Heterogeneous Rock Research Articles

Size-dependent strength behavior of heterogeneous veined gneiss under uniaxial compression

In this paper, 114 uniaxial compressive strength tests were carried out on specimens of veined gneiss with diameters ranging from 14 mm to 100 mm. The main objective of the study was to investigate the influence of the specimen size on the strength behavior of this metamorphic, heterogeneous rock. This size effect results in an increase in strength from small 14-mm diameter specimens up to 50-mm diameter specimens. Thereafter, a mild decrease in results is observed from 50-mm to 100-mm diameter specimens, in line with traditionally considered size-effect approaches. The findings generally agree with previous studies on size effects in sedimentary and igneous rocks, suggesting that metamorphic rocks may also tend to follow the Unified Size-Effect Law (USEL), accounting for general and reverse size-effects in strength. Nevertheless, some variability observed in the results, mainly attributed to inherent heterogeneity of the studied rock could influence how clearly this ascending-descending trend is captured by the model.

Investigation of Rock-Breaking Mechanisms Based on the Adaptive Matching Method for Drilling Loads

Considering stick–slip vibration and the impact loads formed while drilling in strongly heterogeneous formations or soft–hard interbedded formations, an adaptive matching drilling load method is presented in this paper to form dynamic drilling loads to automatically adjust the applied axial load acting on the drill bit. To determine the rock-breaking mechanisms using this method, the structure of a kind of downhole tool was designed and a discrete element simulation model was established with a PDC cutter cutting heterogeneous rock. The effects of the load factor, the applied initial axial force, and the driven force on the variation in the axial force, as well as the moving displacement of the PDC cutter and the rock-breaking characteristic parameters, were studied. The failure states of the simulated rock have a positive correlation with the number of total cracks generated in the rock-breaking process, as opposed to MSE. The decrease in the reaction force suffered by the PDC cutter in the cutting direction was caused by the automatically adapting load, although there was no significant regularity in the axial direction. MSE decreased obviously under the action of the adaptive matching drilling load method so that the contacting states of the PDC cutter could be improved, thus raising the rate of penetration of the PDC bit. This study provides a feasible method for rapidly drilling in highly heterogeneous formations or soft–hard interbedded formations.

Geochemical-process extraction and interpretation using matrix factorization: a framework for verifying effectiveness through forward modeling and inversion analysis

Matrix factorization techniques, such as principal component analysis (PCA) and independent component analysis (ICA), are widely used to extract geological processes from geochemical data. However, their effectiveness in accurately identifying geological processes remains uncertain due to the heuristic nature of these methods. This study introduces a synthetic data-based framework to evaluate the validity of matrix factorization for geochemical process extraction. By constructing a forward model that simulates geochemical weathering, we generated synthetic datasets replicating real-world geochemical compositions, incorporating both the elemental leaching during fluid-rock interactions and the compositional heterogeneity of the original rocks. These datasets were analyzed using PCA and ICA, with preprocessing steps that included standardization and log-ratio transformation to address the challenges posed by compositional data. The results indicate that PCA and ICA effectively extracted the two key geological processes -elemental leaching and original rock heterogeneity-from the synthetic datasets. Among these methods, ICA combined with log-ratio transformation provided the most accurate separation of independent geochemical processes, particularly under ideal conditions with sufficient samples. To quantitatively validate the extracted basis vectors, we estimated elemental mobility parameters during weathering and compared them with known values in the synthetic dataset, demonstrating the applicability of our approach in quantifying geological processes. This study highlights the advantages of a bilateral approach that integrates forward modeling and inversion analysis to enhance the reliability of geochemical process interpretation. The proposed framework offers a systematic methodology for identifying and quantifying underlying geological processes from high-dimensional geochemical data, with potential applications in geochemistry, environmental science, and resource exploration.

