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Performance of free gases during the recovery enhancement of shale gas by CO2 injection: a case study on the depleted Wufeng–Longmaxi shale in northeastern Sichuan Basin, China

Performance of free gases during the recovery enhancement of shale gas by CO2 injection: a case... In this work, a novel thermal–hydraulic–mechanical (THM) coupling model is developed, where the real geological param- eters of the reservoir properties are embedded. Accordingly, nine schemes of C O injection well (IW) and CH production 2 4 well (PW) are established, aiming to explore the behavior of free gases after C O is injected into the depleted Wufeng–Long- maxi shale. The results indicate the free CH or C O content in the shale fractures/matrix is invariably heterogeneous. The 4 2 CO involvement facilitates the ratio of free CH /CO in the matrix to that in the fractures declines and tends to be stable 2 4 2 with time. Different combinations of IW–PWs induce a difference in the ratio of the free CH to the free C O , in the ratio 4 2 of the free CH /CO in the matrix to that in the fractures, in the content of the recovered free CH , and in the content of the 4 2 4 trapped free CO . Basically, when the IW locates at the bottom Wufeng–Longmaxi shale, a farther IW–PWs distance allows more CO in the free phase to be trapped; furthermore, no matter where the IW is, a shorter IW–PWs distance benefits by getting more CH in the free phase recovered from the depleted Wufeng–Longmaxi shale. Hopefully, this work is helpful in gaining knowledge about the shale-based CO injection technique. Keywords CO geological sequestration · Enhanced shale gas recovery · Free gas · Wufeng–Longmaxi Formation · THM coupled modeling 1 Introduction reservoirs is becoming increasingly attractive and has been lauded as a win–win solution for meeting geological C O Current knowledge strongly supports CO sequestration in storage and simultaneous enhanced gas recovery (CS-EGR) geological formations (e.g., shale and coalbed) as a promis- from shales (Liu et al. 2017b, 2019a, b; Kalra et al. 2018; ing approach to respond to the issue of excessive anthropo- Pan et al. 2018; Yang et al. 2019; Zhang et al. 2020). How- genic CO emissions into the atmosphere, which is treated ever, understanding of shale-based CS-EGR is limited, with as carbon-negative technology and thus has been receiv- only few pilot field studies undertaken, in which strategy ing growing attention (Abidoye et al. 2015; Zhang et al. optimization, site characterization/monitoring, and hazard 2015; Wan and Liu 2018; Liu et al. 2020; Rani et al. 2020; assessment & management need to be taken into account Řimnáčová et al. 2020). Therein, injecting CO into shale in a comprehensive manner (Chi et al. 2017; Ajayi et al. 2019; Zhang et al. 2019; Chen et al. 2020; Iddphonce et al. 2020). In other words, despite being proven to be a feasible Edited by Yan-Hua Sun technique, CS-EGR in the shale is not yet mature enough for * Peng Zhao full national or worldwide deployment. scu_zhaopeng@163.com To promote the development of the shale-based CS-EGR 1 technique, considerable work has been organized, in which State Key Laboratory of Hydraulics and Mountain River significant achievements have been drawn (Iddphonce et al. Engineering, Institute of New Energy and Low-Carbon Technology, Sichuan University, Chengdu 610065, China 2020). For example, it has been proven that the CO –CH 2 4 displacement behavior differs in the shales from different College of Architecture and Environment, Sichuan University, Chengdu 610065, China sedimentary environments (Du et al. 2019). Another exam- ple is that the CS-EGR efficiency is considerably affected by Liaohe Oilfield Company, PetroChina, Panjin 124010, China Vol:.