Pore-Scale Modeling of Electrokinetics in Geomaterials

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials developed on the application of an external voltage and pressure difference, respectively. This model is used to predict the macroscale permeabilities of geomaterials via the widely used Carmen–Kozeny equation and through the electrokinetic coupling coefficients. The permeability results for a two-dimensional X-ray tomography-derived sand microstructure are within the same order of magnitude as the experimentally calculated values. The effect of the particle aspect ratio and orientation on the electrokinetic coupling coefficients and subsequently the electrical and hydraulic tortuosity of the porous media has been determined. These calculations suggest a highly tortuous geomaterial can be efficient for applications like decontamination and desalination.

     

Microtomography and Pore-Scale Modeling of Two-Phase Fluid Distribution

Synchrotron-based X-ray microtomography (micro CT) at the Advanced Light Source (ALS) line 8.3.2 at the Lawrence Berkeley National Laboratory produces three-dimensional micron-scale-resolution digital images of the pore space of the reservoir rock along with the spacial distribution of the fluids. Pore-scale visualization of carbon dioxide flooding experiments performed at a reservoir pressure demonstrates that the injected gas fills some pores and pore clusters, and entirely bypasses the others. Using 3D digital images of the pore space as input data, the method of maximal inscribed spheres (MIS) predicts two-phase fluid distribution in capillary equilibrium. Verification against the tomography images shows a good agreement between the computed fluid distribution in the pores and the experimental data. The model-predicted capillary pressure curves and tomography-based porosimetry distributions compared favorably with the mercury injection data. Thus, micro CT in combination with modeling based on the MIS is a viable approach to study the pore-scale mechanisms of CO₂ injection into an aquifer, as well as more general multi-phase flows.     

Predictive Pore-Scale Modeling of Single and Multiphase Flow

We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. The pore space is represented by a topologically disordered lattice of pores connected by throats that have angular cross-sections. We successfully predict single-phase non-Newtonian rheology, and two and three-phase relative permeability for water-wet media. The pore size distribution of the network can be tuned to match capillary pressure data when a network representation of the system of interest is unavailable. The aim of this work is not simply to match experiments, but to use easily acquired data to estimate difficult to measure properties and to predict trends in data for different rock types or displacement sequences.     

Multiblock Pore-Scale Modeling and Upscaling of Reactive Transport: Application to Carbon Sequestration

In order to safely store CO₂ in depleted reservoirs and deep saline aquifers, a better understanding of the storage mechanisms of CO₂ is needed. Reaction of CO₂ with minerals to form precipitate in the subsurface helps to securely store CO₂ over geologic time periods, but a concern is the formation of localized channels through which CO₂ could travel at large, localized rates. Pore-scale network modeling is an attractive option for modeling and understanding this inherently pore-level process, but the relatively small domains of pore-scale network models may prevent accurate upscaling. Here, we develop a transient, single-phase, reactive pore-network model that includes reduction of throat conductivity as a result of precipitation. The novelty of this study is the implementation of a new mortar/transport method for coupling pore networks together at model interfaces that ensure continuity of pressures, species concentrations, and fluxes. The coupling allows for modeling at larger scales which may lead to more accurate upscaling approaches. Here, we couple pore-scale models with large variation in permeability and porosity which result in initial preferential pathways for flow. Our simulation results suggest that the preferential pathways close due to precipitation, but are not redirected at late times.     

Modeling Oil Recovery in Mixed-Wet Rocks: Pore-Scale Comparison Between Experiment and Simulation

Transport in Porous Media - To examine the need to incorporate in situ wettability measurements in direct numerical simulations, we compare waterflooding experiments in a mixed-wet carbonate from a...     

Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element simulations of the Stokes equations for assemblies of 8–200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients.     

Dynamic Pore-Scale Modeling of Residual Trapping Following Imbibition in a Rough-walled Fracture

Transport in Porous Media - We present a new, fully dynamic pore-network modeling platform that is employed to conduct a systematic pore-scale study of capillary trapping under various two-phase...     

Experimental Study of Pore-Scale Mechanisms of Carbonated Water Injection

Carbon dioxide (CO₂) injection is a well-established method for increasing recovery from oil reservoirs. However, poor sweep efficiency has been reported in many CO₂ injection projects due to the high mobility contrast between CO₂ and oil and water. Various injection strategies including gravity stable, WAG and SWAG have been suggested and, to some extent, applied in the field to alleviate this problem. An alternative injection strategy is carbonated water injection (CWI). In CWI, CO₂ is delivered to a much larger part of the reservoir compared to direct CO₂ injection due to a much improved sweep efficiency. In CWI, CO₂ is used efficiently and much less CO₂ is required compared to conventional CO₂ flooding, and hence the process is particularly attractive for reservoirs with limited access to large quantities of CO₂ (offshore reservoirs or reservoirs far away from inexpensive natural CO₂ resources). This article describes the results of a pore-scale study of the process of CWI by performing high-pressure visualisation flow experiments. The experimental results show that CWI, compared to unadulterated (conventional) water injection, improves oil recovery as both a secondary (before water flooding) and a tertiary (after water flooding) recovery method. The mechanisms of oil recovery by CWI include oil swelling, coalescence of the isolated oil ganglia and flow diversion due to flow restriction in some of the pores as a result of oil swelling and the resultant fluid redistribution. In this article the potential benefit of a subsequent depressurisation period on oil recovery after the CWI period is also investigated.     

