Simulation Of Porous Media Research Articles

Dimensionality Analysis of Unsteady-State Core-Flooding Simulations for Homogeneous and Heterogeneous Rock Types

Model quality and computational resources must be carefully balanced in numerical simulations due to the high computational cost that three-dimensional models pose. This is inherently true in the oil and energy industry, where reservoir modelling and complex real experiments are required, in which inaccuracies have a direct impact on financial outcomes. Properly used, one-dimensional simulations yield significant technological and financial benefits by reducing simulation runtime, allowing more efficient operations, and faster and more accurate decision-making. As a result, wherever possible, models with lower dimensionality are preferred. This work aims to analyze the feasibility and effectiveness of the dimensional reduction of three-dimensional to one-dimensional models for unsteady-state core-flooding experiments. For that, 1D and 3D multiphase flow on porous media simulations were performed using the Black Oil IMEX™ software to verify the variability of oil production volume, saturation profiles, and differential pressure numerical responses. According to the results, the oil production volume and pressure differential are not affected by the dimensionality of the problem in homogenous cases. On the other hand, it is found that when dimensionality is reduced, heterogeneities lead to different outcomes in terms of pressure differential and oil volume production, which, in that case, may compromise dimensional reduction.

Deep learning for pore-scale two-phase flow: Modelling drainage in realistic porous media

In order to predict phase distributions within complex pore structures during two-phase capillary-dominated drainage, we select subsamples from computerized tomography (CT) images of rocks and simulated porous media, and develop a pore morphology-based simulator (PMS) to create a diverse dataset of phase distributions. With pixel size, interfacial tension, contact angle, and pressure as input parameters, convolutional neural network (CNN), recurrent neural network (RNN) and vision transformer (ViT) are transformed, trained and evaluated to select the optimal model for predicting phase distribution. It is found that commonly used CNN and RNN have deficiencies in capturing phase connectivity. Subsequently, we develop a higher-dimensional vision transformer (HD-ViT) that drains pores solely based on their size, regardless of their spatial location, with phase connectivity enforced as a post-processing step. This approach enables inference for images of varying sizes and resolutions with inlet-outlet setup at any coordinate directions. We demonstrate that HD-ViT maintains its effectiveness, accuracy and speed advantage on larger sandstone and carbonate images, compared with the microfluidic-based displacement experiment. In the end, we train and validate a 3D version of the model.

Mixed variational formulation and finite-element implementation of second-order poro-elasticity

We present a variational formulation of second-order poro-elasticity that can be readily implemented into finite-element codes by using standard Lagrangian interpolation functions. Point of departure is a two-field minimization principle in terms of the displacement and the fluid flux as independent variables. That principle is taken as a basis for the derivation of continuous and incremental saddle-point formulations in terms of an extended set of independent variables. By static condensation this formulation is then reduced to a minimization principle in terms of the displacement and fluid flux as well as associated higher-order fields. Once implemented into a finite-element code, the resulting formulation can be applied to the numerical simulation of porous media in consideration of second-order effects. Here, we analyze the model response by means of several example problems including two standard tests in poro-elasticity, namely the consolidation problems of Terzaghi and Mandel, and compare the results with those of a corresponding first-order model. As becomes clear, the second-order formulation can unleash its full potential when applied to the study of porous media having spatial dimensions comparable to the size of their microstructure. In particular, it is capable to regularize steep field gradients at external as well as internal surfaces and to describe material dilatation effects known from experiments.

