Erling Fjær

Static and dynamic moduli of a weak sandstone

Static moduli derived from the slope of a stress-strain curve and dynamic moduli derived from the velocity of elastic waves are significantly different for rocks, even though they should be equal according to the theory of linear elasticity. Proper knowledge about this difference might be useful because dynamic measurements are often the only information available about a rock. In tests on a dry sandstone, static and dynamic moduli are always different, except immediately after the direction of loading has been reversed. The results support the assumption that the difference between static and dynamic moduli can be ascribed to the difference in strain amplitude between static and dynamic measurements. At low stress levels, static and dynamic moduli increase with increasing stress during initial loading. In uniaxial compaction tests, the static compaction modulus decreases with increasing stress at higher stress levels, revealing a sensitivity to the location of the failure envelope. However, the correspon...

In-situ stress dependence of wave velocities in reservoir and overburden rocks

Seismic waves propagate through a stressed earth. Sonic waves recorded by a borehole sonic logging tool propagate in the near-well environment—which is also stressed, albeit under different stress conditions than the untouched formation far away. Cores excavated from within the earth undergo stress release, and are then reloaded in the laboratory—but hardly ever to the complete, fully anisotropic in-situ state of stress and pore pressure. Based on this, we easily recognize that stress sensitivity affects our ability to compare and correlate geophysical and petrophysical measurements of wave velocities. On the other hand, it also provides an avenue to extract information about rock stresses. As an example, the presence of abnormally low velocities in seismic or log data is evidence of high pore pressure.

The Scratch Test: An Attractive Technique for Determining Strength and Elastic Properties of Sedimentary Rocks

The Scratch Test is a relatively new technique for determination of mechanical properties of rocks. In a Scratch Test, the surface of the rock is scratched at constant depth (typically less than 1 mm) by a sharp cutter, while the applied forces are being monitored. It is found that these forces are closely related to the mechanical properties of the rock. The Scratch Test thus represents a direct measure on the core material, and provides continuous coverage of data for the entire length of available core material. The work reported here is a detailed study of the Scratch Test as a technique for determining strength and elastic properties of sedimentary rocks. The work is based on extensive laboratory testing of many sedimentary rocks with different mechanical properties. The results of the study show that parameters obtained in a Scratch Test, in particular the Specific Energy, correlate very well with the Uniaxial Compressive Strength (UCS). The accuracy of the Scratch Test for rock strength determination is seen to be at least comparable to the accuracy of the UCS Test, while the resolution is even better. It is also found that the Scratch Test may be used to determine the elastic modulus of rocks with good precision. The Scratch Test only requires access to a free surface of the rock. Hence, it may be run on most available core material. Provided that the core is in a reasonably good shape, no special preparation is required for the test, which is thus both quick and cheap. Unlike the UCS Test, the Scratch Test is almost non-destructive, and provides continuous data coverage. The Scratch Test is therefore a very attractive method for determination of stiffness and strength of core materials when addressing issues like reservoir compaction, hydraulic fracturing, borehole stability and sand production, offering a better resolution and data coverage than any other technique available today. Rock mechanical parameters derived from wire-line log data are continuous but have the disadvantage of being derived indirectly from other measurements, such as sonic velocity, density and porosity.

The Impact of Heterogeneity on the Anisotropic Strength of an Outcrop Shale

Properly accounting for the mechanical anisotropy of shales can be critical for successful drilling of high inclination wells, because shales are known to be weak along bedding planes. To optimize the drilling parameters in such cases, a sufficiently representative, anisotropic rock mechanical model is therefore required. This paper presents such a model developed to better match results from a dedicated, extensive set of uniaxial and triaxial compression tests performed on plugs of Mancos outcrop shale with different orientations relative to the bedding plane. Post failure inspection of the plugs shows that the failure planes are to some extent affected by the orientation of the applied stress relative to the bedding planes, indicating that the bedding planes may represent weak planes which tend to fail before intrinsic failure occurs, whenever the orientation of these planes is suitable. The simple “plane of weakness” model is commonly used to predict strength as function of orientation for such a rock. A comparison of this model to the experimental data shows, however, that the weak planes seem to have an impact on strength even outside the range of orientations where the model predicts such impact. An extension of this model allowing the weak planes to be heterogeneous in terms of patchy weakness was therefore developed. In this model, local shear sliding may occur prior to macroscopic failure, leading to enhanced local stresses and corresponding reduction in strength. The model is found to give better match with strength data at intermediate orientations. The model is also able to partly predict the qualitatively different variation of Young’s modulus with orientation for this data set.

Petrophysical laboratory measurements for basin and reservoir evaluation

The quality of computer modelling in basin and reservoir studies critically depends on the quality of input data. Core measurements may directly provide such data. Cores also help establish correlations between log measured parameters and parameters required in basin or reservoir evaluation. Correlations may also permit simple index measurements to be used for data assessment instead of more tedious laboratory procedures. This paper summarizes different petrophysical laboratory techniques that can be utilized for these purposes. The importance of performing laboratory measurements under representative conditions and to account for core damage effects is underlined.

