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Volume 32 Issue 4
Aug.  2021
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Mutian Qin, Shuyun Xie, Jianbo Zhang, Tianfu Zhang, Emmanuel John M. Carranza, Hongjun Li, Jiayi Ma. Petrophysical Texture Heterogeneity of Vesicles in Andesite Reservoir on Micro-Scales. Journal of Earth Science, 2021, 32(4): 799-808. doi: 10.1007/s12583-021-1409-z
Citation: Mutian Qin, Shuyun Xie, Jianbo Zhang, Tianfu Zhang, Emmanuel John M. Carranza, Hongjun Li, Jiayi Ma. Petrophysical Texture Heterogeneity of Vesicles in Andesite Reservoir on Micro-Scales. Journal of Earth Science, 2021, 32(4): 799-808. doi: 10.1007/s12583-021-1409-z

Petrophysical Texture Heterogeneity of Vesicles in Andesite Reservoir on Micro-Scales

doi: 10.1007/s12583-021-1409-z
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  • It is of great significance to study the spatial distribution patterns and petrophysical complexity of volcanic vesicles which determine whether the reservoir spaces of the volcanic rocks can accumulate oil and gas and enrich high yields or not. In this paper, the digital images of three different textures of vesicular andesite samples, including spherical vesicular andesite, shear deformation vesicular andesite, and secondary filling vesicular andesite, are obtained by microscopic morphology X-CT imaging technology. The spatial micro-vesicle heterogeneity of vesicular andesite samples with different textures is quantitatively analyzed by fractal and multifractal methods such as box-counting dimension and the moment method. It is found that the shear stress weakens the spatial homogeneity since vesicles rupture are accelerated, elongated directionally, and connected with one another under the strain; the secondary filling breaks the vesicles, which significantly enhances the spatial heterogeneity. In addition, shear stress and secondary filling increase the complexity of vesicle microstructures characterized by different fractal and multifractal parameters. These conclusions will provide important theoretical and practical insights into understanding the degassing of volcanic rocks and prediction of high-quality volcanic reservoirs.
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Petrophysical Texture Heterogeneity of Vesicles in Andesite Reservoir on Micro-Scales

doi: 10.1007/s12583-021-1409-z

Abstract: It is of great significance to study the spatial distribution patterns and petrophysical complexity of volcanic vesicles which determine whether the reservoir spaces of the volcanic rocks can accumulate oil and gas and enrich high yields or not. In this paper, the digital images of three different textures of vesicular andesite samples, including spherical vesicular andesite, shear deformation vesicular andesite, and secondary filling vesicular andesite, are obtained by microscopic morphology X-CT imaging technology. The spatial micro-vesicle heterogeneity of vesicular andesite samples with different textures is quantitatively analyzed by fractal and multifractal methods such as box-counting dimension and the moment method. It is found that the shear stress weakens the spatial homogeneity since vesicles rupture are accelerated, elongated directionally, and connected with one another under the strain; the secondary filling breaks the vesicles, which significantly enhances the spatial heterogeneity. In addition, shear stress and secondary filling increase the complexity of vesicle microstructures characterized by different fractal and multifractal parameters. These conclusions will provide important theoretical and practical insights into understanding the degassing of volcanic rocks and prediction of high-quality volcanic reservoirs.

