Static Elastic Properties Research Articles

A New Correlation for Estimating Static Elastic Properties of Sandstone Formations: Case Study from Rumaila Oilfield

Evaluating the elastic characteristics of reservoir's rocks is crucial for the oil and gas sector to reduce risks throughout drilling and production operations. Elastic parameters are essential for prediction of wellbore stability, estimation of in-situ stresses, optimization of drilling performance and design of hydraulic fracturing. Depending on the type of formation, Elastic parameter is varied dramatically. Thus, a precise way to identify these characteristics is needed. Inaccurate assessment of elastic characteristics can result in excessive expenditure and inappropriate field development plans. Static elastic modulus (Est) can be determined through laboratory testing. Although laboratory measurement is the most precise approach to determine the elastic modulus, it requires a continuous core sample to acquire a complete profile of the formation's elastic characteristics. However, just a portion of the well is typically sampled for cores. On the other hand, wireline log data is applied to determine the dynamic modulus (Edyn), allowing for continuous assessment of elastic properties. Numerous characteristics of the rock, including consolidation, pore pressure and lithology affect the dynamic modulus. Thus, it needs to be converted to Static elastic modulus by empirical formulae. Several empirical equations have been proposed to convert dynamic Young's modulus to static Elastic modulus. Nevertheless, the validity of these relationships is restricted and exclusive to certain areas. This research seeks to establish a relationship between Dynamic modulus and static Elastic modulus for sandstone formation of Rumaila oil field. The suggested correlation provides accurate predictions of the static elastic modulus for the complete sandstone segment. The newly created correlation performed better than the previous correlations in predicting static elastic modulus with average absolute error of 8.69 %, and correlation coefficient of 0.9848. The newly established empirical correlation can assist geo-mechanical engineers in estimating continuous profile of the sandstone formation's static modulus.

Geometric effects on impact mitigation in architected auxetic metamaterials

Lightweight materials used for impact mitigation must be able to resist impact and absorb the maximum amount of energy from the impactor. Auxetic materials have the potential to achieve high resistance by drawing material into the impact zone and providing higher indentation and shear resistance. However, these materials must be artificially designed, and the large deformation dynamic effects of the created structures must be taken into consideration when deciding on a protection concept. Despite their promise, little attention has been given to understanding the working mechanisms of high-rate and finite deformation effects of architected auxetic lattice structures. This study compares the static and dynamic elastic properties of different auxetic structures with a honeycomb structure, a typical non-auxetic lattice, at equivalent mass and stiffness levels. In this study, we limit the investigation to elastic material behavior and do not consider contact between the beams of the lattices. It is demonstrated that the equivalent static and dynamic properties of individual lattices at an undeformed state are insufficient to explain the variations observed in impact situations. In particular, the initial Poisson’s ratio does not determine the ability of a structure to resist impact. To gain a thorough comprehension of the overall behavior of these structures during localized, high rate compression, the evolution of the elastic tangent properties under compression and shear deformation was monitored, leading to a more profound understanding. Observations made in one configuration of stiffness and mass are replicated and analyzed in related configurations.

Effects of Regimes of Water Saturation on Static Elastic Properties of Carbonate Rocks

Effects of Regimes of Water Saturation on Static Elastic Properties of Carbonate Rocks

Odd Cosserat elasticity in active materials.

Stress-strain constitutive relations in solids with an internal angular degree of freedom can be modeled using Cosserat (also called micropolar) elasticity. In this paper, we explore Cosserat materials that include chiral active components and hence odd elasticity. We calculate static elastic properties and show that the static response to rotational stresses leads to strains that depend on both Cosserat and odd elasticity. We compute the dispersion relations in odd Cosserat materials in the overdamped regime and find the presence of exceptional points. These exceptional points create a sharp boundary between a Cosserat-dominated regime of complete wave attenuation and an odd-elasticity-dominated regime of propagating waves. We conclude by showing the effect of Cosserat and odd-elasticity terms on the polarization of Rayleigh surface waves.

