Fluids In Porous Media Research Articles

Solving Multiphysics, Multiparameter, Multimodal Inverse Problems: An Application to NMR Relaxation in Porous Media

A general and robust Bayesian optimization framework for the extraction of intrinsic physical properties from an integration of pore-scale forward modeling and experimental measurements of macroscopic system responses is developed. The efficiency of the scheme, which utilizes Gaussian process regression, enables the simultaneous extraction of multiple intrinsic physical properties with a minimal number of function evaluations. Here it is applied to nuclear magnetic resonance (NMR) relaxation responses, paving the way for inverse problem approaches to digital rock physics given its general nature. NMR relaxation responses of fluids in porous media may be described by sums of multiexponential decays resulting in a relaxation time distribution. The shape of this distribution is dependent on intrinsic physical system properties, but also effects like diffusion coupling between different relaxation regimes in heterogeneous porous materials. Forward models based on high-resolution images are employed to naturally incorporate structural heterogeneity and diffusive motion without limiting assumptions. Extracting the required multiple intrinsic parameters of the system poses an ill-conditioned multiphysics multiparameter inverse problem where multiple scales are covered by the underlying microstructure. Exploration of the multidimensional search space given an expensive cost function makes an efficient solution strategy mandatory. We propose a workflow to match experimental measurements with simulations via Bayesian optimization, with special attention paid to the multimodal nature of the topography of the objective function using solution space partitioning. A multimodal search strategy using state-of-the-art evolutionary algorithms and gradient-based optimization algorithms guarantees that the multimodal nature is captured. The workflow is demonstrated on ${T}_{2}$ relaxation responses of Bentheimer sandstone, extracting three physical parameters simultaneously: the surface relaxivity of quartz grains, the effective transverse relaxation time, and the effective diffusion coefficient in clay regions. Multiple mathematically sound and physically plausible solutions corresponding to global minimum and multiple local minima of the objective function are identified within a limited number of function evaluations. Importantly, the shape of the experimental ${T}_{2}$ distribution is recovered almost perfectly, enabling the use of classical interpretation techniques and local analysis of responses based on numerical simulation.

Geometric model of the fracture as a manifold immersed in porous media

In this work, we analyze the flow filtration process of slightly compressible fluids in porous media containing fractures with complex geometries. We model the coupled fracture-porous media system where the linear Darcy flow is considered in porous media and the nonlinear Forchheimer equation is used inside the fracture. We develop a model to examine the flow inside fractures with complex geometries and variable thickness on a Riemannian manifold. The fracture is represented as the normal variation of a surface immersed in R3. Using operators of Laplace–Beltrami type and geometric identities, we model an equation that describes the flow in the fracture. A reduced model is obtained as a low dimensional boundary value problem. We then couple the model with the porous media. Theoretical and numerical analyses have been performed to compare the solutions between the original geometric model and the reduced model in reservoirs containing fractures with complex geometries. We prove that the two solutions are close and, therefore, the reduced model can be effectively used in large scale simulators for long and thin fractures with complicated geometry.

Capillary equilibrium of bubbles in porous media

In geologic, biologic, and engineering porous media, bubbles (or droplets, ganglia) emerge in the aftermath of flow, phase change, or chemical reactions, where capillary equilibrium of bubbles significantly impacts the hydraulic, transport, and reactive processes. There has previously been great progress in general understanding of capillarity in porous media, but specific investigation into bubbles is lacking. Here, we propose a conceptual model of a bubble's capillary equilibrium associated with free energy inside a porous medium. We quantify the multistability and hysteretic behaviors of a bubble induced by multiple state variables and study the impacts of pore geometry and wettability. Surprisingly, our model provides a compact explanation of counterintuitive observations that bubble populations within porous media can be thermodynamically stable despite their large specific area by analyzing the relationship between free energy and bubble volume. This work provides a perspective for understanding dispersed fluids in porous media that is relevant to CO2 sequestration, petroleum recovery, and fuel cells, among other applications.

New Exact Traveling Wave Solutions for Fractional Order System Describing the Second Grade Fluid through Medium with Heat Transfer

The aim of this paper is to determine the time-dependent MHD fractionalized three-dimensional flow of viscoelastic fluid in porous medium with heat transfer by traveling wave solution. The governing nonlinear partial differential equations are altered by utilizing the wave parameter ξ = lx + my + nz + ωtβ/Γ(β+1) into ordinary differential equations. The exact solutions are attained by applying a traveling wave method for two different cases. Here we discuss some precise cases, the solution of MHD Newtonian fluid in porosity can be obtained by substituting α1 → 0 in general solution. The impact of important governing parameters on the movement of a fluid is examined as well as the comparison of Newtonian and non-viscous fluids have been made by 2D and 3D graphical analysis.

