Flow In Porous Media Research Articles

A posteriori-based, local multilevel mesh refinement for the Darcy porous media flow problem

In this work we develop an a posteriori-based adaptive local multilevel mesh refinement strategy for the Darcy porous media flow problem discretized with the finite volume method. Our approach is based on coupling the FIC “flux interface correction” method [1] and the equilibrated flux a posteriori error estimate [2]. The choice of the FIC method is motivated by the fact that it is well-adapted to problems discretized in conservative form since that the FIC provides corrections by balancing fluxes computed from both coarse and fin grids across the interface. The equilibrated flux a posteriori error estimate provides a guaranteed upper bound on the total error in the fluxes and takes advantage of the conservative scheme in such a way that the estimate can be easily coded and cheaply evaluated. We use this a posteriori estimate to detect automatically the zone of interest where the error is dominant in order to defined the local sub-grids. Numerous numerical experiments on practical problems illustrate the performance of our methodology. A comparison with a classical h-adaptive method is also carried out in this work.

A novel micro-continuum lattice Boltzmann approach for multiscale modeling immiscible two-phase flow in porous media

A novel micro-continuum lattice Boltzmann approach for multiscale modeling immiscible two-phase flow in porous media

Effect of chemical absorption on Jeffery Fluid Flow in saturated Porous Media with variable thermal conductivity

This study investigates the impact of species absorption of Jeffery fluid flow through a saturated permeable medium with variable thermal conductivity. The dimensional partial nonlinear derivative model controlling the chemical reacting fluid flow is transformed to invariant form. The resulting flow equations are computed numerically using an approximated finite implicit Crack-Nicolson. A chemical absorption of fluid reactant occurs in a boundless vertical device. Computations are performed for different parameters to examine their sensitivity under isothermal temperature conditions. The computed results are offered graphically for qualitative and quantitative insights into the flow behaviour. The obtained outcomes revealed that the fluid flow rate rises with an increasing values of the parameters and, and it damps with upsurge in the values of the parameters, and. The heat transfer field is reduced with enhancing values of the thermal source, viscous dissipation and time, but declines for a boosted value of the terms suction and Prandtl number. Also, the mass transfer field is higher when mass absorption and time are increased, and diminish with an elevate in the values of Schmidt number and chemical reactions.

Singular value decomposition for single-phase flow and cluster identification in heterogeneous pore networks

Pore networks play a key role in understanding and quantifying flow and transport processes in complex porous media. Realistic pore-spaces may be characterized by singular regions, that is, isolated subnetworks that do not connect inlet and outlet, resulting from unconnected porosity or multiphase configurations. The robust identification of these features is critical for the characterization of network topology and for the solution of the set of linear equations of flow and transport. We propose a robust method based on singular value decomposition to solve for network flow and locate isolated subnetworks simultaneously. The performance of the method is demonstrated for pore networks of different complexity.

The impact of diffusiophoresis on hydrodynamic dispersion and filtration in porous media

It is known that the dispersion of colloidal particles in porous media is determined by medium structure, pore-scale flow variability and diffusion. However, much less is known about how diffusiophoresis, that is, the motion of colloidal particles along salt gradients, impacts large-scale particle dispersion in porous media. To shed light on this question, we perform detailed pore-scale simulations of fluid flow, solute transport and diffusiophoretic particle transport in a two-dimensional hyper-uniform porous medium. Particles and solute are initially uniformly distributed throughout the medium. The medium is flushed at constant flow rate, and particle breakthrough curves are recorded at the outlet to assess the macroscopic effects of diffusiophoresis. Particle breakthrough curves show non-Fickian behaviour manifested by strong tailing that is controlled by the diffusiophoretic mobility. Although diffusiophoresis is a short-time, microscopic phenomenon owing to the fast attenuation of salt gradients, it governs macroscopic colloid dispersion through the partitioning of particles into transmitting and dead-end pores. We quantify these behaviours by an upscaled analytical model that describes both the retention and release of colloids in dead-end pores and the observed long-time tailings. Our results suggest that diffusiophoresis is an efficient tool to control particle dispersion and filtration through porous media.

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.

