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Multifractal study of three-dimensional pore structure of sand-conglomerate reservoir based on CT images You Zhou, Songtao Wu, Zhiping Li, Rukai Zhu, Shuyun Xie, Cheng Jing, and Lei Lei Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00057 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 1, 2018
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Multifractal study of three-dimensional pore structure of sand-conglomerate reservoir based on CT images You Zhou, †, ‡, § Songtao Wu,*, † Zhiping Li, ‡, § Rukai Zhu, † Shuyun Xie, # Cheng Jing, £ and Lei Lei # †
Petrochina Research Institute of Petroleum Exploration & Development, Beijing 100083, China
‡
School of Energy resource, China University of Geosciences(Beijing) , Beijing 100083, China
§
Beijing key laboratory of unconventional natural gas geological evaluation and development engineering ,
Beijing 100083, China #
Earth Science Faculty, China University of Geosciences(Wuhan), Wuhan 430000, Hubei Province, China;
£
School of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710000, Shanxi Province, China;
ABSTRACT Sand-conglomerate reservoir has been scarcely studied, and there is no effective method available for quantitative characterization of pore structure of such reservoir. In this paper, a multifractal study was made on the Triassic Karamay Formation sand-conglomerate reservoir in the Mahu rim region, the Junggar Basin, by using a variety of high-resolution analysis methods, such as Micro-CT, QEMSCAN and MAPS, in order to quantitatively characterize the heterogeneity of pore size distribution, relative differentiation of large and small pores, and mineral composition. The results reveal that the multifractal parameters have more
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influence on permeability than on porosity. The smaller the ∆α (the multifractal spectral width) and the larger the ∆ƒ (the difference in fractal dimension of the maximum and minimum probability subsets), the better the reservoir physical property. To some extent, the relationship between multifractal parameter and mineral composition provides an opportunity to reflect the diagenesis. There is a positive correlation between the clay mineral content and the heterogeneity of the microscopic pore structure of reservoir. Kaolinite and chlorite cementations are the most significant factors that damage the reservoir pore space. This understanding matches well with the MAPS and QEMSCAN results. With outstanding advantage in quantitatively evaluating the heterogeneity of pore structure of sand-conglomerate reservoir, multifractal provides a new idea and method for quantitative characterization of pore structure of other heterogeneous oil reservoirs.
1. INTRODUCTION Sand-conglomerate reservoir is usually characterized by low economic benefit, high exploration cost, great development challenges and low hydrocarbon abundance
1-2
. It has not
been extensively concerned around the world, and not as systematically and thoroughly investigated as conventional sandstone reservoir. In recent years, the successful breakthrough made in the Triassic sand-conglomerate reservoir in the Mahu rim region of the Junggar Basin, China, has unleashed a wave of studies on sand-conglomerate reservoir. However, current studies on tight sand-conglomerate reservoirs mainly involves the tectonic evolution analysis, hydrocarbon-accumulation controlling factor analysis, sedimentary system and other aspects3-6. There is no effective method available for quantitative evaluation of pore structure of tight sandconglomerate reservoir 7. For years, the scholars attempted to characterize the complex pore structure features of
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reservoir with a variety of methods and built corresponding pore models. However, traditional statistical method is not sufficient for quantitative characterization of spatial distribution of rock pores which are irregularly natural and complex. The introduction of the multifractal theory
8-9
provides a powerful tool to precisely and quantitatively study the chaotic complex system in the natural world and has attracted significant attentions of various disciplines. Wong et al. 10 proved for the first time that the pores in sandstone are of fractal characteristics by using the environment scanning electron microscope. Deng et al.
11
and Norbisrath et al.
12
presented a
measurement of fractal dimensions by investigating the fractal characteristics of pore structure of carbonate reservoir and suggested that the fractal dimension ranges from 2 to 3. With the development of the fractal geometry, Essex et al. 13, Hargis et al. 14, Hargrove et al. 15
, Sun et al. 16 and Ge et al. 17 proposed that precise characterization of a complex and variable
fractal requires more than one fractal dimension. This enabled the introduction of “multifractal”. The multifractal spectral function provides an opportunity to characterize a complex fractal at different positions and levels. Xie et al. 18 investigated the fractal and multifractal characteristics of pore structure of carbonate reservoir and proposed that multifractal enables effective quantitative characterization of complexity of pore structure. Stach et al.
19-20
used multifractal
method to characterize the fracture morphology, relating the span of a multifractal spectrum to the fracture shape. Li et al.
