{"paper_id":"18b4cb2d-1e95-4d68-b413-00c9c8f061cf","body_text":"Reconstruction of porous media pore structure and analysis of simulation effect based on SNESIM algorithm | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Reconstruction of porous media pore structure and analysis of simulation effect based on SNESIM algorithm Qing Xie, Jiaqi Gao, Xiaochuang Ye, Jia LI, YiFei Song, SiWen Hu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5021774/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Feb, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract The pore structure of porous media directly affects its permeability characteristics and fluid flow properties, making accurate reconstruction of these structures of great significance. In recent years, multipoint statistics (MPS) methods have been widely used in pore structure modeling. Among them, the SNESIM algorithm, as an advanced MPS technique, has been extensively applied in the study of porous media pore structures. This paper aims to investigate the effectiveness of the SNESIM algorithm in reconstructing pore structures on 2D slices of cores with different porosities taken from the same core. Furthermore, it analyzes the advantages and limitations of the algorithm and its applicable conditions. This study utilizes CT scan images to construct digital core technology and applies the SNESIM algorithm to reconstruct pore structures of core slices with different porosities. By analyzing performance parameters such as porosity, pore throat ratio, average grain radius, coordination number, and permeability, the study found that the reconstructed images in most samples can maintain a trend similar to that of the training images, demonstrating the high applicability and reliability of the SNESIM algorithm in pore structure reconstruction. However, the core slices used in this study were all taken from the same core. Effectively transferring the pore structures from the 2D plane to the 3D pore space and restoring the pore structures to the greatest extent still requires further research. In particular, when dealing with complex pore structures, the accuracy and performance of the SNESIM algorithm need further improvement. Future research will focus on optimizing the algorithm to handle more diverse pore structures and exploring 3D reconstruction methods to more comprehensively describe and analyze the pore characteristics in actual porous media. Physical sciences/Energy science and technology Physical sciences/Mathematics and computing coordination number average grain radius variogram digital core multipoint geostatistics porous media Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Introduction In geological and geophysical research, multipoint geostatistical methods have garnered significant attention due to their superiority in modeling and analyzing complex geological structures. Porous media, as an important natural and artificial material, have extensive applications in fields such as petroleum and natural gas extraction, water resource management, and environmental engineering. However, the internal pore structure of porous media is complex, and accurately predicting fluid flow behavior within them is challenging 1 , 2 . Therefore, accurately reconstructing the pore space structure of porous media has become a hot topic in current research. Currently, there are three main models for pore structure reconstruction: Pore Structure Reconstruction Model, Pore Network Model, and Equivalent Pore Network Model. Among these, the Pore Structure Reconstruction Model is the most commonly used. This model primarily utilizes numerical simulation or computer graphics techniques to digitize the pore space, thereby reproducing the microscopic pores and framework structures of porous media. Presently, the main methods for reconstructing pore structures include the Discrete Element Method (DEM) 3 , 4 and the Image Sequence Reconstruction Method 5 , 6 . The Discrete Element Method (DEM) refers to simulating particle size, pore radius, porosity, and other parameters through a series of particle accumulations to reflect the actual pore structure 7 . However, because DEM typically uses spherical particles to simulate the real reservoir structure, in the absence of realistic shape simulations of the pore structure, this reconstruction method cannot accurately reflect the complex pore morphology and structure of actual rocks 8 , 9 . In contrast, the Image Sequence Reconstruction Method leverages digital technology to reconstruct microscopic pore structures, resulting in a closer approximation to the actual pore structure. Thus, it is widely applied in pore reconstruction research. This method uses two-dimensional scanned images of porous media samples obtained through digital imaging technology and applies these 2D images to pore structure modeling using computer graphics 10 , 11 . Currently, commonly used imaging methods mainly include Computerized Tomography (CT) imaging technology 12 , Scanning Electron Microscopy (SEM) 13 , 14 , and Focused Ion Beam/Scanning Electron Microscopy (FIB/SEM) imaging technology 15 . Among these, CT scanning technology is relatively mature and widely used 16 – 18 . Using CT scan images as prior data for reconstruction images, combined with multipoint statistical methods, is a current research hotspot 19 , 20 . Biswal adopted a physics-based approach to simulate the structure of porous media 21 . Julien Straubhaar proposed a method for editing static images to generate the features of training images while maintaining the consistency of the overall spatial structure 22 . Training images contain prior data information about geological reservoir structures, enabling the replication of multipoint events through information nodes on the training images 23 , 24 . Using prototype elements from training images to construct a non-negative dictionary, the dictionary is then incorporated as prior information into the reconstruction problem 25 . Mingliang Gao et al. (2017) used mathematical modeling to reconstruct the three-dimensional (3D) random spatial structure of porous media from two-dimensional (2D) training images, reconstructing specific morphologies belonging to the training images (Ti) in 3D space 26 . Jeongbin Hwang (2023) built a large, high-quality training image database 27 . Currently, many popular methods also employ training images and multipoint statistics for reproduction, such as neural networks to replicate large pore structure datasets 28 , 29 . Multipoint statistics are often used for the reproduction of features in complex geological reservoirs. Traditional two-point geostatistics based on variogram functions struggle to perform geostatistical simulations when handling large amounts of complex reservoir data. Strebelle and Journel (2000) proposed the single normal equation, which estimates the data distribution of unknown nodes by calculating the probability of node occurrence in training images 30 . However, this method relies on an iterative approach, and the computation speed directly affects the speed of pore structure construction. Strebelle (2002) developed a data storage method based on a search tree, called the single normal equation simulation (SENSIM) algorithm. By scanning the training image once, the obtained multipoint probabilities are stored in the \"search tree\" nodes 31 . Therefore, multipoint statistics (MPS) is a pixel-based direct sampling algorithm. This method first assigns conditional data values as initial data in the simulation grid and then fills the data values of unknown grids in the training image in a random order 32 – 34 . Julien Straubhaar (2021) extended the direct sampling algorithm using multipoint geological simulation tools to address unequal data 35 . Xiaoqi Zhou (2023) simulated the heterogeneity and spatial trends of subsurface formations using a knowledge-based multipoint geostatistics method and combined it with standard permeability test data to improve simulation accuracy 36 , 37 . Gareth R. Chalmers et al. (2013) analyzed pore structure characteristics through total porosity, pore size distribution, surface area, organic geochemistry, mineralogy, and electron microscopy image analysis techniques 38 . By analyzing parameters such as different pore radii, throat radii, and pore granularity, further studies on the anisotropy, permeability, coordination number, and other pore performance parameters of porous media can be conducted 39 . Among these, the seepage characteristics of porous media pores are crucial for evaluating the performance of reconstructed pore structure models. The main methods currently used to study permeability include the Finite Difference Method (FDM) 40 , pore morphology modeling 41 , effective medium theory 42 , computational fluid dynamics (CFD) 43 , 44 , and the lattice Boltzmann method (LBM) 45 . The lattice Boltzmann method (LBM) is an effective method for calculating the permeability of the microstructure of porous media. Siyu Chen (2019) used the LBM method to simulate fluid flow in porous materials and predict their permeability coefficients 19 . Arash Rabbani (2019) proposed a permeability calculation method combining pore network modeling (PNM) with the lattice Boltzmann method (LBM) 46 . Z. Irayani (2018) established three vertical networks, combining the renormalization group method with LBM to calculate the permeability of 3D computed tomography rock images 47 . Budi Dharmala Saputra (2024) studied