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The construction of shale rock physics model and brittleness prediction for high-porosity shale gas-bearing reservoir

The construction of shale rock physics model and brittleness prediction for high-porosity shale... Due to the huge differences between the unconventional shale and conventional sand reservoirs in many aspects such as the types and the characteristics of minerals, matrix pores and fluids, the construction of shale rock physics model is significant for the exploration and development of shale reservoirs. To make a better characterization of shale gas-bearing reservoirs, we first propose a new but more suitable rock physics model to characterize the reservoirs. We then use a well A to demonstrate the feasibility and reliability of the proposed rock physics model of shale gas-bearing reservoirs. Moreover, we propose a new brittleness indicator for the high-porosity and organic-rich shale gas-bearing reservoirs. Based on the parameter analysis using the constructed rock physics model, we finally compare the new brittleness indicator with the commonly used Young’s modulus in the content of quartz and organic matter, the matrix porosity, and the types of filled fluids. We also propose a new shale brittleness index by integrating the proposed new brittleness indicator and the Poisson’s ratio. Tests on real data sets demonstrate that the new brittleness indicator and index are more sensitive than the commonly used Young’s modulus and brittleness index for the high-porosity and high-brittleness shale gas-bearing reservoirs. Keywords Shale gas · Rock physics model · Brittleness prediction 1 Introduction detection with geophysical method are significant for the shale gas reservoirs. Nowadays, the shale gas becomes an important type of Rock physics constructs the relationship between the energy and accounts for about 50% of unconventional gas elastic properties (P-wave velocity, S-wave velocity, density, resources. The current exploration and development of shale etc.) and underground reservoir parameters (porosity, fluid gas are mainly concentrated in the USA, Canada and some saturation, clay content, etc.), which is the foundation of European countries. Though there is a great potential for reservoir prediction and hydrocarbon detection with seismic shale gas resources in China, the exploration and develop- data. It is crucial to the seismic inversion and interpreta- ment of shale gas reservoirs are still at the exploratory stage tion (Wang 2001; King 2005; Xu and Payne 2009; Ma due to the complex geological conditions, strong heteroge- et al. 2010; Zhang et al. 2015a, b; Pan et al. 2018a, 2018b). neities, deep reservoir burials, and so on (Li et al. 2011; Some scholars have studied the rock physics theory of shale Dong et al. 2011; Yu 2012; Pan et al. 2017; Pan and Zhang gas-bearing reservoirs so far. Bayuk et al. (2008) develop 2019). Therefore, to the reservoir characterization and fluid a rock physics model of organic-rich shale, in which the kerogen is treated as the background load-bearing matrix, and the other minerals and pore/cracks are then added. Wu et al. (2012) develop an organic-rich shale anisotropic rock Edited by Jie Hao physics model, who mix the kerogen with the other minerals to calculate the effective rock properties. Zhu et al. ( 2012) * Guang-Zhi Zhang place the organic matter as a part of inclusion space to cal- zhanggz@upc.edu.cn culate the elastic properties, which is in accordance with the School of Geoscience and Info-Physics, Central South well log data. Based on the rock physics model of Zhu et al. University, Changsha 410082, Hunan, China (2012), Bandyopadhyay et al. (2012) analyze the uncertain- School of Geoscience, China University of Petroleum (East ties of rock property inversion in organic-rich shale. Zhang China), Qingdao 266580, Shandong, China Vol:.(1234567890) 1 3 Petroleum Science (2020) 17:658–670 659 et al. (2015a, b) establish an anisotropic rock physics model Young’s modulus is sensitive to changes in mineral content, of shale rocks based on the characterization of anisotropic while the brittleness formula based on Lamé constants is formation, shale minerals, matrix pores, fractures, and fluids sensitive to porosity/pore fluids. filling in pores and fractures. Considering the organic mat- Considering the characteristics of shale gas-bearing reser- ter content and strong anisotropy characteristics, Qian et al. voir, we present the construction process of shale rock phys- (2016) construct a rock physics model suitable for the shale ics model. Using this model, the P- and S-wave velocities gas-bearing reservoirs in Southwest China. According to the can be estimated. Well A in a shale gas-bearing work area is characteristics of high content of shale clay and interlayer taken as an example to verify this model. It is found that the micro-fractures, Liu et al. (2018) build a shale rock physics P- and S-wave velocities and the P-to-S-wave velocity ratio model of Longmaxi Formation in Sichuan Basin, who use are in agreement well with the true logs. For the organic-rich the Backus average theory to describe the elastic parameters and high-porosity shale gas-bearing reservoirs, we propose of shale clay minerals, the Chapman theory to calculate the a new brittleness indicator—E∕ . We compare it with the vertical transversely isotropy (VTI) related to the horizontal commonly used brittleness indicator—E from both theoreti- micro-fractures, and the Bond transformation to consider cal models and real data sets. Results show that compared the influence of dip angles. However, the existing shale rock with E , the new brittleness indicator is more sensitive to the physics models are mainly aimed at the influence of organic characterization of shale gas-bearing reservoirs. matter, and neglect the comprehensive characteristics of shale minerals, organic matter, matrix pores, and fluids. The exploration and development potential of shale gas- 2 T he construction of shale rock physics bearing reservoirs is huge, but it needs large-scale hydrau- model lic fracturing during the process of development due to the ultra-low permeability of reservoirs. The brittle shale 2.1 Voigt–Reuss–Hill (V–R–H) average rocks are conductive to the development of natural frac- tures and hydraulic fracturing network, and therefore, the For the case of an isotropic, completely elastic medium, optimal selection parameters that can effectively represent when the composition and relative content of each phase of the brittleness of rocks are of great significance for identi- rock are known, the upper and lower boundaries of the effec- fying the brittle shale rocks and optimizing the favorable tive elastic moduli of the mixture can be obtained (Mavko fracture zones (Fu et al. 2011; Li et al. 2012; Chen et al. 2009) as 2014). In recent years, many scholars have put forward many elastic parameters to characterize the brittleness of rocks. M = f M (1) V i i Grieser and Bray (2007) propose the most commonly used i=1 shale brittleness index based on Young’s modulus ( E ) and Poisson’s ratio (  ). Goodway et al. (2001, 2010) propose a characterization method of rock brittleness based on the = (2) M M product of Lamé constants ( and  ) and density (i.e., Lamé R i i=1 impedances,  and  ). On this basis, Perez and Marfurt where f and M are the volume fraction and the elastic mod- i i (2013) realize the seismic direct inversion of brittleness ulus of the i t h mater ial. parameters by using the real data. Alzate and Devegowda The arithmetic average of the upper and lower boundaries (2013) comprehensively use the intersection of four param- of the effective elastic moduli is Voigt–Reuss–Hill average, eters, including Young’s modulus, Poisson’s ratio, and Lamé which can be used to estimate the effective elastic moduli of impedances, for the analysis of shale brittleness in the actual isotropous rock expressed as working area. Compared with Young’s modulus, Sharma and Chopra (2012) believe that the product of Young’s modulus M + M V R M = (3) and density (i.e., Young’s impedance) can better character- VRH ize the brittleness of rocks. Liu and Sun (2015) propose two modified relative brittleness factors, and establish the min- 2.2 Self‑consistent approximation (SCA) model eral-elastic parameters-brittleness factor rock physics edition with the organic-rich shale rock physics model, who finally The SCA model is put forward by Budiansky (1965) and realize the spatial distribution prediction of high-quality brittle shale reservoirs. Qian et al. (2017) construct an ani- Hill (1965). Because the effect of pore shape and interaction of inclusions close to each other are taking into account, sotropic rock physics model of organic-rich shale rocks by simulating the coupling between organic matter and clay. this model can be used for the rock with slightly higher concentrations of inclusions. Berryman (1980, 1995) gives Their research is found that the brittleness index based on 1 3 660 Petroleum Science (2020) 17:658–670 a general form of the self-consistent approximations for where K , K , K and K are the effective bulk modulus of d m f N-phase composites saturated rock, dry rock, mineral material, and pore fluid, respectively;  and  are the effective shear modulus of ∗ ∗i saturated rock and dry rock; and  is the porosity. x K − K P = 0 (4) i i SC i=1 2.5 The shale characteristics analysis and construction workflow of rock physics ∗ ∗i model x  −  Q = 0 (5) i i SC i=1 Firstly, we analyze the characteristics of shale minerals. where i refers to the i th mater ial, x , K and  are its volume i i i The commonly used methods for mixing rock mineral fraction, bulk modulus and shear modulus of the i t h mate- compositions are Voigt–Reuss–Hill average, Hashin–Shtrik- rial, respectively, P