Fluid Flow In Porous Media Research Articles

Numerical study on the effect of strategically placed multiple diathermal obstructions within a porous enclosure

A novel strategy to reduce the convection heat transfer across a differentially heated, fluid-saturated porous enclosure has been reported in the present investigation. This objective is achieved by sequentially and strategically embedding multiple diathermal obstructions within the enclosure. To describe it in short, the strategy is to identify the location of maximum convection strength and place a single obstruction at that location. This strategy is re-applied to find an updated location of maximum convection strength and placing another single obstruction at that newly updated location. Darcy flow model is used to describe the fluid flow in porous media and solved using Successive Accelerated Replacement scheme using finite difference method. The parameters under study are type of obstructions (horizontal, vertical, right-inclined, left-inclined, straight-crossed and inclined-crossed), number of obstructions (0 < N <10) and modified Rayleigh number (100 < Ra < 2000). The size of obstruction (Z) has been fixed at 0.1. Flow and temperature distribution are plotted using streamlines and isotherms. The strength of convection is quantified using Nusselt number and maximum absolute stream function. It has been found that introducing obstructions within a differentially heated porous enclosure weakens the convection strength developed within it and the maximum reduction can be obtained for inclined-cross obstruction.

Numerical Simulation of CO Generation and Combustion Efficiency in Sintering Process: Effect of Solid Fuel Particle Size

For sintering pot productive process with various fuel particle size distributions, a transient numerical simulation sintering model based on the computational fluid dynamics approach is developed using Fluent 2021R1. The model combines chemical reaction, mass and heat transfer, Euler–Euler model, and fluid flow in porous media. In this study, CO is employed as the combustion's intermediate product, which is further oxidized by secondary combustion in the high‐temperature zone. Through calculations, the solid fuel combustion behavior of the sintering is explained collectively with the changing bed temperature, CO emission, and solid fuel combustion efficiency of the process under various fuel particle size distribution. In the sintering process, the fuel particle size distribution is crucial for lowering CO emissions and increasing combustion efficiency. The combustion efficiency shows a tendency of increasing initially before decreasing with the reduction of solid fuel particle size, while CO emissions show a trend of reducing first and then increasing. It is advantageous to lower the CO emission in the sintering process, and the combustion efficiency of the sintering process is greatly boosted by 5.13% when the proportion of solid fuel with 5 mm particle size decreases and the proportion of solid fuel with 3 mm particle size increases.

Performance analysis of linearization schemes for modelling multi-phase flow in porous media

Reservoir simulation is crucial for understanding the flow response in underground reservoirs, and it significantly helps reduce uncertainties in geological characterization and optimize methodologies for field development strategies. However, providing efficient and accurate solutions for the strong heterogeneity remains challenging, as most of the discretization methods cannot handle this complexity. In this work, we perform a comprehensive assessment of various numerical linearization techniques employed in reservoir simulation, particularly focusing on the performance of the nonlinear solver for problem dealing with fluid flow in porous media. The primary linearization methods examined are finite difference central (FDC), finite forward difference (FDF), and operator-based linearization (OBL). These methods are rigorously analyzed and compared in terms of their accuracy, computational efficiency, and adaptability to changing reservoir conditions. The results demonstrate that each method has distinct strengths and limitations. The FDC method is more accurate particularly in complex simulations where strong heterogeneity are introduced but is generally slower in convergence. The OBL on the other hand, is more efficient and converges quickly, which makes it suitable for scenarios with limited computational resources and simple physics, while the FDF method provides a balanced combination of precision and computational speed, contingent upon careful step size management of the derivative estimations. This paper aims to guide the selection of appropriate linearization techniques for enhancing nonlinear solvers’ accuracy and efficiency in reservoir simulation .