Mutian Qin, Shuyun Xie, Jianbo Zhang, Tianfu Zhang, Emmanuel John M. Carranza, Hongjun Li, Jiayi Ma. Petrophysical Texture Heterogeneity of Vesicles in Andesite Reservoir on Micro-Scales. Journal of Earth Science, 2021, 32(4): 799-808. doi: 10.1007/s12583-021-1409-z
Citation: Mutian Qin, Shuyun Xie, Jianbo Zhang, Tianfu Zhang, Emmanuel John M. Carranza, Hongjun Li, Jiayi Ma. Petrophysical Texture Heterogeneity of Vesicles in Andesite Reservoir on Micro-Scales. Journal of Earth Science, 2021, 32(4): 799-808. doi: 10.1007/s12583-021-1409-z
  • The decompression during volcanic eruption caused massive degassing of magma and the formation of vesicles during the process of diagenesis (Davydov, 2012). With the release of gas, vesicles in magma nucleated and grew. The density, size distribution and morphology of vesicles may be further modified by coalescence, growth or deformation (Boichu et al., 2008; Papale et al., 1998; Cashman and Mangan, 1994). These vesicles in frozen volcanic rocks record the degassing processes in magmas. Therefore, it is valuable to study the characteristics of vesicles by characterizing the conditions of magma storage, rise and eruption (Spina et al., 2019; Le Gall and Pichavant, 2016). Quantitative analysis and interpretation of volcanic vesicles have been regarded as an important topic of volcanology, and a lot of work has been focused on density and distribution of volcanic vesicles in magma degassing process through 2D images analysis (Giachetti et al., 2010; Blower et al., 2003, 2001; Klug et al., 2002).

    X-ray computed microtomography (CT) is a non-destructive method for imaging textures, which has been demonstrated to be of great potential in the study of quantifying spatial distribution patterns and size frequency distribution of 3D vesicles (Rahner et al., 2018). Papale et al. (1998) first used XRCMT to study the vesicular structure of Hawaiian basalts, and then 3D imaging technology was widely used to study the vesicular space of volcanic rocks (Pistone et al., 2015; Shields et al., 2014; Baker et al., 2012; Degruyter et al., 2009).

    Fractal and multifractal are considered as effective means to describe irregular objects, which can quantitatively describe the spatial distribution, heterogeneity and structural complexity of the target objects, which can be either a tiny pore body (Wang et al., 2019; Xia et al., 2019; García-Gutiérrez et al., 2017) or a large geological activity (Yin et al., 2019; Lyu et al., 2017; Yang et al., 2016; Turcotte, 1989). For oil and gas reservoirs, in recent years, fractal and multifractal methods have been regarded to be of obvious advantages in the quantitative characterization of the complex microstructure and heterogeneity of pore spaces which greatly affect the migration mechanism of reservoir (Cai et al., 2018).

    Krohn (1988) discussed the feasibility of fractal method in characterization of 2D microstructure of sandstone, carbonate rock and shale. Xie et al. (2010) systematically characterize the micro pore structure of carbonate reservoir through fractal and multifractal methods, and considered that corresponding parameters can effectively describe the spatial distribution of micropores. Further combined with micro reservoir analysis methods, such as high-pressure mercury injection (Liu et al., 2020; Wang et al., 2018; Li et al., 2017; Ferreiro et al., 2010), gas adsorption (Yang et al., 2014; Clarkson et al., 2013), NMR (Ge et al., 2015), fractal analysis has been widely utilized in the study of reservoir microstructures (Zhou et al., 2021; Lai et al., 2018).

    In general, natural pores, vesicles in volcanic rocks tend to have larger volume and wider throat than those in tight sandstones and shale. Therefore, the study on the density, size distribution and textures of volcanic vesicles is of great significance for the development and prediction of high-quality volcanic reservoirs (Barreto et al., 2017; Colombier et al., 2017; Wright et al., 2009). In this paper, fractal and multifractal methods are used to quantitatively characterize the different textures of vesicular andesite reservoir samples, to understand the development dynamics of volcanic vesicles from a new perspective, which will provide a basis for the degassing of volcanic lava and the prediction of high-quality reservoirs.

  • Huanghua depression is located in the center of Bohai Bay Basin, with a total area of 1.7×104 km2, which is a secondary negative structural unit in Bohai Bay Basin and is adjacent to Yanshan fold belt in the north, Linqing depression in the south, Chengning uplift in the East and Cangxian uplift in the West. Huanghua depression, which is also an important exploration area in the Bohai Bay Basin, is generally in NNE trending. Several hundred tons of Mesozoic volcanic wells have been discovered and explored in this area. The reservoirs are mainly lava, pyroclastic rocks and pyroclastic sedimentary rocks, and andesite is one of the most important lava reservoirs (Zheng and You, 2019). The sampling area of the three volcanic rocks is located in Wangguantun area, Kongdong oil and gas sag, Huanghua depression as shown in Fig. 1. As is indicated in previous studies, the three samples are located in different areas of the lava effusion region, with different pore evolution forms. The round vesicles, shear-deformed vesicles and secondary filled vesicles were formed under stable degassing conditions in samples W41-1, W6 and G177, respectively. The three samples are selected to explore the development processes and distribution characteristics of high-quality igneous reservoirs in effusive andesites which will facilitate the oil and gas assessment.

