Summary
For many rocks of high economic interest such as chalk, diatomite, shale, tight gas sands, or coal, a submicron-scale resolution is needed to resolve the 3D pore structure, which controls the flow and trapping of fluids in the rocks. Such a resolution cannot be achieved with existing tomographic technologies. A new 3D imaging method based on serial sectioning, which uses the focused-ion-beam (FIB) technology, has been developed. FIB technology allows for the milling of layers as thin as 10 nm by using accelerated gallium (Ga+) ions to sputter atoms from the sample surface. After each milling step, as a new surface is exposed, a 2D image of this surface is generated, and the 2D images are stacked to reconstruct the 3D pore structure. Next, the maximum-inscribed-spheres (MIS) image-processing method computes the petrophysical properties by direct morphological analysis of the pore space. The computed capillary pressure curves agree well with laboratory data. Applied to the FIB data, this method generates the fluid distribution in the chalk pore space at various saturations.
Introduction
Field-scale oil-recovery processes are the result of countless events happening in individual pores. To model multiphase flow in porous media at pore scale, the resolution of the 3D images must be adequate for the rock of interest. Chalk formations in the oil fields of Texas, the Middle East, the North Sea, and other areas hold significant oil reserves. The extremely small typical pore sizes in chalk impose very high requirements on imaging resolution. In the last decade, X-ray microtomography has been used extensively for direct visualization of the pore system and the fluids within sandstone (Jasti et al. 1993; Coles et al. 1998; Wildenschild et al. 2003; Seright et al. 2003). While this approach is fast and nondestructive, its applicability is limited mostly to micron resolutions, although recent developments are bringing the resolution to submicron range (Stampanoni et al. 2002). For chalk pore systems, which are characterized by submicron- to nanometer-length scales, 3D stochastic methods based on 2D scanning-electron-microscope (SEM) images of thin sections have been used to reconstruct the pore system (Talukdar et al. 2001).
The advent of FIB technology has it made possible to reconstruct submicron 3D pore systems for diatomite and chalk (Tomutsa and Radmilovic 2003) (Fig. 1). FIB technology is used in microelectronics to access individual components with nanoscale accuracy for design verification, failure analysis, and circuit modification (Orloff et al. 2002). FIB has been used in material sciences for sectional sample preparation for SEM and for 3D imaging of alloy components (Kubis et al. 2004). In earth sciences, the FIB also has been used for sample preparation for SEM and to access inner regions for performing microanalysis (Heaney et al. 2001).To access the pore structure at submicron scale, the FIB mills successive layers of the rock material as thin as 10 nm. As successive 2D surfaces are exposed, they are imaged with either the electron or the ion beam. After processing, the images are stacked to reconstruct the 3D pore structure. The geometry of the pore space of the obtained structure can be analyzed further to estimate petrophysical rock properties through computer simulations. To analyze the 3D chalk images obtained by the FIB method, we applied the MIS technique (Hazlett 1995; Silin et al. 2003, 2004; Silin and Patzek 2006). The MIS method analyzes the 3D pore-space image directly, without construction of pore networks. It bypasses the nontrivial task of extracting a simple but representative network of pore throats linking pore bodies from the 3D data (Lindquist 2002). Moreover, the pore-network extraction methods, which are based on relatively simple grain and pore shapes in sandstones (Øren and Bakke 2002), may not always be feasible for the complex pore structures of carbonates. Although a pore-network-based flow-modeling approach enjoyed a significant interest from the researchers and resulted in theoretically and practically sound conclusions (Øren et al. 1998; Xu et al. 1999; Patzek 2001; Blunt 2001), we believe that direct pore-space analysis deserves more attention. In addition, direct analysis of the pore space provides an opportunity to study alteration of the rock flow properties (e.g., those resulting from mechanical transformations or mineralization) (Jin et al. 2003).
A Probabilistic Formulation of the Diffusion Coefficient in Porous Media as Function of Porosity
