Images Of Porous Media Research Articles

Reconstruction of reservoir rock using attention-based convolutional recurrent neural network

The digital reconstruction of reservoir rock or porous media is important as it enables us to visualize and explore their real internal structures. The reservoir rocks (such as sandstone and carbonate) contain both spatial and temporal characteristics, which pose a big challenge in their characterization through routine core analysis or x-ray microcomputer tomography. While x-ray micro-computed tomography gives us three-dimensional images of the porous media, it is often impossible to quantify the variability of the pore, grains, structure, and orientation experimentally. Recently, machine learning has successfully demonstrated the reconstruction ability of reservoir rock images or any porous media. These reservoir rock images are crucial for the digital characterization of the reservoir. We propose a novel algorithm consisting of the convolutional neural network, an attention mechanism, and a recurrent neural network for the reconstruction of reservoir rock or porous media images. The attention-based convolutional recurrent neural network (ACRNN) can reconstruct a representative sample of reservoir rocks. The reconstructed image quality was checked by comparing them with the original Parker sandstone, Leopard sandstone, carbonate shale, Berea sandstone, and sandy medium images. We evaluated the reconstruction by measuring pore and throat properties, two-point probability function, and structural similarity index. Results show that ACRNN can reconstruct reservoir rock or porous media of different scales with approximately the same geometrical, statistical, and topological parameters of the reservoir rock images. This deep learning method is computationally efficient, fast, and reliable for synthetic image realizations. The model was trained and validated on real images, and the reconstructed images showed excellent concordance with the real images having almost the same pore and grain structures. The deep learning-based digital rock reconstruction of reservoir rock or porous media images can aid in rapid image generation to better understand reservoir rock or subsurface formation.

Application of space renormalisation technique for spatiotemporal analysis of effective thermal conductivity in multiphase porous materials

Effective thermal conductivity (k¯) is a critical parameter influencing heat transfer in multiphase porous materials. This study introduces a computational approach using the space renormalisation technique to derive k¯ from segmented X-ray micro-CT images of porous media. By accounting for pore-scale heterogeneity, this approach enables detailed spatiotemporal analysis of k¯ in different porous structures. The application of this technique is demonstrated through the prediction and spatiotemporal analysis of k¯ in three different porous rock samples experiencing multiphase fluid flow: (i) steady-state two-phase flow in Estaillades carbonate, (ii) sequential flooding in Bentheimer sandstone, and (iii) immiscible three-phase flow in Ketton limestone. Results show distinct directional variations in k¯ according to phase saturations and redistributions, highlighting the sensitivity of the approach to the microstructural characteristics of porous media. The space renormalisation technique efficiently predicts k¯ with significantly reduced computational costs compared to traditional finite difference methods, making it suitable for real-time applications. The findings provide deeper insights into the dynamic heat transfer mechanisms in heterogeneous porous systems, with implications for various porous media applications such as enhanced oil recovery, geothermal energy extraction, and the design of heat exchangers in engineering systems.

Three-dimensional reconstruction of porous media by fusing multi-grid image features based on extended feature pyramid network

Microstructural analysis of porous media has significant research value in the study of their macroscopic properties. An accurate reconstruction of the digital microstructure model is a prerequisite for understanding their physical properties and transport properties. Deep learning can accurately extract features from training images for a fast and precise reconstruction of porous media. The reconstruction methods based on deep learning have yielded important achievements in the reconstruction of porous media. Aiming at the complex morphology and multi-scale image information of porous media, this paper proposes a generic end-to-end deep learning-based encoder–decoder generative method for the reconstruction of porous media from a single 2D image. This paper designs an extended feature pyramid network encoder to extract image features of different resolutions and different scales, and a generator network incorporating multi-scale image information. Through the training process of the network, the final three-dimensional images that meets certain requirements are generated by means of confrontation. By introducing the loss function of the pattern density function and the loss function of Wasserstein distance with gradient penalty, we constrain the reconstructed 3D structures. Finally, the reconstructed 3D structures and the target 3D structures are visualized to compare their similar morphologies. The morphological parameter indicators of the reconstructed 3D structures were line with those of the target 3D structure. The microstructure parameters of the 3D structures were also compared and analyzed. For complex porous media images, our method can achieve diverse, accurate, and stable 3D reconstruction.