the effect of coordination number on permeability in a 3D rock model using the LBM method, confirming that LBM can serve as a powerful tool for understanding pore-scale seepage 48 . This paper primarily aims to build upon the SNESIM reconstruction algorithm by controlling parameter variables such as template size and grid number. Using porous media core slice samples with different porosities as prior data, the paper reconstructs and generates corresponding pore structure images. By analyzing differences in parameters such as porosity, average pore diameter, pore granularity, pore coordination number, and permeability, the study explores methods to improve reconstruction accuracy. Methodology The main idea of multipoint geostatistics methods consists of three steps: conditional data extraction, feature library construction, and probabilistic simulation. First, real data obtained from geological reservoirs are used as conditional data to extract the actual image structural features of the geological reservoir. These extracted image features are stored using a \"search tree\" structure, forming a library of training image features. Finally, when generating simulated images, the relevant image features are selected from the feature library based on the conditional data and probabilistic principles, creating a reconstructed dataset that resembles the real geological structure. \\(Z(n)\\) is a spatial structural variable defined over the domain of the training image.The data event \\(d{(u)_n}\\) is the state value of size at the center location . The data template \\({\\tau _{\\text{n}}}\\)includes a geometric pattern composed of vectors, \\({\\tau _n}=\\{ {h_\\alpha };\\alpha =1,2,...,n\\}\\), with the template center location set as and other template positions as \\({u_\\alpha }=u+{h_\\alpha }\\left( {\\alpha =1,2,...,n} \\right)\\). As shown in Fig. 1(a), the grid template is composed of 4×4 pixels, determined by the center point and 15 vectors, with each vector represented by a grid point. Figure 1(b) shows the data template for a 2D data event with \\(n=4\\). Figure 1(c) illustrates the scanning of the training image using the data template in the direction indicated by the arrow to construct the search tree, and Fig. 1(e) depicts the structure of the search tree. Figure 1(d) is a data event related to the data template. It illustrates the process of scanning the training image to obtain a data event. In the simulation, the state value of \\(Z(n)\\) is determined by the conditional probability distribution function (cpdf)\\({\\text{d}}\\left( u \\right){\\text{=\\{ z(}}{{\\text{u}}_\\alpha }{\\text{)=}}{{\\text{s}}_{{k_\\alpha }}}{\\text{;}}\\alpha {\\text{=1,2}}...{\\text{,n\\} }}\\) extracted from the training image. According to Bayes' conditional probability formula: \\(\\Pr ob\\left\\{ {Z(u)={s_k}|d({\\text{n}})} \\right\\}=\\frac{{{c_k}\\left( {d\\left( {\\text{n}} \\right)} \\right)}}{{c\\left( {d\\left( {\\text{n}} \\right)} \\right)}}\\) \\(c\\left( {d\\left( {\\text{n}} \\right)} \\right)\\) is the repetition count of \\(d(n)\\)for the data event, \\({c_k}\\left( {d\\left( {\\text{n}} \\right)} \\right)\\) is the inferred repetition count from \\(c\\left( {d\\left( {\\text{n}} \\right)} \\right)\\) when the central node \\(Z(u)\\) has the value \\(Z(n)\\).The probability of occurrence of the conditional data event can be converted to the ratio of the size of the 2D binary image of the effective initial pore \\({N_n}\\). The main process of the SNESIM (Single Normal Equation Simulation) algorithm is as follows: 1.Pre-scan Training Images and Build the Search Tree: Assign sample data to the nearest grid nodes and define a random path to traverse all unsampled nodes. Check if the current node is on the simulation grid; if it is, continue; otherwise, move to the next node according to the random path. If the current node is a location with existing data, skip to the next node. Retain information about the positions in the template where n positions have existing data. 2.Check for Data Positions: Determine if there are any data positions (n' ≠ 0). If not, draw a value from the marginal distribution as the simulation value. Retrieve the number of training data events from the search tree that match the conditional data event, and obtain these events' central values as SK. 3.Verify Event Count: Check if the number of retrieved data events \\(c=\\sum {\\alpha _k}\\)is greater than the minimum value \\({c_{\\hbox{min} }}\\). If not, remove the most distant conditional data and recalculate. 4.Calculate Local Conditional Probability Density Function: Compute the local conditional probability density function \\(p\\left( {u;sk(n')} \\right)={\\raise0.7ex\\hbox{${{\\alpha _k}}$} \\!\\mathord{\\left/ {\\vphantom {{{\\alpha _k}} c}}\\right.\\kern-0pt}\\!\\lower0.7ex\\hbox{$c$}}\\) for subsequent simulation value extraction. 5.Extract and Store Simulation Value: Draw a simulation value from the local conditional probability density function and store it as hard data. Figure 2 illustrates the flowchart of the SNESIM algorithm. Figure 3 SNESIM reconstruction algorithm is shown in the figure. Application example In this experiment, samples were selected from actual reservoir cores from an oil field. Six core slices with porosities of 6%, 10%, 15%, 21%, 25%, and 38% were extracted from the 3D scanned images of the cores, labeled sequentially as A-F, as shown in the first and third columns of Fig. 4. The second and fourth columns in the figure display the binarized images of the CT scan, where the black parts represent the rock matrix and the white parts indicate the pores. Figure 5 shows the reconstructed images of the six samples with porosities of 5%, 10%, 15%, 21%, 25%, and 38%. By comparing the pore structures of the initial training images with those of the reconstructed images, it can be observed that the reconstructed images largely retain the pore structure of the initial training images. Types of pore structures and heterogeneities, such as narrow pores, small pores, and large pores present in the initial images, are also reflected in the reconstructed images. For example, in Fig. 6, samples B and E are illustrated. The bar charts display the frequency of different pore radii in the pore structure, with yellow bars representing the training images and gray bars representing the reconstructed images. It is evident from the images that the pore radii in the two samples are almost identical, and the frequency of occurrence for the same pore size is roughly the same. For instance, in sample E, the heights of the yellow and gray bars for pore radii of 15 µm, 21 µm, and 50 µm are quite similar. In this paper, the \"pore-throat ratio\" index is used for quantitative analysis of the homogeneity within the pore structure of porous media. Within a local range, the variation between pores and throats changes with the pore-throat ratio; that is, the more pronounced the changes in pore structure at a fine scale, the poorer the homogeneity of the porous media. Figure 7 analyzes the reconstruction effects of pore structures at different porosities from the perspective of pore radius distribution. Figure 7(a) presents histograms of the average pore diameter distribution for samples with different porosities. The yellow bars represent the average pore diameter of the initial training images, while the gray bars represent the average pore diameter of the reconstructed images. The bar charts show that the average pore diameter of the reconstructed images generated by the algorithm is quite close to that of the initial training images, indicating high consistency between the two in this metric. Figure 7(b) shows boxplots of pore diameter distributions for samples with different porosities. The yellow and gray parts represent the initial training images and reconstructed images, respectively. Compared to the initial training images, the reconstructed images have a larger interquartile range (IQR) and wider upper and lower range edges, indicating higher variability in the reconstructed images. The median (average pore diameter) of the reconstructed images is slightly higher or comparable to that of the initial training images, but the difference is minimal. The reconstructed images exhibit more frequent outliers, suggesting some deviation from the initial pore structure. Overall, the reconstructed images and initial training images are quite consistent in terms of median (average pore diameter) and general boxplot trends, demonstrating that the reconstruction algorithm is effective in capturing the average pore diameter. However, the increased variability (wider IQR and more outliers) in the reconstructed images may reflect the introduction of new features during the reconstruction process, indicating increased diversity. Figure 8 shows the average pore-throat radius for samples A-F with different porosities. The left side of the figure displays the average pore-throat radius of the initial training images, while the right side shows the boxplots of the average pore-throat radius for the reconstructed pore structures generated by the algorithm. Each boxplot illustrates the distribution of the average pore-throat radius for a sample, including the quartiles, minimum, maximum, and outliers. Overall, the data distribution in the reconstructed images (right side) is very close to that in the training images (left side). The median and interquartile range (IQR) of the reconstructed images are