The elastic response of clastics rocks and grain packs is controlled to a large extend by the arrangements of grains and the strength of the contacts between them. For well-cemented rocks like Fontainebleau sandstone, the elastic moduli of the grains and the contact moduli can be taken as the one of quartz with good agreement to experimental data. In general, and in particular for less well cemented granular rocks, this is not the case, the contact moduli typically being weaker than the surrounding grains. In this study, we utilize microtomographic images and grain-partitioning techniques to assign grain moduli, and employ effective medium theories based on a relation between Xray-CT density and porosity to assign contact moduli between grains. We numerical derive the macroscopic effective elastic moduli of several reservoir rocks, and study their sensitivity to variations of contact moduli between grains in a parametric study.
Developing accurate relationships between pore structure or grain fabric and elastic properties of rocks is a long standing problem in geophysics. The elastic properties of porous rock depend strongly on microstructure. In the absence of full structural information, past attempts to incorporate structure have used rigorous bounds (Hashin and Shtrikman, 1962; Milton, 1981), effective medium theories (Berryman, 1980), simple deterministic models (Wyllie et al., 1956; Raymer et al., 1980), or empirical relationships (Han, 1986). Direct calculations of elastic properties of composite materials from high-resolution 3D images were presented by Garboczi and Day (1995); Roberts and Garboczi (1999); Arns et al. (2002); Knackstedt et al. (2006) for model composites, Fontainebleau sandstone, and industrial foams. These studies, using directly the 3D representations of structure, did consider either materials which are not granular, or well cemented sandstone, where the cement was considered to have the same elastic properties as the grains themselves. In general, the effective elastic properties of granular rock depend strongly on the stiffness of the grain-to-grain contacts (Leurer and Dvorkin, 2000). For larger applied strains, the number of grain contacts increases with increasing pressure (Makse et al., 1999) and grain slippage or cracking of grains could occur. Here, we are interested in the case of linear elastic responses under small applied strains, as characteristic for seismic wave propagation. The digital core group at ANU previously demonstrated the ability to directly measure rock fabric and texture from 3D images of core material and developed robust techniques for partitioning the grain space of a porous material (Saadatfar et al., 2005; Sheppard et al., 2005), in addition to large scale computation of physical properties, including elastic moduli. In this work we expand on our previous work on elastic properties of composite materials and use a combination of Xray-CT density maps, segmented phase fields and grain partitions to assign the elastic properties to the granular phase, and to the contact regions between grains. The purpose of this study is to highlight some of the issues involved in the calculation of elastic properties of non-ideal granular media from tomographic image data.
We discuss the phenomenon of ‘turning noise into signal’ (one of the main properties of seismic interferometry) in the light of changing worldviews, starting with the ordered view of the nineteenth century, via the chaotic world of the twentieth century, to the present view, in which the chaos is tamed.
Bournas, Nasreddine (Geotech Ltd.) | Gacem, Salah (Agence Nationale du Patrimoine Minier) | Fairhead, J. Derek (GETECH Group plc) | Hamoudi, Mohamed (Houari Boumediene University) | Galdeano, Armand (Institut de Physique du Globe de Paris.)
Plona, T. (Schlumberger Oilfield Services) | Valero, H-P. (Schlumberger Oilfield Services) | Bose, S. (Schlumberger Oilfield Services) | Walsh, J. (Schlumberger Oilfield Services) | Wielemaker, E. (Schlumberger Oilfield Services) | Saldungaray, P. (Schlumberger Oilfield Services)
Zishun, Li (Research Institute of E and D of Daqing Oilfield Ltd.,Co) | Xuebin, Guo (Research Institute of E and D of Daqing Oilfield Ltd.,Co) | Xingcai, Fan (Research Institute of E and D of Daqing Oilfield Ltd.,Co)
Telesca, Luciano (Institute of Methodologies for Environmental Analysis, National Research Council,Italy) | Lapenna, Vincenzo (Institute of Methodologies for Environmental Analysis, National Research Council,Italy) | Macchiato, Maria (Dipartimento di Scienze Fisiche, INFM, Universita¿ "Federico II", Naples, Italy) | Hattori, Katsumi (Department of Earth Sciences, Faculty of Science, Chiba University, Japan)
Ivanov, Julia (Kansas Geological Survey, Lawrence, KS) | Miller, Richard D. (Kansas Geological Survey, Lawrence, KS) | Xia, Jianghai (Kansas Geological Survey, Lawrence, KS) | Dunbar, Joseph B. (Engineer Research and Development Center, Vicksburg, MS)