Correlation analysis of element contents and mechanical characteristics of shale reservoirs: A case study in the Cen'gong block, South China

Marine and Petroleum Geology 91 (2018) 19–28

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Research paper

Correlation analysis of element contents and mechanical characteristics of shale reservoirs: A case study in the Cen'gong block, South China

T

Jinshou Liua,b,c,d,∗, Wenlong Dinga,b,c,d, Ruyue Wange,f, Haimeng Yangg, Xinghua Wanga, Ang Lia a

School of Energy Resources, China University of Geosciences, Beijing 100083, China Key Laboratory of Marine Reservoir Evolution and Hydrocarbon Enrichment Mechanism, Ministry of Education, China University of Geosciences, Beijing 100083, China c Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, China University of Geosciences, Beijing 100083, China d Key Laboratory of Strategy Evaluation for Shale Gas, Ministry of Land and Resources, China University of Geosciences, Beijing 100083, China e State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing 100083, China f Petroleum Exploration and Production Research Institute, SINOPEC, Beijing 100083, China g Oil Recovery Plant No. 3, Zhongyuan Oilfield Co. Ltd., SINOPEC, Puyang 066004, Henan, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Element content Mechanical characteristics Correlation analysis Shale reservoirs Brittleness index

The mechanical parameters of shale are some of the most significant assessment indices for shale gas exploitation. The development of element logging offers an opportunity to study the correlations between the elemental concentrations and the mechanical characteristics of shale. Using the Lower Cambrian shale in the Cen'gong area, Guizhou Province, China, as an example, 490 data sets are extracted using formation element and mineralogy (FEM) and cross multipole array acoustic (XMAC) logging. Through Spearman correlation analysis, the correlations between the major elements (Si, Ca, Fe, S, Ti, Mn, Mg, Al, and K) and the mechanical parameters (Young's modulus, Poisson's ratio, shear strength, shear modulus, and brittleness index) are studied. The effects of the Si content on the mechanical parameters (positive/negative correlations, magnitude and significance of the correlations) are discussed based on X-ray diffraction analyses of the minerals in 146 samples. When 1.84% < CSi (Si content) < 28.08%, Young's modulus and the brittleness index decrease with increasing Si content, and Poisson's ratio increases. When 28.08% < CSi < 31.32%, there is no significant correlation between the Si content and the mechanical parameters. When 31.32% < CSi < 44.24%, Young's modulus and the brittleness index increase with increasing Si content, and Poisson's ratio decreases. Thus, it is not reasonable to determine the mechanical properties of shale based only on the elemental composition in different regions.

1. Introduction Commercial exploration for shale gas in the Longmaxi Formation of the Lower Silurian Series in the Jiaoshiba area of Chongqing has demonstrated that southern China, which contains well-developed Paleozoic organic shale, is a significant strategic area for shale gas exploration (Chen et al., 2015a; Guo and Zhang, 2014; Yang et al., 2016). In contrast to North America, the Paleozoic marine organic shale in southern China is characterized by several formations, old age, a high degree of thermal evolution, multiple tectonic movements, complicated tectonic deformation, complicated crustal stress and surface conditions, and poor preservation (Han et al., 2015; Jiang et al., 2015; Xiao et al., 2015; Zhang et al., 2015). The Lower Cambrian shale is characterized by a higher organic abundance, higher degrees of brittleness and thermal evolution, a greater sedimentary thickness and a wider distribution compared to the Longmaxi Formation. Therefore, this shale

∗

reservoir has great potential for shale gas exploitation in southern China (Kříbek et al., 2007; Pi et al., 2013; Zhou et al., 2014). Four shale gas wells have been drilled in the study area; of these, the CY-1 and TX1 wells are two of the rare shale gas wells that targeted the Lower Cambrian shale and were successfully fractured and produced. Hence, understanding the exploration results from these wells can play a significant role and have practical meaning in the exploration and exploitation of the Cambrian Niutitang Formation in complex structural areas of southern China. The mechanical characteristics of shale determine the extent of fracturing of a shale gas reservoir and are significant for shale gas exploration. The mechanical characteristics of shale are typically assessed based on rock mechanics experiments, geophysical methods, the brittle mineral content, and fracturing experiments (Chen et al., 2011; Feignier and Grasso, 1991; Wild et al., 2015). Shale gas exploration has shown that the brittle mineral content is positively correlated with the shale's

Corresponding author. School of Energy Resources, China University of Geosciences, Beijing 100083, China. E-mail address: [email protected] (J. Liu).

https://doi.org/10.1016/j.marpetgeo.2017.12.022 Received 25 September 2017; Received in revised form 8 December 2017; Accepted 14 December 2017 Available online 15 December 2017 0264-8172/ © 2017 Published by Elsevier Ltd.