roughly consistent with those of the training images, indicating that the average pore-throat radius of the reconstructed images is very close to that of the initial pore structure. Although there may be a few outliers in some samples, the boxplots of the reconstructed images are almost identical in distribution to those of the training images, demonstrating that the reconstruction method performs well in preserving the pore-throat radius distribution characteristics. Particularly, the consistency in the median and IQR between the reconstructed and training images shows that the reconstruction method is successful in capturing and reproducing the main statistical features of the original data. The pore-throat ratio, which is the ratio of pore diameter to throat diameter, is an important parameter for characterizing pore structure and a crucial microphysical property of reservoir media. A larger pore-throat ratio indicates a larger pore space and wider channels relative to the throats, which can be more favorable for fluid flow. Figure 9 displays the pore-throat ratios of the pore structures in different core slices, with blue bars representing the training images and red bars representing the reconstructed images. In most slice samples, the pore-throat ratios of the reconstructed images maintain the same trend as those of the training images, indicating that the reconstruction method effectively reproduces the pore structure features of the training images overall. Notably, in sample C, the pore-throat ratio of the reconstructed image closely matches the pore structure features of the training image. In some samples, such as sample E, the pore-throat ratio in the reconstructed images is significantly higher than in the training images. This discrepancy may be due to the reconstruction method's inability to fully capture the features of complex pore structures, reflecting limitations in detail handling and accuracy. However, overall, the reconstructed images for all six samples follow the same trend as the training images, demonstrating that the reconstruction method has high applicability and reliability. This paper uses the average coordination number to quantitatively assess the connectivity of pore structures in porous media. A higher coordination number indicates better pore connectivity. Figure 10 displays histograms of the average coordination number distribution for core slices corresponding to training images and reconstructed images. In the figure, blue represents the coordination numbers of the pore structures in the initial training images, while red represents the coordination numbers in the reconstructed images. For the six samples, which are from the same core slice, the pore coordination numbers are concentrated in the range of 2–4. For samples with the same porosity, the pore coordination numbers in the reconstructed images are generally consistent with those in the training images. As porosity increases, the average coordination number for the six samples with different porosities gradually decreases. This indicates that, at lower porosities, the connectivity of pores at the microscopic scale is better. The grain size radius of pores is a critical parameter affecting pore structure and directly relates to the fluid flow characteristics of the pores. Pores with larger grain size radii typically provide larger fluid flow channels, while pores with smaller grain size radii present greater flow resistance. Figure 11 shows the average grain size radius for training and reconstructed images under different core slices, with blue representing the training images and red representing the reconstructed images. It is observed that the grain size radius of the reconstructed images is similar to that of the training images for most samples, although some differences exist. In certain samples, the grain size radius in the reconstructed images closely matches that of the training images, indicating that the reconstruction method performs well for these samples and can effectively reproduce the pore structure of the training images. However, in some samples, there are noticeable differences in the grain size radius between the reconstructed images and the training images, which may be due to errors or limitations in the reconstruction algorithm for these samples. Overall, the trend of the grain size radius in the reconstructed images is consistent with that of the training images, suggesting that the reconstruction method retains the pore structure characteristics of the training images to a certain extent. For specific samples with significant discrepancies in grain size radius, further optimization of the reconstruction algorithm may be needed to improve accuracy. Porosity is a key parameter describing the size and distribution of pore space and has a significant impact on the fluid flow characteristics of pores. Higher porosity typically indicates larger pore space and lower fluid flow resistance, while lower porosity suggests smaller pore space and higher fluid flow resistance. Figure 12 shows the porosity of the initial and reconstructed two-dimensional pore images for six core slice samples. Analyzing the porosity of the initial and reconstructed pore images is the most direct way to assess reconstruction quality. The figure reveals that, except for the sample with 6% porosity, which shows a very slight difference in porosity between the initial and reconstructed images, the porosity of the reconstructed images for the other samples is consistent with that of the initial images. This indicates that the reconstruction method performs well for these samples and can effectively reproduce the pore structure of the training images. Although some samples show slightly higher or lower porosity in the reconstructed images, which could affect the fluid flow characteristics of the pore structure, overall, the reconstruction method demonstrates excellent performance in retaining the initial pore structure. The variance function reflects the spatial variability of the pore structure. Figure 13 compares the differences between the reconstructed and initial images from the x and y directions in two-dimensional images to analyze the reconstruction effects. Observing the training images (top left and top right), the variance function for different core slices increases with lag distance, indicating that the pore structure has a certain spatial correlation at larger scales. The trends in the variance function in the x and y directions are generally consistent across different slices, showing similar spatial variability in these directions. For the reconstructed images (bottom left and bottom right), the variance function also increases with lag distance for different core slices, but exhibits some fluctuations at certain lag distances. While the variance function trends in the x and y directions for the reconstructed images show some similarity to the training images, there are differences at larger lag distances. Comparing the variance functions of the reconstructed and training images, it is evident that there are significant differences in the variance function values at certain lag distances in the reconstructed images compared to the training images. This may be due to the loss of certain detail information during the reconstruction process or limitations in the reconstruction method when dealing with variability at specific scales. However, the overall trend of the variance function across different core slices is consistent between the training and reconstructed images, indicating that the reconstruction method retains the spatial structural features of the training images to some extent. In summary, the reconstruction method performs well in reproducing the spatial variability of the training images at smaller lag distances but may need further improvement at larger lag distances to better capture the spatial correlations of the training images. The pore structure directly affects the permeability characteristics of porous media. Higher permeability indicates more connected pore spaces and smoother fluid flow. By observing the permeability of different samples in the figure, it can be inferred that the reconstructed images have effectively retained the connectivity of the original pore structure in certain samples, resulting in higher permeability. Figure 14 displays the permeability distribution for six core slice samples, where blue and red squares represent the permeability data of the training images along the x and y axes, respectively, and yellow and green circles represent the permeability data of the reconstructed images along the x and y axes. In some samples (e.g., samples B and E), the permeability of the reconstructed images is close to that of the training images, indicating that the reconstruction method effectively reproduces the permeability characteristics of the original images for these slices. However, in other samples (e.g., samples C and F), there are some differences in permeability between the reconstructed and training images, which may reflect the limitations of the reconstruction method in certain situations. Overall, the reconstruction method performs excellently in preserving the overall connectivity and permeability of the pore structure. However, there may be a need for further optimization and improvement when dealing with complex or highly heterogeneous pore structures. Conclusion Based on the comprehensive analysis of the experiments, the