Lithofacies Types and Physical Characteristics of Organic-Rich Shale in the Wufeng-Longmaxi Formation, Xichang Basin, China.

The shale of the Upper Ordovician Wufeng Formation and the Lower Silurian Longmaxi Formation in the Xichang Basin is the main replacement horizon for the shale gas exploration being conducted in the Sichuan Province, except for the Sichuan Basin. The fine identification and classification of the types of shale facies are important for shale gas exploration and development evaluation. However, the lack of systematic experimental studies on rock physical characteristics and micro-pore structures leads to a lack of physical evidence for the comprehensive prediction of shale sweet spots. Therefore, the present study used different means, such as core observation, total organic carbon content (TOC), helium porosity measurement, X-ray diffraction analysis, and mechanical properties analysis, in combination with the analysis of the whole rock mineral composition and characteristics of shale, for the identification and classification of the lithofacies of the shale layer, the systematic petrology and hardness measurement of the shale samples with different lithofacies, and discussion of the dynamic and static elastic properties of the shale samples and the control factors. It was revealed that nine types of lithofacies existed in the Wufeng Formation- the Long11 sub-member in the Xichang Basin, among which moderate organic carbon content-siliceous shale facies, moderate organic carbon content-mixed shale facies, and high-organic carbon content-siliceous shale facies were the best lithofacies with the optimum reservoir conditions, providing sufficient space for shale gas accumulation. The siliceous shale facies mainly developed organic pores and fractures, and the pore texture was excellent overall. The mixed shale facies mainly developed intergranular pores and mold pores, with a preference toward pore texture. The argillaceous shale facies mainly developed dissolution pores and interlayer fractures, and the pore texture was relatively poor. The geochemical characteristics of the organic-rich shale samples with TOC > 3.5% revealed that the sample was composed of microcrystalline quartz grains as the rock support framework, while the intergranular pores were located between the rigid quartz grains, which exhibited hard pores in the analysis of their mechanical properties. In the relatively organic-poor shale samples with TOC < 3.5%, the quartz source was mainly terrigenous clastic quartz, and the sample was composed of plastic clay minerals as the rock support skeleton, while the intergranular pores were located between argillaceous particles, which exhibited soft pores in the analysis of their mechanical properties. The difference in the rock fabric of the shale samples resulted in an ″initial increase followed by a decrease″ trend of velocity with quartz content, with the organic-rich shale samples exhibiting low velocity-porosity and velocity-organic matter content change rate, and the two kinds of rocks were easier to distinguish in the correlation diagram of the combined elastic parameters such as the P-wave impedance-Poisson ratio and the elastic modulus-Poisson ratio. The samples dominated by biogenic quartz exhibited greater hardness and brittleness, while the samples dominated by terrigenous clastic quartz exhibited lower hardness and brittleness. These results could serve as a basis for logging interpretation and seismic ″sweet spot″ prediction of high-quality shale gas reservoirs in Wufeng Formation-Member 1 of the Longmaxi Formation.

