Images Of Sandstone Research Articles

Image segmentation and flow prediction of digital rock with U-net network

Computed tomography (CT) images of sandstone contain rich reservoir information. Analyzing digital rock images is important for geological research and the flow in the subsurface. This paper presents a workflow for assessing digital rock petrophysical properties based on machine learning techniques, including 1) automatic segmentation of sandstone rock images using U-net networks, 2) permeability prediction using machine learning, and 3) flow simulation by deep learning. First, using the U-net network, the rock images are binary-segmented into matrix and pore, and multisegmented into the matrix, pore, and mineral. The accuracy and intersection over union (IOU) are used to evaluate the performance of image segmentation. The accuracy and IOU of binary segmentation results are 99.87% and 0.9986, and the results for multi-segmentation are 96.77% and 0.7281, respectively. Then, the key features of CT images influencing sandstone permeability are extracted, and the analysis of image features reveals that the hydraulic radius is the most important parameter for permeability prediction. After that, the sandstone permeability is predicted by long short-term memory (LSTM) and random forest (RF) and then compared with the permeability calculated by the lattice Boltzmann (LBM) method. The mean square error (MSE), mean absolute error (MAE), and root mean square error (RMSE) are used to quantitatively evaluate the error of permeability prediction. The studies show that the precision of RF in permeability prediction is higher than that of LSTM, and when all the feature parameters are used as input, the accuracy of permeability prediction is a little higher than that when only the hydraulic radius is used as input. Finally, this paper refines a new U-net model to predict the flow velocity field from CT images, and this new U-net model can reduce the computation time by 98.59% compared with the LBM method. This study will be significant for applying deep learning in simulate the flow in digital rock.

Tight Sandstone Image Augmentation for Image Identification Using Deep Learning

Intelligent identification of sandstone slice images using deep learning technology is the development trend of mineral identification, and accurate mineral particle segmentation is the most critical step for intelligent identification. A typical identification model requires many training samples to learn as many distinguishable features as possible. However, limited by the difficulty of data acquisition, the high cost of labeling, and privacy protection, this has led to a sparse sample number and cannot meet the training requirements of deep learning image identification models. In order to increase the number of samples and improve the training effect of deep learning models, this paper proposes a tight sandstone image data augmentation method by combining the advantages of the data deformation method and the data oversampling method in the Putaohua reservoir in the Sanzhao Sag of the Songliao Basin as the target area. First, the Style Generative Adversarial Network (StyleGAN) is improved to generate high-resolution tight sandstone images to improve data diversity. Second, we improve the Automatic Data Augmentation (AutoAugment) algorithm to search for the optimal augmentation strategy to expand the data scale. Finally, we design comparison experiments to demonstrate that this method has obvious advantages in generating image quality and improving the identification effect of deep learning models in real application scenarios.

A level set approach to Ostwald ripening of trapped gas bubbles in porous media

Ostwald ripening of gas bubbles is a thermodynamic process for mass transfer, which is important for both foam enhanced oil recovery and geological CO2 storage. We present a methodology for simulating Ostwald ripening of gas ganglia surrounded by liquid in arbitrary pore geometries. The method couples a conservative level set model for capillary-controlled displacement and a ghost-bubble technique that calculates mass transfer based on difference in chemical potentials. The methodology is implemented in a software framework for parallel computations. As a validation of the model, we show that simulations of bubble ripening in a pore throat connecting two pore bodies are consistent with previously reported trends in similar geometries. Then we investigate the impact of gas type, compressibility factor, and local capillary pressure on gas-bubble ripening in various water-wet pore geometries. The results confirm that gas solubility and compressibility factor are proportional to the rate of mass transfer. Our simulations suggest that Ostwald ripening has largest impact in heterogeneous or fractured porous structures where differences in gas-bubble potentials are high. However, if the liquid separating the gas bubbles is also a disconnected phase, which can happen in intermediate-wet porous media, the resulting local capillary pressure can limit the coarsening and stabilise smaller bubbles. Finally, we simulated Ostwald ripening on a 3-D pore-space image of sandstone containing a residual gas/water configuration after imbibition. Characterization of gas-bubble morphology during the coarsening shows that large ganglia get more ramified at the expense of small spherical ganglia that cease to exist.

