Field In Porous Medium Research Articles

Predicting the frequency-dependent effective excess charge density: A new upscaling approach for seismoelectric modeling

The seismoelectric method is based on the capacity of seismic waves to generate measurable modifications of the electrical field in porous media. Even though it combines the advantages of seismic and geoelectrical methods, it remains largely underused in hydrogeophysics. Its signal results from an electrokinetic coupling that can be modeled using either the coupling coefficient or the effective excess charge density. The traditional approach is based on the frequency-dependent coupling coefficient, which relates the pressure drop with the change in the electrical potential. A more recent approach consists of describing the excess charge that is effectively dragged by water flowing within the pores. We have developed a new model for the frequency-dependent effective excess charge density. For this, we make use of a mechanistic upscaling of the electrokinetic coupling in a capillary. This novel approach introduces inertial effects arising within the pore space in the flux-averaging procedure to explain the frequency dependence of the effective excess charge density. The presented model is successfully compared to previous models and published data. This new frequency-dependent upscaling approach has the potential of fundamentally improving our current understanding of the seismoelectrical signal in more complex environments, such as partially saturated and fractured media.

Interpolation for the lattice-Boltzmann method to simulate colloid transport in porous media.

The lattice-Boltzmann method is convenient for simulating flow fields in porous media. However, due to its lattice characteristics, the velocity near a solid surface is not accurate, which results in significant errors when simulating colloid transport in porous media. Based on the general properties of a flow field close to a solid surface, we propose an alternative velocity interpolation method in which the velocity at a solid surface is strictly zero. Numerical simulation results show that the proposed method can give more accurate results than the usual bilinear interpolation. In addition, we use this method to simulate the contact efficiency of colloids in porous media and obtain a new power-law form of the contact efficiency.

Computational modeling of intraocular drug delivery supplied by porous implants.

New and efficient drug delivery to the posterior part of the eye is a growing health necessity worldwide. Current treatment of eye diseases, such as age-related macular degeneration (AMD), relies on repeated intravitreal injections of drug-containing solutions. Such a drug delivery has major drawbacks including short drug life, significant medical service, and high medical cost. In this study, we explored a new approach to controlled drug delivery by introducing unique porous implants. Our computational modeling contained key physiological and anatomical traits. Incompressible flow in a porous media field, including the sclera, choroid, and retina layers, is governed by Darcy law and the time evolution of the drug concentration was solved via three convection-diffusion equations in the three layers, respectively. The computational model was validated by established results from independent studies and experimental data. Simulations of the IgG1 Fab drug delivery to the posterior eye were performed to evaluate the effectiveness of the porous implants for controlled delivery. Overall, our results indicate that drug therapeutic levels in the posterior eye sustain for eight weeks similarly to those using intravitreal injection. We first evaluated the effects of the porous implants on the drug delivery in the posterior layers. Subsequent simulations were carried out with varying porosity values in a porous episcleral implant. We found that the time evolution of drug concentration is distinctively correlated to drug source location and pore size. A correlation between porosity and fluid properties for selected porous implants was revealed for the first time in this study.

Physics-constrained deep learning for data assimilation of subsurface transport

Data assimilation of subsurface transport is important in many energy and environmental applications, but its solution is typically challenging. In this work, we build physics-constrained deep learning models to predict the full-scale hydraulic conductivity, hydraulic head, and concentration fields in porous media from sparse measurement of these observables. The model is developed based on convolutional neural networks with the encoding-decoding process. The model is trained by minimizing a loss function that incorporates residuals of governing equations of subsurface transport instead of using labeled data. Once trained, the model predicts the unknown conductivity, hydraulic head, and concentration fields with an average relative error <10% when the data of these observables is available at 12.2% of the grid points in the porous media. The model has a robust predictive performance for porous media with different conductivities and transport under different Péclet number (0.5 < Pe < 500). We also quantify the predictive uncertainty of the model and evaluate the reliability of its prediction by incorporating a variational parameter into the model.