Multiwell-Pressure History Matching in Delaware Play Helps Optimize Fracturing

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 204162, “Multiwell-Pressure History Matching in Delaware Play Helps Optimize Fracturing for Subsequent Pads,” by Roberto Suarez‑Rivera, SPE, and Rohit Panse, W.D. Von Gonten Laboratories, and Javad Sovizi, Baker Hughes, et al. The paper has not been peer reviewed. _ Because hydraulic fracture models include complex physics and uncertainties defined by many variables, the problem of calibrating modeling results with field responses is ill-posed. It is always possible to find a calibrated model that reproduces field data; however, such a model is not unique and multiple matching solutions exist. The objective and scope of the complete paper is to define a work flow for constraining these solutions and obtaining a more-representative model for forecasting and optimization. Introduction In this project, a work flow is presented that uses an ultrafast hydraulic fracturing model with well-known physics and high-confidence rock-property inputs to conduct sensitivity analysis for pad-scale field development. Based on a study of uncertainty on the model variables, the two most-uncertain variables (tectonic strain and leakoff multiplier) are selected for model calibrations. Model results are compared with the field response for all wells and all stages to better understand the discrepancies between the field and the model. Pressure history matching (PHM) is then conducted by adjusting the selected two variables until the global error of all stages and all wells is minimized. The results are nonunique, and uncertainty in the fracture geometry remains high. This can only be reduced by including geometrical constraints from appropriate field measurements. The authors propose that the global response represents the behavior of the entire pad and is unbiased by the behavior of single specific stages. Pad Layout and Model Development The pad in question is in the Delaware Basin and targets two landing zones in the Wolfcamp A formation. The cored well used to generate the geomodel is approximately 2 miles from this pad. Rock-properties modeling was conducted at centimeter-scale resolution using core measurements and petrophysical measurements. These measurements subsequently were integrated with depth-specific measurements of static elastic properties and ultrasonic velocity measurements conducted at elevated stress conditions, representative of the in-situ effective stress. Combining the P- and S-wave velocity and elastic moduli measurements at in-situ stress conditions with the corresponding centimeter-scale resolution velocity measurements along the core surface allowed later correction of in-situ conditions for static-to-dynamic effects and acquisition of centimeter-resolution profiles of anisotropic velocities and corresponding static anisotropic elastic properties along the length of the core. A detailed interface geologic study also was conducted to identify the presence, type, geologic origin, and density of all interfaces present in the core. The core-based measurements provide a high-confidence, high-resolution vertical representation of the reservoir (at the core location). Using multiple wells with consistent field logs and consistent formations tops in the region, a regional geomodel was created for hydraulic fracture modeling. This model possessed a high-confidence representation of the structural geometry of the dominant formations represented in the model. Using these as geometrical boundaries, rock properties were propagated homogeneously along the lateral extent of the model. The authors aim to maintain the model as simply as possible, particularly when no information exists to do otherwise. Their strategy is to start with a simple model, verify the differences between the model and the field measurements, and make changes when necessary if the differences are unacceptable, but not before.

Mechanical Performance of Polystyrene-Based Nanocomposites Filled with Carbon Allotropes

Numerous studies have been performed on different aspects of the mechanical behavior of polymer nanocomposites; however, the results obtained still lack a comprehensive comparative analysis of the mechanical properties of composites containing nanofillers of different shapes and concentrations and subjected to different static and dynamic loads. Carbon nanofillers were shown to provide the most significant improvement in the elastic properties of polymer composites. In this paper, we present a comparative analysis of the mechanical properties of polystyrene-based nanocomposites filled with carbon allotropes of different shapes: spherical fullerene particles, filamentary multi-walled nanotubes, and graphene platelets, fabricated by the same technology. The influence of shape and concentration of dispersed carbon fillers on mechanical and viscoelastic properties of composites in different stress–strain states was evaluated based on the results of tensile and three-point bending tests, and ultrasonic and dynamic mechanical analysis. Comparison of the static and dynamic elastic properties of nanocomposites allowed us to analyze their variations with frequency. At low concentrations of 0.1 wt% and 0.5 wt% all nanofillers did not provide significant improvement of elastic characteristics of composites. More efficient reinforcement was observed at the concentration of 5 wt%. Among the filler types, some increase in composite rigidity was observed with the addition of filamentary particles. The introduction of the layered filler provided the most pronounced rise in the composite rigidity. The weak frequency dependence of the mechanical loss tangent, which is characteristic of amorphous thermoplastics, was demonstrated for all the samples.