A Data-Driven Approach for Efficient Prediction of Permeability of Porous Rocks by Combining Multiscale Imaging and Machine Learning

Digital rock physics has increasingly become an emerging field in which advanced numerical simulation and high-resolution imaging are combined to accurately predict rock properties. In this context, multiscale imaging is crucial for fully capturing the inherent heterogeneity of natural rocks. However, limitations in resolution and field of view (FOV) present significant challenges. Direct numerical simulations at large scales are often not computationally practical or may be too expensive. The compromise between FOV and resolution is particularly pronounced in the complex multiscale pore structures of porous rocks, including carbonates in particular. To address this issue, we propose an innovative machine learning technique that integrates multiscale imaging data at varying resolutions. For the rock sample, we used the imaging data published by Nabipour et al. (Adv Water Resour 104695, 2024) in three resolutions. Our approach employs an optimized neural network design combined with a transfer learning strategy, enabling the identification of complex cross-scale correlations that were previously unattainable with conventional methods. The results demonstrate that this multiscale neural network approach effectively estimates permeability by analyzing various aspects of pore morphology across different scales. In particular, we achieved high accuracy, as evidenced by R-squared coefficients of 0.966 for training and 0.836 for testing in low-resolution domains, and also significantly enhanced computational efficiency, reducing the overall computational time. Despite being tested for images of carbonate rocks, the developed method is adaptable to a wide range of multiscale porous materials and offers a promising solution to the persistent challenge of balancing imaging resolution with FOV.

Geotechnical challenges in crystalline basement terrain: mapping subsurface conditions with electrical resistivity tomography in Ado-Ekiti, Nigeria

Subsoil investigation constitutes a critical step in the planning and execution of any construction project. It is a prerequisite for the design and construction of safe, stable, and sustainable structures. Subsoil investigation using Electrical Resistivity Tomography (ERT) was carried out in Ado-Ekiti, Nigeria to assess the integrity of foundation soils/near-subsurface geomaterials. The study area is underlain by the crystalline basement terrain of southwestern Nigeria. The study delineated low resistivity zones having as low as 63 Ωm at a depth of about 10 m, localized pockets of clay intercalated by lateritic soil, a stretch of geomaterials of high resistivity values over 10000 Ωm observed at a depth of 6 m, and a structural feature diagnostic of fractured zone with intense weathering at depths stretching beyond 25 m. The presence of an underground water channel within the fractured basement rock is significant. The geological variations along the traverses confirm the heterogeneity of the basement complex rocks, even over short distances. This is crucial for foundation design. A gross assumption of uniformity could be hazardous to the stability of the structure. Geophysics remains a very fundamental tool that can be applied in civil engineering work. Use of integrated geophysical methods would reduce ambiguities and enhance site characterization for construction purposes.

Assessment on the thermal efficiency of deep borehole heat exchangers under rock and soil heterogeneity

Assessment on the thermal efficiency of deep borehole heat exchangers under rock and soil heterogeneity

Research on Nuclear Magnetic Resonance Displacement Experiment on Gas–Water Mutual Drive Based on Rock Physical Property Differences

This study addresses the impact of rock physical property differences on the displacement efficiency during the multi-cycle gas–water mutual drive process in water-driven gas storage reservoirs. Utilizing multi-cycle gas–water displacement core experiments and high-pressure nuclear magnetic resonance (NMR) technology, we systematically investigate the relationship between rock physical properties and gas–water flow dynamics. By measuring and dynamically monitoring changes in gas–water distribution within the core, we focus on the effects of differences in permeability, porosity, and pore structure on the non-uniformity and displacement efficiency during the gas–water mutual drive process. The results demonstrate that rock heterogeneity significantly reduces the displacement efficiency, particularly in low-permeability layers where pore structure heterogeneity exacerbates the uneven flow of gas and water, leading to a notable decline in displacement efficiency. Moreover, the impact of micropore structure on displacement efficiency has also been validated. These findings provide important experimental data and theoretical foundations for evaluating and demonstrating the gas–water mutual drive efficiency in water-driven gas storage reservoirs, which is crucial for enhancing gas storage recovery and long-term stability.

