Fluids In Porous Media Research Articles

Analytical investigation of porous medium effects on the flow of two micropolar fluids in a rotating annulus

Fluids with microstructures and microinertia play a vital role in microfluidics and nanfluidics system. One of such significant fluid is micropolar fluid. The characteristic behavior of micropolar fluid flow in conduit/pipe, etc. filled with porous medium helps us understand the flow behavior of biological fluids in porous media, groundwater flow in aquifiers, rotatory machines or viscometer. To understand such real-world problems, it is necessary to get into the mathematical model of such flow models. One such model with wide number of application is presented in this paper. This work investigated the flow of two micropolar fluids between the region formed by two concentric cylinders. Authors have considered inner cylinder to be at rest and outer cylinder rotating at a constant angular velocity. The region between two concentric cylinder is filled with an isotropic porous material. A slip condition at the outer wall and continuity conditions at interface of two fluids has been utilized to obtain an analytical solution for the proposed model. The numerical solution of the obtained solution for present problem is used to graphically analyze the motion of immisicble micropolar fluids rotating in an annulus filled with the porous medium. It is found that an outer cylinder has a notable influence on the flow behavior of immiscible micropolar fluids, contrary to the effect observed within the inner region. An analytical approach of this work not only helps us obtain precise results and analysis of the flow, but it also serves as a useful validation for future approximations within the scope of this work.

An investigation of the behaviour of polymer fluids in the American Petroleum Institute filter press

The American Petroleum Institute (API) filter press test has been used for decades in the construction industry as part of the quality control regime for bentonite-based excavation support fluids. The industry has carried over the use of this test to polymer fluids despite the lack of published evidence of its suitability for these fluids and the very different mechanisms by which polymer fluids and bentonite slurries achieve excavation support. This paper presents the first systematic investigation of this issue through a combination of laboratory testing and theoretical analysis. The investigation demonstrates the very different behaviours of bentonite slurries and polymer fluids. In contrast to the results for bentonite slurries, API filter press results for polymers are shown to be highly sensitive to the filter paper used. In particular, repeatability testing revealed a substantial variation in the polymer fluid loss rates attributable to three primary factors: (a) the filter paper pore size; (b) filter paper damage resulting from the applied test pressure; (c) apparent ‘clogging’ of the filter paper pore space. Furthermore, the study demonstrates the poor repeatability of the API filter press test for polymer fluids even when filter papers of the same type are used. Interestingly, analysis of polymer flow with respect to filter paper pore size and the applied pressure showed that the filter papers were behaving as porous media rather than a simple bundle of capillaries; their behaviour could not be modelled using a simple capillary bundle model. Importantly, this finding shows that the filter press may provide a rapid method of assessing the apparent viscosity of polymer fluids in porous media at high shear rates – data that cannot be obtained by rotational viscometry, and would otherwise require resort to permeameter testing of coarse soils. The investigation demonstrates that the filter press test is not useful for the on-site quality control of polymer fluids but, given the theory presented in the paper, it can be a useful laboratory tool that provides valuable insight into polymer fluid flow behaviour in soils of high hydraulic conductivity, the most challenging soils for polymer fluid support.

A New model of gas-water two-phase seepage based on Newton's law of motion

The pore throat size, structure distribution, and lithology of porous media in gas reservoirs are varied, and the gas-water two-phase seepage law is complex, making it difficult to describe the seepage model. Newton's law of motion is a basic law of motion in classical mechanics, and its application in gas-water two-phase seepage modeling is an innovative practice of classical mechanics in seepage mechanics systems. Based on Newton's three laws of motion, a gas-water two-phase seepage model was established from the force analysis of fluid, and the relationship between velocity and pressure difference, pipe radius, water film thickness, viscosity, etc. was derived under the condition that the model reached a stable state, i.e., force balance. The relationship is referred to as the steady-state model. Subsequently. the equivalent permeability representation model was derived based on the steady-state model to calculate the permeability of rock samples with different channel distribution characteristics. The results were consistent with the measured values, and there is a good correspondence between channel distribution characteristics and permeability. The relative permeability calculation method was established based on the steady-state model and capillary pressure curve. The obtained relative permeability curve aligned with the two-phase seepage law and coincides with the relative permeability curve obtained by Poiseuille's law. Finally, a new productivity equation was derived based on the steady-state model, and the Inflow Performance Relationship (IPR) curve calculated by the gas well example was consistent with the traditional equation. The research results were based on the force analysis of fluid in porous media and fundamentally explored the law of fluid flow. The derived seepage model can be used to calculate reservoir permeability, the gas-water relative permeability curve, and gas well productivity analysis and to effectively guide gas reservoir development. The study was a successful application of the basic theory of mechanics in gas-water two-phase seepage in gas reservoirs.