Rock-mechanical properties and in situ stress state of the Upper Cenomanian Mishrif limestone reservoir, Zubair oil field, southern Iraq

Rock-mechanical properties and tectonic stress state have crucial implications for reservoir stability, drilling, and production optimization. We have developed the first ever in situ stress analysis focused on the Mishrif reservoir from the supergiant Zubair oil field, southern Iraq. We interpreted an overall hydrostatic pore pressure gradient of 9.8 MPa/km and a vertical stress ([Formula: see text]) gradient of 22.17 MPa/km in the Upper Cenomanian Mishrif limestone formation. We inferred a Poisson’s ratio of 0.27–0.31, a Young’s modulus of 27–38 MPa, a coefficient of internal friction range of 0.66–0.76, and estimated a uniaxial compressive strength (UCS) range of 35–70 MPa with a low cohesive strength of 7.8–9.8 MPa from compressional sonic slowness data. We established fitting relationships between the dynamic and static elastic properties from the core-based triaxial test measurements and used the same for estimating the minimum ([Formula: see text]) and maximum ([Formula: see text]) horizontal stress magnitudes by poroelastic horizontal strain model. We validated the reservoir [Formula: see text] with the mini-frac-based fracture closure pressure and interpreted its gradient as 14.5–15.9 MPa/km, whereas we calculated the [Formula: see text] gradient as 19.5–23 MPa/km. We interpreted C-quality breakouts from four-arm caliper data and deciphered a northeast–southwest [Formula: see text] orientation (N45°E–N70°E). Using the compressive failure criteria, we constrained the reservoir [Formula: see text] by stress polygon analysis against the estimated UCS ranges and concluded a normal fault to strike-slip transitional tectonic stress state ([Formula: see text] ≥ [Formula: see text] &gt; [Formula: see text]) in the Mishrif reservoir.

Elastic properties and pore structure characterization of selected shales in the sungai Perlis beds, Terengganu, Peninsular Malaysia

Studied drill core of the Sungai Perlis Beds in the Terengganu State, Peninsular Malaysia, consists of a diverse suite of organic rich shale lithofacies at various subsurface depths. Lithofacies were delineated on the basis bedding thickness, mineralogy, and organic richness carried out by X-ray diffraction and (XRD) total organic content (TOC) analysis. Field-emission scanning electron microscopy (FE-SEM) analysis was carried out to identify the pore structure, range of pore sizes and mineral arrangement within each lithofacies unit Elastic geomechanical properties (Young’s modulus and Poisson’s ratio) were measured on core samples from each lithofacies unit using static and dynamic approaches. The identified lithofacies include moderate TOC massive argillaceous shale (MTOCMAS), high TOC massive argillaceous shale (HTOCMAS) and high TOC massive siliceous shale (HTOCMSS). FE-SEM analysis shows that pores in all the lithofacies are mostly intergranular, associated with phyllosilicate minerals, and ranges from <1 micrometer to approximately 8 micrometer. Static and dynamic elastic properties measurement shows that shale lithofacies having a high content of phyllosilicate minerals has a lower Young’s modulus and a high Poisson’s ratio value while lithofacies rich in brittle minerals has a higher Young’s modulus and a low Poisson’s ratio value. A good correlation exists between mineralogical brittleness index of the lithofacies and their plane strain modulus. The plane strain modulus is found higher in lithofacies having abundance of brittle minerals in the matrix suggesting that the high TOC massive siliceous shale (HTOCMSS) would preferably allow formation of dense hydraulic fractures, as observed in the CT scan analysis of triaxially fractured specimen, compared to argillaceous shale lithofacies.

Surface influence on the stationary shear deformation of a magnetorheological fluid

The study experimentally examines the quasi-static shear deformation of a magnetorheological (MR) fluid structured in an external magnetic field. Experiments are carried out using a rheometer with a plate–plate configuration. The working surfaces of the measuring geometry are modified to demonstrate their influence on the response of the field-structured MR fluid. The simplest possible suspension of microparticles of carbonyl iron in mineral oil without using surfactants or any modifiers is used. The difference in results obtained for structured MR fluid with different concentrations of magnetic particles using different modifications of the surface is demonstrated. The results are intended to motivate more intensive research on the issue and further more in-depth theoretical analysis of static elastic properties of structured MR fluids. Certain related critical issues are briefly highlighted.

