Types Of Porous Media Research Articles

Characterising the role of parametric functions in the van Genuchten empirical model on CO2 storage performance

In the application of two-phase flow in porous media within the context of CO2 sequestration, a non-wetting phase is used to displace a wetting phase residing in-situ to the maximum extent through a network of pore conduits. The storage performance of this physical process can be assessed through numerical simulations where transport properties are usually described using the Brooks & Corey (BC) or van Genuchten (vG) model. The empirical constant, namely the pore geometry index, is a primary parameter in both of these models and experimental evidence shows a variation in the value of this empirical constant. It is, therefore, essential to cast this empirical constant into a ternary diagram for all types of clastic porous media to demarcate the efficiency of two-phase flow processes in terms of the pore geometry index (PGI). In doing so, this approach can be used as a tool for designing more efficient processes, as well as for the normative characterisation of two-phase flow, taking into consideration the predominance of capillary pressure or relative permeability effects. This concept is based on the existence of a PGI estimation for clastic sediments, for which the value for 12 sediment mixtures fall between 1.01 and 3.00. Statistical data obtained from soil physics is used for developing and validating numerical models where a good match is observed in numerical simulations. In this context, a new methodology for the effective characterisation of PGI for different clastic rocks is proposed. This paper presents theoretical observations and continuum-scale numerical simulation results of a PGI characterisation for the prediction of the hydraulic properties of clastic reservoir rocks. The effect of key parameters in the vG empirical model, such as the pressure strength coefficient and the PGI, is incorporated into the simulation analysis. In particular, the model is used to investigate the effects of parameter representation on CO2 storage performance in a saline aquifer. Subsequent analysis shows that the PGI is a very important parameter for defining the flow characteristics of simulation models. It can also be flexibly changed for each rock type and this approach may thus be practical when simulating the evolution of CO2 plume in reservoirs with sedimentary heterogeneities, such as intra-aquifer aquitard layers or graded beds. The use of the realistic PGI boundaries promises a more precise description of the hydraulic behaviour in sandstones and shale when using either the BC or vG model.

Research on Multi-stage Noise Reduction Method of NMR Logging Signal

By inversion calculation of T2 spectrum of echo string, the permeability, saturation, fluid type and other important parameters of porous media can be obtained. However, since the inversion algorithm itself is susceptible to noise signal [1], improving the SNR level of echo signal has been one of the key problems in the application of low-field NMR technology. In order to obtain more accurate analysis results, the corresponding noise reduction method needs to be developed. In the past, the research on noise reduction of NMR signal mainly focused on echo string. This paper constructs a complete NMR signal model and discusses the de-noising of echo and echo string. Aiming at noise reduction of echo, FIR filter and Orthogonal Modulation Filter(OMF) are discussed. Aiming at the de-noising of echo string, this paper proposes an improved CEEMD threshold de-noising, and makes a comparative analysis with the heuristic threshold de-noising based on sym4 wavelet and EMD threshold de-noising proposed by predecessors. It is found that the method proposed in this paper can invert the more accurate T2 spectrum while improving the SNR.

Experimental comparison of agent-enhanced flushing for the recovery of crude oil from saturated porous media

The subsurface remediation of nonaqueous liquid (NAPL) has proven to be challenging even when implementing more aggressive enhanced-flushing techniques. The objective of this study was to evaluate the effectiveness of a combination of alkaline- and surfactant-based enhanced flushing for the removal of crude oil (medium fraction) from saturated porous media. Synchrotron X-ray microtomography (SXM) was used to perform pore-scale examination of NAPL fragmentation and changes in blob morphology, and recovery using three different advective flushing methods: surface-active agent (surfactant) flushing, alkaline flushing, and sequential alkaline-surfactant flushing. This set of experiments was conducted to understand effects on such processes (fragmentation and recovery) as a function of media composition (geochemical/mineralogical) and pH alterations due to calcium-carbonate fraction. Results showed that the sequential flushing technique (alkaline→ surfactant) yielded the highest recovery, 32% after 5 pore volumes (PV) of flushing. The crude oil (NAPL) distribution varied due to differences in porous medium mixture composition and type of fluid (i.e. surfactant vs. alkaline) used for flushing. The results of this study can be used to aid in the understanding of physical and chemical parameters/properties that control mobilization of crude oil in saturated porous media. This can help reduce time and cost during remediation of contaminated sites that contain crude oil or less dense NAPL derivatives consistent with fuel-type petroleum hydrocarbons.