    Figure 1.  Schematic diagram of sampling location of volcanic rocks in Wangguantun area, Kongdong oil and gas sag, Huanghua depression (according to Zheng and You, 2019).

    In order to extract the 3D images of samples, the computer tomography scanner was used to carry out X-ray radiation imaging on the rock pillars. In this experiment, a rock pillar with a diameter of 2.5 cm and a length of 3.0 cm for each sample was cut and used. The scanner was perpendicular to the long axis of the pillar and the image of 16 μm resolution was read according to a certain layer thickness (distance). The images were composed of various gray levels representing different X-ray density units. Light color represents rock skeleton and black represents pore spaces.

    The same method was used to segment each group of images to obtain the binary image of pores and rock skeleton separation, and then the image set of 900×900×900 pixels was taken from each sample, and noise reduction was carried out at the same time. We took a 1.44 cm×1.44 cm×1.44 cm cube column for each sample to carry out 3D reconstruction and fractal and multifractal calculation for each sample.

  • Figure 2 shows the mineralogical characteristics of three samples by microscopical observation (Figs. 2a-2c). Three samples are all vesicular andesites with the matrix composed of plagioclase microcrystalline and volcanic glass, which are interwoven with each other. The phenocrysts are all amphibole with obvious darkening.

    Figure 2.  Mineralogical characteristics shown in micrographs of rock thin sections. (a) W41-1, the matrix is of a vitreous interwoven structure, mainly composed of plagioclase microcrystalline and volcanic glass, with a small amount of dark amphibole phenocrysts; (b) W6, the matrix is mainly composed of plagioclase microcrystalline and volcanic glass, and amphibole phenocrysts show obvious alteration; (c) G177, the matrix is composed of plagioclase distributed in a disordered semi-directional way, with a small amount of altered pyroxene distributed.

    The micrograph of the casting thin sections and digitized images of each 2D CT slice of three samples were taken from different fields of view, showing the microstructural characteristics (Figs. 3a-3c) and planar distribution of vesicles (Figs. 3d-3f). 3D models were reconstructed, as shown in Figs. 4a-4c, showing the distribution of 3D vesicles. Obviously, the pore spaces of the three samples are mainly composed of vesicles (Figs. 3a-3c), but they show different pore evolution patterns due to their location in different parts of the lava area (Farquharson et al., 2015).

    Figure 3.  Micrographs of the casting thin sections ((a), (b), (c)) and digitized images ((d), (e), (f)) of the CT 2D slices. (a) W41-1, large vesicle; (b) W6, Shear deformed vesicles; (c) G177, vesicles with partial filling; (d) W41-1, differentiation of vesicle size; (e) W6, vesicles with shear deformation and rupture; (f) G177, complex vesicle structure.

    Figure 4.  3D vesicle reconstruction of micro CT images for andesite reservoir rock. (a) W41-1, vesicles were different in size and distributed discretized; (b) W6, vesicles present directional deformation; (c) G177, vesicles were partially filled and the structure became extremely complex.

    Huge vesicles of nearly elliptical shape are developed in Sample W41-1 (Fig. 3a), which indicates that the degassing process of magma remained relatively stable during the formation of vesicles (Namiki and Manga, 2006). The sizes of the vesicles are highly differentiated, and vesicles dispersed only some small vesicles gathered (Figs. 3d and 4a). Some large vesicles in Sample W6 are sheared and elongated, some of which are merged (Fig. 3b), which means that the andesite lavas in the region are subjected to shear stress, which may be located in a stress transformation zone (Kushnir et al., 2017). Some small pores were formed due to the rupture of the vesicles (Figs. 3b and 3e). Vesicles of G177 also underwent shear deformation and connection, and extensive secondary filling was developed (Fig. 3c). The vesicles were filled and broken with more micropores (Figs. 3f and 4c).