Determining the static Young’s modulus and Poisson’s ratio, and compressive strength of the friable Erin Formation rocks using P-wave velocity

It is important to understand the mechanical properties (elastic properties and strength) of rocks as these properties are used to model the rock's deformation in civil and underground engineering projects. Determining these properties for friable rocks are very difficult and scarce due to the rock's poor cementation making it challenging to retrieve samples from outcrop and boreholes, and difficult to prepare specimens for laboratory testing. To improve on the lack of mechanical properties of friable rocks, this study aims to measure the mechanical properties and P- and S-wave velocities and determine if empirical relationships exist between them. Experiments were carried out at effective pressures up to 130 MPa under dry and saturated conditions on friable sandstone and thin-bed shale lithofacies from the Erin Formation. The static Young's modulus of the rocks is less than 8 MPa and the unconfined strength ranged from 1.0 to 2.2 MPa, which indicate that the rock is very weak. The confined compressive strength is relatively high due to large strain accumulation (average of 20% strain), which resulted in significant strain hardening. At low effective pressures, velocity measurements were highly attenuated, resulting in limited S-wave velocity measurements. Empirical relationships established between the mechanical properties and P-wave velocities were predominantly weak to strong. Moderate and strong linear relationships were established between the unconfined compressive strength and static elastic properties and between the tensile strength and static Poisson's ratio. The results of this study could be carefully applied to velocity data that are readily available from well logs to estimate the mechanical properties of friable rocks.

COMPARATIVE ANALYSIS OF STATIC SHEAR MODULUS AND DYNAMIC SHEAR MODULUS DETERMINED BY GEOPHYSICAL AND GEOTECHNICAL INVESTIGATION

Due to the occurrence of earth tremors which leads to the vibrations of foundations and perhaps failure of buildings and roads, it is therefore important to understand and have knowledge of the geomechanical soil properties for foundation design, assessment of risks and suggestion of mitigation plans in engineering structures and road construction. A total of 3 boreholes were drilled with the Standard Penetration Test (SPT) performed and Downhole Seismic Test (DST) carried out in the boreholes located within Assa to investigate the Geomechanical soil properties in the area. For the geophysical survey, the downhole seismic test was carried out to determine the P-wave and S-wave. The results were processed using the generalized reciprocal method (GRM) with the Seisimager program. The results of soil dynamic modulus (shear, young and bulk modulus) and Poisson ratio recorded from DST conducted in BH1, BH2 and BH3 ranges from 7300 KPa to 72390 KPa, 0.31 to 0.41 for the Poisson ratio. Meanwhile, soil static modulus and Poisson’s ratio recorded from SPT conducted in BH1, BH2 and BH3 ranges from 2520 to 44687.0 KPa, 0.20 to 0.55 for the Poisson ratio respectively. The results of this study have shown that there is a wide variation between geomechanical properties derived from geotechnical investigations (static properties) and geophysical investigations (dynamic properties). Based on depth trend analysis, the dynamic and static soil elastic properties all increases with depth. Generally, the dynamic soil properties were significantly higher than the static elastic properties. At shallow depths (&lt;12.0 m), the difference between static and dynamic soil modulus was relatively small, but increased with increasing depth. Meanwhile, the difference between static and dynamic Poisson ratio was high at shallow depth and it decreased with increased depths where they almost overlap. Correlation between the derived static and dynamic properties all revealed positive correlation trends. The strength of the correlation was highest for young modulus (r=0.87) which was closely followed by the shear modulus (r=0.63). Meanwhile, Poisson ratio (r=0.40) and bulk modulus (r=0.23) revealed weak positive correlation trends. The regression models generated from this study were used to derive static elastic properties and compared with the static properties obtained from geotechnical investigation thereby deriving the equations Dynamic Shear Modulus = (1.4207 x Static Shear Modulus) + 5022, Dynamic Young Modulus = (2.0241 x static young modulus) + 5054.8, Dynamic Bulk Modulus = (1.7852 x static bulk modulus) + 15458, Dynamic Poisson’s ratio = (0.1812 x Static Poisson’s ratio) + 0.3154. The results showed fairly good match between static (geotechnical) shear modulus and static (from regression model) shear modulus, static (geotechnical) young modulus and static (from regression model) young modulus. There was no good match obtained for bulk modulus and Poisson ratio generally, except at shallow depth (&lt; 12 m depth) where Poisson ratio revealed a good match.

