From a computational point of view non uniform grids can be efficient for computing fluid flows because the grid resolution can be adapted to the spatial complexity of the flow problem. In this contribution an extension of the Finite-Difference Lattice-BGK method on nested grids is presented. This approach is based on multiple nested lattices with increasing resolution. Basically, the discrete velocity Boltzmann equation is solved numerically on each sub-lattice and interpolation between the interfaces is carried out in order to couple the sub-grids consistently. Preliminary results of the method applied on the Taylor vortex benchmark are presented.

Recently developed high resolution computed microtomography (CMT) using synchrotron X-ray sources is analogous to conventional medical CT scanning and provides the ability to obtain three-dimensional images of specimens with a spatial resolution on the order of micrometers. Application of this technique to the study of core samples has previously been shown to provide excellent two- and three- dimensional high resolution descriptions of pore structure and mineral distributions of core material. Recently, computed microtomographic endpoint saturation images of a fluid filled sandstone core sample were obtained using a microtomographic apparatus and a high energy X-ray beam produced by a superconducting wiggler at the National Synchrotron Light Source at Brookhaven National Laboratory. Images of a 6 mm subsection of the one inch diameter core sample were obtained prior and subsequent to flooding to residual oil. Both oil and brine phases were observable within the imaged rock matrix. The rock matrix image data was used as input to a fluid transport simulator and the results compared with the end point saturation images and data. These high resolution images of the fluid filled pore space have not been previously available to researchers and will provide valuable insight to fluid flow, and provide data as input into and validation of high resolution porous media flow simulators, such as percolation-network and lattice Boltzmann models.

The lattice Boltzmann (LB) method is applied to simulating multifluid flow in porous media at sub-pore resolution to determine constitutive behaviors. The authors address the importance of the LB technique for identifying process based constitutive relationships, and demonstrate its application through analysis of the influence of wettability on interfacial areas and constitutive relationships. Porous media surface wettability is varied from uniformly strongly wetted by the resident fluid through strongly wetted by the displacing fluid. Spatially variable wettability is also demonstrated. Primary imbibition and drainage displacements are run, and interfacial areas (IFA) as a function of time are determined and compared. Results indicate that wettability is an important factor in displacement behavior and resulting interfacial area. Primary imbibition in a strongly wet material under capillary dominated flows produces film flow, resulting in high IFAs that decrease with increasing saturation and viscous forces. Primary drainage produces initially high IFA that decreases slightly with increasing saturation or pressure drop. Surfaces with spatially variable wetting can have a strong influence on resulting fluid distributions and fluid flow.

Pore networks derived from synchrotron X-ray microtomographic images of reservoir rocks were used to provide realistic geometries for simulation of oil displacement by water. The Lattice Boltzmann Method was used to compute two-phase flow dynamics with constant pore geometry—but different pressure driving forces and imposed wettability distributions at the pore wall boundaries. Such examinations can be used to formulate more physically meaningful functional forms for multiphase flow relations to replace empirical constructs of relative permeability with only implicit dependencies on wettability and pore structure. Each simulation started with the same low initial water saturation distribution achieved by primary drainage network simulation in an initially strongly water-wet, reasonably homogeneous pore system. Mixed-wet scenarios were produced by altering the boundary conditions of those surfaces contacted by the non-wetting phase in the initial water distribution image. In one set of simulations comparing water-wet and mixed-wet boundary conditions, capillary numbers in the vicinity of 10−4 were not low enough for differences in wettability to give markedly different displacement dynamics. In a second set of simulations, as the driving force for flow was reduced further, we saw differences in the fluid distributions, but only minor changes in the relative permeabilities extracted from simulation output. The biggest difference between waterflood simulations with different wettabilities appears to be the additional recovery possible after breakthrough in the mixed-wet scenario. Capillary pressure, and not relative permeability, controls whether or not a particular saturation state can be observed. It is therefore concluded that capturing wettability effects in capillary pressure relations is probably more important than trying to roll such effects into relative permeability functions. Wettability is expected to play a more important role in heterogeneous systems.