    The quantitative analysis of images and the establishment of the 3D pore model was completed by ImageJ and Avizo software (Houston et al., 2017; Prodanović et al., 2007). The porosity of Sample W41-1, W6 and G177 is 1.94%, 1.96% and 6.27%, respectively, which were obtained by digital image calculation. Through statistical analysis of pore parameters, the regularity of micro pore structure is explored to provide new information for reservoir evaluation.

  • The gray-scale image is binarized into separate vesicle and matrix pixels, and the number of lattices containing vesicle pixels (N) is counted by changing the scale (ε). Under the double logarithmic coordinate axis, the scale size (ε) and the number (N) scatter diagram are plotted (Xie et al., 2010; Mandelbrot, 1977).

    For calculation, the box can be square or round, cubic or spherical. In this paper, we can cover the space with a square of ε and gradually reduce the size of it for 2-Dimensional analysis, and cover the CT columns with a cubic of size (ε) and gradually reduce the size of it for 3-Dimensional pore analysis. The advantage of using the square lattice is that the calculation of the square N(ε) is simpler, and the number of boxes is equal to its covering number.

  • Since the dimension spectrum function had been put forward (Halsey et al., 1987), there are many calculation methods and the moment method is recommended widely (Zhou et al., 2019; Xie et al., 2010). Firstly, the distribution function χ(q, δ) is defined as the quantity representing the degree of multifractal heterogeneity (Tarquis et al., 2009).

    where mi represents the number of pixels circled in the box and M represents the total number of pixels. When the moment q > 0, χ(q, δ) reflects the property of high μi region, highlighting the characteristics of large pore spaces; otherwise, when q < 0, χ(q, δ) reflects the property of low μi region with small and micro pores. The relationship between χ(q, δ) and $ {\delta }^{\tau \left(q\right)} $ under each q is as follows.

    where τ(q) is called mass exponent.

    If τ(q)-q is a straight line, the research object is a single fractal; if τ(q)-q is a convex function, the research object is a multifractal (Evertsz and Mandelbrot, 1992).

    And usually α(q) named as the singularity exponent is obtained by Legendre Transformation (Agterberg, 2001; Bird et al., 2006).

  • Vesicle sizes and textures can reflect magma degassing evolution processes, including nucleation, growth, coalescence and other types of mechanical interactions to different degrees (Parmigiani et al., 2017; Pioli et al., 2017; Toramaru, 1995). As natural reservoir space in volcanic reservoirs, the microstructure of vesicles determines the reservoir property. Usually, shapes of volcanic vesicles are investigated using shape parameters such as shape factors and elongation parameters.

    2D shape factor is denoted as F and the 3D shape factor as FF (Mongrain et al., 2008; Manga et al., 1998; Orsi et al., 1992).

    In Eq. (6), P is the perimeter and S the area of the 2D pores. In Eq. (7), A, the surface area and V, the volume of the 3D pores. Usually, the closer F is to 1, the rounder the pore shape is, and the smaller the value is, the more complex the 2D pore structure is. FF is different from F. The closer FF is to 1, the closer the pore is to the sphere. The more complex the pore is, the higher the FF value is.

    The 2D elongation is denoted as E.

    where a and b are the long axis and the short axis, respectively, of each 2D pore fitted as an ellipse. The ellipse fitted has the same area, center of mass and direction as the real pore. The larger E is, the slender the 2D pore is.

    The 3D elongation is denoted as EE. Calculated by Avizo Software (Ferreira et al., 2018), EE is the ratio of the eigenvalue in the covariance matrix to the maximum eigenvalue, which can reflect the elongation length of the 3D pore. The more elongated pores generally have smaller EEs.

    Table 1 lists the average shape parameters of vesicle group with volume (area) values greater than those of quantile 75%, 50%, 25% and 0% in the 2D and 3D pore spaces. In order to eliminate the specificity of slices, all the pores of 900 slices were selected as the analysis target in 2D characterization.