Dependence of borehole shear‐horizontal‐wave seismoelectric response on soil textures

ABSTRACTThe phenomenon of acoustic waves inducing electric fields in porous media is called the seismoelectric effect. Earlier investigators proposed the usage of seismoelectric effect for well logging. Soil texture has a strong influence on the coupled wave fields during shallow surface explorations. In this article, we study the borehole pure shear‐horizontal wave and the coupling transverse‐electric field (acoustic–electrical coupling wave fields) in the partially saturated soil. Combined with related theories, we expand the formation parameters to partially saturated forms and discuss the influence of soil texture conditions on the seismoelectric wave fields. The results show that the elastic and electrical properties of porous media are sensitive to water saturation. The compositions of the acoustic and electric fields for different soil textures do not change, but the waveforms differ. We also use the secant integral method to simulate the interface‐converted electromagnetic waves. The results show that interface response strength is greatly influenced by soil texture. In addition, considering the sensitivity of the inducing electric field to fluid salinity, we also simulate the time‐domain waveforms of electric field for different pore fluid salinity levels. The results show that as the salinity increases, the electric field amplitude decreases monotonically. The above conclusions have certain significance for the application of borehole shear wave and its coupled electric fields for resource exploration, saturation assessment and groundwater pollution monitoring.

Experimental study of seepage flow properties with biofilm development in porous media with different filter morphologies

Biofilm growth can impact seepage flow properties in the porous media, thereby affecting the performance of the infiltration systems. To better understand and characterize the biofilm distribution and its effect on seepage flow fields in the porous media with different morphologies, two-dimensional transparent flow cells were developed using X-ray images of zeolite, gravel, and ceramsite columns to study the effect of biofilm development and the pore structure on seepage flow properties. The results revealed that the filter morphology and biofilm growth significantly impacted the seepage flow field in porous media. With biofilm growth, a preferential flow pathway was more likely to be formed in angular filter cells (zeolite-shaped cells) than spherical filter cells (ceramsite-shaped cells). It was also found that microbial growth rate was closely related to seepage flowrate in 2D porous media cells. The biofilm grew faster in the areas with higher seepage flowrate. The biofilm accumulation did not seem to affect the location of the preferential seepage flow, probably due to the high permeability of the biofilm in the large pore throats. Although the water head loss of ceramsite-shaped cells was larger than that of two others due to its relatively smaller size of pore throat, the ceramsite-shaped cells presented small dead zone and short-circuiting, which means that ceramiste filter media had higher hydraulic efficiency.

Computational Results With Non-singular and Non-local Kernel Flow of Viscous Fluid in Vertical Permeable Medium With Variant Temperature

Unsteady electrically conducting viscous fluid flow with transversal magnetic field in porous medium over vertical wall with ramped temperature has studied with Atangana-Baleanu derivative. Conjugate impact of heat and mass transfer with slip and non-slip effect are considerable. Solutions of governing equations for temperature gradient, concentration gradient and velocity profile are obtained with Laplace transformation. Inversion calculation of Laplace transformation have been computed with Stehfest’s algorithm. Computational results have been expressed graphically with the effect of various flow physical parameters. Comparative graphical analysis with existing literature as well as Atangana-Baleanu derivative for temperature, concentration and velocity field with slip and non-slip impact shows that the memory effects of Atangana-Baleanu derivative are better than the results existing in literature.

Multi-scale simulation of turbulence and heat transfer characteristics in randomly packed beds

The pore-scale numerical simulation of fluid flow and heat transfer processes in the random structures are given. By comparing the simulation results with the corresponding experimental data, the validity of the structure model and the heat transfer model are verified. The macro analysis is given, it is found that the mean porosity, various flow scalars and heat transfer scalars in the packed structures are all periodically distributed, and the influence of inlet velocities, spheres size and other parameters on the turbulence and temperature field in porous media is described in detail. The large eddy simulation (LES) method is used to study the flow and temperature field under pore-scale in the local porous structure, the distribution characteristic of eddies in porous structure was obtained, and the change regulation of isothermal surface shape (fractal dimension of surface) with heating is also given.

A 3D additive manufacturing approach for the validation of a numerical wall-scale model of catalytic particulate filters

The validation of a numerical model used to predict the permeability of the microporous wall of a coated gasoline particulate filer is arduous due to multiscale effects. To circumvent this, an experimental “magnified twin” approach based on kinematic similarity is proposed. It consists of (1) printing magnified porous wall sections by fused filament additive manufacturing; and (2) characterizing their permeability using a modified falling head permeability measurement device and testing procedure. A detailed approach is also proposed to select the appropriate scaling factor to produce the samples by 3D printing. Comparison between numerical, semi-analytical, and experimental predictions of the impact of coating amount and degree of uniformity on wall permeability is presented. Despite the inherent sensitivity of permeability to pore space characteristics, a very good agreement is reported between simulations and experiments with a 19.3% mean discrepancy for the seven magnified structures tested. The proposed procedure is a relatively easy-to-implement and inexpensive method that may find many applications in the field of porous media.