SNE-SIM algorithm demonstrates high performance in reconstructing pore structures. The analysis of parameters such as porosity, pore-throat ratio, average particle radius, coordination number, and permeability shows that the reconstructed images generally maintain trends similar to those of the training images in most samples. The performance parameters of the reconstructed core slices are largely consistent with those of the initial core slices, indicating that the SNE-SIM algorithm has high applicability and reliability in pore structure reconstruction, effectively reproducing the main pore structure features of the initial training images. However, since the core slices used in this study are all from the same core, this somewhat limits the comprehensive understanding of pore structures. Further analysis and research are needed to effectively transfer the pore structure from a two-dimensional plane to a three-dimensional pore space and to maximize the restoration of the pore structure. Particularly when dealing with complex pore structures, the accuracy and performance of the reconstruction algorithm require further improvement. Future research should focus on optimizing the algorithm to handle more diverse pore structures and explore three-dimensional reconstruction methods to provide a more comprehensive description and analysis of pore features in actual porous media. Declarations Funding This work was supported financially by the National Nature Science Foundation of China [grant numbers 51974247]. Author information Authors and Affiliations College of Petroleum Engineering, Xi’an Shiyou University. Xi’an 710065, China; MOE Engineering Research Center of Development & Management of Western Low & Ultra-Low Permeability Oilfield, Xi’an 710065, China Qing Xie & Jiaqi Gao & Jia Li & Yifei Song NO.3 Gas Production Plant of Changqing Oilfield Company, Petro China Xi’an, Shanxi, 710018, China Xiaochuang Ye College of Electronic Engineering,, Xi’an Shiyou University. Xi’an 710065, China Siwen Hu Contributions Qing Xie, Jiaqi Gao, Siwen Hu, and Jia Li were involved in conceptualization of the study. Qing Xie, Jiaqi Gao, Yifei Song, and Xiaochuang Ye were involved in data acquirement and analysis. All authors involved in interpreting the analyses. Qing Xie and Jiaqi Gao wrote the original draft. All authors reviewed and edited the final draft. Corresponding author Correspondence to Qing Xie. Competing interests The authors declare no competing interests. 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Site-Optimized Training Image Database Development Using Web-Crawled and Synthetic Images. Autom. Constr. 151 , 104886. https://doi.org/10.1016/j.autcon.2023.104886 (2023). Wang, Y., Rahman, S. S. & Arns, C. H. Super Resolution Reconstruction of µ -CT Image of Rock Sample Using Neighbour Embedding Algorithm. Phys. A: Stat. Mech. its Appl. 493 , 177–188. https://doi.org/10.1016/j.physa.2017.10.022 (2018). Wang, Y., Arns, C. H., Rahman, S. S. & Arns, J. Y. Porous Structure Reconstruction Using Convolutional Neural Networks. Math. Geosci. 50 (7), 781–799. https://doi.org/10.1007/s11004-018-9743-0 (2018). Strebelle, S. B. Sequential Simulation Drawing Structures from Training Images (Stanford University.;, 2000). Strebelle, S. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Math. Geol. 34 (1), 1–21. https://doi.org/10.1023/A:1014009426274 (2002). Srivastava, M. An Overviewof Stochastic Methods for Reservoir Characterization, AAPG Computer Applications in Geology. (1995). Journel, A. G. & Geostatistics Roadblocks and Challenges (Springer Netherlands, 1993). Shahraeeni, M. Enhanced Multiple-Point Statistical Simulation with Backtracking, Forward Checking and Conflict-Directed Backjumping. Math. Geosci. 51 (2), 155–186. https://doi.org/10.1007/s11004-018-9761-y (2019). Straubhaar, J. & Renard, P. Conditioning Multiple-Point Statistics Simulation to Inequality Data. Earth Space Sci. 8 (5). https://doi.org/10.1029/2020EA001515 (2021). e2020EA001515. Eschricht, N., Hoinkis, E., Mädler, F., Schubert-Bischoff, P. & Röhl-Kuhn, B. Knowledge-Based Reconstruction of Random Porous Media. J. Colloid Interface Sci. 291 (1), 201–213. https://doi.org/10.1016/j.jcis.2005.05.004 (2005). Zhou, X., Shi, P. & Sheil, B. Knowledge-Based Multiple Point Statistics for Soil Stratigraphy Simulation. Tunn. Undergr. Space Technol. 143 , 105475. https://doi.org/10.1016/j.tust.2023.105475 (2024). Chalmers, G. R., Bustin, R. M. & Power, I. M. Characterization of Gas Shale Pore Systems by Porosimetry, Pycnometry, Surface Area, and Field Emission Scanning Electron Microscopy/Transmission Electron Microscopy Image Analyses: Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig Units. Bulletin . 96 (6), 1099–1119. https://doi.org/10.1306/10171111052 (2012). Zhao, S., Zhang, N., Zhou, X. & Zhang, L. Particle Shape Effects on Fabric of Granular Random Packing. Powder Technol. 310 , 175–186. https://doi.org/10.1016/j.powtec.2016.12.094 (2017). Øren, P. E. & Bakke, S. Process Based Reconstruction of Sandstones and Prediction of Transport Properties. Transp. Porous Media . 46 (2/3), 311–343. https://doi.org/10.1023/A:1015031122338 (2002). Adalsteinsson, D. & Hilpert, M. Accurate and Efficient Implementation of Pore-Morphology-Based Drainage Modeling in Two-Dimensional Porous Media. Transp. Porous Med. 65 (2), 337–358. https://doi.org/10.1007/s11242-005-6091-6 (2006). Hosseini, M., Baghbanan, A. & Seifabad, M. C. Using Effective Medium Theory to Calculate Permeability of Rock with Complex Fractures. Proceedings of the Institution of Civil Engineers - Geotechnical Engineering 1–12. (2021). https://doi.org/10.1680/jgeen.21.00132 Sun, H., Vega, S. & Tao, G. Analysis of Heterogeneity and Permeability Anisotropy in Carbonate Rock Samples Using Digital Rock Physics. J. Petrol. Sci. Eng. 156 , 419–429. https://doi.org/10.1016/j.petrol.2017.06.002 (2017). Zhang, J. et al. Numerical Study on Seepage Flow in Pervious Concrete Based on 3D CT Imaging. Constr. Build. Mater. 161 , 468–478 (2018). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 10 Feb, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 31 Oct, 2024 Reviews received at journal 22 Oct, 2024 Reviews received at journal 20 Oct, 2024 Reviewers agreed at journal 10 Oct, 2024 Reviewers agreed at journal 10 Oct, 2024 Reviewers invited by journal 10 Oct, 2024 Editor assigned by journal 24 Sep, 2024 Editor invited by journal 18 Sep, 2024 Submission checks completed at journal 16 Sep, 2024 First submitted to journal 03 Sep, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-5021774\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":372502976,\"identity\":\"6bc6bd60-2b10-4d90-b727-fcbc469cefc4\",\"order_by\":0,\"name\":\"Qing 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of simulation effect based on SNESIM algorithm\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cp\\u003eIn geological and geophysical research, multipoint geostatistical methods have garnered significant attention due to their superiority in modeling and analyzing complex geological structures. Porous media, as an important natural and artificial material, have extensive applications in fields such as petroleum and natural gas extraction, water resource management, and environmental engineering. However, the internal pore structure of porous media is complex, and accurately predicting fluid flow behavior within them is challenging\\u003csup\\u003e\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e\\u003c/sup\\u003e. Therefore, accurately reconstructing the pore space structure of porous media has become a hot topic in current research.\\u003c/p\\u003e \\u003cp\\u003eCurrently, there are three main models for pore structure reconstruction: Pore Structure Reconstruction Model, Pore Network Model, and Equivalent Pore Network Model. Among these, the Pore Structure Reconstruction Model is the most commonly used. This model primarily utilizes numerical simulation or computer graphics techniques to digitize the pore space, thereby reproducing the microscopic pores and framework structures of porous media. Presently, the main methods for reconstructing pore structures include the Discrete Element Method (DEM) \\u003csup\\u003e\\u003cspan citationid=\\\"CR3\\\" class=\\\"CitationRef\\\"\\u003e3\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e4\\u003c/span\\u003e\\u003c/sup\\u003e and the Image Sequence Reconstruction Method\\u003csup\\u003e\\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e5\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR6\\\" class=\\\"CitationRef\\\"\\u003e6\\u003c/span\\u003e\\u003c/sup\\u003e. The Discrete Element Method (DEM) refers to simulating particle size, pore radius, porosity, and other parameters through a series of particle accumulations to reflect the actual pore structure\\u003csup\\u003e\\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e7\\u003c/span\\u003e\\u003c/sup\\u003e. However, because DEM typically uses spherical particles to simulate the real reservoir structure, in the absence of realistic shape simulations of the pore structure, this reconstruction method cannot accurately reflect the complex pore morphology and structure of actual rocks\\u003csup\\u003e\\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e8\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e9\\u003c/span\\u003e\\u003c/sup\\u003e. In contrast, the Image Sequence Reconstruction Method leverages digital technology to reconstruct microscopic