A simple model incorporating foam rheology to quantify foam penetration behaviour in EPB shield tunnelling

Fulfilling the role of a soil conditioner, foam plays a pivotal role in Earth Pressure Balance (EPB) shield tunnelling by enhancing soil properties such as lowering permeability and increasing flowability. This study introduces a macro-model designed to quantify foam penetration behaviour in saturated sand, utilising rheological properties. To validate this model, experiments were conducted to replicate the foam penetration behaviour. Six sand beds characterised by varying particle sizes, along with foam having an expansion ratio of fifteen, were employed for penetration tests under different hydraulic conditions utilising a sand column device. The rheological profile of the foam is described by the power-law model, as also found by rheometer tests, although with different parameters. The flow behaviour of foam within the sand column conforms to the flow equation that governs power-law fluids in porous media. The developed model effectively predicts the foam penetration process under varying hydraulic conditions compared with the experimental results. Furthermore, the fitting results of the experimental data indicate that the flow behaviour index of the foam remains approximately 0.09 across all tests, regardless of the type of sand used. In contrast, the model-derived generalised permeability coefficient strongly correlates with the effective particle size (d10) of the sand bed. Overall, the model effectively quantifies the foam penetration behaviour, accounting for changes in infiltration velocity and pore water pressure, which is essential for understanding the transfer of support pressure in EPB shield tunnelling.

Fractal permeability model for power-law fluids in embedded tree-like branching networks based on the fractional-derivative theory

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Reflection and transmission characteristic waves on the periodic rough interface of fluid-porous medium

Abstract Nondestructive testing (NDT) is a major method in practical applications such as material exploration and safety assessment. The interaction of ultrasonic waves with roughness material is crucial in NDT, thus the related ultrasonic diffraction theory at the rough interface is widely investigated and analyzed, especially for the periodic elastic medium interface. However, the actual surface is usually porous due to the long-term moisture infiltration. In this paper, the reflection and transmission characteristics of ultrasonic waves on the fluid-porous medium periodic rough surfaces are studied in details.

Convection heat and mass transfer of non-Newtonian fluids in porous media with Soret and Dufour effects using a two-sided space fractional derivative model

Non-Newtonian fluids within heterogeneous porous media may give rise to complex spatial energy and mass distributions owing to non-local mechanisms, the modeling of which remains unclear. This study investigates the natural convection heat and mass transfer of non-Newtonian fluids in porous media, considering the Soret and Dufour effects. A strongly coupled model is developed to quantify the coupled transport of energy and reactive pollutants with the non-Newtonian fluid. The constitutive equation for the non-Newtonian fluid is described by a two-sided Caputo type space fractional velocity gradient. The governing equation, with a symmetric diffusion term, is effectively solved using a stable and convergent shifted Grünwald–Letnikov formula. The influences of three important parameters, which are the average skin friction coefficient, the average Nusselt number, and the Sherwood number, on fluid heat and mass transfer are calculated and analyzed. Numerical results reveal a significant interaction between the fractional derivative and the buoyancy ratio number, both of which affect the average skin friction coefficient. Furthermore, the average Nusselt number increases with the Dufour number while decreasing with the average Sherwood number. These findings enhance our understandings of the dynamics of energy and mass co-transport in non-Newtonian fluids, particularly in relation to their constitutive equation featuring spatial non-local properties.

Molecular Modes Elucidate the Nuclear Magnetic Resonance Relaxation of Viscous Fluids.

The Bloembergen, Purcell, and Pound (BPP) theory of nuclear magnetic resonance (NMR) relaxation in fluids dating back to 1948 continues to be the linchpin in interpreting NMR relaxation data in applications ranging from characterizing fluids in porous media to medical imaging (MRI). The BPP theory is founded on assuming molecules are hard spheres with 1H-1H dipole pairs reorienting randomly; assumptions that are severe in light of modern understanding of liquids. Nevertheless, it is intriguing to this day that the BPP theory was consistent with the original experimental data for glycerol, a hydrogen-bonding molecular fluid for which the hard-sphere-rigid-dipole assumption is inapplicable. To better understand this incongruity, atomistic molecular simulations are used to compute 1H NMR T1 relaxation dispersion (i.e., frequency dependence) in two contrasting cases: glycerol, and a (non hydrogen-bonding) viscosity standard. At high viscosities, simulations predict distinct functional forms of T1 for glycerol compared to the viscosity standard, in agreement with modern measurements, yet both in contrast to BPP theory. The cause of these departures from BPP theory is elucidated, without assuming any relaxation models and without any free parameters, by decomposing the simulated T1 response into dynamic molecular modes for both intramolecular and intermolecular interactions. The decomposition into dynamic molecular modes provides an alternative framework to understand the physics of NMR relaxation for viscous fluids.

