Pore Space Model Research Articles

Study of structural characteristics of hydrocarbon reservoir pore space based on X-ray computed tomography images

Digital studies of pore space and internal structure of hydrocarbon reservoir were conducted on the basis of multiscale X-ray computed tomography images and the analysis of heterogeneities, cavernosity, fracturing and bedding in the rock. Main results. 3D models of rock pore space were created on the basis of computed tomography images through segmentation. Porosity estimation based on the digital approach was performed. It was shown that the digitally obtained data are in good agreement with the results of laboratory measurements. Analysis and visualization of the structure of the main filtration channels in the rock were performed. Pore size distributions in the specimen were obtained, and 3D visualization of the largest pore size was shown. Conclusions. The pore space characteristics obtained on the basis of tomographic approach are valuable data for filling reservoir models and can be used in solving the problems of permeability reduction during different kinds of reservoir impacts. Application of the obtained results in combination with geomechanical tests of rocks is intended to expand existing approaches to complex analysis of core material of reservoirs, as well as to supplement and refine mathematical and operational models of the studied objects.

Numerical Study of Gas Breakthrough in Preferential Rocks for Underground Nuclear Waste Repositories

During the long-term storage of radioactive waste, the continuous generation of gas in the disposal area may influence the integrity of host rock. Thus, the investigation of gas migration and breakthrough in low-permeability rock is indispensable for the stability assessment. In this work, the pore space models of four potential host rocks (Boom clay, COx argillite, Opalinus clay, and Beishan granite) were generated via the binarization of the Gaussian random field. This method provides a randomly formed pore network that does rely on an initial definition of pore shape. The constructed models were analyzed and validated by using the mathematical morphology. A numerical calculation scenario of gas breakthrough on the basis of the Young–Laplace equation was proposed and applied. Results show that the gas breakthrough pressures are 2.62–4.11 MPa in Boom clay and 3.72–4.27 MPa in COx argillite. It enhances the idea that the capillary-induced gas breakthrough is possible at pressures lower than the fracture threshold. For Opalinus clay and Beishan granite, no connected pathway exists, and the breakthrough is more likely to occur through pathway dilation or fractures. The presented method has the advantage of experimental reproducibility and brings a new idea for the investigation of fluid migration in low-permeability rocks.

Experimental and Numerical Research on Water Transport during Adsorption and Desorption in Cement-Based Materials

The durability of cement-based materials is related to water transport and storage in their pore network under different humidity conditions. To understand the mechanism and characteristics of water adsorption and desorption processes from the microscopic scale, this study introduces different points of view for the pore space model generation and numerical simulation of water transport by considering the “ink-bottle” effect. On the basis of the pore structure parameters (i.e., pore size distribution and porosity) of cement paste and mortar with water-binder ratios of 0.3, 0.4 and 0.5 obtained via mercury intrusion porosimetry, randomly formed 3D pore space models are generated using two-phase transformation on Gaussian random fields and verified via image analysis method of mathematical morphology. Considering the Kelvin-Laplace equation and the influence of “ink-bottle” pores, two numerical calculation scenarios based on mathematical morphology are proposed and applied to the generated model to simulate the adsorption-desorption process. The simulated adsorption and desorption curves are close to those of the experiment, verifying the effectiveness of the developed model and methods. The obtained results characterize water transport in cement-based materials during the variation of relative humidity and further explain the hysteresis effect due to “ink-bottle” pores from the microscopic scale.