M.E. Coles, SPE, R.D. Hazlett, and E.L. Muegge, Mobil E& P Technical Center, K.W. Jones, B. Andrews, B. Dowd, P. Siddons, and A. Peskin, Brookhaven National Laboratory, P. Spanne, European Synchrotron Facility, W.E. Soll, Los Alamos National LaboratoryAbstract. High resolution computed microtomography (CMT) using synchrotron X-ray sources provides the ability to obtain three-dimensional images of specimens with a spatial resolution on the order of micrometers. Microimaging capabilities at Brookhaven National Laboratory's National Synchrotron Light Source have been enhanced to provide larger and higher resolution 3-D renderings of pore networks in reservoir rocks at a fraction of the time required in previous first generation scanning methods. Such data are used to model single and multiphase flow properties in digital images of real porous media. Pore networks are analyzed for tortuosity and connectivity measures, which have been elusive parameters in transport property models. We present examples of porosimetry simulation via network modeling to produce initial water saturation and residual oil distributions in a water-wet pore system. Furthermore, pore networks can provide the boundary condition framework for more rigorous simulations of displacement, such as in the lattice Boltzmann simulated waterflood example provided. Direct comparison between simulation and experiment is also possible. CMT images of a 6 mm subsection of a one inch diameter reservoir core sample were obtained prior and subsequent to flooding to residual oil. The fluid distributions from CMT, lattice Boltzmann waterflood simulation, and percolation-based network modeling were found to be highly correlated. Advances in 3-D visualization, implemented in Brookhaven National Laboratory's 3-D theater, will allow even greater digestion and interpretation of phenomena dependent upon pore interconnectivity and multipore interactions.Introduction. Computed Microtomography (CMT) has been available at the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory for many years. First generation scanning methods gave high resolution images of geological and biological samples approaching 1 m resolution. First generation scanning provided necessary detail in moderate to high permeability porous media samples for transport property modeling with computational fluid dynamics methods. The time requirements of first generation methods limited the number of samples which could be investigated and restricted the potential of in-situ experimental monitoring. Implementation of array detection technology enables acquisition of larger 3-D volumes at a fraction of the time required in first generation scanning. Initial implementation, however, was limited by the resolution of fluorescing elements of the detector material, on the order of 10 m rather than 1 m. With the introduction of expansion optics, images of 2.7 m resolution have been obtained containing in the neighborhood of 3x 107 voxels. Improvements in data acquisition, transmission, and reconstruction have reduced the time requirements to produce such a volume to a few hours. Herein we document the status of CMT at the NSLS and display a variety of applications using both first generation and state-of-the-art image data on reservoir rock samples.Advances in Imaging. A schematic of the CMT apparatus is provided as Figure 1, X-ray CMT produces a cross-sectional map, or slice, of linear x-ray attenuation coefficients inside a small sample. To obtain the data for a reconstructed slice, the x-rays transmitted through a single slice of the sample are recorded on a linear array of detectors. The sample is rotated, with the axis of rotation perpendicular to the plane of the incident beam, by a discrete angular interval determined by the linear resolution desired. The transmission of each ray through the sample, along a line from the source to the detector is recorded; this represents a line integral of the attenuation coefficients along this ray. The procedure is repeated for each angular view until the sample has been rotated by 180 in the x-ray beam. P. 413

In response to renewed interest in studying processes in porous and fractured media at the microscale, 30 researchers from universities, national laboratories, and industry gathered recently for a workshop. The group presented, discussed, debated, and brainstormed ideas to encourage interdisciplinary communication and foster new collaboration among researchers.Current microscale research is driven by our limited ability to reliably measure and describe fluid movement, chemical reactions, and other porous media phenomena at the macroscopic (or continuum) scale level. Real breakthroughs that rigorously translate a knowledge of fundamental fluid behavior, complex mineral surface chemistry, or bacterial activity at the pore scale into better models of processes on a macroscopic scale are lacking. Rather than extending traditional models and approaches, researchers are considering how fundamental pore‐scale processes and physical properties are manifested at the continuum scale. Technological advances are allowing us to visualize, measure, simulate, and analyze processes within the pore spaces and discover their intrinsic relationships to macroscopic behavior.