A comparative study of exact and neural network models for wave‐induced multiphase flow in nonuniform geometries: Application of Levenberg–Marquardt neural networks

AbstractMultiphase fluids exhibit immiscible, heterogeneous structures like emulsions, foams, and suspensions. Their complex rheology arises from relative phase proportions, interfacial interactions, and component properties. Consequently, they demonstrate nonlinear effects—shear‐thinning, viscoelasticity, and yield stress. Peristalsis generates fluid flow by propagating contraction waves along channel walls. This mechanism can effectively transport multiphase and non‐Newtonian fluids in microsystems. Accurate modeling requires considering evolving phase relations, variable viscosity, slip, and particle migration anomalies, using approaches like homogenization theory or volume‐averaging. Applications include peristaltic pumping of emulsified biopharmaceuticals, microscale mixing/separating of multiphase constituents, and enhancing porous media fluid flow in oil reservoirs. Analytical and computational approaches to modeling multiphase fluid flows in peristaltic conduits provide an enhanced understanding of their complex dynamics, toward innovating engineering systems. An analytical approach is taken to model non‐Newtonian Ree‐Eyring fluid flows in asymmetric, peristaltic systems. Governing differential equations incorporate key parameters and yield closed‐form solutions for velocity, flow rate, and permeability. Suitable assumptions of long wavelength, and low Reynolds number provide accuracy. In parallel, an artificial neural network (ANN) is developed using supervised learning to predict permeability. The inputs consist of channel asymmetry, Reynolds number, amplitude ratio, and other physical factors. Outcomes validate both methodologies—analytical equations derive precise relationships from first principles, while ANNs reliably learn the system patterns from input‐output data. Additionally, ANNs can tackle more complex fluid dynamics problems with speed and adaptability. Their promising role is highlighted in developing new fluid models, improving the efficiency of simulations, and designing control systems. Side‐by‐side analytical and ANN simulation plots will further highlight ANN capabilities in emulating the system characteristics. This paves the path for employing machine learning to investigate multifaceted flows in flexible, peristaltic systems at scale. Performing a graphical examination of the engineering skin friction coefficient across a range of parameters, encompassing volume fraction, first and second order slip, Ree–Eyring fluid attributes, and permeability.

Computational study on torsional Casson fluid flow through concentric cylinders in a porous medium

The aim of this article is to gain a better knowledge of the non-Newtonian features of Casson fluid flow under torsional motion through two concentric cylinders in a porous medium. This study is crucial because it has the ability to control the flow characteristics of Casson fluids in porous media using rotating cylinders for the optimization of industrial processes. The flow-narrating differential equations are converted into a set of nonlinear differential equations. To obtain numerical results to flow problem, a computational model is developed. Numerical solutions are acquired employing the fourth-order exactness programme (Bvp4c), and findings are validated by comparing them to the Runge-Kutta fourth-order approach. Consequences of various distinct parameters for fluid flow and heat transfer are interpreted in graphical and tabular form. It is found that both fluid velocity and temperature increase with growing inputs of outer angular velocity (0.3≤Ω2≤0.9). Skin friction coefficient (CfsTa) is observed to decline in the case when both cylinders are rotating in same direction (Ω1=0.7andΩ2=0.7) with enhanced inputs of Hartmann number (0.5≤Ha≤2.0), while Nusselt number (Nus) profiles are enhanced with rising inputs of the Forchheimer parameter (0.2≤Fr≤0.8) when both cylinders are rotating in opposite direction (Ω1=0.7andΩ2≤−0.7).

Capillary pressure profile estimation using numerical method and centrifuge test data

Capillary pressure is a crucial parameter that affects the displacement of two or more immiscible fluids in porous media. Measuring capillary pressure as a function of saturation is essential for simulating the process of immiscible flooding in porous media, especially in oil reservoir rocks. The centrifuge method is one of the most widely used techniques for estimating capillary pressure in reservoir rock porous media. This study applied a numerical method to a one-dimensional equation with boundary conditions to simulate the flow of two immiscible fluids in the core plug for a centrifuge experiment. The study also tested oil-water and air-oil systems across various core plugs using a centrifuge device. It involved analyzing the experimental data output through a numerical calculation method to derive the capillary pressure correlation as a function of saturation. The correlation obtained for capillary pressure demonstrates an acceptable match with the experimental data and is applicable in other simulation software.

