Three-dimensional Porous Media Research Articles

Matlab implementation of pore morphology method for modeling liquid residue in porous media with heterogeneous wettabilities

An alternative to the popular volume-of-fluid (VOF) and lattice Boltzmann (LB) methods for simulating fluid flow in porous media is the purely geometric pore morphology method (PMM). The PMM does not require solving partial differential equations and is therefore, orders of magnitude faster than the VOF and LB methods in terms of CPU time (e.g., about a week on 100 cores for the VOF vs. about 30 mins on one core for the PMM in our case). The PMM employs voxel-based morphological operations to provide a quasi-static approximation for capillary flow in porous structures. This paper presents step-by-step instructions for how to implement the PMM in the MATLAB environment, and further to benchmark the method using the simulation results obtained from the VOF and other continuum-based numerical methods. More specifically, this paper presents PMM simulations for the intrusion of a non-wetting fluid in two- and three-dimensional porous media with heterogeneous contact angles. Detailed discussions are also presented for the pros and cons of the PMM and how its non-continuum nature can be used as an advantage to conduct two-phase flow simulations in geometries where a symmetry boundary condition cannot be applied.

Boosting the reconstruction performance of 3D Multi-porous media using double generative adversarial networks

With the continuous improvement of mathematical modeling technology, reconstructing the three-dimensional structure of media from two-dimensional reference images has become an important research method for the three-dimensional modeling of multi-porous media. Deep-learning-based methods are currently popular and form the focus of this research field. However, the performance of deep learning in reconstructing the three-dimensional structure of media from two-dimensional reference images still requires improvement. To enhance the diversity and generalization of network-generated three-dimensional models, this study proposed a preprocessing method that correlated two-dimensional reference images with Gaussian noise, a three-orthogonal random section constraint method, and a dual generative adversarial network (DGAN)-based model. Multiple sets of core samples, a set of building materials, and a set of battery-material samples were used to verify the performance of the proposed network. Both intuitive morphological and statistical feature comparisons showed that the DGAN model solved the problem of insufficient diversity and generalization when reconstructing three-dimensional porous media from a single image using deep-learning-based methods. The morphological and statistical features of the reconstructed three-dimensional structure also exhibited good consistency with the reference two-dimensional image, and the training efficiency of the network was greatly improved.

Impact of Wettability on CO2 Dynamic Dissolution in Three-Dimensional Porous Media: Pore-Scale Simulation Using the Lattice Boltzmann Method.

Understanding the dissolution behavior of supercritical CO2 (scCO2) in porous media is crucial for efficient CO2 storage. However, the precise modeling of dynamic dissolution behavior at this pore scale remains a huge challenge, and the impact of wettability on this process still needs to be clarified. In this study, the influence of rock wettability on CO2 dynamic dissolution in the three-dimensional porous media is investigated using the lattice Boltzmann method (LBM). The LBM is coupled with scCO2-water two-phase flow, solute transport, and heterogeneous and homogeneous reactions. The size, number, and dissolution pattern of scCO2 bubbles during the dissolution process are observed under strongly water-wet, weakly water-wet, intermediate-wet, and mixed-wet conditions. The CO2(aq) concentration and pH are investigated, followed by a quantitative investigation of the impact of wettability on the specific interface area and the mass transfer coefficient. An empirical relationship between the specific interface area and scCO2 saturation is established. The findings reveal that under weakly water-wet and intermediate-wet conditions, the sizes of scCO2 clusters and monomers are small and mostly distributed at the dead end of the pores. In contrast, under strongly water-wet and mixed-wet conditions, the clusters are larger and interconnected, and distributed in the center of the pore. This results in a greater scCO2-water interface area, consequently enhancing the dissolution rate. Furthermore, a strong linear correlation is observed between scCO2 saturation and specific interface area. It is noted that as the hydrophilicity of the rock increases, the mass transfer coefficient initially rises and then declines.