Studying the porosity of graphite foil with different densities: pore space model and gas permeability

Studying the porosity of graphite foil with different densities: pore space model and gas permeability

Quantitative Comparison of 3D Pore Space Properties With Magnetic Pore Fabrics—Testing the Ability of Magnetic Methods to Predict Pore Fabrics in Rocks

AbstractPore fabrics characterize the anisotropy of pore space in rocks and influence the direction of fluid flow. This is important in reservoir characterization, and petroleum and geothermal energy exploitation. X‐ray computed micro‐tomography (XRCT) is commonly used to analyze pore fabrics, but limited by the micron‐scale resolution for representative 1‐inch rock cores. The magnetic pore fabric (MPF) method has been proposed to capture pores down to 10 nm. Although empirical relationships between MPF and pore space properties or permeability anisotropy are available, their application is compromised by large variability. This study integrates He pycnometry and XRCT‐derived pore space models with MPFs, and provides a quantitative comparison for calcarenite (∼50 vol% porosity and complex pore structure), and molasse sandstone (10%–30% porosity and relatively homogeneous pore fabrics). The preferred orientation of pores obtained from XRCT is described by a total shape ellipsoid, calculated by summing the second‐order tensors reflecting the best‐fit ellipsoids of individual pores. This ellipsoid is then compared to the MPF magnitude ellipsoid in terms of fabric orientation, degree and shape of anisotropy. The MPF and total shape ellipsoids are generally coaxial. The MPF has a smaller anisotropy degree than the total shape ellipsoid, and their relationship depends on the ferrofluid properties. The anisotropy shapes show large variability. Nevertheless, the good agreement of principal directions in most samples makes MPFs a valuable and efficient complementary tool to analyze a large number of samples, in combination with XRCT on selected samples, for a field‐scale pore space characterization.

Research on CO2 transfer in basalt and sandstone using 3D pore space model generation and mathematical morphology

The performance of basalt and sandstone for CO2 storage mainly depends on the CO2 migration and solidification in the pore network of rock. This study provides points of view for the simulation of the three-dimensional pore space and the numerical prediction of gas transfer in the microstructure of the studied rocks. The biphasic change on Gaussian random field forms a randomly shaped pore network and the combination of biphasic fields creates a porous model that satisfies the real rock porosity and pore size distribution. Based on the generated model, several calculation scenarios using the mathematical morphology are proposed and numerically implemented to investigate the pore space characteristics, to extract the potential CO2 transfer paths, to analyze the geometric features and thus to evaluate the CO2 storage performance.

Conductivity in partially saturated porous media described by porosity, electrolyte saturation and saturation‐dependent tortuosity and constriction factor

ABSTRACTModelling the relationships among bulk conductivity, electrolyte conductivity, porosity and fractional electrolyte‐saturation continues to be based on empirical relationships such as Archie's law or the Bruggeman correlation. Several authors have attempted to connect such empirical models to first principles. This article presents a complete first principles‐based description of conductivity in partially saturated porous media. A geometrical factor is introduced which, together with porosity and saturation, describes the conductivity of partially saturated porous media. This geometrical factor is separated into two intrinsic geometrical descriptors of the electrolyte distribution accounting for tortuosity and constriction. This tortuosity and constriction factor are obtained from integration over the electrical field lines traversing the electrolyte. Bulk and saturation‐dependent conductance descriptions are illustrated using three‐dimensional pore space models and simulated fluid distributions. Describing conductance through porosity, saturation and a geometrical factor, decomposed into separate terms accounting for tortuosity and constrictivity, permits more insightful understanding of conductance in partially saturated porous media. Use and efficacy of this full conductance description is illustrated throughout this article.