Effects of nonlinear parameter of fluid-solid coupling on acoustic field in porous media.

The purpose of this Letter to the Editor is to demonstrate the effects of the nonlinear parameter of fluid-solid coupling on the acoustic field in porous media. The nonlinear acoustic field excited by a one-dimensional finite-amplitude shear wave propagating in the uniform and infinite saturated porous media is studied. Researchers use the complete strain energy formula with third-order terms of strain in saturated porous media. The formula for calculating the fluid-solid coupling nonlinear parameter γ from the dynamic compatibility condition is given. To illustrate the effect of the fluid-solid coupling nonlinear term on the nonlinear acoustic field excited by the longitudinal and transverse waves, this study compares nonlinear acoustic fields excited by a finite amplitude wave with and without nonlinear parameter γ. The results show that the nonlinear parameter γ has an influence on the nonlinear acoustic field excited by the one-dimensional shear wave, but it has no influence on the nonlinear acoustic field excited by the one-dimensional longitudinal wave.

Mass Transfer Effects on MHD Flow through Porous Medium past an Exponentially Accelerated Inclined Plate with Variable Temperature and Thermal Radiation

The current paper focuses on unsteady MHD free convection flow with mass and heat transfer past an inclined plate. The inclined plate moves with exponential acceleration and is placed in a saturated porous medium having a uniform permeability but a varying concentration and temperature. The important essence of the study is to analyze the angle of inclination on the flow phenomenon with a heat source or sink alongside a destructive reaction. The governing equations are solved with the help of Galerkin Finite Element Method. A detailed discussion on the effects of pertinent material parameters, magnetic field, and permeability of the porous medium is presented. This reveals the flow reversal with an active magnetic field in porous medium. A retarding velocity is observed with angle of inclination and heat source. Applications of the present study include understanding of drag experienced at the heated/cooled inclined surfaces in a seepage flow.

Thermosolutal convective instability of power-law fluid saturated porous layer with concentration based internal heat source and Soret effect

The onset of double-diffusive convective instability in a horizontal porous layer saturated by a power-law fluid that is subjected to concentration based internal heat source and Soret effect is investigated. Both these physical processes have a significant influence on the concentration field in porous media. Here the fluid flow is induced by constant but different temperature and concentration maintained across the boundary planes. The basic flow considered is a uniform throughflow which is inclined with respect to the horizontal x -axis. Considering the heat source ($ \gamma$) and Soret effect (Sr) results in a non-linear basic temperature and concentration profiles. The resulting eigenvalue system of coupled ordinary differential equations along with the boundary conditions is solved to explore the combined effect of internal heat source and Soret parameter on the instability of the power-law fluid. The instability of the base flow appears in the form of oblique rolls, which can be reduced to longitudinal rolls or transverse rolls. Stationary instability is seen for the longitudinal rolls. For transverse rolls, the onset of stationary and oscillatory convective instability depends on Lewis number, Peclet number, Soret parameter and presence of the concentration based internal heat source. It is also evident that $ \gamma$ = 0 and Sr = 0 are singularities for the basic temperature and concentration profiles. The limiting behavior of these parameters is also investigated for their linear stability. Both stationary and oscillatory convective instability corresponding to the pseudoplastic and dilatant fluids is discussed for the case of $ \gamma\rightarrow 0$.

