Rock Elastic Modulus Research Articles

Experimental Study on Mechanical Properties of Freeze-Thaw Damaged Red Sandstone under Combined Dynamic and Static Loading

Using the freeze-thaw cycle test chamber, the red sandstone samples are subjected to cyclic freeze-thaw tests. The physical properties, static mechanical properties of freeze-thaw damage rocks, and the compressional wave velocity at specific axial pressure are measured using conventional physical tests and uniaxial compression tests. The mechanical properties of freeze-thaw damage rocks under dynamic and static loading were studied using Hopkinson pressure bar which can exert axial pressure. The studies show that, with the increase of freeze-thaw cycles, the surface layer of the rock sample undergoes spalling phenomenon, the weight gradually decreases, the sample compactness becomes worse, there are microcracks between the cemented particles, and the compressive strength and elastic modulus decrease. Under the static loading, the longitudinal wave velocity of freeze-thaw damaged samples change significantly compared with that of samples without freeze-thaw. The freeze-thaw damage degree, axial pressure, and strain rate are coupled with each other, which together affect the dynamic mechanical properties of samples, and make the variation of mechanical parameters, such as dynamic peak strength and dynamic elastic modulus of rock. The combined action of freeze-thaw damage and axial pressure weakens the strain rate effect of samples, but when the incident wave of SHPB test is same, the dynamic strength and elastic modulus of freeze-thaw damaged samples are reduced compared with those without freeze-thaw. Combining with strain equivalence principle, the constitutive relation of freeze-thaw damage of red sandstone under dynamic and static combined loading can reflect the influence of coupling damage of axial pressure and freeze-thaw, dynamic impact parameters, and other factors, which are in good agreement with the test results.

Influence of rock heterogeneity on hydraulic fracturing: A parametric study using the combined finite-discrete element method

Hydraulic fracturing has proven to be an efficient technique to enhance production in unconventional reservoirs. Since heterogeneity is commonplace in reservoir rocks, it is vital to investigate the influence of rock heterogeneity on hydraulic fracture propagation. Here, based on the combined finite-discrete element method (FDEM) and cohesive zone model, two series of numerical models with uniformly distributed and Weibull-distributed elastic modulus of rock are assembled, respectively. The comparison with the theoretical solution demonstrates the reliability of the simulation models in both the toughness-dominated regime (TDR) and viscosity-dominated regime (VDR). The parameter analysis demonstrates the rationality of parameters for cohesive elements. The results show that the previous theoretical equations can be used as a preliminary evaluation of simulation parameters. The effects of different parameters such as element size, Weibull distribution type, and far-field stress on hydraulic fracture length, fluid pressure, maximum fracture aperture, and the final fracture morphology are evaluated. The results demonstrate that the distribution type of rock elastic modulus has a significant impact on the hydraulic fracture propagation in both TDR and VDR. The “jump” phenomena have been observed in TDR caused by high fracture toughness. The displacement of fracture location and asymmetrically dynamic propagation are affected by the distribution of rock elastic modulus. Besides, the hydraulic fracture propagation in TDR is more susceptible to element size, the distribution of rock elastic modulus, and far-field stress than that in VDR. This research may shed light on the development of hydraulic fracturing technology in tight reservoirs.

Effect of Spatial Variability of the Elastic Modulus in Composite Ground on the Structural Performance of Large-diameter Tunnels

The spatial variability of soil properties is often neglected in design and construction, resulting in underestimating or overestimating the tunnel structural performance. Furthermore, the risks of ignoring the spatial variability of ground properties increase significantly as the tunnel diameter increases. This study investigates the effects of ground spatial variability on the convergence of shield tunnels in the composite ground, based on a real case of a cross-sea tunnel typically embedded in a ground mixture of soft clay and hard rock in Shenzhen, China. The influence of scale of fluctuation (SOF) for the soil and rock elastic modulus on tunnel convergence is investigated. It is found that the mean value of the tunnel convergence is less affected. In contrast, the tunnel convergence coefficient of variation is strongly affected by changing the elastic modulus SOF of the soil or rock layer. Moreover, the results indicate that as the elastic modulus follows the lognormal distribution, the vertical and horizontal convergence of the tunnel agrees well with the lognormal distribution.

