Relationships between Dynamic Elastic Moduli in Shale Reservoirs

Sheyore John Omovie,John P Castagna

doi:10.3390/en13226001

Sheyore John Omovie, John P Castagna

Open Access

https://doi.org/10.3390/en13226001

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Abstract

Sonic log compressional and shear-wave velocities combined with logged bulk density can be used to calculate dynamic elastic moduli in organic shale reservoirs. We use linear multivariate regression to investigate modulus prediction when shear-wave velocities are not available in seven unconventional shale reservoirs. Using only P-wave modulus derived from logged compressional-wave velocity and density as a predictor of dynamic shear modulus in a single bivariate regression equation for all seven shale reservoirs results in prediction standard error of less than 1 GPa. By incorporating compositional variables in addition to P-wave modulus in the regression, the prediction standard error is reduced to less than 0.8 GPa with a single equation for all formations. Relationships between formation bulk and shear moduli are less well defined. Regressing against formation composition only, we find the two most important variables in predicting average formation moduli to be fractional volume of organic matter and volume of clay in that order. While average formation bulk modulus is found to be linearly related to volume fraction of total organic carbon, shear modulus is better predicted using the square of the volume fraction of total organic carbon. Both Young’s modulus and Poisson’s ratio decrease with increasing TOC while increasing clay volume decreases Young’s modulus and increases Poisson’s ratio.

Highlights

Sonic velocity and density logs provide direct in situ measurement of formation dynamic moduli and derived quantities
To isolate controlling variables strictly within the shale reservoir rock while considering uncertainty in water saturation calculations, we excluded from our analysis datapoints with water saturations greater than 70% as well as low total solid organic carbon (TOC) intervals with weight percent of total organic content less than 1%
Given that density and compressional-wave velocity are often highly correlated [32] the well-defined Vs − Vp relationships in Figure 2 and Table 3 suggest that, as Vp is a good predictor of Vs when shear sonic logs are not available [27], dynamic elastic moduli should be correlated

Summary

Introduction

Sonic velocity and density logs provide direct in situ measurement of formation dynamic moduli and derived quantities. Given compressional-wave velocity, density, and measured or estimated shear-wave velocity, dynamic bulk, P-wave, Young’s and shear moduli and Poisson’s ratio can be directly calculated [1]. With sufficient calibration, these dynamic moduli can potentially be used to estimate static moduli and, especially if anisotropy can be quantified, they may be useful for hydraulic fracturing design in shale reservoirs [2]. Of more direct interest in engineering applications are Poisson’s ratio, ν, and Young’s modulus, E, given by ν = (k/μ − 2/3)/(2k/μ + 2/3) = (Vp /Vs 2 − 2)/(2Vp /Vs 2 − 2), (4)

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