Bayesian Optimization With Transfer Learning: A Study on Spatial Variability of Rock Properties Using NMR Relaxometry

AbstractNuclear magnetic resonance measurements of sedimentary rocks are used to extract various transport properties including hydraulic conductivity and water retention curves. These estimates are controlled by intrinsic physical quantities like surface relaxivities, and effective relaxation time and restricted self‐diffusion coefficient of water in clay. Sampling these properties on a set of core plugs presents a series of inverse problems where some of the extracted parameters are expected to be similar. To leverage such valuable information, we extend a previously developed single‐task inverse solution workflow (ISW) to the multi‐task case, transferring the knowledge gained from previous optimization tasks. Two multi‐task kernels: intrinsic model of coregionalization (ICM) and linear model of coregionalization are compared to capture the underlying correlations. We consider three micro‐CT images of Bentheimer sandstone from two different blocks imaged at different resolutions, following different segmentation pathways, and demonstrate our approach for the case of low and high task similarity. In both scenarios the multi‐task ISW finds lower fitting residuals and uses only one‐third to one‐half of the function evaluations required by the single‐task ISW. The scalability of the multi‐task ISW is demonstrated by transferring knowledge of two completed optimization tasks to a third task, which outperforms the single‐task ISW, with ICM showing faster convergence. The observed 4% difference for the values identified for samples from the same block and around 28% difference across blocks indicates significant spatial variability in surface relaxivity of the main mineral component, while effective clay parameters show a significantly higher variability.

Multistep Super Resolution Double-U-net (SRDUN) for enhancing the resolution of Berea sandstone images

Digital Rock Physics (DRP) has opened a new avenue through the microscale world of rocks leading to more detailed inferences. However, High Resolution (HR) images are problematic from several aspects such as low field of view, huge memory and long time and high cost of image acquisition. Recent advances in Machine Learning (ML) and especially Convolutional Neural Networks (CNN) highly improved the ability of producing HR images from their Low Resolution (LR) counterparts known as Super Resolution (SR) images. In this procedure, the scale-difference between LR and HR images is a key parameter, while a high scale-difference leads to unreliable results regardless of the method. To overcome such a problem, we aim to both propose a multiscale procedure and introduce an efficient network namely Super Resolution Double-U-net (SRDUN). To this end, unlike conventional studies where LR images are synthetically produced from HR images, we capture these images from a Berea sandstone individually in five different scales (16.263, 12.922, 9.499, 5.775 and 3.501 μm for samples with a side of 10, 8, 6, 4 and 2-mm). Then, the SRDUN is introduced, where a first U-net is used to store feature maps of HR images and are imported in a second U-net as informative skip connections. Results show SRDUN could perform more accurate than common networks for small scale-differences. However, when it comes to high scale-differences it becomes more complicated. We propose a multistep procedure, where several mid-step SRDUNs are used to fill the gap of information. Results of this procedure reveal that the multistep procedure could perform much better than the direct approach. These results are then demonstrated by some computations of reservoir parameters such as porosity, pore equivalent diameter distribution, morphometric properties and permeability. Porosity and permeability computations showed that the error of computed values from SR images is increased by increasing scale-difference, however, the multistep procedure leads to more reliable results. The multistep procedure could preserve better the pore size distribution, however, in morphometric properties, the direct approach performs better since the multistep procedure suffers from a smoothing effect.

Deep-learning-based workflow for boundary and small target segmentation in digital rock images using UNet++ and IK-EBM