Effect of Different Shapes of Nanoparticles on Mixed Convective Nanofluid Flow in a Darcy-Forchhiemer Porous Medium

The nanofluid has diverse applications in industries, engineering, and medicine due to its greater thermal characteristics. However, various factors such as the shape and size of nanoparticles, the base fluid, the porous medium, the quadratic drag force, and the viscous dissipation have significant effects on the flow and heat transfer characteristics of nanofluids. Therefore, it is crucial to study the influence of these factors. In this paper, a theoretical investigation is conducted to analyze the mechanisms of thermal conductivities of different shapes of nanoparticles, such as platelet, cylinder, brick and blade on the mixed convective nanofluid flow in a vertical channel saturated with porous medium. Consider ethylene glycol and water as base fluids for the nanoparticles, including copper, aluminum oxide, titanium oxide, silver, and iron oxide. A thin, movable baffle plate of negligible thickness is inserted in the channel and made into double passages. To define the porous matrix, the Darcy-Brinkaman-Forchhiemer model is used, and to define the nanofluid, the Tiwari and Das model is used. Robin boundary conditions are considered for the channel flow. The differential transform method (DTM) is applied to solve non-linear governing equations with inertia, and the perturbation method is applied to solve the problem without inertia. Velocity and temperature cantors are shown graphically using MATLAB and MATHEMATICA. The obtained values by DTM and the perturbation method are well validated and shown graphically. The Nusselt number was evaluated and tabulated for all governing parameters. The objective of this article is to investigate the effect of nonspherical shapes of nanoparticles, the base fluid, the inertial forces of the porous medium, and the buoyancy force on the thermal characteristics of flow and heat transfer of nanofluids. The main findings of this problem are that the optimum velocity and temperature cantor are found for platelet-shaped water-based silver nanofluid.

Absolute permeability estimation from microtomography rock images through deep learning super-resolution and adversarial fine tuning

The carbon capture and storage (CCS) process has become one of the main technologies used for mitigating greenhouse gas emissions. The success of CCS projects relies on accurate subsurface reservoir petrophysical characterization, enabling efficient storage and captured CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{CO}_2$$\\end{document} containment. In digital rock physics, X-ray microtomography (μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}-CT) is applied to characterize reservoir rocks, allowing a more assertive analysis of physical properties such as porosity and permeability, enabling better simulations of porous media flow. Estimating petrophysical properties through numeric simulations usually requires high-resolution images, which are expensive and time-inefficient to obtain with μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu $$\\end{document}-CT. To address this, we propose using two deep learning models: a super-resolution model to enhance the quality of low-resolution images and a surrogate model that acts as a substitute for numerical simulations to estimate the petrophysical property of interest. A correction process inspired by generative adversarial network (GAN) adversarial training is applied. In this approach, the super-resolution model acts as a generator, creating high-resolution images, and the surrogate network acts as a discriminator. By adjusting the generator, images that correct the errors in the surrogate’s estimations are produced. The proposed method was applied to the DeePore dataset. The results shows the proposed approach improved permeability estimation overall.

Assessment of Models for Nonlinear Oscillatory Flow Through a Hexagonal Sphere Pack

We review models for unsteady porous media flow in the volume-averaging framework and we discuss the theoretical relations between the models and the definition of the model coefficients (and the uncertainty therein). The different models are compared against direct numerical simulations of oscillatory flow through a hexagonal sphere pack. The model constants are determined based on their definition in terms of the Stokes flow, the potential flow and steady nonlinear flow. Thus, the discrepancies between the model predictions and the simulation data can be attributed to shortcomings of the models’ parametrisation. We found that an extension of the dynamic permeability model of Pride et al. (PRB 47(9):4964–4978, 1993) with a Forchheimer-type nonlinearity performs very well for linear flow and for nonlinear flow at low and medium frequencies, but the Forchheimer term with a coefficient obtained from the steady-state overpredicts the nonlinear drag at high frequencies. The model reduces to the unsteady Forchheimer equation with an acceleration coefficient based on the static viscous tortuosity for low frequencies. The unsteady Forchheimer equation with an acceleration coefficient based on the high-frequency limit of the dynamic tortuosity has large errors for linear flow at medium and high frequencies, but low errors for nonlinear flow at all frequencies. This is explained by an error cancellation between the inertial and the nonlinear drag.

