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Some examples of soil thin section images and associated simulated images (each image size is 1.6 by 1.2 cm) (a) original images (i.e., soil thin sections); (b) associated simulated image; (c) semivariograms of pore space in original and simulated images.
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The characterization of the soil habitat is of fundamental importance to an understanding of processes associated with sustainable management such as environmental flows, bioavailability, and soil ecology. We describe a method for quantifying and explicitly modeling the heterogeneity of soil using a stochastic approach. The overall aim is to develo...
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... we need to assign states to all the cells in the first row, and the first cell of the next row. The cells in the first row are obtained using a two-neighborhood Markov chain where the state of a cell is conditionally dependent on the state of the cell to its left. The parameters for this Markov chain are obtained as above, but using the smaller two-cell neighborhood. The state of the first cell of the next row is determined using the same two-neighborhood conditional probability. Using these boundary values, the chain runs from the left-hand corner of the image and progresses in raster fashion across the image to the right-hand side. First, the state of cell ( i,j ) in the neighborhood is evaluated, followed by the state of cell ( i,j ϩ 1). The neighborhood is then advanced two cells to the left and the process is repeated. This continues until the last cell on the right-hand side is reached and its state is evaluated. At this point, the cells in the first two rows have been evaluated. Next, the neighborhood remains at the right-hand side but moves one row down. The chain now reverses direction, and instead of deriving the states of the ( i,j ) and ( i,j ϩ 1) cells in terms of the state of the others, it is the states of cells ( i,j ) and ( i , j Ϫ 1) that are determined. However, before the chain can proceed leftwards, the state of the first cell on the right-hand side of the third row must be evaluated. This is done in the same way as when the neighborhood was at the left-hand side of the domain, using the two-neighborhood conditional probability. The chain can now advance leftwards until the left-hand side of the domain is reached. The neighborhood then moves down one row, and the chain reverses as before. Thus, the whole domain is scanned in a raster-like fashion on this basis, until the states of all the required cells are obtained. The scanning scheme algorithm converges rapidly. In the examples reported here, we observed the transition kernel (i.e., the matrix of conditional probabilities for all possible neighborhood configurations), calculated from the recon- structed image as the chain progressed. Almost all the probabilities had become stable after the chain had completed 200 rows, which is equivalent to a depth of 4.0 mm in the original soil section and takes about 10 s of computing time on a 1.7- GHz Pentium IV computer. In other words, the minimum size of a simulated representative soil image should be 0.6 by 0.4 cm 2 , and it takes only a few minutes to generate an image covering several squared. The method was validated using images obtained from soil thin sections and selected to represent a broad contrast in structural properties. Soil cores were collected from an arable field and thin sections were produced using the method described in Nunan et al. (2001). Soil pore maps were obtained by subtracting images obtained with cross-polarized light from images cap- tured using transmitted bright-field light. The resultant images were then segmented into solid and void. The images employed in this study were binary pore maps of dimension 760 by 570 pixels, representing an area of 1.6 by 1.2 cm. Images were selected to represent a range of characteristic soil structural properties, as shown below. To compare the simulated and real images we selected a range of quantitative metrics that characterize the heterogeneity and connectivity of the structures under investigation. The most obvious of these is the porosity and this is readily determined from both the real and simulated structures. The corre- sponding values are listed in Table 1 and range from 7 to 24% in the real structures. There was no significant difference between the porosities in the simulated and real structures ( P Ͼ 0.05, paired t test). The second metric adopted was the mass fractal dimension, which essentially characterizes the degree of aggregation of the solid matrix. The mass (solid) fractal dimension was determined by the box counting method (Hastings and Sugihara, 1993). The calculated values are listed in Table 1, and again there was no significant difference between the simulated and real structures ( P Ͼ 0.05, paired t test). The third and fourth metrics chosen characterize the pore space, where visually obvious differences between the samples were present. The third is the variance of the porosity as measured in a 0.4 by 1.6 mm sampling window placed at 50 random locations in each image. For a given porosity, this is a measure of the connectivity of the pore space (Mandelbrot, 1985). We used the Chi-Square goodness-of-fit test, and tested the null hypothesis that the variances in each pair of simulated and original images were different. This could be rejected at the 95% confidence level indicating that this aspect of the structure of the pore space was not significantly different in the real and simulated images. The fourth metric measured the spatial correlation of the pore space by determining the semivariogram. Figure 3 shows the variograms for the different soil samples used in this study, and there are clear differences in these between the different soil sections. The figure shows the comparison between the variograms for the real and simulated structures. There is no formal statistical way of compar- ing the properties of semivariograms, however the high degree of correspondence between the curves for the measured and simulated structures is good, adding further support for the modeling ...
