Carbonate Rock Physics: Analytical Models and Validations Using Computational Approaches and Lab/Log Measurements
Authors: Xu Shiyu , Chen Ganglin , Zhu Yaping , Zhang Jie , Payne Michael , Deffenbaugh Max , Song Limin , Dunsmuir John H. 
Published: February 2016

Abstract
Developing robust, accurate, and practical carbonate rock physics models is a crucial step for successful geophysical applications in carbonate reservoirs. We extended the Xu-White model, originally designed for clastic rocks, to carbonates and observed some promising results. For example, our shear-wave prediction method was accurate after the mineralogy effect was correctly handled. However, several technical issues still need to be addressed to better understand the seismic response to carbonate rock properties.Carbonates may have complex pore systems, including interparticle, intra-particle, moldic, and vuggy pores. Recent published results suggest seismic wave velocities are strongly affected by pore type.The validity of Gassmann fluid substitution in carbonate rocks is unknown because of the complex pore system and heterogeneity at different scales.Our data show that the effect of mud filtrate invasion on sonic logs is more problematic in carbonates than in clastics. We need a method to quantify the invasion effect and correct the effect if necessary.The effects of other factors, such as stress, lithology and pore fluid are still imperfectly quantified. Improved models could benefit 4D seismic interpretation, as well as fluid and lithology prediction.
In this paper, we will introduce our carbonate rock physics model. In particular, the model will be used to quantify the pore type effect on elastic properties. We will then discuss shear-wave prediction and mud filtrate invasion using examples from East Texas. Examples will also be given to demonstrate how our physics-based log conditioning method improves the seismic/well tie. Finally, some issues on computational rock physics will be discussed.

Introduction
Carbonate reservoirs (limestone and dolomite) account for approximately 50% of oil and gas production worldwide. However, seismic responses in carbonate rocks are poorly understood. For example, it is not known if the DHI ranking system and the AVO classification system developed for clastic rocks are applicable to carbonate rocks. An accurate and physically sound carbonate rock physics model is needed to address those technical issues.
Development of a carbonate rock physics model is extremely difficult because the pore systems in carbonate rocks are complex compared with clastics. While clastic rocks have mainly intergranular pores, carbonate rocks can have a variety of pore types such as moldic, vuggy, interparticle, and intraparticle. Diagenesis often plays a significant role in the development of such a pore system. Recent publications show that pore type strongly affects the porosity-velocity relationship (e.g., Eberli et al. 2003). The complex, multi-scale pore system in carbonates leads some authors to question the applicability of traditional Gassmann fluid substitution (e.g., Wang 1997, Baechle et al. 2005), while others claim that the Gassmann theory works perfectly fine (e.g., Rasolofosaon 2006, Adam et al. 2006). It is important to understand why Gassmann may work in some cases but not in others.
The effect of mud-filtrate invasion on the density log is well-known. However, its effect on sonic logs is difficult to quantify because the invasion profile is determined by many factors, including porosity, permeability, pore structure, fluid properties, and, of course, the pressure difference between the borehole mud and the formation pore fluid. In many cases, our data show that the mud filtrate invasion depth in carbonates is much larger than in clastics, indicating a more significant effect on sonic logs.
Due to the brittle nature of carbonate rocks, fractures are more prevalent than in clastics. These fracture systems act as conduits for fluid flow and can considerably enhance hydrocarbon production in low porosity carbonate rocks or tight gas sands. Understanding the effect of fluid communication between matrix porosity and fracture system(s) on the seismic response is thus a crucial part of carbonate rock physics research.