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include illite, illite-smectite, and some chlorite. The illite content ranges from 23% to 92% with an average of 59.6%, and the illite-smectite content is 6%–62% with an average of 27%. The average smectite content in the illite-smectite is 19.5%. The results of the kerogen maceral and pyrolysis analysis show that the primary organic macerals of the kerogen are sapropel (31–97%) and humic macerals (20–70%), and the samples contain a small amount of non-structural vitrinite and fusinite (Fig. 3B and Table 2). The kerogen maceral of the shale is primarily sapropel with type Ⅰ organic material. The peak pyrolysis temperature ranges from 417 to 600 °C and is generally more than 500 °C. The values of the soluble hydrocarbons (S1), pyrolyzed hydrocarbons (S2) and hydrogen index (HI) are all relatively low, and the equivalent vitrinite reflectance is between 2.27% and 4.42%, which indicates that the shale in the Niutitang Formation is in the overmature stage of late diagenesis.

brittleness; shale with a high content of brittle minerals is typically highly brittle and contains well-developed natural fractures (Ding et al., 2013; Liu et al., 2017a, 2017b). The relationships of the elemental concentrations with the petrology and mineralogy of sedimentary rocks have been investigated in numerous studies (Ajayi and Torres-Verdín, 2016; Anderson et al., 1988; Chen et al., 2015b; Freedman et al., 2015). However, few systematic studies have focused on the relationships between the elemental concentrations and the rock mechanical characteristics to determine the effects of different elements on the mechanical parameters. Recent exploration for shale gas in the Cen'gong area, especially the TX-1 well, applied formation element and mineralogy (FEM) and cross multipole array acoustic (XMAC) logging, which provides an opportunity to study the elemental compositions and mechanical characteristics of shale gas reservoirs. Therefore, we use the Cambrian shale in the Cen'gong area of Guizhou as an example, and we extract 490 data groups from the logs and study the correlations between the major elements (Si, Ca, Fe, S, Ti, Mn, Mg, Al, and K) and the mechanical parameters (Young's modulus, Poisson's ratio, shear strength, and shear modulus) in the formation using Spearman correlation analysis. Based on X-ray diffraction analysis, we discuss the reliability of mechanical parameters calculated using the element content, which provides information for elemental analysis, mechanical assessment, and target selection for the drilling and fracturing of marine shale gas reservoirs in southern China and around the world.

3. Logging identification methods Based on the petrogeochemical study, the sedimentary rock contains tens of major elements, including O, Si, Al, Fe, Ca, Mg, K, and Na, that make up more than 99.5% of the elements. Element capture spectroscopy has been used since the 1970s and can simultaneously measure inelastic scattering and capture gamma rays to quantify the major elemental compositions, including Si, Ca, Fe, S, Ti, Mn, Mg, Al, and K, through spectrum analysis (Bertozzi et al., 1981; Cheng and Yuan, 2005). Several analytical instruments have been developed, including elemental capture spectroscopy (ECS) logs, geochemical (GEM) logs, and formation lithology spectroscopy (FLS) logs. GEM logging can precisely measure the concentrations of Al, Ca, Fe, Mg, Mn, Ti, K, Si, and S and the mineral content of the strata to determine several parameters, such as the petrology and the fluid type and content (Anderson et al., 1988; Weltje and Tjallingii, 2008; Wu et al., 2015a, 2015b). By combining the GEM instrument with other logging tools in a short section with a diameter of 90 mm, compensated neutron logging (CNL), gamma density logging and natural gamma ray (NGR) logging can be performed during one logging run. The upper and lower parts of the detector have an eccentric design that allows the detector to connect to other eccentric devices. With the logging using a high-performance large-size lanthanum bromide crystal gamma photon detector and pulsed neutron emission technology to ensure the quality of the energy spectrum measurement, the output of chemical elements of the formation types and the measurement accuracy are greatly enhanced, and the format of the output data is listed in Table 2. As shown in Fig. 4, according to the element logging results in the TX-1 well, the Si concentration and the quartz content increase from the upper layers to the lower layers of the Niutitang Formation, whereas the concentrations of Al, K, Fe, and the clay minerals decrease from the upper to lower layers. The limestone of the Jiumenchong Formation at a depth of 1760 m contains a significantly higher Ca concentration and calcite content, which indicates good consistency between the element logging and the XRD bulk rock analysis results. The element logging also identified two sections with high gas contents at 1792–1800 m and 1803–1814 m. The cross-dipole array sonic tool is a mature technology and is manufactured by several companies, including the dipole sonic imager (DSI) from Schlumberger, the XMAC instrument from Baker Hughes, and the WaveSonic tool from Halliburton. The anisotropy of a rock layer can result in different S-wave velocities with different polarization orientations, which generates shear wave birefringence. Since the wave shapes are measured in two orthogonal directions, the anisotropy of the stratum can be extracted through the inversion of 4-component (4-C) data. XMAC log data processing provides information about the rock layer, including the P-wave and S-wave velocities, the time interval of the Stoneley wave, the P- and S-wave velocity ratio and the energy (Crampin, 1985; Patterson and Tang, 2001; Tang and Chunduru, 1999; Winterstein and Meadows, 1991). Combined with the density curve, this information can be used to constrain the dynamical Young's