Experimental and statistical investigation of drilling fluid loss in porous media: Part 2 (Fractures)

Drilling fluid loss and mud filtration occur concurrently during overbalanced drilling. Characterization of fluid loss is mostly done via experimental studies with several types of setups and porous media. The first part of this study has been conducted on pore-scale homogenous and heterogenous media. Sequel to the study, this paper presents fracture-scale characterization of drilling fluid loss using experimental and statistical methods. The statistical methods that were used in this study include: experiment design, hypothesis testing, analysis of variance (ANOVA), and multiple linear regression analysis. Dynamic fluid loss experiments were conducted with a setup capable of simulating drillpipe rotation inside thick-walled cylindrical fracture slots that represents natural fractures.The results show that temperature, fracture size and orientation, and type/concentration of lost circulation material (LCM) are the critical factors that influences dynamic fluid loss in fractures. The results from testing the filter cake stability showed that the filter cake layer ruptured on three of the experiments out of the nine that were conducted. For the experimental conditions with the vertical fractures, the regression analysis showed that dynamic fluid loss can be predicted from changes in LCM concentration and fracture width with a considerably high R2 and adjusted R2 values. The R2 value is a parameter that is used to quantify the predictability of an empirical model. The effect of fracture positioning and orientation was also observed and recorded. The originality in this experimental method is the application of thick-walled cylindrical fracture slots (simulating natural fractures) to characterize dynamic drilling fluid loss. Temperature, drillpipe rotation, and pressure conditions were programed to simulate dynamic wellbore conditions under which fluid loss, filter cake evolution, and plastering occur. The methods used in this study can be employed in mud design for wellbore strengthening application and selection of operating conditions.

Natural convection of hybrid nanofluids inside a partitioned porous cavity for application in solar power plants

The present article deals with the CFD simulation of natural convection heat transfer of a hybrid nanofluid in an inverted T-shaped cavity partitioned and saturated by two different types of porous media. Suspensions of organic and inorganic nanoparticles, i.e., MWCNTs and Fe3O4, in water were selected as the working fluid. The macroscopic conservation equations for the flow field and heat transfer were modeled via volume averaging the microscopic equations inside porous media over a representative elementary volume. The effects of many parameters were investigated. The parameters included the Rayleigh number (Ra = 103–106), porosity coefficient ratio of two porous media (er = 0.5–1.8), volume fraction of the dispersed nanoparticles ( $$\varphi$$ = 0–0.003), Richardson number (Ri = 0.1–20), Darcy number ratio of two porous media (Dar = 0.01, 1, 100) and thermal conductivity ratio of two porous media (kr = 0.2, 0.4, 1, 5). The results showed that, with an increase in the Rayleigh number, porosity ratio and Darcy number ratio and decrease in the thermal conductivity ratio, the averaged Nusselt number increased.