Closure behaviour of dislocated rock fractures subject to cyclic normal loadings

Understanding the closure behaviour of rock fractures is of great importance for various rock mechanics and rock engineering issues such as geothermal energy extraction, carbon dioxide capture and sequestration, and geological disposal of radioactive waste. The stress acting on a single bridging asperity results in the surface deformation of itself and the surrounding areas. The aggregate of such deformations exerted by all contacting asperities leads to the total deformation of a fracture. Therefore, the deformation behaviour of a stressed fracture is governed by the mechanical properties of the intact rock (elastic modulus and strength) and the geometrical characteristics of asperities (spatial distribution and local shapes). A contacting asperity may fail when the local stresses have reached some failure criterions, which is responsible to the hysteresis observed in cyclic loading experiments.In the present study, a high-precision contact model that used Boussinesq’s solution to relate contact stresses to surface displacements in two half-spaces was employed to calculate the deformation of rock fractures subject to normal loading-unloading cycles. The normal stress-displacement curves of cyclic loading experiment are in good agreement with the calculation results, and the measured surface damage area fits well the calculated plastic area, which efficiently verifies the validity of the numerical calculation model. An extended parametric study that considered more patterns of dislocation degree was implemented and the numerical calculation results show that the normal stress-displacement curves of different loading cycles show obvious hysterical behaviour. The hysteresis indicated that damages happened on partial contacting asperities, which tended to enhance the closure of a fracture. The hysteresis generated by a loading cycle is typically less than the previous one, showing a gradual weakening trend. More specifically, the damage of the contacted asperities accumulates successively with the increase of loading cycles, and the damage tends to cease after several cycles. The damage-induced permanent change of surface geometry varies the mechanical behaviour of fractures. As the number of loading cycle increases, the normal stiffness of the rock fracture also tends to increase, and eventually approaches a stable value after 4∼5 loading cycles. The numerical calculation provides quantitative estimations on the deformation and asperity damages, which are direct evidence for the hysteretic behaviour of rock fractures subject to cyclic loadings.

The Study on Shale Wellbore Stability with Coupled Mechanical–Chemical Processes in Wushi Oilfield

Wellbore instability (WI) is a challenge in the drilling process, which often causes complex accidents. Measures should be taken to prevent WI in low-strength formation. It is crucial in wellbore engineering to ensure wellbore stability. In fact, WI was solved with large sources of lost time and trouble cost. However, at present, the mechanism of the instability of the shale borehole wall is unclear. To study the shale WI in Wushi Oilfield, the rock mechanics parameters of rocks were tested according to the actual situation of the oilfield. Experimental results were helpful to determine parameters for numerical simulation. A mechanical–chemical coupling model of shale wellbore was established. The numerical simulation results indicated that there was stress concentration around the wellbore wall. The effects of rock elastic modulus, cohesive force, deviation angle, azimuth, drilling fluid density, and hydration time on the stability of the shale borehole were analyzed. The numerical simulation results could provide a reference for on-site drilling optimization.

Determination of Horizontal In-Situ Stress Profiles and Rock Deformation Moduli in Karamay Basin Using a Multiobjective Optimization Technique

Summary We introduce a quick and cost-effective method of estimating horizontal in-situ stress profiles and rock elastic moduli vs. depth from geophysical logs taken in vertical well sections. A multiobjective optimization approach finds the optimum solution for the inversion of in-situ stresses and the rock mechanical parameters from elastic borehole deformations measured by the commonly available four-arm caliper tools. The four-arm caliper log responses also permit quality control (QC) of input and identification and classification of borehole sections that display breakouts and sloughing. The method is applied in the estimation of horizontal in-situ stress profiles and rock deformation moduli vs. depth in Karamay Basin, Northwestern China. The results have demonstrated good agreement with available field in-situ stress measurements, indicating promising broader applications of the method.

