Understanding Brown and Korringa (1975)

Although several studies aimed at linking electrical and hydraulic transport properties in rocks, the existing models remain at most incomplete. Based on this observation, in addition to the transport properties, this contribution investigates the pressure dependence of P wave velocities and porosity for three porous rocks. Apart from hydraulic conductivity, all physical properties show an important dependence to the confining pressure. In particular, electrical resistivity reaches an asymptote at low confining pressures. Using the measured P wave velocities and effective medium theories, the microcrack density (ρ) and its evolution with confining pressure are estimated. For the three rocks, the microcrack density at which electrical resistivity reaches a plateau is of ρ ~0.13. This value corresponds to the threshold for crack percolation in media containing microcracks exclusively. This suggests that in porous and microcracked rocks, electrical resistivity is controlled by two independent hydraulic pathways of tubes and cracks acting in parallel. In contrast, this percolation threshold is not observed in the permeability data. A simple conceptual model is finally introduced that explains the fundamental differences between transport properties.

Elastic properties of rocks play a major and crucial role for the design of any engineering structure. Determination of elastic properties in laboratory is tedious, laborious, very time consuming, as well as expertise is required, whereas determination of uniaxial compressive strength (UCS) and tensile strength in laboratory is simple, easy, and less expertise is required. Here, an attempt has been made to predict the elastic properties (Poisson’s ratio and Young’s modulus) of the schistose rocks from unconfined strength (UCS and tensile strength) using artificial neural network (ANN). A three-layer feed-forward back propagation neural network with 2-5-2 architecture was trained up to 855 epochs to predict the elastic properties of rock mass. The network was trained and tested by 120 data sets, and validation of the network was done by 20 new randomly selected data sets of UCS and tensile strength. The samples were collected from the schistose rocks of Nathpa-Jhakri hydropower project site, SJVNL, Himachal Pradesh, India. To check the validity and suitability of the artificial neural network technique, multivariate regression analysis (MVRA) is also performed, and comparison has been made. It was found that ANN gives closer values of predicted Poisson’s ratio and Young’s modulus as compared to MVRA. The coefficient of determination for Poisson’s ratio was 0.9809 and 0.843 by ANN and MVRA, respectively, whereas 0.9922 and 0.9362 for Young’s modulus by ANN and MVRA, respectively. The mean absolute percentage error (MAPE) for Young’s modulus is 11.13 and 28.21 by ANN and MVRA, respectively; whereas MAPE for Poisson’s ratio is 3.64 and 9.23 by ANN and MVRA, respectively.

The aim of the current study is to determine the elastic properties of carbonate rocks using ultrasonic method. Forty rock samples of Anah formation were collected at different depths from four wells drilled at the study area . The relationship between wave velocities and elastic properties of rocks was defined. Regression analyses to define these relations were applied. The results indicate that the elastic properties of the rocks show a linear relationship with both P- and S-wave velocities. The best relationship was obtained between both Young's modulus and Shear modulus with Vs in the determination of the coefficient ( R2 ), with values of 0.91 and 0.94, respectively. Bulk modulus and Lame’s constant were better correlated with Vp than with Vs in the determination of R2,with values of 0.92 and 0.83, respectively. Poisson’s ratio showed a good correlation using the ratio of Vp/Vs in the determination of R2, with a value of 0.81. The main output of this study shows that the ultrasonic method is a useful tool for the prediction of the elastic dynamic properties of sample rocks and that it can be used as an economical , simple and non- destructive method, especially for engineering purposes. 

The classic differential effective medium (DEM) theory can be used to determine the elastic properties of the porous medium, but the final elastic properties of multiple-porosity rock depend on the added order of the different pore-type inclusions. This paper presents a differential effective medium model for multiple-porosity rock and derives the analytical solutions of the bulk and shear moduli for dry rock. The validity of these analytical approximations is tested by integrating the full DEM equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range. The analytical formulae have been used to predict the elastic moduli for the sandstone experimental data by assuming that the porous rock contains dual-porosity of both cracks and pores. The results show that they can accurately predict the variations of elastic moduli with porosity for dry sandstones.