Correlations between the static and anisotropic dynamic elastic properties of lacustrine shales under triaxial stress: Examples from the Ordos Basin, China

Shales are abundant and are increasingly important for the hydrocarbon industry as source rocks and unconventional reservoirs. The anisotropic dynamic elastic properties of shales are important in the exploration stage of shale reservoirs whereas their static elastic properties are key for the hydraulic fracturing for the more efficient development of shale gas and oil. However, the correlations between the static and anisotropic dynamic elastic properties that could provide a basis for the seismic methods to potentially evaluate the fracturing ability of shales without the need of cored samples from the borehole are still poorly understood. We have demonstrated, through dedicated simultaneous laboratory measurements of the anisotropic velocities and the strains of samples under triaxial stress, how the static and anisotropic dynamic elastic properties are correlated in seven lacustrine shales from the Ordos Basin, one of the major shale gas plays in China. The results show that the static and anisotropic dynamic elastic properties are stress-dependent. More importantly, the anisotropic velocities are found to be approximately linearly correlated with the axial strains of the samples at differential stress (the difference between axial stress and confining stress) greater than 30 MPa, with the slopes of the linear correlations in excellent linear relationship with Young’s moduli determined from the static elastic measurements. The results not only reveal the internal link between the static and anisotropic dynamic elastic properties of lacustrine shales, but they also pave a potential way for the anisotropic seismic explorations to remotely evaluate the fracturing ability of shales.

Feasibility Study on the Application of Dynamic Elastic Rock Properties from Well Log for Shale Hydrocarbon Development of Brownshale Formation in the Bengkalis Trough, Central Sumatra Basin, Indonesia.

In modeling the hydraulic fracking program for unconventional reservoir shales, information about elasticity rock properties is needed, namely Young's Modulus and Poisson's ratio as the basis for determining the formation depth interval with high brittleness. The elastic rock properties (Young's Modulus and Poisson's ratio) are a geomechanical parameters used to identify rock brittleness using core data (static data) and well log data (dynamic data). A common problem is that the core data is not available as the most reliable data, so well log data is used. The principle of measuring elastic rock properties in the rock mechanics lab is very different from measurements with well logs, where measurements in the lab are in high stresses / strains, low strain rates, and usually drained, while measurements in well logging use the principle of measured downhole by high frequency sonic. vibrations in conditions of very low stresses / strains, High strain rate, and Always undrained. For this reason, it is necessary to convert dynamic to static elastic rock properties (Poisson's ratio and Young's modulus) using empirical equations. The conversion of elastic rock properties (well logs) from dynamic to static using the empirical calculation method shows a significant shift in the value of Young's Modulus and Poisson's ratio, namely a shift from the ductile zone dominance to the dominant brittle zone. The conversion results were validated with the rock mechanical test results from the analog outcrop cores (static) showing that the results were sufficiently correlated based on the distribution range.

Determining the transverse isotropic rocks’ static elastic moduli with cylindrical plugs: Shortfalls, challenges, and expected outcomes