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

A novel meshless numerical simulation of oil-water two-phase flow with gravity and capillary forces in three-dimensional porous media

This paper presents a novel fully implicit scheme for simulating three-dimensional (3D) oil-water two-phase flow with gravity and capillary forces using the meshless generalized finite difference method (GFDM). The approach combines an implicit Eulerian scheme in time with a GFDM discretization method in space to compute implicit solutions for the pressure and saturation in the flow control equations. The research introduces an L2 norm error formula and conducts a sensitivity analysis on the impact of varying influence domain radii on computational accuracy within the Cartesian node collocation scheme. Findings suggest that larger influence domain radii correspond to reduced computational accuracy, providing a preliminary guideline for selecting the domain radius in 3D GFDM applications. Overall, this paper presents an effective and precise meshless method for addressing two-phase flow challenges in 3D porous media, highlighting the promising prospects of GFDM in numerical simulations.

Pore-scale flame oscillations and patterns of upstream combustion wave propagation in a one-layer porous burner

Upstream propagation of filtration combustion wave in a one-layer porous burner is studied experimentally using thermal imaging and high-speed filming. The burner is the one-layer packed bed of spheres modeling porous media and providing optical access to the flame. This design allowed us to study macroscopic propagation of the combustion wave as well as non-stationary flame behavior at the pore scale. Experimental results demonstrate that upstream propagating combustion wave forms non-uniform porous medium temperature distribution in transverse direction which consists of hot areas separated by low-temperature regions. Macroscopic flame propagation can be accompanied by oscillations of some flame fragments at the pore scale. The mechanism of these pulsations is identical to the flames with repetitive extinction and ignition in narrow channels with external heating. Experimental results suggest that large scale evolution of the thermal wave affects the non-stationary behavior of the flame fragments at the pore scale and vice versa. The interplay between pore-scale and macro-scale processes manifests itself in the multiple repetitions of some patterns of the combustion wave propagation. Two most typical and common patterns are described and discussed. These patterns are step-wise transition of the flame fragment into the upstream pore and transition through the series of flame oscillations with repetitive extinction and ignition. It is shown that highly simplified one-dimensional model describes flame propagation in externally heated variable cross-section channel with heat conducting walls is capable to describe main features of these two patterns. Parametric study allows to predict the effect of problem parameters on the regions of existing of one or another pattern of upstream flame propagation.Novelty and Significance StatementThis paper presents new experimental data on temperature characteristics of upstream propagating filtration combustion wave in a one-layer porous burner. For the first time the patterns of combustion wave propagation uniting macro-scale processes of the thermal wave propagation and oscillations of the flame fragments at the pore scale are described on the basis of experimental data and numerical modeling. Results obtained for the one-layer burner can apparently be generalized to the case of combustion in three-dimensional porous media and packed beds. These results are significant because extend fundamental knowledge on porous media combustion by information on pore- and macro- scale flame dynamics as well as on the interplay of these scales. Experimental results can also be useful for validation of pore-resolved numerical simulations actively developed in the last decade.

A pore-scale lattice Boltzmann model for solute transport coupled with heterogeneous surface reactions and mineral dissolution

In this paper, we propose a pore-scale lattice Boltzmann model to simulate fluid flow coupled with heterogeneous surface reactions and mineral dissolution. The primary innovation lies in the transformation of surface reactions, originally treated as a boundary condition, into a volume-source term through dimensional augmentation within the framework of sharp liquid–solid interfaces. This significantly simplifies the implementation, particularly for reactions occurring in porous media with intricate geometric structures. Several benchmark tests were performed to validate the accuracy of this model, including a reaction–diffusion problem in a rectangular domain, a two-dimensional reaction and dissolution of a circular grain, as well as a three-dimensional calcite crystal dissolution in a micro-channel. All the obtained simulation results agree well with the reference solutions. In addition, a dissolution problem in a three-dimensional porous medium built with the sand pack is then investigated. Cases with different Péclet numbers (Pe) and Damköhler numbers (Da) were simulated, and five dissolution modes were obtained, which were finally summarized in a diagram of Pe and Da.

