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Model comparisons of multivariate statistics with theoretical predictions of elastic properties in sandstones
Akarapatima, Thanyanat
Akarapatima, Thanyanat
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2018
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This research is on acoustic properties of sandstones and shaly sandstones for various sedimentary basins. P- and S- wave velocities are investigated and correlated with physical properties. In seismic and well log interpretations, modeling the relation of rock properties helps to identify and to characterize reservoirs. Previous studies have shown that wave velocities in rock samples can be expressed as a linear relation between porosity and clay content when the experimental pressure is sufficient to close internal cracks. This research focuses on modeling the empirical multivariate linear regressions of elastic moduli by principal component analysis and multiple linear regression analysis. The comparisons to literature models show that to better predict acoustic properties, all models require prior knowledge about the rock formation of interest. Statistical analyses of data from eight different sandstones and shaly sandstone formations show that linear combinations between porosity (phi) and clay content (clay) of sandstone explain changes in elastic moduli. The equation derived in this thesis is only valid within the condition used to develop the model, sandstones with porosity 0 to 33% and clay content 0 to 51%, measured at ultrasonic frequency. To remove density effects, I derived relationship for elastic moduli as K = 37.19 - 80.04(phi) - 2.70(clay) R2 = 0.79 and Mu= 29.21- 72.43(phi) - 21.10(clay) R2 = 0.80. These equations can be used for quality checking data and predicting Vs from Vp. In summary, principal component analysis and multiple linear regression allow the uses of porosity and clay content to explain the variations of bulk and shear moduli in sandstones. This work eliminates systematic errors in measurements, obtained from literature and expands the range for shaly sandstone to low clay content and low porosity for prediction purposes.
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