Cylindrical-shaped plugs can be tested using a Hoek-cell-like apparatus that allows for efficient and inexpensive measurements of a rock’s static elastic properties. However, when it comes to transverse isotropic material, this approach has a natural limitation due to the isotropic radial stresses; particular attention to the boundary conditions and the proper design of pressurization steps is warranted. Typical attempts to constrain the complete set of compliances ([Formula: see text]), using multiple plugs of different orientations, are impeded by the heterogeneity and pressure-dependent elasticities inherent to sedimentary rocks. Through stepwise pressure increases, we can constrain four normal compliances [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], describing two Young’s moduli and three Poison’s ratios, using a single horizontal plug drilled parallel to the rock’s isotropic plane, contrary to the common assumption that both horizontal and vertical plugs are needed. The measurement of the shear modulus [Formula: see text] needs to be obtained using a plug that is drilled oblique to the isotropic plane; replicating the in situ stress environment is not possible using this approach. Finally, the specimen’s anisotropic plane’s geometry is elliptical under isotropic radial stress; this causes a discrepancy between the strain gauge’s contraction and the actual strain. We have developed an iterative inversion approach to account for this issue and calculate the exact strains useful for inferring [Formula: see text] from measurements reported by strain gauges. The example included in this writing indicates that, without correction, inferred values of [Formula: see text] may suffer errors of 20%.

Static and Dynamic Mechanical Properties of Organic-Rich Gas Shale

Rock mechanical properties are critical for drilling, wellbore stability, and well stimulation. There are usually two laboratory methods to determine rock mechanical properties: static compression tests and acoustic velocity measurements. Rocks are heterogeneous, so there are significant differences between static elastic constants and the corresponding dynamic ones. Usually, static test results are more representative than dynamic methods but the static tests are time consuming and costly. Dynamic methods are nondestructive and less expensive, which are practical in the laboratory and field. In this paper, we compare the static and dynamic elastic properties of Eagle Ford Shale by triaxial compressive tests and ultrasonic velocity tests. Correlations between static and dynamic elastic properties are developed. Conversion from dynamic mechanical properties to static mechanical properties is established for better estimating reservoir mechanical properties. To better understand the relationship of static and dynamic mechanical properties, 30 Eagle Ford Shale samples were tested. According to the test results, the dynamic properties are considerably different from the static counterparts. For all tested samples, static Young’s modulus is lower than dynamic Young’s modulus, ranging from 55% to 90%. The difference of the static and dynamic Young’s moduli decreases with the increasing of confining pressure. The reason may be because the microcracks closed in high confining pressure. Correlations between static and dynamic Young’s modulus are developed by regression analysis, which are crucial to understand the rock mechanical properties and forecast reservoir performance when direct measurement of static mechanical properties is not available or expensive. There are no strong correlations between static and dynamic Poisson’s ratios observed for the tested samples. Two potentially major reasons for the discrepancy of the static and dynamic properties of Eagle Ford Shale are discussed. Lithology and heterogeneity may be the inherent reasons, and external causes are probably the difference in strain amplitude and frequency.

Low-Frequency Elastic Properties of a Polymineralic Carbonate: Laboratory Measurement and Digital Rock Physics

We demonstrate that the static elastic properties of a carbonate sample, comprised of dolomite and calcite, could be accurately predicted by Digital Rock Physics (DRP), a non-invasive testing method for simulating laboratory measurements. We present a state-of-the-art algorithm that uses X-ray Computed Tomography (CT) imagery to compute the elastic properties of a lacustrine rudstone sample. The high-resolution CT-images provide a digital sample that is used for analyzing microstructures and performing quasi-static compression numerical simulations. Here, we present the modified Segmentation-Less method withOut Targets method: a combination of segmentation-based and segmentation-less DRP. This new method assigns the spatial distribution of elastic properties of the sample based on homogenization theory and overcomes the monomineralic limitation of the previous work, allowing the algorithm to be used on polymineralic rocks. The method starts by partitioning CT-images of the sample into smaller sub-images, each of which contains only two phases: a mineral (calcite or dolomite) and air. Then, each sub-image is converted into elastic property arrays. Finally, the elastic property arrays from the sub-images are combined and fed into a finite element algorithm to compute the effective elastic properties of the sample. We compared the numerical results to the laboratory measurements of low-frequency elastic properties. We find that the Young’s moduli of both the dry and the fully saturated sample fall within 10% of the laboratory measurements. Our analysis also shows that segmentation-based DRP should be used cautiously to compute elastic properties of carbonate rocks similar to our sample.