and Q are geometric factors of inclu- man–Hill average, etc. (Ba et al. 2013). In this paper, we sions, and the superscript ∗ i on P and Q indicates that the consider the characteristics of shale minerals to calculate factors are used for an inclusion of material i in a back- the elastic modulus of rock matrix. ground medium with self-consistent effective moduli K SC The main mineral compositions of shale are clay, sand, and  . SC carbonate, etc. (Wang et al. 2010). In this work, the main rock compositions are clay, quartz, and calcite. Among 2.3 Kuster–Toksöz (K–T) model them, carbonate minerals are very few, mainly formed in the process of evolution after shale deposition and filled in Assuming that the dry-rock Poisson’s ratio is observed to be the pores or fractures in the form of calcite (Nie and Zhang constant with respect to the porosity, Keys and Xu (2002) 2011). From the scanning electron microphotographs pub- obtain simple analytic expressions for the effective bulk lished in Hornby et al. (1994) and Ruppel et al. (2008), it modulus of dry rock can be seen that the clay can be regarded as the background mineral of shale and filled with quartz and organic matter. K = K (1 − ) (6) d m So the traditional methods are not applicable for calculating the elastic parameters of the matrix minerals. According to =  (1 − ) (7) d m the distribution characteristics of shale minerals, we pro- ∑ ∑ 1 1 pose a new method of using the SCA model to calculate the where p = ∕ u T ( ) , q = ∕ u F( ) , and 3 l iijj l 5 l l l=p,s,m l=p,s,m equivalent elastic modulus of rock matrix, in which the clay F()= T ()− T () 3. ijij iijj is the solid mineral, the mixture of quartz and calcite getting In Eqs. (6) and (7), K and  are the effective bulk modu- d d by V–R–H average, and organic matter are inclusions with lus and shear modulus of dry rock with the porosity of  ; K different shapes. and  are the effective bulk modulus and shear modulus of Secondly, we analyze the characteristics of pores and mineral materials making up rock, respectively; u is the pore fluids. volume fraction;  is the aspect ratio of pores; p and q are The shale reservoir is a tight reservoir with low porosity the coefficients related to the pore aspect ratio; T ( ) and iijj and low permeability. Generally, its porosity is less than T ( ) are the functions of pore aspect ratio. ijij l 10%. There are some disconnected micro-pores distrib- uted in shale, especially in the clay component of it. The 2.4 Gassmann’s equation main fluids in shale are water and gas. Among them, water can be divided into two types: free water (water can move Under the condition of low frequency, Gassmann (1951) freely) and bound water (water cannot move freely). The calculates the modulus of saturated rock using the known shale gas is mainly composed of adsorbed gas and free gas, moduli of dry rock, mineral material and pore fluids, which each accounting for about 50%. The adsorbed gas mainly can be expressed as occurs in the surface of clay particles and pores, while the 2 free gas occurs in matrix pores and natural fractures (Jiang 1 − et al. 2010). K =K + (8) 1− K With high micro-pore volume and large surface area, + − K K K f m m the clay mineral has relatively greater capacity of adsorb- ing fluids (Ding et  al. 2012). Therefore, there are much bound water and adsorbed gas in it. So the pores are divided d (9) into two types in this paper, including the disconnected micro-pore containing immovable fluid and the connected 1 3 Petroleum Science (2020) 17:658–670 661 micro-pore containing movable fluid (Zhang et al. 2015a, b). 2.6 Model test It is supposed that the micro-pores containing immovable fluid are sparsely distributed in clay with poor connectivity, The input parameters of the constructed shale rock physics which is added using the K-T model. And the micro-pores model in this paper mainly include: (1) the volume frac- containing movable fluid have some connectivity. So the tion, elastic moduli, and density of each component of shale combination of K-T model and DEM model are used to add matrix minerals (quartz, calcite, and clay); (2) the content the dry pores and then saturate them with the Gassmann of organic matter; (3) shale porosity, fluid saturation, elastic low-frequency relations. moduli, density, and other information. According to the analysis above, the workflow of shale A well A in a shale gas work area is used to test the con- rock physics effective model is obtained: structed shale rock physics model. We use the rock physics model to calculate P- and S-wave velocities of well A and (1) We calculate the elastic modulus parameters of “pure” then compare the results with the well log data to verify the shale by assuming that the clay is the background reliability and applicability of this model. medium, and then use the K-T model to add the dis- Table 1 gives the elastic moduli and density parameters of connected micro-pores with the immovable fluid. shale mineral components and filling fluids. Figure  2 shows (2) We calculate the elastic modulus parameters of the the well log data of clay content, quartz content, calcite con- mixture of quartz and calcite by using the formula of tent, TOC content, porosity, and water saturation obtained V–R–H average. from the logging interpretation of well A. Figure 3 shows (3) We use the SCA model to add the organic matter and the mixture of quartz and calcite to calculate the elastic moduli of “rock matrix.” Table 1 The mineral composition parameters used in rock physics (4) We use the K-T model and DEM model to add the dry model connected micro-pores and get the elastic moduli of “dry” skeleton. We simulate the different types of con- Minerals or fluids ρ, g/cm K, Gpa μ, Gpa nected micro-pores (such as intergranular pore and Calcite 2.71 76.8 32 fracture) by adjusting the pore aspect ratios. Quartz 2.65 21 45 (5) We use the Gassmann equation to add the pore fluids to Clay 2.6 2.9 7 the dry connected micro-pores and calculate the elastic Organic matter 1.3 2.7 parameters of saturated rock. Then we calculate the P- Water 1.02 2.25 0 and S-wave velocities. The flowchart is shown in Fig.  1. Gas 0.00065 0.00013 0 Organic Clay Micro-pores with immovable Quartz Calcite matter (Background medium) fluid (disconnected) V-R-H average K-T model Mineral mixture “Pure” shale SCA model “Rock matrix” Dry pores with some connectivity K-T model and DEM model Fluids “Dry” skeleton Gassmann equation Density, P- and S-wave velocities Saturated rock of rocks Fig. 1 The flowchart of constructed shale rock physics model 1 3 662 Petroleum Science (2020) 17:658–670 2200 2200 2200 2200 (a) (b) 2250 2250 2250 2250 2300 2300 2300 2300 2350 2350 2350 2350 2400 2400 2400 2400 2450 2450 2450 2450 2000 4000 6000 -0.1 0 0.1 2000 3000 4000 -0.10 0.1 V , m/s Error_V , / V , m/s Error_V , / P P S S 2200 2200 (c) 2250 2250 2300 2300 2350 2350 2400 2400 2450 2450 1.0 1.5 2.0 -0.10 0.1 V /V , / Error_V /V , / P S P S Fig. 2 The comparison of P- and S-wave velocities and P-to-S-wave velocity ratio estimated by shale rock physics model with well log data of well A. a P-wave velocity and estimation errors; b S-wave velocity and estimation errors; c P-to-S-wave velocity ratio and estimation errors the estimated results of P- and S-wave velocities, and P-to- 10%. The marked area indicates the target reservoir and the S-wave velocity ratio. estimated P- and S-wave velocities decrease in this target From Fig. 3a, b, we can see that the P- and S-wave veloci- area. ties calculated by the shale rock physics model are in good agreement with the well log data. Moreover, the estimated P-to-S-wave velocity ratio also agrees well with the true logs. The relative errors are very small and almost less than 1 3 Depth, m Depth, m Depth, m Petroleum Science (2020) 17:658–670 663 2200 2200 2200 2200 2200 2200 2250 2250 2250 2250 2250 2250 2300 2300 2300 2300 2300 2300 2350 2350 2350 2350 2350 2350 2400 2400 2400 2400 2400 2400 2450 2450 2450 2450 2450 2450 00.5 1.0 0.51.0 00.5 1.0 00.1 0.2 00.1 0.2 00.5 1.0 Clay content, / TOC content, /W Porosity, / ater saturation, / Quartz content, / Calcite content, / Fig. 3 Well log interpretation of clay content, quartz content, calcite content, organic matter content, porosity, and water saturation of well A 2 2 3 Brittleness analysis of high‑porosity shale V − 2V P S = = (11) gas‑bearing reservoir 2 2 2( + 2) 2V − 2V P S Due to the low-permeability characteristic of shale, the most E − E min effective way to improve the shale gas productivity is the E = (12) brittleness E − E artificial fracturing. Study found that in the same condition max min of geodynamic background, rock mineralogical composi- tions and mechanical properties, shale with high contents of max brittleness (13) organic matter and quartz is more brittle and easier to form min max natural and induced fractures under the action of tectonic stress in shale rocks. This is conducive to the gathering and E + brittleness brittleness BI = (14) seepage of shale gas (Jiang et al. 2010; Ding et al. 2012). Moreover, the fractures produced by fracturing and the frac- where V , V , and  represent the P- and S-wave velocities, ture network formed by primary pores and micro-fractures P S in shale gas-bearing reservoir both play a role in storage and and density, respectively; E and E represent the max min maximum and minimum of Young’s modulus ( E ) of rocks; migration of shale gas. Therefore, the high porosity of shale plays a positive role in the effect of artificial fracturing. In  and  represent the maximum and minimum of max min Poisson’s ratio (  ) of rocks; BI represents the brittleness addition, the area with high gas content is undoubtedly the target location of high gas production in shale gas-bearing index of rocks, which is the average of the sum of