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The purpose of this paper is to investigate the utilization of artificial neural networks (ANNs) in learning models that address the nonlinear anisotropic flow and hysteresis retention behavior of deformable porous materials. Herein, the micro‐geometries of various networks of porous Bentheimer Sandstones subjected to several degrees of strain from the literature are considered. For the generation of the database required for the training, validation, and testing of the machine learning (ML) models, single‐phase and biphasic lattice Boltzmann (LB) simulations are performed. The anisotropic nature of the intrinsic permeability is investigated for the single‐phase LB simulations. Thereafter, the database contains the computed average fluid velocities versus the pressure gradients. In this database, the range of applied fluid pressure gradients includes Darcy as well as non‐Darcy flows. The generated output from the single‐phase flow simulations is implemented in a feed‐forward neural network, representing a path‐independent informed graph‐based model. Concerning the two‐phase LB simulations, the Shan‐Chen multiphase LB model is used to generate the retention curves of the cyclic drying/wetting processes in the deformed porous networks. Consequently, two different ML path‐dependent approaches, that is, 1D convolutional neural network and the recurrent neural network, are used to model the biphasic flow through the deformable porous materials. A comparison in terms of accuracy and speed of training between the two approaches is presented. Conclusively, the outcomes of the papers show the capability of the ML models in representing constitutive relations for permeability and hysteretic retention curves accurately and efficiently. [ABSTRACT FROM AUTHOR]

The following proceeding presents a multiscale approach to investigate the hydraulic anisotropy and retention behavior in porous materials involving deformation effects. Concerning the former, single‐phasic fluid flow simulations using the lattice Boltzmann method (LBM) are initially accomplished at the pore‐level geometry of Bentheimer sandstones provided by X‐ray microscopy at several degrees of compression to compute the intrinsic permeability. Due to the anisotropic nature of the Bentheimer sandstones, favored pore channels for fluid flow are witnessed within the domain. Therefore, it is important to understand the alteration of the preferred flow paths at each degree of compression. In this regard, we propose a new upscaling approach between the LBM and the macroscopic Theory of Porous Media (TPM) to accurately compute the macroscopic hydraulic structural tensor, which plays a crucial role in the calculation of the deformation‐dependent anisotropic specific permeability. As for the latter, the Shan‐Chen (SC) model of the LBM is applied at each strain level to model biphasic fluid flow via the unsaturated porous domain. Herein, the retention curves of the drainage and imbibition processes of each deformed state are computed. In turn, the comparison among the results shows the effect of variation of the strain degree on the retention behavior. [ABSTRACT FROM AUTHOR]

In this paper, we present a reliable micro‐to‐macroscale framework to model multiphase fluid flow through fractured porous media. This is based on utilizing the capabilities of the lattice Boltzmann method (LBM) within the phase‐field modeling (PFM) of fractures in multiphase porous media. In this, we propose new physically motivated phase‐field‐dependent relationships for the residual saturation, the intrinsic as well as relative permeabilities. In addition, an anisotropic, phase‐field‐dependent intrinsic permeability tensor for the fractured porous domains is formulated, which relies on the single‐ and multiphasic LBM flow simulations. Based on these results, new relationships for the variation of the macroscopic theory of porous media (TPM)–PFM model parameters in the transition zone are proposed. Whereby, a multiscale concept for the coupling between the multiphasic flow through the crack on one hand and the porous ambient, on the other hand, is achieved. The hybrid model is numerically applied on a real microgeometry of fractured porous media, extracted via X‐ray microcomputed tomography data of fractured Berea Sandstone. Moreover, the model is utilized for the calculation of the fluid leak‐off from the crack to the intact zones. Additionally, the effects of the depth of the transition zone and the orientation of the crack channels on the amount of leakage flow rates are studied. The outcomes of the numerical model proved the reliability of the multiscale model to simulate multiphasic fluid flow through fractured porous media. [ABSTRACT FROM AUTHOR]

In this contribution, the Shan‐Chen (SC) two‐phase flow model of the lattice Boltzmann method (LBM) is numerically implemented to simulate multiphase fluid flow on microtomography (µ‐CT) data of a sphere packing. From the model, the saturation degrees of the fluid phases, i.e. invading and displaced fluids, are extracted from the computed lattice density distribution functions. Several simulations are run with different degrees of kinetic viscosity contrast between the fluid phases within increasing increments of capillary pressure. At each increment, the relative permeability regarding each fluid phase is computed as a function of the saturation degree. The motivation of this study is to (1) investigate the effect of the kinetic viscosity contrast between the fluid phases on the retention behavior, (2) analyze the range of validity of the van Genuchten relation according to the computed retention data and (3) propose an extension towards an upscaling micro‐to‐macroscopic hierarchic scheme for the simulation of multiphasic fluid flow in unsaturated porous media. [ABSTRACT FROM AUTHOR]

• A multi-scale modelling of fluid flow in deformable porous materials via a combined approach that includes Lattice Boltzmann Method (LBM) and Theory of Porous Media (TPM). • Studying the permeability in the Darcy and non-Darcy pore-fluid flow via LBM-TPM approach. • Based on LBM, the work proposes a correction factor of the intrinsic permeability used in TPM when non-Darcy flow occurs. • Addressing numerical stability challenges in the saddle-point problem of poroelasticity, with focus on compaction state. • Proposing two stabilization schemes, i.e. pseudo-compressibility vs. minimum permeability, in solving the strongly-coupled system of differential equations of porous media. This paper presents a numerical approach for the simulation of fluid flow through porous media by proposing a theoretical and numerical meso-to-macro multiscale framework, which combines the advantages of the lattice Boltzmann method (LBM) with the continuum Theory of Porous Media (TPM) to efficiently and accurately model fluid transport in heterogeneous porous media. In particular, LBM presents an alternative to experiments by studying the flow from a mesoscopic perspective, which in turn, allows the derivation of the material parameters needed for simulating the flow in the macroscopic TPM model. In this work, a meso-macro hierarchic upscaling scheme is applied to investigate the deformation-dependent intrinsic permeability properties and the Darcy/non-Darcy fluid flow regime. Concerning the mesoscale, the intrinsic permeability of the porous domain is computed by means of the LBM model at the first stage. Subsequently, deformation of the medium takes place in furtherance of determining the relation of the aforementioned deformation dependency. Thereupon, these findings are input into the TPM model in order to compute the primary unknown variables, where special focus is laid on the stability challenges in the compaction and near compaction states. With respect to the criteria of non-Darcy fluid flow, the conditions of its onset, i.e. the induced pressure gradient and mean fluid flow velocity, are computed as well using the LBM solver and conveyed afterwards to the macroscopic TPM model. Herein, the non-Darcy intrinsic permeability has been investigated in the TPM approach based on the Forchheimer equation. Simulations done on a synthetic porous micro-structure show that the combined framework proved to stand well between the two approaches. [ABSTRACT FROM AUTHOR]