    Parameter
    Sample
    Area/volume ≥0% Area/volume ≥25% Area/volume ≥50% Area/volume ≥75%
    2D 3D 2D 3D 2D 3D 2D 3D
    Area/volume fraction (%) W41-1 100.00 100.00 99.61 99.97 97.43 99.87 89.89 98.83
    W6 100.00 100.00 99.34 99.96 96.60 99.74 87.07 98.60
    G177 100.00 100.00 99.29 99.96 95.87 99.82 83.70 98.98
    F/FF W41-1 0.901 5 1.162 2 0.875 3 1.365 2 0.857 3 1.532 9 0.835 9 1.492 2
    W6 0.814 1 1.938 5 0.762 2 2.394 6 0.693 1 2.987 4 0.643 8 4.098 4
    G177 0.709 4 3.643 4 0.633 3 4.544 8 0.516 5 6.084 7 0.399 7 10.171 0
    E/EE W41-1 0.142 5 0.565 4 0.137 2 0.607 3 0.117 2 0.633 1 0.108 3 0.758 4
    W6 0.239 0 0.447 6 0.252 8 0.462 2 0.284 4 0.436 1 0.266 9 0.442 8
    G177 0.292 6 0.491 5 0.322 0 0.473 7 0.369 0 0.433 3 0.370 5 0.400 3

    Table 1.  Shape parameters of vesicle groups in 2D and 3D with different partitions

    In the 2D slices, the first 25% of the vesicles occupy more than 80% of the area space. While in the 3D vesicle space, the first 25% of the vesicles occupy more than 98% of the volume space. This phenomenon indicates that there is a huge difference in the size of vesicles, and a small number of vesicles occupy the majority of the vesicle space. Certainly, it also reflects the existence of a large number of micropores, which may be invalid or "fuzzy" due to the influence of resolution or noise. The presence of these vesicles greatly limits the characterization effects of the average vesicle shape parameters which change significantly in different vesicle groups (Fig. 5).

    Figure 5.  Line charts of shape parameters of vesicle groups in 2D and 3D with different quantiles. (a) 3D shape factor FF; (b) 3D elongation factor EE; (c) 2D shape factor F; (d) 2D elongation factor E.

    Specifically, the average FF of the first 25% vesicles of W6 sample is higher than that of all the vesicles of G177, but lower than that of the first 75%, 50% and 25% vesicles of G177 sample (Fig. 5a). For 2D slices, the average F of all vesicles of G177 is higher than that of 50% and 25% of vesicles than W6 (Fig. 5c).

    The deformation of vesicles is also obvious. The variation of 2D and 3D vesicle elongation of different vesicle groups is disordered. The EE of the first 50% vesicles and the first 25% vesicles of W6 is higher than the first 50% and the first 25% vesicles of G177, but the situation is different in the first 75% and the first 100% pores (Fig. 5b).

    In order to accurately characterize the texture of vesicles, it is necessary to select appropriate vesicle group as the target. We selected the 2D vesicles with the first 50% of the area and the 3D vesicles with the first 25% of the volume as the research objectives. These vesicles occupy more than 95% of the total volume (area) (Table 1), which can represent the main characteristics of vesicles.

    Among them, Sample W41-1 vesicles have the smoothest edge and the simplest structure, indicating that the volcanic vesicles were formed under slow decompression (Namiki and Manga, 2006), and their shapes were nearly spherical. Vesicles in W6 has a more complex structure and higher elongation ratio than vesicles in W41-1, which indicates that the vesicles underwent shear deformation, coalescence and rupture (Okumura et al., 2016, 2008; Degruyter et al., 2009). In addition, due to the influence of partial filling, FF of G177 was significantly higher than that of others, indicating that the vesicles were broken and the structure became extremely complex.

    We also found larger vesicles have lower FF and higher F (Figs. 5a and 5c). It is worth mentioning that the shape factor of W41-1 does not change much, but changes obviously in W6 and G177. Since the larger vesicle bodies of W6 and G177 are mainly of deformation and partial filling vesicles, the difference of pore structure morphology between large and small pores is huge, which leads to significant differences in shape parameters.

