Three-dimensional Porous Media Research Articles

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.

Toward pore-scale simulation of combustion in porous media using a low-Mach hybrid lattice Boltzmann/finite-difference solver

A hybrid numerical model previously developed for combustion simulations is extended in this article to describe flame propagation and stabilization in porous media. The model, with a special focus on flame/wall interaction processes, is validated via corresponding benchmarks involving flame propagation in channels with both adiabatic and constant-temperature walls. Simulations with different channel widths show that the model can correctly capture the changes in flame shape and propagation speed as well as the dead zone and quenching limit, as found in channels with cold walls. The model is further assessed considering a pseudo two-dimensional porous burner involving an array of cylindrical obstacles at constant temperature, investigated in a companion experimental study. Furthermore, the model is used to simulate pore-scale flame dynamics in a randomly generated three-dimensional porous media. Results are promising, opening the door for future simulations of flame propagation in realistic porous media.

Effects of the geothermal gradient on the convective dissolution in CO2sequestration

Convective dissolution is an important mechanism for long-term CO$_2$sequestration in deep saline aquifers. The presence of an unstable geothermal gradient can affect the process of dissolution. In this paper, we present direct numerical simulations in a three-dimensional porous medium at three different concentration Rayleigh numbers$Ra_S$with a set of thermal Rayleigh numbers$Ra_T$. Simulations reveal that the flow structures alter when${\textit {Ra}}_T$increases for a fixed${\textit {Ra}}_S$. Strong thermal gradient can yield large-scale convection rolls which change the horizontal distribution and motions of concentration fingers. The time evolution of fluxes also has different responses to different${\textit {Ra}}_T$. A theoretical model is developed and successfully describes the evolution of concentration flux and volume averaged concentration during the final shutdown stage. We further calculate the dissolved CO$_2$into the interior over time, which shows non-monotonic variations as${\textit {Ra}}_T$increases. At the end of our simulations, the maximum increment of dissolved CO$_2$occurs when density ratio is around unity for all three concentration Rayleigh numbers we have explored. We apply our results to a typical geological reservoir and discuss their implications.

New Geometry Models for Calculating Tortuosity of Flow Paths in 3D Porous Media

The pore tortuosity of flow paths in porous media plays a crucial role in the simulation of various petrophysical properties (e.g., absolute permeability). A geometric model composed of tortuous stream tubes in the three-dimensional porous media with cubic particles (grains) representing solid grains to calculate tortuosity is proposed under the assumption that the particles are allowed to overlap unrestrictedly and fluids are incompressible. The model is formulated as a function of porosity and contains no empirical constants, which helps to reveal the physical mechanism of tortuous pore paths for fluids to flow within porous media. The result performs better in approximating the results on three-dimensional porous rocks.

Reconstruction of three-dimensional porous media using multi-scale generative adversarial networks

Numerical simulation methods have been widely used in the reconstruction of porous media, but their applicability usually suffers from the huge hardware burden and computational time. Recently, with the rapid development of deep learning, its powerful ability in feature extraction has been applied to reconstruct porous media. As an important branch of deep learning, generative adversarial network (GAN) has been considered as an effective method to extract features from training images (TIs). Based on GAN, this paper proposes a method for the reconstruction of porous media using multi-scale GAN (multi-GAN), which learns the features of the TI at different scales separately by using a convolutional pyramid structure. The proposed method uses only a single three-dimensional (3D) TI of porous media for reconstruction and the reconstructed images contain structural information of the TI at different scales. Compared with some typical methods, this method has certain advantages in terms of reconstruction quality and efficiency.