DIGITAL CLUSTER MODEL OF PORE SPACE AT FLOW OF THREE-PHASE FLOW IN POROUS MEDIUM

The work is devoted to one of the urgent problems of the oil and gas industry — the study of three-phase filtration. The creation of pore space models is an important stage in the study of the flow of oil and gas mixtures for the subsequent determination of the filtration and reservoir properties of reservoir rocks. The aim of the study is to develop a physical and mathematical model of a porous medium on the scale of a core sample. A digital cluster model for calculating the geometric parameters of the pore space is presented. The structure of the pore space of the cluster model is based on the distribution of pores by diameters obtained from capillary pressure curves (KCD). The core contains clusters consisting of a big channel (B) through which oil, water and gas move in a clear mode, average channels (A) with moving water and gas and small channels (S) with moving gas, as well as bridges between these channels. The division of the pore diameter distribution function into regions related to big, average and small channels is based on empirically determined relationships between the numbers of channels through which fluids move in the pore space in the above combinations. At the same time, the transition from the physical core model to the digital cluster model is carried out with the preservation of porosity, absolute permeability and taking into account the tortuosity of the channels. The dependence of the tortuosity of channels on their diameter is assumed according to a decreasing power law. The model presented in this paper is tested on two examples at different values of effective porosity and the number of intervals of the pore distribution function by diameter. The model has the potential for further development and calculation of the filtration flow of a three-phase mixture (oil, gas and water) on the scale of a core sample.

Pore-scale simulation of remaining oil distribution in 3D porous media affected by wettability and capillarity based on volume of fluid method

Characterizing the trapped phase in porous media is essential for many engineering applications, such as enhanced oil recovery, nuclear storage, and geological sequestration of CO2. This study aims to study the distribution, evolution, and influencing factors of the remaining oil in the process of water flooding at the pore scale. The single-connected pore space model was established by reconstructing the real micron CT scanned images of carbonate rocks. The VOF (volume of fluid) method using FSF (filtered surface force) formulation was adopted on OpenFOAM platform to simulate the oil-water two-phase flow process at the pore scale. Different wettability and capillary number were considered in the model. The accuracy of the model was proved by comparing with previous experimental results. The results showed that in the process of water flooding, the complex pore structure would lead to the generation of remaining oil, and the phase circulation phenomenon can be observed in the remaining oil and presents two distribution forms: co-current driven flow and lid-cavity driven flow. It also revealed that the phase recirculation increases the viscous dissipation. Further research also showed that the two forms of recirculation could be transferred by changing the wettability and that a higher capillary number was more beneficial for reducing the remaining oil saturation.

Fast simulation of two-phase flow in three-dimensional digital images of heterogeneous porous media using multiresolution curvelet transformation

Advances in instrumentation have made it possible to obtain high-resolution images of heterogeneous porous media. Such advances and the rapid increase in computational power mean that direct numerical simulation of multiphase flow in two- and three-dimensional (3D) images of porous media is feasible and, therefore, models of pore space that represent simplification and approximation of the actual morphology are dispensable. The bottleneck for image-based simulation is its long computation time. We propose an approach for speeding-up simulation of multiphase flow in 3D images of porous media that utilizes curvelet transformations (CTs). The CTs are designed for denoising of images that contain complex curved surfaces, such as those of heterogeneous porous media. This is possible because the morphology of most porous media contain extended correlations, implying that their images carry redundant information that can be eliminated by a suitable CT. As a result, simulation of multiphase flow in the coarser images are far less computationally intensive. The new approach is used to simulate two-phase flow of CO2 and brine in a 3D image of Berea sandstone. We demonstrate that the results with the CT-processed image are as accurate as those with the original one, while computations are significantly faster by a speedup factor between one and more than two orders of magnitude.

Speeding-up Simulation of Multiphase Flow in Digital Images of Heterogeneous Porous Media by Curvelet Transformation

Multiphase fluid flow in porous media is important to a wide variety of processes of fundamental scientific and practical importance. Developing a model for the pore space of porous media represents the first step for simulating such flows. With rapid increase in the computation power and advances in instrumentation and imaging processes, it has become feasible to carry out simulation of multiphase flow in two- and three-dimensional images of porous media, hence dispensing with development of models of pore space that are based on approximating their morphology. Image-based simulations are, however, very time consuming. We describe an approach for speeding-up image-based simulation of multiphase flow in porous media based on curvelet transformations, which are specifically designed for processing of images that contain complex curved surfaces. Most porous media contain correlations in their morphology and, therefore, their images carry redundant information that, in the curvelet transform space, can be removed efficiently and accurately in order to obtain a coarser image with which the computations are far less intensive. We utilize the methodology to simulate two-phase flow of oil and water in two-dimensional digital images of sandstone and carbonate samples, and demonstrate that while the results with the curvelet-processed images are as accurate as those with the original ones, the computations are speeded up by a factor of 110–150. Thus, the methodology opens the way toward achieving the ultimate goal of simulation of multiphase flow in porous media, namely, making image-based computations a standard practice.