Three-dimensional (3D) X-ray micro-computed tomography (μCT) has been widely used in petroleum engineering because it can provide detailed pore structural information for a reservoir rock, which can be imported into a pore-scale numerical model to simulate the transport and distribution of multiple fluids in the pore space. The partial volume blurring (PVB) problem is a major challenge in segmenting raw μCT images of rock samples, which impacts boundaries and small targets near the resolution limit. We developed a deep-learning (DL)-based workflow for accurate and fast partial volume segmentation. The DL model's performance depends primarily on the training data quality and model architecture. This study employed the entropy-based-masking indicator kriging (IK-EBM) to segment 3D Berea sandstone images as training datasets. The comparison between IK-EBM and manual segmentation using a 3D synthetic sphere pack, which had a known ground truth, showed that IK-EBM had higher accuracy on partial volume segmentation. We then trained and tested the UNet++ model, a state-of-the-art supervised encoder-decoder model, for binary (i.e., void and solid) and four-class segmentation. We compared the UNet++ with the commonly used U-Net and wide U-Net models and showed that the UNet++ had the best performance in terms of pixel-wise and physics-based evaluation metrics. Specifically, boundary-scaled accuracy demonstrated that the UNet++ architecture outperformed the regular U-Net architecture in the segmentation of pixels near boundaries and small targets, which were subjected to the PVB effect. Feature map visualization illustrated that the UNet++ bridged the semantic gaps between the feature maps extracted at different depths of the network, thereby enabling faster convergence and more accurate extraction of fine-scale features. The developed workflow significantly enhances the performance of supervised encoder-decoder models in partial volume segmentation, which has extensive applications in fundamental studies of subsurface energy, water, and environmental systems.

GeoChemFoam: Direct modelling of flow and heat transfer in micro-CT images of porous media

GeoChemFoam is an open-source OpenFOAM-based numerical modelling toolbox that includes a range of custom packages to solve complex flow processes including multiphase transport with interface transfer, single-phase flow in multiscale porous media, and reactive transport with mineral dissolution. In this paper, we present GeoChemFoam’s novel numerical model for simulation of conjugate heat transfer in micro-CT images of porous media. GeoChemFoam uses the micro-continuum approach to describe the fluid-solid interface using the volume fraction of fluid and solid in each computational cell. The velocity field is solved using Brinkman’s equation with permeability calculated using the Kozeny-Carman equation which results in a near-zero permeability in the solid phase. Conjugate heat transfer is then solved with heat convection where the velocity is non-zero, and the thermal conductivity is calculated as the harmonic average of phase conductivity weighted by the phase volume fraction. Our model is validated by comparison with the standard two-medium approach for a simple 2D geometry. We then simulate conjugate heat transfer and calculate heat transfer coefficients for different flow regimes and injected fluid analogous to injection into a geothermal reservoir in a micro-CT image of Bentheimer sandstone and perform a sensitivity analysis in a porous heat exchanger with a random sphere packing.

Pore scale image analysis for petrophysical modelling

Sedimentary rocks are known for their complex pore system with varying morphology due to intricate diagenetic processes. The present study demonstrates the applicability of image analysis in analysing and defining reservoir rock properties. Conventional techniques provide quantitative results but fail to give information about the internal microstructure of the rock. On the other hand, digital image techniques reveal the micro and macro-pore types and their connectivity across multiple scales. Hence, we performed the digital image analysis on Field Emission Scanning Electron Microscopy (FESEM) images of sandstone and carbonate samples collected from the upper Assam and Bombay offshore basins. FESEM derived image analysis was used exclusively due to its several unique features over contemporary techniques involving lesser data acquisition, simulation time and performing analysis even on a rock chip obtained while drilling the borehole. Porosity was evaluated based on the percentage of pores available within the image, and permeability was evaluated using the Kozeny-Carman equation. Further, we developed statistical equations to understand the existence of coherence amongst these parameters. Our study shows that we could determine both open and closed porosities by this method. In addition, there is an agreement between the conventional porosity measurement and image-derived porosity for most rock samples, especially for very low and high porosity. Further, this study highlights the importance of thresholding, an essential component in evaluating porosity using digital images. We propose that the methodology developed can accurately characterise reservoirs based on pore networks using high-resolution imaging techniques. The developed methodology may be adopted to promote best practices. Since we used digital images obtained from small chip size rock samples, this method is advantageous to quickly calculate the porosity and permeability from rock chips retrieved from the sieve shaker while drilling. Digital datasets extracted from this analysis will be helpful for reservoir description and characterisation based on image-derived petrophysical parameters.

