Estimating permeability of carbonate rocks from porosity and v p / v s Ida L. Fabricius 1 , Gregor Baechle 2 , Gregor P. Eberli 2 , and Ralf Weger 2 ABSTRACT We present a method for predicting permeability from son- ic and density data. The method removes the porosity effect on the ratio v p /v s of dry rock, and it addresses the specific sur- face as an indirect measure of permeability. We look at ultra- sonic data, porosity, and the permeability of 114 carbonate core plugs. In doing so, we establish an empirical relationship between the specific surface of the solid phase as calculated by Kozeny’s equation and v p /v s linearly transformed to re- move the porosity effect. One must view the specific surface derived by using Kozeny’s equation as an effective specific surface because Kozeny’s equation only holds for homoge- neous rock with interconnected pores. The ratio v p /v s of dry rocks, on the other hand, seems to be controlled by the true specific surface, pointing to an inherent limitation in the method. The 114 carbonate plugs originate in three geologi- cal settings and comprise 83 calcitic and 31 dolomitic sam- ples. Their depositional texture varies from mud-dominated to grain-dominated and recrystallized types. Our research ap- plies the relationship to 137 carbonate samples from two dif- ferent depositional settings. We find a reasonable match be- tween predicted and measured permeability. The match is better for samples with carbonate mud-filled depositional textures than for carbonate mud-poor depositional textures. Diagenetic factors such as vuggy porosity decrease the pre- dictability of permeability. INTRODUCTION Attempts to predict permeability from porosity and sonic data have been made by several researchers Klimentos and McCann, 1990; Akbar et al., 1993; Prasad, 2003; Tsuneyama et al., 2003; Yamamoto, 2003. The historical focus has been on predicting per- meability from P-wave velocity and attenuation. Klimentos and Mc- Cann 1990 report on the P-wave attenuation of water-saturated sandstone, both clay-free and clay-bearing. For clay-free sandstone, they find attenuation in accordance with the theory of Biot 1956. In contrast, for clay-bearing sandstone, they find a higher attenuation. They propose that the higher attenuation might reflect viscous inter- action between clay particles and pore fluid. Klimentos and McCann 1990 conclude that attenuation depends on porosity and clay con- tent. They propose that for a given porosity, attenuation systemati- cally increases with decreasing permeability and that this increase is because of the permeability-reducing effect of clay. Akbar et al. 1993 similarly note that whereas P-wave velocity of sandstone is only moderately influenced by clay content, P-wave attenuation and permeability are both strongly dependent on clay content. This de- pendency indicates that attenuation is a key factor in determining permeability. From a porosity model of parallel tubes, they find at- tenuation to have a sharp peak at low permeability. Accordingly, Yamamoto 2003 models permeability of high-porosity aquifer limestone from attenuation data. Interestingly, from a study of bio- clastic carbonates, Tsuneyama et al. 2003 find that the v p /v s ratio carries information on permeability: High v p /v s at high permeability corresponds to grainstone facies v p is sonic P-wave velocity and v s is sonic shear wave velocity. Tsuneyama et al. 2003 can predict the relationship from a rock-frame model. Prasad 2003 studies a wide range of rock types, including sandstone and limestone. She finds that for a given flow zone unit, P-wave velocity of water-satu- rated samples correlates with permeability. On the other hand, she does not find a convincing correlation between permeability and P-wave attenuation. Thus there is a lack of a pattern among the published results on permeability versus P-wave attenuation. Perhaps porosity so strong- ly controls permeability, that the effect of porosity on permeability may mask the influence of other factors. Permeability is related not just to the porosity, but also to the interface between the pores and the solid material the specific surfaceKozeny, 1927. For homoge- neous sediments with high pore-connectivity, such as chalk, perme- ability may be predicted directly from porosity and specific surface by using Kozeny’s equation without empirical factors Mortensen et Manuscript received by the Editor February 4, 2007; revised manuscript received May 12, 2007; published online August 3, 2007. 1 Technical University of Denmark, Department of Environment and Resources, Kgs. Lyngby, Denmark. E-mail: ilf@er.dtu.dk. 2 University of Miami, Rosenstiel School of Marine and Atmospheric Science, Miami, Florida. E-mail: gbaechle@rsmas.miami.edu; geberli@ rsmas.miami.edu; rweger@rsmas.miami.edu. © 2007 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 72, NO. 5 SEPTEMBER-OCTOBER 2007; P. E185–E191, 10 FIGS. 10.1190/1.2756081 E185 Downloaded 15 Nov 2011 to 130.79.10.178. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/