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods.

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid-fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. We discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

Pore-scale simulation of miscible viscous fingering with dissolution reaction in porous media

Global climate change is happening but may be mitigated by the technology of geological carbon dioxide (CO2) sequestration. To gain comprehensive insights into this approach, we perform pore-scale simulations of displacement between two miscible fluids in porous media using a new multiple-relaxation-time lattice Boltzmann model. This study marks the first attempt to investigate viscous fingering dynamics in miscible displacement, considering the coexistence of viscosity contrast and dissolution reaction. Simulation results capture different fingering patterns that depend on dissolution (Damköhler number Da), diffusion (Peclet number Pe), and viscosity contrast (viscosity ratio R). From simulations of unstable viscous flows, dissolution is found to delay fingering onset, slow down fingering propagation, and inhibit or reinforce the late-stage fingering intensity. In simulations with stable viscosity contrasts, the displacement features fingering phenomena when dissolution is fast enough. In addition, we conduct a parametric study to assess the impact of Pe, R, and Da. The results suggest that increasing Pe or R destabilizes fingering, but increasing Da first suppresses and gradually intensifies fingering. Finally, for every fixed Da, we determine the phase boundary between stable and unstable regimes in a Pe–R phase plane. A unified scaling law is developed to approximate boundary lines obtained under different Da values. By comparing reactive and nonreactive cases, we classify four distinct regimes: stable, unstable, reactive stable, and reactive unstable. These pore-scale insights are helpful in understanding and predicting the displacement stability during the geological CO2 sequestration, which is of importance to the pre-evaluation of the storage efficiency and safety.

Effect of electro-kinetic processes on filtration of fluids and gas in porous medium

The paper reviews the fluid and gas flow in the porous medium considering electro-kinetic phenomena – electro-phoresis and electro-osmosis, as well as the charges associated with them. These phenomena are due to the double electric layer on the border of division of disperse system phases. Electro-kinetic phenomena are follows: electro-phoresis, electro-osmosis, flow potential (Quincke effect) and sedimentation potential (Dorn effect). The formulas for the motion of fluid and gas in porous medium considering the properties of porous medium and saturating them fluids, as well as the interaction between them, which is described with electro-kinematic phenomena, have been obtained. Obtained formulas have been evaluated via the results of laboratory researches.

Lattice Boltzmann Modeling of the Apparent Viscosity of Thinning–Elastic Fluids in Porous Media

Many non-Newtonian fluids, including polymers, exhibit both shear-thinning and viscoelastic rheological properties. A lattice Boltzmann (LB) model is developed for simulation of the flow of thinning–elastic fluids through porous media. This model applies the Oldroyd-B constitutive equation and the Carreau model, respectively, to account for the viscoelastic and shear-thinning behaviors of the thinning–elastic fluid in porous media. Both rheological features are captured well by this model and are verified against analytical solutions. The thinning-then-thickening viscosity curve of the thinning–elastic fluid observed in experiments is reproduced by the present pore-scale simulations. In addition to the traditional extensional theory, we propose other important mechanisms for the increase in apparent viscosity of viscoelastic fluids at higher shear rates. The mechanisms proposed include the reduction in conductivity due to stagnant fluid, the compressed effective flow region, and larger energy dissipations caused by the viscoelastic instability. We find that the viscoelastic thickening effect is more prominent in porous geometries with a large pore–throat ratio.

Numerical model of gravity segregation of two-phase fluid in porous media based on hybrid upwinding

Abstract The paper discusses the numerical algorithm constructing a three-dimensional model for a flow of two-phase incompressible fluid caused by the mass force of gravity in a porous medium. The algorithm is based on a combination of a hybrid upwind method with an explicit scheme for determination of the saturation. The hybrid upwinding allows us to take into account flows of fluid of various nature (in this case, viscous and gravitational flows) separately, which is extremely important in the case of gravitational flow with opposite directions of phase flows. The explicit scheme being extremely simple in implementation provides a small dispersion of solutions on discontinuities. The proposed algorithm is illustrated by the results of numerical experiments demonstrating the monotonicity of the method considered in this paper.