Effect of confining pressure on the mechanical properties of heterogeneous rocks under cyclic loading

To investigate the influence of mesoscopic heterogeneity and confining pressure on the mechanical properties of granite under cyclic loading, a series of biaxial compression tests were conducted on granite samples with different mineral crystal size distributions using Particle Flow Code (PFC) software. A grain-based model was established to explore the effects of crystal size distribution-induced mesoscopic heterogeneity, confining pressure, and cyclic loading on rock mechanics parameters. The mesoscopic damage mechanism was analyzed from a microscopic perspective. The results showed that confining pressure and heterogeneity significantly affected the mechanical behavior and damage mechanisms of rock samples under both compressive and cyclic loading. As confining pressure increased, the peak strength, elastic modulus, and strain of the rock gradually increased, but the growth rate slowed down, mainly due to the micro-crack closure and compaction effects induced by the confining pressure. The increase in heterogeneity led to a gradual decrease in the peak stress and elastic modulus of the rock, and the influence of heterogeneity on these mechanical parameters weakened as confining pressure increased. The number of micro-cracks in the rock passed through three stages: slow growth, lag growth, and accelerated growth. Under high confining pressure, the failure mode of the rock tended to be ductile, accompanied by plastic deformation and crack closure, while heterogeneity accelerated crack propagation. The mechanical properties of granite were significantly affected by its mineral composition and hardness differences. The existence of a hardness gradient intensified local crack propagation and affected the overall mechanical behavior and damage evolution of granite.

Homogeneity Equation for the Effective Elastic Properties of Heterogenous Rocks Developed From Machine Learning

AbstractThis study develops an artificial neural network (ANN) model designed to estimate the effective elastic properties of heterogeneous rocks with inclusions. The ANN addresses the limitations of traditional effective medium models by avoiding theoretical assumptions, such as low inclusion percentages, and it incorporates the effects of inclusion length, spacing and orientation. This approach enables the accurate calculation of an equation that links dimensionless geometrical and physical features of rocks to their equivalent Young's modulus and Poisson's ratio. A two‐dimensional finite element model is employed to calculate, through dynamic loading, the effective Young's modulus and Poisson's ratio of an elastic matrix with properties comparable to sandstones and shales that has ellipsoidal inclusions representing cracks. While this study focuses on a single matrix and inclusion type, the results demonstrate that the method can be extended to any combination of matrix and inclusion elastic properties. The numerical model is validated against experimental and analytical solutions for simple geometries and then used to generate the training data, with inputs including crack length, crack density, aspect ratio, and distances between cracks. The ANN, though dependent on the numerical model for training and testing, operates much faster and can be applied to a broader range of scenarios. By training a single‐layer neural network, an accurate homogeneity equation is derived, relating effective elastic properties to dimensionless inclusion parameters. This approach to obtain a homogeneity equation has applications in rock mechanics, geophysics, and composite materials.

Characterizing heterogeneous rocks in 3D with a multimodal deep learning approach – Implications for transport simulations

Characterizing heterogeneous rocks in 3D with a multimodal deep learning approach – Implications for transport simulations

On Dislocation Modeling of Megathrust Tsunami Sources

AbstractModeling tsunamis due to subduction earthquakes for scientific research and hazard assessment requires accurate quantification of coseismic seafloor deformation. Although the widely used analytical model of shear dislocation in a uniform elastic half space can accommodate complex fault geometry and slip distribution, it fails to capture the sloping seafloor topography and heterogeneous rock rigidity (shear modulus) in real subduction zones. In practice, these real‐world complexities are either ignored or addressed by adjusting fault geometry and/or applying corrections to the deformation results, with consequences poorly understood. This study investigates the validity or errors of these simplifications by comparing dislocation model results with those from finite element models that account for these complexities. Our analysis reveals that the absence of the seafloor slope can be accurately compensated by adjusting the shallow geometry of the megathrust such that the fault depth below the flat model surface approximates the actual fault depth below the seafloor. Effects of short‐wavelength bathymetry can be effectively incorporated by adding a commonly used gradient‐based correction. For slip‐to‐trench ruptures, it is crucial to adjust fault geometry to ensure that the fault reaches the model surface at the trench; otherwise, the abrupt slip termination at a small depth creates an uplift spike which is a commonly seen artifact in tsunami source models. Our findings highlight the secondary or minimal effects of heterogeneous rigidity on tsunamigenic deformation if fault slip is kinematically assigned. This research offers guidance for the development of more accurate tsunami source models using analytical dislocation solution.