E brittleness and  . reservoirs. To sum up, the region with high porosity, high brittleness organic matter content, and high brittle mineral content is Young’s modulus ( E ) indicates the stiffness of rocks, which also known as the stiffness modulus. The greater the sweet spot of shale reservoirs with high brittleness. Generally speaking, Young’s modulus ( E ) and Poisson’s the value is, the greater the stiffness of rock is. Because the harder shales are better at fracturing than tough ratio (  ) are the most commonly used parameters to charac- terize the brittleness of rock. Greiser and Bray (2007) pro- shales, they increase the permeability of the area. There- fore, Young’s modulus ( E ) is usually used as an impor- pose the shale brittleness index expression based on Young’s modulus ( E ) and Poisson’s ratio (  ), which can be expressed tant index for the measurement of rock brittleness. Pois- son’s ratio (  ) can be used to characterize the transverse as deformation intensity of rocks. The higher its value is, the 2 2 3V − 4V (3 + 2) P S more prone it is to transverse deformation of rocks. Gen- E = = V (10) 2 2 ( + ) erally, the reservoir area with high Young’s modulus ( E ) , V − V P S low Poisson’s ratio (  ), and high brittleness index ( BI ) is 1 3 Depth, m 664 Petroleum Science (2020) 17:658–670 the sweet spot of shale brittleness (Goodway et al. 2010; modulus ( E ), Poisson’s ratio (  ), brittleness index ( BI ) , Sharma and Chopra 2012). new brittleness indicator ( E  ), and new brittleness index However, it is found that the sensitivity of Young’s modu- ( BI ). NEW lus ( E ) to shale brittleness is reduced by factors such as shale It is assumed that the matrix minerals of rocks only organic matter, porosity, and fluid (see Sect.  3.1 for details). contain quartz (its bulk modulus and shear modulus are Therefore, Young’s modulus ( E ) cannot be fully applied to 36.6  GPa and 45.0  GPa, respectively) and clay (its bulk the indication of brittleness of high gas shale with high TOC modulus and shear modulus are 21.0  GPa and 7.0  GPa, content and high porosity under certain circumstances. respectively), and the rocks are fully saturated with gas (its The first and second Lamé constants (  and  ) are related bulk modulus and shear modulus of 0.00013 GPa and 0 GPa, to the compressibility and rigidity of rocks and can improve respectively). The porosity range of the matrix pores is about the sensitivity to pore fluids and lithologic changes, further 0%–10%. On this basis, the above established rock phys- improving the effective identification of reservoir areas ics model of shale rocks is used to analyze the influence of (Goodway 2001). According to the analysis of hydrocarbon quartz content and porosity on Young’s modulus ( E ), Pois- content and brittleness properties of Texas Barnett shale, son’s ratio (  ), brittleness index ( BI ), new brittleness indica- Goodway et al. (2010) propose the areas of high Young’s tor ( E∕ ), and new brittleness index ( BI ), and the results NEW modulus ( E ), high first Lamé constants (  ) or Lamé imped- are shown in Fig. 4a–e, in which the different lines represent ance (  ) and low Poisson’s ratio (  ) to be the high shale the different quartz content. gas-bearing reservoirs. Combining the brittleness analysis of Figure 4a shows that Young’s modulus ( E ) increases with high gas shale in this work area, we propose a new brittle- the increase in quartz content and the decrease in poros- ness indicator—E  , namely the ratio of Young’s modulus ity. Therefore, Young’s modulus ( E ) in the high-porosity ( E ) to the first Lamé constants (  ). Meanwhile, similar to shale areas is less sensitive to the brittle minerals (quartz). the expression of shale brittleness index based on Young’s Figure 4b shows that Poisson’s ratio (  ) decreases with the modulus ( E ) and Poisson’s ratio (  ) proposed by Greiser increase in quartz content and decreases rapidly with the and Bray (2007), we propose a new shale brittleness index increase in porosity when the porosity of rock matrix is ( BI ) based on new brittleness indicator ( E∕ ) and Pois- greater than 4%. Therefore, Poisson’s ratio (  ) in the high- NEW son’s ratio (  ), which can be expressed as porosity shale areas is more sensitive to the brittle minerals (quartz). Figure 4c shows that the new brittleness indicator 2 2 2 V 3V − 4V (3 + 2) S P S ∕ ( E  ) increases with the increase in quartz content and the E∕ = = (15) 2 2 2 2 ( + ) rapid increase in porosity when the porosity of rock matrix is V − 2V V − V P S P S greater than 6%. Moreover, the change range of new brittle- ness indicator ( E∕ ) is more than Poisson’s ratio (  ). There- E∕ − (E∕) min fore, the new brittleness indicator ( E  ) in the high-porosity (E∕) = (16) brittleness (E∕) − (E∕) max min shale area is the most sensitive to brittle minerals (quartz). It can be seen from the comparison between Fig. 4d, e that (E∕) +  the quartz content has no correlation with the brittleness brittleness brittleness BI = (17) NEW index ( BI ) and the new brittleness index ( BI ). The new NEW brittleness index ( BI ) increases monotonously with the NEW where (E∕) and (E∕) represent the maximum and max min increase in porosity, but the brittleness index ( BI ) decreases minimum of new brittleness indicator ( E∕ ) of rocks; BI NEW first and then increases slowly with the increase in poros- represents the new brittleness index of rocks, which is the ity. In summary, the new brittleness index ( BI ) is more NEW average of the sum of (E∕) and  . brittleness brittleness sensitive to high-porosity shale areas. Because the area of high porosity, high brittleness, Secondly, we analyze the influence of organic matter and high gas reservoir can be regarded as the sweet spot content and fluid types on these five parameters, such as of shale gas-bearing reservoirs, we analyze the effects of Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index quartz, porosity, organic matter, and pore fluids to these five ( BI ), new brittleness indicator ( E∕ ), and new brittleness parameters of brittleness indicator, including Young’s modu- index ( BI ). NEW lus ( E ), Poisson’s ratio (  ), brittleness index ( BI ), new brit- It is assumed that the matrix minerals of rocks contain tleness indicator ( E∕ ), and new brittleness index ( BI ). NEW organic matter (its bulk modulus and shear modulus are 2.9 GPa and 2.7 GPa, respectively) and clay (its bulk modu- 3.1 Model analysis of brittleness parameters lus and shear modulus are 21.0 GPa and 7.0 GPa, respec- tively), and the range of the organic matter is about 0%–25%. Firstly, we analyze the influence of brittle minerals (quartz) The rocks are fully saturated with gas (its bulk modulus and and porosity on these five parameters, such as Young’s shear modulus are 0.00013 GPa and 0 GPa, respectively) 1 3 Petroleum Science (2020) 17:658–670 665 60 0.3 (a) (b) Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% 40 0.2 20 0.1 Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% 0 0 00.010.020.030.04 0.05 0.06 0.07 0.08 0.09 0.10 00.010.020.030.040.050.060.070.080.090.10 Porosity, / Porosity, / (c) Quartz content = 0% Quartz content = 40% (d) Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% Quartz content = 20% Quartz content = 60% 0.5 00.010.020.030.04 0.05 0.06 0.07 0.08 0.09 0.10 00.010.020.030.040.050.060.070.080.090.10 Porosity, / Porosity, / 1.0 (e) Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% 0.5 00.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Porosity, / Fig. 4 The influence of quartz content and porosity on Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index ( BI ), new brittleness indica- tor ( E∕  ), and new brittleness index ( BI ). a Young’s modulus ( E ); b Poisson’s ratio (  ); c brittleness index ( BI ); d new brittleness indicator NEW ( E∕  ); e new brittleness index ( BI ) NEW or water (its bulk modulus and shear modulus are 2.25 GPa range is very small. In contrast, the new brittleness index and 0 GPa, respectively). On this basis, the above estab- ( BI ) is more sensitive to the shales with high organic NEW lished rock physics model of shale rocks is used to analyze matter content. the influence of organic matter content and fluid types on In summary, compared with Young’s modulus ( E ) and Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index brittleness index ( BI ), the new brittleness indicator ( E∕ ) ( BI ), new brittleness indicator ( E∕ ), and new brittleness and new brittleness index ( BI ) are more sensitive to the NEW index ( BI ), and the results are shown in Fig. 5a–e, in sweet spot of shales with high quartz content, high organic NEW which the different lines represent the different fluid types. matter content, high porosity, and high gas content. Figure 5a, b shows that Young’s modulus ( E ) and Pois- son’s ratio (  ) reduce with the increase in organic matter 3.2 Case study content, and the water-saturated shale has lower values of Young’s modulus ( E ) and Poisson’s ratio (  ) than gas-sat-3.2.1 Cross‑plots analysis urated shale. Therefore, the high value of Young’s modu- lus ( E ) is less sensitive to the gas-bearing shales with high We use two sets of real data from different work areas to organic matter content. Figure 5c shows that the new brit- analyze Young’s modulus ( E ) and the new brittleness indica- tleness indicator ( E∕ ) increase with the increase in organic tor ( E∕ ) by cross-plots, and Figs. 6 and 7 show the results. matter content, and the gas-saturated shale has high value From Fig. 6, it can be seen that compared with Young’s of new brittleness indicator ( E∕ ) than the water-saturated modulus ( E ), the new brittleness indicator ( E∕ ) is more shale. Therefore, the new brittleness indicator ( E∕ ) is effective to separate the ductile shale from brittle sandstone, more sensitive to the shales with high organic matter con- and the gas-bearing sandstone has a higher value of the new tent. Moreover, it can be seen from Fig. 5d, e that the shale brittleness indicator ( E∕ ) than water-bearing one, so it is brittleness index ( BI ) first decreases and then increases with easy to separate them (dividing line 1). But it is difficult to the increase in organic matter content, and the variation separate the ductile shale and sandstone containing different 1 3 E/ ,  / E, GPa BI new, / BI, /  , / 666 Petroleum Science (2020) 17:658–670 12 15 (a) (b) Water saturated Water saturated Gas saturated Gas saturated 7 0 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 TOC content, / TOC content, / 2.5 1.0 (d) (c) Water saturated Water saturated 2.0 Gas saturated Gas saturated 1.5 0.5 1.0 0.5 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 TOC content, /TOC content, / 1.0 (e) Water saturated Gas saturated 0.5 0 0.05 0.10 0.15 0.20 0.25 TOC content, / Fig. 5 The influence of organic matter content and fluid types on these five parameters, such as Young’s modulus ( E ), Poisson’s ratio (  ), br ittle- ness index ( BI ), new brittleness indicator ( E∕  ), and new brittleness index ( BI ). a Young’s modulus ( E ); b Poisson’s ratio (  ); c brittleness NEW index ( BI ); d new brittleness indicator ( E∕  ); e new brittleness index ( BI ) NEW Gas bearing glauconitic sandstone Gas bearing sandstone Gas bearing lithic sandstone Water bearing sandstone Ductile shale Ductile shale Dividing line Dividing line 1 Dviding line 2 4 2 5 10 15 20 25 30 35 40 05 10 15 20 25 30 E, Gpa E, Gpa Fig. 7 Cross-plot of Young’s modulus ( E ) and the new brittleness Fig. 6 Cross-plot of Young’s modulus ( E ) and the new brittleness indicator ( E∕ ) indicator ( E∕ ) fluids by Young’s modulus ( E ). So the new brittleness indi- The data in Fig. 7 are the well log data from Mannville cator ( E  ) comes out as a superior attribute for the estima- region (Goodway 2001), in which the porosity of gas-bear- tion of rock brittleness and fluids. ing glauconitic sandstone and gas-bearing lithic sandstone 1 3 E/ ,  / E E/ , GP / , GP  a a E, GPa BI new, / BI, / , GPa E/ ,  / Petroleum Science (2020) 17:658–670 667 is about 15%–25% and 10%–18%, respectively. It can be 3.2.2 Well log data analysis observed from horizontal axis that the data of gas-bearing sandstone and background shale are partially overlap, and Using the same well log data set of well A that was used cannot be distinguished well by using Young’s modulus ( E ). to do model test above, Young’s modulus ( E ), Poisson’s However, the new brittleness indicator ( E∕ ) can distinguish ratio (  ), brittleness index ( BI ), new brittleness indicator gas-bearing sandstone and the background shale obviously ( E  ) and new brittleness index ( BI ) are compared and NEW (dividing line). In addition, for glauconitic sandstone with analyzed. larger porosity and lithic sandstone with smaller porosity, From Fig. 8a, it can be seen that Young’s modulus ( E ) the new brittleness indicator ( E∕ ) can also differentiate to has low value in the background ductile shale and gas- some extent. But if Young’s modulus ( E ) as the indicative bearing brittle shale, while it has high value in sand-shale factor, brittleness of lithic sandstone is higher than glauco- interbedding and carbonate rock formation. Combining the nitic sandstone, which obviously does not agree with the well log interpretation of Fig. 8b with rock physics analy- actual situation. sis above, it is found that in the background ductile shale section, the rock exhibits apparently ductile and Young’s modulus ( E ) is low due to its high clay content and low 2200 2200 2200 2200 2200 (a) Ductile shale 2250 2250 2250 2250 2250 2300 2300 2300 2300 2300 Sand-shale interbedding 2350 2350 2350 2350 2350 Gas bearing brittle shale 2400 2400 2400 2400 2400 Carbonate rocks 2450 2450 2450 2450 2450 20 40 60 80 0.2 0.3 24 00.5 1.0 00.5 1.0 E, GPa , / E/ ,  / BI, / BI new, / 2200 2200 2200 2200 (b) Ductile shale 2250 2250 2250 2250 2300 2300 2300 2300 Sand-shale interbedding 2350 2350 2350 2350 Gas bearing brittle shale 2400 2400 2400 2400 Carbonate rocks 2450 2450 2450 2450 20 40 60 05 10 15 05 10 15 050 100 Quartz content, %TOC content, %Porosity, %Water saturation, % Fig. 8 Parameter curves of well A. a Parameter curves of Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index ( BI ), new brittleness indi- cator ( E∕  ), and new brittleness index ( BI ); b well log interpretation of quartz content, organic matter content, porosity, and water saturation NEW 1 3 Depth, m Depth, m 668 Petroleum Science (2020) 17:658–670 quartz content. In sand-shale interbedding, Young’s high contents of organic matter, porosity and gas, while the modulus ( E ) has a high value because of the increase in new brittleness indicator ( E  ) can characterize gas-bearing quartz content and the low contents of porosity, fluids, and brittle rocks better. Besides quartz content, the new brittle- organic matter. In gas-bearing shale section, high quartz ness indicator ( E  ) is also sensitive to the comprehensive content can increase Young’s modulus ( E ), but the high effects of organic matter, porosity, and fluids. So this factor value of organic content, porosity and gas content reduce has better guiding significance for the selection of fracturing it. Therefore, the comprehensive effects of all these factors area of shale gas-bearing reservoirs. reduce the sensitivity of Young’s modulus ( E ) to quartz content, and the result shows low value. In carbonate rock section, the contents of carbonate minerals (calcite, dolo- 4 Conclusions mite, etc.) are high, and contents of quartz, organic mat- ter, pore are low, so the value of Young’s modulus ( E ) In this study, based on the comprehensive analysis of shale is high. While Poisson’s ratio (  ) shows high values in gas-bearing reservoir, we propose a new process of shale the background ductile shale section, intermediate values rock physics model to estimate the P- and S-wave veloci- in the sand-shale interbedding and carbonate rock forma- ties. The trial result shows that the estimated velocities are tion, and low values in gas-bearing sandstone section. In in good agreement with the well log data. background shale section, the new brittleness indicator We use the constructed rock physics model to make the ( E  ) shows low values. But in sand-shale interbedding analysis of the brittleness of organic-rich shale gas-bearing and carbonate rock section, it shows immediate values, reservoirs, and propose a new brittleness indicator ( E∕ ). and in gas-bearing sandstone section, it shows high values. Compared with the conventional brittleness indicator of Similarly, we find that in the background shale section, the Young’s modulus ( E ), the new brittleness indicator ( E∕ ) value of new brittleness indicator ( E  ) is low due to the is more sensitive to the high brittle shales with high organic high clay content and low quartz content and the result is matter content, high porosity, and high gas content, which consistent with Young’s modulus ( E ). In sand-shale inter- can be used to better indicate the sweet spot of shale gas- bedding, porosity and organic matter content are low and bearing reservoirs. Moreover, compared with the conven- the new brittleness indicator ( E  ) increases but Pois- tional shale brittleness index ( BI ) based on Young’s modu- son’s ratio (  ) decreases with the increase in the quartz lus ( E ) and Poisson’s ratio (  ), the new shale brittleness content. In gas-bearing shales, the high values of quartz index ( BI ) based on the new brittleness indicator ( E∕ ) NEW content, organic matter content, porosity and gas content and Poisson’s ratio (  ) is more sensitive to the characteriza- all enhance the new brittleness indicator ( E  ) and reduce tion of high-porosity shale gas-bearing reservoirs. There- Poisson’s ratio (  ); therefore, the new brittleness indica- fore, the combination of the new brittleness indicator ( E∕ ), tor ( E  ) has the maximum value, and Poisson’s ratio Poisson’s ratio (  ), and new shale brittleness index ( BI ) NEW (  ) shows the minimum value. In carbonate rock section, can better indicate the strong fracturing zone of shale gas- because the carbonate minerals (calcite, dolomite, etc.) bearing reservoirs. have some brittleness and high content, the values of the new brittleness indicator ( E  ) and Poisson’s ratio (  ) Open Access This article is licensed under a Creative Commons Attri- bution 4.0 International License, which permits use, sharing, adapta- are medium. tion, distribution and reproduction in any medium or format, as long The shale brittleness index ( BI ), which combines Young’s as you give appropriate credit to the original author(s) and the source, modulus ( E ) and Poisson’s ratio (  ), has high values in sand- provide a link to the Creative Commons licence, and indicate if changes shale interbedding and carbonate rock sections, immediate were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated values in gas-bearing shales, and low values in background otherwise in a credit line to the material. If material is not included in shale section. However, the new brittleness index ( BI ), NEW the article’s Creative Commons licence and your intended use is not which combines the new brittleness indicator ( E∕ ) and permitted by statutory regulation or exceeds the permitted use, you will Poisson’s ratio (  ), has the largest values in gas-bearing need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativ ecommons .or g/licenses/b y/4.0/. shales, medium values in sand-shale interbedding section, and low values in background shale section. Moreover, the values of each section show obvious differences. 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The construction of shale rock physics model and brittleness prediction for high-porosity shale gas-bearing reservoir

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Abstract

Due to the huge differences between the unconventional shale and conventional sand reservoirs in many aspects such as the types and the characteristics of minerals, matrix pores and fluids, the construction of shale rock physics model is significant for the exploration and development of shale reservoirs. To make a better characterization of shale gas-bearing reservoirs, we first propose a new but more suitable rock physics model to characterize the reservoirs. We then use a well A to demonstrate the feasibility and reliability of the proposed rock physics model of shale gas-bearing reservoirs. Moreover, we propose a new brittleness indicator for the high-porosity and organic-rich shale gas-bearing reservoirs. Based on the parameter analysis using the constructed rock physics model, we finally compare the new brittleness indicator with the commonly used Young’s modulus in the content of quartz and organic matter, the matrix porosity, and the types of filled fluids. We also propose a new shale brittleness index by integrating the proposed new brittleness indicator and the Poisson’s ratio. Tests on real data sets demonstrate that the new brittleness indicator and index are more sensitive than the commonly used Young’s modulus and brittleness index for the high-porosity and high-brittleness shale gas-bearing reservoirs. Keywords Shale gas · Rock physics model · Brittleness prediction 1 Introduction detection with geophysical method are significant for the shale gas reservoirs. Nowadays, the shale gas becomes an important type of Rock physics constructs the relationship between the energy and accounts for about 50% of unconventional gas elastic properties (P-wave velocity, S-wave velocity, density, resources. The current exploration and development of shale etc.) and underground reservoir parameters (porosity, fluid gas are mainly concentrated in the USA, Canada and some saturation, clay content, etc.), which is the foundation of European countries. Though there is a great potential for reservoir prediction and hydrocarbon detection with seismic shale gas resources in China, the exploration and develop- data. It is crucial to the seismic inversion and interpreta- ment of shale gas reservoirs are still at the exploratory stage tion (Wang 2001; King 2005; Xu and Payne 2009; Ma due to the complex geological conditions, strong heteroge- et al. 2010; Zhang et al. 2015a, b; Pan et al. 2018a, 2018b). neities, deep reservoir burials, and so on (Li et al. 2011; Some scholars have studied the rock physics theory of shale Dong et al. 2011; Yu 2012; Pan et al. 2017; Pan and Zhang gas-bearing reservoirs so far. Bayuk et al. (2008) develop 2019). Therefore, to the reservoir characterization and fluid a rock physics model of organic-rich shale, in which the kerogen is treated as the background load-bearing matrix, and the other minerals and pore/cracks are then added. Wu et al. (2012) develop an organic-rich shale anisotropic rock Edited by Jie Hao physics model, who mix the kerogen with the other minerals to calculate the effective rock properties. Zhu et al. ( 2012) * Guang-Zhi Zhang place the organic matter as a part of inclusion space to cal- zhanggz@upc.edu.cn culate the elastic properties, which is in accordance with the School of Geoscience and Info-Physics, Central South well log data. Based on the rock physics model of Zhu et al. University, Changsha 410082, Hunan, China (2012), Bandyopadhyay et al. (2012) analyze the uncertain- School of Geoscience, China University of Petroleum (East ties of rock property inversion in organic-rich shale. Zhang China), Qingdao 266580, Shandong, China Vol:.(1234567890) 1 3 Petroleum Science (2020) 17:658–670 659 et al. (2015a, b) establish an anisotropic rock physics model Young’s modulus is sensitive to changes in mineral content, of shale rocks based on the characterization of anisotropic while the brittleness formula based on Lamé constants is formation, shale minerals, matrix pores, fractures, and fluids sensitive to porosity/pore fluids. filling in pores and fractures. Considering the organic mat- Considering the characteristics of shale gas-bearing reser- ter content and strong anisotropy characteristics, Qian et al. voir, we present the construction process of shale rock phys- (2016) construct a rock physics model suitable for the shale ics model. Using this model, the P- and S-wave velocities gas-bearing reservoirs in Southwest China. According to the can be estimated. Well A in a shale gas-bearing work area is characteristics of high content of shale clay and interlayer taken as an example to verify this model. It is found that the micro-fractures, Liu et al. (2018) build a shale rock physics P- and S-wave velocities and the P-to-S-wave velocity ratio model of Longmaxi Formation in Sichuan Basin, who use are in agreement well with the true logs. For the organic-rich the Backus average theory to describe the elastic parameters and high-porosity shale gas-bearing reservoirs, we propose of shale clay minerals, the Chapman theory to calculate the a new brittleness indicator—E∕ . We compare it with the vertical transversely isotropy (VTI) related to the horizontal commonly used brittleness indicator—E from both theoreti- micro-fractures, and the Bond transformation to consider cal models and real data sets. Results show that compared the influence of dip angles. However, the existing shale rock with E , the new brittleness indicator is more sensitive to the physics models are mainly aimed at the influence of organic characterization of shale gas-bearing reservoirs. matter, and neglect the comprehensive characteristics of shale minerals, organic matter, matrix pores, and fluids. The exploration and development potential of shale gas- 2 T he construction of shale rock physics bearing reservoirs is huge, but it needs large-scale hydrau- model lic fracturing during the process of development due to the ultra-low permeability of reservoirs. The brittle shale 2.1 Voigt–Reuss–Hill (V–R–H) average rocks are conductive to the development of natural frac- tures and hydraulic fracturing network, and therefore, the For the case of an isotropic, completely elastic medium, optimal selection parameters that can effectively represent when the composition and relative content of each phase of the brittleness of rocks are of great significance for identi- rock are known, the upper and lower boundaries of the effec- fying the brittle shale rocks and optimizing the favorable tive elastic moduli of the mixture can be obtained (Mavko fracture zones (Fu et al. 2011; Li et al. 2012; Chen et al. 2009) as 2014). In recent years, many scholars have put forward many elastic parameters to characterize the brittleness of rocks. M = f M (1) V i i Grieser and Bray (2007) propose the most commonly used i=1 shale brittleness index based on Young’s modulus ( E ) and Poisson’s ratio (  ). Goodway et al. (2001, 2010) propose a characterization method of rock brittleness based on the = (2) M M product of Lamé constants ( and  ) and density (i.e., Lamé R i i=1 impedances,  and  ). On this basis, Perez and Marfurt where f and M are the volume fraction and the elastic mod- i i (2013) realize the seismic direct inversion of brittleness ulus of the i t h mater ial. parameters by using the real data. Alzate and Devegowda The arithmetic average of the upper and lower boundaries (2013) comprehensively use the intersection of four param- of the effective elastic moduli is Voigt–Reuss–Hill average, eters, including Young’s modulus, Poisson’s ratio, and Lamé which can be used to estimate the effective elastic moduli of impedances, for the analysis of shale brittleness in the actual isotropous rock expressed as working area. Compared with Young’s modulus, Sharma and Chopra (2012) believe that the product of Young’s modulus M + M V R M = (3) and density (i.e., Young’s impedance) can better character- VRH ize the brittleness of rocks. Liu and Sun (2015) propose two modified relative brittleness factors, and establish the min- 2.2 Self‑consistent approximation (SCA) model eral-elastic parameters-brittleness factor rock physics edition with the organic-rich shale rock physics model, who finally The SCA model is put forward by Budiansky (1965) and realize the spatial distribution prediction of high-quality brittle shale reservoirs. Qian et al. (2017) construct an ani- Hill (1965). Because the effect of pore shape and interaction of inclusions close to each other are taking into account, sotropic rock physics model of organic-rich shale rocks by simulating the coupling between organic matter and clay. this model can be used for the rock with slightly higher concentrations of inclusions. Berryman (1980, 1995) gives Their research is found that the brittleness index based on 1 3 660 Petroleum Science (2020) 17:658–670 a general form of the self-consistent approximations for where K , K , K and K are the effective bulk modulus of d m f N-phase composites saturated rock, dry rock, mineral material, and pore fluid, respectively;  and  are the effective shear modulus of ∗ ∗i saturated rock and dry rock; and  is the porosity. x K − K P = 0 (4) i i SC i=1 2.5 The shale characteristics analysis and construction workflow of rock physics ∗ ∗i model x  −  Q = 0 (5) i i SC i=1 Firstly, we analyze the characteristics of shale minerals. where i refers to the i th mater ial, x , K and  are its volume i i i The commonly used methods for mixing rock mineral fraction, bulk modulus and shear modulus of the i t h mate- compositions are Voigt–Reuss–Hill average, Hashin–Shtrik- rial, respectively, P and Q are geometric factors of inclu- man–Hill