The Impact of Wettability on the Co-moving Velocity of Two-Fluid Flow in Porous Media

The impact of wettability on the co-moving velocity of two-fluid flow in porous media is analyzed herein. The co-moving velocity, developed by Roy et al. (Front Phys 8:4, 2022), is a novel representation of the flow behavior of two fluids through porous media. Our study aims to better understand the behavior of the co-moving velocity by analyzing simulation data under various wetting conditions. We analyzed 46 relative permeability curves based on the Lattice–Boltzmann color fluid model and two experimentally determined relative permeability curves. The analysis of the relative permeability data followed the methodology proposed by Roy et al. (Front Phys 8:4, 2022) to reconstruct a constitutive equation for the co-moving velocity. Surprisingly, the coefficients of the constitutive equation were found to be nearly the same for all wetting conditions. On the basis of these results, a simple approach was proposed to reconstruct the relative permeability of the oil phase using only the co-moving velocity relationship and the relative permeability of the water phase. This proposed method provides new information on the interdependence of the relative permeability curves, which has implications for the history matching of production data and the solution of the associated inverse problem. The research findings contribute to a better understanding of the impact of wettability on fluid flow in porous media and provide a practical approach for estimating relative permeability based on the co-moving velocity relationship, which has never been shown before.

Multilayer Commingled Production Effects in Hydrate Reservoirs with Underlying Gas

Multilayer commingled production is a widely used development method to improve the production capacity of gas reservoirs. However, there is currently limited research on the gas production characteristics of multilayer commingled production in hydrate reservoirs with underlying gas. The objective of this study was to analyze the characteristics of multilayer commingled production in order to determine suitable hydrate reservoirs for such a development method. Firstly, we employed analytical solutions to the equations of fluid flow in porous media to determine the factors affecting the production capacity. Then, by employing numerical simulation and depressurization methods, the rates of gas production and gas release from hydrate dissociation in a single production well were estimated. Additionally, the production capacity ratio of multilayer commingled production and separated-layer production was proposed. The influence of different reservoir characteristics on multilayer commingled production yield was determined and plotted. When there is an interlayer between hydrates and the underlying gas, the formation pressure ratio is the decisive factor affecting the multilayer commingled production yield. When there is no interlayer, the multilayer commingled production rate will increase with an increase in the permeability ratio, hydrate saturation, and underlying gas saturation. This study provides a theoretical foundation for predicting the production capacity of hydrate reservoirs, as well as assistance in selecting the hydrate reservoirs most suitable for multilayer commingled production.

A new pixel-free algorithm of pore-network extraction for fluid flow in porous media: Flashlight search medial axis

A new pixel-free algorithm of pore-network extraction for fluid flow in porous media: Flashlight search medial axis

Effects of fluid composition in fluid injection experiments in porous media

Experiments on fluid flow in porous media, using fluids loaded with solids of various grain sizes, have been conducted in a modified Hele-Shaw setup. This setup utilised weakly cemented porous media with specific hydraulic and mechanical properties. Fluid injection in coarse granular media with clean or low-concentration fine particles, results in infiltration only, with pressure close to the material tensile strength, while injection in finer granular material causes damage alongside infiltration, with the fluid pressure still close to the material tensile strength. When larger particle sizes or higher particle concentrations are used in the mixture, the fluid travels further within the porous medium, primarily influenced by the grain size of the granular medium. In the latter case, the Darcy flow equation with an effective permeability term can be employed to determine the pressure differential. For the largest particle sizes included in the fluid, the equation is still applicable, but the effective permeability requires adjustment for particle size within the fluid rather than the granular medium. This is crucial when the injection point is locally clogged. The experiments show that fracturing conditions are controlled by different mechanisms. Dimensional and statistical analysis was used to classify the injection pressures to regimes predicted by fracturing theory or by Darcy law with modified effective permeabilities. The findings show that both the material properties and fluid composition are important designing parameters.