A five field formulation for flow simulations in porous media with fractures and barriers via an optimization based domain decomposition method

The present work deals with the numerical resolution of coupled 3D–2D problems arising from the simulation of fluid flow in fractured porous media modeled via the Discrete Fracture and Matrix (DFM) model. According to the DFM model, fractures are represented as planar interfaces immersed in a 3D porous matrix and can behave as preferential flow paths, in the case of conductive fractures, or can actually be a barrier for the flow, when, instead, the permeability in the normal-to-fracture direction is small compared to the permeability of the matrix. Consequently, the pressure solution in a DFM can be discontinuous across a barrier, as a result of the geometrical dimensional reduction operated on the fracture. The present work is aimed at developing a numerical scheme suitable for the simulation of the flow in a DFM with fractures and barriers, using a mesh for the 3D matrix non conforming to the fractures and that is ready for domain decomposition. This is achieved starting from a PDE-constrained optimization method, currently available in literature only for conductive fractures in a DFM. First, a novel formulation of the optimization problem is defined to account for non permeable fractures. These are described by a filtration-like coupling at the interface with the surrounding porous matrix. Also the extended finite element method with discontinuous enrichment functions is used to reproduce the pressure solution in the matrix around a barrier. The method is presented here in its simplest form, for clarity of exposition, i.e. considering the case of a single fracture in a 3D domain, also providing a proof of the well posedness of the resulting discrete problem. Four validation examples are proposed to show the viability and the effectiveness of the method.

A mixed nonlocal finite element model for thermo‐poro‐elasto‐plastic simulation of porous media with multiphase fluid flow

SummaryA new mixed nonlocal finite element framework is developed for nonlinear thermo‐poro‐elasto‐plastic simulation of porous media with multiphase pore fluid flow and thermal coupling. The solid‐fluid interaction is accounted for using the mixture theory of Biot based on the volume fractions concept. Different sources of nolinearities arising from the multiphase fluid flow effects, advective‐diffusive heat transfer, inelastic deformation, fluid flux injection induced mechanical tractions, solid skeleton deformation permeability dependence, and temperature dependent viscosity are included in developing a robust numerical solver for the targeted coupled multiphysics problem. To address the effect of microstructure in inelastic localized deformation behaviour with dilational softening, a nonlocal plasticity model is proposed based on a characteristic length scale which rectifies the non‐physical pathological mesh dependence problem encountered in conventional plasticity. The accuracy and strength of the developed model is shown with comparing the obtained numerical results of a benchmark bilateral compression test with existing published data in the literature. To show the versatility and robustness of the developed computational framework in modelling the geomechanics of real‐case engineering practices, large scale thermo‐hydro‐mechanical (THM) subsurface stimulation processes with applications in enhanced oil recovery (EOR) are effectively simulated and the targeted enhanced recovery and performances are demonstrated. The current formulation does not include phase transformation modelling capability, and therefore, the developed models may not be applicable for simulation of the engineering processes that involve phase change behaviour (e.g., steam injection).

Dynamic changes in dissolved organic matter during transport of landfill leachate in porous medium.

The dynamic changes in dissolved organic matter (DOM) during the transport of landfill leachate (LL) in porous medium should be explored, considering the high levels of DOM in the LL of municipal solid waste. Column experiments were carried out at 25°C at a Darcy's flux of 0.29cm/h for 2722h to compare the transport of Cl-, ultraviolet absorbance at 254nm (UV254), chemical oxygen demand (COD), and dissolved organic carbon (DOC) in the simulated porous medium by using the CXTFIT2.1 code. Results showed that the convection-dispersion equation (CDE) could describe Cl- transport well. The high levels of λ and D could be highly correlated with the physicochemical properties of the porous medium. The transport of the studied DOM with evident aromatic character could be described appropriately by the CDE model with the first-order reaction assumption, considering the similar variation trends of UV254, COD, and DOC in the effluent during experiments. Specifically, the values of retardation factor (R) were in the following order: DOC > UV254 > COD, whereas the low values of the first-order decay coefficient (k1) for DOC and COD were still higher than that for UV254. High contents of humic-like substances in the DOM with complex toxic components resulted in the natural low removal efficiencies of COD, DOC, and UV254 (≤ 23%), which could be confirmed by the variations of fluorescence index (FI) and humification index (HIX) in the effluent. The results should be helpful in evaluating the environmental risk induced by the LL leakage in a landfill site.