Evaluation of the Diametrical Core Deformation and Discing Analyses for In-Situ Stress Estimation and Application to the 4.9\xa0km Deep Rock Core from the Basel Geothermal Borehole, Switzerland

The in situ state of rock mass stresses is a key design parameter, e.g., for deep engineered geothermal systems. However, knowledge of the stress state at great depths is sparse mostly because of the lack of possible in situ tests in deep boreholes. Among different options, core-based in situ stress estimation may provide valuable stress information though core-based techniques have not yet become a standard. In this study we focus on the Diametrical Core Deformation Analysis (DCDA) technique using monzogranitic to monzonitic rock drill cores from 4.9 km depth of the Basel-1 borehole in Switzerland. With DCDA the maximum and minimum horizontal stress (SHmax and Shmin) directions, and the horizontal differential stress magnitudes (∆S) can be estimated from rock cores extracted from vertical boreholes. Our study has three goals: first, to assess photogrammetric core scanning to conduct DCDA; second, to compare DCDA results with borehole breakout and stress-induced core discing fracture (CDF) data sets; and third, to investigate the impact of rock elastic anisotropy on ∆S. Our study reveals that photogrammetric scanning can be used to extract reliable core diametrical data and CDF traces. Locally aligned core pieces showed similar SHmax orientations, conform to borehole breakout results. However, the variability of core diametrical differences was large for the Basel-1 core pieces, which leads to a large spread of ∆S. Finally, we demonstrate that core elastic anisotropy must be considered, requiring robust estimates of rock elastic moduli, to receive valuable stress information from DCDA analyses.

Petroleum rock mechanics: An area worthy of focus in geo-energy research

Petroleum rock mechanics: An area worthy of focus in geo-energy research

Effect of high temperature and strain rate on the elastic modulus of rocks: a review

Effect of high temperature and strain rate on the elastic modulus of rocks: a review

Numerical simulation of stress field distribution before re-fracturing treatment

Due to the first fracturing failure at the middle and final stages of oil and gas field development, re-fracturing technology has become a key method to increase production in oilfield. So, stress field distribution should be the key successful factor to impact re-fracturing technology after the initial fracturing in reservoir. In order to accurately describe the initial stress field distribution of reservoir after fracturing and provide theoretical basis for subsequent re-fracturing, this paper with theory of rock fracture mechanics and fluid-solid coupling equation had built several ABAQUS numerical model of hydraulic fracturing according to the basic theory of XFEM, to analyses the stress influence by horizontal stress difference, rock elastic modulus, Poisson’s ratio and production time before re-fracturing. Numerical simulation results show that due to the initial crack and the change of pore pressure in the process of production, the direction and size of the original stress field change a lot, which lead a stress field redirection; Reservoir and rock physical mechanical parameters bring a significantly change of reservoir stress field distribution; with the difference of horizontal stress, rock elastic modulus and oil field production time increasing, induced stress effect and stress redirection area decrease; the greater of Poisson’s ratio, the induced stress effect and redirection area is smaller.

Study on Stress-Dependent Permeability of Fracture Networks in Fractured Porous Media

