0
Research Papers: Petroleum Engineering

A New Method of Porous Space Reconstruction Using Multipoint Histogram Technology

[+] Author and Article Information
Na Zhang

Petroleum Engineering,
Texas A&M University at Qatar,
Education City,
P.O. Box 23874,
Doha, Qatar
e-mail: na.zhang@qatar.tamu.edu

Qian Sun

Petroleum Engineering,
Texas A&M University at Qatar,
Education City,
P.O. Box 23874
Doha, Qatar e-mail: qian.sun@qatar.tamu.edu

Mohamed Fadlelmula

Petroleum Engineering,
Texas A&M University at Qatar,
Education City,
P.O. Box 23874
Doha, Qatar e-mail: mohamed.fadlelmula@qatar.tamu.edu

Aziz Rahman

Petroleum Engineering,
Texas A&M University at Qatar,
Education City,
P.O. Box 23874
Doha, Qatar e-mail: marahman@tamu.edu

Yuhe Wang

Petroleum Engineering,
Texas A&M University at Qatar,
Education City,
P.O. Box 23874
Doha, Qatar e-mail: yuhe.wang@qatar.tamu.edu

1These authors contributed equally to this work.

2Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received January 30, 2017; final manuscript received October 31, 2017; published online November 28, 2017. Assoc. Editor: Daoyong (Tony) Yang.

J. Energy Resour. Technol 140(3), 032909 (Nov 28, 2017) (12 pages) Paper No: JERT-17-1046; doi: 10.1115/1.4038379 History: Received January 30, 2017; Revised October 31, 2017

