Application of T-matrix model for static moduli approximation from dynamic moduli determined by sonic well logging

Abstract

The paper examines the proposed approach of using T-matrix model to convert dynamic moduli (Young's modulus and Poisson's ratio) determined by sonic well logging to values equivalent to values of static moduli (called effective moduli). The chosen approach is particularly suitable for rock masses consisting of solid rocks with irregular local cracking. The proposed approach is based on the fact that for intact rock with Young's modulus values on the order of several tens of GPa and strength σc on the order of several tens of MPa, the values of static and dynamic moduli are equivalent. Any fractures in the rock will cause the elastic behaviour to cease being linear and a difference will appear between the values of static and dynamic moduli. It is possible to approximate this difference using the T-matrix model.The starting point for creating a T-matrix model is a simplified layered geological model of a borehole profile. Added to this are values of static moduli determined by a uniaxial compression test on representative samples of the borehole core. Additional input data for calculating the T-matrix model include porosity determined from well logging measurements, and the presence of cracks as interpreted from an acoustic scan of the borehole wall. The given approach is demonstrated in the experimental measurement of a borehole in Silurian limestone. The procedure was verified by comparing the calculated effective moduli with values of static moduli, measured on control samples prepared from borehole core outside the collection intervals of samples used as input for calculation of the T-matrix model. This comparison showed that for majority of samples there was a decrease in the difference from nearly 40% (dynamic moduli) to under 10% (effective moduli).