    In addition, the larger EE in W41-1 3D vesicles indicates that the larger vesicles are closer to the sphere shape with lower elongation ratios. However, the EE of W6 and G177 decreased with the increase of the vesicle volumes, implying that the shear deformation of the larger vesicles is more obvious than that of the small vesicles. This tendency is also shown in the 2D aspect. The first 50% and the first 25% vesicle groups show higher E values (Figs. 5b and 5d).

  • Figure 6 shows the rose diagram of the first 25% 3D vesicles direction calculated by Avizo software (Table 1). These 25% vesicles can reflect the overall characteristics of the vesicles and avoid the influence of micro pores. The direction of vesicles is determined by two parameters, elevation φ (0-90°) and azimuth θ (0-360°). In this paper, elevation φ is divided into two groups, φ≥45° and φ < 45°.

    Figure 6.  Rose diagrams of 3D vesicles orientation. (a) φ≥45°, the azimuth θ rose diagram of vesicles in W41-1; (b) φ < 45°, the azimuth θ rose diagram of vesicles in W41-1; (c) φ≥45°, the azimuth θ rose diagram of vesicles in W6; (d) φ < 45°, the azimuth θ plum blossom rose diagram of vesicles in W6; (e) φ≥45°, the azimuth θ rose diagram of vesicles in G177; (f) φ < 45°, the azimuth θ rose diagram of vesicles in G177.

    We found that the azimuth θ of vesicles in W41-1 are mostly concentrated at 270°-360° and 90°-180° (Figs. 6a and 6b), which may be due to the influence of pressure and gravity during the nucleation process that the vesicles are slightly ellipsoid. The azimuth θ vesicles in W6 show a trend of convergence towards 180°-270° (Figs. 6c and 6d), indicating that the vesicles began to deform in the shear direction owing to the influence of shear strain, and the anisotropy of vesicles distribution increased. The vesicles in G177 were broken by partial filling, resulting in disordered azimuth θ of the fragments and weakening of anisotropy (Figs. 6e and 6f).

  • In general, the smaller the box dimension Db is, the smoother the surface of pore and throat is, with weaker complexity and stronger homogeneity, and the better the reservoir performance of rock would be; while Db is closer to 2, that is, the larger Db, the less smooth the surface of pore and throat is, and the more complex the structure of spatial junctions are, the more inhomogeneous the size distribution, which means stronger heterogeneity (Xie et al., 2010; Mandelbrot, 1977). Fractal characteristics of pore structure of 900 samples in each of the three samples are analyzed. The results are presented in Table 2, in which the 2D box dimension, Db, was the average value of 900 slices, and the higher Db represents the relatively more complex microstructure (Xie et al., 2010; Yu, 2006). The average Db show that W6 and G177 had more complex microstructure than W41-1, but there was a small difference between W6 and W41-1, which indicates that shear strain does not cause significant deformation of vesicle microstructure. Figure 7 shows the change in Dbs in 900 slices. In the two-dimensional scale, the vesicular structure of W6 has higher Db than that of W41-1 sample with the same porosity, but the difference is small, which indicates that shear deformation can complicate the vesicle structure, although the effect is limited. The Db of G177 is obviously different from W41-1 and W6, which indicates that mineral filling has a more obvious effect on the microstructure of vesicles than shear deformation in the two-dimensional space.

    Sample Db Δα ΔαL ΔαR R
    W41-1 1.082 3 1.102 1 0.443 0 0.659 1 -0.204 7
    W6 1.150 9 1.085 3 0.457 4 0.627 9 -0.161 5
    G177 1.476 8 1.073 5 0.416 3 0.657 2 -0.225 4

    Table 2.  Fractal and multifractal parameters describing the 2D vesicles

    Figure 7.  Distribution of Db of 2D vesicles on different slices.