In order to investigate the stress-sensitive characteristics of fracture networks under reservoir actual stress condition and its influence on the seepage in fractured porous media, we carried out permeability tests on experimental models with fracture networks under constant-volume boundary condition. In addition, a novel analytical stress-dependent permeability model of fracture networks in different directions was derived. Based on the test results and the proposed analytical model, the effects of various parameters (e.g., initial fracture aperture, fluid pressure, rock elastic modulus, effective-stress coefficient, and fracture dip) on deformation characteristics of fracture networks and the corresponding permeability tensor of fracture networks were studied. The research results show that, for a fractured porous media with a single group of fractures, the principal value of permeability is always parallel to the fracture-development direction. With increasing effective stress, the principal value of permeability decreases; however, the principal value direction remains unchanged. Moreover, for the fractured porous media with multiple sets of fractures, the principal direction of equivalent permeability will be inclined to the fractures with larger fracture aperture. Specifically, for the fractured porous media with two sets of intersecting fractures, the principal direction of equivalent permeability is parallel to the angular bisector of these two sets of intersecting fractures. Furthermore, the greater the difference of the fracture aperture change rate under effective stress, the more obvious the deviation of the permeability principal direction. The derived analytical model is of great theoretical and scientific significance to deepen the understanding of the stress-sensitive permeability of fractured reservoirs.

Statistical models for estimating the uniaxial compressive strength and elastic modulus of rocks from different hardness test methods

In engineering projects (dams, tunnels, slope stability) the strength characteristics of the rocks affect the construction operations. It is sometimes difficult, time-consuming, and expensive to evaluate the engineering properties of solid rocks by performing direct tests. For this reason, various laboratory studies have been carried out by many researchers to predict important engineering properties such as uniaxial compressive strength (UCS) and elastic modulus (E) of rocks in a practical way. One of the engineering properties used to estimate UCS-E practically is the hardness of rocks. Hardness tests are easy to apply and non-destructive, and in many of these tests very small specimens are needed. The main objective of this study is to analyze the relations between the UCS-E of the rocks and the various hardness methods (Schmidt hammer hardness, SHH; Shore Scleroscope hardness, SSH; Vickers hardness, HV; Brinell hardness, HB; and Indentation hardness index, IHI). For this purpose, the most appropriate and meaningful relations between hardness tests and UCS-E were determined by simple regression (SR) techniques. Relationships between main engineering properties (UCS, E) and physicomechanical properties were analyzed by multiple regression (MR) techniques using SPSS software. The statistical analyses made revealed the existence of strong correlations between UCS-E and hardness properties of rocks.

The impact of geomechanical units (GMUs) classification on reducing the uncertainty of wellbore stability analysis and safe mud window design

The current study proposed an improved approach for application of Geomechanical Units (GMUs) classification in reducing the uncertainty of wellbore stability models. For this purpose, the optimal drilling direction and safe mud window were modeled in the Iranian Offshore oilfield, Persian Gulf basin. Two main normal faults created a graben with three geomechanical sectors in the study area including northern, middle and southern sectors. The middle sector, which is under high compression, is the main target of this study. A set of well logs and Fullbore Formation Micro Imager (FMI) data associated with the rock mechanical tests including Uniaxial Compressive Strength (UCS), Triaxial Compressive Strength (TCS) and ultrasonic results were used to establish and tune the geomechanical models. The dynamic rock elastic moduli including UCS, Poisson's ratio, Young's modulus, shear modulus and bulk modulus were estimated from well logs data. Through appropriate correlations between well logs and laboratory results, the dynamic modules were converted to static data. Five geomechanical units were obtained based on the classification of rock elastic moduli by using multi-resolution graph-based clustering.The interpretation of FMI logs and their incorporation in the geomechanical models showed that most safe drilling direction is in the 120° azimuth which is parallel to the direction of minimum horizontal stress, σh (NW-SE direction). Higher mud weight is expected at N030E azimuth to overcome collapse pressure, which is the worst drilling direction, σH (NE-SW direction). Wellbore inclination more than 60° angle is not recommended for formations comprising of GMU E and partially GMU D (mainly shales and clayey limestones). The results of this study showed that GMUs classification is an effective way of updating the wellbore stability models and reducing the uncertainty of safe mud window design.