A blob method for diffusion

As a counterpoint to classical stochastic particle methods for diffusion, we develop a deterministic particle method for linear and nonlinear diffusion. At first glance, deterministic particle methods are incompatible with diffusive partial differential equations since initial data given by sums of Dirac masses would be smoothed instantaneously: particles do not remain particles. Inspired by classical vortex blob methods, we introduce a nonlocal regularization of our velocity field that ensures particles do remain particles and apply this to develop a numerical blob method for a range of diffusive partial differential equations of Wasserstein gradient flow type, including the heat equation, the porous medium equation, the Fokker–Planck equation, and the Keller–Segel equation and its variants. Our choice of regularization is guided by the Wasserstein gradient flow structure, and the corresponding energy has a novel form, combining aspects of the well-known interaction and potential energies. In the presence of a confining drift or interaction potential, we prove that minimizers of the regularized energy exist and, as the regularization is removed, converge to the minimizers of the unregularized energy. We then restrict our attention to nonlinear diffusion of porous medium type with at least quadratic exponent. Under sufficient regularity assumptions, we prove that gradient flows of the regularized porous medium energies converge to solutions of the porous medium equation. As a corollary, we obtain convergence of our numerical blob method. We conclude by considering a range of numerical examples to demonstrate our method’s rate of convergence to exact solutions and to illustrate key qualitative properties preserved by the method, including asymptotic behavior of the Fokker–Planck equation and critical mass of the two-dimensional Keller–Segel equation.

Experimental Investigation on Additively Manufactured Transpiration and Film Cooling Structures

The last 50 years has witnessed significant improvement in film cooling technologies while transpiration cooling is still not implemented in turbine airfoil cooling. Although transpiration cooling could provide higher cooling efficiency with less coolant consumption compared to film cooling, the fine pore structure and high porosity in transpiration cooling metal media always raised difficulties in conventional manufacturing. Recently, the rapid development of additive manufacturing (AM) has provided a new perspective to address such challenge. With the capability of the innovative powder bed selective laser metal sintering (SLMS) AM technology, the complex geometries of transpiration cooling part could be precisely fabricated and endued with improved mechanical strength. This study utilized the SLMS AM technology to fabricate the transpiration cooling and film cooling structures with Inconel 718 superalloy. Five different types of porous media including two perforated plates with different hole pitches, metal sphere packing, metal wire mesh, and blood vessel shaped passages for transpiration cooling were fabricated by EOS M290 system. One laidback fan-shaped film cooling coupon was also fabricated with the same printing process as the control group. Heat transfer tests under three different coolant mass flow rates and four different mainstream temperatures were conducted to evaluate the cooling performance of the printed coupons. The effects of geometry parameters including porosity, surface outlet area ratio, and internal solid–fluid interface area ratio were investigated as well. The results showed that the transpiration cooling structures generally had higher cooling effectiveness than film cooling structure. The overall average cooling effectiveness of blood vessel-shaped transpiration cooling reached 0.35, 0.5, and 0.57, respectively, with low (1.2%), medium (2.4%), and high (3.6%) coolant injection ratios. The morphological parameters analysis showed the major factor that affected the cooling effectiveness most was the internal solid–fluid interface area ratio for transpiration cooling. This study showed that additive manufactured transpiration cooling could be a promising alternative method for turbine blade cooling and worthwhile for further investigations.

Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part I: Theory

We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \;...

A variational approach to doubly nonlinear equations

This article presents a variational approach to the existence of solutions to equations of Porous Medium type. More generally, the method applies also to doubly nonlinear equations with a nonlinearity in u and Du , whose prototype is given by \partial_t u^m-\mathrm {div}(|D u|^{p-2}D u) = 0, where m > 0 and p > 1 . The technique relies on a nonlinear version of the Minimizing Movement Method which has been introduced in [14] in the context of doubly nonlinear equations with general nonlinearities \partial_t b(u) and more general operators with variational structure. The aim of this article is twofold. On the one hand it provides an introduction to variational solutions and outlines the method developed in [14]. In addition, we extend the results of [14] to initial data with potentially infinite energy. This requires a detailed discussion of the growth conditions of the variational energy integrand. The approach is flexible enough to treat various more general evolutionary problems, such as signed solutions, obstacle problems, time dependent boundary data or problems with linear growth.