pore structures, resulting in a closer approximation to the actual pore structure. Thus, it is widely applied in pore reconstruction research. This method uses two-dimensional scanned images of porous media samples obtained through digital imaging technology and applies these 2D images to pore structure modeling using computer graphics\\u003csup\\u003e\\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e10\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e11\\u003c/span\\u003e\\u003c/sup\\u003e. Currently, commonly used imaging methods mainly include Computerized Tomography (CT) imaging technology\\u003csup\\u003e\\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e12\\u003c/span\\u003e\\u003c/sup\\u003e, Scanning Electron Microscopy (SEM)\\u003csup\\u003e\\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e13\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR14\\\" class=\\\"CitationRef\\\"\\u003e14\\u003c/span\\u003e\\u003c/sup\\u003e, and Focused Ion Beam/Scanning Electron Microscopy (FIB/SEM) imaging technology\\u003csup\\u003e\\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e15\\u003c/span\\u003e\\u003c/sup\\u003e. Among these, CT scanning technology is relatively mature and widely used\\u003csup\\u003e\\u003cspan additionalcitationids=\\\"CR17\\\" citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e18\\u003c/span\\u003e\\u003c/sup\\u003e. Using CT scan images as prior data for reconstruction images, combined with multipoint statistical methods, is a current research hotspot\\u003csup\\u003e\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e19\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e20\\u003c/span\\u003e\\u003c/sup\\u003e. Biswal adopted a physics-based approach to simulate the structure of porous media\\u003csup\\u003e\\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e21\\u003c/span\\u003e\\u003c/sup\\u003e. Julien Straubhaar proposed a method for editing static images to generate the features of training images while maintaining the consistency of the overall spatial structure\\u003csup\\u003e\\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e22\\u003c/span\\u003e\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eTraining images contain prior data information about geological reservoir structures, enabling the replication of multipoint events through information nodes on the training images \\u003csup\\u003e\\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e23\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e24\\u003c/span\\u003e\\u003c/sup\\u003e. Using prototype elements from training images to construct a non-negative dictionary, the dictionary is then incorporated as prior information into the reconstruction problem\\u003csup\\u003e\\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e25\\u003c/span\\u003e\\u003c/sup\\u003e. Mingliang Gao et al. (2017) used mathematical modeling to reconstruct the three-dimensional (3D) random spatial structure of porous media from two-dimensional (2D) training images, reconstructing specific morphologies belonging to the training images (Ti) in 3D space\\u003csup\\u003e\\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e26\\u003c/span\\u003e\\u003c/sup\\u003e. Jeongbin Hwang (2023) built a large, high-quality training image database\\u003csup\\u003e\\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e27\\u003c/span\\u003e\\u003c/sup\\u003e. Currently, many popular methods also employ training images and multipoint statistics for reproduction, such as neural networks to replicate large pore structure datasets\\u003csup\\u003e\\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e28\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e29\\u003c/span\\u003e\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eMultipoint statistics are often used for the reproduction of features in complex geological reservoirs. Traditional two-point geostatistics based on variogram functions struggle to perform geostatistical simulations when handling large amounts of complex reservoir data. Strebelle and Journel (2000) proposed the single normal equation, which estimates the data distribution of unknown nodes by calculating the probability of node occurrence in training images\\u003csup\\u003e\\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e30\\u003c/span\\u003e\\u003c/sup\\u003e. However, this method relies on an iterative approach, and the computation speed directly affects the speed of pore structure construction. Strebelle (2002) developed a data storage method based on a search tree, called the single normal equation simulation (SENSIM) algorithm. By scanning the training image once, the obtained multipoint probabilities are stored in the \\\"search tree\\\" nodes\\u003csup\\u003e\\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e31\\u003c/span\\u003e\\u003c/sup\\u003e. Therefore, multipoint statistics (MPS) is a pixel-based direct sampling algorithm. This method first assigns conditional data values as initial data in the simulation grid and then fills the data values of unknown grids in the training image in a random order\\u003csup\\u003e\\u003cspan additionalcitationids=\\\"CR33\\\" citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e32\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR34\\\" class=\\\"CitationRef\\\"\\u003e34\\u003c/span\\u003e\\u003c/sup\\u003e. Julien Straubhaar (2021) extended the direct sampling algorithm using multipoint geological simulation tools to address unequal data\\u003csup\\u003e\\u003cspan citationid=\\\"CR35\\\" class=\\\"CitationRef\\\"\\u003e35\\u003c/span\\u003e\\u003c/sup\\u003e. Xiaoqi Zhou (2023) simulated the heterogeneity and spatial trends of subsurface formations using a knowledge-based multipoint geostatistics method and combined it with standard permeability test data to improve simulation accuracy\\u003csup\\u003e\\u003cspan citationid=\\\"CR36\\\" class=\\\"CitationRef\\\"\\u003e36\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e37\\u003c/span\\u003e\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eGareth R. Chalmers et al. (2013) analyzed pore structure characteristics through total porosity, pore size distribution, surface area, organic geochemistry, mineralogy, and electron microscopy image analysis techniques\\u003csup\\u003e\\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e38\\u003c/span\\u003e\\u003c/sup\\u003e. By analyzing parameters such as different pore radii, throat radii, and pore granularity, further studies on the anisotropy, permeability, coordination number, and other pore performance parameters of porous media can be conducted\\u003csup\\u003e\\u003cspan citationid=\\\"CR39\\\" class=\\\"CitationRef\\\"\\u003e39\\u003c/span\\u003e\\u003c/sup\\u003e. Among these, the seepage characteristics of porous media pores are crucial for evaluating the performance of reconstructed pore structure models.\\u003c/p\\u003e \\u003cp\\u003eThe main methods currently used to study permeability include the Finite Difference Method (FDM)\\u003csup\\u003e\\u003cspan citationid=\\\"CR40\\\" class=\\\"CitationRef\\\"\\u003e40\\u003c/span\\u003e\\u003c/sup\\u003e, pore morphology modeling\\u003csup\\u003e\\u003cspan citationid=\\\"CR41\\\" class=\\\"CitationRef\\\"\\u003e41\\u003c/span\\u003e\\u003c/sup\\u003e, effective medium theory\\u003csup\\u003e\\u003cspan citationid=\\\"CR42\\\" class=\\\"CitationRef\\\"\\u003e42\\u003c/span\\u003e\\u003c/sup\\u003e, computational fluid dynamics (CFD)\\u003csup\\u003e\\u003cspan citationid=\\\"CR43\\\" class=\\\"CitationRef\\\"\\u003e43\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR44\\\" class=\\\"CitationRef\\\"\\u003e44\\u003c/span\\u003e\\u003c/sup\\u003e, and the lattice Boltzmann method (LBM)\\u003csup\\u003e45\\u003c/sup\\u003e. The lattice Boltzmann method (LBM) is an effective method for calculating the permeability of the microstructure of porous media. Siyu Chen (2019) used the LBM method to simulate fluid flow in porous materials and predict their permeability coefficients\\u003csup\\u003e\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e19\\u003c/span\\u003e\\u003c/sup\\u003e. Arash Rabbani (2019) proposed a permeability calculation method combining pore network modeling (PNM) with the lattice Boltzmann method (LBM)\\u003csup\\u003e46\\u003c/sup\\u003e. Z. Irayani (2018) established three vertical networks, combining the renormalization group method with LBM to calculate the permeability of 3D computed tomography rock images\\u003csup\\u003e47\\u003c/sup\\u003e. Budi Dharmala Saputra (2024) studied the effect of coordination number on permeability in a 3D rock model using the LBM method, confirming that LBM can serve as a powerful tool for understanding pore-scale seepage\\u003csup\\u003e48\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eThis paper primarily aims to build upon the SNESIM reconstruction algorithm by controlling parameter variables such as template size and grid number. Using porous media core slice samples with different porosities as prior data, the paper reconstructs and generates corresponding pore structure images. By analyzing differences in parameters such as porosity, average pore diameter, pore granularity, pore coordination number, and permeability, the study explores methods to improve reconstruction accuracy.