Revealing soil‐borne hydrogel effects on soil hydraulic properties using a roughness‐triangular pore space model

AbstractUnderstanding the influence of soil‐borne hydrogels (e.g., bacterial extracellular polymeric substances [EPS] and biofilm or root‐derived mucilage) on soil hydraulic properties is crucial for accurate modeling of flow and transport in porous media. The underlying mechanisms of how hydrogels modify soil physical and hydraulic properties, however, remain unclear. In this study, we applied a roughness‐triangular pore space model (R‐TPSM) to simulate water retention curve and hydraulic conductivity of hydrogel‐affected soils. The model considers the effective soil pore size distribution and physicochemical properties (e.g., surface tension and surface roughness) of soil and soil solution. The modeling results are in good agreement with measured water retention curves and hydraulic conductivity for different textured soils. Comparison of the fitted model parameters between control and hydrogel‐treated soil samples indicates that hydrogels reduce surface tension and shift the effective pore size distribution to a narrower size range. Hydrogels generally increase water retention in the form of adsorptive films and reduce film flow under relatively dry conditions. This study highlights the importance of considering reduced surface tension and mean pore size by hydrogels in changing soil hydraulic properties, which has important implications for accurate modeling of water distribution and flow in the rhizosphere.

THE BASIC LAWS OF THE CONCEPT OF PORE SPACE CONNECTEDNESS FOR PETROPHYSICAL MODELING OF RESERVOIR PROPERTIES OF TERRIGENOUS OIL ROCKS

The paper presents mathematical patterns that allow petrophysical modeling of the basic static and dynamic filtration-capacitive properties of rocks. The considered generalized laws are a mathematical expression of the concept of connected pore space and are obtained on the basis of a general model of effective pore space, based on the results of computer modeling of 3D percolation gratings.

Analysis of Seepage Characteristics of Complex Pore Structure Rock by Digital Core Method

Application of traditional rock physics experimental methods in investigating the macroscopic pertrophysical properties of low porosity, low permeability, and high complexity pore structure reservoirs is limited by the high cost, long cycle, large error, and specific difficulties of such reservoirs. It is also difficult to evaluate quantitatively the influence of microscopic reservoir structure on rock physical properties. Application of micro-CT scanning and advanced imaging processing technology enables one to establish an accurate representative pore space model equivalent to the true core structure. Numerical simulation with Avizo-XLab solver method was used to calculate the pore fluid flow based on the Navier-Stokes equation and the Darcy seepage law. The visualization method helped to display the pore-space fluid flow in a three-dimensional streamline, and the pore pressure distribution field is displayed, making the simulation results clear and intuitive. Research shows that numerical simulation based on the digital platform provides an instrument for the measurement of the fluid micro flow and the rock seepage parameters. This paper provides a new method for digital research on rock physical properties which helps to overcome the deficiency of traditional rock physics experimental research.