A hybrid pore-network-continuum modeling framework for flow and transport in 3D digital images of porous media

Understanding flow and transport in multiscale porous media is challenging due to the presence of a wide range of pore sizes. Recent imaging advances offer high-resolution characterization of the multiscale pore structures. However, simulating flow and transport in 3D digital images requires models to represent both the resolved and sub-resolution pore structures. We develop a hybrid pore-network-continuum modeling framework. The hybrid framework treats the smaller pores below the image resolution as a continuum using the Darcy-scale formalism and explicitly represents the larger pores resolved in the images employing a pore network model. We validate the hybrid model against direct numerical simulations for single-phase flow and solute transport and further demonstrate its applicability for simulating two-component gas transport in a shale rock sample. The results indicate that the new hybrid model represents the flow and transport process in multiscale porous media while being much more computationally efficient than direct numerical simulation methods for the range of simulated conditions.

An improved convolutional neural network for predicting porous media permeability from rock thin sections

Permeability prediction is a crucial aspect of investigating fluid flow capacity in porous media, and rapidly predicting the permeability of rock thin sections aids in reservoir assessment. In recent years, significant progress has been made regarding the use of deep learning for predicting porous media permeability, effectively overcoming the limitations associated with time-consuming conventional permeability determination methods. To address the issues of low prediction accuracy and insufficient generalization capability of previous permeability prediction models, this study proposes an improved convolutional neural network for porous media permeability and applies it to predict the permeability of rock thin sections. Given the difficulty of obtaining a large amount of rock thin section data, we synthetically generated 1000 binary images of porous media and calculated the corresponding permeability labels using computational fluid dynamics. These data were used as foundational data for training the model. The proposed model achieved accurate and efficient permeability prediction of porous media with a correlation of 0.9667 on testing set. Simultaneously, we employed class activation mapping technology to visualize the permeability prediction process of the neural network, thereby elucidating the working principles of the neural network during porous media permeability prediction. Subsequently, based on an optimally pretrained neural network, transfer learning was utilized to predict the permeability of rock thin sections, which achieved a correlation of 0.9032. Our study extends the rock thin section applications and provides technical support for reservoir evaluation.

Effects of microscopic pore-throat structure on gas–liquid relative permeability: Porous media construction and pore-scale simulation

The porous media structure of the oil/gas reservoir changes greatly after long-term development, which subsequently influences the macroscopic relative permeability. To clarify the effects of microscopic pore-throat structure on macroscopic relative permeability, we first proposed a method to generate two-dimensional porous media images with adjustable structure parameters. The method is based on Delaunay triangulation and is similar to the pore-network generation process, which can provide binary images for direct numerical simulation of flow through porous media. Then, we established the single component multiphase Shan–Chen lattice Boltzmann method coupling the real gas equation of state. Finally, we discussed the effect of pore radius, coordination number, pore-throat ratio, pore shape, and wettability on the gas–liquid relative permeability curve using the lattice Boltzmann simulation. This study provides an effective method to generate porous media and explain the mechanism of relative permeability change at the pore scale.

Swin transformer based transfer learning model for predicting porous media permeability from 2D images

