Mixing models and frame moduli bounds in complex lithologies
Asian Gassiyev, John Patrick Castagna · 2009
This paper investigates the use of bounding equations in complex porous multiminerallic lithologies to determine limits for frame elastic moduli by considering different scenarios for porosity distribution. Two different schemes for selection of end-member components are considered. A porosity-explicit mixing model considers each of the mineral constituents and the pore fluid as end-members of the mixture. This approach requires the mixing of dissimilar constituents such as solids and fluids, resulting in elastic moduli bounds, which are, generally too wide to be useful in porous composites. Alternatively, a porosity—implicit mixing model incorporates the porosity into single-phase end-member components. This model is theoretically exact for dry rocks. For an evenly distributed porosity in a quartz-calcite mixture, Hashin-Shtrikman bounds (KHS) derived from the porosity-implicit mixing model are close. However, these bounds are violated by the assumption of a linear relationship between velocity and composition and suggest a relationship of compressional velocity to the 3/2 power of calcite fractional volume. When the effect of uneven porosity distribution is added to the model, significant deviations may occur.