2. Geological setting The Cen'gong shale gas section in southwest Tongren, eastern Guizhou Province, is located on the transitional slope between the Yunnan-Guizhou Plateau and the Xiangxi Mountain area. Tectonically, this region is located in the Qianbei area on the southeastern edge of the Yangtze plate in the west Xiang'e syncline (Fig. 1A). The significant tectonic events in this area include the Xuefeng orogeny, the Caledonian orogeny, the Yanshanian orogeny, and the Himalayan movement, of which the Yanshanian orogeny formed the basis of the current geological structure and topography (Liu et al., 2017c; Wang et al., 2016; Zeng et al., 2013). The folds and faults in the study area are oriented trending NE and NNE, and the main fault is a thrust fault with a dip angle of 50–80°, which had a significant effect on the distribution of the formation (Fig. 1B). The sedimentary environment of the area is composed of a Cambrian outer shelf deposit on the slope of a platform margin with water depths that decrease from southeast to northwest (Feng et al., 2002; Liu et al., 2016; Wu et al., 2016). The Lower Cambrian shale developed stably and is primarily composed of black carbonaceous shale and black silica shale. The shale contains type I organic material with a total organic carbon (TOC) content of 1.7–10.5% and an average of 4.6%; the equivalent vitrinite reflectance is 2.3–4%, and the shale gas content is 1.1–2.88 m3/t, which indicates that it is a good potential shale gas reservoir. The exposed strata include Sinian, Cambrian, Ordovician, some Silurian, and Quaternary rocks. The Cambrian system is widely distributed and includes the Niutitang Formation, Jiumenchong Formation, Bianmachong Formation, Balang Formation, Qingxudong Formation, Gaotai Formation, and Loushanguan Formation (Fig. 2). The mineralogy of the Cambrian shale was analyzed with a Rigaku SmartLab 9 X-ray diffractometer (XRD). X-ray diffraction and mineral analysis of 146 samples from the CY-1 and TX-1 wells were performed using a “Panalytical X'Pert PRO MPD” XRD with CuKα radiation (λ¼1.5406 for CuKα1). As shown in Fig. 3A and Table 1, the major minerals of the black shale in the Lower Cambrian Niutitang Formation are detrital minerals and clay minerals with small amounts of carbonate, pyrite, and barite. The concentration of detrital minerals ranges from 29% to 86% with an average of 68.7%, and the minerals include quartz and some feldspar. The concentration of clay minerals ranges from 7.3% to 71.4% with an average of 22.3%, and the clay minerals 20

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Fig. 1. (A) Location of the Cen'gong block and (B) cross-section through the Cen'gong block. The location is shown in (A).

modulus and Poisson's ratio and determine the stress and degree of fracture development (Huang et al., 2012; Li et al., 2006; Moon and Ku, 2016; Wang et al., 2008). Many methods can be used to assess rock brittleness. Grieser and Bray (2007) proposed using the elasticity parametric method with Young's modulus and Poisson's ratio from XMAC logs to characterize rock brittleness; after the calculation, the format of the output mechanical parameters is provided in Table 2. The vertical variation of the shale's brittleness in the TX-1 well can be determined using this method to calculate the shale brittleness. The equations of the elasticity parameters and the brittleness indices are as follows:

Ed = G

μd =

3Δts2 Δtp2

2 2 1 Δts − 4Δtp ⋅ 2 2 2 3Δts Δtp

μBrit =

μmax − μ × 100 μmax − μmin

(4)

G=

EBrit + μBrit 2

(5)

ρb Δts2

(7)

(8)

where G is the shear modulus (MPa); K is the bulk modulus (MPa); SS is the shear strength (MPa); Vsh is the clay content (%); ρb is the rock density (g/cm3); Ed is the dynamical Young's modulus (GPa); μd is the dynamical Poisson's ratio; Δtp and Δts are the time intervals of the Pand S-waves (μs/ft) (1 ft = 0.3048 m), respectively; EBrit is the normalized Young's modulus (GPa); μBrit is the normalized Poisson's ratio; BI is the non-dimensional brittleness index; E is the dynamical Young's modulus determined from the logging information (GPa); μ is the Poisson's ratio determined from the logging information; Emax and Emin are the maximum and minimum values of Young's modulus, respectively (GPa); and μmax and μmin are the maximum and minimum values of Poisson's ratio, respectively. As shown in Fig. 4, the Young's modulus and brittleness index of the Niutitang Formation have similar vertical distributions; the upper shale has low brittleness and Young's modulus, both parameters increase gradually with increasing depth, and the degree of fracture development in the rock core is consistent with the brittleness. In addition, the shale at the bottom and middle of the well has a low Poisson's ratio and a high Young's modulus, and it contains well-developed fractures.

(2)

(3)

3Δts2 Δtp2 2

(1)

E − Emin × 100 Emax − Emin

3Δts2 − 4Δtp2

1 + μd ⎞ 1 + 0.78Vsh SS = 0.00544ρb2 ⎜⎛ ⎟ (1 − 2μd ) 1 μ − 4Δtp4 d⎠ ⎝

3Δts2 − 4Δtp2

EBrit =

BI =

K = ρb

(6) 21

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Fig. 2. Stratigraphic and lithological systems of the study area.

4. Theory and methods

When selecting the correlation coefficient, the frequency distribution of the variables should be used to determine whether the data follow a normal distribution. The normal distribution is tested using a probability-probability (P-P) plot and a non-parametric test (Wu et al., 2015b). The P-P plot is obtained based on the correlation between the variable's cumulative ratio and that of the specific distribution. When the data follow a specific distribution, the points plot in a line on the PP plot. Therefore, if the points approach a line or most of the points plot on the line, the data have a highly normal distribution (Fig. 5). Non-parametric tests include the Kolmogorov-Smirnov test (D-test) and the Shapiro-Wilk test (W-test) (Mohammadkarimi and Dobre, 2014; Wu et al., 2015b). According to the principles of the Statistical Analysis System, the W-test is preferred when the sample size

The correlations between different mechanical parameters and different elements are studied using correlation analysis. Correlation analysis is defined as an analysis of two or more variables to evaluate the degrees of correlation between them. The correlation coefficient is the index used to quantitatively assess the degree of correlation. Common correlation coefficients include the Pearson coefficient, Kendall coefficient, and Spearman coefficient (Yue et al., 2002). In this paper, we use the Cambrian shale in the Cen'gong area of Guizhou as an example, extract 490 data groups (Tables 2 and 3) from the logs, and study the correlations between the major elements and the mechanical parameters.