The first open channel for yield-stress fluids in porous media

Abstract

A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media

During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid.

Heat transfer of large Prandtl number fluids in porous media by a new lattice Boltzmann model

With the fast development of sustainable energy technologies and the extreme urgency to protect the living environment, it is crucial to deepen our understanding on the heat transfer characteristics of natural convection of large Prandtl number fluids in porous media. In this study a novel lattice Boltzmann approach is developed as a powerful numerical tool to close the knowledge gap on this important topic. With the aid of this new numerical tool, four new findings are reported and they show that the heat transfer characteristics and correlations of natural convection of large Prandtl number fluids in porous media are quite different from their small Prandtl number counterparts. Through the present analysis, it is found that such inconsistences result from that a transition from a convection-dominated heat transfer process to a conduction-dominated one will appear more easily for large Prandtl number fluids in porous media.

On Boundedness and Growth of Unsteady Solutions Under the Double Porosity/Permeability Model

There is a recent surge in research activities on modeling the flow of fluids in porous media with complex pore-networks. A prominent mathematical model, which describes the flow of incompressible fluids in porous media with two dominant pore-networks allowing mass transfer across them, is the double porosity/permeability (DPP) model. However, we currently do not have a complete understanding of unsteady solutions under the DPP model. Also, because of the complex nature of the mathematical model, it is not possible to find analytical solutions, and one has to resort to numerical solutions. It is therefore desirable to have a procedure that can serve as a measure to assess the veracity of numerical solutions. In this paper, we establish that unsteady solutions under the transient DPP model are stable in the sense of Lyapunov. We also show that the unsteady solutions grow at most linear with time. These results not only have a theoretical value but also serve as valuable a posteriori measures to verify numerical solutions in the transient setting and under anisotropic medium properties, as analytical solutions are scarce for these scenarios under the DPP model.This figure shows that the evolution of an unsteady solution under the DPP model satisfies the theoretical bound derived in this paper. \(\Vert \varvec{\Upsilon }\Vert _{{\mathcal {V}}}\) denotes a norm defined in terms of the velocities in the 2 pore-networks

Darcy–Carreau Model and Nonlinear Natural Convection for Pseudoplastic and Dilatant Fluids in Porous Media

The linear and weakly nonlinear stability analyses are carried out to study instabilities in Darcy–Benard convection for non-Newtonian inelastic fluids. The rheological model considered here is the Darcy–Carreau model, which is an extension to porous media of Carreau rheological model usually used in clear fluid media. The linear stability approach showed that the critical Rayleigh number and wave number corresponding to the onset of convection are the same as for Newtonian fluids. By employing weakly nonlinear theory, we derived a cubic Landau equation that describes the temporal evolution of the amplitude of convection rolls in the unstable regime. It is found that the bifurcation from the conduction state to convection rolls is always supercritical for dilatant fluids. For pseudoplastic fluids, however, the interplay between the macroscale properties of the porous media and the rheological characteristics of the fluid determines the supercritical or subcritical nature of the bifurcation. In the parameter range where the bifurcation is supercritical, we determined and discussed the combined effects of the fluid properties and the porous medium characteristics on the amplitude of convection rolls and the corresponding average heat transfer for both pseudoplastic and dilatant fluids. Remarkably, we found that the curves describing these effects collapse onto the universal curve for Newtonian fluids, provided the average apparent viscosity is used to define Rayleigh number.

A lattice Boltzmann study of dynamic immiscible displacement mechanisms in pore doublets

An advanced chromodynamics, Rothmann-Keller (RK) type lattice Boltzmann model (LBM) is used in this study. The new model benefits from high stability and capability of independently setting the interfacial tension of the fluids as an input parameter. In addition, the model is coupled with a wall-density approach to simulate the hydrophilic or hydrophobic properties of wall surfaces. Finally, injection of a wetting (non-wetting) fluid in a pore doublet geometry which is initially filled with non-wetting (wetting) fluid is simulated. The results of simulation reveal the capability of RK-LBM to simulate relative permeabilities of fluids in porous media for future studies of two-immiscible phase flow in various geoenvironmental problems.

Calculation of the relative phase permeabilities in the case of filtration of power law fluids in porous media

Calculation of the relative phase permeabilities in the case of filtration of power law fluids in porous media

Gibbs Ensemble Monte Carlo for Reactive Force Fields to Determine the Vapor-Liquid Equilibrium of CO2 and H2O.