Volumetric measurement of a Newtonian fluid flow through three-dimensional porous media using Lagrangian particle tracking (Shake-the-Box) technique

This work experimentally investigates the pressure-driven flow of a pure Newtonian fluid through three-dimensional (3D) porous media models. The porous media model consists of square arrays of rods that also could be interpreted as a periodic tandem rod arrangement. We employed a time-resolved three-dimensional particle tracking velocimetry (3D Shake-the-Box) technique for a range of Reynolds numbers 111 ≤ R e ≤ 890 to observe flow structures and vortex formation between the rods in porous media structures with different porosities of ε = 0.7 , 0.8 , and 0.9 , which corresponds to the spacing ratio of L D = 1.75 , 2 , and 3, where L is the distance between the centers of the rods, and D is the diameter of the rods. For all the examined cases, we further analyzed the effect of the Reynolds number and the spacing ratio on the instantaneous and averaged patterns of velocity, vorticity, and the other flow parameters after obtaining the two-dimensional velocity fields using the bin-averaging method. We observed both symmetrical and asymmetrical patterns of structure and recirculation regions between the rods depending on the Reynolds number and spacing ratio. Increasing the Reynolds number reduced the symmetrical patterns of flow structures with respect to the centerline of the gap region, while the spacing ratio was randomly affecting the symmetry degree. Vortex shedding was considerable for the two examined high Reynolds numbers of Re = 444 and Re = 890 behind the upstream rod as the porosity increased. The backward movement of the reattachment point has been observed by increasing the Reynolds number.

Optimum Volume Fraction and Inlet Temperature of an Ideal Nanoparticle for Enhanced Oil Recovery by Nanofluid Flooding in a Porous Medium

Nowadays, oil companies employ nanofluid flooding to increase oil production from oil reservoirs. Herein the present work, a multiphase flow in porous media was used to simulate oil extraction from a three-dimensional porous medium filled with oil. Interestingly, the finite element method was used to solve the nonlinear partial differential equations of continuity, energy, Darcy’s law, and the transport of nanoparticles (NPs). The proposed model used nanofluids (NFs) empirical formulas for density and viscosity on NF and oil relative permeabilities and NP transport equations. The NPs thermophysical properties have been investigated and compared with their oil recovery factor (ORF) to determine the highest ORF. Different NPs (SiO2, CuO, and Al2O3) were used as the first parameter, keeping all parameters constant. The simulation was run three times for the injected fluid using the various NPs to compare the effects on enhanced oil recovery. The second parameter, volume fraction (VF), has been modeled six times (0.5, 1, 2, 3, 4, and 5%), with all other parameters held constant. The third parameter, the injected NF inlet temperature (293.15–403.15 K), was simulated assuming that all other parameters are kept constant. The energy equation was applied to choose the inlet temperature that fits the optimum NP and VF to determine the highest ORF. Findings indicated that SiO2 shows the best ORF compared to the other NPs. Remarkably, SiO2 has the lowest density and highest thermal capacity. The optimum VF of SiO2 was 4%, increasing the ORF but reduced when the VF was higher than 4%. The ORF was improved when the viscosity and density of the oil decreased by increasing the injected inlet temperature. Furthermore, the results indicated that the highest ORF of 37% was obtained at 353.15 K when SiO2 was used at a VF of 4%. At the same time, the lowest recovery is obtained when a volume of 5% was used at 403.15 K.

Pore-scale investigation of wettability effects on drying process of three-dimensional porous medium

Pore-scale investigation of wettability effects on drying process of three-dimensional porous medium

Spatial Moment Analysis of Convective Mixing in Three-Dimensional Porous Media Using X-ray CT Images

Spatial Moment Analysis of Convective Mixing in Three-Dimensional Porous Media Using X-ray CT Images

Spatial Moment Analysis of Convective Mixing in Three-Dimensional Porous Media Using X-ray CT Images

Spatial Moment Analysis of Convective Mixing in Three-Dimensional Porous Media Using X-ray CT Images

Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

• Features of log-conductivity, Y , fields are captured by a non-Gaussian (GSG) model. • Expressions of flow and transport moments in three-dimensional GSG fields are derived. • Head and velocity fields are more correlated in GSG than in Gaussian Y structures. • Non-Gaussianity of Y heavily influences pre-asymptotic macrodispersion values. • Late time transport exhibits a Fickian behavior also in non-Gaussian Y fields. In this work, we explore the implications of modeling the logarithm of hydraulic conductivity, Y , as a Generalized Sub-Gaussian (GSG) field on the features of conservative solute transport in randomly heterogeneous, three-dimensional porous media. Hydro-geological properties are often viewed as Gaussian random fields. Nevertheless, the GSG model enables us to capture documented non-Gaussian traits that are not explained through classical Gaussian models. Our formulation yields lead- (or first-) order analytical solutions for key statistical moments of flow and transport variables. These include flow velocities, hydraulic head, and macrodispersion coefficients, as obtained across GSG log-conductivity fields. The analytical model is based on a first-order spectral theory, which constrains the rigorous validity of our results to small values of log-conductivity variance ( σ Y 2 < < 1 ). Analytical results are then compared against detailed numerical estimates obtained through a Monte Carlo scheme encompassing various levels of domain heterogeneity. An asymptotic Fickian transport regime is attained at late times in both Gaussian and GSG Y fields. Convergence to such regime is slower for GSG as compared to Gaussian fields. This suggests a strong impact of the heterogeneity structure on non-Fickian pre-asymptotic behaviors of the kind documented in the literature. The quality of the comparison between analytical and numerical results deteriorates with increasing σ Y 2 . Otherwise, our lead-order solutions frame macrodispersion coefficients in appropriate orders of magnitude also for values of σ Y 2 up to approximately 1.7, which are consistent with the spatial variability of Y across a single geological unit. In this sense, our analytical approach enables one to obtain prior information on solute plume evolution and to grasp the effects of non-Gaussian medium heterogeneity while favoring simplicity. Our findings also enhance the current level of understanding of the nature of mass transfer across heterogeneous media characterized by complex variability structures which cannot be reconciled with classical Gaussian scenarios.

Study of fluid displacement in three-dimensional porous media with an improved multicomponent pseudopotential lattice Boltzmann method

We generalize a recently developed improved multicomponent pseudopotential lattice Boltzmann method in three dimensions and analyze its applicability to simulate flows through realistic porous media. The model is validated and characterized via benchmarks, and we investigate its performance by simulating the displacement of immiscible fluids in three-dimensional geometries. Two samples are considered, namely, a pack of spheres obtained numerically and a Bentheimer sandstone rock sample obtained experimentally. We show that with this model, it is possible to simulate realistic viscosity ratios, to tune surface tension independently, and, most importantly, to preserve the volume of trapped fluid. We also evaluate the computational performance of the model on the graphical processing unit and mention the implemented optimizations to increase the computational speed and reduce the memory requirements.

Minireview on Solar Desalination and Hydropower Generation by Water Evaporation: Recent Challenges and Perspectives in Materials Science

Environmental energy harvesting holds great promise for sustainable development of society. Today, there are many kinds of available energy sources, such as hydropower, nuclear energy, thermal power, etc., but all of these suffer from requiring massive infrastructure investment, producing environmental pollution, and/or having the potential to experience catastrophic failure. In this review, we introduce novel methodology for harvesting energy, using evaporation of water from three-dimensional porous media, low-dimensional nanotubes, or microfibrous structures. We can produce fresh water driven by harnessing sunlight and can generate hydroelectric power via water transpiration. The former is driven by nanoscale photothermal heating, which induces rapid evaporation of water, while its bulk remains near room temperature. The latter is coupled with mass transport of water comprising ions that are condensed adjacent to the charged surface of the porous or fibrous media. These proposed schemes are clean, simple, and useful, which can be employed anywhere, because they operate as a result of spontaneous capillary action of water, solar power, or coulombic attraction occurring at the water–solid interface. The low-cost micro- and nanostructured materials presented here are readily available, suitable for securing potable water, and offer ubiquitous, clean, permanent energy sources for self-powered sensor networks and night-time energy harvesters that do not require energy inputs.