HR: 1340h
AN: MR23C-1514    [Abstracts]
TI: Transport Properties at Different Scales Using Digital Rocks
AU: * Richa, R
EM: richa7@pangea.stanford.edu
AU: Mukerji, T
EM: mukerji@pangea.stanford.edu
AF: Stanford University, Department of Geophysics 397 Panama Mall, Stanford, CA 94305, United States
AU: Mavko, G
EM: mavko@stanford.edu
AF: Stanford University, Department of Geophysics 397 Panama Mall, Stanford, CA 94305, United States
AB: In this paper we explore how rock heterogeneity translates into scale-dependent permeability and formation factor, as well as the relation between them. We used a detailed 3-D representation of pore structure of unconsolidated sand obtained from X-ray CT scan. For the samples, loose sand grains were collected from Pomponio Beach and Ano Nuevo costal dune (eolian). These loose sand grains were mixed with epoxy, packed and 3D images were digitized by High-resolution X-ray tomography (CT- scanning). Fluid flow and electrical current were computationally simulated through subsets of the microstructure at different scales. The autocorrelation lengths, a, of the entire sample were calculated in three different directions. The autocorrelation lengths show slight anisotropy in Z-direction in both samples. Since the anisotropy wasn't large so it wasn't considered further in the current analysis. Further, the anisotropy in Z-direction can be attributed to change in the resolution in Z-direction as the artifact of the 3D CT scans. The average autocorrelation, however, was used to calculate the Representative Elementary Volume (REV). Keehm (2003) suggested for single phase fluid flow the REV should be approximately ten times the autocorrelation length, a. Hence for the current analysis a REV of 200 x 200 x 200 pixels for the Pomponio Beach sands (a = 20 pixels) while a REV of 120 x 120 x 120 pixels for Aņo Nuevo costal dune sands (a = 12 pixels) were considered. The size of the subsets randomly selected from the microstructure varied from 200 x 200 x 200 pixels (= 10a x 10a x 10a) to 25 x 25 x 25 pixels (= 1.25a x 1.25a x 1.25a) for Pomponio Beach sands where as the size of the subsets for Aņo Nuevo costal dune sands altered from 175 x 175 x 175 pixels (= 14.5a x 14.5a x 14.5a) to 25 x 25 x 25 pixels (= 2.1a x 2.1a x 2.1a). The number of subsets selected for the analysis increased as the size of subset decreased in order to obtain statistically meaningful results. As can be observed the maximum size of subsets chosen was approximately equal to or greater than the REV of the sample. The size of subsets was significantly reduced from the REV sizes in order to study the effect of scales on the transport properties as well as the relationships between these transport properties. Electrical conductivity and single-phase permeability simulations were carried out for the subsets thus obtained. As the size of subsets decreased, the scatter in the computed permeability and resistivity increased although they still followed the expected trends of effective medium relations in each case. Different effective medium relations used to compare with the simulated data in current paper were: (a) For porosity-permeability relation: Kozeny- Carman relation (Carman, 1961), (b) For porosity-formation factor relation: Archie's equation (Archie, 1942) and (c) For permeability-formation factor: Katz and Thompson (Katz and Thompson, 1987). The clouds of the simulated data of different size subsets as well as their corresponding means tended towards a higher value as the size of subsets was decreased though they still fell on the effective medium trend line. However, the computational time required for calculating the bigger subset sizes was far greater than for smaller subset sizes.
DE: 0545 Modeling (4255)
DE: 0560 Numerical solutions (4255)
DE: 5114 Permeability and porosity
DE: 5139 Transport properties
SC: Mineral and Rock Physics [MR]
MN: 2007 Fall Meeting