussion of the general frame of the TPM, its extensions, solution schemes, applications and historical development, the interested reader is referred to [20,24,31,35,36,49,50,52,71,85,101] among others. Besides, the phase-field model (PFM) is employed for deriving a unified kinematics formulation for the phase changing fluid constituent.…”

Section: Introductionmentioning

confidence: 99%

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Experimental study and numerical modeling of the thermo-hydro-mechanical processes in soil freezing with different frost penetration directions

et al. 2021

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This research work presents an experimental and numerical study of the coupled thermo-hydro-mechanical (THM) processes that occur during soil freezing. With focusing on the artificial ground freezing (AGF) technology, a new testing device is built, which considers a variety of AGF-related boundary conditions and different freezing directions. In the conducted experiments, a distinction is made between two thermal states: (1) The thermal transient state, which is associated with ice penetration, small deformations, and insignificant water suction. (2) The thermal (quasi-) steady state, which has a much longer duration and is associated with significant ice lens formation due to water suction. In the numerical modeling, a special focus is laid on the processes that occur during the thermal transient state. Besides, a demonstration of the micro-cryo-suction mechanism and its realization in the continuum model through a phenomenological retention-curve-like formulation is presented. This allows modeling the ice lens formation and the stiffness degradation observed in the experiments. Assuming a fully saturated soil as a biphasic porous material, a phase-change THM approach is applied in the numerical modeling. The governing equations are based on the continuum mechanical theory of porous media (TPM) extended by the phase-field modeling (PFM) approach. The model proceeds from a small-strain assumption, whereas the pore fluid can be found in liquid water or solid ice state with a unified kinematics treatment of both states. Comparisons with the experimental data demonstrate the ability and usefulness of the considered model in describing the freezing of saturated soils.

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“…The underlying study considers a fluid-saturated porous medium consisting of immissible solid and fluid constituents ϕ α (α = S : solid, α = F : fluid). Within the framework of theory of porous media (TPM), the saturation condition is defined as n S + n F = 1 with n α being the volume fraction, whereas the partial density ρ α and material density ρ αR are related to each other via ρ α = n α ρ αR (references in [1][2][3]). In this study, the solid material (rock) is considered incompressible ρ SR = const., while the pore-fluid (water) is treated as a compressible material with the material time derivative defined as (ρ F R ) S := K F (p) S with K F as the fluid compressibility parameter and p as the fluid pressure [4].…”

Section: Mathematical Modellingmentioning

confidence: 99%

Thermomechanical phase‐field fracture modeling of fluid‐saturated porous media

Nguyen

Sweidan

Heider

et al. 2021

Proc Appl Math and Mech

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In this work, the problem of brittle fracture in a fluid-saturated porous material is extended by considering the non-isothermal states of the sample. The temperature field will affect the problem in two aspects: 1) Temperature-dependent material parameters, such as elasticity modulus (E) and critical energy release rate (Gc). 2) Thermal expansion due to thermo-mechanical volume coupling. In hydraulic fracturing, we further study the effect of the temperature difference between the injected fluid and the surrounding porous media ambient on the crack behavior. The modeling of the porous media domain is based on the macroscopic theory of porous media (TPM), whereas the phase-field method (PFM) is applied to approximate the sharp crack edges by diffusive ones. In the numerical implementation, the coupled system of partial differential equations will be solved using the FEM in order to simulate the heat transition in the crack and non-crack regions.

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Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable, heterogeneous porous media

Cited by 28 publications

References 41 publications

An offline multi‐scale unsaturated poromechanics model enabled by self‐designed/self‐improved neural networks

An offline multi‐scale unsaturated poromechanics model enabled by self‐designed/self‐improved neural networks

Experimental study and numerical modeling of the thermo-hydro-mechanical processes in soil freezing with different frost penetration directions

Thermomechanical phase‐field fracture modeling of fluid‐saturated porous media

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