(1234567890) 1 3 Petroleum Science (2021) 18:530–545 531 the CO proportion in the injected CO –N mixture (Li and to several hundred meters, where vertical heterogeneity 2 2 2 Elsworth 2019). In one other example, NMR-based investi- emerges in many reservoir parameters, such as the porosity/ gation indicated that the properties (e.g., mineral composi- permeability, the Langmuir volume, and Young’s modulus tion) of shale reservoir can interfere with the CS-EGR out- (Tang et al. 2016; Liu et al. 2017a). Clearly, the development puts (Liu et al. 2019b). However, the examples mentioned of a comprehensive model that contains as many realistic above mainly pay attention to the gases (CO /CH ) in the conditions as possible is, therefore, the need of the hour, 2 4 adsorbed phase during the CO –CH interaction, in which aiming to enhance understanding of the free gases behavior 2 4 the performance of the free gases (CO /CH ) tends to be during the CS-EGR process in shales. 2 4 ignored. Unfortunately, neglecting the free gases in the pro- In this work, because the Wufeng–Longmaxi Forma- cess of shale-based CS-EGR does not exist in isolation and tion in the northeastern Sichuan Basin (SW China) has even is a common phenomenon reported in many literatures huge potential resources of shale gas (Liu et al. 2017a), it (Liu et al. 2017b; Zhou et al. 2019; Řimnáčová et al. 2020). is selected for simulation where the CS-EGR technique has Although the competitive adsorption of CO /CH is the the opportunity to be implemented. Accordingly, a ther- 2 4 primary element enabling CS-EGR in shales (Wang et al. mal–hydraulic–mechanical (THM) coupled model is devel- 2018b; Liu et al. 2019a), the gases in free phase inevitably oped using the COMSOL Multiphysics software, attempting appear to the spaces of the pores and fractures in shale res- to simulate the depleted condition of the Wufeng–Longmaxi ervoirs during the C O –CH interaction (Fathi and Akkutlu, shale. Herein, this integrated model not only contains the 2 4 2014). Basically, free gas is crucial for shale gas explora- responses of the rock deformation, competitive CH /CO 4 2 tion/exploitation and even occupies over 50% of in situ gas sorption, gas/water two-phase flow, and thermal expansion content in shales (Liu et al. 2016b). To separately study in the dual-porosity system but also involves the real hetero- the multiphase (free/adsorbed) gas in shales, experimental geneity of the reservoir properties of the Wufeng–Longmaxi approaches have been conducted, and sound achievements shale. Using a mathematical approach, this work focuses on have been made. For instance, isotopic geochemistry (Liu the dynamic interaction of free CO and free CH during the 2 4 et al. 2016b) and low-field NMR (Yao et al. 2019) were suc-continuous CO injection into the depleted Wufeng–Long- cessfully introduced to quantitatively identify the CH in the maxi shale, with a run time of roughly 30 years (10,000 free and adsorbed phase. Nevertheless, it was found that a d). Accordingly, in a quantitative manner, a series of simu- single experimental methodology was usually performed at lations are set to clarify the anisotropic content variation a restricted scale, and could hardly recognize the free CO of free gases (CO and CH ) in the modeling reservoir, 2 2 4 and free CH from the C O –CH mixture at the same time under different relative locations of the CO injection well 4 2 4 2 during the dynamic CO –CH interaction in shales. Given (IW) and the CH production well (PW). Furthermore, the 2 4 4 this situation, physics-based numerical simulations can be strengths and weaknesses of each IW–PWs combo are also employed to address concerns about the free gases during discussed, in terms of the different desired objectives. Hope- the shale-based CS-EGR process, in which multi-factors can fully, the peculiar perspectives from the gases in the free be investigated in a clear and transparent manner. phase during the CO –CH interaction in shales will help to 2 4 Up to a point, numerical attempts have given rise to deepen awareness on the potential