Magnetohydrodynamic instability of fluid flow in a bidisperse porous medium

Magnetohydrodynamic instability of fluid flow in a bidisperse porous medium

Impact of activation energy and cross-diffusion effects on 3D convective rotating nanoliquid flow in a non-Darcy porous medium

PurposeThis study aims to investigate numerically the impact of the three-dimensional convective nanoliquid flow on a rotating frame embedded in the non-Darcy porous medium in the presence of activation energy. The cross-diffusion effects, i.e. Soret and Dufour effects, and heat generation are included in the study. The convective heating condition is applied on the bounding surface.Design/methodology/approachThe control model consisted of a system of partial differential equations (PDE) with boundary constraints. Using suitable similarity transformation, the PDE transformed into an ordinary differential equation and solved numerically by the Runge–Kutta–Fehlberg method. The obtained results of velocity, temperature and solute concentration characteristics plotted to show the impact of the pertinent parameters. The heat and mass transfer rate and skin friction are also calculated.FindingsIt is found that both Biot numbers enhance the heat and mass distribution inside the boundary layer region. The temperature increases by increasing the Dufour number, while concentration decreases by increasing the Dufour number. The heat transfer is increased up to 8.1% in the presence of activation energy parameter (E). But, mass transfer rate declines up to 16.6% in the presence of E.Practical implicationsThe applications of combined Dufour and Soret effects are in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The nanofluid with porous medium can be used in chemical engineering, heat exchangers and nuclear reactor.Social implicationsThis study is mainly useful for thermal sciences and chemical engineering.Originality/valueThe uniqueness in this research is the study of the impact of activation energy and cross-diffusion on rotating nanoliquid flow with heat generation and convective heating condition. The obtained results are unique and valuable, and it can be used in various fields of science and technology.

Iterative schemes for coupled flow and transport in porous media -- Convergence and truncation errors

Nonlinearities of coupled flow and transport problems for partially saturated porous media are solved with explicit iterative L-schemes. Their behavior is analyzed with the aid of the computational orders of convergence. This approach allows highlighting the influence of the truncation errors in the numerical schemes on the convergence of the iterations. Further, by using manufactured exact solutions, error-based orders of convergence of the iterative schemes are assessed and the convergence of the numerical solutions is demonstrated numerically through grid-convergence tests.

Relative permeabilities for two-phase flow through wellbore cement fractures

Multiple fluids are likely to exist in fractures and flow paths associated with leaky wellbores, including liquids (e.g., crude oil) and gases (e.g., gas exsolved from liquid). These fluids occupy and move through different portions of the pore spaces within the fractures depending on many factors, including fluid properties, fracture size, and the amount of the different fluids. Upward leakage of any phase, through the fracture, can contaminate water-bearing formations, create hazardous surface conditions, and compromise the functionality of the wellbore. Early signs of wellbore leaks may be expressed by anomalous pressure behavior at surface monitoring points on cavern storage wells. These pressure anomalies are difficult to interpret, necessitating knowledge of the factors that affect the multiphase flow in fractures and porous media. These parameters are critical to modeling multiphase flow in fractures. This insight can guide further diagnosis and maximize leak remediation. Our study focuses on the relationship of the liquid–gas relative permeabilities for representative variable-aperture wellbore cement fracture. To obtain the relative permeability of each phase, two-phase flow tests were conducted where both fluids were flowing simultaneously through a fractured wellbore cement specimen under a range of factors, namely (1) aperture size, (2) capillary numbers, and (3) viscosity ratio. The flow experiments were conducted under a range of confining stresses and flow velocities, using nitrogen gas and silicone oils (of different viscosities) in a specially designed pressure vessel. The sum of gas and oil relative permeabilities were found to be less than one under all conditions, which indicates that the presence of one phase affects the permeability of the other phase, and vice versa. Since the gas phase flow conditions include a significant inertial flow component in addition to viscous flow, the inertial flow coefficients at different saturation states are presented. The factors affecting the relationship between the relative permeabilities are discussed in detail. A new mathematical model for estimating the relative permeability of wellbore cement fracture is presented and experimentally validated.

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 .

Numerical simulation and thermodynamic test analysis of plate heat exchanger based on topology optimization