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... The construction methods of digital rock mainly include two categories: physical experimental methods and numerical reconstruction methods. Numerical reconstruction methods, such as the four-parameter random growth method [20], sequential indicator simulation method [21], simulated annealing method [22], multipoint statistics method [23], and Markov chain-Monte Carlo method [24], although cost-effective, have limitations in terms of accuracy and simulation fidelity due to their reliance on numerical calculations for simulating rock structures [25,26]. ...
The microscopic pore-fracture structure and wettability have a significant influence on the two-phase seepage of shale gas and water. Due to the limitation of experimental conditions, the seepage patterns of gas and water in shale pores and slits under different wetting conditions have not been clarified yet. In this study, the three-dimensional digital rock models of shale inorganic pores, organic pores, and microfractures are established by focused ion beam-scanning electron microscopy scanning, and gas-driven water seepage simulation in shale microscopic pore-fracture structure under different wetting conditions is carried out based on volume of fluid method. The simulation results show that the gas–water relative permeability curves of microfractures are up-concave, and the gas–water relative permeability curves of inorganic and organic pores are up-convex; the gas–water two-phase percolation in microfractures is least affected by the change of wettability, the gas–water two-phase percolation in inorganic pores is most affected by the change of wettability, and the organic pores are in between; the gas–water two-phase percolation zone of microfractures is the largest, and the isotonic saturation is the highest; under the water-wet conditions, the critical gas saturation of microfractures, inorganic pores, and organic pores are 0.13, 0.315, and 0.34, respectively, and the critical gas saturation of organic pores under non-water-wet conditions is 0.525, indicating that under water-bearing conditions, the shale gas flow capacity in water-wet microfractures is the strongest, followed by water-wet inorganic pores, water-wet organic pores, and hydrophobic organic pores, respectively.
... However, reconstructed rock samples have similar structural features in different directions, the calculation speed is slow, and hard data constraints need to be given in advance (Ting et al. 2010). The Markov Chain Monte Carlo algorithm (Keijan et al. 2004) is a method that creates a state sequence of a Markov chain. The state value at each position depends on a limited number of positions in front of it, and the probability of this state is called conditional probability. ...
The 3D digital rock technology is extensively utilized in analyzing rock physical properties, reservoir modeling, and other related fields. This technology enables the visualization, quantification, and analysis of microstructures in rock cores, leading to precise predictions and optimized designs of reservoir properties. Although the accuracy of 3D digital rock reconstruction algorithms based on physical experiments is high, the associated acquisition costs and reconstruction processes are expensive and complex, respectively. On the other hand, the 3D digital rock random reconstruction method based on 2D slices is advantageous in terms of its low cost and easy implementation, but its reconstruction effect still requires significant improvement. This article draws inspiration from the Concurrent single-image generative adversarial network and proposes an innovative algorithm to reconstruct 3D digital rock by improving the generator, discriminator, and noise vector in the network structure. Compared to traditional numerical reconstruction methods and generative adversarial network algorithms, the method proposed in this paper is shown to achieve good agreement with real samples in terms of Dykstra-Parson coefficient, porosity, two-point correlation function, Minkowski functionals, and visual display.
... Compared with physical experimental methods, the numerical reconstruction methods employ a number of 2D thin-sections or 3D porous media images as training images (TIs) and reconstruct porous media using the statistical information drawn from TIs. Numerous numerical reconstruction techniques are available, including the simulated annealing method [12], Markov chain Monte Carlo [51], multi-point statistics (MPS) [35], sequential indicator simulation [13], the denoising diffusion probabilistic models [23] and the truncated Gaussian random field method [3]. If only two phases in porous media need to be reconstructed, the two-point cluster function has been proven to be a superior descriptor for the structural information of porous media [19]. ...
