Journal of Engineering Geology

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Abstract
(Paper pages 1159-1178)
Young’s modulus measured as the slope of the stress-strain curve under static loading conditions (Es) in the lab is one of the most essential parameters for reservoir geomechanical modeling. However, information on the value of Es along the well length is often discontinuous and limited to cross well with the core. On the other hand, well log data for wave velocities Vp and Vs are often available for most hydrocarbon reservoirs. Hence, well-known equations are needed to calculate static Young’s modulus based on the compressional and shear wave velocities (Vp and Vs) that is dynamic Young’s modulus (Ed). Unfortunately, because of porosity and micro cracks in rock texture, Es and Ed are not equal. Therefore, correlation between static and dynamic parameters could result in a continuous and more reliable knowledge on the elastic parameters along the well length. In this research, laboratory experiments were carried out on limestone rock core specimens of Sarvak formation obtained from an oil well in the South West of Iran. Empirical relations were suggested to estimate UCS and static Young’s modulus from compressional wave velocity (Vp) and dynamic Young’s modulus. These empirical relations are prerequisite for continuous wellbore stability analysis in oil and gas well drilling

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Non-destructive methods such as ultrasonic wave velocity are extensively used for estimating physical and mechanical properties of rock due to the simplicity, economical, fast and harmless nature. Rock constructions have been made worldwide from past to present. Determination of strength of rock constructions such as archeological evidence is not possible using conventional rock strength tests. Developing a cheap, simple, non-destructive, efficient and accurate method to estimate the strength of such constructions can be useful. Rock blocks and constructions have various shapes and sizes. Rock blocks having various shapes and sizes have been prepared from marble, travertine, granite, and limestone and ultrasonic wave velocity at various directions of the blocks dimensions and the uniaxial compressive strength of cylindrical core obtained from the blocks have been measured. The results show that shapes and sizes have no effect on the ultrasonic wave velocity. At the end relationships between uniaxial compressive strength and ultrasonic wave velocity have been determined. The uniaxial compressive strength of blocks and rock constructions can be estimated by the obtained relationships using non-destructive, simple and indeed low cost method of ultrasonic wave velocity.

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In geotechnical engineering, rock mechanics and engineering geology, depending on the project design, uniaxial strength and static Youngchr('39')s modulus of rocks are of vital importance. The direct determination of the aforementioned parameters in the laboratory, however, requires intact and high-quality cores and preparation of their specimens have some limitations. Moreover, performing these tests is time-consuming and costly. Therefore, in this study, it was tried to precisely predict the desirable parameters using physical characteristics and ultrasonic tests. To do so, two methods, i.e. principal components regression and support vector regression, were employed. The parameters used in modelling included density, P- wave velocity, dynamic Poisson’s ratio and porosity. Accordingly, the experimental results conducted on 115 limestone rock samples, including uniaxial compressive and ultrasonic tests, were used and the desired parameters in the modelling were extracted using the laboratory results. By means of correlation coefficient (R²), normalized mean square error (NMSE) and Mean absolute error (MAE), the developed models were validated and their accuracy were evaluated. The obtained results showed that both methods could estimate the target parameters with high accuracy. In support vector regression, Particle Swarm Optimization method was used for determining optimal values of box constraint mode and epsilon mode, and the modelling was conducted using four kernel functions, including linear, quadratic, cubic and Gaussian. Here, the quadratic kernel function yielded the best result for UCS and cubic kernel function yielded the best result for E_s. In addition, comparing the results of the principal components regression and the support vector regression indicated that the latter outperformed the former.

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