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Accurately determining rock elastic modulus (EM) and uniaxial compressive strength (UCS) using laboratory methods requires considerable time and cost. Hence, the development of models for estimating the mechanical properties of rock is a very attractive alternative. The current research was conducted to predict the UCS and EM of sandstone rocks using quartz%, feldspar%, fragments%, compressional wave velocity (PW), the Schmidt hardness number (SN), porosity, density, and water absorption via simple regression, multivariate regression (MVR), K-nearest neighbor (KNN), support vector regression (SVR) with a radial basis function, the adaptive neuro-fuzzy inference system (ANFIS) using the Gaussian membership (GM) function, and the back-propagation neural network (BPNN) based on various training algorithms. The samples were categorized as litharenite and feldspathic litharenite. By increasing the feldspar% and quartz% and decreasing the fragments%, the static properties increased. The results of the statistical analysis showed that the SN and porosity have the greatest effect on the UCS and EM, respectively. Among the Levenberg–Marquardt (LM), Bayesian regularization, and Scaled Conjugate Gradient training algorithms using the BPNN method, the LM achieved the best results in forecasting the UCS and EM. The ideal obtained BPNN, using a trial-and-error process, contains four neurons in a hidden layer with eight inputs. All five models attained acceptable accuracy (correlation coefficient greater than 70%) for estimating the static properties. By comparing the methods, the ANFIS showed higher precision than the other methods. The UCS and EM of the samples can be determined with very high accuracy (R2 > 99%). [ABSTRACT FROM AUTHOR]

Digital rock physics is at the forefront of characterizing porous media, leveraging advanced tomographic imaging and numerical simulations to extract key rock properties like permeability. However, fully capturing the heterogeneity of natural rocks necessitates imaging increasingly larger sample volumes, presenting a significant challenge. Direct numerical simulations at these scales become either prohibitively expensive or computationally unfeasible due to limitations in resolution and field of view (FOV). This issue is particularly pronounced in carbonate rocks, known for their complex, multiscale pore structures, which exacerbate the resolution-FOV tradeoff. To address this, we introduce a machine learning strategy that merges multiscale imaging data from various resolutions with a 3D convolutional neural network (CNN) model. This approach is innovative in its ability to identify cross-scale correlations, thereby enabling the estimation of transport properties in larger volumes—properties that are difficult to simulate directly—using trainable proxies. The integration of multiscale imaging with deep learning allows for accurate permeability predictions at scales beyond those feasible with traditional direct simulation methods. By employing transfer learning across different scales during the training phase, our multiscale machine learning model achieves robust performance, with an R² exceeding 0.96 when evaluated on diverse lower-resolution domains with larger FOVs. Notably, this method significantly enhances computational efficiency, reducing the computational time by orders of magnitude. Originally developed for the intricate pore structures of carbonate rocks, our approach shows promise for application to a wide range of multiscale porous media, offering a viable solution to the longstanding tradeoff between imaging resolution and FOV in digital rock physics. [ABSTRACT FROM AUTHOR]