Machine Learning Assisted Prediction of Porosity and Related Properties Using Digital Rock Images.

Accurately estimating reservoir rock properties is paramount for modeling the storage and flow of fluids (hydrocarbon, carbon dioxide, and groundwater) in porous media. However, existing laboratory techniques to measure rock properties are usually time-consuming, expensive, and computationally intensive. This work proposes an efficient workflow that uses the machine learning algorithm, based on the convolutional neural network (CNN) framework, to predict rock properties from microcomputed tomography (micro-CT) X-ray images. The workflow involves data preprocessing, label extraction, training, and prediction using the segmented images of the rock to predict porosity, throat area, and pore surface area, which are essential for pore-scale modeling. The model was trained and validated on the Bentheimer sandstone, which was then used to predict properties of other sandstones (Castlegate and Leopard) with different pore structures and flow properties. The model yielded a good prediction for the throat and pore surface area but a significant error for porosity. Subsequently, a new complex model was trained and validated using diverse images from Bentheimer and an additional rock Castlegate, which was then used to predict the properties of Leopard sandstone. The new model improved the prediction of each property, resulting in mean absolute percentage error (MAPE) values of 2.19%, 3.04%, and 6.08% for porosity, pore surface area, and throat area with the binary images, respectively. In addition, we present a novel data-driven method using a simple regression model to predict the absolute permeability of a digital rock sample using the pore network parameters as predictors. The extreme gradient boost (XGBoost), which performed the best among several machine algorithms, was trained and validated using digital rock images from Bentheimer and Castlegate sandstone. The generated model was then used to predict the absolute permeability of the Leopard sandstone with an R 2 of 0.813, which was a significant improvement over the model generated solely by using either the Bentheimer or the Castlegate sandstone images. Furthermore, our analysis showed that the tortuosity had the most significant effect on the absolute permeability prediction of the rock sample. This study showed that we can reliably predict the morphological properties of porous media using computationally efficient models generated from digital rock images, which can be used to build a regression model to predict the crucial petrophysical properties needed to model the flow of fluids in porous media.

Influence of the imposed flow rate boundary condition on the flow of Bingham fluid in porous media

Influence of the imposed flow rate boundary condition on the flow of Bingham fluid in porous media

General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media

A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence.Graphical abstract

Submodels of 2-d model of the motion of fluid or gas in a porous medium with an external non-stationary source or absorption

The motion of fluid or gas in a porous medium is the main object of investigation of underground hydromechanics. The model describing this motion was called “Porous medium”.In our paper, we study a general 2-d model of the motion of fluid or gas in porous medium with an external non-stationary source or absorption. As the main research method, we use the method of group (symmetry) analysis, which is one of the most effective ways to obtain information about the properties of solutions to differential equations that define a physical model. A group classification of the differential equation defining studied physical model is carried out. As a result, all basic models with different symmetry properties are obtained. For the basic model, which admits the widest group a classification of all its invariant submodels is performed and all invariant submodels, defined by invariant solutions of rank 1 are studied. All solutions found have physical meaning.The set of explicitly found solutions forms a 47-parametric family of exact solutions. Each solution in this family depends on an arbitrary function defining an external non-stationary source or absorption. For each solution, for the specific values of the parameters on which it depends and for this specific function, we obtained a graph of the pressure distribution.Other solutions are used to describe the movement of a liquid or gas if either the pressure and its rate of change, or the pressure and one of its gradient components, are given at an initial time at a fixed point. The set of these solutions depends on 13 parameters and a function defining an external non-stationary source or absorption. For specific values of this function and specific values of the parameters on which each solution depends, the existence and uniqueness of a solution to the corresponding boundary value problem under some additional conditions has been established. Each such problem is solved numerically. The results of these decisions we reflected in the graphs.The significance of obtained solutions lies in the fact that we have obtained a database consisting of two multiparameter families of invariant solutions of rank 1 of the equation describing the motion of fluid or gas in a porous medium in the presence of an external non-stationary source or absorption. Every solution depends on an empirically determined function. These solutions describe specific physical processes. They can also be used as test solutions in numerical calculations related to the study of the motion of fluid or gas in a porous medium during fluids filtering, engineering surveys in the construction of building structures and in the extraction of shale oil or gas.