Absorption and reactive properties of fluids in porous media are key to the design and improvement of numerous energy related applications. Molecular simulations of these systems require accurate force fields that capture the involved chemical reactions and have the ability to describe the vapor–liquid equilibrium (VLE). Two new reactive force fields (ReaxFF) for CO2 and H2O are developed, which are capable of not only modeling bond breaking and formation in reactive environments but also predicting their VLEs at saturation conditions. These new force fields include extra terms (ReaxFF-lg) to improve the long-range interactions between the molecules. For validation, we have developed a new Gibbs ensemble Monte Carlo (GEMC–ReaxFF) approach to predict the VLE. Computed VLE data show good agreement with National Institute of Standards and Technology reference data as well as existing nonreactive force fields. This validation proves the applicability of the GEMC–ReaxFF method to test new reactive force fields, and simultaneously it proves the applicability to extend newly developed ReaxFF force fields to other more complex reactive systems.

Experimental Study on the Cyclic Steam Stimulation Assisted by Flue Gas Under Shallow Heavy-Oil Reservoir Conditions: Optimization of the Steam-Flue Gas Ratio

Normally, the recovery effect of a heavy-oil reservoir gradually deteriorates after multiple rounds of cyclic steam stimulation (CSS). However, the injection of flue gas can effectively increase the utilization degree of steam heat energy, which improves the recovery effect. In this paper, an experimental method for CSS using an energy storage container was established. Based on this method, a one-dimensional core physical simulation experiment for CSS under different flue gas ratios was performed. During the experiment, the changes in temperature field, oil production rate, increase in backpressure, and oil recovery factors were tested. In addition, differences in these data under different injection steam-flue gas ratios were compared. The results show that the flue gas provides a channel of fluids in porous media for steam, which is conducive to the heat transfer of steam to the deeper part of the sandpack. The sandpack has a higher temperature in each cycle than the CSS. The core temperature of each round of flue-gas-assisted CSS is higher than that of the CSS. The final oil recovery factors of flue-gas-assisted CSS using different steam-flue gas ratios are 22.2, 26.7, 30.8, 24.4, and 21.6%, while that of CSS is only 17.2%. According to the experiment, it is concluded that the best steam-flue gas ratio to optimize the flue-gas-assisted CSS is 1:10. With the combined effect of three factors (the temperature field of the sandpack, energizing effect of the flue gas, and degree of oil during recovery), the flue-gas-assisted CSS using the steam-flue gas ratio of 1:10 maximizes the steam heat transfer, increases the energy of return discharge, replenishes formation energy, and improves the oil recovery factor. Through the experiment, the research results provide theoretical guidance for improving the effectiveness of the CSS of heavy-oil reservoirs.

Two-dimensional nonlinear time fractional reaction\u2013diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

In the present article, an efficient operational matrix based on the famous Laguerre polynomials is applied for the numerical solution of two-dimensional non-linear time fractional order reaction–diffusion equation. An operational matrix is constructed for fractional order differentiation and this operational matrix converts our proposed model into a system of non-linear algebraic equations through collocation which can be solved by using the Newton Iteration method. Assuming the surface layers are thermodynamically variant under some specified conditions, many insights and properties are deduced e.g., nonlocal diffusion equations and mass conservation of the binary species which are relevant to many engineering and physical problems. The salient features of present manuscript are finding the convergence analysis of the proposed scheme and also the validation and the exhibitions of effectiveness of the method using the order of convergence through the error analysis between the numerical solutions applying the proposed method and the analytical results for two existing problems. The prominent feature of the present article is the graphical presentations of the effect of reaction term on the behavior of solute profile of the considered model for different particular cases.

Effects of nonlinear thermal radiation over magnetized stagnation point flow of Williamson fluid in porous media driven by stretching sheet

AbstractIn this study, the stagnation point flow of a magnetized Williamson fluid past a stretching sheet in the presence of nonlinear thermal radiation and buoyancy effect is studied. The present situation is remodeled using similarity transformation that transforms the flow model of partial differential equations into the set of nonlinear ordinary differential equations. The fourth‐order Runge‐Kutta scheme and shooting method are employed to solve these reduced equations. The effects of various associated parameters over the velocity and temperature profiles are plotted and the outcome of each associated parameter is discussed through graphs. The key findings are noted as follows: the velocity profile declines with an increase in the magnetic force number, and an increment in buoyancy parameter leads to the increase in the boundary layer thickness and decrease in the thickness of the thermal boundary layer.