Pressure In Porous Media Research Articles

Numerical study of CO2 trans-critical process inside micromodel based porous structures under supercritical pressures

Understanding the flow, heat transfer, and trans-critical process of carbon dioxide in porous media is crucial for various applications, including CO2 sequestration, soil remediation and oil and gas recovery, due to its unique physical properties in the critical region. In this study, a porous media model on a microfluidic chip structure was simulated to emphasize the heat transfer and trans-critical process of CO2 under supercritical pressure in porous media. The study aims to observe the behaviors of CO2 during its transition from subcritical to supercritical temperature under supercritical pressure. The main objective is to observe the temperature distribution and pressure change of CO2 in a porous media model under the influence of bottom heating. At the same time, we observe the changes in the position of the critical temperature point of CO2 in porous media and analyze its heat exchange process in porous media. After the flow reaches a steady state, the temperature span near the grains is 1.6 K, and the pressure drop per unit length is 1480.3 Pa/mm. As the flow time progresses, the critical temperature line migrates from outlet region to inlet region, the range of sCO2 narrows from 81.7 % to 84.7 % in the porous media region. Finally, the influence of different working conditions on the trans-critical region is studied. It is hoped that this study will contribute to the understanding of the trans-critical process of CO2 in porous media.

Note on a Novel Model for Capillary Pressure in Porous Media

Note on a Novel Model for Capillary Pressure in Porous Media

A Closed-Form Equation for Capillary Pressure in Porous Media for All Wettabilities

A saturation–capillary pressure relationship is proposed that is applicable for all wettabilities, including mixed-wet and oil-wet or hydrophobic media. This formulation is more flexible than existing correlations that only match water-wet data, while also allowing saturation to be written as a closed-form function of capillary pressure: we can determine capillary pressure explicitly from saturation, and vice versa. We propose Pc=A+Btanπ2-πSeCfor0≤Se≤1,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{{\ ext{c}}} = A + B\ an \\left( {\\frac{\\pi }{2} - \\pi S_{e}^{C} } \\right)\\,{\ ext{for}}\\,0 \\le S_{{\ ext{e}}} \\le 1,$$\\end{document}where S_{{text{e}}} is the normalized saturation. A indicates the wettability: A>0 is a water-wet medium, A<0 is hydrophobic while small A suggests mixed wettability. B represents the average curvature and pore-size distribution which can be much lower in mixed-wet compared to water-wet media with the same pore structure if the menisci are approximately minimal surfaces. C is an exponent that controls the inflection point in the capillary pressure and the asymptotic behaviour near end points. We match the model accurately to 29 datasets in the literature for water-wet, mixed-wet and hydrophobic media, including rocks, soils, bead and sand packs and fibrous materials with over four orders of magnitude difference in permeability and porosities from 20% to nearly 90%. We apply Leverett J-function scaling to make the expression for capillary pressure dimensionless and discuss the behaviour of analytical solutions for spontaneous imbibition.

Experimental and theoretical investigation of the migration and plugging of the particle in porous media based on elastic properties

Particle migration in porous media is of great significance in the areas of formation-water filtration and oil field development. The current theories and methods ignore the effect of particle elasticity on its flow resistance, which is the key point for particle parameters design toward reservoir profile control. Therefore, this paper focuses on the research on the migration process and flow resistance prediction of elastic particles in porous media. Based on the Hertzian contact theory, a migration and plugging model of the elastic particle in porous media is established. Then, core slice injection and microfluidic experiments were used to study the migration process of particles in porous media, which can provide an accurate coefficient for the migration and plugging model. And long core injection experiments were carried out using three kinds of elastic particles (3.7 μm, 8.4 μm, and 21.1 μm) to verify the accuracy of the model. The results show that elastic particles will form a filter cake within 3 cm of the injection end of the core. Combined with the microfluidic visualization experiment, the transport process of elastic particles in porous media can be summarized as the “Gathered and Energized” transport mode with three stages: particles accumulate at the injection end and increase the injection pressure, particles squeeze into the core, and particles deep migration. The migration and plugging model of elastic particles can predict its injection pressure in porous media, which is highly consistent with the experimental data, with an average error of 8.4%. When the reservoir permeability is constant, the injection pressure of elastic particles changes exponentially with the matching factor. In addition, the reservoir permeability also directly affects the injection pressure of elastic particles. When the permeability increases from 1.7 D to 6.0 D, the injection pressure decreases by >70%. This model provides a new method to study the migration of elastic particles in porous media and predict the flow resistance, which is of guiding significance to the bilateral matching design of elastic particles and reservoirs.

Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities

In this article we consider the numerical modeling and simulation via the phase field approach for coupled two-phase free flow and two-phase porous media flow of different densities and viscosities. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled by several domain interface conditions. It is showed that the coupled model satisfies an energy law. Then we first propose a coupled unconditionally stable finite element method for solving this model and analyze the energy stability for this method. Furthermore, based on the ideas of pressure stabilization and artificial compressibility, we propose an unconditionally stable time stepping method that decouples the computation of the phase field variable, the velocity and pressure of free flow, the velocity and pressure of porous media, hence significantly reduces the computational cost. The energy stability of this decoupled scheme with the finite element spatial discretization is rigorously established. We verify numerically that our schemes are convergent and energy-law preserving. Numerical experiments are also performed to illustrate the features of two-phase flows in the coupled free flow and porous media setting.

A Thermodynamic Analysis of the Impact of Temperature on the Capillary Pressure in Porous Media

AbstractA thermodynamic analysis of the capillary drainage, imbibition and hysteresis pressure in two‐phase porous media systems at different temperatures has been performed. Expressions for the work required or gained when the fluid saturations change, proportional to the capillary pressures, are presented. The expressions are determined using the criterion that changes in Helmholtz free energy equals zero at equilibrium. From these expressions, the variation of capillary drainage, imbibition and hysteresis pressures for increasing temperature are determined without calculating the actual capillary pressure values. The temperature dependency results show that the capillary drainage pressure declines with a fractional rate for increasing temperature with contribution from two terms, the air‐water interfacial tension and the entropy term, which give a total fractional reduction of −0.0082 K−1, close to the value −0.0084 K−1 found experimentally. The capillary imbibition pressure increases with a total fractional rate versus temperature equal +0.004 K−1 in line with the observation that water tables in soils are lifted upon day‐time heating. The total fractional temperature variation of the hysteresis capillary pressure term declines with a rate of −0.0143 K−1 for increasing temperature in qualitative agreement with experimental data. The results support the hypothesis that the thermodynamic approach applied under given assumptions can account for the major effects determining the temperature dependency of two‐phase capillary pressure in porous media. Furthermore, the entropy term adds an additional hysteresis term to the conventional term, even under isothermal conditions. The capillary pressure hysteresis phenomenon is therefore caused by two effects: Differences in interfacial areas including contact angle hysteresis plus the entropic contribution.

Frequency domain spectral element method for modelling poroelastic waves in 3-D anisotropic, heterogeneous and attenuative porous media

SUMMARY Simulating poroelastic waves in large-scale 3-D problems having porous media coupled with elastic solids and fluids is computationally challenging for traditional methods. It is well established that the spectral element method (SEM) is more effective than the traditional methods like the finite element method (FEM) when dealing with complex geophysical problems, for its high-order accuracy with exponential convergence. However, at present, little research has been done for SEM in the frequency domain, which will be more efficient than the time-domain SEM for narrowband simulations with multiple sources, material dispersion and attenuation. Herein, we systematically develop a SEM in the frequency domain to simulate coupled poroelastic, elastic and acoustic waves in anisotropic (i.e. porosity, permeability and elastic coefficients with anisotropy), heterogeneous, and lossy media. Furthermore, we completely remove the dimension inconsistency between the displacement field and the pressure in porous media to reduce the condition number of the system matrix by around 16 orders of magnitude while maintaining the symmetry of the system matrix. To solve the multiphysics coupling problems, we apply different coupling conditions to different interface types, and use basis functions to discretize the corresponding governing equations. Numerical examples show that the proposed SEM can obtain higher accuracy with much fewer unknowns compared with the FEM and has the capacity to solve the large-scale real coupling problems.

Pipe network modeling for analysis of flow in porous media

In this paper, a new matrix framework has been developed for the simulation of flow and pressure in porous media. In this framework, the pressure gradient formulation in Darcy’s law is considered as the head-loss equation in pipe network modeling. Then, an artificial pipe network has been constructed to find the pressure head profile in porous media. Two explicit and implicit formulations have been advanced for linear and nonlinear analysis, which the latter is an implementation of the Newton–Raphson algorithm. Both formulations iteratively solve a linear system of equations for calculating the nodal heads and apply a matrix multiplication for updating the flow vector. While the explicit method needs few iterations, the implicit method requires at least 20 iterations to converge with acceptable accuracy. For testing these formulations, four different types of network configurations were tested. The analysis of three laboratory tests showed that the application of the implicit method provides reliable and accurate results.

