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.

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Fig. 1

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

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Fig. 2

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

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Fig. 3

The D3Q19 lattice velocity vectors model

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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)

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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)).

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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

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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.)

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Fig. 12

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

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Fig. 13

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

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Fig. 15

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

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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

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Fig. 5

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

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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

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Fig. 7

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

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Fig. 14

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



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