The accurate reconstruction of porous media is difficult to accomplish in practical research due to the intricacy of the internal structure of porous media, which cannot be described only using some equations or languages. The emerging deep learning methods open up a new research field for the reconstruction of porous media. One of the classic deep learning methods is generative adversarial network (GAN), which has been applied to the reconstruction of porous media, but also requires sufficient training samples as well as a long simulation process. Some GAN’s variants, such as the single-image GAN (SinGAN), are proposed to achieve desired results with only one training image (TI), but its serial structure still necessitates lengthy training time. Based on SinGAN, a stochastic reconstruction method of porous media combining attention mechanisms with multiple-stage GAN is proposed, focusing on important features of porous media with a single TI to achieve favorable simulation quality and using two discriminators to maintain enough diversity (one discriminator prefers real data, and the other favors fake data). Experiments prove that our method outperforms some numerical reconstruction methods and SinGAN in terms of practicality and efficiency.
... Three high resolution binary SEM images ( Fig. 1) gathered from shale oil reservoir are used to reconstruct the 3D nanoporous shale based on Markov chain Monte Carlo algorithm (Wu et al., 2004). The pixel size and resolution of each SEM image are 400 × 400 and 27.5 nm, respectively. ...
Hydrocarbon mass transport in nanoporous media notably differs from that in traditional micro-scale porous media due to strong solid-fluid interaction in nanoscale confined pore space. Accurate prediction of hydrocarbon thermodynamic transport in nanoporous shale must consider the bound water distribution pattern, fluid occurrence in dual-wet pores (organic and inorganic), thermodynamic phase equilibrium, boundary slippage and rheological property. So far, there is no such a model that incorporates the above mentioned factors into assessing the multicomponent hydrocarbon mass transport in nanoporous shale. In this work, we propose a pore network based multicomponent hydrocarbon mass transport model considering above mentioned factors and the multicomponent hydrocarbon thermodynamic transport mechanisms are elucidated in detail. The bound water film stability and induced capillary condensation are first analyzed according to Kelvin equation and the extended DLVO theory. A thermodynamic phase equilibrium-fluid occurrence coupling model is further developed considering the oil-gas capillary pressure change with oil saturation on pore network model (PNM). The multicomponent hydrocarbon single pore transport model is derived considering boundary slippage, adsorption layer thickness and fluid rheology and is extended to PNM transport simulation. The multicomponent hydrocarbon permeability variations at different pressure, pore size, relative humidity and total organic carbon (TOC) are analyzed in detail. The predicted hydrocarbon flux change with pressure gradient matches well with the previous observed trend in the laboratory experiments. Study results reveal that the multicomponent hydrocarbon exhibits non-linear transport behavior determined by the fluid rheology and the threshold pressure gradient for hydrocarbon starting to flow is mutually controlled by the yield stress and pore size.
... physical experimental methods, numerical simulation methods use statistical information extracted from real 2D or 3D images of porous media to reconstruct porous media. Typical numerical simulation methods include the processbased method (Ji et al. 2018), the simulated annealing method (Jiao et al. 2008), the Markov chain Monte Carlo method (Wu et al. 2004), the truncated Gaussian random field method (Hélène and Didier 2016), multi-point statistics (MPS) Blunt 2004, 2005), etc. Compared with physical experiment methods, numerical simulation methods have the advantages of low cost and high efficiency. ...
The fluid flow and heat transfer in porous media are not only related to the physical properties of the fluid itself, but also related to the structure and distribution of the pore space of porous media. The reconstruction of porous media has become a prerequisite for the research and analysis of the microscopic pore structure. At present, numerical simulation methods are widely used in the field of porous media reconstruction, which can achieve reconstructed results similar to the real pore structure, but generally the whole process is CPU-intensive and time-consuming. With the widespread application of deep learning in many scientific fields, although generative adversarial network (GAN), as a branch of deep learning generative models, has the strong ability of feature extraction and prediction, it is challenged by the large CPU/memory consumption in training. One solution is to perform multi-scale reconstruction, which has been used in the variants of GAN. Based on multi-scale reconstruction, smaller-scale training samples can be used to reconstruct larger-scale samples with the benefits of a much faster speed than traditional numerical simulation methods and lower burdens on CPU/memory. Hence, this paper proposes a progressively growing multi-scale GAN model for the reconstruction of porous media. Compared with some variants of GAN and traditional numerical simulation methods, the effectiveness and practicability of our method are proved.