Non-hysteretic functional form of capillary pressure in porous media

Models of flow of two immiscible fluids in a porous medium overwhelmingly involve use of an equilibrium correlation between what is identified as capillary pressure and the saturation of one of the fluids. This correlation is said to be hysteretic with the functional relation depending on which of the two fluids has displaced the other in a flow scenario. This correlation was proposed when abilities to investigate porous medium systems experimentally for the distribution of fluids or using computer simulation were limited. Because of advances, we can now assert that the quantity called capillary pressure is ambiguously defined and the alleged hysteretic behaviour, even at equilibrium, is actually due to incompleteness in the functional dependence. We provide a path forward for a theoretically sound formulation that corrects the assertion that capillary pressure is a hysteretic function of saturation, and we advocate for moving beyond ingrained erroneous notions.

Numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure

In this paper, we propose and analyze the convergence of a TPFA (Two Points Flux Approximation) finite volume scheme to approximate the two incompressible phase flow with dynamic capillary pressure in porous media. The fully implicit scheme is based on nonstandard approximation on mobilities and capillary pressure on the dual mesh. We derive a discrete variational formulation and we present a new result of convergence in a two or three dimensional porous medium. In comparison with static capillary pressure, the non-equilibrium capillary model requires more powerful techniques; especially the discrete energy estimates are not standard.

Lattice Boltzmann simulation of resistance coefficient of the oil and water migration in porous media

The coefficients of oil and water transfer resistance in porous media are the basis of numerical study on the migration of contamination in the pipeline, soil cleaning, oilfield water flooding, and oilfield water treatment. Based on the quartet structure generation set, the porous media with random distribution are constructed. The lattice Boltzmann method is used to simulate the mesoscopic migration of oil and water in porous media. Then the distribution law of oil and water velocity and pressure in porous media is analyzed, and the fitting equations of oil and water resistance coefficients are obtained under different porosity. The results show that when the oil and water migrate in porous media, the viscous resistance coefficient is larger than the inertia resistance factor, and the viscosity resistance coefficient of water is obviously higher than that of oil, while the coefficient of inertia resistance of oil and water is nearly same.

Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow in porous media incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behavior. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks–Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.

Study on relations between porosity and damage in fractured rock mass

The porosity is often regarded as a linear function of fluid pressure in porous media and permeability is approximately looked as constants. However, for some scenarios such as unconsolidated sand beds, abnormal high pressured oil formation or large deformation of porous media for pore pressure dropped greatly, the change in porosity is not a linear function of fluid pressure in porous media, and permeability can't keep a constant yet. This paper mainly deals with the relationship between the damage variable and permeability properties of a deforming media, which can be considered as an exploratory attempt in this field.

Homogenization of two fluid flow in porous media.

The macroscopic behaviour of air and water in porous media is often approximated using Richards' equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e. constant gas pressure, this model is shown to reduce to the simpler form of Richards' equation. The starting point for this derivation is the Cahn–Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media with the underlying geometrical and material properties.

Mechanisms of surfactant-enhanced air sparging in different media

This article presents the results of a laboratory investigation of the mechanisms of surfactant-enhanced air sparging (SEAS) in different media. Two kinds of media (medium sand and gravel) were used in one-dimensional column experiments, designed to determine (1) the functional relationship between the air saturation and surface tension of water during SEAS, and (2) the contaminant removal mechanisms in different air travel modes (channels and bubbles) under different surface tension values. The results demonstrated that when air traveled in the form of channels, a decrease in surface tension accordingly reduced capillary pressure in porous media. Air saturation therefore increased, thereby considerably improving contaminant removal. The variations in removal efficiency under different surface tension values coincide with the trend of air saturation change. When air traveled in the form of bubbles, the SEAS-induced air saturation in the column was directly affected by foam stability and foamability, rather than by the surface tension of water. Surfactant addition improved only the contaminant removal rate, but the decrease in lingering concentration was insignificant. The results of this study can serve as theoretical bases for SEAS application in contaminated sites.

