Modeling velocity in carbonates using a dual porosity DEM model

The differential effective medium theory is used to model the velocity of carbonates with two predefined end-member pore types and under dry and water saturated conditions. The dual porosity DEM takes into account input parameters derived from digital image analysis of thin sections. In particular the respective amount of microporosity and macroporosity and the aspect ratio of the macropores are incorporated. A conceptual aspect ratio of 0.1 for micropores and a measured aspect ratio of 0.5 for macropores is used as input parameters for the differential effective medium (DEM) model. The model predicts that the compliant micropores have a strong influence on the sonic velocity of porous carbonates because increasing concentrations of micropores reduce the rock stiffness. The model values are compared to high frequency (1MHz) laboratory velocity measurements. These velocity predictions with the dual porosity DEM model show significant better velocity prediction than empirical models, e.g. the Wyllie times average equation. We obtain a root-mean-square-error of 392 m/s when comparing predicted with measured velocity values. Our results also show that a differential effective medium model that uses measured input parameters from quantitative digital image analysis improves estimates of acoustic properties of carbonates.