\\u003c/p\\u003e\"},{\"header\":\"Methodology\",\"content\":\"\\u003cp\\u003eThe main idea of multipoint geostatistics methods consists of three steps: conditional data extraction, feature library construction, and probabilistic simulation. First, real data obtained from geological reservoirs are used as conditional data to extract the actual image structural features of the geological reservoir. These extracted image features are stored using a \\\"search tree\\\" structure, forming a library of training image features. Finally, when generating simulated images, the relevant image features are selected from the feature library based on the conditional data and probabilistic principles, creating a reconstructed dataset that resembles the real geological structure.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\\\(Z(n)\\\\)\\u0026nbsp; is a spatial structural variable defined over the domain of the training image.The data event \\\\(d{(u)_n}\\\\) is the state value of size at the center location . The data template \\\\({\\\\tau _{\\\\text{n}}}\\\\)includes a geometric pattern composed of vectors, \\\\({\\\\tau _n}=\\\\{ {h_\\\\alpha };\\\\alpha =1,2,...,n\\\\}\\\\), with the template center location set as and other template positions as \\\\({u_\\\\alpha }=u+{h_\\\\alpha }\\\\left( {\\\\alpha =1,2,...,n} \\\\right)\\\\). As shown in Fig.\\u0026nbsp;1(a), the grid template is composed of 4×4 pixels, determined by the center point and 15 vectors, with each vector represented by a grid point. Figure\\u0026nbsp;1(b) shows the data template for a 2D data event with \\\\(n=4\\\\). Figure\\u0026nbsp;1(c) illustrates the scanning of the training image using the data template in the direction indicated by the arrow to construct the search tree, and Fig.\\u0026nbsp;1(e) depicts the structure of the search tree. Figure\\u0026nbsp;1(d) is a data event related to the data template. It illustrates the process of scanning the training image to obtain a data event.\\u003c/p\\u003e\\n\\u003cp\\u003eIn the simulation, the state value of \\\\(Z(n)\\\\) is determined by the conditional probability distribution function (cpdf)\\\\({\\\\text{d}}\\\\left( u \\\\right){\\\\text{=\\\\{ z(}}{{\\\\text{u}}_\\\\alpha }{\\\\text{)=}}{{\\\\text{s}}_{{k_\\\\alpha }}}{\\\\text{;}}\\\\alpha {\\\\text{=1,2}}...{\\\\text{,n\\\\} }}\\\\) extracted from the training image.\\u003c/p\\u003e\\n\\u003cp\\u003eAccording to Bayes' conditional probability formula:\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\\\(\\\\Pr ob\\\\left\\\\{ {Z(u)={s_k}|d({\\\\text{n}})} \\\\right\\\\}=\\\\frac{{{c_k}\\\\left( {d\\\\left( {\\\\text{n}} \\\\right)} \\\\right)}}{{c\\\\left( {d\\\\left( {\\\\text{n}} \\\\right)} \\\\right)}}\\\\)\\u0026nbsp;\\u003c/p\\u003e\\n\\u003cp\\u003e\\u0026nbsp;\\\\(c\\\\left( {d\\\\left( {\\\\text{n}} \\\\right)} \\\\right)\\\\)\\u0026nbsp; is the repetition count of \\\\(d(n)\\\\)for the data event, \\\\({c_k}\\\\left( {d\\\\left( {\\\\text{n}} \\\\right)} \\\\right)\\\\) is the inferred repetition count from \\\\(c\\\\left( {d\\\\left( {\\\\text{n}} \\\\right)} \\\\right)\\\\) when the central node \\\\(Z(u)\\\\) has the value \\\\(Z(n)\\\\).The probability of occurrence of the conditional data event can be converted to the ratio of the size of the 2D binary image of the effective initial pore \\\\({N_n}\\\\).\\u003c/p\\u003e\\n\\u003cp\\u003eThe main process of the SNESIM (Single Normal Equation Simulation) algorithm is as follows:\\u003c/p\\u003e\\n\\u003cp\\u003e1.Pre-scan Training Images and Build the Search Tree: Assign sample data to the nearest grid nodes and define a random path to traverse all unsampled nodes. Check if the current node is on the simulation grid; if it is, continue; otherwise, move to the next node according to the random path. If the current node is a location with existing data, skip to the next node. Retain information about the positions in the template where n positions have existing data.\\u003c/p\\u003e\\n\\u003cp\\u003e2.Check for Data Positions: Determine if there are any data positions (n' ≠ 0). If not, draw a value from the marginal distribution as the simulation value. Retrieve the number of training data events from the search tree that match the conditional data event, and obtain these events' central values as SK.\\u003c/p\\u003e\\n\\u003cp\\u003e3.Verify Event Count: Check if the number of retrieved data events \\\\(c=\\\\sum {\\\\alpha _k}\\\\)is greater than the minimum value \\\\({c_{\\\\hbox{min} }}\\\\). If not, remove the most distant conditional data and recalculate.\\u003c/p\\u003e\\n\\u003cp\\u003e4.Calculate Local Conditional Probability Density Function: Compute the local conditional probability density function \\\\(p\\\\left( {u;sk(n')} \\\\right)={\\\\raise0.7ex\\\\hbox{${{\\\\alpha _k}}$} \\\\!\\\\mathord{\\\\left/ {\\\\vphantom {{{\\\\alpha _k}} c}}\\\\right.\\\\kern-0pt}\\\\!\\\\lower0.7ex\\\\hbox{$c$}}\\\\) for subsequent simulation value extraction.\\u003c/p\\u003e\\n\\u003cp\\u003e5.Extract and Store Simulation Value: Draw a simulation value from the local conditional probability density function and store it as hard data.\\u003c/p\\u003e\\n\\u003cp\\u003eFigure\\u0026nbsp;2 illustrates the flowchart of the SNESIM algorithm. Figure\\u0026nbsp;3 SNESIM reconstruction algorithm is shown in the figure.\\u003c/p\\u003e\\n\"},{\"header\":\"Application example\",\"content\":\"\\u003cp\\u003eIn this experiment, samples were selected from actual reservoir cores from an oil field. Six core slices with porosities of 6%, 10%, 15%, 21%, 25%, and 38% were extracted from the 3D scanned images of the cores, labeled sequentially as A-F, as shown in the first and third columns of Fig.\\u0026nbsp;4. The second and fourth columns in the figure display the binarized images of the CT scan, where the black parts represent the rock matrix and the white parts indicate the pores.\\u003c/p\\u003e\\u003cp\\u003eFigure 5 shows the reconstructed images of the six samples with porosities of 5%, 10%, 15%, 21%, 25%, and 38%. By comparing the pore structures of the initial training images with those of the reconstructed images, it can be observed that the reconstructed images largely retain the pore structure of the initial training images. Types of pore structures and heterogeneities, such as narrow pores, small pores, and large pores present in the initial images, are also reflected in the reconstructed images.\\u003c/p\\u003e\\u003cp\\u003eFor example, in Fig.\\u0026nbsp;6, samples B and E are illustrated. The bar charts display the frequency of different pore radii in the pore structure, with yellow bars representing the training images and gray bars representing the reconstructed images. It is evident from the images that the pore radii in the two samples are almost identical, and the frequency of occurrence for the same pore size is roughly the same. For instance, in sample E, the heights of the yellow and gray bars for pore radii of 15 µm, 21 µm, and 50 µm are quite similar.\\u003c/p\\u003e\\u003cp\\u003eIn this paper, the \\\"pore-throat ratio\\\" index is used for quantitative analysis of the homogeneity within the pore structure of porous media. Within a local range, the variation between pores and throats changes with the pore-throat ratio; that is, the more pronounced the changes in pore structure at a fine scale, the poorer the homogeneity of the porous media.\\u003c/p\\u003e\\u003cp\\u003eFigure\\u0026nbsp;7 analyzes the reconstruction effects of pore structures at different porosities from the perspective of pore radius distribution.\\u003c/p\\u003e\\u003cp\\u003eFigure\\u0026nbsp;7(a) presents histograms of the average pore diameter distribution for samples with different porosities. The yellow bars represent the average pore diameter of the initial training images, while the gray bars represent the average pore diameter of the reconstructed images. The bar charts show that the average pore diameter of the reconstructed images generated by the algorithm is quite close to that of the initial training images, indicating high consistency between the two in this metric.\\u003c/p\\u003e\\u003cp\\u003eFigure 7(b) shows boxplots of pore diameter distributions for samples with different porosities. The yellow and gray parts represent the initial training images and reconstructed images, respectively. Compared to the initial training images, the reconstructed images have a larger interquartile range (IQR) and wider upper and lower range edges, indicating higher variability in the reconstructed images. The median (average pore diameter) of the reconstructed images is slightly higher or comparable to that of the initial training images, but the difference is minimal. The reconstructed images exhibit more frequent outliers, suggesting some deviation from the initial pore structure. Overall, the reconstructed images and initial training images are quite consistent in terms of median (average pore diameter) and general boxplot trends, demonstrating that the reconstruction algorithm is effective in capturing the average pore diameter. However, the increased variability (wider IQR and more outliers) in the reconstructed images may reflect the introduction of new features during the reconstruction process, indicating increased diversity.\\u003c/p\\u003e\\u003cp\\u003eFigure 8 shows the average pore-throat radius for samples A-F with different porosities. The left side of the figure displays the average pore-throat radius of the initial training images, while the right side shows the boxplots of the average pore-throat radius for the reconstructed pore structures generated by the algorithm.