Haar wavelet collocation technique for numerical solution of porous media equations

This paper focuses on using efficient Haar wavelet collocation method to nonlinear parabolic differential equations in order to solve steady state pore-scale creeping fluid flow in porous medium, substituting finite Haar series for space derivatives, incontrast forward difference approach is used to estimate the time derivative for porous media equation. These equations has vast number of application in engineering and various other fields such as, in petroleum engineering, there are often situations where fluids are near critical conditions. As oil pressure reduces below the bubble point when gas forms liquid condensations, or when the surface tension become very low i.e, transition from miscibility to immiscibility. To model gas production by pressure decline requires an accurate description of physical mechanism involved in the appearance of the gas bubbles. The observed stability with theoretical convergence assertion, the conservation law of mass and energy are stated. This supports the convergence of the preferred paradigm. A convergent approximation to the porous media equation is obtained by suggested approach. By calculating the maximum error norm and the experimental rate of convergence for various problems, the method efficiency and dependability are demonstrated. The method is accurate, easily applicable, and efficient.

Embedded Finite Element formulation for fluid flow in fractured porous medium

The presence of discontinuities, such as fractures or geological faults, can significantly influence the fluid flow in a porous medium. In general, the discontinuities can act as preferential flow paths. However, depending on their aperture and filling material, they can act as barriers to fluid flow. To model these different possibilities, this paper presents an embedded approach in the context of the finite element method to model the presence of discontinuities inside a porous medium in transient analyses. The formulation is attractive since it does not require the mesh used to discretize the porous medium to conform to the discontinuities. The derivation of the formulation is based on the Strong Discontinuity Approach by enriching the pressure field of the finite element with a Heaviside function. The enriched part of the pressure field is discretized based on the pressure jumps evaluated at the nodes where the discontinuity intersects the finite element. The discontinuity internal pressure is taken as an independent field, allowing the modeling of high pressures inside the discontinuity. A strategy to condense the discontinuity internal pressure degrees of freedom is presented. Numerical examples are presented showing the flexibility of the formulation to capture the influence of discontinuities on the fluid flow in porous medium. The results obtained with the proposed formulation are compared with interface element models, showing a good agreement between the two approaches.

A manufacturing method of rock samples with specific porosity and permeability for large-scale 3-D physical simulations

Making an artificial rock sample with specific porosity and permeability at a low cost to restore heterogeneous characteristics of target formation is significant to improving quality in large-scale 3-D physical simulations. To achieve this goal, the effects of effective stress of compaction (ESC), mass fraction of cements (MFC) and average diameter of grain (ADG) on porosity and permeability of rock samples are primarily analyzed by making 80 artificial core plugs using pressing synthesis technique. The results show that both ESC and MFC are negatively correlated with porosity and permeability. Meanwhile, if rock grains are enough homogeneous in size, only permeability is affected by ADG dramatically and the impact of ADG on porosity is not obvious. Based on the above achievements, two empirical models on the relationships between manufacturing parameters and porosity, manufacturing parameters and permeability are developed respectively, and then they are used to design a sub-meter scale rock sample and calculate its manufacturing parameters. Lastly, this rock sample is used to demonstrate the reliability of method by testing actual porosity and permeability. The validation indicates that absolute error between designing and actual porosity is 2.50% and absolute error of permeability is 20.30%. Manufacturing errors are lower than that of previous works. Additionally, production cost of rock samples is also very low and the total cost of the above sample is about 6000 CN Yuan (900 US Dollars). Thus, this method is reliable and it has great developing potential in large-scale 3-D physical simulations on fluid flow in porous media.

Effect of particle size distribution variability on the permeability of hydrate-bearing sediments: A CFD study