Pre-Jurassic seismogeological complexes typification in the South-east of Western Siberia

Relevance. The heterogeneity of the lithological composition (alternation of carbonate, effusive, clay-siliceous and other rocks), steep angles of strata incidence, the neighborhood of ancient rocks with much younger rocks, tectonic activity evidences and metamorphosis processes make it difficult to predict the objects of the Pre-Jurassic depositional complex that are promising from the point of view of the presence of hydrocarbons. Object. Seismic wavefield of the Pre-Jurassic complex of deposits in the southeastern part of the West Siberian oil and gas province (Tomsk and Novosibirsk regions). Aim. Carrying out a morphological description followed by systematization of images of the seismic wave field of lithologically heterogeneous rocks of the Pre-Jurassic complex. Methods. The study of the seismic wave field behavior in various geological formations of the Pre-Jurassic depositional complex. Seismic stratigraphy and seismic formation analysis of time seismic sections. Generalization and systematization of accumulated data. Classification of various typical objects of the Pre-Jurassic complex according to the wave pattern. Results and conclusions. The author has typified the main seismogeological complexes of the Pre-Jurassic deposits of the south-east of Western Siberia (Tomsk and Novosibirsk regions). The considered criteria of seismogeological typification are recommended for assessing and zoning the seismic wave field of Paleozoic objects according to their degree of prospects. The limestones overlain by weathering crust, as well as monocline and submerged blocks of organogenic limestones and dolomites stand out most vividly on the seismic record. The protrusions of igneous rocks are least energetically pronounced. An additional seismogeological class of regular recording was identified. It is characterized by the deflection of the central part of blocks of horizontally layered rocks. This may be characteristic of clustic deposits (volcanogenic sedimentary formations of the Triassic), which may be unpromising in the deposits of the Pre-Jurassic complex in the territory under consideration. The aithor proposed the approaches for further development of the study.

Investigation of the Effects of Rock Components for Different Pyroclastic Rocks on Leeb Hardness

The aim of this study is to research the effect of rock components on Leeb hardness (HL), a non-destructive test commonly used in recent periods. With this aim, cube samples of two different pyroclastic rocks containing dominantly pumice (P) or volcanic rock fragments (VRF) were prepared. Later, the proportions of different components (P and VRF) on the surfaces of the cube samples were determined using the Image Pro Plus 6.0 image processing program. The effect of the variation in these components on HL values was researched with simple regression analysis and strong correlation coefficients were found between these values. According to the data obtained, the HL test was identified not to be suitable for heterogeneous rocks comprising different components.

Nanoindentation-Based Random Field Model for Fracture of Heterogeneous Rock

Nanoindentation-Based Random Field Model for Fracture of Heterogeneous Rock

Experimental Techniques and Rock Physics Modeling to Study the Effects of Mineral Content and Thermal Maturation on Elastic Properties of the Organic-Rich Shale: Case Study of the Longmaxi Formation