field deployment of the knowledge improvement on the performance of free gases CS-EGR project in the shale reservoir. during the CS-EGR operation in shales. There are two exam- ples; one is that numerical work advocated that the portion of free gas is always less than that of adsorbed gas in the pro-2 Geological background cess of C O –CH interplay in shales, under variable reser- 2 4 voir permeability and temperature/pressure (Mohagheghian In this work, the case Wufeng–Longmaxi shale is from the et al. 2019). Another modeling study has suggested that an Well-WQ2 that is a shale gas exploration well and is located increase in the ratio of the free CH to adsorbed CH would in the northeastern Sichuan Basin, Southwest (SW) China 4 4 decrease the CO sequestration potential of the Utica shale (Fig. 1a). In this region, an arc tectonic belt system with a formation (Tao et al. 2014). Unfortunately, current simula- thrust belt trending to the southwest was formed by a series tions about free C H /CO in shales are usually run with a of tectonic activities, in which the Chengkou-Fangxian and 4 2 plain mathematical model with only a single layer or/and Shashi Buried fault zones are quintessential examples (Li isotropic conditions being simulated, which is contrary to et al. 2013; Ji et al. 2015; Liu et al. 2017a). field fact that multilayer and heterogeneous characteristics Figure 1b shows the continuous sedimentary succession exist extensively in shale reservoirs (Tang et al. 2016; Liu in the study area from the late Sinian to the Cenozoic Era, et  al. 2017a). For this reason, limited existing numerical except for the missing strata from the Devonian to the Car- achievements can be directly generalized and carried out boniferous period (Meng and Zhang 2000; Shi et al. 2012; in a real shale formation that usually has a thickness of tens Li et al. 2013). Under this sedimentary background, previous 1 3 Dabashan Epiplatform Sag Shashi Buried Fault Zone 532 Petroleum Science (2021) 18:530–545 (a) (b) Stratigraphy HC Lithology System system Formation Shaanxi Province 0 30 km ... ... ... ... Sandstone, mudstone . . . . Baitianba Jurassic . . . . basal conglomerate . . . Zhenping Mudstone Chengkou Xujiahe coal beds ... ... ... ... . . . . sandstone . . . . Chengkou-Fangxian Fault Zone Gypsum, halite Leikoupo Sichuan Province limestone Triassic Gypsum, halite Hubei Province Jialingjiang dolomite . . Tongjiezi Oolitic limestone . . . WQ2 . . . . Bioclastic limestone . . . Feixianguang dolostone Wuxi . . . . Changxing . . . Bioclastic limestone Wushan Mudstone, coal beds Wujiaping limestone Permian Wanzhou Sag Fold Belts Chert-bearing Chengdu Maokou limestone Chongqing Limestone Qixia mudstone Wa ... ... ... ... Sichuan Basin Cuijiagou ... ... ... ... Siltstone, shale Silurian Longmaxi Shale (c) -18 2 3 ... ... ... ... φ, % V , m /t P , MPa k, 10 m L L Wufeng Mudstone, siltstone -1 Layer No. Depth, m E, GPa v, 10 φ φ m f k k V V P P Ordovician . . . h v L-CH4 L-CO2 L-CH4 L-CO2 . . . . Baota Limestone 1 1200-1210 44.4 2.27 3.54 0.51 4.20 4.12 4.12 10.68 4.12 10.68 . . . . . . 2 1210-1220 45.6 2.70 2.78 0.32 1.82 3.84 3.84 8.75 3.84 8.75 Oolitic dolostone Sanyoudong . . . 3 1220-1230 51.5 2.52 2.07 0.43 3.20 3.58 3.58 8.69 3.58 8.69 . . . Qinjiamiao Limestone 4 1230-1240 63.8 2.08 2.84 0.66 4.60 3.04 3.04 9.50 3.04 9.50 Cambrian Shipai Dolostone 5 1240-1250 62.4 2.13 1.36 0.44 1.68 2.28 2.28 11.75 2.28 11.75 ... ... ... ... Carbonaceous 8.79 6 1250-1260 60.7 2.19 2.88 0.42 6.40 3.16 3.16 3.16 8.79 Guojiaba mudstone 5.00 2.60 2.60 13.99 2.60 13.99 7 1260-1270 60.9 2.18 1.72 0.53 HC-hydrocarbon system; E-Young's modulus; v-Poisson's ratio; 8 1270-1280 61.3 2.17 5.54 0.66 8.10 3.21 3.21 10.09 3.21 10.09 φ-Porosity; φ -Fracture porosity; φ -Matrix porosity; k-Permeability; f m 9 1280-1290 58.6 2.26 1.26 0.51 3.80 2.87 2.87 9.11 2.87 9.11 k -Horizontal permeability; k -Vertical permeability; V -Langmuir volume h v L 