Soil and rock, as typical porous media, widely exist in natural slopes and landslides and underground reservoirs. Accurate predicting the permeability of porous media is crucial in preventing geological disasters and extracting underground energy. The conventional methods for obtaining the porous media permeability involve experiments or numerical simulations, both of which are usually time-consuming. In recent years, a new approach to predicting the porous media permeability has emerged, utilizing porous media images and leveraging deep learning algorithms. However, previous image-based permeability prediction frameworks have been dominated by convolutional neural networks (CNNs). CNNs require extensive data and intricate network architectures to achieve reasonably accurate predictive performance. State-of-the-art neural networks and methods are employed to overcome the shortcomings of CNNs. To initiate this research, we generated 1200 two-dimensional porous media images. The permeability labels for the target porous media were acquired through computational fluid dynamics. Subsequently, an end-to-end permeability prediction surrogate model was established based on the Swin Transformer architecture. The proposed model falls under the category of transfer learning models, where pre-trained weights and bias from other datasets serve as the initial weights and bias for our dataset. Our model has achieved State-of-the-art performance, outperforming CNN by a significant margin on small-size datasets. Even with a small dataset size as 200, the proposed model still achieves an R2 score of 0.9717 on the testing set. Both transfer learning and the Swin Transformer architecture have demonstrated robust predictive capabilities in the context of predicting permeability in small-size dataset porous media based on computer vision.

Enhancing pore network extraction performance via seed-based pore region growing segmentation

Pore-scale modeling, aided by imaging advancements and computational power, is now a vital tool for comprehending fluid flow and transport in porous media. It allows detailed exploration of pore structures and analysis of fluid dynamics and mass transport at smallest scales. This work presents the Pore Region Growing (PREGO) Algorithm, a novel approach to address segmentation challenges encountered in large-sized 3D images used for pore network modeling. The algorithm overcomes limitations of traditional methods like the watershed algorithm, in both computational time and memory of the pore segmentation. Like the watershed method, the proposed work involves identifying seed points, then grows each to fill their respective basis. The algorithm differs from existing approaches in that it efficiently prioritizes and grows the seed points using a FIFO queue, resulting in well-defined segmentation with clear and smooth boundaries between neighboring regions. The output was validated by demonstrating the algorithm's robustness in predicting diffusive behavior and viscous fluid flow within the pore phase network, with excellent agreement in comparison to lattice Boltzmann simulations and experimental data. The proposed algorithm was also shown to accurately predict transport properties under varying porosity, and different types of real porous media images. The evaluation of the Intersection over Union (IoU) and Dice Similarity Coefficient (DSC) metrics revealed that the PREGO technique had a maximum error of 5.44%, whereas the Watershed method exhibited a comparatively higher error rate of 22.3%. Structural analysis of physical properties revealed PREGO captures pore and throat sizes in close agreement with existing approaches. Crucially, computational performance analysis demonstrated its efficiency, significantly reducing memory consumption by 50% and CPU time speed up of 3.35X compared to the standard watershed algorithm using a priority queue.

Characterization of synthetic porous media images by using fractal and multifractal analysis

Fractal and multifractal analysis of porous images allow the description of porous media through a scale-invariant understanding. There have been numerous works that have used these analysis techniques for the description of a great variety of real porous media. However, these studies are usually comparative, being difficult to discern the role played by the pore size and pore distribution in the results of fractal and multifractal analysis. This works develops an in-depth study of different synthetic porous media from a fractal and multifractal approach, in which both the pore size and its distribution in the medium are parameterized. Thus, a set of synthetic binary images have been generated obtaining deterministic and random structures with different fixed pore sizes and also with different rates of pore sizes. Lacunarity is also calculated in order to complete the aforementioned analysis. Results evinces that fractal dimension increases with pore size and that it is higher when the pore distribution obeys a random distribution versus a deterministic one. However, when the pore size is very large, fractal dimension is similar regardless of the pore distribution. From a multifractal approach, pore size is negatively correlated with the degree of multifractality. In fact, in images with mixtures of different pore sizes it is also found that the greater the ratio of small pores, the greater degree of multifractality. By contrast, when the ratio of large pores is relevant, the degree of multifractality also increases due to the merging of macro-pores.