Enhancing unsteady heat transfer simulation in porous media through the application of convolutional neural networks

This research describes a novel technique for anticipating unstable heat transfer in porous media. Convolutional neural networks (CNNs) are used with finite volume method (FVM) and long short-term memory (LSTM) networks to accomplish this. Heat transport networks are difficult to characterise using traditional numerical methodologies owing to their nonlinearity and complexity. The proposed solution combines FVM’s precise physical modelling with CNN’s and LSTM’s superior pattern identification and temporal analysis. This collaboration supports the suggested strategy. Heat transport dynamics simulations in porous materials are more accurate, efficient, and adaptable when employing this hybrid framework. The experimental setup focused on porous material properties and gathered and processed a large amount of data. The building’s three-dimensional shape, heat transfer, and time were investigated. Temporal fluctuations were also used. Multiple indicators are used to evaluate the overall performance of the model. These criteria include convergence speed, F1 score, accuracy, precision, recall, and computational cost. In the most notable numerical results, the proposed strategy surpasses both the Finite Element and the Lattice Boltzmann methods. The presented method enabled fast convergence and reduced processing costs. These results were: accuracy (0.92), precision (0.93), recall (0.91), and F1 score (0.92). The proposed method is generalizable and adaptable, and it can address a variety of heat transport simulation problems in porous media. Unlike CNNs, which can identify significant spatial patterns, LSTM cells can only see temporal dynamics. These two components are required to show heat transfer, which is a continually changing phenomenon. Modern technology enables more complex simulations. Processing expenses are lowered, and estimations are more accurate. These two discoveries were obtained through the inquiry and methodologies. Finally, the CNN-FVM-LSTM technique simulates heat transport using complicated computer models. Predicting unusually high temperatures in porous materials may improve the model’s accuracy, computational efficiency, and flexibility.

Accelerating fluid flow simulations through doubly porous media using a FEM-assisted machine learning approach

This paper introduces an innovative methodology for simulating fluid flow through doubly porous media. This technique combines finite element (FE) simulations and machine learning (ML) methods. The approach involves training ML models with a dataset of FE simulation outcomes, enabling predictions of macroscopic permeability under varied conditions. This strategy addresses the limitations of conventional simulation methods, which suffer from high computational demands and lack of systematic insight. The approach's precision and efficiency are confirmed through numerical experiments, achieving a coefficient of determination of 0.998. The outcomes underline the potential of the FEM-assisted ML strategy to considerably enhance fluid flow simulations in porous media. The technique can find applications across diverse domains within civil engineering. Furthermore, developing an intuitive graphical user interface (GUI) streamlines the application of the proposed approach.

A benchmark study for quasi-static numerical upscaling of seismic wave attenuation and dispersion in fractured poroelastic rocks

Numerical simulation is an effective tool for comprehending fluid flow behavior and solid skeleton deformation within porous media, as well as obtaining valid seismic information. The elastic response of seismic waves, serving as an intermediary linking material properties and seismic attributes, is influenced by a combination of the wave-induced fluid flow (WIFF) effects and stress interactions. However, the impact of stress interactions is frequently overlooked in numerous studies, primarily due to the complex distribution of subsurface fractures makes it difficult to clarify the effects caused by local stress perturbations. Therefore, we present a numerical upscaling procedure as a benchmark process to quantify seismic wave attenuation and dispersion in fractured porous media simulations. The procedure is based on COMSOL Multiphysics and allows for the simulation of the energy dissipation resulting from the compression of a model with arbitrary forms of fluid saturation, geometry, and petrophysical parameters by seismic waves. We analyze the fracture models with different spatial distributions and infills to understand the mechanism. Our simulation results show the efficient and accurate capabilities of the numerical upscaling procedure in simulating the acoustic properties of fractured porous media and demonstrate the physical processes at various frequencies. In addition, our study yielded corresponding results: 1) the diverse spatial distribution of fractures not only gives rise to peak anomalies but also influences both the attenuation peaks and characteristic frequencies of seismic waves, thus reflecting the attenuation phenomena occurring at different scales; 2) various infills exhibit distinct sensitivities to fracture morphology and stress interactions.

