Micromechanics modelling for mineral volume fraction determination: application on a terrigenous formation

This work presents a non-linear Self-Consistent (SC) micromechanics method to model the observed physical elastic properties of a terrigenous formation with the purpose to obtain its depth mineral volume fractions profile. In this approach, it is first assumed that the observed physical elastic properties obtained from well logs, such as the density ρ_o and the elastic compressional Vp_o and shear Vs_o velocities, are a non-linear relationship of the unknown mineral volume fractions α. Then, a gradient descent algorithm is implemented to seek for those volume fractions α for which differences between modelled and observed physical elastic properties are minimum. It is assumed that quartz, calcite and clay are the main comprising minerals of the formation. Obtained volume fractions profile follow the same general trends to those estimated by implementing the Linear Least-Squares Inversion LLSI method which is widely used in petrophysical analysis to obtain mineral concentrations from density ρ_o, photoelectric effect Pe_o and compressional slowness Δ tp_o well logs. Results also show that calcite and clay volume fractions from these two methods are highly correlated while quartz volume fractions show low correlation. Further comparison between clay concentrations from SC method with clay concentrations calculated from direct measurements of gamma ray GR well logs used as a guideline also exhibits high correlation. These results suggest that the SC method is better suited to obtain clay and calcite volume fractions rather than quartz volume fractions. However, SC method can provide with insights about the general distribution of quartz along the borehole.