3D tight sandstone digital rock reconstruction with deep learning

Tight oil and gas reservoirs have attracted an increasing amount of attentions and have become one of the focus of research field in recent years. Tight sandstones have complex pore structures and narrow pores and throats with pore sizes varying from nanometers to micrometers, and studying flow mechanisms in tight sandstones is of great importance to tight oil/gas reservoir development. Reconstructing digital rock, which can comprehensively represent the petrophysical properties of tight sandstone, is key to simulating the fluid flow in micro/nanopores. This paper proposes a new method of reconstructing 3D digital rock from CT images of tight sandstones based on a deep convolutional generative adversarial network (DCGAN), and 3D convolution in the generator and discriminator are adopted to realize reconstruction from 1D data to a 3D digital rock model. The model adopts pore area, volume, spatial distribution and connectivity, Fréchet inception distance score to evaluate the proposed model. Studies show that when the training effect is slightly poor, the generated digital rock model will exhibit noise, which can be reduced by postprocessing; when the training effect is good, DCGAN can accurately reconstruct the 3D digital rock model of tight sandstones, and the reconstructed digital rock is very consistent with the pore size, geometric structure, and connectivity of natural tight sandstones. When multiple 3D tight sandstone CT images are used for training, the DCGAN can learn the pore structure characteristics of entire tight sandstone bodies, which have strong heterogeneous, and the porosity distribution obtained from the generated digital rock is similar to that of the original tight sandstone. • Reconstructing 3D digital rock of tight sandstone based DCGAN with 3D convolution in the generator and discriminator. • Evaluating digital rock with pore area, volume, spatial distribution, connectivity, and the Fréchet inception distance score. • The reconstructed digital rock has a similar porosity distribution compared to the original heterogeneous tight sandstone.

Minimising the impact of sub-resolution features on fluid flow simulation in porous media

Resolution of micro-computed tomography (micro-CT) images of rocks affects flow simulation results, especially on low resolution images where the pore-grain boundary is not well resolved. However, there are two occasions where conducting flow simulations on low resolution images may be beneficial. The first case is when computation costs need to be reduced, and second is when high-resolution scanned images are unavailable and segmentation on available low-resolution images is difficult due to uncertainty at the pore boundary. A novel analytical formulation, the concentric pipes method, is introduced in this paper to include the effect of sub-resolution features in flow simulation. For the first case, we compare porosity, permeability, pore connectivity, and the velocity field obtained from applying different approaches to solve for flow on images with sub-resolution features. We find that the permeabilities obtained from downsampled images using the concentric pipes method have 13.2% errors on average compared to results from high-resolution images, while computation time decreases by at least 80%. For the second case, three phase segmentation can be applied to low resolution images and the concentric pipes method can be applied to the uncertain region which allows flow in the system to be solved. Permeability estimations in this case are within 0.5% error for a sandstone image and 11% error for carbonate images. We also simulate transport of particles on downsampled images and compare the transport properties with the high-resolution images.

Upscaling permeability anisotropy in digital sandstones using convolutional neural networks

Pore-scale modelling and implementation of micro x-ray Computed Tomography (μxCT) images have become a reliable method to predict the petrophysical properties of rocks. However, the prediction of porosity and investigation of permeability anisotropy is highly reliant on image resolution. The trade-off between image resolution and field of view makes properties prognostication of large-scales low-resolution models challenging. To estimate the properties of single-phase flow accurately, implementing the upscaling method is vital to correlate different scales. We have combined Convolutional Neural Networks (CNNs) with the downsampling technique as an upscaling approach and then carried it out on multiscale images of Fontainbleau sandstone. By employing pore-scale simulation, the normalized downsampled high-resolution images are labelled with their porosity, permeability in X-direction (kx), Y-direction (ky), and Z-direction (kz), used to train the CNNs. The upscaled properties of low-resolution images are predicted using trained CNNs. A continuum-scale simulator has been used to simulate single-phase flow in different directions to observe the anisotropy effect and compute the overall values of upscaled properties. The results suggest that the represented upscaling method can significantly close the properties of the low-resolution to the same properties of the high-resolution model while enormously reduces the computational time and cost.