A coupled MPM and CBFEM framework for large deformation simulation of porous media interacting with pore and free fluid

The hydromechanical interaction of porous media with pore and free fluid widely exists in geotechnical engineering. In some situations, the solid phase would exhibit large deformation, and the boundaries between the solid and fluid phases might change substantially, making it challenging for computational simulation. A framework coupling the material point method (MPM) with the characteristic-based finite element method (CBFEM) was proposed for simulating the behavior of porous media and fluid systems with large deformation. It employs the MPM to discretize the solid domain and solve corresponding momentum equations in the Lagrangian framework in favor of its advantage for large deformation simulation, and the CBFEM to discretize the fluid domain and solve the Navier-Stokes and free-surface equations of the fluid phase in the Eulerian framework in favor of its maturity and high efficiency. The fractional-step approach was adopted to solve velocity and pressure separately in a time step to make the MPM-CBFEM coupling more flexible. In addition, an implicit drag-force term was proposed to grow the time step in undrained conditions. A series of quasi-static and transient problems were simulated to show the performance and prospects of the proposed framework for the large deformation of the porous media and fluid systems.

Новая модель течения жидкости на базе метода решетчатых уравнений больцмана для сред со сложной геометрической структурой

Modelling porous media finds its application in many industries and human life, namely from the oil industry and construction to washing dishes. The article considers the processes of filtrating single-phase liquid through a porous structure, the description of which is based on lattice Boltzmann method in two-dimensional space. The problem of taking into account the structure of a simulated porous medium when applying the algorithm of lattice Boltzmann equations has many solutions. Nevertheless, at the microlevel, large errors in approximating the pore boundaries can occur, due to the fact that the lattice sites are assumed to be absolutely liquid or absolutely impenetrable. The paper proposes a model in which the lattice nodes are considered to be partially permeable. Partial permeability in this case refers to having a proportion of solids in the lattice site. As a result, it is possible to derive an equation that obeys the laws of mass and momentum conservation, the validity of which has been proven empirically. Due to the equation symmetry, it can be easily used not only on a plane, but also in three-dimensional space.The new lattice Boltzmann method can be employed, for example, in modelling water filtration through sandy soils, which is used in calculating subsidence of the foundations

3D reconstruction of unlimited-size real-world porous media by combining a BicycleGAN-based multimodal dictionary and super-dimension reconstruction

Three-dimensional reconstruction from a single two-dimensional image is important in the field of numerical simulation of porous media (including sandstones, composite, and alloys). Owing to limitations of computer storage space, the algorithm itself, and GPU memory, traditional algorithms and increasingly popular deep-learning algorithms cannot reconstruct complete real-size core images. To solve this problem, we propose a generative adversarial network dictionary-based super-dimension (GANDB-SD) algorithm that uses a BicycleGAN model to establish eight multimodal mappings of small-size structures. These mapping relations are used as the mapping dictionary when the super-dimension reconstruction framework is used to reconstruct the real core images without size limitation. Based on this algorithm, we further propose a three-dimensional co-occurrence matrix function as the loss function for the first time and propose a diversity preservation strategy to solve the pattern repetition problem during reconstruction. We performed an experiment to reconstruct a 5123 image, in which the morphological parameters and reconstruction time of different algorithms were compared. Results show that the algorithm has advantages in reconstruction accuracy and time. We further reconstructed 10003 real cores, and the statistical and morphological similarities between the reconstructed and target structures proved that the proposed algorithm is competent in the task of reconstructing real-world cores with unlimited size. We remark that our approach opens the door to a new methodology that incorporating machine learning/deep learning techniques into conventional super-dimension methods to address 3D reconstruction of unlimited-size real-world porous media issues in a wide range of related fields.