Fig. 3. (A) The mineral composition of the Lower Cambrian shale in the northern Guizhou area; and (B) the kerogen macerals of the Lower Cambrian shale in the northern Guizhou area.

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Table 1 Quantitative detection of mineral composition of the Lower Cambrian shale by X - ray diffraction. Sample number

Depth (m)

Quartz (%)

Potash feldspar (%)

Plagioclase (%)

Calcite (%)

Dolomite (%)

Pyrite (%)

Clay (%)

TX-01 TX-02 TX-03 TX-04 TX-05 TX-06 TX-07 TX-08 TX-09 TX-10 TX-11 TX-12 TX-13 TX-14 TX-15 … TX-137 TX-138 TX-139 TX-140 TX-141 TX-142 TX-143 TX-144 TX-145 TX-146

1770.55 1771.05 1771.55 1772.05 1772.55 1773.05 1774.1 1774.6 1775.1 1775.6 1776.05 1776.5 1777 1777.5 1778 … 1787.8 1788.4 1789 1789.5 1790 1790.5 1792 1793 1793.5 1794

44.2 45.5 55.8 40.6 56.1 51.1 56.9 38.3 42.9 53.5 49.2 53.3 40.3 40.3 50.3 … 71.2 69.4 66.2 63.2 58.3 64.4 61.5 80.8 58.2 65.1

1.0 1.2 1.2 1.0 0.9 1.1 1.3 1.5 1.4 1.4 / 0.9 2.5 2.6 1.7 … / 2.1 2.4 2.0 1.9 / 2.2 / 2.6 /

8.7 7.8 6.9 6.2 6.2 6.8 8.0 7.7 6.9 7.0 6.1 5.6 8.4 8.7 7.0 … 4.4 4.3 4.7 5.4 6.9 8.1 6.7 4.6 8.9 4.4

/ / / / / / / 8.7 / 3.1 8.8 3.8 / / / … / / 0.5 3.7 4.5 / 0.7 1.8 0.6 2.5

4.4 6.8 1.5 8.7 2.3 2.4 6.9 7.5 5.1 3.2 5.7 5.2 9.6 12 5.0 … 2.3 / 4.0 5.6 6.8 4.5 5.7 3.2 4.2 3.1

6.3 5.9 6.0 14.5 6.2 8.2 8.5 13.9 9.2 10.9 8.5 7.5 11.1 16.8 8.2 … 5.9 7.9 8.9 4.9 9.0 10.2 12.0 6.6 11.6 7.8

35.3 32.9 28.6 28.9 28.3 30.5 18.4 22.4 34.5 20.9 21.7 23.7 28.0 19.5 27.8 … 16.2 16.3 13.3 15.1 12.7 12.8 11.3 3.0 13.9 17.0

Table 2 Sorting table of element content and mechanical parameters. Number

1

2

3

4

5

6

…

485

486

487

488

489

490

Ti/% S/% Si/% Mn/% Mg/% K/% Fe/% Ca/% Al/% Μ/% E/104MPa BM/104MPa SM/104MPa SS/MPa BI

0.0003 2.0066 32.0407 0.0914 0.0082 0.1088 0.0007 4.2349 5.3868 0.19 4.44 2.39 1.86 8.23 49.92

0.0005 2.1560 30.8382 0.0735 0.0287 0.1424 0.0010 6.3711 4.8269 0.24 5.76 3.65 2.33 16.33 52.80

0.0021 2.4336 32.6989 0.0966 0.0669 0.4696 0.0048 3.0575 6.4018 0.24 6.11 3.92 2.46 18.58 51.55

0.0016 2.3247 34.3548 0.0751 0.0521 0.6268 0.0104 2.9179 5.1488 0.24 5.56 3.50 2.25 15.09 51.23

0.0019 1.7738 32.6744 0.1076 0.0615 0.6892 0.1245 5.9065 4.1249 0.16 7.34 3.63 3.15 20.68 71.74

0.0019 3.0066 33.0723 0.0632 0.0541 0.5628 0.1371 4.1610 4.5400 0.17 5.06 2.57 2.16 10.08 56.31

… … … … … … … … … … … … … … …

0.4921 0.5241 28.4647 0.0488 0.2958 3.2501 5.5061 0.7205 7.1725 0.28 4.36 3.30 1.70 11.17 24.89

0.4456 0.1364 27.4051 0.0103 0.3810 3.9088 5.5536 0.6656 8.2099 0.30 4.49 3.71 1.73 12.91 26.33

0.3682 0.2979 30.6583 0.0269 0.1317 3.7052 5.6305 0.4015 5.9539 0.31 3.53 3.15 1.34 8.60 16.42

0.3872 0.3084 30.6763 0.0293 0.1949 3.6919 5.6970 0.4284 5.6087 0.28 4.46 3.36 1.74 11.62 24.81

0.4754 0.1353 29.9523 0.0127 0.0835 3.7477 5.8519 0.1895 6.4871 0.30 4.31 3.57 1.66 11.96 21.12

0.3878 0.6192 28.9343 0.0356 0.1794 3.1729 5.8915 1.0203 6.0327 0.30 4.41 3.63 1.70 12.41 25.45

In Table 1, μ is Poisson ratio; E is Young's modulus; BM = bulk modulus; SM = shear modulus; SS = shear strength; and BI = brittleness index.

