Prediction of relative permeability in simple porous media

A Statistical Analysis of Fluid Interface Fluctuations: Exploring the Role of Viscosity Ratio

Understanding multiphase flow through porous media is integral to geologic carbon storage or hydrogen storage. The current modelling framework assumes each fluid present in the subsurface flows in its own continuously connected pathway. The restriction in flow caused by the presence of another fluid is modelled using relative permeability functions. However, dynamic fluid interfaces have been observed in experimental data, and these are not accounted for in relative permeability functions. In this work, we explore the occurrence of fluid fluctuations in the context of sizes, locations, and frequencies by altering the viscosity ratio for two-phase flow. We see that the fluctuations alter the connectivity of the fluid phases, which, in turn, influences the relative permeability of the fluid phases present.

Characterisation of hydraulic properties of commercial gas diffusion layers: Toray, SGL, MGL, woven carbon cloth

This study utilises computational fluid dynamics simulations with the OpenFOAM computational framework to investigate and compare the in-plane and through-plane permeability properties of four different gas diffusion layers (GDLs). Also the through-plane water and air relative permeability values and water saturations at different rates were simulated. Permeability analysis enhances our understanding of fluid flow, ways to decrease pressure loss in the GDL, and methods to enhance oxygen concentration at the catalyst layer interface through convection. The analysis reveals that the investigated GDL materials have spatial heterogeneity of porosity and permeability, especially in the Sigracet SGL 25 BA GDL. However, the porosity and permeability of the Toray TGP-H 060 and AvCarb 370 MGL GDLs exhibit less variations. The two-phase flow studies on GDL saturation show that at the same water injection flowrate, the AvCarb 370 MGL GDL has the largest remaining water saturation, with Sigracet SGL 25 BA GDL being the less saturated GDL among the four investigated GDLs. The compression from the ribs significantly affected the in-plane permeabilities of both Toray TGP-H 060 and especially impacted Sigracet SGL 25 BA GDL. This impact was expected as the pore size distribution varied significantly in the areas under the ribs versus the channel.

Break-up and mobilization of DNAPL by acoustic excitation: Experimental evidence and pore network modeling

Dense non-aqueous phase liquids (DNAPLs) are long-term groundwater contaminants due to their high toxicity and slight solubility in water. The use of acoustic waves to remobilize trapped ganglia in subsurface porous systems have some advantages over pre-existing solutions including eliminating the bypassing effect and new environmental hazards. Designing an effective acoustically assisted remediation method for such purposes relies on understanding the underlying mechanisms and developing validated models. In this work, pore-scale microfluidic experiments were run to investigate the interplay between break-up and remobilization under sonication at different levels of flow rate and wettability conditions. Based on the experimental observation and pore-scale physical characteristics, a pore network model was developed and verified against the experimental results. Such a model was developed based on a two-dimensional network and scaled up to three-dimensional networks. In the experiments, processing of two-dimensional images showed that acoustic waves can remobilize trapped ganglia. The other observed effect of vibration is to break up blobs and reduce the mean ganglia size. Recovery enhancements were greater in hydrophilic micromodels as compared to hydrophobic system. A strong correlation was found between the remobilization and breakup indicating that the trapped ganglia are breaking up due to acoustic stimulation firstly and then a background viscous force may get them flowing under the new generated fluid distribution. In modeling, the simulation results of residual saturation reasonably matched with experimental observations. The differences between the prediction by the model and the experimental data at verification points is less than 2% for data before and after the acoustic excitation. The transitions from three-dimensional simulations were used to propose a modified capillary number. This study gives a better understanding of the mechanisms behind the effect of acoustic waves in porous media and provides a predictive tool for evaluating enhancement in fluid displacement.

