Flow In Porous Media Research Articles

Variable Temperature Plate Heat Transfer: MHD Fluid Natural Convection Flow in Porous Medium

The heat transfer from a variable temperature plate has been studied under the presence of porous medium and MHD fluid. Solutions for flat plate in porous medium are usually numeric, in this work an exact solution is found. Free convection governing equations were nondimensionalized and solved using Laplace transform. Exact solutions for the dependent non-dimensional variables were obtained. Velocity and temperature solutions that satisfy the governing equations and exponential boundary conditions were validated with a special case from the existing literature and found to be in good agreement. The temperature and velocity distributions within the porous medium were analysed for different non-dimensional numbers such as Prandtl number and Grashof number and for Newtonian and non-Newtonian fluids. It has been found that the Pr number decreases the velocity variation as a result of the increased viscosity. Higher Grashof number increases the velocity variation for the extra potential it supplies in the momentum equation. Heat generation term raises the dimensionless temperature variation in the energy equation, in its turn the dimensionless temperature increases the velocity variation.

Fractional analysis of time-fractional Emden–Fowler model arising in fluid flow of porous media and physical sciences

The concept of time-fractional Emden–Fowler (EF) model is used to describe the fluid flow in porous media, where the flow displays fractional-order behavior due to intricate microstructures. This study aims to analyze the fractional analysis of a linear and nonlinear time-fractional EF model, in which the fractional derivatives are taken in the Caputo form. We establish the Sumudu perturbation transform method (SPTM) by combining the Sumudu transform (ST) with the homotopy perturbation method (HPM). The ST discretizes the fractional-order model to a Sumudu space where the utilization of HPM handles the nonlinear parameters in the recurrence relation very effectively. We provide two numerical tests of the time-fractional EF model to check the legitimacy and reliability of the suggested scheme. The derived outcomes by SPTM enhance the excellence over a longer period by reducing the parameters of the truncated series. Some graphical representations at different fractional orders are provided to validate our proposed scheme. This approach offers a clear and concise procedure with symbolic computation to derive the series results which converge very promptly.

A class of high-order physics-preserving schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media

A class of high-order physics-preserving schemes for thermodynamically consistent model of incompressible and immiscible two-phase flow in porous media

A universal structure of neural network for predicting heat, flow and mass transport in various three-dimensional porous media

A universal structure of neural network for predicting heat, flow and mass transport in various three-dimensional porous media

Simulation of CO2–water two‐phase fluid displacement characteristics based on the phase field method

AbstractThe two‐phase flow in porous media is affected by multiple factors. In the present study, a two‐dimensional numerical model of porous media was developed using the actual pore structure of the core sample. The phase field method was utilized to simulate the impact of displacement velocity, the water–gas viscosity ratio, and the density ratio on the flow behavior of two‐phase fluids in porous media. The effectiveness of displacement was evaluated by analyzing CO2 saturation levels. The results indicate that the saturation of CO2 in porous media increased as the displacement velocity increased. When the displacement velocity exceeded 0.01 m/s, there was a corresponding increase in CO2 saturation. Conversely, when the displacement velocity was below this threshold, the impact on CO2 saturation was minimal. An “inflection point,” M3, was present in the viscosity ratio. When the viscosity of CO2 is less than 8.937 × 10−5 Pa·s (viscosity ratio below M3), variations in the viscosity of CO2 had little impact on its saturation. Conversely, when the viscosity of CO2 exceeded 8.937 × 10−5 Pa·s (viscosity ratio greater than M3), saturation increased with an increase in the viscosity ratio. In terms of the density ratio, the saturation of CO2 increased monotonically with an increase in the density ratio. Similarly, increasing density ratios resulted in a monotonic increase in CO2 saturation, though this trend was less pronounced in numerical simulations. Analysis results of displacement within dead‐end pores using pressure and velocity diagrams reveal eddy currents as contributing factors. Finally, the impact of pore throat structure on the formation of dominant channels was examined.

Stefan blowing effects on forced convective chemically reactive nanofluid flow over a porous plate in Darcy-Forchheimer porous medium