Pore-scale modeling is becoming a hot topic in overall reservoir characterization process. It is an important approach for revealing the flow behaviors in porous media and exploring unknown flow patterns at pore scale. Over the past few decades, many reconstruction methods have been proposed, and among them the simulated annealing method (SAM) is extensively tested and easier to program. However, SAM is usually based on the two-point probability function or linear-path function, which fails to capture much more information on the multipoint connectivity of various shapes. For this reason, a new reconstruction method is proposed to reproduce the characteristics of a two-dimensional (2D) thin section based on the multipoint histogram. First, the two-point correlation coefficient matrix will be introduced to determine an optimal unit configuration of a multipoint histogram. Second, five different types of seven-point unit configurations will be used to test the unit configuration selection algorithm. Third, the multipoint histogram technology is used for generating the porous space reconstruction based on the prior unit configuration with a different calculation of the objective function. Finally, the spatial connectivity, patterns reproduction, the local percolation theory (LPT), and hydraulic connectivity are used to compare with those of the reference models. The results show that the multipoint histogram technology can produce better multipoint connectivity information than SAM. The reconstructed system matches the training image very well, which reveals that the reconstruction captures the geometry and topology information of the training image, for instance, the shape and distribution of pore space. The seven-point unit configuration is enough to get the spatial characters of the training image. The quality of pattern reproduction of the reconstruction is assessed by computing the multipoint histogram, and the similarity is around 97.3%. Based on the LPT analysis, the multipoint histogram can describe the anticipated patterns of geological heterogeneities and reproduce the connectivity of pore media with a high degree of accuracy. The two-point correlation coefficient matrix and a new construction theory are proposed. The new construction theory provides a stable theory and technology guidance for the study of pore space development and multiphase fluid flow rule in the digital rock.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Yue, W. , and Wang, J. Y. , 2015, “ Feasibility of Waterflooding for a Carbonate Oil Field Through Whole-Field Simulation Studies,” ASME J. Energy Resour. Technol., 137(6), p. 064501. [CrossRef]
Wang, W. D. , Shahvali, M. , and Su, Y. L. , 2017, “ Analytical Solutions for a Quad-Linear Flow Model Derived for Multistage Fractured Horizontal Wells in Tight Oil Reservoirs,” ASME J. Energy Resour. Technol., 139(1), p. 012905. [CrossRef]
Shirman, E. , Wojtanowicz, A. K. , and Kurban, H. , 2014, “ Enhancing Oil Recovery With Bottom Water Drainage Completion,” ASME J. Energy Resour. Technol., 136(4), p. 042906. [CrossRef]
Zhou, D. Y. , and Yang, D. Y. , 2017, “ Scaling Criteria for Waterflooding and Immiscible CO2 Flooding in Heavy Oil Reservoirs,” ASME J. Energy Resour. Technol., 139(2), p. 022909. [CrossRef]
Caers, J. , 2001, “ Geostatistical Reservoir Modelling Using Statistical Pattern Recognition,” J. Pet. Sci. Eng., 29(3–4), pp. 177–188. [CrossRef]
Yu, J. , Armstrong, R. T. , Ramandi, H. L. , and Mostaghimi, P. , 2016, “ Coal Cleat Reconstruction Using Micro-Computed Tomography Imaging,” Fuel, 181, pp. 286–299. [CrossRef]
Liu, X. F. , Sun, J. M. , Wang, H. T. , and Yu, H. W. , 2009, “ The Accuracy Evaluation on 3D Digital Cores Reconstructed by Sequence Indicator Simulation,” Acta Pet. Sin., 30, pp. 391–395. http://en.cnki.com.cn/Article_en/CJFDTOTAL-SYXB200903014.htm
Zhao, X. C. , Yao, J. , and Yi, Y. J. , 2007, “ A New Stochastic Method of Reconstructing Porous Media,” Transp. Porous Media, 69(1), pp. 1–11. [CrossRef]
Okabe, H. , and Blunt, M. J. , 2007, “ Pore Space Reconstruction of Vuggy Carbonates Using Microtomography and Multiple-Point Statistics,” Water Resour. Res., 43(12), p. W12S02. [CrossRef]
Jing, Y. , Armstrong, R. T. , and Mostaghimi, P. , 2017, “ Rough-Walled Discrete Fracture Network Modelling for Coal Characterisation,” Fuel, 191, pp. 442–453. [CrossRef]
Xu, Z. , Teng, Q. Z. , He, X. H. , and Li, Z. J. , 2013, “ A Reconstruction Method for Three-Dimensional Pore Space Using Multiple-Point Geology Statistic Based on Statistical Pattern Recognition and Microstructure Characterization,” Int. J. Numer. Anal Methods Geomech., 37(1), pp. 97–110. [CrossRef]
Liu, X. H. , Srinivasan, S. , and Wong, D. , 2002, “ Geological Characterization of Naturally Fractured Reservoirs Using Multiple Point Geostatistics,” SPE/DOE Improved Oil Recovery Symposium, Tulsa, OK, Apr. 13–17, SPE Paper No. SPE-75246-MS.
Yao, J. , Wang, C. C. , Yang, Y. F. , and Yan, X. , 2012, “ A Stochastic Upscaling Analysis for Carbonate Media,” ASME J. Energy Resour. Technol., 135(2), p. 022901. [CrossRef]
Bryant, S. , and Blunt, M. , 1992, “ Prediction of Relative Permeability in Simple Porous Media,” Phys. Rev. A, 46, pp. 2004–2011. [CrossRef] [PubMed]
Safavisohi, S. R. F. B. , and Sharbati, E. , 2007, “ Porosity and Permeability Effects on Centerline Temperature Distributions, Peak Flame Temperature, Flame Structure, and Preheating Mechanism for Combustion in Porous Media,” ASME J. Energy Resour. Technol., 129(1), pp. 54–65. [CrossRef]
Strebelle, S. , 2002, “ Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics,” Math. Geol., 34(1), pp. 1–21. [CrossRef]
Yeong, C. L. Y. , and Torquato, S. , 1998, “ Reconstructing Random Media—II: Three-Dimensional Media From Two-Dimensional Cuts,” Phys. Rev. E, 58, pp. 224–233. [CrossRef]
Joshi, M. Y. , 1974, “ A Class of Stochastic Models for Porous Media,” Ph.D. dissertation, University of Kansas, Lawrence, KS.
Keehm, Y. , Mukerji, T. , and Nur, A. , 2004, “ Permeability Prediction From Thin Sections: 3D Reconstruction and Lattice-Boltzmann Flow Simulation,” Geophys. Res. Lett., 31(4), p. L04606. [CrossRef]
Guardiano, F. , and Srivastava, R. M. , 1993, Multivariate Geostatistics: Beyond Bivariate Moments, Vol. 1, Kluwer, Dordrecht, The Netherlands, pp. 133–144.
Strebelle, S. , and Cavelius, C. , 2014, “ Solving Speed and Memory Issues in Multiple-Point Statistics Simulation Program SNESIM,” Math. Geosci., 46, pp. 171–186. [CrossRef]
Hajizadeh, A. , Safekordi, A. , and Farhadpour, F. A. , 2011, “ A Multiple-Point Statistics Algorithm for 3D Pore Space Reconstruction From 2D Images,” Adv. Water Resour., 34(10), pp. 1256–1267. [CrossRef]
Okabe, H. , and Blunt, M. J. , 2004, “ Prediction of Permeability for Porous Media Reconstructed Using Multiple-Point Statistics,” Phys. Rev. E, 70(6), p. 066135. [CrossRef]
Tahmasebi, P. , and Sahimi, M. , 2012, “ Reconstruction of Three-Dimensional Porous Media Using a Single Thin Section,” Phys. Rev. E, 85(6), p. 066709. [CrossRef]
Hajizadeh, A. , and Farhadpour, Z. , 2012, “ An Algorithm for 3D Pore Space Reconstruction From a 2D Image Using Sequential Simulation and Gradual Deformation With the Probability Perturbation Sampler,” Transp. Porous Media, 94(3), pp. 859–881. [CrossRef]
Naraghi, M. E. , Spikes, K. , and Srinivasan, S. , 2016, “ 3-D Reconstruction of Porous Media From a 2-D Section and Comparisons of Transport and Elastic Properties,” SPE Western Regional Meeting, Anchorage, AK, May 23–26, SPE Paper No. SPE-180489-MS.
Farmer, C. L. , 1989, “ The Mathematical Generation of Reservoir Geology,” Joint IMA/SPE European Conference on the Mathematics of Oil Recovery, Cambridge, UK, July 25–27, pp. 1–12.
Qiu, W. Y. , and Kelkar, M. G. , 1995, “ Simulation of Geological Models Using Multipoint Histogram,” SPE Annual Technical Conference & Exhibition, Dallas, TX, Oct. 22–25, SPE Paper No. SPE-30601-MS.
Metropolis, N. , Rosenbluth, A. W. , Rosenbluth, M. N. , Teller, A. H. , and Teller, E. , 1953, “ Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys., 21, pp. 1087–1092. [CrossRef]
Honarkhah, M. , and Caers, J. , 2010, “ Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling,” Math. Geosci., 42(5), pp. 487–517. [CrossRef]
Hilfer, R. , 1992, “ Local-Porosity Theory for Flow in Porous Media,” Phys. Rev. E, 45, pp. 7115–7121. [CrossRef]
Hilfer, R. , 2002, “ Review on Scale Dependent Characterization of the Microstructure of Porous Media,” Transp. Porous Media, 46(2–3), pp. 373–390. [CrossRef]
Mei, R. W. , Luo, L. S. , and Shyy, W. , 1999, “ An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method,” J. Comput. Phys., 155(2), pp. 307–330. [CrossRef]
Okabe, H. , and Blunt, M. J. , 2005, “ Pore Space Reconstruction Using Multiple-Point Statistics,” J. Pet. Sci. Eng., 46(1–2), pp. 121–137. [CrossRef]
Liang, Z. R. , Fernandes, C. P. , Magnani, F. S. , and Philippi, P. C. , 1998, “ A Reconstruction Technique for Three-Dimensional Porous Media Using Image Analysis and Fourier Transforms,” J. Pet. Sci. Eng., 21(3–4), pp. 273–283. [CrossRef]
Hu, J. , and Stroeven, P. , 2005, “ Local Porosity Analysis of Pore Structure in Cement Paste,” Cem. Concr. Res., 35(2), pp. 233–242. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Configuration for multipoint histogram example and (b) 16 possible combinations of four-point unit configuration