A Stochastic Filling and Modeling Algorithm of Non-Equal Diameter Particles with Specified Probability Density for Porous Permeable Materials

In this paper, a model generation algorithm for non-equal diameter particles with a specified probability density distribution is proposed. Based on considering the randomness of the size and distribution of the particles, the compact stacking of the particles is realized by the compactness algorithm, and then the spatial distribution of the tightly compacted particles is made to meet the random distribution of the specified probability density and the specified volume fraction by the filtering algorithm. The computational efficiency and effectiveness of the algorithm are verified, and the effects of the particle size and volume fraction on the distribution are analyzed. Finally, the proposed model has been used to study the permeability of a titanium porous filter cartridge. The results show that the size and location of the particle samples that are generated by the proposed algorithm follow specified probability distributions according to the requirements, and the volume fraction can be adjusted. Compared with the traditional algorithm, the computational effort and complexity are reduced. The resultant model can be used to study the permeability of porous materials and provide modeling support for structural optimization and further simulation of porous materials.

A review on reactive transport model and porosity evolution in the porous media

This work comprehensively reviews the equations governing multicomponent flow and reactive transport in porous media on the pore-scale, mesoscale and continuum scale. For each of these approaches, the different numerical schemes for solving the coupled advection-diffusion-reactions equations are presented. The parameters influenced by coupled biological and chemical reactions in evolving porous media are emphasised and defined from a pore-scale perspective. Recent pore-scale studies, which have enhanced the basic understanding of processes that affect and control porous media parameters, are discussed. Subsequently, a summary of the common methods used to describe the transport process, fluid flow, reactive surface area and reaction parameters such as porosity, permeability and tortuosity are reviewed.

Dissolution and remobilization of NAPL in surfactant-enhanced aquifer remediation from microscopic scale simulations

In this paper, the dissolution and mobilization of non-aqueous phase liquid (NAPL) blobs in the Surfactant-Enhanced Aquifer Remediation (SEAR) process were upscaled using dynamic pore network modeling (PNM) of three-dimensional and unstructured networks. We considered corner flow and micro-flow mechanisms including snap-off and piston-like movement for two-phase flow. Moreover, NAPL entrapment and remobilization were evaluated using force analysis to develop the capillary desaturation curve (CDC) and predict the onset of remobilization. The corner diffusion mechanism was also applied in the modeling of interphase mass transfer to represent NAPL dissolution as the dominant mass transfer process. In addition, the effect of pore-scale heterogeneity on mass transfer rate coefficient and recovered residual NAPL was considered in the simulations. Sodium dodecyl sulfate (SDS) and Triton X-100 were used as the surfactant for the SEAR process. The results indicate that although surfactants enhance NAPL recovery during two-phase flow, surfactant-enhanced remediation of residual NAPL through dissolution is highly dependent on surfactant type. When SDS ─as a surfactant with high critical micelle concentration (CMC) and low micelle partition coefficient (K_m)─ was injected into a NAPL contaminated site, the mass transfer rate coefficient decreased (due to considerable changes in interface chemical potentials) which leads to a significant reduction in NAPL recovery after the end of two-phase flow. In contrast, Triton X-100 (with low CMC and high K_m) improved NAPL recovery, by enhancing solubility at surfactant concentrations greater than CMC which overcompensates the interphase mass transfer reduction.

Research on the Correction Method of the Capillary End Effect of the Relative Permeability Curve of the Steady State

Relative permeability curve is a key factor in describing the characteristics of multiphase flow in porous media. The steady-state method is an effective method to measure the relative permeability curve of oil and water. The capillary discontinuity at the end of the samples will cause the capillary end effect. The capillary end effect (CEE) affects the flow and retention of the fluid. If the experimental design and data interpretation fail to eliminate the impact of capillary end effects, the relative permeability curve may be wrong. This paper proposes a new stability factor method, which can quickly and accurately correct the relative permeability measured by the steady-state method. This method requires two steady-state experiments at the same proportion of injected liquid (wetting phase and non-wetting phase), and two groups of flow rates and pressure drop data are obtained. The pressure drop is corrected according to the new relationship between the pressure drop and the core length. This new relationship is summarized as a stability factor. Then the true relative permeability curve that is not affected by the capillary end effect can be obtained. The validity of the proposed method is verified against a wide range of experimental results. The results emphasize that the proposed method is effective, reliable, and accurate. The operation steps of the proposed method are simple and easy to apply.