Nonlocal time porous medium equation with fractional time derivative

We consider nonlinear nonlocal diffusive evolution equations, governed by a Levy-type nonlocal operator, fractional time derivative and involving porous medium type nonlinearities. Existence and uniqueness of weak solutions are established using approximating solutions and the theory of maximal monotone operators. Using the De Giorgi–Nash–Moser technique, we prove that the solutions are bounded and Holder continuous for all positive time.

Strength Tortuosity - Porosity Relation in Locally Types of Porous Media (Experimental Model)

The experimental model of five types of porosity media (fine sand, gravel, sand, porcelanite and composed media) was conducted to determine the relationship between tortuosity and porosity. The red colour (Carmoisine E122) was used as a tracer. The results have good agreement with an empirical relation based on performing regression analysis on test result through the use of the trial version 9 of data Fit software of Oakdale Engineering computer programs. The proposed empirical equation was correlated as a function of three basic variables of media characteristics; porosity (n), shape factor (φ) and sphericity factor (P) by τ = 1 + C1 * pφ(1 − nc2

Experimental study on flow and rheological behavior of oil-in-water emulsions in unconsolidated porous media: Effect of particle size and phase volume fractions

Flow of oil-in-water (o/w) emulsions through porous media was studied experimentally. Details of the theoretical developments of effective viscosity of emulsions flowing through unconsolidated porous media were presented. The emulsion rheological data were coupled with the hydraulic radius concept and the Navier-Stokes (NS) equation to account for the pressure gradient dependence of effective viscosity of emulsions in porous media. Thereafter, the emulsion flow through different type of porous media (packed bed with different size of particle diameter) was studied. The rheological behavior of o/w emulsions in porous bed with oil volume fraction ranging from 10 to 80 % (v/v) was investigated. Emulsions behaved like non-Newtonian shear thinning (n<1) fluids. The effect of emulsion volume fraction, flow rate and number of pore volume (PV) injected on bed pressure drop and flow resistance of different types of porous media were studied and discussed. The observed blocking/resistance mechanisms could be attributed in part to the pressure drop-flow rate response of behavior of emulsion flow in porous media. These showed the potential use of emulsions as conformance agents.

Multiple large-time behavior of nonlocal interaction equations with quadratic diffusion

In this paper we consider a one-dimensional nonlocal interaction equation with quadratic porous-medium type diffusion in which the interaction kernels are attractive, nonnegative, and integrable on the real line. Earlier results in the literature have shown existence of nontrivial steady states if the $L^1$ norm of the kernel $G$ is larger than the diffusion constant $\varepsilon$. In this paper we aim at showing that this equation exhibits a 'multiple' behavior, in that solutions can either converge to the nontrivial steady states or decay to zero for large times. We prove the former situation holds in case the initial conditions are concentrated enough and 'close' to the steady state in the $∞$-Wasserstein distance. Moreover, we prove that solutions decay to zero for large times in the diffusion-dominated regime $\varepsilon≥ \|G\|_{L^1}$. Finally, we show two partial results suggesting that the large-time decay also holds in the complementary regime $\varepsilon &lt; \|G\|_{L^1}$ for initial data with large enough second moment. We use numerical simulations both to validate our local asymptotic stability result and to support our conjecture on the large time decay.

Pore-level visual analysis of heavy oil recovery using chemical-assisted waterflooding process – Use of a new chemical agent

Chemical-assisted waterflooding enhances the ultimate recovery of a conventional waterflooding process through several mechanisms such as reducing interfacial tension between water and oil, formation of in-situ emulsions, treatment of adverse mobility ratio, and wettability modification. Application of chemical-assisted waterflooding for recovery of heavy oil is still an active research topic. A new chemical technology (i.e. IPC Technology as referred to in this paper) has been developed. A proprietary mixture of surfactants is used in several techniques associated with surface extraction as well as in-situ recovery of heavy oil and bitumen. This formulation of solvents and surfactants is reusable, low foaming, non-flammable, not acutely toxic, and non-carcinogenic. The efficacy of using IPC as an additive for waterflooding was presented earlier through a systematic coreflooding study, which showed increased ultimate recovery of different types of oils when compared with commercial surfactant and alkali flooding. In order to investigate the mechanisms behind the enhanced macro-scale oil recovery, a series of pore-scale tests were designed and conducted in this study. Glass micromodel type of porous media was used in the presence of brines with different ion compositions. The pore-scale chemical-assisted waterflooding tests were carried out in four consecutive stages: brine flooding, chemical flooding, soaking period, and extended brine flooding. High quality pore-scale images were captured for qualitative and quantitative analysis of the IPC-assisted waterflooding at the pore-level. IPC intensified water wettability of grain particles in the presence of NaCl; however in the presence of MgCl2, use of IPC makes solid surfaces oil-wet. The phenomenon of water-in-oil and oil-in-water emulsification was observed when IPC was used along with different brine compositions. This phenomenon is weakened for lighter oils. When the acid number of the oil was low, extension of soaking period intensified wettability alteration and emulsification mechanisms. Other pore-scale phenomena were also observed during visualization tests such as coalescence of microdroplets during the extended waterflooding stage, snap-off mechanism creating daughter droplets during the extended waterflooding stage, occasional flow of bulk oil films toward the production end, and wettability reversal during various flooding stages. Attempts were also made to conduct statistical analysis of emulsion droplet sizes under different test conditions. Several parameters, including chemical concentration as well as ion concentration in brines, were found to significantly affect the emulsion droplet size distribution.

Lattice Boltzmann simulations for invasion patterns during drying of capillary porous media

Drying of capillary porous media involves coupled heat and mass transfer in complex void space geometry, which makes it very difficult to model and simulate invasion patterns. Thus far, modeling of drying was done using either continuum methods or pore network models (PNM), both of which have some limitations on representing the geometry of void space and underlying transport mechanism. Pore network models were in general applied to reconstructed void space, therefore, dynamic invasion patterns, cluster formations and dependency on drying kinetics may not be accurate. Alternatively, Lattice Boltzmann Method (LBM) is ideal for simulation of drying in capillary porous media as it can incorporate complex effects in a simple and natural way. In this work, the Lattice Boltzmann Method (LBM) using Shan Chen multiphase representation is used to simulate invasion patterns during the drying of four different void space computation domains, differing in both pore and throat geometries.The dynamics of invasion patterns and cluster formation were captured in all four computation domains. Due to the complex geometries present in porous media, capillary instabilities are often observed which leads to sudden jumps in the fluid-fluid interface. In this work, the effects of such instabilities on the liquid distribution are studied. The invasion patterns are compared to identify the dependence of capillary instabilities on the pore structure. It was observed that fluid-fluid interface motion could be classified into two types- evaporation-diffusion invasion, which constituted of slow invasion of voids by diffusion, and Haines jumps, which involved fast invasion of voids due to capillary instabilities. It was observed that some types of porous media exhibited an abundance of the former, particularly in irregular pore structures. However, regular pore structures showed a combination of both evaporation-diffusion invasions and Haines jumps. Lastly, it was observed that the rate of invasion of pores depends on its structure. Pores with sharp edges take a considerably longer period to invade due to a liquid holdup at the edges. This work emphasizes the advantages of using the LBM to simulate the drying of porous media for complex regular/irregular geometries.