Stress-dependent fluid dynamics of shale gas reservoirs: A pore network modeling approach

In this study, the pore network modeling approach is implemented to study the flow behavior of the methane gas in shale reservoirs in the presence of slip flow and gas desorption under different effective stress conditions through the effect on apparent permeability. A single pore and a pore network are constructed using a down-scaled Berea sandstone image. The compressible Stokes is applied with proper boundary conditions to capture slip flow and gas desorption effects. To include the effect of stress, poroelasticity principles are applied to describe the interaction between fluid flow and solid deformation. The model performance is verified against an experimental data taken from the literature. Both models show a negative effect of stress on gas flow when slip flow and desorption mechanisms are activated in the models. In the single pore model, slip has a positive and complementary effect on desorption at a specific stress value when their coupled contributions are summative. However, the results of pore network model show that slip has a destructive effect on desorption contribution specially at low effective stress values. That is, the changes in pore pressure induced by the slip mechanism act to limit the desorption contribution. This is clearly noted with the consideration of stress effects. At high effective stress values, the slip effect is limited due to the increase in pore pressure by compression, hence a closer matching between the permeability enhancement produced by the desorption mechanism alone and the coupled effect of desorption and slip can be noticed. Stress acts to limit the slip flow and also the desorption mechanism as they both are a function of pore pressure, however, as stress increases the contribution of desorption no longer would be reduced by slip flow. This study provides insights into stress role in multiphysics gas flow in shale reservoirs.

GeoChemFoam: Direct Modelling of Multiphase Reactive Transport in Real Pore Geometries with Equilibrium Reactions

GeoChemFoam is an open-source OpenFOAM-based toolbox that includes a range of additional packages that solve various flow processes from multiphase transport with interface transfer, to single-phase flow in multiscale porous media, to reactive transport with mineral dissolution. In this paper, we present a novel multiphase reactive transport solver for simulations on complex pore geometries, including microfluidic devices and micro-CT images, and its implementation in GeoChemFoam. The geochemical model includes bulk and surface equilibrium reactions. Multiphase flow is solved using the Volume-Of-Fluid method, and the transport of species is solved using the continuous species transfer method. The reactive transport equations are solved using a sequential operator splitting method, with the transport step solved using GeoChemFoam, and the reaction step solved using Phreeqc, the US geological survey’s geochemical software. The model and its implementation are validated by comparison with analytical solutions in 1D and 2D geometries. We then simulate multiphase reactive transport in two test pore geometries: a 3D pore cavity and a 3D micro-CT image of Bentheimer sandstone. In each case, we show the pore-scale simulation results can be used to develop upscaled models that are significantly more accurate than standard macro-scale equilibrium models.

Reconstructing porous media using generative flow networks

One area of intense scientific interest for the study of sandstones, carbonates, and shale at the pore scale is the use of limited image and petrophysical data to generate multiple realizations of a rock’s pore structure. Such images aid efforts to quantify uncertainty in petrophysical properties, including porosity–permeability transforms. We develop and evaluate a deep learning-based method to synthesize porous media volumes using a so-called generative flow model trained on x-ray microscope images of rock texture and pore structure. These models are optimized on a log-likelihood objective and they synthesize large and realistic three-dimensional images. We demonstrate the rapid generation of sandstone image volumes that display realism as gauged by quantitative comparison of topological features using Minkowski functionals of porosity, specific surface area, and the Euler–Poincaré characteristic (i.e., pore connectivity). We also evaluate the single-phase permeability using Navier–Stokes and lattice Boltzmann methods and show that transport properties of the generated samples match measured trends.

Fractal analysis of CT images of tight sandstone with anisotropy and permeability prediction

For developing unconventional oil and gas resources, it is necessary to quantify the heterogeneity embodied in both pore-size distribution (PSD) and pore spatial distribution, on the basis of which the relationship between the seepage characteristics and the microstructure of heterogeneous porous media could then be clarified. In this work, micro computed tomography (μCT) and image processing technology were applied to characterise matrix pore structure in tight sandstone. Fractal theory was used to investigate the image-based heterogeneity of tight porous media. On the basis of the verification that the PSD of the tight rock is statistically self-similar at a certain scale, we investigated the relationships between porosity and fractal dimension, and between 2D and 3D fractal dimensions, respectively. The results showed that the pore structure characteristic parameters with anisotropy, i.e., the ratio of the minimum pore size to the maximum pore size λ max /λ min and a proportionality constant C KT , could be obtained by liner fitting fractal dimension and porosity. Moreover, the 2D PSD characteristics of the ‘standard cross section’ were consistent with the 3D PSD characteristics of pore network. A fractal permeability model was established by treating the connected pores in the matrix as a bundle of conical micropipes. The permeability values predicted by the proposed model agreed well with those predicted by finite volume method simulation under the condition where irreducible pores were removed. A sensitivity analysis indicated that increasing the heterogeneity of the PSD and pore spatial distribution reduced the flow capacity of the matrix, particularly for low-porosity porous media. • A method to verify the fractal self-similarity of pore size distribution in CT images. • D f-2 vs D f-3 of microstructure in heterogeneous porous media was explored. • Fractal anisotropic model for permeability prediction in heterogeneous porous media.