Reconstruction of 3D greyscale image for reservoir rock from a single image based on pattern dictionary

Most methods that model 3D porous media from 2D images are based on binary images. In this paper, we propose a method for reconstructing 3D greyscale isotropic porous media images from a single image. Our proposed method incorporates a fast-sampling procedure to control the continuity and variability between adjoining reconstruction layers, a new similarity calculation method to obtain the most similar patterns from a pattern dictionary, and a central area simulation procedure to solve the block effect problem. The reconstruction results from application of our proposed method to a real reservoir 3D model obtained via computed tomography (CT) and a comparison with the original CT structure demonstrate that our proposed method can reproduce properties such as autocorrelation function, linear function, shape distribution, average shape factor, average pore radius size, average throat radius size, average pore volume, permeability and grey histogram. Further, the comparison results indicate that the statistical characteristics of the reconstructions match the training image and the CT model perfectly.

An intercomparison of the pore network to the Navier-Stokes modeling approach applied for saturated conductivity estimation from X-ray CT images

Different modeling techniques can be used to estimate the saturated conductivity of a porous medium based on computed tomography (CT) images. In this research, two methods are intercompared: direct modeling using the Navier–Stokes (NS) approach and simplified geometry pore network (PN) modeling. Both modeling approaches rely on pore media geometry which was determined using an X-ray CT scans with voxel size 2 μm. An estimate of the saturated conductivity using both methods was calculated for 20 samples prepared from sand with diverse particle size distributions. PN-estimated saturated conductivity was found to be statistically equivalent to the NS-determined saturated conductivity values. The average value of the ratio of the PN-determined conductivity to the NS-determined conductivity (K_satPN/NS) was equal to 0.927. In addition to the NS and PN modeling approaches, a simple Kozeny-Carman (KC) equation-based estimate was made. The comparison showed that the KC estimate overestimated saturated conductivity by more than double (2.624) the NS estimate. A relationship was observed between the porous media specific surface and the K_satPN/NS ratio. The tortuosity of analyzed samples was estimated, the correlation between the porous media tortuosity and the specific surface of the samples was observed. In case of NS modelling approach the difference between pore media total porosity and total porosity of meshes, which were lower, generated for simulations were observed. The average value of the differences between them was 0.01. The method of NS saturated conductivity error estimation related to pore media porosity underestimation by numerical meshes was proposed. The error was on the average 10% for analyzed samples. The minimum value of the error was 4.6% and maximum 19%.

Microphysical Modeling of Carbonate Fault Friction at Slip Rates Spanning the Full Seismic Cycle

Laboratory studies suggest that seismogenic rupture on faults in carbonate terrains can be explained by a transition from high friction, at low sliding velocities (V), to low friction due to rapid dynamic weakening as seismic slip velocities are approached. However, consensus on the controlling physical processes is lacking. We previously proposed a microphysically based model (the "Chen-Niemeijer-Spiers" [CNS] model) that accounts for the (rate-and-state) frictional behavior of carbonate fault gouges seen at low velocities characteristic of rupture nucleation. In the present study, we extend the CNS model to high velocities (1 mm/s ≤ V ≤ 10 m/s) by introducing multiple grain-scale deformation mechanisms activated by frictional heating. As velocity and hence temperature increase, the model predicts a continuous transition in dominant deformation mechanisms, from frictional granular flow with partial accommodation by plasticity at low velocities and temperatures, to grain boundary sliding with increasing accommodation by solid-state diffusion at high velocities and temperatures. Assuming that slip occurs in a localized shear band, within which grain size decreases with increasing velocity, the model results capture the main mechanical trends seen in high-velocity friction experiments on room-dry calcite-rich rocks, including steady-state and transient aspects, with reasonable quantitative agreement and without the need to invoke thermal decomposition or fluid pressurization effects. The extended CNS model covers the full spectrum of slip velocities from earthquake nucleation to seismic slip rates. Since it is based on realistic fault structure, measurable microstructural state variables, and established deformation mechanisms, it may offer an improved basis for extrapolating lab-derived friction data to natural fault conditions.