Efficient heat transfer in PHEs relies on optimizing flow distribution to minimize thermal dead zones. Existing studies have predominantly focused on single-phase fluids as working media and employed density-based methods for structural optimization of microchannel heat exchangers at small scales. In this study, the Brinkman term from the porous media flow model is introduced in an innovative manner, along with the utilization of a material density interpolation model, which builds upon the density-based approach. A novel two-phase fluid topology optimization method is proposed, specifically tailored for large-scale PHE operating conditions, resulting in the successful design of a new PHE topology. To compare the performance of the two heat exchangers, finite element simulation, visualization experiments, and thermodynamic performance testing are conducted. The simulation results reveal that the heat transfer capacity of the topological PHE is 810 W with pressure drops of 18.8 kPa, while the dimple PHE exhibits heat transfer capacity of 652 W with pressure drops of 25.9 kPa. Compared to the dimple PHE, the topological PHE demonstrates 24.2 % improvement in heat transfer performance and 27.8 % reduction in pressure drop. The dimensionless comprehensive heat transfer coefficient (j/f) indicates that the overall performance of the topological PHE significantly surpasses that of the traditional PHE. Furthermore, the visualization experiment results demonstrate that the complex texture structure of the topological PHE effectively induces fluid motion, compelling the fluid to flow along the texture direction. This significantly mitigates the issue of uneven flow within the PHE, thus enhancing heat transfer efficiency. Specifically, the topological PHE exhibits inlet–outlet temperature difference of 10.3 °C and pressure drops of 11.2 kPa, while the dimple PHE shows inlet–outlet temperature difference of 6 °C and pressure drops of 12.9 kPa. The findings of this study provide guidance for future research endeavors aimed at evaluating potential solutions to advance heat transfer in PHEs and facilitate the implementation of thermal management strategies.

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.

From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

AbstractExtensive experiments have demonstrated that fluid flow in low‐permeability media deviates from Darcy's law at low pressure gradients, which is called pre‐Darcy flow. Although numerous pre‐Darcy flow models have been proposed, these models generally contain one or more empirical parameters with no clear physical meaning. In this paper, we present a simple unified model to describe pre‐Darcy flow in porous media by introducing the concept of loss permeability. The physical meaning of the loss permeability parameter and its relationship to permeability are analyzed. Based on the statistics of the loss permeability parameter results of 24 core samples, we found that there is a good positive correlation between the loss permeability parameter and the absolute permeability. A smaller loss permeability indicates a stronger fluid‐solid interaction and a stronger nonlinearity between the flow velocity and the pressure gradient. Taking a one‐dimensional linear unsteady flow of a slightly compressible fluid in a homogeneous porous medium as an example, we solve the pressure diffusion equation based on the proposed model using a finite difference method. Our results demonstrate that the rate of pressure propagation for pre‐Darcy flow is slower than that for Darcy flow for the entire observation period, which corrects previous conclusions. This study is highly important for improving the understanding of fluid flow in low‐permeability media.

A unified macroscopic equation for creeping, inertial, transitional, and turbulent fluid flows through porous media

Over the course of several decades, numerous model equations of the macroscopic fluid flow through porous media have been proposed. The application of such equations is, however, often complicated due to the requirement of variant specifications of parameters and empirical factors for different flow regimes. It is, therefore, necessary and desirable to have a unified fundamental equation that is capable of predicting porous media flows for the entire spectrum of flow regimes that are practically encountered. This work aims to fulfill that requirement. With the aid of a hypothesis-based analysis, finite-element simulations, and published experimental data, a new macroscopic transport equation has been proposed to predict statistically stationary single-phase incompressible flows through a non-deformable stationary porous medium. The new model may be written as a drag law associated with a dimensionless resistance parameter that is a function of the porous medium geometry and the flow forces. Though complex, this resistance parameter may be modeled as a power function in terms of three predictable parameters. Overall, the proposed transport equation has been found to be a more extensive form of other key models in existence. Using approximately 6000 analytical, numerical, and experimental data points, the equation has been validated as an excellent model for creeping, inertial, transitional, and turbulent porous media flows. The results show that the proposed equation is applicable to simple and complex porous media of 30%–90% porosity. Moreover, a dimensionless group in terms of the equation's resistance parameter has been established as useful for scaling.

Visualization of Potential Flow: Dealing with the Branch Cuts

The theory of potential flow is important in several application fields, in particular: in aero dynamics, fluid dynamics, electrostatics, porous media flow. In the classical approach flow is described by a potential function of the complex plane into the complex plane. Using potential function contouring the visualizing of streamlines in flow nets can reveal important characteristics of the flow in question, for which alternative methods fail. However, branch cuts of important potential functions pose a problem for the visual representation. Here methods are outlined how to deal with the problem: (1) to be aware that equalities, common in real number algebra, may not hold in the complex number space; (2) to partition the complex plane into sub-domains on which the functions are evaluated sequentially. The description of the methods uses superpositions of complex logarithms as examples, but the ideas can be adopted for the visualisation to other potentials as well.

New Criteria to Estimate Local Thermal Nonequilibrium Conditions for Heat Transport in Porous Aquifers

AbstractA fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm.