Linear and nonlinear modulus surfaces in stress space, from stress-strain measurements on Berea sandstone

International audienceThe elastic response of many rocks to quasistatic stress changes is highly nonlinear and hysteretic, displaying discrete memory. Rocks also display unusual nonlinear response to dynamic stress changes. A model to describe the elastic behavior of rocks and other consolidated materials is called the Preisach-Mayergoyz (PM) space model. In contrast to the traditional analytic approach to stress-strain, the PM space picture establishes a relationship between the quasistatic data and a number density of hysteretic mesoscopic elastic elements in the rock. The number density allows us to make quantitative predictions of dynamic elastic properties. Using the PM space model, we analyze a complex suite of quasistatic stress-strain data taken on Berea sandstone. We predict a dynamic bulk modulus and a dynamic shear modulus surface as a function of mean stress and shear stress. Our predictions for the dynamic moduli compare favorably to moduli derived from time of flight measurements. We derive a set of nonlinear elastic constants and a set of constants that describe the hysteretic behavior of the sandstone

KG2B, a collaborative benchmarking exercise for estimating the permeability of the Grimsel granodiorite - Part 1: Measurements, pressure dependence and pore-fluid effects

Measuring the permeability of tight rocks remains a challenging task. In addition to the traditional sources of errors that affect more permeable formations (e.g. sample selection, non-representative specimens, disturbance introduced during sample acquisition and preparation), tight rocks can be particularly prone to solid–fluid interactions and thus more sensitive to the methods, procedures and techniques used to measure permeability. To address this problem, it is desirable to collect, for a single material, measurements obtained by different methods and pore-fluids. For that purpose a collaborative benchmarking exercise involving 24 laboratories was organized for measuring the permeability of a single low permeability material, the Grimsel granodiorite, at a common effective confining pressure (5 MPa). The objectives of the benchmark were: (i) to compare the results for a given method, (ii) to compare the results between different methods, (iii) to analyze the accuracy of each method, (iv) to study the influence of experimental conditions (especially the nature of pore fluid), (v) to discuss the relevance of indirect methods and models and finally (vi) to suggest good practice for low permeability measurements. In total 39 measurements were collected that allowed us to discuss the influence of (i) pore-fluid, (ii) measurement method, (iii) sample size and (iv) pressure sensitivity. Discarding some outliers from the bulk data set (4 out of 39) an average permeability of 1.11 × 10−18 m² with a standard deviation of 0.57 × 10−18 m² was obtained. The most striking result was the large difference in permeability for gas measurements compared to liquid measurements. Regardless of the method used, gas permeability was higher than liquid permeability by a factor approximately 2 (kgas = 1.28 × 10−18 m² compared to kliquid = 0.65 × 10−18 m²). Possible explanations are that (i) liquid permeability was underestimated due to fluid-rock interactions (ii) gas permeability was overestimated due to insufficient correction for gas slippage and/or (iii) gases and liquids do not probe exactly the same porous networks. The analysis of Knudsen numbers shows that the gas permeability measurements were performed in conditions for which the Klinkenberg correction is sufficient. Smaller samples had a larger scatter of permeability values, suggesting that their volume were below the Representative Elementary Volume. The pressure dependence of permeability was studied by some of the participating teams in the range 1–30 MPa and could be fitted to an exponential law k = ko.exp(–γPeff) with γ = 0.093 MPa−1. Good practice rules for measuring permeability in tight materials are also provided

Characterization of rock for constraining reservoir scale tomography at the Geysers geothermal field

A suite of laboratory measurements are being conducted on Geysers graywacke recovered from a drilled depth of 2599 meters in NEGU-17. The tests are being conducted to characterize the effect of pressure and fluid saturation on the seismic properties of the graywacke matrix. The measurements indicate that the graywacke is an unusual rock in many respects. Both compressional and shear velocities exhibit relatively little change with pressure. Water saturation causes a slight increase in the compressional velocity, quantitatively consistent with predictions from the Biot-Gassmann equations. Shear velocity decreases with water saturation by an amount greater than that predicted by the Biot-Gassmann equations. This decrease is attributed to chemomechanical weakening caused by the presence of water. Measurements of Q, from torsion experiments on room dry samples at seismic frequencies indicate unusually high Q, (~500). Water saturation decreases the shear modulus by 12 percent, again indicative of chemomechanical weakening. Q, is lower for the water saturated condition, but still relatively high for rock at low stress. Results of ultrasonic pulse propagation experiments on partially saturated samples are typical of low porosity rocks, being characterized by a monotonic decrease in compressional and shear velocity with decrease in saturation. An increase in shear velocity and low frequency shear modulus after vacuum drying indicates the presence of chemo-mechanical weakening resulting from the presence of small amounts of water