Blind zones in radiating dispersion at high Péclet number driven by non-Newtonian fluids in porous media

A wide range of environmental, energy, medical and biological processes rely on dispersive transport through complex media. Yet, because of the stagnant and opaque nature of the microscopic system, the role of disordered flow and structure in the dispersive transport of solutes remains poorly understood. Here, we use a circular porous microfluidic system to investigate the radial dispersion in porous media driven by non-Newtonian fluids with strong advection rate (or at high Péclet number) and low-to-moderate Reynolds numbers. We observe for the first time the presence of diffusion ‘blind zones’ in the microstructure for high solution injection velocities. More specifically, an in-depth analysis uncovers that the circumferential flow frame, coformed by obstacles and vortices especially the ‘twin-vortex’ with same rotation direction, is responsible for the diffusion ‘blind zones’ and transport heterogeneity. The vortices are induced by the coupling of microfluidics and porous structures, and correlated to inertial flow-induced instabilities. The trade-off between diffusion efficiency and quality/completeness with respect to the high Péclet number (or high inlet velocity) serves to enhance our comprehension of intricate fluid dynamics and affords a set of principles to aid a diverse range of practical implementations.

Framework for simulating the partially miscible multi-component hydrocarbon fluids in porous media via the pseudo-potential lattice Boltzmann model

framework for simulating the partially miscible multi-component hydrocarbon fluids in porous media via the pseudo-potential lattice Boltzmann model

Hydraulic tortuosity of porous media: comparison of different modeling methods

Abstract Hydraulic tortuosity is a crucial parameter affecting the movement of fluid in porous media. Currently, researchers have used different methods to construct porous media models and studied the variation of hydraulic tortuosity with porosity. In this paper, we use Monte Carlo random particle, quartet structure generation set (QSGS), and CT-scan reconstruction to construct porous media models with different porosity. The finite element method is used to simulate the fluid passing through the models. The effectiveness of the QSGS algorithm in constructing porous media is verified. The hydraulic tortuosity of the three types of model is computed using the streamline length ratio method, and its variation law with porosity is explored. The results show that the change law of the three models is consistent. The law of power function change is satisfied between the two for all models, which means the increase in porosity causes a decrease in tortuosity. Different models are constructed to explore the effect of tortuosity on permeability. An increase in tortuosity results in a smaller permeability when other conditions are equal. This paper aims to provide effective methods for constructing porous media models and a reference for studying hydraulic tortuosity.

Study of the Flow Field and Permeability Characteristics in the Goaf using the OpenPNM Package

The roof-caving step scale goaf behind the working face is sensitive to the region’s spontaneous combustion and gas concentration distribution, including many rock block cracks and holes. A severe deviation from the dynamics of fluids in porous media by representative element volume (REV), leading to the results of Computational Fluid Dynamics (CFD) simulation, has a significant error. A heterogeneous two-dimensional pore network model was established to simulate the goaf flow accurately. The network was first created using the simple cubic lattice in the OpenPNM package, and the spatial distribution of the “O-ring” bulking factor was mapped to the network. The bulking factor and Weibull distribution were combined to produce the size distribution of the pore and throat in the network. The constructed pore network model was performed with single-phase flow simulations. The study determined the pore structure parameters of the pore network through the goaf’s risked falling characteristics and described the flow field’s distribution characteristics in the goaf. The permeability coefficient increases as pore diameter, throat diameter, pore volume and throat volume increase and increases as throat length decreases. The correlation between throat volume and permeability coefficient is the highest, which indicates that the whole throat is the main control factor governing the air transport capacity in the goaf. These results may provide some guidelines for controlling thermodynamic disasters in the goaf.

Multiplex vortex instability in the flow of non-Newtonian fluids through microcavity arrays

Complex fluids always possess obvious non-Newtonian properties that facilitate the occurrence and development of vortex instability in porous media, which is of critical significance in many natural and industrial processes. It is widely known that this flow instability is regulated by both fluid flow and solid structure. However, the quantitative understanding of how structural characteristics of porous space affect the evolution of vortex instability is still nascent, especially in the case of fluids with varying rheological properties. Herein, the flow of polymer solutions with distinct non-Newtonian properties through microcavity arrays is experimentally studied, by which we systematically explore the effect of structural parameters of the cavity array on vortex instability. We find that, for both Newtonian and shear-thinning fluids with negligible elasticity, the vortex evolution behavior in each cavity of the cavity array is identical to those in an isolated cavity. In contrast, for viscoelastic fluids, the vortex instability is visibly affected by cavity number and cavity–cavity interval, and this effect exhibits different forms when the fluid shear-thinning participates or not. Multiplex vortex instabilities are observed under these tested conditions. By multiplex, we mean the vortex formation dynamics and evolution patterns are diversified. These unusual evolution phenomena are then interpreted in terms of the interplay between the elongation and relaxation of polymers as they navigate among neighboring cavities. These results can help us to further understand the flow instability of complex fluids in porous media and evoke new strategies for microfluidic applications of efficient mixing.