Implementation of a direct-addressing based lattice Boltzmann GPU solver for multiphase flow in porous media

GPU accelerated lattice Boltzmann (LB) simulations of multiphase flow in porous media have become a powerful tool to study fluid displacement process in porous media. For porous structures with a very low porosity, indirect-addressing memory access methods are preferred due to significantly reduction of the memory footprint despite that those methods are more difficult to implement and the resulting performance may be more sensible to the computing architectures, such as cache hierarchy and size. The direct-addressing methods are straightforward to implement and are able to archive high throughput when the porosity is large, while the methods become less efficient when the structures are too sparse. Nevertheless, the direct-addressing methods combined with multi-block grid technique are promising for many applications. In this work, we present a hybrid-way to tackle multiphase flow simulations in porous media, where the direct-addressing method is employed for the main LB evolution while the indirect-addressing method is employed for the complex boundary conditions. The CSF-based LB color-gradient multiphase model and the geometry-based wetting model are employed to increase accuracy and stability. Thanks to the utilization of AA-pattern streaming scheme, non-slip boundary condition of arbitrary orientation can be enforced without extra cost. We perform comprehensive analysis of the computational performance of the present solver on NVIDIA GPUs. For typical sandstones, our results show that the present implementation is able to achieve over 1.5 speedup compared with other direct-addressing schemes on V100 and A100, respectively and, particularly, the computational performance of the boundary kernels is greatly increased thanks to the increased L2 cache size of the latest GPUs.

Physics-informed data-driven model for fluid flow in porous media

A physics-informed machine learning model is developed that can replace the numerical simulations of porous media. By learning the communications among grid cells in the numerical domain, this model is capable of accurately predicting flow fields for new sets of simulation runs. Because of the many possible random arrangements of particles and their orientation with respect to each other, generalization of permeability with high accuracy is not trivial — nor is it practical using conventional means. Furthermore, building a comprehensive database for different grain/pore arrangements is not possible because of the cost of running numerical simulations to generate the database that represent all possible arrangements. The objective is to predict grid-level flow fields in porous media as a priori to determining permeability of porous media. The rationale is that once the detailed grid-level dynamics can be accurately predicted using data-driven approach, for any configuration/topology of the porous media, the detailed dynamics could be predicted without any need for new expensive numerical simulation runs. In this work, a physics-informed deep learning model is developed by using the results from Lattice-Boltzmann simulations of randomly distributed circular grains to represent the porous media. A variety of porous structures are developed by changing the number, size, and location of circular grains. The deep U-Net and ResNet neural network architectures are combined to train a deep learning model which avoids the vanishing gradient issues. The continuity and momentum conservation equations are embedded into the loss function of deep learning architecture. Robustness of the developed model is then tested for numerous variations of porous media which have not been used for developing the model.

A generic workflow of projection-based embedded discrete fracture model for flow simulation in porous media

A generic workflow of projection-based embedded discrete fracture model for flow simulation in porous media

Stream and Potential Functions for Transient Flow Simulations in Porous Media with Pressure-Controlled Well Systems

Gaussian solutions of the diffusion equation can be applied to visualize the flow paths in subsurface reservoirs due to the spatial advance of the pressure gradient caused by engineering interventions (vertical wells, horizontal wells) in subsurface reservoirs for the extraction of natural resources (e.g., water, oil, gas, and geothermal fluids). Having solved the temporal and spatial changes in the pressure field caused by the lowered pressure of a well’s production system, the Gaussian method is extended and applied to compute and visualize velocity magnitude contours, streamlines, and other relevant flow attributes in the vicinity of well systems that are depleting the pressure in a reservoir. We derive stream function and potential function solutions that allow instantaneous modeling of flow paths and pressure contour solutions for transient flows. Such analytical solutions for transient flows have not been derived before without time-stepping. The new closed-form solutions avoid the computational complexity of time-stepping, required when time-dependent flows are modeled by superposing steady-state solutions using complex analysis methods.