Prediction of rock elastic moduli based on a micromechanical finite element model

We present a finite element simulation approach to compute rock elastic moduli that is based on a grain-grain contact methodology, moving away from the common approach of modeling the solid framework as a whole, thus, the individual grains are not distinguished. In this approach we are able to address the grain-grain contact problem associated with the different degrees of consolidation found in reservoir rocks. Three important elements in this workflow are, a robust grain-grain segmentation method, a conformal meshing algorithm, and the grain-grain contact physics. We present benchmark results in four cases from literature and compare with laboratory and other results from elastic solvers that do not model explicitly grain-grain contacts. Finally, we discuss options to estimate and model the strength of the contacts, relating to the degree of consolidation of the rocks.

Determination of Shape Coefficient in Elastic Modulus Estimation with Penetration Test

Elastic modulus is a significant parameter in design and construction for rock engineering. Rock penetration test as a convenient method to evaluate the modulus of rocks has a great potential to be used. Based on the elastic theory, the relationship between rock penetration behavior and elastic modulus was established. In order to evaluate the elastic modulus, the shape coefficient is an important parameter to be determined. However, due to many factors, the value of this parameter is still uncertain. To provide a better insight into the shape coefficient and its factors, a series of penetration tests which used several types of rock samples with different sizes were conducted to study the determination of shape coefficient under different conditions. The test results show that sample size influences the shape coefficient, and with the increase in size, the shape coefficient decreases gradually to a stable value. In contrast, confining pressure has less effect on shape coefficient, and in the moderate and low stresses region, a fixed value can be selected for the test. Different types of rocks correspond to different shape coefficients. The shape coefficient of hard rock is higher than that of soft rock. Shape coefficient should be selected reasonably according to the penetration depth in practical application, and the reason, furthermore, why back-calculated shape coefficient deviates from the theoretical value is also discussed.

Theoretical Analysis of Proppant Embedment and Fracture Conductivity in Fractured Reservoir

Proppant embedment mainly accounts for diminishing fracture aperture and conductivity. The conductivity decrease could greatly restrict fluid flow, thereby affecting the well performance. In this paper, new mathematical models are derived to calculate the proppant embedment and fracture conductivity after hydraulic fracturing. These models take three crucial factors into consideration, including proppant instantaneous elastic deformation, the conductivity change over time, and effective fracture geometry and corresponding proppants amount. Fitting correction is performed for the new theoretical model based on the experimental data. The results show that the theoretical model proposed matches well with the experimental data. The fracture conductivity is in proportion to proppant viscosity, elastic modulus of proppant and in inverse proportion to closure pressure, while elastic modulus of rock and large value of formation rock viscosity have slight impact on fracture conductivity. Moreover, with the increase of proppant viscosity, it takes longer for the conductivity to come to the steady state. These new mathematical models can provide some insights for proppant size selection and sand ratio optimization of fracturing treatment, and it is also a good method to predict the proppant embedment and the fracture conductivity.

Estimation of tensile strength and moduli of a tension compression bi modular rock

The Brazilian test has been widely used to determine the indirect tensile strength of rock, concrete and other brittle materials. The basic assumption for the calculation formula of Brazilian tensile strength is that the elastic moduli of rock are the same both in tension and compression. However, the fact is that the elastic moduli in tension and compression of most rocks are different. Thus, the formula of Brazilian tensile strength under the assumption of isotropy is unreasonable. In the present study, we conducted Brazilian tests on flat disk-shaped rock specimens and attached strain gauges at the center of the disc to measure the strains of rock. A tension-compression bi-modular model is proposed to interpret the data of the Brazilian test. The relations between the principal strains, principal stresses and the ratio of the compressive modulus to tensile modulus at the disc center are established. Thus, the tensile and compressive moduli as well as the correct tensile strength can be estimated simultaneously by the new formulas. It is found that the tensile and compressive moduli obtained using these formulas were in well agreement with the values obtained from the direct tension and compression tests. The formulas deduced from the Brazilian test based on the assumption of isotropy overestimated the tensile strength and tensile modulus and underestimated the compressive modulus. This work provides a new methodology to estimate tensile strength and moduli of rock simultaneously considering tension-compression bi-modularity.