Modeling Flow and Pressure Fields in Porous Media with High Conductivity Flow Channels and Smart Placement of Branch Cuts for Variant and Invariant Complex Potentials

A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time. Invariant complex potentials describe physical flows where a switch of the real and imaginary parts of the function will still describe the same type of physical flow (but only rotated by π/2). Such invariants can be formulated with Euler’s formula to depict the same flow for any arbitrary orientation with respect to the coordinate system used. In contrast, variant complex potentials, when swapping their real and imaginary parts, will result in two fundamentally different physical flows. Next, we show that the contour integrals of the real and imaginary part of simple variant and invariant complex potentials generally do not generate any discernable branch cut problems. However, complex potentials due to the multiple superpositions of simple flows, even when invariant, may involve many options for selecting the branch cut locations. Examples of such branch cut choices are given for so-called areal doublets and areal dipoles, which are powerful tools to describe the streamlines and pressure fields for flow in porous media with enhanced permeability flow channels. After a discussion of the branch cut solutions, applications to a series of synthetic and field examples with enhanced permeability flow channels are given with examples of the streamline and pressure field solutions.

A new bi‐fidelity model reduction method for Bayesian inverse problems

SummaryThis work presents a new bi‐fidelity model reduction approach to the inverse problem under the framework of Bayesian inference. A low‐rank approximation is introduced to the solution of the corresponding forward problem and admits a variable‐separation form in terms of stochastic basis functions and physical basis functions. The calculation of stochastic basis functions is computationally predominant for the low‐rank expression. To significantly improve the efficiency of constructing the low‐rank approximation, we propose a bi‐fidelity model reduction based on a novel variable‐separation method, where a low‐fidelity model is used to compute the stochastic basis functions and a high‐fidelity model is used to compute the physical basis functions. The low‐fidelity model has lower accuracy but efficient to evaluate compared with the high‐fidelity model; it accelerates the derivative of recursive formulation for the stochastic basis functions. The high‐fidelity model is computed in parallel for a few samples scattered in the stochastic space when we construct the high‐fidelity physical basis functions. The required number of forward model simulations in constructing the basis functions is very limited. The bi‐fidelity model can be constructed efficiently while retaining good accuracy simultaneously. In the proposed approach, both the stochastic basis functions and physical basis functions are calculated using the model information. This implies that a few basis functions may accurately represent the model solution in high‐dimensional stochastic spaces. The bi‐fidelity model reduction is applied to Bayesian inverse problems to accelerate posterior exploration. A few numerical examples in time‐fractional derivative diffusion models are carried out to identify the smooth field and channel‐structured field in porous media in the framework of Bayesian inverse problems.

New finite volume multiscale finite element model for simultaneously solving groundwater flow and darcian velocity fields in porous media

This paper proposes a new finite volume multiscale finite element model (NFVMSFEM) for groundwater flow and velocity simulation in porous media. The main goal of this method is to simultaneously obtain the heads and continuous x,y direction Darcian velocities, thereby simplifying the simulation process and improving the efficiency. This goal is accomplished by introducing a novel velocity matrix in the control volume boundary flux estimation of the finite volume multiscale finite element method (FVMSFEM) framework. The velocity matrix allows for the NFVMSFEM to directly represent continuous fine-scale velocities by coarse-scale heads, thus merging the two kinds of unknowns into one. Through a modified Yeh’s Galerkin model, the velocity matrix is constructed in each local coarse element before the head computation; thus, the computational cost is very little. Furthermore, the NFVMSFEM inherits the advantageous features of the FVMSFEM, which ensures the local conservation of heads and further improves the efficiency. The results of the comparison between the NFVMSFEM and certain classical methods for head and velocity computation demonstrate its effectiveness and high efficiency.

Numerical simulation of the seismic wave propagation and fluid pressure in complex porous media at the mesoscopic scale

In this study, we apply an improved high-order staggered-grid finite difference method to model seismic wave propagation in complex heterogeneous porous media with cracks. Upon changing the mesh step and applying a broadband wavelet, we obtain numerical simulation results at the mesoscopic scale. As a fundamental result of applying Biot’s theory, three types of waves are also found. We discuss the relationship between the shear wave splitting parameter and the crack density of an equivalent medium in detail. Based on Darcy’s law, the finite element method is used to investigate the distribution of the fluid pressure field in porous media at the mesoscopic scale. A flat ellipse is used as an approximation of a crack. According to the simulation results, we further study the influence of variations in the crack angle on the distribution of the fluid pressure. Moreover, the formulas derived from the Fourier transform are used to calculate the inverse attenuation quality factors and phase velocities of the fast compressional wave, slow compressional wave and shear wave. The effects of the porosity and elastic modulus of an equivalent medium on wave attenuation are also taken into account in this study.

