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An Investigation of Static and Dynamic Data Using Multistage Triaxial Test

Abstract

This work is to develop an improved understanding of the relationship between static and dynamic data for a suite of four rock samples. “Static data” are defined as the large strain (> 10^-3) measurements on unloading and reloading tri-axial stress paths. “Dynamic data” are the small strain (<10^-6) data acquired using acoustic velocity measurement techniques. The results are analyzed in terms of Young's Modulus. A quadratic fit has been applied to the static data, this allows us to separate the response into a linear and nonlinear elastic terms. M1, and M2 respectively. M1 is interpreted to be dominated by the contact modulus and is constant throughout the entire unload and reload cycles. M2 the nonlinear elastic term is interpreted to be due to the opening and closing of compliant pores. These interpretations result from the correlation we find between the linear term and the measured velocity and the nonlinear term with the measured irrecoverable strains. The motivation behind this work is therefore to provide a more robust conversion between the Young's modulus than that derived from empirically based correlations. It is expected this will ultimately involve the use of thin section and/or microCT data to provide a mineralogical and textural based model, allowing the up scaled wellbore and field models to be developed. To our knowledge this is the first time a delineation of the separate mechanisms i.e. linear versus nonlinear effects in the static elastic moduli has been observed. Consistent with previously published results, the dynamic Young's modulus is always greater than or equal to the static modulus. The static Young's modulus decreases with increasing axial stress. This is interpreted to be consistent with increasing sample damage generating more compliant pores. When the unload-reload cycles are fit with a quadratic equation, the parameters M1 (linear) and M2 (quadratic) were not sensitive to the fraction of the unload reload cycle data fit at low stress. At high stress the damage associated with initial loading impacts the fit. M1 is equal to the modulus obtained from velocity data at small strains and M2 correlates with the total percent irrecoverable strains on both the unload and reload cycles. M1 is relatively independent of confining stress on the reload cycle. A small stress dependence is observed on the unload cycle. M2 however shows significant stress dependence. M2 decreases with increasing confining stress.