... Different from the physical experiment methods, numerical reconstruction methods reconstruct porous media using the statistical information extracted from real 2D or 3D images of porous media. The numerical reconstruction methods include the truncated Gaussian random field method (Hélène and Didier 2015), the simulated annealing method (Hazlett 1997), the sequential indicator simulation method , the Markov chain Monte Carlo method (Wu et al. 2004), the multi-point statistics (MPS) method (Okabe and Blunt 2005), etc. Compared to physical experiment methods, numerical reconstruction methods have the advantages of low cost and high efficiency. ...
Because of the complex internal porous structures, the reconstruction of porous media has encountered many difficulties in practical research and development. At present, numerical simulation methods are widely used in the field of reconstructing porous media, which can reconstruct results similar to the true pore structure, but generally are CPU-intensive and time-consuming. Recently, with the rapid development of deep learning, the powerful ability of feature extraction and structure prediction owned by deep learning can be transferred to reconstruct porous media. The convolutional neural network (CNN) is one of the classical methods in deep learning. A traditional CNN is unable to specially focus on the effective features in learning and possibly has degradation problem with the increase of layers. To address the degradation problem and make CNNs extract important features, residual networks and attention mechanisms are combined in CNNs to respectively alleviate network degradation and focus on the important features in the reconstruction of porous media. Besides, the bilinear interpolation is used to enlarge the size of compressed data. Compared with some traditional numerical reconstruction methods, CNN, GAN and some variants of GAN, our method has shown its practicability and effectiveness.
... The calculating transfer probability is the core in the application of Markov chain, but the calculation procedures are very complex. To address this issue, Wu et al. [43] introduced the neighborhood concept, namely, that the state of a certain point only depends on the states of several nearby points. In this work, we use a traversal scanning algorithm (based on the MCMC method) to generate sufficient image size to ensure the formed digital core has the same statistical characteristics with the original image. ...
... Reconstruction of digital core based on the MCMC method[43]. ...
Characterizing internal microscopic structures of porous media is of vital importance to simulate fluid and electric current flow. Compared to traditional rock mechanics and geophysical experiments, digital core and pore network modeling is attracting more interests as it can provide more details on rock microstructure with much less time needed. The axis extraction algorithm, which has been widely applied for pore network modeling, mainly consists of a reduction and burning algorithm. However, the commonly used methods in an axis extraction algorithm have the disadvantages of complex judgment conditions and relatively low operating efficiency, thus losing the practicality in application to large-scale pore structure simulation. In this paper, the updated algorithm proposed by Palágyi and Kuba was used to perform digital core and pore network modeling. Firstly, digital core was reconstructed by using the Markov Chain Monte Carlo (MCMC) method based on the binary images of a rock cutting plane taken from heavy oil reservoir sandstone. The digital core accuracy was verified by comparing porosity and autocorrelation function. Then, we extracted the central axis of the digital pore space and characterize structural parameters through geometric transformation technology and maximal sphere method. The obtained geometric parameters were further assigned to the corresponding nodes of pore and throat on the central axis of the constructed model. Moreover, the accuracy of the new developed pore network model was measured by comparing pore/throat parameters, curves of mercury injection, and oil-water relative permeability. The modeling results showed that the new developed method is generally effective for digital core and pore network simulation. Meanwhile, the more homogeneity of the rock, which means the stronger “representative” of binary map the rock cutting plane, the more accurate simulated results can be obtained.
... In order to analyze and obtain the structures of pore space with lower costs, numerical reconstruction methods have been widely studied, which reconstruct pore space using the statistical information extracted from real 2D or 3D images of rocks or other materials. Typical numerical reconstruction methods include the truncated Gaussian simulation method [13], the simulated annealing method [9], the Monte Carlo method [31], the sequential indicator simulation method [10], the multiple-point statistics (MPS) [24,25], etc. Some numerical reconstruction methods, e.g. ...