A Fractal Model for Capillary Pressure of Porous Media

Capillary pressure is a basic parameter in the study of the behavior of porous media containing two or more immiscible fluid phases. In this study, the capillary pressure of porous media is predicted based on based on fractal property of pore in porous media. The formula of calculating the capillary pressure of porous media is given. The capillary pressure of porous media is expressed as a function of porosity, fractal dimension of pore and saturation. Based on the parametric effect analysis, we conclude that the capillary pressure of porous media is negatively correlated with the porosity and saturation. Besides, it is shown that the capillary pressure of unsaturated porous media decreases with the increase of saturation. No additional empirical constant is introduced. This model contains less empirical constants than the conventional correlations. The model predictions are compared with the existing experimental data and good agreement between the model predictions and experimental data is found. The validity of the present fractal model is thus verified.

Experiments on foam texture under high pressure in porous media

Foam flooding has become one of the most effective methods to improve oil recovery in high water-cut oilfields. In order to obtain images of the texture of foam in the cores under high pressure, this paper developed an experimental real-time image acquisition device for detecting the foam's texture as the bubbles flowed in the porous media. Image processing and statistic analysis methods for describing the foam's texture were also established. Experimental results showed that the bubble distribution became homogeneous and stabilized, and the pressure difference between two ends of the core increased gradually during the process of foam flooding. In the initial stage, the bubbles presented a flake-like distribution. The liquid phase flowed continuously, as did the gas phase. As the displacement continued, the volume of a single bubble lessened, while the number of bubbles increased. When the bubbles reached a steady state, the pressure difference between the two ends of the core was stable, and the bubbles presented a uniform distribution. A larger injection rate, a higher core permeability and a larger gas–liquid ratio all can cause a larger-than-average bubble diameter, poor stability and a decreased degree of homogeneity.

Empirical Formula of Chemical Grouting Pressure in Porous Media Based on Similarity Theory

Based on similarity theory and model test, this paper proposes the empirical formula of chemical grouting pressure in porous media that mainly reflects the characteristics of grouting machine, grouting materials, and the propriety of geotechnical medium. This formula reflects the complex grouting process in a simple way. And the orthogonal experiment results indicate that the factors affecting grouting pressure are the permeability of rock mass, grout viscosity, and grouting pump flow. Based on the empirical formula, and according to the achievement in fluid mechanics, this paper further studies and proposes the empirical formula of grouting pressure influenced by pipelines

Study on fluid flow in nonlinear elastic porous media: Experimental and modeling approaches

A theoretical model for describing the changes in the porosity and permeability with fluid pressure in elastic deformed porous media was presented firstly. Secondly, the changes in porosity and permeability of sandstones were studied by experimental approach, and the exponential correlations between porosity, permeability and fluid pressure in porous media were obtained by regression based on these experimental data. Thirdly, based on the theory of nonlinear deformation of porous media and the continua theory on porous media and fluids, a fluid filtration mathematical model considering nonlinear elastic deformation of porous media was developed. To get insights into the performances of fluid flow in the media, exact analytical solutions of the nonlinear model were obtained by traveling-wave transmission. The main parameters were input to analyze the difference of the solutions and their effects on the characteristics of the fluid pressure distribution with space and time. It is found that the effect of nonlinear elastic deformation may lead to the nonlinear distribution of fluid pressure in porous media at one-dimensional case at a one-dimensional case. However, the distribution of fluid pressure in porous media is linear only when the pressure-dependent factors of pressure rock permeability, porosity, fluid density and viscosity satisfy a special correlation.

A Multiphase, Two-Fluid Model for Water Transport in a PEM Fuel Cell

A finite volume based computational method for predicting two-phase flows in fuel cells is presented. The model formulation and numerical algorithms are selected to provide robustness and accuracy, while allowing the treatment of important phenomena relevant to fuel cell water management such as segregation of the phases to form films and slugs in gas channels. Variations in the algorithms for computing pressure corrections and phase fractions are assessed using water-air flows in fuel cell channel geometries. The accuracy of the model is evaluated by comparison to benchmark simulations, measured pressure drop data for air-water flows, and analytical solutions for capillary pressure in porous media. The results indicate that the selected formulation is sufficiently stable and accurate to serve as the basis for a detailed model of water transport in fuel cells.