  • The heterogeneous properties of vesicle system reflect the process of degassing and nucleation of vesicles to some extents, and also affect the migration mechanism of vesicular volcanic rock reservoir. To some extent, the heterogeneity of pore distribution in porous media affects the connectivity and permeability of pore structure (Chen et al., 2017). The multifractal method is used to quantitatively characterize the multi-dimensional spatial heterogeneity of volcanic vesicles with different textures, which enhances the characterization of spatial distribution pattern of volcanic vesicles. At the same time, the evolution process of igneous rock vesicles is dynamic, so the study of vesicle heterogeneity can offer new ideas for the analysis of magma degassing evolution and volcanic reservoir prediction.

    According to the calculation method of multifractal dimension, the statistical order q of multifractal moment method is selected in the range of [5-5], and the 2D multifractal parameters of the sample vesicle structure are obtained by covering the 2D pore space with boxes of different scales.

    Table 2 shows the 2D multifractal parameters, where ΔααLαR is the width of multifractal singular spectrum, reflecting the spatial differentiation degree of irregular aggregates under different measures. The larger the Δα of vesicle system is, the more inhomogeneity its distribution is, which often indicates lower permeability (Chen et al., 2017). Since ΔαL and ΔαR, the width of the left and the right part of the multifractal singular spectrum, show the difference between relatively larger and smaller vesicles. And thus R=(ΔαLαR)/Δα, is used to reflect the asymmetry of multifractal spectrum curve and then to describe the differentiation degree of large vesicles and small vesicles.

    It is found that the Δα values of W6 and G177 are lower than that of W41-1, which indicates that the 2D vesicles of W6 and G177 have lower heterogeneity. The asymmetry index R is negative, indicating that vesicles (pores) are differentiated in the slices and micro vesicles (pores) are dominant.

    Figures 8 and 9 show the distribution of 2D fractal parameters on different slices. The multifractal spectrum width Δα and the asymmetry index R have great changes on different slices, indicating that there are obvious differences in the characteristics of 2D slices at different positions of the same vesicle system. In addition, the multifractal parameters of G177 have the smallest difference among different slices, while those of W41-1 parameters have the largest variation range and those of W6 are between the two samples.

    Figure 8.  Distribution of Δα of 2-D vesicles on different slices.

    Figure 9.  Distribution of R of 2-D vesicles on different slices.

  • Table 3 lists the 3D Db of the three samples. Compared with W41-1, W6 and G177 have higher Db, which is due to the deformation, fracture and coalescence of vesicles caused by shear strain. Moreover, partial filling can break the original vesicle space and make the microstructure extremely complex.

    Sample Db Δα ΔαL ΔαR R
    W41-1 2.147 3 2.815 0 1.406 6 1.406 6 -0.000 6
    W6 2.427 2 2.265 2 1.039 9 1.216 5 -0.078 3
    G177 2.631 8 2.440 6 0.747 2 1.692 3 -0.387 4

    Table 3.  Fractal and multifractal parameters describing the 3D vesicles

    Compared with 2D Db, 3D Db has a higher distinction between W41-1 and W6 (Tables 2 and 3). 2D slices only contain plane information of vesicles structure, while 3D data are the superposition of 2D information, which can more accurately describe the characteristics of vesicle microstructure and show the differences of different vesicle structure.

  • According to the multifractal analysis method, the plot of f(α) vs. α to represent the 3D multifractal spectrum characteristics of the vesicle structure is obtained (Fig. 10). The multifractal spectrum of the three samples shows typical right partial continuous spectrum distribution pattern, which further reflects the spatial heterogeneity of the samples (Fig. 10). It is obvious that indeed all of the 3D vesicle networks analyzed of the three andesite samples have multifractal geometries.

    Figure 10.  Multifractal spectrum function f(α) curves of 3-D vesicle distribution Patterns.