Effect of Elastic Deformation and Rough Grain Surface on Heat Conduction in Partially Saturated Granular Porous Media

AbstractAccurate prediction of the effective thermal properties of partially saturated rock, soil, and other types of porous media is essential to a wide variety of phenomena and processes in engineering and natural sciences. The effective thermal conductivity of porous media depends strongly on the morphology of the media and the fluid distribution in the pore space, as well as on geomechanical processes such as dilation and microcracking. A precursor to such processes is the deformation of the grains' surface due to the overburden pressure that is dependent on pore‐scale features, such as the surface texture of the grains. We report on the results of the extensive two‐dimensional computer simulations of heat conduction of granular porous media in which the grains have rough, self‐affine fractal surface, and water partially saturates the pore space, and the media are subjected to an external compressive pressure. The Young's modulus of the grains and the fractal dimension of their surface profile dictate the contact area for the deformation. The spatial distribution of the fluids and the resulting saturation is generated by a lattice Boltzmann method, while the conduction process is simulated by a thermal lattice Boltzmann. Two essentially linear dependence of the effective thermal conductivity on the water saturation emerge, separated at a critical water saturation Sc that signals the formation of percolation clusters of water‐filled pores. One interval, below Sc, is dominated by heat conduction through the solid phase, assisted by conducting water globules that bridge the noncontacting grains. The second interval emerges above Sc in which the water‐filled pores create a percolating conductive cluster that dominates heat conduction through the medium. The effect of various factors on the conduction process is studied in detail.

Global solvability of chemotaxis–fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions

In this work we extend a recent result to chemotaxis–fluid systems which include matrix-valued sensitivity functions S(x,n,c):Ω×[0,∞)2→R3×3 in addition to the porous medium type diffusion, which were discussed in the previous work. Namely, we will consider the system nt+u⋅∇n=Δnm−∇⋅(nS(x,n,c)∇c),x∈Ω,t>0,ct+u⋅∇c=Δc−c+n,x∈Ω,t>0,ut+(u⋅∇)u=Δu+∇P+n∇ϕ,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0,in a bounded domain Ω⊂R3 with smooth boundary. Assuming that m≥1, α≥0 satisfy m+α>43, that the matrix-valued function S(x,n,c):Ω×[0,∞)2→R3×3 satisfies |S(x,n,c)|≤S0(1+n)α for some S0>0 and suitably regular nonnegative initial data, we show that the corresponding no-flux-Dirichlet boundary value problem emits at least one global very weak solution. Upon comparison with results for the fluid-free system this condition appears to be optimal. Moreover, imposing a stronger condition for the exponents m and α, i.e. m+2α>53, we will establish the existence of at least one global weak solution in the standard sense.

Analysis and Finite Element Modelling of Water Flow in Concrete

Due to the construction of underground structures and hazardous waste storages, understanding and modelling of seepage in concrete has become an important issue in life-span analyses. The theories and calculation methods of unsaturated soil mechanics provide an opportunity to analyze water flow in other types of porous media (e.g. concrete) as well. This study deals with the determination of the permeability for unsaturated and saturated concrete and modelling the water flow in concrete. The direct measurement of the saturated permeability, the preparation of the drying water retention curve and determination of the depth of penetration of water under pressure are involved in the series of tests. For the fitting method of the experimental water retention curves were used Fredlund and Xing (1994) and van Genuchten (1980) model. The theory of lateral shift was applied to estimate the wetting water retention curve from the drying WRC. Thus, we could calculate the unsaturated permeability functions with Fredlund et al. (1994) and van Genuchten (1980) model. The finite element modelling of the standard test for watertightness were performed with Midas GTS using the measured and calculated unsaturated property functions.

Existence result for degenerate cross-diffusion system with application to seawater intrusion

In this paper we study a degenerate parabolic system, which is strongly coupled. We prove general existence result, but the uniqueness question remains open. Our proof of existence is based on a crucial entropy estimate which controls the gradient of the solution together with its non-negativity. Our system is of porous medium type which is applicable to models in seawater intrusion.

Solutions with moving singularities for equations of porous medium type

We construct positive solutions of equations of porous medium type with a singularity which moves in time along a prescribed curve and keeps the spatial profile of singular stationary solutions. It turns out that there appears a critical exponent for the existence of such solutions.