Transport scaling in porous media convection

We present a theory to describe the Nusselt number,$\operatorname {\mathit {Nu}}$, corresponding to the heat or mass flux, as a function of the Rayleigh–Darcy number,$\operatorname {\mathit {Ra}}$, the ratio of buoyant driving force over diffusive dissipation, in convective porous media flows. First, we derive exact relationships within the system for the kinetic energy and the thermal dissipation rate. Second, by segregating the thermal dissipation rate into contributions from the boundary layer and the bulk, which is inspired by the ideas of the Grossmann and Lohse theory (J. Fluid Mech., vol. 407, 2000;Phys. Rev. Lett., vol. 86, 2001), we derive the scaling relation for$\operatorname {\mathit {Nu}}$as a function of$\operatorname {\mathit {Ra}}$and provide a robust theoretical explanation for the empirical relations proposed in previous studies. Specifically, by incorporating the length scale of the flow structure into the theory, we demonstrate why heat or mass transport differs between two-dimensional and three-dimensional porous media convection. Our model is in excellent agreement with the data obtained from numerical simulations, affirming its validity and predictive capabilities.

Sliced Wasserstein Distance-Guided Three-Dimensional Porous Media Reconstruction Based on Cycle-Consistent Adversarial Network and Few-Shot Learning

Sliced Wasserstein Distance-Guided Three-Dimensional Porous Media Reconstruction Based on Cycle-Consistent Adversarial Network and Few-Shot Learning

Application of meshless generalized finite difference method (GFDM) in single-phase coupled heat and mass transfer problem in three-dimensional porous media

This paper achieves effective and precise meshless modeling of three-dimensional (3D) single-phase coupled heat and mass transfer problems based on the generalized finite difference method (GFDM). It utilizes the Taylor formula and the weighted least squares method in the node influence domains to derive a generalized finite difference scheme for spatial derivatives of pressure and temperature. Consequently, a sequential coupled discrete scheme for the pressure diffusion equation and heat convection–conduction equation is formulated, resulting in the determination of pressure and temperature. An example conducts sensitivity analysis with different schemes of node collocation and different radius of influence domains. The calculation results demonstrate that this method exhibits good convergence. Two 3D model examples with regular and irregular boundaries illustrate the advantages of the GFDM in handling complex geometric problems within the computational domain, showcasing its superior flexibility and simplicity. This paper demonstrates the significant potential of GFDM in addressing complex geometric multi-physics field coupling challenges, offering innovative ideas for geothermal resource development, groundwater management, and thermal recovery in oil and gas reservoirs.

Numerical simulation and experimental study of three-phase distribution characteristics of leaked light non-aqueous phase liquid from buried pipelines in soils containing groundwater and gas.

Leakage accidents of buried pipelines have become increasingly common due to the prolonged service of some pipelines which have been in use for more than 150years. Therefore, there is an urgent need for accurate prediction of pollution scope to aid in the development of emergency remediation strategies. This study investigated the distribution of a light non-aqueous phase liquid in soils containing gas and water through numerical simulations and laboratory experiments. Firstly, a three-dimensional porous medium model was established using ANSYS FLUENT, and for the first time, the distribution of gas and groundwater in soil environments was simulated in the model. Subsequently, the distribution of the three phases of diesel, gas, and water in soil was studied with different leakage velocities and it was found that the leakage velocity played a significant role in the distribution. The areas of diesel in soils at 60min were 0.112m2, 0.194m2, 0.217m2, and 0.252m2, with corresponding volumes of 0.028m3, 0.070m3, 0.086m3, and 0.106m3, respectively, for leakage velocities of 1.3m/s, 3.4m/s, 4.6m/s, and 4.9m/s. Calculation formulas for distribution areas and volumes were also developed to aid in future prevention and control strategies under different leakage velocities. The study also compared the distribution areas and volumes of diesel in soils with and without groundwater, and it was found that distribution scopes were larger in soils containing groundwater due to capillary force. In order to validate the accuracy of the numerical simulation, laboratory experiments were conducted to study the diffusion of oil, gas, and water under different leakage velocities. The results showed good agreement between the experiments and the simulations. The research findings are of great significance for preventing soil pollution and provide a theoretical basis for developing scientifically sound soil remediation strategies.