Stability of non-linear flow in heterogeneous porous media simulations using higher order and continuity basis functions

Using isogeometric analysis, we present a highly optimized FORTRAN code for simulations of three-dimensional non-linear flow problem in heterogeneous media. This includes deriving the weak formulations, discretizing with the forward Euler scheme, and implementing computation of the right-hand side. Some properties of exact solutions of heat transport and non-linear flow in heterogeneous media problems have been derived to validate the numerical solution. Stability analysis of the employed explicit time-stepping scheme has been performed. First, the properties of the discrete form of the heat transfer problem have been systematically investigated, leading to the conjecture concerning the sufficient condition of stability of the scheme, which numerical computations have subsequently confirmed. A similar analysis has been carried out for the non-linear flow in heterogeneous media problem. For this problem, the bound on the time step was conjectured to decrease exponentially, which has been verified experimentally. The simulation’s behavior close to the stability limit has been investigated and found to be considerably more complex than for the heat transport problem. Detailed experimental analysis of the time complexity of the particular parts of the simulator algorithm has been described. In addition, dependence on both mesh size and order of continuity of B-spline basis has been investigated.

Capacitive platform for real-time wireless monitoring of liquid wicking in a paper strip.

Understanding the phenomenon of liquid wicking in porous media is crucial for various applications, including the transportation of fluids in soils, the absorption of liquids in textiles and paper, and the development of new and efficient microfluidic paper-based analytical devices (μPADs). Hence, accurate and real-time monitoring of the liquid wicking process is essential to enable precise flow transport and control in microfluidic devices, thus enhancing their performance and usefulness. However, most existing flow monitoring strategies require external instrumentation, are generally bulky and unsuitable for portable systems. In this work, we present a portable, compact, and cost-effective electronic platform for real-time and wireless flow monitoring of liquid wicking in paper strips. The developed microcontroller-based system enables flow and flow rate monitoring based on the capacitance measurement of a pair of electrodes patterned beneath the paper strip along the liquid path, with an accuracy of 4 fF and a full-scale range of 8 pF. Additionally to the wired transmission of the monitored data to a computer via USB, the liquid wicking process can be followed in real-time via Bluetooth using a custom-developed smartphone application. The performance of the capacitive monitoring platform was evaluated for different aqueous solutions (purified water and 1 M NaCl solution), various paper strip geometries, and several custom-made chemical valves for flow retention (chitosan-, wax-, and sucrose-based barriers). The experimental validation delivered a full-scale relative error of 0.25%, resulting in an absolute capacitance error of ±10 fF. In terms of reproducibility, the maximum uncertainty was below 10 nl s-1 for flow rate determination in this study. Furthermore, the experimental data was compared and validated with numerical analysis through electrical and flow dynamics simulations in porous media, providing crucial information on the wicking process, its physical parameters, and liquid flow dynamics.

An improved pressure drop correlation for modeling localized effects in a pebble bed reactor

Advances in the development of pebble bed reactors (PBRs) has created a desire for accurate and cost-effective simulation tools for design scoping studies and safety analysis. The current state-of-the-art for these simulations is the use of porous media models, although these models rely on correlations to capture the effects of flow features that are not explicitly modeled. One of the areas where correlation accuracy is currently lacking is in the near-wall region of the bed. In this region, the presence of the wall causes the pebbles to pack more orderly, drastically changing the geometry and flow behavior in this region.This work presents a new generalized pressure drop correlation for PBRs based on the KTA equation. A high-to-low methodology is applied, where large eddy simulation (LES) is performed on two beds of 1568 and 1700 pebbles to generate a high-fidelity dataset. The flow fields are then averaged in time and separated into concentric rings of 0.05 Dpeb width. Average porosity, velocity, and pressure drop are extracted for each ring and the friction and form losses are calculated. The Reynolds number range for this study is 625–10,000, and thus the form losses are dominant over the friction losses. The form losses across the rings are investigated, and a correction term for the form loss calculation is determined and applied to the KTA equation to drastically improve the capability of modeling localized porosity effects in a porous media code. The improved correlation reduces near-wall velocity prediction error from over 50% with the KTA correlation to around 5%. Agreement in pressure drop prediction between LES and porous media simulations is also improved.

Parallel OpenMP and OpenACC porous media simulation

Parallel OpenMP and OpenACC porous media simulation