Summary
X-ray computed microtomography (XMT) is used for high-resolution, nondestructive imaging and has been applied successfully to geologic media. Despite the potential of XMT to aid in formation evaluation, currently it is used mostly as a research tool. One factor preventing more widespread application of XMT technology is limited accessibility to microtomography beamlines. Another factor is that computational tools for quantitative image analysis have not kept pace with the imaging technology itself.
In this paper, we present a new grain-based algorithm used for network generation. The algorithm differs from other approaches because it uses the granular structure of the material as a template for creating the pore network rather than operating on the voxel set directly. With this algorithm, several advantages emerge: the algorithm is significantly faster computationally, less dependent on image resolution, and the network structure is tied to the fundamental granular structure of the material. In this paper, we present extensive validation of the algorithm using computer-generated packings. These analyses provide guidance on issues such as accuracy and voxel resolution. The algorithm is applied to two sandstone samples taken from different facies of the Frontier Formation in Wyoming, USA, and imaged using synchrotron XMT. Morphologic and flow-modeling results are presented.
Introduction
Subsurface transport processes such as oil and gas production are multiscale processes. The pore scale governs many physical and chemical interactions and is the appropriate characteristic scale for the fundamental governing equations. The continuum scale is used for most core or laboratory scale measurements (e.g., Darcy velocity, phase saturation, and bulk capillary pressure). The field scale is the relevant scale for production and reservoir simulation.
Multiscale modeling strategies aim to address these complexities by integrating the various length scales. While pore-scale modeling is an essential component of multiscale modeling, quantitative methods are not as well-developed as their continuum-scale counterparts. Hence, pore-scale modeling represents a weak link in current multiscale techniques.
The most fundamental approach for pore-scale modeling is direct solution of the equations of motion (along with other relevant conservation equations), which can be performed using a number of numerical techniques. The finite-element method is the most general approach in terms of the range of fluid and solid mechanics problems that can be addressed. Finite-difference and finite-volume methods are more widely used in the computational fluid dynamics community. The boundary element method is very well suited for low-Reynolds number flow of Newtonian fluids (including multiphase flows). Finally, the lattice-Boltzmann method has been favored in the porous-media community because it easily adapts to the complex geometries found in natural materials.
A less rigorous approach is network modeling, which gives an approximate solution to the governing equations. It requires discretization of the pore space into pores and pore throats, and transport is modeled by imposing conservation equations at the pore scale. Network modeling involves two levels of approximation. The first is the representation of the complex, continuous void space as discrete pores and throats. The second is the approximation to the fluid mechanics when solving the governing equations within the networks. The positive tradeoff for these significant simplifications is the ability to model transport over orders-of-magnitude larger characteristic scales than is possible with direct solutions of the equations of motion. Consequently, the two approaches (rigorous modeling of the conservation equations vs. network modeling) have complementary roles in the overall context of multiscale modeling. Direct methods will remain essential for studying first-principles behavior and subpore-scale processes such as diffusion boundary layers during surface reactions, while network modeling will provide the best avenue for capturing larger characteristic scales (which is necessary for modeling the pore-to-continuum-scale transition).
This research addresses one of the significant hurdles for quantitative network modeling: the use of high-resolution imaging of real materials for quantitative flow modeling. We focus in particular on XMT to obtain 3D pore-scale images, and present a new technique for direct mapping of the XMT data onto networks for quantitative modeling. This direct mapping (in contrast to the generation of statistically equivalent networks) ensures that subtle spatial correlations present in the original material are retained in the network structure.
Dynamic coupling of pore-scale and reservoir-scale models for multiphase flow