N ≤ 2000, whereas the D-test is preferred when the sample size N > 2000. For these two tests, a P value greater than 0.05 indicates that the data follow a normal distribution. As shown in Table 4, all the P values of the variables are less than 0.05 for the D-test and the W-test, which implies that most of the data are not significantly normal. Thus, a non-parametric test is applied to assess the correlation of the variables (i.e., the Spearman rank coefficient Rs). The detailed procedure is as follows:

Rs2 =

− 2TY ⋅

(n3 − n) 6

− 2TX

(10)

(3) Establish a hypothesis test to determine the significance level. (4) Calculate the test statistics. If the same di value does not occur in the correlation analysis of the two variables, then the correlation between the variables is calculated using Eq. (6); otherwise, Eq. (7) is used. The levels of correlation between different variables can be calculated using Eqs. (6) and (7) (Table 5). Negative values represent negative correlations between two variables, and positive values represent positive correlations.

The Spearman rank correlation coefficient (Rs) has two equations: n

6 ∑i = 1 di2 n (n2 − 1)

(n3 − n) 6

where di is the rank order difference of the ith pair of variables (X, Y), n is the number of data groups, TX (or TY) = ∑t3-t, and t is the number of the same rank in X (or Y). When TX = TY = 0, the equations are equivalent.

(1) Coding rank: Sequentially code the observed values of the X and Y variables from small to large. (2) Substitute the data into the equation for calculation.

Rs1 = 1 −

[(n3 − n)/6] − (TX + TY ) − ∑ di2

(9)

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Fig. 4. The GEM and XMAC logging interpretation of the Niutitang Formation in the TX-1 well. PSIW = porosity of shaly irreducible water; PMF = porosity of movable fluid; PCIW = porosity of capillary irreducible water; SM = shear modulus; BM = bulk modulus; DREWF = Dry rock elemental weight fraction; CSWR = compressional and shear wave ratio; CWS = compressional wave slowness; SWS = shear wave slowness; and STWS=Stoneley wave slowness.

with all nine elements in the following order: K > Fe > Al > Ti > Si > Mg > Ca > Mn. The bulk modulus has no significant correlations with the Ti, Si, and Mg contents, a correlation of low significance with the Mn content, and highly significant correlations with S, Fe, K, Ca, and Al in the order Fe > Al > K > Ca > S. The shear modulus has highly significant correlations with all nine elements: Fe > K > Al > Ti > Si > Mg > S > Ca > Mn. The shear strength has no significant correlations with the S and Mn contents and highly significant correlations with the other elements: Fe > K > Al > Ti > Si > Ca > Mg.

Table 3 Statistical distribution of the element content and mechanical parameters.

Ti S Si Mn Mg K Fe Ca Al μ E BM SM SS BI

N

Average (%)

Minimum (%)

Maximum (%)

SD

490 490 490 490 490 490 490 490 490 490 490 490 490 490 490

0.25 0.73 31.32 0.03 0.18 2.42 3.28 2.68 5.30 0.25 5.39 3.62 2.17 15.37 43.18

0.00 0.00 1.84 0.00 0.00 0.11 0.00 0.00 0.00 0.04 2.54 2.23 0.94 5.74 12.46

0.62 4.21 44.24 0.41 4.58 4.83 5.89 36.54 15.01 0.35 8.33 7.35 3.56 41.89 85.72

0.12 0.68 6.92 0.03 0.34 1.10 1.39 5.94 2.69 0.05 1.12 0.68 0.52 5.37 15.24

5.2. Unreliable determination of mechanical parameters using only the element contents Several mathematical models have been developed to determine the mineralogy and petrology of rocks based on their elemental compositions (Ajayi and Torres-Verdín, 2016; Anderson et al., 1988; Chen et al., 2015b; Freedman et al., 2015). In this study, the elemental contents of the shale, especially the Si content, have different correlations and significance with the mechanical characteristics in different ranges. As shown in Table 6, the correlations of Si with Poisson's ratio (μ), Young's modulus (E), shear strength (SS), and the brittleness index (BI) are different for different Si contents (CSi). Through the change in the magnitude and significance of the correlation, the range of “Si” for different classes is determined. When 1.84% < CSi < 28.08%, the Si content has a slightly significant positive correlation with Poisson's ratio (Rs: 0.227) and highly significant negative correlations with E, SS, and BI in the order SS > E > BI. With increasing Si content in this range of contents, E, SS, and BI decrease, and Poisson's ratio increases. When 28.10% < CSi < 31.32%, the Si content has correlations of low significance with μ, E, SS, and BI; that is, the relationships between the Si content and the mechanical parameters are unclear in this range of Si contents. When 31.37% < CSi < 44.24%, the Si content has a highly significant negative correlation with Poisson's ratio (Rs: -0.524) and highly significant positive correlations with E, SS, and BI in the order E > BI > SS. In this range of Si contents, E, SS, and BI increase with

In Table 3, SD = standard deviation.