Effect of the Filtrate Fluid of Water-Based Mud on Sandstone Rock Strength and Elastic Moduli.

During drilling operations, the filtrate fluid of the drilling mud invades the drilled rock. The invading filtrate fluid will interact with the rock and therefore alter the rock internal topography, pore system, elastic moduli, and rock strength. The objective of this study is to evaluate the effect of the mud filtrate of barite-weighted water-based mud on the geomechanical properties of four types of sandstone rocks (Berea Buff, Berea Spider, Bandera Brown, and Parker). The mud filtrate was collected to provide mud filtrate–rock exposure at a pressure of 300 psi and 200 °F temperature for 10 days. The study assessed the alteration in the rock geomechanics employing an integrated laboratory analysis of X-ray diffraction (XRD), scanning electron microscopy (SEM), nuclear magnetic resonance (NMR), and scratch testing. The ultrasonic results showed changes after exposure to the mud filtrate and an obvious reduction trend in the shear wave velocities due to the dissolution and mineralogical modifications in rock samples. The obtained results displayed a general strength reduction for the four sandstone types with different levels. The strength reduction ranged from 6% reduction for Berea Spider to a record 23% reduction for Parker. For all sandstone types, Young’s modulus showed a general reduction ranging from 11 to 40%, while Poisson’s ratio recorded an increase by 62–155% after the filtrate interaction. The study illustrated the role of pore-system alteration in controlling the rock strength and dynamic moduli.

Experimental study on the influence of locked-in stress on the uniaxial compressive strength and elastic modulus of rocks

The rock contains many inclusions which produce high locked-in stress under the ground stress. In order to study the influence of locked-in stress on the mechanical properties of rocks, the rock-like materials and nitrile rubber particles are used to make a test block of the rock-like model which contains inclusions. The rubber particles will expand as the test block is heated, which creates locked-in stress in the inclusions. Uniaxial compression tests of similar model blocks with different locked-in stresses and different inclusion contents were performed by using a water bath and MTS-5T uniaxial compression testing machine. The results show that the peak strength and elastic modulus decreased with the increasement of locked-in stress and inclusion content. In the meantime, the relationship among the peak strength, the elastic modulus of the test piece, the locked-in stress and the inclusion content were obtained with the help of a mathematical fitting analysis of the quantitative formula. Furthermore, the expression and value curve of the joint impact factor are calculated. This paper evaluates the importance of the locked-in stress in the mechanical properties of the rock-like material and provide a guide for other researchers to further investigate the locked-in stress in rocks.

Study on Fracturing and Diffusion Mechanism of Nonslab Fracturing Grouting

The coupling effect of a slurry and the fractured rock layer controls a spatial attenuation of the fracture channel width and grouting pressure from a grouting hole to the slurry top of fracture diffusion. This paper comprehensively considers the influencing factors such as the mechanical properties of the injected rock mass and the time-varying characteristics of the serous viscosity and introduces the control equation of the fracture channel width to establish a single-fracture nonslab fracturing grouting model. Combining the motion law of the slurry with the extension form of fracture, the equation of slurry diffusion motion, considering the fracture geometry and the time-varying characteristics of the serous viscosity, is derived. Comparing this equation with the existing theories and experiments, the validity and reliability of the theory are verified. In this paper, the effects of rock elastic modulus, slurry viscosity, and grouting rate on the fracturing grouting diffusion law of rock mass are analyzed. It is pointed out that when fracturing grouting in deep rock layers, a larger initial grouting rate and grouting pressure should be selected in the early stages of grouting to generate or penetrate fractures in the rock layer. Also, when the grouting pressure is stable, it is appropriate to increase the viscosity so that the slurry can quickly gel in the fractures thus sealing the fractures.