Darcy-Forchheimer model is used in several areas for designing the infiltration of drainage system, enhanced oil recovery, fuel injection system in automobile and aerodynamics and many others. Motivated by these uses, present work aims to investigate the forced convective slip flow and heat transmissions in a two-dimensional Darcy-Forchheimer porous medium under the influences of Stefan suction(blowing) and convective boundary conditions. In the energy equation heat source/sink and in concentration equation first-order chemical reaction are incorporated. Two phase model for nanofluid that includes Brownian motion and thermophoresis has been considered. These make the mathematical model of flow more realistic and valuable. Interestingly, there exists self-similar solutions of the leading equations under suitable approach. Numerical solutions are obtained for the self-similar nonlinear ordinary differential equations. The fourth order Runge-Kutta (RK-4) method associated with the Shooting technique is used on the converted equations to obtain numerical solutions. The thorough discussions and demonstrations of effects involving fluid and medium parameters on velocity, temperature and concentration similar solutions are attained systematically. It reveals that the reduction of velocity boundary layer is found to increase for both permeability and inertial parameters. On the other hand, temperature is decreasing in this situation. However, concentration rises at first but diminishes after crossing over point. Temperature increase is noticed as heat source/sink parameter rises. Fluid velocity is enhanced, whereas, temperature and concentration both diminish within the boundary layer for the rising values of permeability parameter and inertial parameter of the porous medium. With the rise in Stefan blowing parameter, fluid velocity reduces but temperature and concentration both are found to rise. Other parameters including the impacts of chemical reaction and boundary slip have been explored. Finally, the physical explanations are provided as far as practicable.

Kinetic modeling and CFD simulation of in-situ heavy oil upgrading using batch reactors and porous media

The depletion of conventional oil reserves and rising global energy demand necessitate efficient extraction methods for unconventional resources like heavy oil. This study successfully applies the coupling of chemical reaction kinetics with fluid dynamics in porous media for in-situ heavy oil upgrading, extending existing models to dynamic conditions. Using advanced kinetic modeling and Computational Fluid Dynamics (CFD), catalytic reactions are analyzed employing a Ni–W–Mo catalyst. The primary aim of this study is to investigate the effects of temperature, oil composition, and residence time on the upgrading process and the resulting product distribution. Simulations were first performed in a non-porous batch reactor to identify optimal reaction conditions, followed by modeling reactive flow in porous media to better simulate real-world reservoir conditions. The results show that temperature and residence time significantly influence conversion rates and product yields, with a 30% increase in lighter hydrocarbon production as the reaction temperature is raised from 575 to 700 K. These findings emphasize the importance of dynamic modeling in optimizing in-situ upgrading processes and provide insights into improving unconventional oil recovery techniques. This research provides a comprehensive framework to enhance the understanding of complex chemical and hydrodynamic interactions in porous media, contributing to the development of more effective oil recovery strategies for unconventional resources.

Numerical analysis of time-fractional MHD prandtl fluid flow in porous media using radial basis functions and Crank–Nicolson scheme

In this study, the magnetohydrodynamic (MHD) flow of a Prandtl fluid through a porous medium confined between two parallel plates is investigated. The lower plate is stationary, while the upper plate exhibits oscillatory motion. A novel numerical approach is employed, combining radial basis function (RBF) collocation with the Crank–Nicolson scheme to solve the time-fractional partial differential equation governed by the Caputo fractional derivative. The method’s robustness and accuracy are demonstrated through detailed numerical results, emphasizing the influence of key parameters such as the MHD parameter, Prandtl fluid parameter, porous medium parameter and fractional derivative orders. Graphical illustrations highlight the dynamic interplay between these parameters and the fractional behavior, offering deeper insights into the impact of fractionality on fluid flow characteristics.

Contour analysis for entropy generation in stagnation point of EMHD tangent hyperbolic nanofluid over dual stratified porous stretching sheet

Purpose The analysis of stagnation point in non-Newtonian fluid is of considerable interest among the scientific communities; however, very few studies are reported on double-stratified porous mediums. This paper aims to elucidate electromagnetohydrodynamic hyperbolic tangent nanofluid. Thermal and solutal stratification effects are considered and stagnant flow in porous medium adds more intricacy and novelty to the findings, which contribute to understanding specific structural designs of aircraft and transport modelling, groundwater contamination and bio-energy production. Entropy generation analysis adds intensification of heat transfer. Design/methodology/approach Fifth-order Runge–Kutta–Fehlberg method via shooting technique is used to solve highly nonlinear ODEs. Numerical analysis to understand the nature of surface drag force, local Nusselt number and Sherwood number with various parameters are incorporated. Findings Key findings reveal that a temperature and concentration profile diminishes with increasing stratification parameter. Heat transfer rate rises by 17.8% due to the Prandtl number, whereas mass transfer rate increases as 108.5% due to thermophoresis parameter. Furthermore, systems entropy generation reduced by 10.77% while increasing power law index parameter and porous parameter. Originality/value The concept of stratified scenarios represents a significant advancement, appearing across diverse natural and engineering systems such as oceanography, geophysics and environmental science. Minimizing total entropy production is essential for enhancing efficiency and achieving superior outcomes in numerous engineering applications.