The observation and analyses of cores are the bases of various studies on oil and gas exploration and development. However, the real natural cores suffer from their own instability and constant weathering or erosion as well as experimental damages, leading to the changes of their physical and chemical characteristics. Digital cores can address the above issues by core digitalization and then reusing the original core images or data without damaging the real samples. The 3D reconstruction of pore space actually is an important step for the construction of 3D digital cores. There are two main ways for the reconstruction of pore space including physical experimental methods and numerical reconstruction methods. Physical experimental methods usually are quite time-consuming and expensive while numerical reconstruction methods are relatively inexpensive and more efficient. With the flourishing development of deep learning and its variants, the reconstruction of pore space possibly can benefit from the strong inherent ability of extracting characteristics from training images (TIs) hidden in deep learning. This paper proposes a reconstruction method using a deep residual deconvolution network (DRDN), considered as a variant of deep learning, in which the characteristics of TI are learned by using constant residual convolution in training and then the pore space is reconstructed by adding the previous residual convolution results to each deconvolution layer. Compared to some other typical numerical reconstruction methods, our method shows its efficiency and practicability in the reconstruction of 3D pore space.
... The first attempt is to construct multi-resolution 2D or 3D digital images that integrate SEM images information acquired at different magnifications. A Markov Chain Monte Carlo (MCMC) method is developed to reconstruct multi-scale heterogeneous porous media using the thin section images at various resolutions (Wu et al. 2004(Wu et al. , 2006. Okabe and Blunt (2007) established a two-step approach to combine microtomography at the microscale resolution to resolve large pores and vugs with statistically reconstructed high-resolution images for smaller features by multiple-point statistics (MPS). ...
Due to the multi-scale pore size and complex gas-bound water distribution, it is challenging to accurately predict gas transport property in shale. Given the known heterogeneities, single-resolution pore-scale imaging is not reliable for representative pore structure characterization. In this study, the image-based shale multi-scale pore network model (MPNM) is proposed and the impacts of pore structure and relative humidity (RH) on gas transport are analyzed in detail. 3D binary images are constructed by the multiple-point statistics method from a section of low-resolution SEM image which covers the large-scale pore structure and fine-scale SEM images with the same physical size at high resolution. The maximal ball fitting method is applied to extract large-scale pore network model (LPNM) and fine-scale pore network models (FPNMs) from the 3D binary images, respectively. MPNM is obtained by merging the LPNM and FPNMs based on the proposed procedure. The confined gas-bound water distribution at different RH is calculated considering the disjoining pressure resulting from van der Waals force, electric double-layer interactions and structural force. Gas slippage in irregular pores is considered for gas transport. Pore structure parameters and gas permeabilities are calculated based on the MPNM, LPNM and FPNMs. Study results indicate that the gas permeability of MPNM is more close to the laboratory pressure pulse decay measured gas permeability of studied sample. Gas permeability decreases with the increasing RH and drops to zero at average pore radius less than 12 nm and RH larger than 0.7.
... Digital core reconstruction is mainly focused on the analysis and construction of core structure [7,8]. At present, the pores of digital cores in shale gas reservoirs are distributed from nanometer to millimeter. ...
Conventional digital core reconstruction methods are not suitable for deep shale gas reservoirs with low porosity and permeability, anisotropy and complex mineral composition, and conventional single resolution three-dimensional digital core structure model cannot fully describe the core structure of shale gas reservoirs of different scales. In this paper, the advantages and disadvantages of different digital core reconstruction methods are summarized by analyzing examples. It is found that MCMC core reconstruction method is more suitable for image reconstruction of 3D digital structure model core of deep shale gas reservoir in China; Finally, in view of the problems existing in conventional digital core reconstruction methods, combining CT imaging with ion beam focused electron microscopy (FIB-SEM) imaging technology, a 3D digital core structure model with multi-scale, multi-component and corresponding macro pore and micro pore of the corresponding reservoir is proposed. The micro spatial distribution structure of the model is similar to that of real shale gas reservoir core, it overcomes the difficulty that the resolution of single scale 3D digital gas reservoir core model and the micro size characteristics of gas reservoir core cannot be perfectly considered. It can not only accurately describe the micro pore space distribution structure of real core gas reservoir, but also accurately describe the macro heterogeneity of deep shale gas reservoir core.