10 1290-1300 57.8 2.29 2.59 0.78 3.60 4.01 4.01 6.01 4.01 6.01 P -Langmuir pressure Fig. 1 Geological background of Well-WQ2 and the vertical heterogeneous reservoir characteristics (Shi et al. 2012; Li et al. 2013; Zhu et al. 2016; Liu et al. 2017a; Zhao et al. 2020). a Geological information of the Northeastern Sichuan Basin. b Integrated stratigraphic column of the Northeastern Sichuan Basin. c Vertical heterogeneity of the Wufeng–LongMaxi shales in the WQ2 shale well studies have identified two conventional hydrocarbon source which also has anisotropic characteristics in the reservoir systems (Fig. 1b): the bottom one (from the Cambrian Guo- properties (e.g., porosity/permeability) (Liu et al. 2016a, jiaba Formation to the Silurian Cuijiagou Formation) and the 2017a) (Fig. 1c). In addition, the well logs of Well-WQ2 upper one (from the Permian Qixia Formation to the Trias- indicate the temperature of the Wufeng–Longmaxi shale is sic Leikoupo Formation) (Li et al. 2013; Liu et al. 2017a). 36 °C (310 K), the water saturation is 0.3, and the in-situ Therein, during the shale gas exploration and exploitation, stresses in the horizontal and vertical directions are 30 MPa the Wufeng–Longmaxi shale is usually treated as a close and 36 MPa, respectively (Zhao et al. 2020). Such field data combination due to the conformable contact relationship provide a basis for the model development in this numerical between the upper Ordovician Wufeng Formation and the work, ensuring this model is as close to the real formation lower Silurian Longmaxi Formation (Zhu et al. 2016; Ye conditions as possible. et al. 2017; Wang et al. 2018a). The Wufeng–Longmaxi shale in the Well-WQ2 has a thickness of roughly 100  m with a buried depth of 3 Development of the mathematical model 1200–1300  m, where the bottom section (about 10  m) belongs to the Wufeng shale (Liu et  al. 2016a, 2017a). 3.1 Model description for the Wufeng–Longmaxi At such a buried depth, the depleted pressure of the shale Wufeng–Longmaxi shale is estimated at about 1.7  MPa (Zhang et al. 2015). Statistics suggest that the vertical het- Figure 2a exhibits the schematic of the simulation model in erogeneity is strong in the involved Wufeng–Longmaxi shale this work, which is treated as a typical pattern and contains 1 3 Huayingshan Mountain Convex Fold Belts Qiyaoshan Mountain Convex Fold Belts Reservoir beds Seal beds Source rocks Reservoir beds Seal beds Lower hydrocarbon system Upper hydrocarbon system Petroleum Science (2021) 18:530–545 533 300 m Layer 1 (a) (b) PWs candidate Layer 2 Layer 3 Layer 4 50 m Layer 5 100 m Layer 6 Layer 7 Layer 8 Layer 9 150 m Layer 10 (c) CO2 injection well (IW) CH4 production well (PW) CH4 CO2 Water Fractures Matrix pores Gas and water Mass exchange at Gas diffusion and flow in fracture matrix surface adsorption/desorption Shale skeleton Fig. 2 Schematic diagram of the process of CS-EGR in a shale reservoir (Zhao et al. 2020). All involved wells have a radius of 0.1 m. a Typical pattern of IW–PWs. b Relative locations of IW–PWs. c Mass transport of multi-fluids in the shale one injection well (IW) in the center and four production combos, when the IW is located at the lower section and is wells (PWs) in the corners (Li and Elsworth 2019). This pat- 50 m far away from the PWs in the horizontal direction, the tern is axisymmetric, so a two-dimensional representative is modeling case is labeled as L50. In a similar fashion, the selected for the numerical simulation (Fig. 2b). According to rest of the cases are marked as L100, L150, M50, M100, the geological parameters, the model height is determined as M150, H50, H100, and H150, respectively (Fig. 2). Herein, 100 m and is equally divided into ten sections to reveal the the layer 3, interface of layers 5–6, and layer 8, where the vertical heterogeneity of the reservoir properties. The model IW candidate is set, represent the upper, middle, and lower width is set 300 m