Application of deep learning for semantic segmentation of sandstone thin sections

Sedimentary petrology is the basis for most mineral and textural identification in sandstones. Automating mineralogical interpretation of an entire thin section image has many practical applications, including improved geological understanding, input of spatial distribution of mineralogy and grain size for petrophysical evaluations, and integration with 3D imaging modalities (micro-CT, nano-CT). We investigate the application of Convolutional Neural Network (CNN) based supervised semantic segmentation methods for predicting pixel-scale mineralogy using 2D RGB images of sandstones acquired by transmission light microscopy. Models were trained to interpret a simple binary pore-mineral (grain) segmentation and a 10-class segmentation (porosity, quartz, feldspar, rock fragments, carbonate grains, opaque grains, quartz cement, carbonate cement, clay cement, and hydrocarbons filling pores). For the 2-class classification framework to distinguish between pores and minerals, most models lead to satisfactory results with acceptable accuracy. For the 10-class classification framework, models trained with Deeplab V3+ Resnet-18 network yield more continuous results compared to those based on VGG networks. We conclude that the effectiveness of the models, in predicting a petrology class in a thin section, strongly correlates with the amount of labeled data available to train the model to interpret the class in question. Semantic segmentation models, based on CNNs, can produce encouraging results for a 10-class petrological classification framework of an entire thin section image and thus provide a complete scene understanding which is difficult to produce manually.

Experimental investigation and two-phase flow simulation of oil and nanofluids on micro CT images of sandstone for wettability alteration of the system

This work provides an analysis of the effect of nanofluids on the wettability of sandstone for the application of enhanced oil recovery. The wettability of sandstone with brine and nanofluids of ZnO, BiFeO 3, and SrFeO 3 is studied experimentally using contact angle calculations. Also, the direct simulations for the displacement of oil with brine and nanofluids are carried out on a micro-CT scanned porous sandstone structure for the measurement of capillary pressure and relative permeability. Fluid properties such as viscosity and density of the nanofluids, brine, and oil to be used in simulations were obtained using viscometer and densimeter. The experimental results show that the contact angle of crude oil on the sandstone surface has a higher value for nanofluids as 125.89° for ZnO, 122.88° for BiFeO 3, and 104.98 for SrFeO 3 as compared to brine 28.66°, which means the wettability of the system changes from oil-wet to water-wet by the addition of nanofluids. The simulation results indicate that BiFeO 3 nanofluid has a greater tendency to change the wettability of porous medium as compared to brine, ZnO, and SrFeO 3 nanofluids, as it shows better values of relative permeability and capillary pressure. • Micro-CT imaging of sandstone samples and image processing is explained. • Mathematical model and boundary conditions for two-phase flow simulation are described. • Experimental calculations for fluid properties i.e. contact angle, viscosity and density. • Saturation profiles for two-phase flow of oil and brine/nanofluids are studied. • Relative permeability and capillary pressure curves are evaluated.

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.

Pore-Scale Modelling of Three-Phase Capillary Pressure Curves Directly in Uniformly Wet Rock Images

In this work, we developed a semianalytical model to compute three-phase capillary pressure curves and associated fluid configurations for gas invasion in uniformly wet rock images. The fluid configurations and favorable capillary entry pressures are determined based on free energy minimization by combining all physically allowed three-phase arc menisci. The model was first validated against analytical solutions developed in a star-shaped pore space and subsequently employed on an SEM image of Bentheim sandstone. The simulated fluid configurations show similar oil-layer behavior as previously imaged three-phase fluid configurations. The simulated saturation path indicates that the oil-water capillary pressure can be described as a function of the water saturation only. The gas-oil capillary pressure can be represented as a function of gas saturation in the majority part of the three-phase region, while the three-phase displacements slightly reduce the accuracy of such representation. At small oil saturations, the gas-oil capillary pressure depends strongly on two-phase saturations.