Direct comparison of density-driven convective mixing in a three-dimensional porous medium using experiments and simulation

Direct comparison of density-driven convective mixing in a three-dimensional porous medium using experiments and simulation

Flow prediction of heterogeneous nanoporous media based on physical information neural network

The simulation and prediction of fluid flow in porous media play a profoundly significant role in today's scientific and engineering domains, particularly in gaining a deeper understanding of phenomena such as the migration and fluid flow in underground rock formations and the enhancement of oil recovery rates. The flow of fluids in nanoscale porous media requires consideration of the effects of microscale phenomena, which are challenging to accurately describe using traditional physical models. Currently, research in deep learning for porous media predominantly focuses on conventional porous media, and there is an urgent need for investigations into heterogeneous nanoporous media. Simultaneously, there is a necessity to overcome the limitations of traditional data-driven models lacking physical prior knowledge. Therefore, the integration of physics-informed neural networks, which combine deep learning with physical principles, becomes essential for inferring relatively accurate results from sparse data. In this work, based on the heterogeneity of porous media in shale, we have introduced a deep learning model that couples physical information to predict the flow in heterogeneous nanoscale porous media. In the Physical Information Neural Network model, we utilize point clouds and couple them with deep residual networks. Discrete sampling points are used as inputs, and a multi-level residual connection, along with dimension concatenation, is employed to fuse feature information. The network, through backpropagation, takes into account the Navier-Stokes equations and wall conditions in heterogeneous nanoscale porous media. The results indicate that the apparent permeability and pressure field accuracy are over 90% and 95%, respectively. The Physical Information Neural Network demonstrates promising prospects for predicting flow in nanoscale porous media. Future work will extend to the multiphase complex flow in three-dimensional porous media.

Mathematical Model for Dynamic Adsorption with Immiscible Multiphase Flows in Three-dimensional Porous Media

Mathematical Model for Dynamic Adsorption with Immiscible Multiphase Flows in Three-dimensional Porous Media

Detailed simulation of a commercial radial fixed bed reactor for isomerization of C8 aromatics

Numerical simulations of C8 aromatics isomerization in radial reactors are important for understanding fluid flow, heat and mass transfer, complex reactions, and operational optimization. To investigate these aspects, we develop a three-dimensional porous media model integrated with modified reaction kinetics. This model accurately accounts for the actual reactor structure while parametrizing Ergun's equation to describe the pressure drop of the fluid passing through the scallop and center pipe. The catalyst seal exhibited an inverted U-shaped velocity distribution, resulting in a dead zone in the upper-right corner and an approximately 50 % reduction in catalyst utilization rate. Under 381 ℃ and 0.71 MPa conditions, the reactor exhibited an axial distribution uniformity value of 0.183, a pressure drop of 18.61 kPa, and an isomerization activity of 23.83 %. The calculated product profiles closely match the actual production data. Our validated and credible model provides valuable guidance for industrial radial reactors.

Study on early shrinkage and cracking of slab in UHPC light-weight composite deck based on ambient temperature and humidity effects

This study investigates the early performance and potential issues of ultra-high-performance concrete (UHPC) light-weight composite decks (LCBDs) used in municipal highway bridge design. The major objective of this research was to understand the complex evolution of temperature and humidity within immature UHPC thin layers, which can lead to deformation and secondary stress, potentially causing cracks and threatening the long-term applicability and safety of steel-concrete composite bridges. Understanding of the mechanism of this process will be the basis for subsequent work. The early performance of UHPC with ordinary concrete is compared. Besides, discussions are conducted on the basic thermal conductivity theory of three-dimensional porous media and the hydration mechanism of cement-based materials that are appropriate for early-stage UHPC. Subsequently, a refined thermo-mechanical coupling analysis method for steel-UHPC LCBD was proposed, implemented using ABAQUS, and validated through a UHPC composite beam test. This method was applied to calculate the early shrinkage of the UHPC layer in a steel-UHPC LCBD and evaluate the risk of cracking in an actual bridge expansion project, providing a rationality evaluation of a bridge design and its construction procedure.