    The Δα value of 3D vesicles of W41-1 sample is higher than that of W6 (Table 3), reflecting that the spatial distribution of W41-1 vesicles is highly heterogeneous, because the process of small vesicles gathering to form large vesicles makes the spatial distribution of vesicles more chaotic, which is consistent with the characteristics of 2D slices. The vesicles in Sample W6 are deformed, elongated and connected due to shear strain, forming a directional arrangement similar to tubular pumice, and the heterogeneity is reduced. Generally speaking, the connectivity and permeability of volcanic vesicles after shear deformation are enhanced (Farquharson et al., 2016). On the other hand, the permeability of vesicles with similar extension direction is better than that of the pore throat system with high structural complexity. (Lai et al., 2018; Kushnir et al., 2017; Pistone et al., 2017; Vona et al., 2016; Degruyter et al., 2009).

    The 3D multifractal spectrum width Δα of G177 is between W41-1 and W6, which indicates that shear deformation reduces the heterogeneity of the original vesicle space distribution, while the filling effect makes the vesicles broken, the spatial distribution becomes complex and the heterogeneity is enhanced.

    The asymmetry index R of the 3D multifractal spectrum of W6 is slightly lower than that of W41-1, indicating that the smaller vesicles have a higher bulk density. This is due to the formation of micro pores due to the rupture of vesicles under shear strain, and the larger vesicles are easier to gather and connect under shear deformation, which further decreases the density of large vesicles (Okumura et al., 2008). The multifractal spectrum of G177 is strongly right biased, and correspondingly the asymmetry index R reaches -0.387 4, indicating well that the differentiation degree of larger vesicles and small vesicles is relatively smaller.

    We found that the 2D and 3D Δα can effectively characterize the heterogeneity of W41-1 and W6. For the complexly reconstructed vesicle space such as G177, due to the limited information contained in the 2D slices, the shape and spatial distribution of the vesicles are ignored, which makes the 2D heterogeneity and 3D heterogeneity different (Tables 2 and 3).

  • (1) Both 2D and 3D vesicles in andesite are of fractal and multifractal characteristics. The fractal dimension and multifractal parameters of 3D vesicle structure extracted in this paper quantitatively characterized the microstructure and spatial heterogeneity of spherical vesicles, shear deformation vesicles and partial filling vesicles with obvious differences in parameters. The 2D fractal dimension is effective to characterize the microstructure of partial filling vesicles and primary vesicles, but it is limited to differentiate the spherical vesicles and shear deformation vesicles. Moreover, 2D multifractal parameters are useful to characterize the spatial heterogeneity of spherical vesicles and shear deformation vesicles, although there are recognizable differences between different slices.

    (2) The parameters can be recommended to analyze the dynamic evolution of andesite reservoir rocks. Noticeable differences were found in microstructure and spatial heterogeneity of different textures of vesicular andesite. W41-1 belongs to vesicular andesite formed under stable degassing. The size of the vesicles is obviously different and its distribution is disorderly with higher 3D Δα values and the strongest heterogeneity. Vesicles in W41-1 own the simplest microstructure with the lowest 3D Db value. Once these smooth and huge vesicles are connected, high quality reservoir space will be established. Thus, the stable degassing magma belt is of great potential for reservoir formation. W6 belongs to vesicular andesite formed by shear stress during the degassing process of magma. After shear deformation, fracture and connection, the microstructure complexity of vesicles is slightly improved (3D Db is 2.427 2), but it still has relatively smooth and wide pore-throat structure. The vesicles are arranged orderly and the heterogeneity is weaker with 3D Δα of 2.265). Compared with the stable degassing vesicular volcanic rocks, vesicular volcanic rocks subjected to shear deformation are of higher potential connectivity and permeability. The vesicles of G177 have been broken by partial filling, and the 2D and 3D Db are much higher than those of W41-1 and W6, indicating the microstructure of G177 is extremely complex. Although the vesicles have undergone directional deformation and the heterogeneity has been reduced, the heterogeneity is still stronger than W6 due to the fragmentation of these broken vesicles. In this way, partial filling can reduce the reservoir performance of vesicular andesite reservoir. It is clear that classical measures with traditional porosity parameters alone were insufficient to distinguish differences in micro-vesicle structures from images of different heterogeneity. However, such differences could be detected from comparisons of multifractal spectrum parameters. Finally, we found Δα and Db values provided the most sensitive measure of changes in micro-vesicle morphology.

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