Within Otway Basin CO2 sequestration program, a small amount of CO2 is currently being injected into a depleted Naylor gas field, onshore Victoria. The reservoir is relatively deep (2 km) and complex with area extent of approximately 0.5 km2 limiting the monitoring program to the application of seismic methods only. However the injection of CO2 into this heterogeneous reservoir, where residual gas saturation is present throughout most of the sand column, is expected to cause very subtle changes in elastic properties of the reservoir rock. Indeed initial approximate modelling of 4D seismic response showed that only 4-6 % change in the elastic parameters could be expected. Such small effect could be ?lost? even through approximate fluid substitution methodology. Considering inherently low repeatability of land seismic it becomes even more important to accurately predict 4D seismic at this site. For that purpose we have investigated various methodologies that could increase the accuracy of the predicted changes in elastic properties of the reservoir rock. We derived a methodology for accurate prediction of elastic properties of the reservoir rock through calibration of the log and petrophysical data with core sample. The result showed core saturated velocities and log measurement agree with each other when the ?effective? Kgrain is applied. It suggested that ?effective? Kgrain could be used to represent the average mineralogy of the grains if we do not know the exact mineral composition making up the rock. However, comparative analysis and calibration of log measurement with core sample proved that accurate fluid substitution methodology at this site is hard to achieve without having dense core sample test results within the reservoir interval. In this paper, we present a methodology to derive elastic properties of the reservoir rock through calibration of the log and petrophysical data with core sample measurement.

Using core samples of the Kola ultradeep borehole (SG-3) and their surface analogues, variations in the density and elastic properties of some crystalline rocks of the Earth’s crust are estimated by modeling of in situ conditions. It is shown that the bulk density and the elastic wave velocities in the rocks have a weak depth gradient. In the SG-3 section under consideration, this gradient is negative. The resulting dependences for estimating the variations in the properties of the crystalline rocks are suitable for the depth range from the surface to 20–30 km. The initial data for the linear approximation of the characteristics can be obtained from the results of tests of surface analogue samples. It is shown that the velocity anisotropy of the metamorphic rocks can vary within wide limits.

Gassmann equations predict effective elastic properties of an isotropic homogeneous bulk rock frame filled with a fluid. This theory has been generalized for an anisotropic porous frame by Brown and Korringa equations. Recently, Ciz and Shapiro (2008) developed a generalization of Gassmann equations for porous media saturated with a solid material. In this paper we present an overview of the new theory and compare to numerical simulations of effective elastic properties of porous rocks filled with an additional solid component. Moreover, we model the effective elastic prroperties of clay-sand mixtures and rocks saturated with heavy oils. The latter application we validate by comparing to experimental data. A very good agreement between numerical and experimental data has been obtained. Thus, this new generalized Gassmann's model is directly applicable as useful rock physics model, e.g.: in proper seismic data interpretation.

The concept of critical porosity was introduced to the rock physics community in the 1990s by Amos Nur and colleagues at Stanford University. Critical porosity has proved useful in reservoir characterization using seismic, borehole acoustic waves, and sonic logs, as well as in geomechanical applications such as prediction of rock strength and in-situ stress. This article reviews the concept and its relation to the phenomenon of mechanical percolation in statistical physics. Estimates of the critical porosity using laboratory measurements, computer simulations, and effective medium and effective field theories are discussed. Effective medium and effective field theories are not able to describe accurately the behavior of rocks in the vicinity of the critical porosity due to assumptions of idealized pore shapes and failure to explicitly account for pore connectivity. However, they do prove useful for understanding the effect of porosity, pore shape, and pore orientation distribution on elastic wave velocities, and suggest relations between porosity and elastic moduli useful for modeling of elastic waves in porous rocks.