On the global existence and analyticity of the mild solution for the fractional Porous medium equation

In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces are to show the existence of unique global mild solution under the condition of small initial data. Applying Fourier transform methods gives an equivalent integral equation of the model equation. The linear and nonlinear terms are then estimated in the corresponding Lei and Lin spaces. Further, the analyticity of solution to the fractional Porous medium equation is also obtained.

Influence of vibration on droplet dynamics in a three-dimensional porous medium

In this study, the effects of vibration on droplet dynamics inside a three-dimensional (3D) porous medium are investigated with a focus on frequency, amplitude, and surface wettability. A lattice Boltzmann method based on the Allen–Cahn equation (A-C LBM) is used. The results show that the volume of the drained drop and drainage duration of the droplet are significantly affected by the contact angle. The hydrophilic nature of the pores causes the droplet to spread inside the medium and resist the vibration force, resulting in a lower discharged liquid volume and delayed drainage. In contrast, a hydrophobic surface repels the droplet and leads to quicker drainage. It is also observed that the speed of droplet drained from the porous medium is higher for hydrophobic conditions, causing the separated drop to rebound and jump back toward the medium after impacting the surrounding wall boundaries. A thorough investigation is conducted on the combined implication of the surface adhesion, amplitude, and frequency of vibration on the first separation time of the droplet from the porous medium and full drainage duration. The results show that with increasing the hydrophobicity, the required vibration amplitude for complete drainage has decreased. In this way, the interplay between the adhesive force and the vibration force impedes the liquid phase separation from the hydrophilic porous medium at a low vibration amplitude. However, the results demonstrate that even in these conditions, an increase in the vibration frequency can enhance the separation and improve the drainage of the liquid phase from the pores.

Simulation of Reactive Transport in Fractured Porous Media

Numerical simulations of reactive transport in fractured porous media require the solution of coupled physical and chemical processes that depend on the fractures. Such coupled processes are described by a system of nonlinear partial differential-algebraic equations, while strong heterogeneities characterise fractures. This paper presents an approach to simulate single-phase flow and non-isothermal reactive transport with mineral dissolution and precipitation in fractured porous media. Our numerical solution strategy is based on two ingredients. First, the model equations consist of coupled partial differential equations for the fluid flow, heat transfer and solute transport and nonlinear algebraic equations representing the chemical reactions. Second, fractures are explicitly represented and treated as lower-dimensional objects. The partial differential equations are discretised using finite-volume methods, and at each time step, we solve a nonlinear system of equations using Newton’s method. With numerical simulations, we illustrate our model’s ability to accurately describe the two-way interaction between coupled multi-physical processes and two- and three-dimensional porous media with intersecting fractures.

A New Method to Three-dimensional Dual Medium Geometry Model Construction

Dual medium geometric model is widely used in soil and rock mass environment, which can only reflect the material exchange between cracks and matrix. The dual medium geometric model ignores the hydraulic relationship between the pores and cracks. The paper develops a new method to construct the three-dimensional dual medium geometry model. This method is completely written by Matlab scripting language, can describe the real spatial distribution state of fracture in bedrock. In the method, three-dimensional random fracture network geometric models with different parameters and three-dimensional porous media geometric models with Berlin Noise characteristics are constructed respectively, and then use the three-dimensional direct superposition method to construct the dual medium geometric model. The paper introduces the construction of three-dimensional random fracture network geometry model, three-dimensional porous media geometric model and the dual medium geometric model by direct superposition method. This research is of great significance to the construction of dual medium model and numerical simulation in related fields.