\\u003c/p\\u003e\\u003cp\\u003eEach boxplot illustrates the distribution of the average pore-throat radius for a sample, including the quartiles, minimum, maximum, and outliers. Overall, the data distribution in the reconstructed images (right side) is very close to that in the training images (left side). The median and interquartile range (IQR) of the reconstructed images are roughly consistent with those of the training images, indicating that the average pore-throat radius of the reconstructed images is very close to that of the initial pore structure.\\u003c/p\\u003e\\u003cp\\u003eAlthough there may be a few outliers in some samples, the boxplots of the reconstructed images are almost identical in distribution to those of the training images, demonstrating that the reconstruction method performs well in preserving the pore-throat radius distribution characteristics. Particularly, the consistency in the median and IQR between the reconstructed and training images shows that the reconstruction method is successful in capturing and reproducing the main statistical features of the original data.\\u003c/p\\u003e\\u003cp\\u003eThe pore-throat ratio, which is the ratio of pore diameter to throat diameter, is an important parameter for characterizing pore structure and a crucial microphysical property of reservoir media. A larger pore-throat ratio indicates a larger pore space and wider channels relative to the throats, which can be more favorable for fluid flow.\\u003c/p\\u003e\\u003cp\\u003eFigure\\u0026nbsp;9 displays the pore-throat ratios of the pore structures in different core slices, with blue bars representing the training images and red bars representing the reconstructed images. In most slice samples, the pore-throat ratios of the reconstructed images maintain the same trend as those of the training images, indicating that the reconstruction method effectively reproduces the pore structure features of the training images overall. Notably, in sample C, the pore-throat ratio of the reconstructed image closely matches the pore structure features of the training image.\\u003c/p\\u003e\\u003cp\\u003eIn some samples, such as sample E, the pore-throat ratio in the reconstructed images is significantly higher than in the training images. This discrepancy may be due to the reconstruction method's inability to fully capture the features of complex pore structures, reflecting limitations in detail handling and accuracy. However, overall, the reconstructed images for all six samples follow the same trend as the training images, demonstrating that the reconstruction method has high applicability and reliability.\\u003c/p\\u003e\\u003cp\\u003eThis paper uses the average coordination number to quantitatively assess the connectivity of pore structures in porous media. A higher coordination number indicates better pore connectivity. Figure\\u0026nbsp;10 displays histograms of the average coordination number distribution for core slices corresponding to training images and reconstructed images. In the figure, blue represents the coordination numbers of the pore structures in the initial training images, while red represents the coordination numbers in the reconstructed images.\\u003c/p\\u003e\\u003cp\\u003eFor the six samples, which are from the same core slice, the pore coordination numbers are concentrated in the range of 2–4. For samples with the same porosity, the pore coordination numbers in the reconstructed images are generally consistent with those in the training images. As porosity increases, the average coordination number for the six samples with different porosities gradually decreases. This indicates that, at lower porosities, the connectivity of pores at the microscopic scale is better.\\u003c/p\\u003e\\u003cp\\u003eThe grain size radius of pores is a critical parameter affecting pore structure and directly relates to the fluid flow characteristics of the pores. Pores with larger grain size radii typically provide larger fluid flow channels, while pores with smaller grain size radii present greater flow resistance. Figure\\u0026nbsp;11 shows the average grain size radius for training and reconstructed images under different core slices, with blue representing the training images and red representing the reconstructed images.\\u003c/p\\u003e\\u003cp\\u003eIt is observed that the grain size radius of the reconstructed images is similar to that of the training images for most samples, although some differences exist. In certain samples, the grain size radius in the reconstructed images closely matches that of the training images, indicating that the reconstruction method performs well for these samples and can effectively reproduce the pore structure of the training images. However, in some samples, there are noticeable differences in the grain size radius between the reconstructed images and the training images, which may be due to errors or limitations in the reconstruction algorithm for these samples.\\u003c/p\\u003e\\u003cp\\u003eOverall, the trend of the grain size radius in the reconstructed images is consistent with that of the training images, suggesting that the reconstruction method retains the pore structure characteristics of the training images to a certain extent. For specific samples with significant discrepancies in grain size radius, further optimization of the reconstruction algorithm may be needed to improve accuracy.\\u003c/p\\u003e\\u003cp\\u003ePorosity is a key parameter describing the size and distribution of pore space and has a significant impact on the fluid flow characteristics of pores. Higher porosity typically indicates larger pore space and lower fluid flow resistance, while lower porosity suggests smaller pore space and higher fluid flow resistance.\\u003c/p\\u003e\\u003cp\\u003eFigure\\u0026nbsp;12 shows the porosity of the initial and reconstructed two-dimensional pore images for six core slice samples. Analyzing the porosity of the initial and reconstructed pore images is the most direct way to assess reconstruction quality. The figure reveals that, except for the sample with 6% porosity, which shows a very slight difference in porosity between the initial and reconstructed images, the porosity of the reconstructed images for the other samples is consistent with that of the initial images. This indicates that the reconstruction method performs well for these samples and can effectively reproduce the pore structure of the training images.\\u003c/p\\u003e\\u003cp\\u003eAlthough some samples show slightly higher or lower porosity in the reconstructed images, which could affect the fluid flow characteristics of the pore structure, overall, the reconstruction method demonstrates excellent performance in retaining the initial pore structure.\\u003c/p\\u003e\\u003cp\\u003eThe variance function reflects the spatial variability of the pore structure. Figure\\u0026nbsp;13 compares the differences between the reconstructed and initial images from the x and y directions in two-dimensional images to analyze the reconstruction effects.\\u003c/p\\u003e\\u003cp\\u003eObserving the training images (top left and top right), the variance function for different core slices increases with lag distance, indicating that the pore structure has a certain spatial correlation at larger scales. The trends in the variance function in the x and y directions are generally consistent across different slices, showing similar spatial variability in these directions. For the reconstructed images (bottom left and bottom right), the variance function also increases with lag distance for different core slices, but exhibits some fluctuations at certain lag distances. While the variance function trends in the x and y directions for the reconstructed images show some similarity to the training images, there are differences at larger lag distances.\\u003c/p\\u003e\\u003cp\\u003eComparing the variance functions of the reconstructed and training images, it is evident that there are significant differences in the variance function values at certain lag distances in the reconstructed images compared to the training images. This may be due to the loss of certain detail information during the reconstruction process or limitations in the reconstruction method when dealing with variability at specific scales. However, the overall trend of the variance function across different core slices is consistent between the training and reconstructed images, indicating that the reconstruction method retains the spatial structural features of the training images to some extent.\\u003c/p\\u003e\\u003cp\\u003eIn summary, the reconstruction method performs well in reproducing the spatial variability of the training images at smaller lag distances but may need further improvement at larger lag distances to better capture the spatial correlations of the training images.\\u003c/p\\u003e\\u003cp\\u003eThe pore structure directly affects the permeability characteristics of porous media. Higher permeability indicates more connected pore spaces and smoother fluid flow. By observing the permeability of different samples in the figure, it can be inferred that the reconstructed images have effectively retained the connectivity of the original pore structure in certain samples, resulting in higher permeability.