Summary To evaluate favorable fracturing locations and layers of shale gas reservoirs, it is essential to comprehend how thermal maturity and mineral composition affect geomechanical characteristics. The effects of kerogen thermal maturation on elastic properties of organic-rich shale under consideration of the vitrinite reflectance and how it relates to kerogen density and organic porosity demand in-depth investigation. We propose rock physics modeling of heterogeneous shale rock samples to model kerogen as a function of thermal maturity and elastic properties as a function of shale composition. Nine Longmaxi shale samples from different depths of Well A were collected and tested by using X-ray diffraction (XRD), light microscope, open system pyrolysis gas chromatography, nanoindentation, and uniaxial-triaxial compression techniques to examine mineralogy, geochemical, and geomechanical characteristics. Using the Voigt-Reuss-Hill average and differential effective medium approach, shale matrix was modeled first and incorporated kerogen matter in terms of incremental thermal maturation. The acoustic characteristics of Longmaxi laminated shale affected by the thermal maturation were also studied using the Hudson model. The results indicate that the Longmaxi shale is part of highly brittle hard rocks; more brittle minerals increase their strength. As clay minerals increase, we observe that at 10-MPa confining pressure, triaxial compression strength (TCS) decreases from 72 MPa to 43 MPa in the Longmaxi upper member sample (SUM), 63 MPa to 39 MPa in the Longmaxi middle member sample (SMM), and 55 MPa to 36 MPa in the Longmaxi lower member sample (SLM). However, with the rise of the quartz + carbonate + feldspar mineral group, we observe an increase in TCS, which goes from 58 MPa to 75 MPa in the SUM, 52 MPa to 68 MPa in the SMM, and 48 MPa to 66 MPa in the SLM. Research indicates that the effective modulus and P-wave velocity of Longmaxi shale falls with increasing of Ro from 0 to 3. In the SUM, Young’s modulus decreased from 11.4 GPa to 1.3 GPa. SMM shows a reduction of Young’s modulus from 11.1 GPa to 0.5 GPa, while SLM shows a decrease from 10.9 GPa to 1.14 GPa. Also, the Vp falls from 5.63 km/s to 4.2 km/s, while the Vs decreases from 3.4 km/s to 2.16 km/s in the SUM. However, in the SMM, Vp decreases from 5.58 km/s to 4.22 km/s, and Vs falls from 2.9 km/s to 1.7 km/s, while Vp and Vs are reduced in the SLM. The results of our modeling approach are confirmed by the variation of elastic properties measured in the laboratory and interpreted in well logs, which show a satisfying validity and usefulness. However, given the extreme variety of reservoir characteristics and basin evolution conditions, we also recommend that it be locally calibrated when applied to particular shale reservoirs.

Enhanced Oil Recovery in Heterogeneous Carbonate Rocks Using a Gemini Surfactant under Harsh Conditions

Enhanced Oil Recovery in Heterogeneous Carbonate Rocks Using a Gemini Surfactant under Harsh Conditions

Carbonate Rocks Grouping Using Critical Porosity Approach in Miocene Rocks, Banggai Basin

Abstract Reservoir is the trapped location of hydrocarbons with diverse physical rock properties or high heterogeneity. The characteristics of rock heterogeneity significantly influence the rock’s ability to flow fluids, especially hydrocarbons contained within the reservoir rock. Several methods have been developed to classify the heterogeneity of reservoir rocks, such as the Amaful, Wibowo and Permadi methods, among others. These methods are developed based on experiments using sandstone rocks, although in some studies, they are also frequently employed in categorizing carbonate reservoir rocks. However, these commonly used methods still face challenges in rock classification when actual rock samples are unavailable. In this study, the classification of carbonate reservoir rocks is conducted using a critical porosity approach compared to the classification using the Wibowo and Permadi methods, as well as the hydraulic flow unit method employed in previous research. The data utilized in this study consists of experimental 43 rock samples from the Miocene era of the Banggai Basin. The analysis results reveal that using the Wibowo and Permadi method, 10 rock classifications are obtained, whereas employing the critical porosity approach results in 6 rock groups. Both methods demonstrate a correlation between rock pore structure and rock geometry, where rocks categorized under RT-10 in the Wibowo and Permadi method and RT-6 in the critical porosity method exhibit the smallest pore geometry values compared to other rock groups. Each rock classification signifies the rock’s fluid flow capability, with rocks categorized under RT-1 indicating better fluid flow capability as they possess finer geometries.