Preparation and Tensile Properties of Novel Porous Plates Made by Stainless Steel Wire Mesh and Powder Composites

Porous metal materials have important mechanical properties, and there are various manufacturing methods to produce them. In this paper, a porous, thin strip was fabricated by the composite rolling of stainless steel wire mesh and stainless steel powder. Then, a porous plate of stainless steel wire mesh and powder composite (SWMPC) was prepared by folding, pressing, and vacuum sintering the thin strip, and its structural characteristics and permeability were studied. The effects of the gap of the roller, gap of the powder box, number of layers by folding, and sintering parameters on the porosity and mechanical properties were also studied. The results indicated that the permeability increased with the increasing of porosity. Sintering parameters had a great influence on the mechanical properties. The larger the roll gap, the higher the porosity and the weaker the mechanical properties. As the gap of the powder box increased, the porosity decreased and the mechanical properties improved. The number of layers had no effect on the porosity. The first three stages of tensile curves of 10 and 15 layers were deformation stages and generally coincided, the time was short at the fracture stage. However, the mechanical properties got a raise when layers was 15.

Three-dimensional multiscale fusion for porous media on microtomography images of different resolutions

Accurately acquiring the three-dimensional (3D) image of a porous medium is an imperative issue for the prediction of multiple physical properties. Considering the inherent nature of the multiscale pores contained in porous media such as tight sandstones, to completely characterize the pore structure, one needs to scan the microstructure at different resolutions. Specifically, low-resolution (LR) images cover a larger field of view (FOV) of the sample, but are lacking small-scale features, whereas high-resolution (HR) images contain ample information, but sometimes only cover a limited FOV. To address this issue, we propose a method for fusing the spatial information from a two-dimensional (2D) HR image into a 3D LR image, and finally reconstructing an integrated 3D structure with added fine-scale features. In the fusion process, the large-scale structure depicted by the 3D LR image is fixed as background and the 2D image is utilized as training image to reconstruct a small-scale structure based on the background. To assess the performance of our method, we test it on a sandstone scanned with low and high resolutions. Statistical properties between the reconstructed image and the target are quantitatively compared. The comparison indicates that the proposed method enables an accurate fusion of the LR and HR images because the small-scale information is precisely reproduced within the large one.

Microphysical Model Predictions of Fault Restrengthening Under Room-Humidity and Hydrothermal Conditions: From Logarithmic to Power-Law Healing

The maximum fault strength and rate of interseismic fault strengthening ("healing") are of great interest to earthquake hazard assessment studies, as they directly relate to event magnitude and recurrence time. Previous laboratory studies have revealed two distinct frictional healing behaviors, referred to as Dieterich-type and non-Dieterich-type healing. These are characterized by, respectively, log-linear and power-law increase in the strength change with time. To date, there is no physical explanation for the frictional behavior of fault gouges that unifies these seemingly inconsistent observations. Using a microphysical friction model previously developed for granular fault gouges, we investigate fault strengthening analytically and numerically under boundary conditions corresponding to laboratory slide-hold-slide tests. We find that both types of healing can be explained by considering the difference in grain contact creep rheology at short and long time scales. Under hydrothermal conditions favorable for pressure solution creep, healing exhibits a power-law evolution with hold time, with an exponent of ~1/3, and an "apparent" cutoff time (α) of hundreds of seconds. Under room-humidity conditions, where grain contact deformation exhibits only a weak strain-rate dependence, the predicted healing also exhibits a power-law dependence on hold time, but it can be approximated by a log-linear relation with α of a few seconds. We derive analytical expressions for frictional healing parameters (i.e., healing rate, cutoff time, and maximum healing), of which the predictions are consistent with numerical implementation of the model. Finally, we apply the microphysical model to small fault patches on a natural carbonate fault and interpret the restrengthening during seismic cycles.

Experimentally based pore network modeling of NAPL dissolution process in heterogeneous porous media

Practical designs of non-aqueous phase liquids (NAPLs) remediation strategies require reliable modeling of interphase mass transfer to predict the retraction of NAPL during processes such as dissolution. In this work, the dissolution process of NAPL during two-phase flow in heterogeneous porous media is studied using pore-network modeling and micromodel experiments. A new physical-experimental approach is proposed to enhance the prediction of the dissolution process during modeling of interphase mass transfer. In this regard, the normalized average resident solute concentration is evaluated for describing the dissolution process at pore-level. To incorporate the effect of medium heterogeneities, a new experimental factor is considered for enhancing corner diffusion modeling. In addition, capillary desaturation curves (CDCs) are predicted during hydraulic flow modeling to estimate initial residual NAPL saturation. The developed network model can predict residual NAPL saturations and mass transfer rate coefficient for a NAPL-water system at different injection rates and fluid saturations. The evaluated mass transfer rate coefficients using the proposed physical-experimental approach show a significant improvement compared to either mechanistic or empirical methods. The proposed approach in this study can be attractive for possible applications in commercial simulators of contaminant transport in porous media.