Petrophysical properties of deep Longmaxi Formation shales in the southern Sichuan Basin, SW China

Abstract Deep shale layer in the Lower Silurian Longmaxi Formation, southern Sichuan Basin is the major replacement target of shale gas exploration in China. However, the prediction of “sweet-spots” in deep shale gas reservoirs lacks physical basis due to the short of systematic experimental research on the physical properties of the deep shale. Based on petrological, acoustic and hardness measurements, variation law and control factors of dynamic and static elastic properties of the deep shale samples are investigated. The study results show that the deep shale samples are similar to the middle-shallow shale in terms of mineral composition and pore type. Geochemical characteristics of organic-rich shale samples (TOC > 2%) indicate that these shale samples have a framework of microcrystalline quartz grains; the intergranular pores in these shale samples are between rigid quartz grains and have mechanical property of hard pore. The lean-organic shale samples (TOC

The stress dependence anisotropic elastic properties of shale

The stress dependence anisotropic elastic properties of shale is experimentally evident. It is well explained by the homogenization theory for a medium containing imperfect contact areas (ICA) of which the elastic properties are functions of the effective confining stress. For practical purpose, a minimum number of parameters related to the ICA is considered and calibrated on experimental data. It is observed that the trends of the five transversely isotropic elastic stiffnesses versus the effective confining stress can be well captured by four microscopic parameters: (1) a parameter that characterizes the orientation distribution of the contacts; (2) a ratio between the normal and in-plane compliances of the contacts; (3) the magnitude of the contact compliance at the stress-free condition; and (4) a curvature parameter that defines the dimensionless evolution of the contact compliance versus the effective confining stress. More importantly, these parameters can be fixed for different groups of materials: e.g. wet shale, dry shale, kerogen-rich shale, etc. therefore, a strong predictive capacity of the proposed method is approved. It is then used to predict the effective stiffnesses of shale at a high stress range using the measured data at a low stress range. It can also be used to explain the difference between the elastic properties of in-situ shale and shale samples at a stress-free or a modified stress condition in laboratory. Taking into account the stress dependence contact effect can also offers a capacity to analyze the relationship between its dynamic and static elastic properties.

Low Static Shear Modulus Along Foliation and Its Influence on the Elastic and Strength Anisotropy of Poorman Schist Rocks, Homestake Mine, South Dakota

We investigate the influence of foliation orientation and fine-scale folding on the static and dynamic elastic properties and unconfined strength of the Poorman schist. Measurements from triaxial and uniaxial laboratory experiments reveal a significant amount of variability in the static and dynamic Young’s modulus depending on the sample orientation relative to the foliation plane. Dynamic P-wave modulus and S-wave modulus are stiffer in the direction parallel to the foliation plane as expected for transversely isotropic mediums with average Thomsen parameters values 0.133 and 0.119 for epsilon and gamma, respectively. Static Young’s modulus varies significantly between 21 and 117 GPa, and a peculiar trend is observed where some foliated sample groups show an anomalous decrease in the static Young’s modulus when the symmetry axis (x3-axis) is oriented obliquely to the direction of loading. Utilizing stress and strain relationships for transversely isotropic medium, we derive the analytical expression for Young’s modulus as a function of the elastic moduli E1, E3, ν31, and G13 and sample orientation to fit the static Young’s modulus measurements. Regression of the equation to the Young’s modulus data reveals that the decrease in static Young’s modulus at oblique symmetry axis orientations is directly influenced by a low shear modulus, G13, which we attribute to shear sliding along foliation planes during static deformation that occurs as soon as the foliation is subject to shear stress. We argue that such difference between dynamic and static anisotropy is a characteristic of near-zero porosity anisotropic rocks. The uniaxial compressive strength also shows significant variability ranging from 21.9 to 194.6 MPa across the five sample locations and is the lowest when the symmetry axis is oriented 45° or 60° from the direction of loading, also a result of shear sliding along foliation planes during static deformation.