Hydrocarbon reservoirs generally are composed of rocks with pores and cracks that are filled with different fluids: gas, water, oil, etc. The fluids filling the pores have a significant impact on the effective characteristics of the reservoir. Methods of Effective Medium Theory (EMT) can simulate the effective elastic properties of porous-fractured media, such as rocks. The practical applications of EMT methods for fractured porous rocks are important for fracking, reservoir property prediction using seismic data and understanding the AVO properties of reservoirs. To date, a huge number of different EMT approaches exist and it is very difficult to choose the best one. Each of the most popular EMT methods for the modeling of effective elastic properties of reservoir rocks, of course, generate different results. However, different conclusions on method’s applicability are drawn from the differences in the experimental and theoretical results. The main goal of the paper is to find the most optimal method of effective medium theory. It can be shown that the T-matrix approach is the most general, modern and adequate for the rock physics applications. A practical application of the T-matrix approach was developed for the inverse problem with a special choice of comparison body. Also, other theories exist for simulation the effective proprieties of rocks: poroelasticity, contact models etc. The EMT has a close connection with these theories. A connection between the Effective Medium Theory and Poroelasticity are shown. Our conclusions are verified on experimental data. As an example of practical utilization of the T-matrix approach mathematical models for the effective elastic properties of carbonate reservoir rocks including oolitic limestone are constructed.

The in-situ mechanical strengths of rocks are very difficult properties to determine or measure because of variation in stress states and rock anisotropics. On the other hand, drilling penetration rates in rocks which are related to some rock strengths can be measured with a higher degree of reliability in the field. From penetration rate and other drilling data, a rock's drilling strength may be determined and related to its mechanical properties. Wireline electrical log data have been extensively used in reservoir characterization and sometimes give direct measurements of some elastic properties of the rocks. However, there is still the need to evolve some universally acceptable rock strength determination method from wireline electric log data. This approach has the advantage of not requiring extensive drilling and laboratory data and also provides a realistic estimate of in-situ rock strength. This paper discusses relationships between rock drilling strength and some wireline log properties and shows how a formation's drilling strength can be estimated from log data.

In this study the elastic properties of crystalline rocks – amphibolites from different boreholes were studied. We studied the depth effect on the elastic properties of mineralogically quite homogenous rocks – amphibolites. The samples were taken from three different crustal levels – shallow (tens of meters) Stařechov (Czech Republic), medium deep (first thousands of meters) KTB (Germany), and deep crustal depths (up to 12 km) KSDB3 (Russia). The elastic properties were first determined experimentally using high-pressure apparatus and 3D ultrasonic testing. The effect of main rock fabric components were evaluated using the method of inverse calculation from experimental data. There was found an increase of P-wave velocity, P-wave stiffness elastic constants with the depth for 19 samples, collected from different depth, and all loaded to 400 MPa of hydrostatic pressure. This fact can be explained by the stress memory effect. Stiffness constants and Young modulus were determined for primary material orientation INTRODUCTION Elastic anisotropy is a crucial physical property of crustal rocks namely when reflecting deformational history of the rock. Knowledge of the anisotropy of deep crustal rocks (e.g., Kern et al. 1991) is of special interest for studies focused on the evolution of the crust. The relationship between amphibolite elastic properties and mineral composition and/or rock fabric has been extensively studied in the past (Siegesmund et al. 1989). The influence of microcracks on the elastic wave velocity and its anisotropy has been noted in many previous studies (Crampin 1977, Babuška and Pros 1984 among others). Numerous studies are focused on the systematic study of elastic properties of rocks extracted from boreholes e.g., KTB (Berckhemer et al. 1997) or KSDB3 (Nikitin et al., 2001, Saikia et al. 2021). In all of these studies, there is missing comparative research concentrated on the relationship between the actual depth of rock occurrence and its elastic properties.

We present a new technique for static computations of effective elastic properties of multiple fractured rocks. This approach is based on the viscoelastic rotated staggered finite‐difference (FD) grid wave propagation technique. Our simulations are used to explain discrepancies of some recent numerical studies. The focus is on scale effects of a so‐called representative volume element (RVE). From the point of view of classical micromechanics we review different numerical techniques: Static as well as dynamic numerical experiments. We show that the differential effective medium theory (DEM) is capable of producing satisfactory predictions of effective elastic moduli. For non‐dilute crack densities this is not the case for the non‐interacting approximation (NIA).