Natural gas hydrates (NGH) are considered as a future clean energy in the era of carbon neutrality. The seepage behaviour of hydrate-bearing sediment (HBS) and its controlling factors are significant for developing effective production strategies. In this study, we aim to elucidate how the heterogeneous spatial distribution of clayey-silty sediment particles, particularly the non-uniform particle size distribution (PSD) affects the permeability of HBS. An algorithm was developed to generate the heterogeneous spatial distribution of sediment particles based on the PSD of hydrate-bearing cores extracted from Japan Nankai Trough (D50 = 122 μm). A series simulation of fluid flow in porous media based on CFD was conducted for the HBS with varying hydrate saturations (SH). The watershed segmentation algorithm was employed for the identification of pore structure, including pore space and pore throat with a detailed analysis on the pore structure evolution with SH. Host sediments with higher uniformity result in initial high permeability but the permeability reduction with increasing SH is more significant compared with that of lower uniformity. Pore throat width reduced to less than 5 μm with SH above 50% compared with its original width of ∼30 μm. Tortuosity exhibits a linear increase with SH, while permeability decreases exponentially with increasing tortuosity. We propose an improved permeability model (KCpro) based on the classical Kozeny-Carman model accounting for the change in specific surface area for non-uniform PSD in HBS with good agreement. This study confirmed the applicability of CFD modelling as a promising tool to study the seepage behaviour of HBS complementary to classical permeability experimental tests. Results of this study provide fundamental understanding on how permeability evolves in HBS with significant PSD variations in natural gas hydrate reservoirs in nature.

Assessing Rheology Effects and Pore Space Complexity in Polymer Flow Through Porous Media: A Pore‐Scale Simulation Study

AbstractNon‐Newtonian fluid flow within porous media, exemplified by polymer remediation of contaminated groundwater/aquifer systems, presents complex challenges due to the fluids' complex rheological behavior within 3D tortuous pore structures. This paper introduces a pore‐scale flow simulator based on the OpenFOAM open‐source library, designed to model shear‐thinning flow within porous media. Leveraging this developed solver, extensive pore‐scale flow simulations were conducted on μ‐CT images of various real and synthetic porous media with varying complexity for both power‐law and Cross‐fluid models. We focused on the macroscale‐averaged deviation between bulk viscosity and the in‐situ viscosity, commonly denoted by a shift factor. We provided an in‐depth evaluation of the shift factor's dependency on the fluid's rheological attributes and the rock's pore space complexity. The least‐squares fitted values of the shift factor fell in the range of 1.6–9.5. Notably, the most pronounced shift factor emerged for extreme flow behavior indices. Our findings highlight not just the critical role of rheological parameters, but also demonstrate how the shift factor fluctuates based on tortuosity, characteristic pore length, and the cementation exponent. In particular, less porous/permeable systems with smaller characteristic pore lengths exhibited larger shift factors due to higher variations of shear rate and local viscosity in narrower flow paths. Additionally, the shift factor increased as rock became more tortuous and heterogeneous. The introduced pore‐scale simulation proves instrumental in determining the macroscopic averaged shift factor. This, in consequence, is vital for precise computations of viscosity and pressure drop when dealing with non‐Newtonian fluid flow in porous media.

Computational analysis of power-law fluids for convective heat transfer in permeable enclosures using Darcy effects

Natural convection is a complex environmental phenomenon that typically occurs in engineering settings in porous structures. Shear thinning or shear thickening fluids are characteristics of power-law fluids, which are non-Newtonian in nature and find wide-ranging uses in various industrial processes. Non-Newtonian fluid flow in porous media is a difficult problem with important consequences for energy systems and heat transfer. In this paper, convective heat transmission in permeable enclosures will be thoroughly examined. The main goal is to comprehend the intricate interaction between the buoyancy-induced convection intensity, the porosity of the casing, and the fluid’s power-law rheology as indicated by the Rayleigh number. The objective is to comprehend the underlying mechanisms and identify the ideal conditions for improving heat transfer processes.The problem’s governing equations for a scientific investigation are predicated on the concepts of heat transport and fluid dynamics. The fluid flow and thermal behavior are represented using the energy equation, the Boussinesq approximation, and the Navier–Stokes equations. The continuity equation in a porous media represents the conservation of mass. Finite Element Analysis is the numerical method that is suggested for this challenging topic since it enables a comprehensive examination of the situation. The results of the investigation support several important conclusions. The power-law index directly impacts heat transmission patterns. A higher Rayleigh number indicates increased buoyancy-induced convection, which increases the heat transfer rates inside the shell. The porosity of the medium significantly affects temperature gradients and flow distribution, and it is most noticeable when permeability is present. The findings show how, in the context of porous media, these parameters have complicated relationships with one another.

