Gas Shale Anisotropy and Mechanical Property: Laboratory Measurements and Mathematical Modeling
Lu, Kefei 1975-
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This dissertation focus on the study of elasticity, permeability, mechanical properties, and the mathematical modeling of Barnett shale. This study is based on the laboratory core measurements, literature data, and data set provided by industry. We noticed that the difference between assumed 45o to bedding planes and real cutting angle could reach to 5o, which leads to more than 15% of C13 estimation error. To reduce the angle error, we use both Vp and Vsv measured from core samples to determine the cutting angle and then calculate C13 with the real angle, other than traditional way of using Vp at 45 o to calculate C13. This method can be applied to permeability tensor measurements. Velocity and permeability anisotropy have been measured on 12 core samples. High velocity anisotropy has been observed. P-wave anisotropy parameter ε ranges from 5% to 73% and S-wave parameter γ ranges from 7% to 47% at unconfined conditions. Anisotropy increases with clay and TOC contents increase. Both velocity and permeability reach to the highest values when parallel to bedding planes. The permeability and velocity anisotropy behaviors are the same along the symmetry axis. Permeability is much more sensitive than velocity to the existing anisotropy. Effects are more than 100%. Literature data and core measurement data from Marathon Oil Company have been analyzed. Shales have Vp/Vs ratios range from 1.5 to 1.8. Besides Vp/Vs ratios, we found that velocities vertical to beddings are closely correlated with those horizontal to beddings with correlation coefficient 0.61 for both P- and S-wave. This relation may vary from reservoir to reservoir. The Young’s modulus and Poisson’s ratios have been calculated in anisotropic formulae and compared with isotropic case for common minerals in shale. For the anisotropic case, negative Poisson’s ratios exist at certain direction as reported. Form Marathon data on Barnett core, the static/dynamic Young’s modulus ratios range from 0.52 to 0.74. Empirical relations between static and dynamic Young’s modulus have been proposed (correlation coefficient for horizontal modulus was 0.81 and for vertical modulus was 0.93, standard errors were 0.16 and 0.05, respectively). With mineralogy composition and other rock properties, shale medium was estimated using a general singular approximation (GSA). The modeling results fit well with ultrasonic and sonic velocity measurements. The anisotropic Young’s modulus and Poisson’s ratio calculated from modeled effective elastic constants also show good fit with measured moduli. This means the GSA method can be used to interpret the anisotropic properties of shale reservoirs. We developed a new method of determining the measuring angle and elastic constant C13. Our measurements showed that permeability anisotropy and velocity anisotropy have good correlation behaviors along the symmetry directions. In respect of Thomson anisotropy parameters, the anisotropic Young’s modulus and Poisson’s ratios behave differently. In general, results obtained in this study will help to better understand the reservoir structure and stimulate the possibility to predict the unmeasured parameters (permeability) based on measured one (velocity).