average, etc. (Ba et al. 2013). In this paper, we sions, and the superscript ∗ i on P and Q indicates that the consider the characteristics of shale minerals to calculate factors are used for an inclusion of material i in a back- the elastic modulus of rock matrix. ground medium with self-consistent effective moduli K SC The main mineral compositions of shale are clay, sand, and  . SC carbonate, etc. (Wang et al. 2010). In this work, the main rock compositions are clay, quartz, and calcite. Among 2.3 Kuster–Toksöz (K–T) model them, carbonate minerals are very few, mainly formed in the process of evolution after shale deposition and filled in Assuming that the dry-rock Poisson’s ratio is observed to be the pores or fractures in the form of calcite (Nie and Zhang constant with respect to the porosity, Keys and Xu (2002) 2011). From the scanning electron microphotographs pub- obtain simple analytic expressions for the effective bulk lished in Hornby et al. (1994) and Ruppel et al. (2008), it modulus of dry rock can be seen that the clay can be regarded as the background mineral of shale and filled with quartz and organic matter. K = K (1 − ) (6) d m So the traditional methods are not applicable for calculating the elastic parameters of the matrix minerals. According to =  (1 − ) (7) d m the distribution characteristics of shale minerals, we pro- ∑ ∑ 1 1 pose a new method of using the SCA model to calculate the where p = ∕ u T ( ) , q = ∕ u F( ) , and 3 l iijj l 5 l l l=p,s,m l=p,s,m equivalent elastic modulus of rock matrix, in which the clay F()= T ()− T () 3. ijij iijj is the solid mineral, the mixture of quartz and calcite getting In Eqs. (6) and (7), K and  are the effective bulk modu- d d by V–R–H average, and organic matter are inclusions with lus and shear modulus of dry rock with the porosity of  ; K different shapes. and  are the effective bulk modulus and shear modulus of Secondly, we analyze the characteristics of pores and mineral materials making up rock, respectively; u is the pore fluids. volume fraction;  is the aspect ratio of pores; p and q are The shale reservoir is a tight reservoir with low porosity the coefficients related to the pore aspect ratio; T ( ) and iijj and low permeability. Generally, its porosity is less than T ( ) are the functions of pore aspect ratio. ijij l 10%. There are some disconnected micro-pores distrib- uted in shale, especially in the clay component of it. The 2.4 Gassmann’s equation main fluids in shale are water and gas. Among them, water can be divided into two types: free water (water can move Under the condition of low frequency, Gassmann (1951) freely) and bound water (water cannot move freely). The calculates the modulus of saturated rock using the known shale gas is mainly composed of adsorbed gas and free gas, moduli of dry rock, mineral material and pore fluids, which each accounting for about 50%. The adsorbed gas mainly can be expressed as occurs in the surface of clay particles and pores, while the 2 free gas occurs in matrix pores and natural fractures (Jiang 1 − et al. 2010). K =K + (8) 1− K With high micro-pore volume and large surface area, + − K K K f m m the clay mineral has relatively greater capacity of adsorb- ing fluids (Ding et  al. 2012). Therefore, there are much bound water and adsorbed gas in it. So the pores are divided d (9) into two types in this paper, including the disconnected micro-pore containing immovable fluid and the connected 1 3 Petroleum Science (2020) 17:658–670 661 micro-pore containing movable fluid (Zhang et al. 2015a, b). 2.6 Model test It is supposed that the micro-pores containing immovable fluid are sparsely distributed in clay with poor connectivity, The input parameters of the constructed shale rock physics which is added using the K-T model. And the micro-pores model in this paper mainly include: (1) the volume frac- containing movable fluid have some connectivity. So the tion, elastic moduli, and density of each component of shale combination of K-T model and DEM model are used to add matrix minerals (quartz, calcite, and clay); (2) the content the dry pores and then saturate them with the Gassmann of organic matter; (3) shale porosity, fluid saturation, elastic low-frequency relations. moduli, density, and other information. According to the analysis above, the workflow of shale A well A in a shale gas work area is used to test the con- rock physics effective model is obtained: structed shale rock physics model. We use the rock physics model to calculate P- and S-wave velocities of well A and (1) We calculate the elastic modulus parameters of “pure” then compare the results with the well log data to verify the shale by assuming that the clay is the background reliability and applicability of this model. medium, and then use the K-T model to add the dis- Table 1 gives the elastic moduli and density parameters of connected micro-pores with the immovable fluid. shale mineral components and filling fluids. Figure  2 shows (2) We calculate the elastic modulus parameters of the the well log data of clay content, quartz content, calcite con- mixture of quartz and calcite by using the formula of tent, TOC content, porosity, and water saturation obtained V–R–H average. from the logging interpretation of well A. Figure 3 shows (3) We use the SCA model to add the organic matter and the mixture of quartz and calcite to calculate the elastic moduli of “rock matrix.” Table 1 The mineral composition parameters used in rock physics (4) We use the K-T model and DEM model to add the dry model connected micro-pores and get the elastic moduli of “dry” skeleton. We simulate the different types of con- Minerals or fluids ρ, g/cm K, Gpa μ, Gpa nected micro-pores (such as intergranular pore and Calcite 2.71 76.8 32 fracture) by adjusting the pore aspect ratios. Quartz 2.65 21 45 (5) We use the Gassmann equation to add the pore fluids to Clay 2.6 2.9 7 the dry connected micro-pores and calculate the elastic Organic matter 1.3 2.7 parameters of saturated rock. Then we calculate the P- Water 1.02 2.25 0 and S-wave velocities. The flowchart is shown in Fig.  1. Gas 0.00065 0.00013 0 Organic Clay Micro-pores with immovable Quartz Calcite matter (Background medium) fluid (disconnected) V-R-H average K-T model Mineral mixture “Pure” shale SCA model “Rock matrix” Dry pores with some connectivity K-T model and DEM model Fluids “Dry” skeleton Gassmann equation Density, P- and S-wave velocities Saturated rock of rocks Fig. 1 The flowchart of constructed shale rock physics model 1 3 662 Petroleum Science (2020) 17:658–670 2200 2200 2200 2200 (a) (b) 2250 2250 2250 2250 2300 2300 2300 2300 2350 2350 2350 2350 2400 2400 2400 2400 2450 2450 2450 2450 2000 4000 6000 -0.1 0 0.1 2000 3000 4000 -0.10 0.1 V , m/s Error_V , / V , m/s Error_V , / P P S S 2200 2200 (c) 2250 2250 2300 2300 2350 2350 2400 2400 2450 2450 1.0 1.5 2.0 -0.10 0.1 V /V , / Error_V /V , / P S P S Fig. 2 The comparison of P- and S-wave velocities and P-to-S-wave velocity ratio estimated by shale rock physics model with well log data of well A. a P-wave velocity and estimation errors; b S-wave velocity and estimation errors; c P-to-S-wave velocity ratio and estimation errors the estimated results of P- and S-wave velocities, and P-to- 10%. The marked area indicates the target reservoir and the S-wave velocity ratio. estimated P- and S-wave velocities decrease in this target From Fig. 3a, b, we can see that the P- and S-wave veloci- area. ties calculated by the shale rock physics model are in good agreement with the well log data. Moreover, the estimated P-to-S-wave velocity ratio also agrees well with the true logs. The relative errors are very small and almost less than 1 3 Depth, m Depth, m Depth, m Petroleum Science (2020) 17:658–670 663 2200 2200 2200 2200 2200 2200 2250 2250 2250 2250 2250 2250 2300 2300 2300 2300 2300 2300 2350 2350 2350 2350 2350 2350 2400 2400 2400 2400 2400 2400 2450 2450 2450 2450 2450 2450 00.5 1.0 0.51.0 00.5 1.0 00.1 0.2 00.1 0.2 00.5 1.0 Clay content, / TOC content, /W Porosity, / ater saturation, / Quartz content, / Calcite content, / Fig. 3 Well log interpretation of clay content, quartz content, calcite content, organic matter content, porosity, and water saturation of well A 2 2 3 Brittleness analysis of high‑porosity shale V − 2V P S = = (11) gas‑bearing reservoir 2 2 2( + 2) 2V − 2V P S Due to the low-permeability characteristic of shale, the most E − E min effective way to improve the shale gas productivity is the E = (12) brittleness E − E artificial fracturing. Study found that in the same condition max min of geodynamic background, rock mineralogical composi- tions and mechanical properties, shale with high contents of max brittleness (13) organic matter and quartz is more brittle and easier to form min max natural and induced fractures under the action of tectonic stress in shale rocks. This is conducive to the gathering and E + brittleness brittleness BI = (14) seepage of shale gas (Jiang et al. 2010; Ding et al. 2012). Moreover, the fractures produced by fracturing and the frac- where V , V , and  represent the P- and S-wave velocities, ture network formed by primary pores and micro-fractures P S in shale gas-bearing reservoir both play a role in storage and and density, respectively; E and E represent the max min maximum and minimum of Young’s modulus ( E ) of rocks; migration of shale gas. Therefore, the high porosity of shale plays a positive role in the effect of artificial fracturing. In  and  represent the maximum and minimum of max min Poisson’s ratio (  ) of rocks; BI represents the brittleness addition, the area with high gas content is undoubtedly the target location of high gas production in shale gas-bearing index of rocks, which is the average of the sum of E brittleness and  . reservoirs. To sum up, the region with