Toward a New Generation of Two-Fluid Flow Models Based on the Thermodynamically-Constrained Averaging Theory

Traditional models of two-fluid flow through porous media at the macroscale have existed for nearly a century. These phenomenological models are not firmly connected to the microscale; thermodynamic constraints are not enforced; empirical closure relations are well known to be hysteretic; fluid pressures are typically assumed to be in a local equilibrium state with fluid saturations; and important quantities such as interfacial and curvilinear geometric extents, tensions, and curvatures, known to be important from microscale studies, do not explicitly appear in traditional macroscale models. Despite these shortcomings, the traditional model for two-fluid flow in porous media has been extensively studied to develop efficient numerical approximation methods, experimental and surrogate measure parameterization approaches, and convenient pre- and post-processing environments; and they have been applied in a large number of applications from a variety of fields. The thermodynamically constrained averaging theory (TCAT) was developed to overcome the limitations associated with traditional approaches, and we consider here issues associated with the closure of this new generation of models. It has been shown that a hysteretic-free state equation exists based upon integral geometry that relates changes in volume fractions, capillary pressure, interfacial areas, and the Euler characteristic. We show an analysis of how this state equation can be parameterized with a relatively small amount of data. We also formulate a state equation for resistance coefficients that we show to be hysteretic free, unlike traditional relative permeability models. Lastly, we comment on the open issues remaining for this new generation of models.

The Investigation of Permeability Calculation Using Digital Core Simulation Technology

Digital core simulation technology, as an emerging numerical simulation method, has gradually come to play a significant role in the study of petrophysical properties. By using this numerical simulation method, the influence of micro factors on seepage properties of reservoir rock is taken into consideration, making up the shortcomings of the traditional physical experiment. Three-dimensional core images are reconstructed by a computed tomography scanning technique. Different sizes of the sub-region were simulated by three methods including the direct computation of Navier-Stokes equations, the simulation of the pore network model, and the lattice Boltzmann method. The permeability computed by each simulation was compared. After comparison between these three methods, the results of the direct computation method based on Navier-Stokes equations were found to be higher than the other two methods. The pore network model simulation has an obvious advantage on the computation speed and the simulation area. The lattice Boltzmann method shows the low efficiency due to the time-consuming process. At last, the permeability calculated by the three methods is matched by the Kozeny-Carman equation. A more accurate formula can be obtained by a series of numerical simulations, which can be applied to marco-scale simulation.

Pore-scale statistics of flow and transport through porous media

Flow in porous media is known to be largely affected by pore morphology. In this work, we investigate the effects of pore geometry on the transport and spatial correlations of flow through porous media in two distinct pore structures arising from three-dimensional assemblies of overlapping and nonoverlapping spheres. Using high-resolution direct numerical simulations (DNS), we perform Eulerian and Lagrangian analysis of the flow and transport characteristics in porous media. We show that the Eulerian velocity distributions change from nearly exponential to Gaussian distributions as porosity increases. A stretched exponential distribution can be used to represent this behavior for a wide range of porosities. Evolution of Lagrangian velocities is studied for the uniform injection rule. Evaluation of tortuosity and trajectory length distributions of each porous medium shows that the model of overlapping spheres results in higher tortuosity and more skewed trajectory length distributions compared to the model of nonoverlapping spheres. Wider velocity distribution and higher tortuosity for overlapping spheres model give rise to non-Fickian transport while transport in nonoverlapping spheres model is found to be Fickian. Particularly, for overlapping spheres model our analysis of first-passage time distribution shows that the transport is very similar to those observed for sandstone. Finally, using three-dimensional (3D) velocity field obtained by DNS at the pore-scale, we quantitatively show that despite the randomness of pore-space, the spatially fluctuating velocity field and the 3D pore-space distribution are strongly correlated for a range of porous media from relatively homogeneous monodisperse sphere packs to Castlegate sandstone.