Simulation of non-Newtonian fluid seepage into porous media stacked by carbon fibers using micro-scale reconstruction model

Ceramic matrix composite of carbon fiber framework reinforced by silicon carbide (Cf/SiC) is a new material with excellent properties. In order to improve its preparation process, the flow of polycarbosilane solution in carbon fiber is studied based on the computational fluid dynamics method. CT images of carbon fiber porous media are obtained by Micro-CT imaging technology and optimized by means of ImageJ software. The 3D solid matrix and pore space models of carbon fiber porous media are established by using Mimics software, and the pore space model is meshed. Using the computational fluid dynamics software Fluent, the VOF multiphase flow model is adopted, the surface tension model and contact angle model are introduced considering the micro-pore effect of porous media, and a suitable mathematical model for the transport of gas–liquid two-phase flow in carbon fiber porous media is established. The validity of CFD mathematical model is verified by comparing experimental data with simulation results. Based on the CFD simulation results, the effects of feed pressure, surface tension coefficient and contact angle on fluid flow are studied. It is found that the larger the feed pressure and contact angle, the more uniform the distribution of liquid phase, pressure and velocity in the medium, which is conducive to the flow of liquid phase in porous media. The larger the surface tension coefficient, the longer the breakthrough time of liquid, and the more uneven the liquid distribution. This study is helpful to understand the law of fluid transport in porous media and provides theoretical basis for the preparation of Cf/SiC composites.

Pore size distribution and reservoir characterization: evaluation for the Eocene beach-bar sequence, Dongying Depression, China

Pore size distribution and associated heterogeneities of thinly bedded beach-bar sandstone reservoir from upper fourth member of Eocene Shahejie Formation (Es4s) are characterized with the help of mercury injection capillary pressure (MICP) and nuclear magnetic resonance (NMR) transversal relaxation time (T2) data. Permeability and porosity are two represented important characteristics of rocks that control the movement and storage of fluids. The aim of this paper is to establish relationships between pore throat sizes and reservoir quality. The results derived from thin-section petrography, scanning electron microscopy (SEM), MICP, NMR T2 relaxation time, and 3D micro-CT (μ-CT) are compared to characterize pore space dimensions and types comprehensively. Average pore throat size from MICP ranges between 0.47 μm and 2.83 μm while maximum pore throat size ranges between 2.48 μm and 7.36 μm. The combination of pore size distribution obtained from MICP and NMR seems appropriate to cover the range of pore size from beach-bar sand and overcome the individual method limits. Afterwards, digital 3D μ-CT tomographic images are used to characterize and visualize pore space and pore network model to compare with the experimental data. MICP and NMR experiment showed generally bimodal (meso and micro) pore size distribution. Usually mesopore corresponding to intergranular pores is dominant, while heavily cemented sandstones show large amounts of intercrystalline micropores. Complex and heterogeneous beach-bar sandstone reservoir requires comprehensive study program to evaluate the reservoir.

On the challenges of greyscale-based quantifications using X-ray computed microtomography.

For X-ray computed microtomography (μ-CT) images of porous rocks where the grains and pores are not fully resolved, the greyscale values of each voxel can be used for quantitative calculations. This study addresses the challenges that arise with greyscale-based quantifications by conducting experiments designed to investigate the sources of error/uncertainty. We conduct greyscale-based calculations of porosity, concentration and diffusivity from various μ-CT experiments using a Bentheimer sandstone sample. The dry sandstone is imaged overtime to test the variation of greyscale values over sequential scans due to instrumentation stability. The sandstone is then imaged in a dry and contrast-agent saturated state at low resolution to determine a porosity map, which is compared to a porosity map derived from segmented high-resolution data. Then the linearity of the relationship between the concentration of a contrast agent and its corresponding attenuation coefficient is tested by imaging various solutions of known concentration. Lastly, a diffusion experiment is imaged at low resolution under dynamic conditions to determine local diffusivity values for the sandstone, which is compared to values derived from direct pore-scale simulations using high-resolution data. Overall, we identify the main errors associated with greyscale-based quantification and provide practical suggestions to alleviate these issues. LAY DESCRIPTION: X-ray computed microtomography (CT) imaging has become an important way to study the pore space of a porous medium. Using segmented images, we can build 3D pore space models for porous media and characterize the morphology and/or run simulations on the models. So, image segmentation is a critical image processing step. However, for low resolution images where image segmentation is not possible, grayscales are directly used for quantifications such as porosity and concentration calculations. Although these types of calculations have been widely accepted and used, the uncertainties and errors associated with grayscale-based quantifications are not fully discussed. Here we specifically design experiments with X-ray CT imaging to address the challenges that arise in grayscale-based quantifications. For instance, in order to validate porosity calculation results from low resolution images (with the help of high attenuating tracer), high resolution images are also acquired, which serve as a benchmark. The errors associated with concentration calculation using grayscale values are also discussed. In addition, numerical simulations using grayscale values are performed on a diffusion experiment images with X-ray CT. The problems that arise in dynamic imaging and the subsequent numerical simulations are discussed. The experiments, calculations and discussions provide a more comprehensive understanding on grayscale-based quantifications and aid in designing better X-ray CT experiments.

