Anisotropic elastic constants from dipole flexural dispersions in unconventional shale-gas reservoirs

Abstract

Anisotropic elastic constants are required to estimate the minimum horizontal stress magnitude using sonic data from a pilot vertical wellbore in unconventional shale-gas formations. Generally, the borehole Stoneley and flexural dispersions in a TI- (transversely isotropic) formation exhibit frequency-dependent sensitivities to all five TI-elastic constants. A frequency-dependent integral formulation relates fractional changes in the Stoneley or flexural velocities to incremental changes in the TI-elastic constants from an assumed equivalent isotropic reference state. Consequently, fractional changes in the Stoneley or flexural velocities at different frequencies can be inverted to obtain incremental changes in the TI-elastic constants from a chosen equivalent isotropic reference state. A linear relationship between fractional changes in the measured dispersion from a carefully chosen reference state to corresponding changes in the five TI-elastic constants is a reliable way to invert for multiple anisotropic constants. Based on the sensitivity of modal velocities to small changes in the anisotropic elastic constants, the inversion algorithm successfully inverts multiple elastic moduli from either the borehole Stoneley or dipole flexural dispersions. Validation of the inverted elastic constants is obtained by a good agreement between the reconstructed and measured dispersions.