Construction of pore structure geometry model from digital images of porous media and its application in pore-scale flow simulation

Pore-scale imaging and modeling has been regarded as an effective means to reveal the micro-control mechanism of macrophysical properties of various porous media materials. Nevertheless, it is challenging and intractable to construct their geometric models accurately because of the extreme intricacy of real pore structure geometries. In order to address the issue, based on the Chebyshev distance transform of digital image, this paper presents a universal algorithm for constructing the corresponding geometric model directly from the digital image of pore structure. Based on digital images acquired by advanced imaging technology, the pore structure geometry models of different types of porous media materials (silicon wafer, carbonate rock and sandstone) have been successfully constructed, which makes the validity of the presented algorithm verified. In addition, the constructed geometric models are imported into the finite element analysis software to carry out single-phase flow simulation experiments, the numerical results of which show that the predicted absolute permeabilities have high consistency with laboratory measurements, thus further verifying the accuracy and effectiveness of the presented algorithm.

Robust surface-correlation-function evaluation from experimental discrete digital images.

Correlation functions (CFs) are universal structural descriptors; surface-surface F_{ss} and surface-void F_{sv} CFs are a subset containing additional information about the interface between the phases. The description of the interface between pores and solids in porous media is of particular importance and recently Ma and Torquato [Phys. Rev. E 98, 013307 (2018)2470-004510.1103/PhysRevE.98.013307] proposed an elegant way to compute these functions for a wide variety of cases. However, their "continuous" approach is not always applicable to digital experimental 2D and 3D images of porous media as obtained using x-ray tomography or scanning electron microscopy due to nonsingularities in chemical composition or local solid material's density and partial volume effects. In this paper we propose to use edge-detecting filters to compute surface CFs in the "digital" fashion directly in the images. Computed this way, surface correlation functions are the same as analytically known for Poisson disks in case the resolution of the image is adequate. Based on the multiscale image analysis we developed a C_{0.5} criterion that can predict if the imaging resolution is enough to make an accurate evaluation of the surface CFs. We also showed that in cases when the input image contains all major features, but do not pass the C_{0.5} criterion, it is possible with the help of image magnification to sample CFs almost similar to those obtained for high-resolution image of the same structure with high C_{0.5}. The computational framework as developed here is open source and available within the CorrelationFunctions.jl package developed by our group. Our "digital" approach was applied to a wide variety of real porous media images of different quality. We discuss critical aspects of surface correlation functions computations as related to different applications. The developed methodology allows applying surface CFs to describe the structure of porous materials based on their experimental images and enhance stochastic reconstructions or super-resolution procedures, or serve as an efficient metrics in machine learning applications due to computationally effective GPU implementation.

Multiple-Point Geostatistics Simulation of the Natural Gas Hydrate Distribution at the Pore Scale

Heat and mass transfer in a natural gas hydrate reservoir is strongly affected by the hydrate pore habit. Some present simplified models used in numerical simulation of a hydrate-bearing sediment are difficult to catch features of the hydrate distribution in sediments precisely. Using an improved multiple-point geostatistics simulation method, this study generates a series of images of porous media that reproduce the hydrate distribution information on a training image. The improved algorithm completely solves the problem that the hydrate blocks the boundary and makes the variogram and visual properties similar to the training image. Some typical phenomena of hydrate formation appear in the results, such as Ostwald ripening and the shift of hydrate pore habit from grain coating toward pore filling. The feasibility of predicting the pore habit of a hydrate with time using this novel method is proven by the verification case. This study offers a new approach to predict the distribution behavior of a hydrate, and this algorithm may be applied widely by scanning training images from different reservoirs.

Prediction of local concentration fields in porous media with chemical reaction using a multi scale convolutional neural network