high porosity, high brittleness organic matter content, and high brittle mineral content is Young’s modulus ( E ) indicates the stiffness of rocks, which also known as the stiffness modulus. The greater the sweet spot of shale reservoirs with high brittleness. Generally speaking, Young’s modulus ( E ) and Poisson’s the value is, the greater the stiffness of rock is. Because the harder shales are better at fracturing than tough ratio (  ) are the most commonly used parameters to charac- terize the brittleness of rock. Greiser and Bray (2007) pro- shales, they increase the permeability of the area. There- fore, Young’s modulus ( E ) is usually used as an impor- pose the shale brittleness index expression based on Young’s modulus ( E ) and Poisson’s ratio (  ), which can be expressed tant index for the measurement of rock brittleness. Pois- son’s ratio (  ) can be used to characterize the transverse as deformation intensity of rocks. The higher its value is, the 2 2 3V − 4V (3 + 2) P S more prone it is to transverse deformation of rocks. Gen- E = = V (10) 2 2 ( + ) erally, the reservoir area with high Young’s modulus ( E ) , V − V P S low Poisson’s ratio (  ), and high brittleness index ( BI ) is 1 3 Depth, m 664 Petroleum Science (2020) 17:658–670 the sweet spot of shale brittleness (Goodway et al. 2010; modulus ( E ), Poisson’s ratio (  ), brittleness index ( BI ) , Sharma and Chopra 2012). new brittleness indicator ( E  ), and new brittleness index However, it is found that the sensitivity of Young’s modu- ( BI ). NEW lus ( E ) to shale brittleness is reduced by factors such as shale It is assumed that the matrix minerals of rocks only organic matter, porosity, and fluid (see Sect.  3.1 for details). contain quartz (its bulk modulus and shear modulus are Therefore, Young’s modulus ( E ) cannot be fully applied to 36.6  GPa and 45.0  GPa, respectively) and clay (its bulk the indication of brittleness of high gas shale with high TOC modulus and shear modulus are 21.0  GPa and 7.0  GPa, content and high porosity under certain circumstances. respectively), and the rocks are fully saturated with gas (its The first and second Lamé constants (  and  ) are related bulk modulus and shear modulus of 0.00013 GPa and 0 GPa, to the compressibility and rigidity of rocks and can improve respectively). The porosity range of the matrix pores is about the sensitivity to pore fluids and lithologic changes, further 0%–10%. On this basis, the above established rock phys- improving the effective identification of reservoir areas ics model of shale rocks is used to analyze the influence of (Goodway 2001). According to the analysis of hydrocarbon quartz content and porosity on Young’s modulus ( E ), Pois- content and brittleness properties of Texas Barnett shale, son’s ratio (  ), brittleness index ( BI ), new brittleness indica- Goodway et al. (2010) propose the areas of high Young’s tor ( E∕ ), and new brittleness index ( BI ), and the results NEW modulus ( E ), high first Lamé constants (  ) or Lamé imped- are shown in Fig. 4a–e, in which the different lines represent ance (  ) and low Poisson’s ratio (  ) to be the high shale the different quartz content. gas-bearing reservoirs. Combining the brittleness analysis of Figure 4a shows that Young’s modulus ( E ) increases with high gas shale in this work area, we propose a new brittle- the increase in quartz content and the decrease in poros- ness indicator—E  , namely the ratio of Young’s modulus ity. Therefore, Young’s modulus ( E ) in the high-porosity ( E ) to the first Lamé constants (  ). Meanwhile, similar to shale areas is less sensitive to the brittle minerals (quartz). the expression of shale brittleness index based on Young’s Figure 4b shows that Poisson’s ratio (  ) decreases with the modulus ( E ) and Poisson’s ratio (  ) proposed by Greiser increase in quartz content and decreases rapidly with the and Bray (2007), we propose a new shale brittleness index increase in porosity when the porosity of rock matrix is ( BI ) based on new brittleness indicator ( E∕ ) and Pois- greater than 4%. Therefore, Poisson’s ratio (  ) in the high- NEW son’s ratio (  ), which can be expressed as porosity shale areas is more sensitive to the brittle minerals (quartz). Figure 4c shows that the new brittleness indicator 2 2 2 V 3V − 4V (3 + 2) S P S ∕ ( E  ) increases with the increase in quartz content and the E∕ = = (15) 2 2 2 2 ( + ) rapid increase in porosity when the porosity of rock matrix is V − 2V V − V P S P S greater than 6%. Moreover, the change range of new brittle- ness indicator ( E∕ ) is more than Poisson’s ratio (  ). There- E∕ − (E∕) min fore, the new brittleness indicator ( E  ) in the high-porosity (E∕) = (16) brittleness (E∕) − (E∕) max min shale area is the most sensitive to brittle minerals (quartz). It can be seen from the comparison between Fig. 4d, e that (E∕) +  the quartz content has no correlation with the brittleness brittleness brittleness BI = (17) NEW index ( BI ) and the new brittleness index ( BI ). The new NEW brittleness index ( BI ) increases monotonously with the NEW where (E∕) and (E∕) represent the maximum and max min increase in porosity, but the brittleness index ( BI ) decreases minimum of new brittleness indicator ( E∕ ) of rocks; BI NEW first and then increases slowly with the increase in poros- represents the new brittleness index of rocks, which is the ity. In summary, the new brittleness index ( BI ) is more NEW average of the sum of (E∕) and  . brittleness brittleness sensitive to high-porosity shale areas. Because the area of high porosity, high brittleness, Secondly, we analyze the influence of organic matter and high gas reservoir can be regarded as the sweet spot content and fluid types on these five parameters, such as of shale gas-bearing reservoirs, we analyze the effects of Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index quartz, porosity, organic matter, and pore fluids to these five ( BI ), new brittleness indicator ( E∕ ), and new brittleness parameters of brittleness indicator, including Young’s modu- index ( BI ). NEW lus ( E ), Poisson’s ratio (  ), brittleness index ( BI ), new brit- It is assumed that the matrix minerals of rocks contain tleness indicator ( E∕ ), and new brittleness index ( BI ). NEW organic matter (its bulk modulus and shear modulus are 2.9 GPa and 2.7 GPa, respectively) and clay (its bulk modu- 3.1 Model analysis of brittleness parameters lus and shear modulus are 21.0 GPa and 7.0 GPa, respec- tively), and the range of the organic matter is about 0%–25%. Firstly, we analyze the influence of brittle minerals (quartz) The rocks are fully saturated with gas (its bulk modulus and and porosity on these five parameters, such as Young’s shear modulus are 0.00013 GPa and 0 GPa, respectively) 1 3 Petroleum Science (2020) 17:658–670 665 60 0.3 (a) (b) Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% 40 0.2 20 0.1 Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% 0 0 00.010.020.030.04 0.05 0.06 0.07 0.08 0.09 0.10 00.010.020.030.040.050.060.070.080.090.10 Porosity, / Porosity, / (c) Quartz content = 0% Quartz content = 40% (d) Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% Quartz content = 20% Quartz content = 60% 0.5 00.010.020.030.04 0.05 0.06 0.07 0.08 0.09 0.10 00.010.020.030.040.050.060.070.080.090.10 Porosity, / Porosity, / 1.0 (e) Quartz content = 0% Quartz content = 40% Quartz content = 20% Quartz content = 60% 0.5 00.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Porosity, / Fig. 4 The influence of quartz content and porosity on Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index ( BI ), new brittleness indica- tor ( E∕  ), and new brittleness index ( BI ). a Young’s modulus ( E ); b Poisson’s ratio (  ); c brittleness index ( BI ); d new brittleness indicator NEW ( E∕  ); e new brittleness index ( BI ) NEW or water (its bulk modulus and shear modulus are 2.25 GPa range is very small. In contrast, the new brittleness index and 0 GPa, respectively). On this basis, the above estab- ( BI ) is more sensitive to the shales with high organic NEW lished rock physics model of shale rocks is used to analyze matter content. the influence of organic matter content and fluid types on In summary, compared with Young’s modulus ( E ) and Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index brittleness index ( BI ), the new brittleness indicator ( E∕ ) ( BI ), new brittleness indicator ( E∕ ), and new brittleness and new brittleness index ( BI ) are more sensitive to the NEW index ( BI ), and the results are shown in Fig. 5a–e, in sweet spot of shales with high quartz content, high organic NEW which the different lines represent the different fluid types. matter content, high porosity, and high gas content. Figure 5a, b shows that Young’s modulus ( E ) and Pois- son’s ratio (  ) reduce with the increase in organic matter 3.2 Case study content, and the water-saturated shale has lower values of Young’s modulus ( E ) and Poisson’s ratio (  ) than gas-sat-3.2.1 Cross‑plots analysis urated shale. Therefore, the high value of Young’s modu- lus ( E ) is less sensitive to the gas-bearing shales with high We use two sets of real data from different work areas to organic matter content. Figure 5c shows that the new brit- analyze Young’s modulus ( E ) and the new brittleness indica- tleness indicator ( E∕ ) increase with the increase in organic tor ( E∕ ) by cross-plots, and Figs. 6 and 7 show the results. matter content, and the gas-saturated shale has high value From Fig. 6, it can be seen that compared with Young’s of new brittleness indicator ( E∕ ) than the water-saturated modulus ( E ), the new brittleness indicator ( E∕ ) is more shale. Therefore, the new brittleness indicator ( E∕ ) is effective to separate the ductile shale from brittle sandstone, more sensitive to the shales