A deep learning-based workflow for fast prediction of 3D state variables in geological carbon storage: A dimension reduction approach

Deep learning (DL) models are extensively used as surrogate models for high-fidelity simulations of multiphase fluid flow in porous media at large scales, enabling fast forecasts of the spatial–temporal evolution of three-dimensional (3D) state variables in geological carbon storage (GCS). However, training these models in high-dimensional space remains computationally demanding and prone to overfitting because of limited training data. This paper presents a novel workflow to address these challenges by integrating dimension reduction (DR) methods. The proposed workflow employed pre-trained DR models to extract the latent variables of geological models and state variables and utilized the multi-layer perceptron (MLP) for constructing mapping functions between the input and output variables in latent spaces. Subsequently, the pre-trained reconstruction models converted the MLP-predicted latent state variables to their original high-dimensional form. Furthermore, we proposed a novel strategy for the DR and reconstruction of 3D saturation fields to account for the unique data characteristics of sparsity, nonuniformity, and discontinuity. The proposed strategy applied PCA and inverse PCA for 2D average saturation fields and developed a DL-based 3D reconstruction model, leveraging three 2D average saturation fields as input to produce a 3D saturation field as output. The pre-training of DR and reconstruction models and training of MLP models were conducted on 84 Gulf of Mexico (GoM) simulations and evaluated on 12 testing simulations. Each simulation contained 720 monthly time steps, with the first 360 months as the injection period and the rest as the post-injection period. The proposed workflow, incorporating DR and DL models, accurately predicts the normalized 3D pressure fields, achieving mean square error (MSE) of 2.92 × 10−7 compared to the ground truth obtained from a full-physics simulator. Furthermore, the proposed strategy outperformed PCA and convolutional autoencoder (CAE) models on 3D saturation fields, resulting in minor workflow prediction errors with an MSE of 2.93 × 10−5. The results suggest the proposed workflow provides sufficient predictive fidelity across temporal and spatial scales, and enables a speedup of 160 times compared to the full-physics simulator, facilitating improved decision-making and risk assessment for large-scale GCS management in real-time scenarios.

Overview of the Application of Physically Informed Neural Networks to the Problems of Nonlinear Fluid Flow in Porous Media

To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differential equations. To solve this direct problem, it is necessary to linearize the equation system. Algorithm construction for inverse problem solution is problematic since the numerical solution is unstable. The application of implicit methods is reduced to matrix equations with a high rank of the coefficient matrix, which requires significant computational resources. The authors of this paper investigated the possibility of parameterized function (physics-informed neural networks) application to solve direct and inverse problems of non-Newtonian fluid flows in porous media. The results of laboratory experiments to process core samples and field data from a real oil field were selected as examples of application of this method. Due to the lack of analytical solutions, the results obtained via the finite difference method and via real experiments were proposed for validation.

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.

THE EFFECT OF POLYMER GEL ON THE OIL AND WATER PERMEABILITY DAMAGE IN A MICROFLUIDIC DEVICE

Microfluidics, a rapidly advancing field, finds wide applications in various domains, including enhanced oil recovery. This study delineates the methodology for fabricating a microchip with channels having a width of 50 μm, designed to simulate and visualize fluid flow in porous media. The microfluidic device was constructed using NOA81, a UV-curable polymer. Upon curing, it forms a robust and transparent microchip structure suitable for precise fluid control and analysis in microfluidic applications. Flood experiments conducted on the microchip revealed that the introduction of a 0.5 wt% polymer gel into the model's channels resulted in a reduction of water permeability by a factor of 106 and 25 at the shock front and after injection pressure stabilized, respectively. In contrast, oil permeability was reduced by at least 40 times.