On the dynamic response of a layered heterogeneous rough irregular double porous composite rock structure due to a moving line load

On the dynamic response of a layered heterogeneous rough irregular double porous composite rock structure due to a moving line load

Analysis of Surrounding Rock Stability Based on Refined Geological and Mechanical Parameter Modeling—A Case Study

Metallic ore deposits are generally formed through magmatic intrusions, followed by metamorphism. The geological structures in such regions are often complex, with mechanical parameters exhibiting significant variability. These characteristics dictate the need for refined geological modeling and heterogeneous mechanical parameters for rock mass stability analysis to ensure reliability. Therefore, this paper proposes a novel method for rock mass stability analysis. The method fully leverages high-density drilling data from the mine and introduces an intelligent rock quality designation (RQD) identification technique, facilitating characterization of the spatial heterogeneity of rock mass RQD. Building on this, laboratory experiment data and in situ measurements are integrated, and the Hoek–Brown criterion is employed to achieve a refined characterization of heterogeneous rock mass mechanical parameters. This method allows for a realistic inversion of in situ rock mass mechanical conditions, overcoming the limitations inherent in assigning uniform parameters. Finally, the computed rock mass mechanical parameters are assigned to the refined computational model to conduct rock mass stability analysis. Taking the Jiangfeng Iron Mine, with its complex geological conditions, as an example, this method enables the accurate evaluation of the rock mass stability, determines the feasibility of joint mining, and calculates the appropriate thickness of the isolation pillars, effectively mitigating safety risks in mining operations. This method provides a valuable reference for the rock mass stability analysis of underground joint mining operations for similar mines.

Practical Applications of Space-Time Fractional Diffusion in Naturally Fractured Reservoirs

Summary This study introduces a radial space-time fractional-diffusion (ST-FD) model, now adapted for Laplace space. This model incorporates dual-porosity factors and, when applied to well tests in naturally fractured reservoirs, addresses the effects of rock heterogeneity in fractured or fissured formations by solving a multi-index ST-FD equation through the Laplace transformation. For the first time, pressure distributions in cylindrical coordinates for heterogeneous fractured rocks with space- and time-dependent properties are presented. These findings are novel and unreported in existing literature, highlighting the utility of this approach in analyzing fractured reservoirs. The method developed in this paper was applied to five example well tests from fractured carbonate fields in northern Iraq, demonstrating the practical application of this methodology. Two key models commonly used in the industry to study naturally fractured reservoirs are the Warren and Root (1963) dual-porosity model and de Swaan (1976) model. The Warren and Root model assumes a pseudosteady-state flow between the matrix and fractures, while de Swaan’s model addresses transient flow between these components. When applied to pressure buildup (BU) responses in fractured reservoirs from northern Iraq that exhibit a power-law pattern, these traditional models could lead to misinterpretations, attributing the behavior to boundary effects such as faults. In contrast, using the continuous time random walk framework, specifically the ST-FD model developed by Raghavan and Chen (2021 and 2023), and now modified in this paper with solutions in Laplace space, provides a more accurate interpretation of these pressure responses. The analysis of real-world data using this modified ST-FD model reveals that the power-law behavior in pressure BU responses is linked to the reservoir’s complex heterogeneity as shown in five example well tests presented here. The effectiveness of the modified ST-FD model in Laplace space is validated, offering practical insights for well testing and accurate evaluations of reservoir recovery potential. Although the system is intricate at a fine scale, the results are applicable in the conventional sense at the Theis (1935) scale. Long-range connectivity and distorted flow paths that result in pauses, flow reversals, and related phenomena are quantified through three exponents and fractional derivatives. The findings highlight the influence of diverse heterogeneity indexes and introduce an effective workflow for interpretation and reservoir assessment. These insights significantly enhance comprehension of the reservoir’s complex heterogeneity, leading to better estimations of ultimate recovery.