Transport Properties of Porous Media Reconstructed From Thin-Sections
- I. Hidajat (U. of Houston) | A. Rastogi (U. of Houston) | M. Singh (U. of Houston) | K.K. Mohanty (U. of Houston)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2002
- Document Type
- Journal Paper
- 40 - 48
- 2002. Society of Petroleum Engineers
- 5.3.4 Integration of geomechanics in models, 5.3.1 Flow in Porous Media, 1.2.3 Rock properties, 5.3.2 Multiphase Flow, 5.1 Reservoir Characterisation, 1.14 Casing and Cementing, 5.6.2 Core Analysis, 1.6.9 Coring, Fishing, 5.1.5 Geologic Modeling, 5.6.4 Drillstem/Well Testing, 5.5.2 Core Analysis, 5.6.1 Open hole/cased hole log analysis, 4.3.4 Scale
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The objective of this work is to predict transport properties within any complex porous medium from its 2D microimage. 3D porous media are generated that have the same porosity, autocorrelation, chord length distribution, and lineal path function as a given 2D microimage of a medium. The properties of the reconstructed media are compared with those of the original media. A pore skeleton and Euclidean distance map are determined for the 3D pore-space from which body radius, throat radius, and connectivity distributions are extracted. This network structure is used in calculation of transport properties. Specific surface area is estimated accurately. Permeability and formation factor are estimated approximately. The correlations between adjacent pore bodies and throats are identified.
Formation evaluation is an important task in the development of oil and gas reservoirs. It involves many operations such as seismic, well testing, logging, and core analysis. Of all these methods, core analysis has the highest spatial resolution. Cores are analyzed for their transport properties such as permeability, relative permeability, capillary pressure, and electrical conductivity, etc. These tests are performed only on a few cores because these experiments are expensive and time-consuming.1
In the past, several pore-scale mechanistic techniques have been developed to relate pore structure to macroscopic transport properties of porous media (e.g., Lattice-Boltzmann method2,3) and network models.4-6 Lattice-Boltzmann method starts with a particulate description of fluids, and Boltzmann transport equation is solved with specific collision rules that approximate Navier- Stokes equation on an average. This method readily lends itself to parallelization and is effective in describing single-phase flow through complex geometries.7 This method is still very computationally intensive for multiphase flow through porous media.2 Network models idealize the pore space as a network of pore bodies or junctions interconnected by pore throats or bonds.8 Given the pore-level displacement physics9 in each body and throat, one can compute single phase10 and multiphase transport properties of a medium.11 Percolation theory can be used if pseudostatic invasions are modeled in idealized regular networks.12 These techniques have been successful in estimating the trends of transport properties of porous media.13,14 They have been successful quantitatively only for a few cases15-17 in which detailed pore geometry is available. In many applications in the past, the detailed 3D pore structure has not been available.
It is possible to get the 3D pore structure of a porous rock by serial sectioning,8,18 X-ray microtomography,19,20 and image reconstruction. 21-24 Serial sectioning involves imaging hundreds of polished sections of a porous rock and is performed rarely because it is very time-consuming. Microtomography (or micro CT) uses synchrotron X-ray sources and is thus not routinely available. Image reconstruction involves generation of a 3D pore structure from a 2D image of a thin-section. Thin-sections are often taken from formation cores and imaged for geological evaluation, such as mineralogy and sorting. Thin-section images are seldom used to estimate formation transport properties. If a reliable method can be developed to reconstruct 3D pore structures from their 2D sectional images, then thin-sections can be used to estimate transport properties.
Two methods have been developed in the past for porous media reconstruction: process-based16,17 and statistics-based.21-24 In the process-based method, thin-section images are analyzed to determine the grain diameter distribution. Sedimentation of these spherical grains is then simulated, followed by a certain amount of compaction. This simulated pore space is further modified for quartz cement overgrowth and clay coating. It is a mechanistic method, and initial results appear promising.17 Its limitation lies in the presumed spherical shape of the particles. The statistics-based method does not make any assumptions about the shapes of particles. Certain spatial statistics of the 2D image are measured, and a 3D medium is generated that reproduces those statistics.21-24 If accurate, this reconstruction technique offers a fast and viable way to generate realistic porous media.
An infinite set of statistical functions (e.g., n-point correlation functions, n=1, 2, 3 . . . ) is needed to represent a porous medium exactly. However, the time of computation makes this scheme impractical. The key challenge for the statistical method of porous media reconstruction is selecting appropriate statistical properties or functions that can capture important features of the porous media without excessive amounts of computation. The 3D reconstruction is considered successful if it has transport properties similar to the experimental values determined for a core sample.
There are essentially two statistical function reconstruction techniques available in the literature. The first method is called a linear combination method and is described in detail in the next section.21 This method generates media that match only one- and two-point correlation functions with those of the 2D images. This method does not work well for low-porosity media; a lot of isolated porosity is generated. The second method is a simulated annealing method.22,23 One starts with a random initial field and allows modifications that lower the error in statistical functions to be matched. Here it is possible to include as many statistical functions or properties as desired. However, as more functions are included, the simulated annealing method requires more computation. The minimum set of statistical functions needed to capture the essential structure of porous media is not clear. Roberts24 employed two-point autocorrelation and chord-distribution functions to reconstruct random isotropic composite materials. Yeong and Torquato23 had included one-point pore correlation function (porosity), two-point pore-pore correlation function, and lineal path length distribution to reconstruct Fontainebleau sandstone. It was shown that the combination of two-point autocorrelation function and lineal path function gave better macroscopic properties such as permeability. Hazlett22 showed that one- and two-point correlation functions were not sufficient to reproduce the connectivity of the medium. His results may have been affected by the limited size of the simulated media. Hazlett22 included primary drainage capillary pressure information to improve the connectivity of the simulated media, but the computation time was excessive.
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