The study of solute transport in porous media is of interest in many chemical engineering systems. Some example applications include packed bed catalytic reactors, filtration devices, and batteries. The pore scale modeling of these systems is time consuming and may require large computing resources, for this reason computational fluid dynamics (CFD) simulations are not practical if a large number of simulations is required, like in multiscale modeling, where a model at a large scale calls for pore scale simulations. It has been shown that neural networks can be trained with a dataset of flow simulations and then predict fields orders of magnitude faster, and with less computational resources, in new domains. However, it is crucial to provide the neural network with an effective description of the domain and the undergoing operating conditions to be able to train models that generalize accurately in unseen samples. Therefore, research is needed to employ neural networks in new complex systems. The appropriate training of a network for predicting coupled flow and solute transport processes is an outstanding problem due to the complex interplay between geometry and operating conditions. In this work, we train a multi scale convolutional neural network (MSNet) with a diverse dataset of simulations of transport and chemical reaction in porous media to predict the local concentration fields in images of porous media. Our dataset contains a wide diversity of sphere pack arrangements under different operating conditions (Péclet and Reynolds numbers). We train a robust model by employing different input descriptors that represent the medium and the different operating conditions of each system. Our trained model is able to provide nearly instantaneous predictions, compared to around twenty hours of the CFD workflow, with less than 3.5% error on new geometries and transport conditions. Thus the model could be easily integrated in a multiscale workflow where fast response is needed.

An accelerated process-based method for the accurate computation of relative permeability from direct simulations of two-phase flow on micro-computed tomography images of porous media

Pore-scale forces have significant effects on the macroscopic behavior of multi-phase flow through porous media. We develop a robust and accurate accelerated process-based method for the computation of relative permeability from direct simulations of pore-scale two-phase flow on micro-computed tomography images. In the pressure drop calculation, we take advantage of an existing analysis that establishes a relationship between pore-scale forces and Darcy-scale pressure drops using an energy-conservation approach. We establish a thermodynamically consistent approximation of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each flowing phase for the first time within the context of a free-energy lattice Boltzmann method (LBM). In addition, we propose and test a new computationally efficient partial-mirror periodic boundary condition for a fully coupled visco-capillary pore-scale flow simulator based on a free-energy LBM. The new boundary condition is imposed only in the main flow direction and significantly reduces the computational cost of the process-based relative-permeability computation protocol at a small compromise on accuracy.We first compute primary-drainage and subsequent imbibition relative permeability curves for a reservoir sandstone rock sample. We use this real-reservoir dataset to validate the pressure drop computation method and the partial-mirror periodic boundary condition. We then simulate the entire drainage and imbibition cycle using an extensively studied Berea sandstone dataset. We quantitatively demonstrate that pore-scale direct numerical simulation-based relative permeability curves computed with our novel process-based method agree well with experimental steady-state relative permeability measurements. We also quantitatively demonstrate that the new partial-mirror periodic boundary condition accelerates the relative permeability computations 4 to 13 times.

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.

Prediction of diffusional conductance in extracted pore network models using convolutional neural networks

Pore network modeling (PNM) based on networks extracted from tomograms is a well-established tool for simulating pore-scale transport behavior in porous media. A key element of this approach is the accurate determination of pore-to-pore conductance values, which is a complex task that greatly affects the accuracy of flow and diffusive mass transport studies. Classic methods of conductance estimation based on analytical solutions and shape factors only apply to simple pore geometries, whereas real porous media contain irregular-shaped pores. Although direct numerical simulations (DNS) can accurately estimate conductance considering pores' real morphology, it has a high computational cost that becomes infeasible for large tomograms. The present work remedies this problem using a deep learning (DL) approach, with a specific focus on diffusional transport which has received less attention than hydraulic conductance. A convolutional neural network (CNN) model was trained to estimate diffusive conductance of PNM elements from volumetric images of porous media. The developed framework estimates the diffusive conductance by analyzing individual pore-to-pore 3D images isolated from the tomogram to fully capture the topology and shapes. A key outcome of the present work is that only images of the pore regions are used as input data, avoiding excessive preprocessing time for data preparation. The results of the diffusive conductance prediction show good agreement with the test data obtained by DNS method, with 0.94 R2 prediction accuracy and a speedup of 500x in prediction runtime.