Modeling the spectral features of acoustic noise produced by gas flow in rock samples based on the theory of ensemble of interconnected pore resonators

A new model describing the pore space as an ensemble of interconnected Helmholtz resonators is proposed. This model makes it possible to improve the description of spectral peculiarities of the experimentally recorded acoustic noise during gas flow through a porous medium. The results of the resonance frequency calculation are presented by the example of the pore space model of the Indiana Limestone. Microvortexes in the pores are considered as the main mechanism of acoustic noise generation by gas flow. The presented numerical simulations on COMSOL Multiphysics show that the generation of microvortexes begins when the Reynolds number in the pores reaches 1 to 10.

Modeling the Spectral Features of Acoustic Noise Produced by Gas Flow in Rock Samples Based on the Theory of Ensemble of Interconnected Pore Resonators

A new model describing the pore space as an ensemble of interconnected Helmholtz resonators is proposed. This model makes it possible to improve the description of spectral peculiarities of the experimentally recorded acoustic noise during gas flow through a porous medium. The results of the resonance frequency calculation are presented by the example of the pore space model of the Indiana Limestone. Microvortexes in the pores are considered as the main mechanism of acoustic noise generation by gas flow. The presented numerical simulations on COMSOL Multiphysics show that the generation of microvortexes begins when the Reynolds number in the pores reaches 1 to 10.

Rheological Properties and Tomographically Determined Pore Space of Undisturbed Samples of Typical Chernozems and Soddy-Podzolic Soils

Coupled studies of pore space and rheological behavior of undisturbed samples from soddypodzolic soils (Albic Glossic Retisols (Loamic, Aric, Cutanic)) of Moscow oblast under forest and under cropland and from typical chernozems (Haplic Chernozems (Loamic, Aric, Pachic)) of Kursk oblast under oak forest, shelterbelt, and cropland were conducted. Soil pore space was investigated using a Bruker SkyScan 1172 G (Belgium) microtomograph, and 3D models of pore space were constructed. The total pore space (in percent of the volume of analyzed samples) and the volumes of open and closed pores were determined from these models. The nondestructive tomographic method made it possible to analyze the rheological properties of soils for the same samples using the amplitude sweep method on an MCR-302 (Anton Paar, Austria) rheometer. The following parameters of the rheological behavior were determined: storage modulus in the range of linear viscoelastic behavior, the range of linear viscoelastic behavior, and the range of plastic behavior. A joint analysis of the rheological properties and morphometric characteristics of the undisturbed samples of soddy-podzolic soils and chernozems demonstrated the dependence of the rheological behavior of these soils on their physicochemical properties and pore space structure reflecting the differences in the genesis and physical and chemical properties of soil horizons. The correlation analysis attested to direct (positive) relationships between the values of the total and open tomographic porosities, the range of linear viscoelastic behavior, and the deformation upon the destruction of soil structure. Negative relationships were found between the values of open and total porosity and the structural strength of the soil monoliths. A hypothesis about an increase in the range of plastic behavior of soils and a decrease in the strength of soil structure with an increase in porosity was suggested.