\\u003c/p\\u003e\\u003cp\\u003eFigure\\u0026nbsp;14 displays the permeability distribution for six core slice samples, where blue and red squares represent the permeability data of the training images along the x and y axes, respectively, and yellow and green circles represent the permeability data of the reconstructed images along the x and y axes. In some samples (e.g., samples B and E), the permeability of the reconstructed images is close to that of the training images, indicating that the reconstruction method effectively reproduces the permeability characteristics of the original images for these slices. However, in other samples (e.g., samples C and F), there are some differences in permeability between the reconstructed and training images, which may reflect the limitations of the reconstruction method in certain situations.\\u003c/p\\u003e\\u003cp\\u003eOverall, the reconstruction method performs excellently in preserving the overall connectivity and permeability of the pore structure. However, there may be a need for further optimization and improvement when dealing with complex or highly heterogeneous pore structures.\\u003c/p\\u003e\"},{\"header\":\"Conclusion\",\"content\":\"\\u003cp\\u003eBased on the comprehensive analysis of the experiments, the SNE-SIM algorithm demonstrates high performance in reconstructing pore structures. The analysis of parameters such as porosity, pore-throat ratio, average particle radius, coordination number, and permeability shows that the reconstructed images generally maintain trends similar to those of the training images in most samples. The performance parameters of the reconstructed core slices are largely consistent with those of the initial core slices, indicating that the SNE-SIM algorithm has high applicability and reliability in pore structure reconstruction, effectively reproducing the main pore structure features of the initial training images.\\u003c/p\\u003e \\u003cp\\u003eHowever, since the core slices used in this study are all from the same core, this somewhat limits the comprehensive understanding of pore structures. Further analysis and research are needed to effectively transfer the pore structure from a two-dimensional plane to a three-dimensional pore space and to maximize the restoration of the pore structure. Particularly when dealing with complex pore structures, the accuracy and performance of the reconstruction algorithm require further improvement. Future research should focus on optimizing the algorithm to handle more diverse pore structures and explore three-dimensional reconstruction methods to provide a more comprehensive description and analysis of pore features in actual porous media.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eFunding\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThis work was supported financially by the National Nature Science Foundation of China [grant numbers 51974247].\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAuthor information\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eAuthors and Affiliations\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCollege of Petroleum Engineering, Xi’an Shiyou University. Xi’an 710065, China; MOE Engineering Research Center of Development \\u0026amp; Management of Western Low \\u0026amp; Ultra-Low Permeability Oilfield, Xi’an 710065, China\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eQing Xie\\u0026nbsp;\\u0026amp;\\u0026nbsp;Jiaqi Gao\\u0026nbsp;\\u0026amp;\\u0026nbsp;Jia Li\\u0026nbsp;\\u0026amp;\\u0026nbsp;Yifei Song\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eNO.3 Gas Production Plant of Changqing Oilfield Company, Petro China Xi’an, Shanxi, 710018, China\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eXiaochuang Ye\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCollege of Electronic Engineering,, Xi’an Shiyou University. Xi’an 710065, China\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eSiwen Hu\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eContributions\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eQing Xie, Jiaqi Gao,\\u0026nbsp;Siwen Hu,\\u0026nbsp;and Jia Li were involved in conceptualization of the study. Qing Xie, Jiaqi Gao, Yifei Song, and Xiaochuang Ye were involved in data acquirement and analysis. All authors involved in interpreting the analyses. Qing Xie and Jiaqi Gao wrote the original draft. All authors reviewed and edited the final draft.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCorresponding author\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eCorrespondence to\\u0026nbsp;Qing Xie.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eCompeting interests\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors declare no competing interests.\\u003c/p\\u003e\\u003ch2\\u003eData Availability\\u003c/h2\\u003e\\u003cp\\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eAndr\\u0026auml;, H. et al. Digital Rock Physics Benchmarks\\u0026mdash;Part I: Imaging and Segmentation. \\u003cem\\u003eComput. 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Mater.\\u003c/em\\u003e \\u003cb\\u003e161\\u003c/b\\u003e, 468\\u0026ndash;478 (2018).\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true},\"keywords\":\"coordination number, average grain radius, variogram, digital core, multipoint geostatistics, porous media\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-5021774/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-5021774/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe pore structure of porous media directly affects its permeability characteristics and fluid flow properties, making accurate reconstruction of these structures of great significance. In recent years, multipoint statistics (MPS) methods have been widely used in pore structure modeling. Among them, the SNESIM algorithm, as an advanced MPS technique, has been extensively applied in the study of porous media pore structures. This paper aims to investigate the effectiveness of the SNESIM algorithm in reconstructing pore structures on 2D slices of cores with different porosities taken from the same core. Furthermore, it analyzes the advantages and limitations of the algorithm and its applicable conditions.\\u003c/p\\u003e \\u003cp\\u003eThis study utilizes CT scan images to construct digital core technology and applies the SNESIM algorithm to reconstruct pore structures of core slices with different porosities. By analyzing performance parameters such as porosity, pore throat ratio, average grain radius, coordination number, and permeability, the study found that the reconstructed images in most samples can maintain a trend similar to that of the training images, demonstrating the high applicability and reliability of the SNESIM algorithm in pore structure reconstruction. However, the core slices used in this study were all taken from the same core. Effectively transferring the pore structures from the 2D plane to the 3D pore space and restoring the pore structures to the greatest extent still requires further research. In particular, when dealing with complex pore structures, the accuracy and performance of the SNESIM algorithm need further improvement. Future research will focus on optimizing the algorithm to handle more diverse pore structures and exploring 3D reconstruction methods to more comprehensively describe and analyze the pore characteristics in actual porous media.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Reconstruction of porous media pore structure and analysis of simulation effect based on SNESIM algorithm\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2024-11-18 09:52:10\",\"doi\":\"10.21203/rs.3.rs-5021774/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2024-10-31T06:12:15+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2024-10-22T23:33:09+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2024-10-20T15:07:11+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"57523952611736853521181019530770650260\",\"date\":\"2024-10-10T13:28:09+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"126929652749059253366236360928888054116\",\"date\":\"2024-10-10T11:34:27+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2024-10-10T09:46:27+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2024-09-24T08:00:29+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvited\",\"content\":\"\",\"date\":\"2024-09-18T04:17:40+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2024-09-17T03:49:23+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Scientific Reports\",\"date\":\"2024-09-03T04:11:19+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"3706a0bf-99ea-4f4b-924c-d323220b21a7\",\"owner\":[],\"postedDate\":\"November 18th, 2024\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[{\"id\":39649317,\"name\":\"Physical sciences/Energy science and technology\"},{\"id\":39649318,\"name\":\"Physical sciences/Mathematics and computing\"}],\"tags\":[],\"updatedAt\":\"2025-02-17T15:59:11+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-5021774\",\"link\":\"https://doi.org/10.1038/s41598-025-88730-w\",\"journal\":{\"identity\":\"scientific-reports\",\"isVorOnly\":false,\"title\":\"Scientific Reports\"},\"publishedOn\":\"2025-02-10 15:57:02\",\"publishedOnDateReadable\":\"February 10th, 2025\"},\"versionCreatedAt\":\"2024-11-18 09:52:10\",\"video\":\"\",\"vorDoi\":\"10.1038/s41598-025-88730-w\",\"vorDoiUrl\":\"https://doi.org/10.1038/s41598-025-88730-w\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-5021774\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-5021774\",\"identity\":\"rs-5021774\",\"version\":[\"v1\"]},\"buildId\":\"qtupq5eGEP_6zYnWcrvyt\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}