Investigation on synthesis of cordierite bonded porous SiC ceramics with emphasis on bond phase formation

Abstract Cordierite-bonded porous SiC ceramics were synthesized from SiC, Al2O3 and MgO powders with varying petroleum coke (PC) as the sacrificial pore former. To trace the path of development of the oxide binder phase and mechanistic steps of oxidation reaction of a PC pore former powder, thermal analysis (up to 1400 °C in air) of the precursor powders was studied with non-isothermal method varying different heating rates. The results indicated the transformation of cordierite binder phase and the average activation energy was determined to be 840 ± 27 kJ mol−1. The formation of the oxide binder phase (cristobalite (24–31 wt%) and cordierite (21–28 wt%)) and pore phase (porosity of 30–67 vol% and average pore size of 3–36 μm) were further analysed by conducting X-ray diffraction test, chemical analysis and microstructure examination for better understanding the formation of the pore phase and the binder phases of the ceramics for its applicability in the field of porous media at hostile conditions.

Pore-scale simulation and statistical investigation of velocity and drag force distribution of flow through randomly-packed porous media under low and intermediate Reynolds numbers

Fluid flow through packed porous media and fluid–particle interactions are of importance in various industrial and natural processes. However, the lack of knowledge about the velocity field in the pore space and distribution of drag force on individual particles has been a source of uncertainties in modeling these processes. Therefore, an improved understanding of the velocity field and fluid–particle interactions is a fundamental step for better understanding of these systems. In this article, the pore-scale velocity field and fluid–solid interaction from a single particle to randomly-packed mono-sized porous media are investigated using a 3D GPU-based parallel Lattice Boltzmann model. The packed porous media are generated by means of discrete element method and have a wide range of porosity values. The developed model is first validated by experimental results of fluid flow around single and two interactive particles; the validated model is then used to conduct statistical analysis of velocity in the pore space and drag force on individual particles. The results suggest that the velocity field in porous media can be divided into four zones, namely: zero-velocity zone, low-velocity zone, high-velocity zone, and recirculation zone. Moreover, the probability density distribution of velocity is highly dependent on Reynolds number and porosity and can be bi-modal, depending on a combination of Reynolds number and porosity. The probability density distribution of the drag force always shows a single peak at the mean value with a skewness to the right. Finally, a simpler and more accurate correlation for the mean drag force over a wide range of Reynolds number and porosity is proposed based on the numerical results. The accuracy and reliability of several empirical equations, including the one proposed in this study, for the mean drag force are compared through a statistical analysis.

Pore-scale simulation of vortex characteristics in randomly packed beds using LES/RANS models

Turbulent flow characteristics and vortex behaviors in the pore space of real packed beds under different flow conditions is numerically investigated. Real geometric structure of randomly packed beds is modeled using the discrete element software LIGGGHTS. Both LES and RANS methods are employed to predict vortex shape and evolution features at pore scale in actual packed beds. The numerical model is validated corresponding to experimental data, a good agreement is achieved between predicted results and measurements. Based on the computational results, the distribution characteristics of vorticity and velocity in multiple representative special structures are analysed, such as the channel formed by two pellets, similar triangle area formed by compact spherical walls and channel. Besides the effects of special structures on vortex shape and turbulence intensity is studied, such as the guiding and friction effect by the side spherical wall on gas motion, and strong shear force on both sides of the main channel. The Q criterion is used to identify vortex structures and capture distribution and evolution of vortexes in the computational domain. Moreover, the effect of inlet velocity on the position and shape of eddies is investigated, and eddy morphological changes under unsteady inlet conditions are also discussed., At last, a comparison between LES and RANS methods shows that the LES method can capture more details of the distribution and shape of the vortexes in the pore space, and therefore it is more suitable to the complicated flow field in porous media.

Effect of Suspended Particles and Magnetic Field on Thermal Convection in Ferromagnetic Fluid with Varying Gravitational Field in Porous Medium.

30Apr 2016 Effect of Suspended Particles and Magnetic Field on Thermal Convection in Ferromagnetic Fluid with Varying Gravitational Field in Porous Medium. Sumit Pant , Naveen Bhagat and Hema Kharayat. Department of Mathematics, M. B. Govt. P. G. College, Haldwani (Nainital), 263139, India. Department of Physics, M. B. Govt. P. G. College, Haldwani (Nainital), 263139, India.