Computational multiphase micro‐periporomechanics for dynamic shear banding and fracturing of unsaturated porous media

AbstractDynamic shearing banding and fracturing in unsaturated porous media are significant problems in engineering and science. This article proposes a multiphase micro‐periporomechanics (PPM) paradigm for modeling dynamic shear banding and fracturing in unsaturated porous media. Periporomechanics (PPM) is a nonlocal reformulation of classical poromechanics to model continuous and discontinuous deformation/fracture and fluid flow in porous media through a single framework. In PPM, a multiphase porous material is postulated as a collection of a finite number of mixed material points. The length scale in PPM that dictates the nonlocal interaction between material points is a mathematical object that lacks a direct physical meaning. As a novelty, in the coupled PPM, a microstructure‐based material length scale is incorporated by considering micro‐rotations of the solid skeleton following the Cosserat continuum theory for solids. As a new contribution, we reformulate the second‐order work for detecting material instability and the energy‐based crack criterion and J‐integral for modeling fracturing in the PPM paradigm. The stabilized Cosserat PPM correspondence principle that mitigates the multiphase zero‐energy mode instability is augmented to include unsaturated fluid flow. We have numerically implemented the novel PPM paradigm through a dual‐way fractional‐step algorithm in time and a hybrid Lagrangian–Eulerian meshfree method in space. Numerical examples are presented to demonstrate the robustness and efficacy of the proposed PPM paradigm for modeling shear banding and fracturing in unsaturated porous media.

Equivalent Radius for Well Inflow Calculations at Different Regimes in Reservoir Flow Simulations

A problem of well representation in numerical simulation of fluid flows in porous media is considered. When modelling hydrocarbon reservoirs, underground gas storages and other natural porous media, there’s a large typical difference in scales of wells (about 10 cm) and inter-well distances (from hundreds to thousands meters), so wells aren’t resolved on the grid as explicit boundaries in large-scale reservoir simulations. Instead, wells are represented by sources/sinks. The problem is that the average pressure in a grid block containing the well (well block pressure, WBP) isn’t equal to the well pressure (bottomhole pressure, BHP). D. Peaceman showed that WBP can be interpreted as the pressure at equivalent radius inside the well grid block. He derived the classical formula for the equivalent radius for steady-state (SS) Darcy flow. Though Peaceman showed it could be used for pseudo steady-state (PSS) flow as well, his derivation for PSS was not accurate. In this paper we compute the equivalent radius for PSS and boundary dominated (BD) regimes of Darcy flow and examine the impact of flow regime and distance to external boundary (or inter-well distance) on it. The results are important for accurate well representation in numerical flow simulations of underground reservoirs.

Simulations of CO2 Dissolution in Porous Media Using the Volume-of-Fluid Method

Traditional investigations of fluid flow in porous media often rely on a continuum approach, but this method has limitations as it does not account for microscale details. However, recent progress in imaging technology allows us to visualize structures within the porous medium directly. This capability provides a means to confirm and validate continuum relationships. In this study, we present a detailed analysis of the dissolution trapping dynamics that take place when supercritical CO2 (scCO2) is injected into a heterogeneous porous medium saturated with brine. We present simulations based on the volume-of-fluid (VOF) method to model the combined behavior of two-phase fluid flow and mass transfer at the pore scale. These simulations are designed to capture the dynamic dissolution of scCO2 in a brine solution. Based on our simulation results, we have revised the Sherwood correlations: We expanded the correlation between Sherwood and Peclet numbers, revealing how the mobility ratio affects the equation. The expanded correlation gave improved correlations built on the underlying displacement patterns at different mobility ratios. Further, we analyzed the relationship between the Sherwood number, which is based on the Reynolds number, and the Schmidt number. Our regression on free parameters yielded constants similar to those previously reported. Our mass transfer model was compared to experimental models in the literature, showing good agreement for interfacial mass transfer of CO2 into water. The results of this study provide new perspectives on the application of non-dimensional numbers in large-scale (field-scale) applications, with implications for continuum scale modeling, e.g., in the field of geological storage of CO2 in saline aquifers.