Effects of Nonlinear Thermal Density Variation and Radiation on MHD Mixed Convection Through a Porous Medium Over a Permeable Vertical Plate: A Numerical Approach

ABSTRACTIn the present paper, we study the effect of nonlinear thermal radiation on magnetohydrodynamic (MHD) flow through a porous medium subject to a convective boundary condition over a permeable vertical plate. The Boussinesq approximation is used to predict nonlinear density variation with temperature (NDT), which enhances thermal transport. Similarity transformations facilitate the conversion of the governing nonlinear partial differential equations into nonlinear ordinary differential equations, enabling further analysis. The solutions are obtained and presented graphically using the bvp4c method in MATLAB. The primary objective of our study is to analyze the effects of suction/injection, NDT, and nonlinear thermal radiation on MHD flow dynamics and temperature distribution. The conclusions reveal that the nonlinear Boussinesq approximation parameter and Grashof number enhance buoyancy forces, increasing velocity boundary layer thickness and improving heat dissipation. Higher nonlinear thermal radiation raises fluid temperature, reduces viscosity, and thickens both boundary layers. Suction enhances flow stability by thinning boundary layers and facilitating efficient heat transfer, whereas strong injection increases the boundary layer thickness, retains heat, and disrupts flow stability. A higher magnetic parameter slows velocity more in suction and thickens the thermal boundary layer in injection. A greater Prandtl number reduces boundary layer thickness and enhances the Nusselt number, while a higher convective heat transfer parameter increases both boundary layer thickness and skin friction in suction. We have compared our numerical results with those of previous studies and observed an excellent agreement. The novelty of this study lies in its unique approach to modeling nonlinear thermal radiation, suction/injection, and its impact on MHD flow and heat transfer in porous media. The findings have practical implications for various engineering fields, including energy systems, aerospace, biomedical engineering, chemical processing, and environmental engineering, contributing to the optimization of heat transfer in technological applications.

Characterization of N2 foam flow with in-situ capillarypressure measurements in a high-permeability homogeneous sandpack: effect of surfactant concentration and flowrate

Determining the capillary pressure during foam flow in porous media is important because bubbles are thought to coalesce by lamella rupture as the "limiting capillary pressure" is approached. In this study, the role of surfactant concentration on capillary pressure and apparent viscosity of a foam flowing, at different flowrates, through porous media was explored. An in-house capillary-pressure probe was constructed, and it was utilized to characterize the capillary pressure of a foam flowing in a 145-Darcy homogenous sandpack. In-situ capillary pressures were determined for seven foam-quality-scan experiments with different gas velocities and surfactant concentrations. By comparing the test results, collected under different flowrates and surfactant concentrations, the apparent viscosity and the capillary pressure decreased for a quality greater than the transition foam quality, at the peak of apparent viscosity. The transition foam quality increases with increasing surfactant concentration and flow rate. For the slowest velocity, a minimum surfactant concentration is required to generate strong foam. While above this minimum surfactant concentration, foam-apparent viscosity is similar for different surfactant concentrations at the same velocity.

Gradient flows of interacting Laguerre cells as discrete porous media flows

Gradient flows of interacting Laguerre cells as discrete porous media flows

A two-stage computational approach for stochastic Darcy-forchheimer non-newtonian flows

The study of stochastic non-Newtonian fluid flows in porous media has significant applications in engineering and scientific fields, particularly in geophysical transport, biomedical flows, and industrial filtration systems. This research develops a high-order numerical scheme to solve deterministic and stochastic partial differential equations governing the Darcy–Forchheimer flow of Williamson fluid over a stationary sheet. This study aims to formulate and validate a computationally efficient two-stage method that accurately captures the effects of non-Newtonian behavior, porous media resistance, and stochastic perturbations. The proposed two-stage numerical method integrates a modified time integrator with a second-stage Runge-Kutta scheme, ensuring second-order accuracy in time for deterministic problems. The Euler-Maruyama approach handles Wiener processes for stochastic models, providing robust performance under random fluctuations. A compact sixth-order spatial discretization scheme enhances solution accuracy while maintaining computational efficiency. Numerical experiments, including Stokes’ first problem, demonstrate the superior accuracy and reliability of the proposed method compared to existing second-order Runge-Kutta schemes. The results confirm that the technique effectively captures complex interactions between deterministic and stochastic effects while significantly improving computational efficiency. This study advances numerical techniques for stochastic fluid dynamics, providing a practical framework for modeling and analyzing non-Newtonian fluid flows in porous media with real-world applications in engineering, geophysics, and industrial systems.