21
computed the multifractal parameters using 2D casting thin
sections and defined the relationship between the parameters and the geometric mean of NMR T2. While the fractal and multifractal theories have been applied broadly to the studies of microscopic pore structure, these studies are based mainly on 2D images 22. In contrast, 3D pore structure provides a more comprehensive and realistic reflection of the pore space in real samples,
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and hence can exploit more valid information that is neglected by 2D images. In this paper, with the Micro-CT data cube as a core and the multifractal theory as a guidance, the multifractal spectra in 3D space is computed by programming with MATLAB (R2014a) in order to quantitatively characterize the multifractal of 3D pore space. Then, QEMSCAN and MAPS are utilized to identify the relationship between the multifractal parameters and the relative mineral content, for the purpose of improving the application of the multifractal theory in the petroleum geology sector.
2. EXPERIMENTS AND METHODS 2.1 Samples The Mahu rim region is located at the northwestern margin of the Junggar Basin geographically, and in the Wu-Xia fault belt and the southeastern part of the Ke-Bai fault belt structurally. It is a petroleum-rich range and major production area in the Xinjiang Oilfield. The primary target layer is the Karamay Formation, which ranges from 200 to 300 m thick and consists of two members, i.e. Lower Karamay and Upper Karamay. Clastic reservoirs in the study area are dominated by fan delta sand-conglomerate, with low textural and composition maturities
23
. The Karamay Formation sand-conglomerate, with average porosity of 8% and
average permeability of less than 1 mD, can be classified as typical extra-low porosity and extralow permeability reservoir. Table 1 shows the tested conventional physical properties of 15 typical sand-conglomerate samples of the Karamay Formation recovered from the Mahu rim region. The porosity ranges from 7.4% to 14% with an average value of 11.02%, and the permeability ranges from 0.0054mD to 1.2mD with an average value of 0.33 mD. Having a relatively high average porosity but an extremely low permeability indicates that the pore connectivity of Karamay Formation is poor, which may results from the strong heterogeneity of
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pore structures. Table 1 Physical properties of typical sand-conglomerate samples Sample No.
Lithology
Depth / m
Porosity / %
Permeability / mD
B64-16
Medium conglomerate
2484.5
7.8
0.05
B64-29-1
Fine sandstone
2644.4
10
0.03
B64-29-2
Fine sandstone
2644.4
12.1
0.033
B64-3-1
Fine conglomerate
2303.1
11.3
0.183
B64-3-2
Fine conglomerate
2303.1
10.58
0.14
B64-33-1
Fine conglomerate
2655.1
14
0.4
B64-33-2
Fine conglomerate
2655.1
14
0.5
B64-36
Medium-coarse sandstone
2665.8
13.3
0.395
B64-38-1
Medium-coarse sandstone
2678.5
13.5
1.2
B64-38-2
Medium-coarse sandstone
2678.5
9.5
0.551
B64-4
Medium conglomerate
2304
12.9
0.329
B64-42
Fine conglomerate
2685.7
8.8
0.45
B64-43-1
Fine conglomerate
2686
10.6
0.6
M101-2-2
Pebbly coarse sandstone
3366.6
9.5
0.072
M5-6
Medium-coarse sandstone
3373.95
7.4
0.0054
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Fig. 1 Core photos and major pore types of sand-conglomerate reservoirs in the study area a. B64-38-1, medium-coarse sandstone; b. M101-2-2, pebbly coarse sandstone; c. B64-4, conglomerate; d. B64-36, primary intergranular pore, Micro-CT 2D grayscale slice; e. B64-382, intergranular dissolved pore, Micro-CT 2D grayscale slice; f. B64-42, intragranular dissolved pore, Micro-CT 2D grayscale slice; g. M5-6, intercrystalline pore of clay mineral, MAPS imaging analysis; h. B64-29-1, nano-scale microfracture, MAPS imaging analysis; i. B64-42, feldspar dissolution, casting thin section, plane-polarized light
2.2 Experiments High-resolution scanning tests, including Micro-CT, QEMSCAN and MAPS, were conducted on all 15 typical sand-conglomerate samples by the Petroleum Geological Experiment & Research Center of PetroChina Research Institute of Petroleum Exploration and Development. 2.2.1 Micro-CT The XRM-400 CT scanner manufactured by Carl Zeiss (Germany), with the maximum
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resolution of 0.7 µm/pixel, was used. The 16-bit CCD camera used as the detector has the grayscale of 65536 (i.e. 216). Avizo Fire 9.0, a professional image processing software, was used for display, analysis and quantitative computation of 3D images. The resolution of Micro-CT scanning is irreconcilable to the vision of study. During the trial scanning, the resolution was defined as 2 µm for realizing the best match between the resolution and the vision of study. The diameter of the core samples to be tested is 2 mm, the designed voltage is 60 kV, the power is 5 W, and the field of view is 2 mm × 2 mm. All samples were scanned under the same parameter setting. For every sample, about 1004 2D CT slices with the resolution of 1024 pixels × 1024 pixels were acquired. A 3D pore model (Fig.3) was built after the image cropping, filtering and binarization of 2D slices (Fig.2).