Understanding the mechanical properties of formations has its importance in the drilling, production, and management phases of reservoirs. In petroleum engineering, measurements through wire-line logs, which run in the boreholes after the drilling phase, are of the most common methods to estimate mechanical properties of different layers. Elastic rock mechanic measurements from logs are dynamic values and need to be upscaled and calibrated to fit the corresponding pseudo-static measurements that are obtained from cores in the laboratory. As a practical approach to having a continuous profile of these static parameters and surmount the arduousness that confronts by using core samples and laboratory tests, many researchers tried to deploy predictive methods and empirical correlations. However, it will be a great advantage to have a real-time estimation of these static parameters while drilling based on bit and formation rock interaction. Artificial neural networks are powerful tools for estimation of complex functions subjected to availability of large enough data sets that present samples of actual behavior of the function. In this study, artificial neural networks were implemented to estimate in situ rock mechanical properties, including Unconfined Compressive Strength, Young's Modulus of Elasticity, and the ratio of these parameters known as Modulus Ratio, by using operational drilling parameters as inputs. Required data were gathered from drilling reports, logging operations, and core samples from nine wells placed in Ahwaz Oilfield located in south-west Iran. The trained networks showed satisfactory low errors in the testing process and sketched the capability of artificial neural networks in estimation of complex functions. The accuracy of the presented model was then compared with the results of calibrated regional correlations and modified Warren's equation. These correlations are used in the candidate wells to estimate Unconfined Compressive Strength and Young's Modulus of Elasticity. It was observed that the new artificial neural network approach is a competent and accurate method for real-time calculation of static elastic properties of formation rocks. The results of this work could be used for drilling optimization, reducing stability problems, and lithologic boundary detection while drilling.

The knowledge of seismic, elastic and physical properties of the deep-seated rocks, like density, porosity, P- and S-wave velocities, elastic modulii and seismic wave attenuation, is extremely important to study various geophysical and geodynamical problems. Since major part of the Earth’s continental crust, remains inaccessible to direct observations, the laboratory measurement of such properties becomes essential, which are used to model the crustal composition, rheological behaviour and physical and thermal state of the crust and the underlying mantle. This is specially true for the geodynamically active areas, like Deccan Volcanic Province, which is concealed below 1 to 3 km thick suite of basaltic lavas. This volcanic terrain is also experiencing high level of intraplate seismic activity. Deep scientific drillings in two such prominent seismic zones, provided unique opportunity to study such properties. Results obtained on Deccan volcanic and basement cores from 617 m deep Killari borehole, have given some very interesting clues to geological evolution of this terrain.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 30359, “Reservoir Characterization Supported by Rock Physics Diagnostics,” by Stephan Gelinsky, Shell. The paper has not been peer reviewed. Copyright 2021 Offshore Technology Conference. Reproduced by permission. Rock physics models are often perceived as too complicated and dependent on too many difficult-to-measure parameters to be of practical use for reservoir characterization. In the complete paper, the author demonstrates how careful calibration of a common and simple rock physics model can provide valuable insights into the reservoir and seal elastic properties such as function of porosity, fluid, and mineral properties and net-to-gross. The model can be used for quantitative seismic interpretation of reservoirs with variable net-to-gross and porosity away from well control. Methodology Rock physics describes the application of fundamental physical principles to establish the elastic properties of porous rocks as a function of their mineral composition, pore fill, and microstructure and texture. Once a suitable rock physics model is calibrated locally, the use of seismic data to estimate reservoir rock and fluid properties from the elastic rock properties is possible—specifically, from the observed seismic amplitudes and if seismic data were inverted from the seismically derived acoustic and shear impedances. The Hashin-Shtrikman (HS) effective medium bounds can be used to characterize both sandstones and shales. While the application of this model for clean sandstones is straightforward and, thus, is not included in this synopsis, the application for shales is more complex.