Abstract
Two significant questions in carbonate petrophysics are: (1) which objective, quantifiable, and parameterizable aspects of thin section pore geometry best explain commonly observed scatter in carbonate velocity-porosity cross plots; and (2) what is the importance of geometrical characteristics of the pore space on acoustic velocity relative to other physical properties? In this dissertation, quantitative description of the pore geometries of carbonate rocks and measurements of acoustic properties are used to develop an empirical link between general qualitative geological descriptions and a rigorous theoretical rock physics model.Comparison of petrophysical attributes of carbonate core plugs, geologic description, and quantitative geometric parameters derived from thin sections using digital image analysis demonstrate that: (1) geometric information captured by geological descriptions of pore type in carbonates explains aspects of scatter in velocity-porosity cross-plots; (2) four quantitative geometrical parameters that capture pore size, pore surface roughness, aspect-ratio, and pore network complexity statistically capture characteristics that quantitatively differentiate thin sections from each other; (3) two of these parameters (perimeter-over-area and dominate pore size) are related to the deviation of acoustic velocity from Wyllie's time average equation (R 2 = 0.65 and R2 = 0.62 respectively); (4) comparing geometric characteristics and laboratory measurements of velocity and porosity with Extended Biot Theory (EBT) frame flexibility factors confirms the validity of EBT; (5) the two geometrical parameters (2D specific surface and dominate size) are strongly correlated to geometrical frame flexibility parameters derived from acoustic measurements ( R2 = 0.68 and R2 = 0.60 respectively); and (6) internal rock geometry influences acoustic velocity most strongly in high porosity carbonate rocks.The findings from this study imply that: (1) estimating porosity from acoustic data can be substantially improved by incorporating information on quantitative pore space geometry; and (2) in cases where good estimates of porosity are available (e.g. from well-log data or seismic with extensive well control) quantitative pore geometric characteristics can be estimated directly from acoustic data. These quantitative geometric characteristics of the pore space can be used to estimate permeability indirectly from acoustic data.