Incorporating the Effect of Gravity Into Image‐Based Drainage Simulations on Volumetric Images of Porous Media

AbstractSimulating drainage in volumetric images of porous materials is a key technique for studying multiphase flow and transport. Image‐based techniques based on sphere insertion are popular due to their computational efficiency and reasonable predictions, though they lack physical rigor. Since most tomograms are small, the impact of gravity on the fluid distributions has not been previously considered. With the advent of stochastically generated images of arbitrary size, and ever larger field‐of‐view images, the validity of neglecting gravity is becoming questionable. In this work, an image‐based technique that includes the effect of gravity during gravity stabilized displacements was developed and validated. Results compared favorably with analytical solutions of capillary rise in tubes, and to micromodel experiments in terms of the pseudo‐capillary pressure curves. The compactness of the invasion front was also shown to vary linearly with the inverse Bond number. Finally, a contour map of expected error as a function of image size and Bond number was generated to help identify when gravitational effects cannot be ignored. The presented algorithm utilizes only basic image processing tools and offers the same computational advantage as other image‐based sphere insertion methods.

Diffraction by image processing and its application in materials science

Abstract A spectral theory for constituents of macroscopically homogeneous random microstructures is developed and provided with a sound mathematical basis, where the spectrum obtained by Fourier methods corresponds to the angular intensity distribution of X-rays scattered by this constituent. It is shown that the fast Fourier transform applied to three-dimensional images of microstructures obtained by micro-tomography is a powerful tool of image processing. The applicability of this technique is demonstrated in the analysis of images of porous media.

Study on the linkages between microstructure and permeability of porous media using pore network and BP neural network

In applying porous media air bearings (PMABs), designing the pore microstructure of porous media to obtain the desired permeability is challenging. The key parameters in this design are to map the pore microstructure characteristics to permeability and adapt to manufacturing process with the characteristics. For this purpose, a framework is proposed to characterize pore microstructure with morphology descriptor and predict permeability. 3D digital images of porous media are obtained using X-ray micro-computed tomography and various image construction techniques. The complex pore microstructure of porous media is represented with a pore network. Permeability is calculated based on the pore network. Sixteen pore microstructure morphology descriptors are initially calculated to characterize pore microstructure. A back-propagation neural network (BPNN) is built to learn the correlation between morphology descriptors and permeability. Pearson correlation coefficient (PCC) and feature importance scores of morphology descriptors are obtained based on the dataset and trained BPNN. The results demonstrate that the prediction performance of BPNN is excellent. The following six morphology descriptors (porosity, coordination number, average pore diameter, average throat diameter, average pore throat ratio, average throat length) are reserved to characterize pore microstructure. Finally, two types of pore microstructure are designed with the help of knowledge obtained by this research.

3D reconstruction of porous media by combining scaling transformation and multi-scale discrimination using generative adversarial networks

The modeling and characterization of porous media is quite significant to explore and develop oil and natural gas resources . Traditional numerical simulation methods obtain reconstruction results through the statistical probability in training images (TIs), while the reconstruction process is lengthy and the probability information cannot be reused. The development of deep learning has provided reliable support for the reconstruction of porous media due to its strong ability of learning and extracting characteristics from TIs and the reuse of network parameters. As a common deep learning method, generative adversarial networks (GANs) can obtain images highly similar to the structural characteristics of the TI through adversarial training between the generator and the discriminator . Based on GAN, a three-dimensional multi-scale pattern generative adversarial network (3D-MSPGAN) that can achieve 3D super-resolution reconstruction of porous media is proposed in this paper. The use of scaling transformation allows 3D-MSPGAN to reconstruct super-resolution images of porous media that are much larger than the TI, while the multi-scale discrimination in the discriminator provides a guarantee for the generation of high-quality super-resolution images, by which the discriminator can retain the global structure and local characteristics of the TI simultaneously during the reconstruction process. In addition, due to the multi-scale patch information used in the discriminator, only a single TI is needed to complete the reconstruction of porous media. Experimental comparison with some typical methods proves that 3D-MSPGAN can achieve the reconstruction of 3D porous media with faster speed and higher quality. • Our method can achieve super-resolution reconstruction of porous media. • Our method only needs a single training image for the reconstruction. • Our method can complete large-quantity reconstructions quickly.