An evaluation of empirical and rock physics models to estimate shear wave velocity in a potential shale gas reservoir using wireline logs

Abstract

Shear wave velocity (Vs) is essential for determining the elastic properties of rocks, which are useful for shale gas reservoir characterization. Many investigators have developed empirical models of varying form and complexity, and simplified rock physics models for the estimation of Vs using conventional well logs and/or laboratory measurements on core samples. Other investigators have developed rock physics models and used them to estimate velocities based on fundamental rock properties such as mineralogy, pore geometry and fluid saturations. The selection of a suitable model based on well logs is challenging, especially in cases where cores are not available. This study evaluates various relationships in the literature for the estimation of shear wave velocity applied to sandy shale and shale intervals of the Lower Goru Formation, Lower Indus Basin, Pakistan. Some inputs (e.g., compressional wave velocity) are directly taken from conventional log measurements, while others (e.g., petrophysical and elastic properties) are estimated using available log and the literature data. A statistical analysis has been used to quantify the difference between measured and predicted Vs. The results reveal that some empirical models can produce a coefficient of determination (R2) of roughly 0.8 when cross-plotted against measured Vs values, and R2 values can be further increased by 10%–20% if the coefficients are adjusted based on available Vs data. However, these models do not explicitly account for the mechanisms of velocity variations in sandy shale and shale due to pore geometry (aspect ratio), consolidation and fluid saturations in the manner that rock physics models do. The rock physics modeling conducted for this work demonstrated that the use of Biot's model (rather than Gassmann's model) for fluid substitution improved model performance for Vs estimation in gas-saturated sandy shale and shale of the Lower Goru Formation. Although statistical analysis showed this model to be slightly less accurate than the best empirical models (R2 of approximately 0.77), it is suggested that the rock physics model should be reliable when applied to a broader range of saturations and lithologies in the Lower Goru Formation. Also, using the rock physics approach, model input parameters can be optimized using Vp data, which represents a significant advantage over the empirical models which require Vs data for optimization. The modified rock physics model is thus deemed to be the best option available at present for the study area, and it is suggested that it should be appropriate for use in other settings – assuming that Vp data are available and sufficient knowledge regarding rock lithology is available.