Evolution of Pore-Scale Morphology of Oil Shale During Pyrolysis: A Quantitative Analysis

This article describes experimental results and the numerical validation for multiphase, multicomponent evaporation in porous media 1d flow. We apply the model of Lindner et al. (Transp. Porous Media 112(2):313–332, 2016. doi: 10.1007/s11242-016-0646-6). The permeability of the porous medium is measured in an additional setup with a constant head permeameter to verify the validity of Darcy flow. The heat losses are considered in an analytical approach of correlating measured temperatures and heat inputs with enthalpies. A method of interpreting the experimental results is discussed to determine the phase state. We can show good qualitative agreement of the shift and position of the evaporation region when varying boundary conditions such as mass flux, concentration and heat input.     

Pore-Scale Lattice Boltzmann Modeling and 4D X-ray Computed Microtomography Imaging of Fracture-Matrix Fluid Transfer

We present sequential X-ray computed microtomography (CMT) images of matrix drainage in a fractured, sintered glass-granule-pack. Sequential (4D) CMT imaging captured the capillary-dominated displacement of the oil-occupied matrix by the surfactant-brine-occupied fracture at the pore scale. The sintered glass-granule-pack was designed to have minimal pore space beyond the resolution of CMT imaging, ensuring that the pore space of the matrix connected to the fracture could be captured in its entirety. This provided an opportunity to validate the increasingly common lattice Boltzmann modeling technique against experimental images at the pore scale. Although the surfactant was found to alter the wettability of the originally weakly oil-wet glass to water-wet, the fracture-matrix fluid transfer is found to be a drainage process, showing minimal counter-current migration of the initial wetting phase (decane). The LB simulations were found to closely match experimental rates of fracture-matrix fluid transfer, and trends in the saturation profiles, but not the irreducible wetting-phase saturation behind the flooding front. The underestimation of the irreducible wetting phase saturation suggests that finer image and lattice resolutions than those reported here may be required for accurate prediction of some macroscale multiphase flow properties, at a sizable computational cost.     

Pore-Scale Analysis of NAPL Blob Dissolution and Mobilization in Porous Media

A pore-scale analysis of nonaqueous phase liquid (NAPL) blob dissolution and mobilization in porous media was presented. Dissolution kinetics of residual NAPLs in an otherwise water-saturated porous medium was investigated by conducting micromodel experiments. Changes in residual NAPL volume were measured from recorded video images to calculate the mass transfer coefficient, K and the lumped mass transfer rate coefficient, k. The morphological characteristics of the blobs such as specific and intrinsic area were found to be independent of water flow rate except at NAPL saturations below 2%. Dissolution process was also investigated by separating the mass transfer into zones of mobile and immobile water. The fractions of total residual NAPL perimeters in contact with mobile water and immobile water were measured and their relationship to the mass transfer coefficient was discussed. In general, residual NAPLs are removed by dissolution and mobilization. Although these two mechanisms were studied individually by others, their simultaneous occurrence was not considered. Therefore, in this study, mobilization of dissolving NAPL blobs was investigated by an analysis of the forces acting on a trapped NAPL blob. A dimensional analysis was performed to quantify the residual blob mobilization in terms of dimensionless Capillary number (Ca _I). If Ca _I is equal to or greater than the trapping number defined as , then blob mobilization is expected.     

Grain Shape Effects on Permeability,Formation Factor,and Capillary Pressure from Pore-Scale Modeling

We invoke pore-scale models to evaluate grain shape effects on petrophysical properties of three-dimensional (3D) images from micro-CT scans and consolidated grain packs. Four sets of grain-packs are constructed on the basis of a new sedimentary algorithm with the following shapes: exact angular grain shapes identified from micro-CT scans, ellipsoids fitted to angular grains, and spheres with volume and surface-to-volume ratio equal to original angular grains on a grain-by-grain basis. Subsequently, a geometry-based cementation algorithm implements pore space alteration due to diagenesis. Eight micro-CT scans and 144 grain-pack images with $500 \times 500 \times 500$ voxels (the resolution units of 3D images) are analyzed in this study. Absolute permeability, formation factor, and capillary pressure are calculated for each 3D image using numerical methods and compared to available core measurements. Angular grain packs give rise to the best agreement with experimental measurements. Cement volume and its spatial distribution in the pore space significantly affect all calculated petrophysical properties. Available empirical permeability correlations for non-spherical grains underestimate permeability between 30 and 70 % for the analyzed samples. Kozeny–Carman’s predictions agree with modeled permeability for spherical grain packs but overestimate permeability for micro-CT images and non-spherical grain packs when volume-based radii are used to calculate the average grain size in a pack. We identify surface-to-volume ratio and grain shape as fundamental physical parameters that control fluid distribution and flow in porous media for equivalent porosity samples.     