Spontaneous imbibition in fractal tortuous micro-nano pores considering dynamic contact angle and slip effect: phase portrait analysis and analytical solutions

Shales have abundant micro-nano pores. Meanwhile, a considerable amount of fracturing liquid is imbibed spontaneously in the hydraulic fracturing process. The spontaneous imbibition in tortuous micro-nano pores is special to shale, and dynamic contact angle and slippage are two important characteristics. In this work, we mainly investigate spontaneous imbibition considering dynamic contact angle and slip effect in fractal tortuous capillaries. We introduce phase portrait analysis to analyse the dynamic state and stability of imbibition. Moreover, analytical solutions to the imbibition equation are derived under special situations, and the solutions are verified by published data. Finally, we discuss the influences of slip length, dynamic contact angle and gravity on spontaneous imbibition. The analysis shows that phase portrait is an ideal tool for analysing spontaneous imbibition because it can evaluate the process without solving the complex governing ordinary differential equations. Moreover, dynamic contact angle and slip effect play an important role in fluid imbibition in fractal tortuous capillaries. Neglecting slip effect in micro-nano pores apparently underestimates imbibition capability, and ignoring variations in contact angle causes inaccuracy in predicting imbibition speed at the initial stage of the process. Finally, gravity is one of the factors that control the stabilisation of the imbibition process.

Spontaneous and Flow-Driven Interfacial Phase Change: Dynamics of Microemulsion Formation at the Pore Scale

The dynamic behavior of microemulsion-forming water-oil-amphiphiles mixtures is investigated in a 2.5D micromodel. The equilibrium phase behavior of such mixtures is well-understood in terms of macroscopic phase transitions. However, what is less understood and where experimental data are lacking is the coupling between the phase change and the bulk flow. Herein, we study the flow of an aqueous surfactant solution-oil mixture in porous media and analyze the dependence of phase formation and spatial phase configurations on the bulk flow rate. We find that a microemulsion forms instantaneously as a boundary layer at the initial surface of contact between the surfactant solution and oil. The boundary layer is temporally continuous because of the imposed convection. In addition to the imposed flow, we observe spontaneous pulsed Marangoni flows that drag the microemulsion and surfactant solution into the oil stream, forming large (macro)emulsion droplets. The formation of the microemulsion phase at the interface distinguishes the situation from that of the more common Marangoni flow with only two phases present. Additionally, an emulsion forms via liquid-liquid nucleation or the Ouzo effect (i.e., spontaneous emulsification) at low flow rates and via mechanical mixing at high flow rates. With regard to multiphase flow, contrary to the common belief that the microemulsion is the wetting liquid, we observe that the minor oil phase wets the solid surface. We show that a layered flow pattern is formed because of the out-of-equilibrium phase behavior at high volumetric flow rates (order of 2 m/day) where advection is much faster than the diffusive interfacial mass transfer and transverse mixing, which promote equilibrium behavior. At lower flow rates (order of 30 cm/day), however, the dynamic and equilibrium phase behaviors are well-correlated. These results clearly show that the phase change influences the macroscale flow behavior.

Local Pore Size Correlations Determine Flow Distributions in Porous Media

The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from δ-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.

Generalized network modeling: Network extraction as a coarse-scale discretization of the void space of porous media

A generalized network extraction workflow is developed for parameterizing three-dimensional (3D) images of porous media. The aim of this workflow is to reduce the uncertainties in conventional network modeling predictions introduced due to the oversimplification of complex pore geometries encountered in natural porous media. The generalized network serves as a coarse discretization of the surface generated from a medial-axis transformation of the 3D image. This discretization divides the void space into individual pores and then subdivides each pore into sub-elements called half-throat connections. Each half-throat connection is further segmented into corners by analyzing the medial axis curves of its axial plane. The parameters approximating each corner-corner angle, volume, and conductivity-are extracted at different discretization levels, corresponding to different wetting layer thickness and local capillary pressures during multiphase flow simulations. Conductivities are calculated using direct single-phase flow simulation so that the network can reproduce the single-phase flow permeability of the underlying image exactly. We first validate the algorithm by using it to discretize synthetic angular pore geometries and show that the network model reproduces the corner angles accurately. We then extract network models from micro-CT images of porous rocks and show that the network extraction preserves macroscopic properties, the permeability and formation factor, and the statistics of the micro-CT images.