Grahic Jump Location
Fig. 2

(a) Part examples of contiguous four-point template and (b) part examples of noncontiguous four-point template

Grahic Jump Location
Fig. 3

The D3Q19 lattice velocity vectors model

Grahic Jump Location
Fig. 4

(a) Digital image of a thin section containing 200 × 200 pixels and (b) the entropy of the training image as a function of template size

Grahic Jump Location
Fig. 5

Different types of seven-point unit configuration chosen for the generation (The black pixel represents the center of the correlation coefficient matrix.)

Grahic Jump Location
Fig. 6

A simple transition diagram from the training image to the simulated reconstruction: (a) training image with the porosity of 0.159, (b) the structure of the initial random generation, and (c) reconstructed image by using multipoint histogram technology

Grahic Jump Location
Fig. 7

Comparison between (a) the original image (ϕ = 0.159) and (b) the smoothed image (ϕ = 0.161) after the noise canceling process

Grahic Jump Location
Fig. 8

Generated constructions with different types of seven-point unit configuration: (a) simulated image using unit configuration in Fig. 5(a), (b) simulated image using unit configuration in Fig. 5(b), (c) simulated image using unit configuration in Fig. 5(c), (d) simulated image using unit configuration in Fig. 5(d), and (e) simulated image using unit configuration in Fig.5(e)

Grahic Jump Location
Fig. 9

Comparison of autocorrelation and lineal-path properties for training image and simulated images. (Simulated Image_a using unit configuration in Fig. 5(a); Simulated Image_b using unit configuration in Fig. 5(b); and Simulated Image_e using unit configuration in Fig.5(e)).

Grahic Jump Location
Fig. 10

(a) Autocorrelation function for training image in the x and y directions, (b) autocorrelation function of the training image and reconstructed one in the x direction, and (c) autocorrelation function of the training image and reconstructed one in the y direction

Grahic Jump Location
Fig. 11

Comparison of the porosity distribution in the 30 reconstructed generations with that of training image (The dot line represents the porosity of the training image.)

Grahic Jump Location
Fig. 12

Local porosity distribution for different samples with side length L = 375 μm

Grahic Jump Location
Fig. 13

Local porosity distribution for different samples with side length L = 500 μm

Grahic Jump Location
Fig. 14

Local percolation probability for different samples with side length L = 125 μm

Grahic Jump Location
Fig. 15

Local percolation probability for different samples with side length L = 250 μm

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In