with high organic matter con- and the gas-bearing sandstone has a higher value of the new tent. Moreover, it can be seen from Fig. 5d, e that the shale brittleness indicator ( E∕ ) than water-bearing one, so it is brittleness index ( BI ) first decreases and then increases with easy to separate them (dividing line 1). But it is difficult to the increase in organic matter content, and the variation separate the ductile shale and sandstone containing different 1 3 E/ ,  / E, GPa BI new, / BI, /  , / 666 Petroleum Science (2020) 17:658–670 12 15 (a) (b) Water saturated Water saturated Gas saturated Gas saturated 7 0 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 TOC content, / TOC content, / 2.5 1.0 (d) (c) Water saturated Water saturated 2.0 Gas saturated Gas saturated 1.5 0.5 1.0 0.5 0 0.05 0.10 0.15 0.20 0.25 0 0.05 0.10 0.15 0.20 0.25 TOC content, /TOC content, / 1.0 (e) Water saturated Gas saturated 0.5 0 0.05 0.10 0.15 0.20 0.25 TOC content, / Fig. 5 The influence of organic matter content and fluid types on these five parameters, such as Young’s modulus ( E ), Poisson’s ratio (  ), br ittle- ness index ( BI ), new brittleness indicator ( E∕  ), and new brittleness index ( BI ). a Young’s modulus ( E ); b Poisson’s ratio (  ); c brittleness NEW index ( BI ); d new brittleness indicator ( E∕  ); e new brittleness index ( BI ) NEW Gas bearing glauconitic sandstone Gas bearing sandstone Gas bearing lithic sandstone Water bearing sandstone Ductile shale Ductile shale Dividing line Dividing line 1 Dviding line 2 4 2 5 10 15 20 25 30 35 40 05 10 15 20 25 30 E, Gpa E, Gpa Fig. 7 Cross-plot of Young’s modulus ( E ) and the new brittleness Fig. 6 Cross-plot of Young’s modulus ( E ) and the new brittleness indicator ( E∕ ) indicator ( E∕ ) fluids by Young’s modulus ( E ). So the new brittleness indi- The data in Fig. 7 are the well log data from Mannville cator ( E  ) comes out as a superior attribute for the estima- region (Goodway 2001), in which the porosity of gas-bear- tion of rock brittleness and fluids. ing glauconitic sandstone and gas-bearing lithic sandstone 1 3 E/ ,  / E E/ , GP / , GP  a a E, GPa BI new, / BI, / , GPa E/ ,  / Petroleum Science (2020) 17:658–670 667 is about 15%–25% and 10%–18%, respectively. It can be 3.2.2 Well log data analysis observed from horizontal axis that the data of gas-bearing sandstone and background shale are partially overlap, and Using the same well log data set of well A that was used cannot be distinguished well by using Young’s modulus ( E ). to do model test above, Young’s modulus ( E ), Poisson’s However, the new brittleness indicator ( E∕ ) can distinguish ratio (  ), brittleness index ( BI ), new brittleness indicator gas-bearing sandstone and the background shale obviously ( E  ) and new brittleness index ( BI ) are compared and NEW (dividing line). In addition, for glauconitic sandstone with analyzed. larger porosity and lithic sandstone with smaller porosity, From Fig. 8a, it can be seen that Young’s modulus ( E ) the new brittleness indicator ( E∕ ) can also differentiate to has low value in the background ductile shale and gas- some extent. But if Young’s modulus ( E ) as the indicative bearing brittle shale, while it has high value in sand-shale factor, brittleness of lithic sandstone is higher than glauco- interbedding and carbonate rock formation. Combining the nitic sandstone, which obviously does not agree with the well log interpretation of Fig. 8b with rock physics analy- actual situation. sis above, it is found that in the background ductile shale section, the rock exhibits apparently ductile and Young’s modulus ( E ) is low due to its high clay content and low 2200 2200 2200 2200 2200 (a) Ductile shale 2250 2250 2250 2250 2250 2300 2300 2300 2300 2300 Sand-shale interbedding 2350 2350 2350 2350 2350 Gas bearing brittle shale 2400 2400 2400 2400 2400 Carbonate rocks 2450 2450 2450 2450 2450 20 40 60 80 0.2 0.3 24 00.5 1.0 00.5 1.0 E, GPa , / E/ ,  / BI, / BI new, / 2200 2200 2200 2200 (b) Ductile shale 2250 2250 2250 2250 2300 2300 2300 2300 Sand-shale interbedding 2350 2350 2350 2350 Gas bearing brittle shale 2400 2400 2400 2400 Carbonate rocks 2450 2450 2450 2450 20 40 60 05 10 15 05 10 15 050 100 Quartz content, %TOC content, %Porosity, %Water saturation, % Fig. 8 Parameter curves of well A. a Parameter curves of Young’s modulus ( E ), Poisson’s ratio (  ), brittleness index ( BI ), new brittleness indi- cator ( E∕  ), and new brittleness index ( BI ); b well log interpretation of quartz content, organic matter content, porosity, and water saturation NEW 1 3 Depth, m Depth, m 668 Petroleum Science (2020) 17:658–670 quartz content. In sand-shale interbedding, Young’s high contents of organic matter, porosity and gas, while the modulus ( E ) has a high value because of the increase in new brittleness indicator ( E  ) can characterize gas-bearing quartz content and the low contents of porosity, fluids, and brittle rocks better. Besides quartz content, the new brittle- organic matter. In gas-bearing shale section, high quartz ness indicator ( E  ) is also sensitive to the comprehensive content can increase Young’s modulus ( E ), but the high effects of organic matter, porosity, and fluids. So this factor value of organic content, porosity and gas content reduce has better guiding significance for the selection of fracturing it. Therefore, the comprehensive effects of all these factors area of shale gas-bearing reservoirs. reduce the sensitivity of Young’s modulus ( E ) to quartz content, and the result shows low value. In carbonate rock section, the contents of carbonate minerals (calcite, dolo- 4 Conclusions mite, etc.) are high, and contents of quartz, organic mat- ter, pore are low, so the value of Young’s modulus ( E ) In this study, based on the comprehensive analysis of shale is high. While Poisson’s ratio (  ) shows high values in gas-bearing reservoir, we propose a new process of shale the background ductile shale section, intermediate values rock physics model to estimate the P- and S-wave veloci- in the sand-shale interbedding and carbonate rock forma- ties. The trial result shows that the estimated velocities are tion, and low values in gas-bearing sandstone section. In in good agreement with the well log data. background shale section, the new brittleness indicator We use the constructed rock physics model to make the ( E  ) shows low values. But in sand-shale interbedding analysis of the brittleness of organic-rich shale gas-bearing and carbonate rock section, it shows immediate values, reservoirs, and propose a new brittleness indicator ( E∕ ). and in gas-bearing sandstone section, it shows high values. Compared with the conventional brittleness indicator of Similarly, we find that in the background shale section, the Young’s modulus ( E ), the new brittleness indicator ( E∕ ) value of new brittleness indicator ( E  ) is low due to the is more sensitive to the high brittle shales with high organic high clay content and low quartz content and the result is matter content, high porosity, and high gas content, which consistent with Young’s modulus ( E ). In sand-shale inter- can be used to better indicate the sweet spot of shale gas- bedding, porosity and organic matter content are low and bearing reservoirs. Moreover, compared with the conven- the new brittleness indicator ( E  ) increases but Pois- tional shale brittleness index ( BI ) based on Young’s modu- son’s ratio (  ) decreases with the increase in the quartz lus ( E ) and Poisson’s ratio (  ), the new shale brittleness content. In gas-bearing shales, the high values of quartz index ( BI ) based on the new brittleness indicator ( E∕ ) NEW content, organic matter content, porosity and gas content and Poisson’s ratio (  ) is more sensitive to the characteriza- all enhance the new brittleness indicator ( E  ) and reduce tion of high-porosity shale gas-bearing reservoirs. There- Poisson’s ratio (  ); therefore, the new brittleness indica- fore, the combination of the new brittleness indicator ( E∕ ), tor ( E  ) has the maximum value, and Poisson’s ratio Poisson’s ratio (  ), and new shale brittleness index ( BI ) NEW (  ) shows the minimum value. In carbonate rock section, can better indicate the strong fracturing zone of shale gas- because the carbonate minerals (calcite, dolomite, etc.) bearing reservoirs. have some brittleness and high content, the values of the new brittleness indicator ( E  ) and Poisson’s ratio (  ) Open Access This article is licensed under a Creative Commons Attri- bution 4.0 International License, which permits use, sharing, adapta- are medium. tion, distribution and reproduction in any medium or format, as long The shale brittleness index ( BI ), which combines Young’s as you give appropriate credit to the original author(s) and the source, modulus ( E ) and Poisson’s ratio (  ), has high values in sand- provide a link to the Creative Commons licence, and indicate if changes shale interbedding and carbonate rock sections, immediate were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated values in gas-bearing shales, and low values in background otherwise in a credit line to the material. If material is not included in shale section. However, the new brittleness index ( BI ), NEW the article’s Creative Commons licence and your intended use is not which combines the new brittleness indicator ( E∕ ) and permitted by statutory regulation or exceeds the permitted use, you will Poisson’s ratio (  ), has the largest values in gas-bearing need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativ ecommons .or g/licenses/b y/4.0/. shales, medium values in sand-shale interbedding section, and low values in background shale section. Moreover, the values of each section show obvious differences. 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