Gravity stabilized drainage in porous media with controlled disorder

This work presents an experimental, numerical, and theoretical investigation of slow drainage processes in porous media, focusing on systematic variations in pore-scale disorder. We examine a system comprising a monolayer of cylinders in a quasi-two-dimensional (2D) geometry, where the medium's disorder is controlled via a disorder parameter, ε. By systematically altering ε, we randomly shift the positions of the cylinders and analyze the resulting effects on the gravity stabilized invasion front. Our results show that increasing ε has a significant impact on the stable width of the invasion front, with this width scaling with the disorder parameter according to an exponent β=0.57, which closely matches the theoretical value predicted by percolation theory for 2D systems. Additionally, we derive a reciprocal relationship between the dimensionless fluctuation number and the disorder parameter ε. Moreover, we find a correlation between the invasion front width and the size of trapped clusters in the system, and we explore how pore disorder affects the air saturation left behind the invasion front. Both our experimental and numerical findings exhibit exponent values that align with theoretical scaling predictions. This study advances the current understanding of multiphase flows in porous media by specifically addressing the influence of pore-scale disorder on the morphology of invasion fronts. Published by the American Physical Society 2025

Microscopic simulations of oil–water two-phase flow in high-porosity and low-permeability carbonate porous media

The pore types in carbonate reservoirs are highly diverse, and a detailed characterization of the flow behavior of oil–water two-phase flow at the pore scale within different pore storage types holds significant importance. In this work, digital core reconstruction based on computed tomography scanning technology has quantitatively characterized the micro-pore structures of these rocks, and typical core samples representing diverse pore storage types have been selected for microscopic visualization simulation studies. Utilizing the volume of fluid method, we conducted visual simulations of oil–water two-phase flow in porous media. Comparisons were made under varying conditions of wettability, displacement pressure, and viscosity ratio regarding breakthrough time, residual oil distribution, and changes in residual oil saturation, revealing the dynamic flow characteristics of oil–water phases within different pore types during water flooding. The results demonstrate that complex pore-throat structures (large pores, small throats) significantly reduce the displacement efficiency during microscopic water flooding. Specifically, moldic pores exhibit high permeability, leading to oil phase retention; biological chamber pores (intraparticle pores) are characterized by the most pronounced high-porosity and low-permeability features, with numerous blind-end voids and poor connectivity, resulting in limited displacement effectiveness, whereas intergranular dissolution pores show good connectivity, achieving more efficient oil recovery. The mobility of the water phase among the three pore types follows the order: intergranular dissolution pores > moldic pores > biological chamber pores. Furthermore, improvements in wettability, increased displacement pressure, and reduced oil–water viscosity ratio serve to optimize the flow process at the microscopic level, thereby enhancing overall oil recovery efficiency.

Entropy optimization of MHD nanofluid flow in porous media over a stretching surface

Entropy optimization of MHD nanofluid flow in porous media over a stretching surface

Gravity‐dominated three‐phase flow in porous media

Gravity‐dominated three‐phase flow in porous media

Simulation on detachment and migration behaviors of mineral particles induced by fluid flow in porous media based on CFD-DEM

Simulation on detachment and migration behaviors of mineral particles induced by fluid flow in porous media based on CFD-DEM

Meshless spline-based DQ methods of high-dimensional space–time fractional advection–dispersion equations for fluid flow in heterogeneous porous media

Meshless spline-based DQ methods of high-dimensional space–time fractional advection–dispersion equations for fluid flow in heterogeneous porous media

Dual-fractal nuclear magnetic resonance to relative permeability conversion: A novel framework for multiphase flow characterization

Based on dual-fractal theory, this paper proposes a novel methodology to transform nuclear magnetic resonance (NMR) measurements into relative permeability model, thereby realized the challenge of accurately quantifying multiphase fluid flow in dual-fractal porous media. The novel relative permeability model integrates a multitude of parameters associated with the microscopic pore architecture of porous media. It can be verified through case studies that the newly constructed relative permeability model demonstrates excellent applicability. Furthermore, we have discovered a correlation between the segmentation characteristics of the relationship between the pore radius (r) and transverse relaxation time (T2) in low-permeability sandstone reservoirs and the number of peaks in the NMR curve. Specifically, the single-peak type can usually be divided into two segments, while the multi-peak type can generally be divided into three segments. The comprehensive fractal dimension (Dc) derived from the weighting method effectively captures the holistic core heterogeneity. The characteristics of small diameter pores are particularly sensitive to variations in the pore tortuosity fractal dimension (Dτ), the pore structure fractal dimension (Df), Dc, and ε (represents the pore size ratios). Given that the wetting phase preferentially occupies small pores, its relative permeability is significantly affected by these parameter changes. Conversely, the non-wetting phase mainly flows through large pores and is thus less influenced by changes in these parameters.