A Relation Between Adiabatic and Isothermal Moduli

Exploration in shale formations has experienced substantial popularity growth in recent history. With this, the importance of understanding the elastic properties of the sub-surface in exploration areas has also grown. Dynamic elastic properties can be extracted from seismic or well log velocity information; however for geomechanical modeling purposes, it is often desirable to obtain static measurements directly from core samples. Accurate static measurements are of significant importance to many applications, namely hydraulic fracturing and reservoir engineering, and are often used to determine reservoir behavior in completions engineering. Widely unavailable or not properly preserved core data has resulted in the development of correlation functions to relate dynamic and static measurements for estimation of static rock properties in exploration regions where static data are not available. The relationship between static and dynamic measurements of both Poisson’s Ratio and Young’s Modulus has attracted some interest with regard to exploration, and has even been proposed as a product indicator for shales. This work is targeted at investigation of this relationship from the perspective of thermodynamics. Results here provide a schematic for relating adiabatic and isothermal measurements of elastic properties in shales and various aggregates, and the effect due to anisotropy. This method uses elastic velocity data to extract the adiabatic material properties, coupled with compositional information and thermal characteristics for estimation of the isothermal material properties. Variation due to anisotropy is examined by manipulating the tensor of thermal expansion for the isothermal calculations. Analysis was conducted for several core samples found throughout the referenced literature for Barnett, Haynesville, and Bossier shales. Results of this work conclude only a qualitative understanding of the extent to which static properties can be estimated via the adiabatic-isothermal relationship. As such, the developed formulae described here do not accurately depict the differences between static and dynamic deformation, and consequently cannot be used for estimation of static properties from dynamic measurements as originally hypothesized. Further developments in this area may provide an alternative mechanism for estimation of these properties.