This study is on elastic properties of sandstones and shaly sandstones for various sedimentary basins. P- and S- wave velocities (Vp and Vs) are investigated and correlated with physical properties. In seismic and well log interpretations, modeling the relationship of rock properties helps to identify and characterize reservoirs. Previous studies have shown that velocities in rock samples linearly relate to porosity (ϕ) and clay content (clay) when the pressure is sufficient to close internal cracks. This study focuses on modeling the empirical multivariate linear regressions of elastic moduli by principal component analysis (PCA) and multiple linear regression analysis.
Statistical analyses of data from eight different sandstones and shaly sandstone formations show that linear combinations between porosity and clay content explain changes in elastic moduli. The empirically derived equation is valid within the condition used to develop the model, sandstones with porosity 0 to 0.33 and clay content 0 to 0.51, measured at ultrasonic frequency. To remove density effects, I derived relationship for elastic moduli as K = 37.19 − 80.04(ϕ) − 2.70(clay) R2 = 0.79 and µ = 29.21− 72.43(ϕ) − 21.10(clay) R2 = 0.80. The modelled elastic moduli matches ones of laboratory dataset within +/-1SD. The outliers highlight a mineralogy effect on elastic rock properties. The model underestimates all moduli with stiff cements (calcite and pyrite) since it is developed for sandstones with weak cements (clay minerals). Thus, the model can be used for quality checking data and predicting Vs from Vp.
A blind test of the model was performed, using ultrasonic core measurements and log data from two wells. For core data, the model results in under-prediction of shear moduli of Oseberg sandstones. A possible reason is that the clean sandstone has lower Poisson's ratio than shaly sandstone; however, the model was developed from cleaner sandstones than blind test sandstones. For well log data, the model overestimates bulk modulus and underestimates shear modulus of the North Kalikpik well. However, the model underestimates bulk modulus and overestimates shear modulus of the Mesaverde well log. Three possible sources of errors are: (a) dispersion effect from differences in measurement frequencies; (b) Vs estimation and fluid substitution calculations; (c) errors in the logs and varying borehole conditions.
In general, all models require prior knowledge about the rock formation of interest. The study also reflects on an improper linear model because log measurements are pressure dependent. The suggestion for well log measurement prediction is modeling in a nonlinear equation form.