Theoretically derived pore geometry in carbonates using the extended biot theory

Abstract

Carbonates typically display a large scatter in velocity-porosity cross plots that is caused by the difference in stiffness that the highly variable pore geometry produces in carbonate rocks at a given porosity. In recent years, digital image analysis (DIA) made it possible to capture objective, quantifiable parameters of the pore geometry to explain the scatter in carbonate velocity-porosity cross plots. The geometrical parameters most influential for acoustic velocity are Perimeter over Area (measuring the complexity of the pore space) and Dominant Size (measuring pore sizes as equivalent diameter). Most theoretical models of acoustic wave propagation in porous media, however, do not incorporate those geometrical characteristics of the natural pore spaces? In contrast, the frame flexibility and coupling factors (fk and γk) embedded in the Extended Biot Theory capture the geometrical characteristics using poroelastic data. Here, these theoretically derived parameters are tested and validated with experimental data. In 95 limestone samples, Extended Biot Theory parameters fk and γk can be derived reliably from measured acoustic data. Both parameters correlate well to Perimeter over Area (r = 0.702, p < 0.0001), and Dominant Size (r = 0.792, p < 0.0001) derived using digital image analysis of thin section photographs. These correlations confirm the existence and the strength of the relationship between theoretical parameters from the Extended Biot Theory and quantitative pore geometry parameters. Thus, this study illustrates 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 pore geometry characteristics can be used to estimate permeability indirectly from acoustic data. For example, permeability estimates based on a Kozeny-Carman type function incorporating geometrical information derived from the topological Extended Biot Theory parameters fk and γk, yield a statistically significant, high Pearson correlation coefficient of r = 0.713 (p < 0.0001).