Ensemble distribution for immiscible two-phase flow in porous media

We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In particular, we find an expression for the overall mobility of the system from the ensemble distribution. The entropy production at the scale of the porous medium is shown to give the expected product of the average flow and its driving force, obtained from a black-box description. We test numerically some of the central theoretical results.

Review of pore network modelling of porous media: Experimental characterisations, network constructions and applications to reactive transport

Pore network models have been applied widely for simulating a variety of different physical and chemical processes, including phase exchange, non-Newtonian displacement, non-Darcy flow, reactive transport and thermodynamically consistent oil layers. The realism of such modelling, i.e. the credibility of their predictions, depends to a large extent on the quality of the correspondence between the pore space of a given medium and the pore network constructed as its representation. The main experimental techniques for pore space characterisation, including direct imaging, mercury intrusion porosimetry and gas adsorption, are firstly summarised. A review of the main pore network construction techniques is then presented. Particular focus is given on how such constructions are adapted to the data from experimentally characterised pore systems. Current applications of pore network models are considered, with special emphasis on the effects of adsorption, dissolution and precipitation, as well as biomass growth, on transport coefficients. Pore network models are found to be a valuable tool for understanding and predicting meso-scale phenomena, linking single pore processes, where other techniques are more accurate, and the homogenised continuum porous media, used by engineering community.

Pattern density function for reconstruction of three-dimensional porous media from a single two-dimensional image

Three-dimensional (3D) structures are useful for studying the spatial structures and physical properties of porous media. A 3D structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. Among many reconstruction algorithms, an optimal-based algorithm was developed and has strong stability. However, this type of algorithm generally uses an autocorrelation function (which is unable to accurately describe the morphological features of porous media) as its objective function. This has negatively affected further research on porous media. To accurately reconstruct 3D porous media, a pattern density function is proposed in this paper, which is based on a random variable employed to characterize image patterns. In addition, the paper proposes an original optimal-based algorithm called the pattern density function simulation; this algorithm uses a pattern density function as its objective function, and adopts a multiple-grid system. Meanwhile, to address the key point of algorithm reconstruction speed, we propose the use of neighborhood statistics, the adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism. The pattern density function is a high-order statistical function; thus, when all grids in the reconstruction results converge in the objective functions, the morphological features and statistical properties of the reconstruction results will be consistent with those of the TI. The experiments include 2D reconstruction using one artificial structure, and 3D reconstruction using battery materials and cores. Hierarchical simulated annealing and single normal equation simulation are employed as the comparison algorithms. The autocorrelation function, linear path function, and pore network model are used as the quantitative measures. Comprehensive tests show that 3D porous media can be reconstructed accurately from a single 2D training image by using the method proposed in this paper.

Multiscale and multiresolution modeling of shales and their flow and morphological properties

The need for more accessible energy resources makes shale formations increasingly important. Characterization of such low-permeability formations is complicated, due to the presence of multiscale features, and defies conventional methods. High-quality 3D imaging may be an ultimate solution for revealing the complexities of such porous media, but acquiring them is costly and time consuming. High-quality 2D images, on the other hand, are widely available. A novel three-step, multiscale, multiresolution reconstruction method is presented that directly uses 2D images in order to develop 3D models of shales. It uses a high-resolution 2D image representing the small-scale features to reproduce the nanopores and their network, a large scale, low-resolution 2D image to create the larger-scale characteristics, and generates stochastic realizations of the porous formation. The method is used to develop a model for a shale system for which the full 3D image is available and its properties can be computed. The predictions of the reconstructed models are in excellent agreement with the data. The method is, however, quite general and can be used for reconstructing models of other important heterogeneous materials and media. Two biological examples and from materials science are also reconstructed to demonstrate the generality of the method.