5. Results and discussion 5.1. Correlations between the element contents and mechanical parameters In this paper, the correlation is highly significant when the confidence level is 0.95, and the correlation has low significance when the confidence level is 0.99; the others have no significant correlation (Tables 5 and 6). As shown in Table 5, Poisson's ratio has no significant correlation with the Ca content and high correlations (99% confidence) with the other eight elements. The correlations are in the following order: Si > Ti > Fe > K > Al > Mg > S > Mn. Young's modulus has a low significance correlation (95% confidence) with the Mn content and highly correlates (99% confidence) with the other eight elements in the following order: Fe > K > Al > Ti > Si > Mg > Ca > S. In addition, the brittleness has highly significant correlations

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Fig. 5. (A) Frequency distribution of the K elemental content; (B) P-P plot of the K elemental content; (C) Frequency distribution of Young's modulus; and (D) PP plot of Young's modulus.

Si content is greater than 31%, the Si is provided by the quartz due to the high Si content of quartz (46.24%). Hence, with increasing Si content, the quartz content increases, and the clay content decreases, which results in an increasing Young's modulus, shear strength, and brittleness index and a decreasing Poisson's ratio. These results demonstrate that it is risky to determine the mechanical properties of shale based only on the elemental composition in different regions. Rather, mathematical models are required to constrain the rock mechanical parameters, mineralogy and petrology corresponding to different elemental and mineral compositions.

Table 4 Normal distribution test of element contents and mechanical parameters. K-S

Ti Sul Si Mn Mg K Fe Ca Al μ E BM SM SS BI

S-W

Statistic

P

Statistic

P

0.074 0.186 0.121 0.195 0.301 0.104 0.114 0.326 0.046 0.074 0.096 0.095 0.134 0.133 0.097

.000 .000 .000 .000 .000 .000 .000 .000 .015 .000 .000 .000 .000 .000 .000

0.981 0.798 0.862 0.580 0.404 0.953 0.939 0.402 0.986 0.977 0.943 0.862 0.923 0.898 0.963

.000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000

5.3. Brittleness index mathematical model of the niutitang shale The brittleness of shale is an important index to evaluate the rock mechanics characteristics of reservoirs, which determines the fracturing of shale gas reservoirs and has a significant impact on the exploration and development of shale gas (Chong et al., 2010; Kahraman and Altindag, 2004). The mineral composition method is based on the amount of quartz, feldspar, carbonate and other brittle minerals as a percentage of the total mineral content to indicate shale brittleness. The brittleness index is calculated as follows:

increasing Si content, and Poisson's ratio decreases. The XRD analysis (Fig. 3A and Table 1) and the mineral elemental contents (Table 7) of the shale samples demonstrate that the Si in the shale in the Cen'gong area is primarily from quartz and clay minerals, which consist of illite and illite-smectite (Fig. 6A). The Si content of the quartz is 46.24%, and that of the clay minerals in the Lower Cambrian shale is 23 ± 1% (Table 7). The XRD analyses demonstrate a negative correlation between the quartz and the clay minerals (Fig. 6B), and the total content of quartz and clay minerals is greater than 50% (Fig. 6C). The Si variation in the shale samples may be due to the relative variation of the quartz and clay minerals. When the Si content is less than 28%, most of the Si is from clay minerals, which results in a decreasing Young's modulus, shear strength, and brittleness index and an increasing Poisson's ratio with increasing Si content. In contrast, when the

BRIT m =

V Qtz+V Fs+V Cal+V Dolo+V Pyr × 100 V Qtz+V Fs+V Cal+V Dolo+V Pyr + V Clay

(11)

In Eq. (11), VQtz, VFs, VCal, VDolo, VPyr, and VClay are the volume contents of quartz, feldspar, calcite, dolomite, pyrite, and clay minerals, respectively. The elemental content method is based on the content of the elements Si, Ca, and Mg to indicate shale brittleness. The brittleness index is calculated as follows:

BRIT e =

ω (Si + Ca + Mg ) − ω (Si + Ca + Mg )min × 100 ω (Si + Ca + Mg )max−ω (Si + Ca + Mg )min

(12)

Fig. 7 shows the brittleness index of shale calculated by the 25

Marine and Petroleum Geology 91 (2018) 19–28

0.666 −0.313∗∗ −0.658∗∗ −0.136∗∗ 0.338∗∗ 0.732∗∗ 0.644∗∗ −0.270∗∗ 1 0.527∗∗ −0.710∗∗ −0.229∗∗ −0.717∗∗ −0.572∗∗ −0.747∗∗ 0.804 −0.348∗∗ −0.449∗∗ −0.206∗∗ 0.411∗∗ 0.844∗∗ 1 −0.362∗∗ 0.644∗∗ 0.548∗∗ −0.766∗∗ −0.275∗∗ −0.767∗∗ −0.632∗∗ −0.816∗∗