A Network Modeling Approach to Derive Unsaturated Hydraulic Properties of a Rough-Walled Fracture

The hydraulic properties of a rough-walled fracture in a limestone sample are estimated using a network model based on three-dimensional representations of the fracture apertures. Two different scenarios are considered: drainage of water out of a fracture and infiltration of water into a fracture. Besides capillary effects, the model takes into account an accessibility criterion (invasion percolation) and, in the case of infiltration, the rate dependence of the water movement. A hysteresis effect between drainage and imbibition hydraulic properties can be observed, which increases with increasing capillary number. The measured permeability is overestimated by 15% by the network model. In a sensitivity analysis the influence of the main fracture field characteristics (field size and fracture segment size in relation to correlation length) on the calculated hydraulic properties is investigated. Field size has an important influence on the inverse of the water/air entry value for imbibition, making it difficult to scale this parameter to other field sizes. A parameter analysis investigating the influence of the main fracture characteristics (mean fracture aperture, roughness, and correlation length) on the hydraulic properties shows that the mean fracture aperture is the most important fracture parameter influencing both strongly the saturated permeability K and . The effect of varying the variance and the correlation length on K and is much less than the influence of the mean fracture aperture. The effective permeability of the fracture is also calculated by the geometric mean K _g . Up to (log_e(K)) = 1, the discrepancy between K _g and K _n (network model result) is less than 15%. At larger correlation lengths (for a constant (log_e(K))), the discrepancy between K _g and K _n increases.     

Thermographical Analysis of Paper During Tensile Testing and Comparison to Digital Image Correlation

The thermal response in paper has been studied by thermography. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of warmer streaks could be observed in the samples. On the same samples digital image correlation (DIC) was used to study local strain fields. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Because of its fibrous network structure, paper has an inhomogeneous micro-structure, which is called formation. It could be shown that the formation was the cause of the inhomogeneous deformations in paper. Finite element simulations was used to show how papers with different degrees of heterogeneity would deform. Creped papers, where the strain at break has been increased, were analysed. For these paper it was seen that an overlaid compaction of the paper was created during the creping process. During tensile testing this was recovered as the paper network structure was strained.     

Droplet Imbibition into Paper Coating Layer: Pore-Network Modeling Simulation

Liquid penetration into thin porous media such as paper is often simulated using continuum-scale single-phase Darcy’s law. The underlying assumption was that a sharp invasion front percolates through the layer. To explore this ambiguous assumption and to understand the controlling pore-scale mechanisms, we have developed a dynamic pore-network model to simulate imbibition of a wetting phase from a droplet into a paper coating layer. The realistic pore structures are obtained using the FIB-SEM imaging of the coating material with a minimum resolution of 3.5 nm. Pore network was extracted from FIB-SEM images using Avizo software. Data of extracted pore network are used for statistically generating pore network. Droplet sizes are chosen in the range of those applicable in inkjet printing. Our simulations show no sharp invasion front exists and there is the presence of residual non-wetting phase. In addition, penetration of different sizes of droplets of different material properties into the pore network with different pore body and pore throat sizes are performed. We have found an approximately linear decrease in droplet volume with time. This contradicts the expected \(\sqrt{t}\)-behavior in vertical imbibition that is obtained using macroscopic single-phase Darcy’s law. With increase in flow rate, transition of imbibition invasion front from percolation-like pattern to a more sharper one with less trapping of non-wetting phase is also reported. Our simulations suggest that the single-phase Darcy’s law does not adequately describe liquid penetration into materials such as paper coating layer. Instead Richards equation would be a better choice.     

基于图像分析法的水稻茎秆力学性能测量与分析

水稻茎秆力学性能的准确描述是水稻抗倒伏力学分析的关键。由于茎秆是由生物活性材料组成的形状不规则柔性结构,传统的测试方法难以对其力学性能进行准确测量。以南方水稻为研究对象,采用拉伸试验机对水稻茎秆进行了拉伸试验。首先采用传统的应变片方法测量应变,继而探索采用图像分析法实现非接触、高精度地测量水稻茎秆的截面尺寸、拉伸变形。用数字摄像机记录不同荷载水平下试件表面的数字图像,采用数字图像相关分析法(DIC)进行分析,通过两种方法计算茎秆的轴向应变;将完成拉伸实验的试件切片,采集其横截面的数字图像,通过数字图像分析技术得到其几何特性,并对大量实验数据进行了统计分析,实现了对水稻茎秆弹性模量、抗弯刚度等的合理描述。实验结果表明,采用传统的应变片测量求得的水稻茎秆的弹性模量的离散性极大,超出样本差异性的范围,而采用数字图像分析方法得到的弹性模量、抗弯刚度的结果有一定的离散性,但分布比较合理,比较准确地反映了水稻茎秆相关的力学性能。     

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.