(a) Selecting the range of study
(b) Original 2D slice
(c) Slice after filtering
(d) Binarization
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Fig. 2 Processing of original 2D slice of Micro-CT
(a) B64-33-1
(b) B64-38-1
(c) B64-3-1
(d) M101-2-2
Fig. 3 3D pore model of CT scanning for typical sand-conglomerate samples
2.2.2 QEMSCAN QEMSCAN is a mineral auto-identification system that utilizes the point-by-point spectral scanning function to run scanning and stitching of multiple fields of view on a one-to-one basis, thereby identifying minerals over a large area. This method eliminates the human influences and enhances the precision of reservoir petrographic study (Fig. 4). In this study, Qunta 450 field emission scanning electron microscope manufactured by FEI was used. This instrument allows simultaneous testing of two samples. Every sample was scanned with 9 fields of view. The total size of field of view is 3 mm × 3 mm, the resolution is 2.9 µm and the length of testing speech is
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14 h per sample.
Fig.4 QEMSCAN quantitative analysis result of Sample M5-6
2.2.3 MAPS MAPS is an image stitching technique that scans the selected study area to generate hundreds to thousands of small images with very high resolution (as high as 10 nm) and identical pixel size and then stitches and combines these small images under the pre-set parameter to form a 2D back-scattered electron (BSE) image that has high resolution and covers a large area (Fig. 5). The utilization of MAPS allows the continuous characterization of the sand-conglomerate reservoir space from the nano-scale to the micron-scale and the millimeter-scale. With the combination of the QEMSCAN quantitative in-situ scanning, MAPS can provide an important basis for studying the heterogeneity, microscopic pore structure and mineral occurrence of the sand-conglomerate reservoir.
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Fig. 5 MAPS image a. MAPS 2D BSE image, Zone I shows the kaolinite cement; b. Zoom-in of Zone I; c, Zoom-in of Zone II; d. Zoom-in of Zone III
In this study, totally 660 small images with high-resolution were scanned. The pixel size of the stitched image is 30000 pixels × 28000 pixels, the total size of the field of view is 2.7 mm × 2.5 mm, the resolution reaches 15 nm and the length of testing speech is 12 h per sample. The Hellios Nanolab 650 field emission scanning electron microscope manufactured by FEI was used. The Microsoft HD View plug-in is required for displaying the scanning result. 2.3 Multifractal methods 2.3.1 The concept of multifractal Let F be a set of the d-dimensional Euclidean space Rd, a support of measure P. As for a zone small enough, under a certain division regulation, the heterogeneity of the partial measure P follows the power-law distribution feature with exponent α. If δ→0, the following formula is obtained 16: P(δ)~δα
(1)
If the set (F,δ) is covered with N boxes with the scale of δ, Pi(δ) is the measure of the No.i box. The measure Pi(δ) varies over boxes. a is the singular exponent. The relationship of the number N(δ) of box sharing the same α and δ in fractal is defined as 16
: N(δ)~δ-ƒ(α)
(2)
The physical significance of ƒ(α) is the fractal dimension sharing the same α subset. Different values of α can be utilized for determining different fractals. In this way, (F,µ) can be divided into infinite fractal subsets that have different dimensions ƒ(α), thereby forming the multifractal spectra.
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2.3.2 Computing method of multifractal There are two languages available for characterizing the multifractal spectral function, i.e. α~ƒ(α) and q~Dq, which are equivalent under the Legendre transform. Usually, characterization of multifractal spectra is based on the relationship between the singular exponent α and the fractal dimension ƒ(α) of subsets sharing the same α. Since the introduction of the fractal dimension spectral function by Halsey et al.
24
, a variety of methods for computing the
multifractal spectral function have been proposed by Cheng
25
, Grau et al.
26
and Bird et al.
27
,
such as the moment, wavelet and histogram methods, of which the moment method is the most common 28. Unlike the 2D image-based method, the Micro-CT-based 3D pore model enables the coverage of the 3D pore space with the grid consisting of a series of cubes (3D boxes) with the side length of δ (δ0, that is, the property of relatively large pore space. The maximum probability plays a crucial role and the other probabilities are negligible if q→+∞; otherwise, if q