−0.299 0.768∗∗ −0.245∗∗ 0.371∗∗ 0.048 −0.422∗∗ −0.362∗∗ 1 −0.270∗∗ 0.032 0.195∗∗ 0.201∗∗ 0.163∗∗ 0.230∗∗ 0.225∗∗

∗∗

Al

∗∗

Ca

0.777 −0.473∗∗ −0.486∗∗ −0.413∗∗ 0.422∗∗ 1 0.844∗∗ −0.422∗∗ 0.732∗∗ 0.536∗∗ −0.724∗∗ −0.228∗∗ −0.727∗∗ −0.583∗∗ −0.832∗∗

∗∗

Fe

0.396 0.02 −0.369∗∗ 0.027 1 0.422∗∗ 0.411∗∗ 0.048 0.338∗∗ 0.278∗∗ −0.288∗∗ −0.032 −0.305∗∗ −0.192∗∗ −0.361∗∗

∗∗

K

Ti S Si Mn Mg K Fe Ca Al μ E BM SM SS BI

1 −0.385∗∗ −0.513∗∗ −0.267∗∗ 0.396∗∗ 0.777∗∗ 0.804∗∗ −0.299∗∗ 0.666∗∗ 0.569∗∗ −0.613∗∗ −0.044 −0.643∗∗ −0.417∗∗ −0.732∗∗

−0.385 1 −0.007 0.549∗∗ 0.02 −0.473∗∗ −0.348∗∗ 0.768∗∗ −0.313∗∗ −0.216∗∗ 0.172∗∗ −0.117∗∗ 0.188∗∗ 0.046 0.301∗∗

−0.513 −0.007 1 0.029 −0.369∗∗ −0.486∗∗ −0.449∗∗ −0.245∗∗ −0.658∗∗ −0.717∗∗ 0.573∗∗ −0.012 0.616∗∗ 0.350∗∗ 0.667∗∗

−0.267 0.549∗∗ 0.029 1 0.027 −0.413∗∗ −0.206∗∗ 0.371∗∗ −0.136∗∗ −0.154∗∗ 0.111∗ −0.103∗ 0.133∗∗ 0.02 0.220∗∗

∗∗

Mg

∗∗

Mn

∗∗

Si

∗∗

S Ti

Table 5 Magnitude and significance of the correlation coefficient between element contents and mechanical parameters.

Table 6 Magnitude and significance of the correlation coefficient between rock mechanical parameters and Si content.

In Table 5, "*" indicates that the correlation is of low significance when the confidence level is 0.95; "**" indicates that the correlation has high significance when the confidence level is 0.99; the others have no significant correlation.

−0.732∗∗ 0.301∗∗ 0.667∗∗ 0.220∗∗ −0.361∗∗ −0.832∗∗ −0.816∗∗ 0.225∗∗ −0.747∗∗ −0.801∗∗ 0.886∗∗ 0.169∗∗ 0.919∗∗ 0.653∗∗ 1 −0.417 0.046 0.350∗∗ 0.02 −0.192∗∗ −0.583∗∗ −0.632∗∗ 0.230∗∗ −0.572∗∗ −0.237∗∗ 0.888∗∗ 0.813∗∗ 0.813∗∗ 1 0.653∗∗ −0.643 0.188∗∗ 0.616∗∗ 0.133∗∗ −0.305∗∗ −0.727∗∗ −0.767∗∗ 0.163∗∗ −0.717∗∗ −0.706∗∗ 0.985∗∗ 0.361∗∗ 1 0.813∗∗ 0.919∗∗ −0.044 −0.117∗∗ −0.012 −0.103∗ −0.032 −0.228∗∗ −0.275∗∗ 0.201∗∗ −0.229∗∗ 0.308∗∗ 0.484∗∗ 1 0.361∗∗ 0.813∗∗ 0.169∗∗ −0.613 0.172∗∗ 0.573∗∗ 0.111∗ −0.288∗∗ −0.724∗∗ −0.766∗∗ 0.195∗∗ −0.710∗∗ −0.616∗∗ 1 0.484∗∗ 0.985∗∗ 0.888∗∗ 0.886∗∗ 0.569 −0.216∗∗ −0.717∗∗ −0.154∗∗ 0.278∗∗ 0.536∗∗ 0.548∗∗ 0.032 0.527∗∗ 1 −0.616∗∗ 0.308∗∗ −0.706∗∗ −0.237∗∗ −0.801∗∗

∗∗

E

∗∗

μ

BM

SM

∗∗

SS

∗∗

BI

J. Liu et al.

Si content

N

Rs (Si, μ)

Rs (Si, E)

Rs (Si, SS)

Rs (Si, BI)

1.84–28.08 28.10–31.32 31.37–44.24

110 110 270

0.227* −0.370* −0.524**

−0.482** 0.231* 0.708**

−0.538** 0.074 0.642**

−0.470** 0.301* 0.703**

elemental content method and the mineral composition method. After linear fitting of shale brittleness calculated by the two methods, the relative error of BRITe is -14–30%. In shale layers with higher shale content, BRITe is greater than BRITm, and the relative error of BRITe is small in shale layers with low shale content (Fig. 7B), which may be related to the mineral composition of the Niutitang shale. When the clay content is high, more of the Si, Mg and Ca contents come from illite, montmorillonite, and illite mixed layers, which leads to larger calculated BRITe (Fig. 7A and C). Based on the composition of the minerals in the Niutitang shale (Figs. 3A and 6A) and the mineral chemical composition (Table 7), a brittleness correction model for the Niutitang shale based on the elemental content of the Cen'gong block is proposed:

ω (Si/ Al) − ω (Si/ Mg )min BRIT c = ⎡ ⎢ ⎣ ω (Si/ Al)max−ω (Si/ Mg )min ω (Si/ Al) − ω (Si/ Mg )min ⎤ × 50 + ω (Si/ Al)max−ω (Si/ Mg )min ⎥ ⎦

(13)

Using Eq. (13), the corrected shale brittleness index (BRITc) is obtained, and the BRITc relative errors calculated after linear fitting with BRITm are determined. The calculated errors are concentrated in the range of -10–10%. With the new model, the relative error of BRITc is significantly reduced. Therefore, when evaluating the mechanical properties of shale based on the element contents, mathematical models are required to constrain the rock mechanical parameters, mineralogy, and petrology corresponding to different elemental compositions or to establish a mathematical model for evaluating shale brittleness based on the shale composition in the study area. In the actual evaluation of shale brittleness, the shale mineral composition is obtained by XRD analysis. Based on the mineral composition, a suitable rock brittleness correction model can be established to evaluate the continuous brittleness of a single well. 6. Conclusions (1) In the analyzed shale reservoir, the magnitude, significance and sign (positive or negative) of the correlations between the Si content and the rock's mechanical characteristics are different in different Si content ranges. When 1.84% < CSi < 28.08%, clay minerals are the primary source of Si, which results in a decreasing Young's modulus and brittleness index and an increasing Poisson's ratio with increasing Si content. When 28.10% < CSi < 31.32%, the Si is provided by both quartz and clay minerals, and there are no significant correlations between the Si content and the mechanical characteristics. When 31.37% < CSi < 44.24%, quartz is the primary source of Si, which results in an increasing Young's modulus and brittleness index and a decreasing Poisson's ratio with increasing Si content. (2) In general, Poisson's ratio is correlated with Si (negative), Ti (positive), Fe (positive), K (positive), and Al (positive). Young's modulus and the brittleness index are also highly significantly correlated with these five elements, although the positive-negative correlations are opposite to those of Poisson's ratio. The bulk modulus is highly significantly correlated with Fe, Al, K, and Ca with consistent correlations. The shear modulus and strength are generally highly correlated with Fe (negative), K (negative), Al (positive), Ti (negative), and Si (positive). 26

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Table 7 Mineral chemical composition (according to Harvey and Lovell, 1992a, 1992b).

Quartz Plagioclase Potash feldspar Illite Montmorillonite Chlorite Kaolinite Glauconite Muscovite Calcite Dolomite Anhydrite Siderite Pyrite Hematite

Si

Al

Ti

Fe

Mg

Ca

K

Mn

46.24 30.15 30.02 23.23 22.96 11.6 22.23 23.03 20.97 – – – – –

0.12 11.36 10.08 13.95 9.08 21.34 20.09 3.23 17.74 – – – – –

0.006 – 0.006 0.254 – – 0.036

0.105 0.403 0.077 2.788 1.12 17.22 0.455 19.55 1.73 – – – 48.3 46.67 70

0.078 0.09 0.006 1.652 3.048 2.916 0.006 0.48 0.486 0.024 12.672 – – –

1.793 0.026 0.229 1.086 0.135 0.021 0.079 0.264 39.944 22.336 29.43 – – -

0.017 0.929 10.92 5.824 – – 0.714 5 8.688 – – – – –

0.008 0.008 – – 0.008 – 0.039 – 0.17 – – –

0.246 – – – – –

S 0.01 – – – – – – – – 23.52 53.33 –

Fig. 6. (A) The clay mineral composition of the shale in the Cen'gong area; (B) the relationship between the quartz content and clay content; and (C) statistics of the total quartz and clay content. G represents the sample points with total quartz and clay content less than 50%.

Fig. 7. Comprehensive columnar section of rock brittleness indices of the Niutitang shale in the TX-1 well.

Acknowledgments

(3) In elemental logging, it is not reasonable to rely on only the elemental composition to determine the mechanical properties of shale in different regions. Instead, mathematical models are required to constrain the rock mechanical parameters, mineralogy, and petrology corresponding to different elemental and mineral compositions.

This research was supported by the Fundamental Research Funds for the Central Universities (2652017308), the National Natural Science Foundation of China (Grant Nos. 41372139 and 41072098), and the National Science and Technology Major Project of China 27

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(2016ZX05046-003-001 and 2016ZX05034-004-003). The authors would like to thank the staff of all the laboratories that cooperated in performing the tests and analyses. We are also grateful to the anonymous reviewers, whose comments improved the quality of this manuscript.

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Nomenclature G SS K(BM) ρb Ed μd Δtp: Δts EBrit μBrit BI XRD VQtz VFs VCal VDolo VPyr VClay Vsh XMAC

Shear modulus Shear strength Bulk modulus Rock density Dynamical Young's modulus Dynamical Poisson's ratio Time intervals of the P-waves Time intervals of the S-waves Normalized Young's modulus Normalized Poisson's ratio Brittleness index X-ray diffractometer Quartz content Feldspar content Calcite content Dolomite content Pyrite content Clay content Clay content Cross multipole array acoustic

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