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 rootmean- 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.
Elastic moduli are affected directly by three influencing factors: rock framework, pore fluid and pore space. Indirect factors, such as, changes in temperature and pressure have the potential to modify the effect of the direct factors on elastic moduli. Carbonate rocks, in contrast to sandstone, display complex pore structures with an astonishing range of pore sizes and pore shapes. Although the pore shape is the most significant rock property, affecting the elastic property of the rock (Wang, 2001), it can not be easily quantified. In comparison to the pore shape, the pore size is relatively easily to measure and quantify. A positive correlation between pore size and velocity was first been observed by Hamilton et al. (1956). Anselmetti and Eberli (1993) observed a relationship between pore type and velocity, where rock samples containing moldic and intraparticle porosity have a higher velocity than samples containing micro-moldic porosity and microporosity. Effective medium models have the potential to capture the effect of those pore geometries on acoustic properties. Many experimental and numerical studies use the aspect ratios as pore type indicators. The aspect ratio is either assigned (Goldberg and Gurevich, 1998, Xu and White, 1995 and Markov et al., 2005), derived from velocitypressure measurements (Sun and Goldberg, 1997), derived from joint inversion of acoustic and resistivity measurements (Kazatchenko et al., 2004) or estimated using neural networks (Yan et al., 2002). Only a few studies used aspect ratios determined from thin sections and they proved not to capture the observed velocity variations (Colpaert et al., 2007 and Rossebø et al., 2005). Effective medium models with various concentrations of pores and assigned pore shapes or pore types have been used to characterize the acoustic properties of carbonate rocks. In this study we emphasize the importance of separating the effects of micropores and macropores when evaluatingacoustic properties of carbonates..