Evaluating the Poroelastic Effect on Anisotropic, Organic-Rich, Mudstone Systems

Understanding the poroelastic effect on anisotropic organic-rich mudstones is of high interest and value for evaluating coupled effects of rock deformation and pore pressure, during drilling, completion and production operations in the oilfield. These applications include modeling and prevention of time-dependent wellbore failure, improved predictions of fracture initiation during hydraulic fracturing operations (Suarez-Rivera et al. Presented at the Canadian Unconventional Resources Conference held in Calgary, Alberta, Canada, 15–17 November 2011. CSUG/SPE 146998 2011), improved understanding of the evolution of pore pressure during basin development, including subsidence and uplift, and the equilibrated effective in situ stress (Charlez, Rock mechanics, vol 2 1997; Katahara and Corrigan, Pressure regimes in sedimentary basins and their prediction: AAPG Memoir, vol 76, pp 73–78 2002; Fjær et al. Petroleum related rock mechanics. 2nd edn 2008). In isotropic rocks, the coupled poro-elastic deformations of the solid framework and the pore fluids are controlled by the Biot and Skempton coefficients. These are the two fundamental properties that relate the rock framework and fluid compressibility and define the magnitude of the poroelastic effect. In transversely isotropic rocks, one desires to understand the variability of these coefficients along the directions parallel and longitudinal to the principal directions of material symmetry (usually the direction of bedding). These types of measurements are complex and uncommon in low-porosity rocks, and particularly problematic and scarce in tight shales. In this paper, we discuss a methodology for evaluating the Biot’s coefficient, its variability along the directions parallel and perpendicular to bedding as a function of stress, and the homogenized Skempton coefficient, also as a function of stress. We also predict the pore pressure change that results during undrained compression. Most importantly, we provide values of transverse and longitudinal Biot’s coefficients and the homogenized Skempton coefficient for two important North American, gas-producing, organic-rich mudstones. These results could be used for petroleum-related applications.

Rock acoustics and rock mechanics: Their link in petroleum engineering

Seismic data represent the most important source of information about underground formations that have not been accessed by excavations or drilling. When target formations can be reached by drilling, more accurate velocity data are available via logging. The primary use of the seismic information is still to map structure. However, there is a growing interest in using seismic data to derive intrinsic information about rock properties such as porosity, clay content, etc. Porosity estimation has traditionally also been the main application of sonic logs. In fact, an established school of thought holds that velocities in sedimentary rocks are primarily a measure of porosity—the lower the velocity, the higher the porosity.

Stress-Induced Fracturing of Reservoir Rocks: Acoustic Monitoring and μCT Image Analysis

Stress-induced fracturing in reservoir rocks is an important issue for the petroleum industry. While productivity can be enhanced by a controlled fracturing operation, it can trigger borehole instability problems by reactivating existing fractures/faults in a reservoir. However, safe fracturing can improve the quality of operations during CO2 storage, geothermal installation and gas production at and from the reservoir rocks. Therefore, understanding the fracturing behavior of different types of reservoir rocks is a basic need for planning field operations toward these activities. In our study, stress-induced fracturing of rock samples has been monitored by acoustic emission (AE) and post-experiment computer tomography (CT) scans. We have used hollow cylinder cores of sandstones and chalks, which are representatives of reservoir rocks. The fracture-triggering stress has been measured for different rocks and compared with theoretical estimates. The population of AE events shows the location of main fracture arms which is in a good agreement with post-test CT image analysis, and the fracture patterns inside the samples are visualized through 3D image reconstructions. The amplitudes and energies of acoustic events clearly indicate initiation and propagation of the main fractures. Time evolution of the radial strain measured in the fracturing tests will later be compared to model predictions of fracture size.

Stress-induced versus lithological anisotropy in compacted claystones and soft shales

Shales are anisotropic. Most definitions of shale in-corporate this attribute, either by referring to fissility and existence of cleavage planes, or to anisotropic texture resulting in anisotropy of physical properties on many length scales. Definitions of shale scatter though; some focus on a high content of clay minerals as characteristic of a shale, while others consider a large amount of fine grains (< 2μm) as sufficient. In a rock mechanical context, it is natural to define shale as a rock in which clay minerals constitute the load-bearing framework. This means that “gas shales” in oil-field terminology are, strictly speaking, not shales according to a geological or a geomechanical perspective. Still, these materials have a lot in common with classically defined shales (e.g., low permeability) and anisotropy.

Elastic Dispersion Derived from a Combination of Static and Dynamic Measurements

Utilization of laboratory tests for calibration and interpretation of data from seismic surveys requires knowledge about elastic dispersion in the range from seismic to ultrasonic frequencies. Data on such dispersion are hard to obtain because it requires specially designed equipment and also relies on simplifying assumptions about rock symmetry. A new method for estimation of dispersion in this frequency range is presented here. This method requires only standard rock mechanical equipment with ultrasonic velocity measurements, and is based on comparison of static and dynamic data. A key element in this method is a procedure for elimination of strain amplitude as a source for differences between static and dynamic moduli. High-quality data is necessary, but the required accuracy is not extreme. Application of the method on one partly saturated shale and two dry sandstone samples indicates that dispersion increases with clay content, and decreases with stress.