to avoid possible influence of the right sections of the simulative shale reservoir, respectively. boundary condition (e.g., formation overpressure) (Li et al. 2017). Accordingly, the simulation area of 100 m × 300 m is divided into 5085 elements, and all boundaries are air- 3.2 THM coupling process and governing equations tight for flux, except for the right boundary with the initial gas pressure being set. As the CS-EGR operation is con- Since many parameters are involved in this simulation work ducted in the depleted conditions of the Wufeng–Longmaxi (see "Appendix"), CS-EGR in shales is identified as a com- shale, the initial pressure of the simulative reservoir is set as plicated process and involves integral feedback in the THM 2 MPa (that is, 0.3 MPa for C O and 1.7 MPa for CH ). In coupling phenomenon. Basically, the hydraulic field contains 2 4 this modeling process, under a temperature of 305 K, con- complex mass transport of binary gases (CO /CH ) with the 2 4 stant pressures of 0.1 MPa and 7 MPa are applied to the gas–water represented as two-phase flows superposed on PWs and IW during the CS-EGR process, respectively. To competitive non-isothermal adsorption (Fig. 2c). Once the develop the mathematical model, the primary parameters shale reservoir captures the nonthermally equilibrated C O , (see "Appendix") are obtained from the existing literatures heat transfer, such as thermal conduction/convection, occurs (Dahaghi 2010; Sun et al. 2013; Fathi and Akkutlu 2014; Li among the CH, CO , water, and shale skeleton, which is 4 2 and Elsworth 2015, 2019; Fan et al. 2019a, b, c; Ma et al. accompanied by energy release/adsorption associated with 2020; Zhao et al. 2020), while the key heterogeneous infor- gas adsorption/desorption, in turn impacting on the thermal mation on the Wufeng–Longmaxi shale is derived from real field (Fan et al. 2019a). Furthermore, the dynamic variation fieldwork (Fig.  1). in the hydraulic and thermal fields can interfere with the As shown in Fig. 2b, three IW candidates and three PWs mechanical field (e.g., shrink/swelling of the shale matrix), candidates are organized to investigate how the relative influencing the anisotropic porosity/permeability and thus locations of IW and PWs affect the free gas behavior of the affecting the convective fluxes of the water, gas, and energy CS-EGR operation in shales. Among these nine IW–PWs (Fan et al. 2019a). 1 3 Wufeng-Longmaxi Formation IW candidate a b a 100 m 534 Petroleum Science (2021) 18:530–545 The shale reservoir in this work is described as a dual- porosity media (Fig. 2c), which is used extensively in previ- ous numerical works (Bandis et al. 1983; Nassir et al. 2014; CH in matrix Li and Elsworth 2015, 2019; Zhou et al. 2018; Zhao et al. CH in fracture 2020). According to these works above, a series of govern- ing equations representing rock deformation, competitive CH /CO sorption, gas/water two-phase flow, and thermal 4 2 expansion are used for the CS-EGR model development in this work. 4 Results and discussion 0 200 400 600 80010001200140016001800 In the dual-porosity media, fractures and matrix pores are Free CH , kg the internal spaces of shale for trapping free gases ( CO / CH ). In this work, four types of free gases are classified Fig. 3 Original free CH content in modeling reservoir of the to investigate the behavior of free C O /CH during the CS- 2 4 depleted Wufeng–Longmaxi shale EGR process in the depleted Wufeng–Longmaxi shale— CH in the fracture, CO in the fracture, CH in the matrix 4 2 4 and CO in the matrix. Accordingly, this work separately After a production period of 10,000 d, the CS-EGR studies the performance of free CH or free CO , and then 4 2 operation enables the content difference of free CH in the the dynamic interaction between free CH and free C O dur- 4 2 fracture/matrix under variable IW–PWs combos. Accord- ing the recovery enhancement of shale gas by C O injection ing to the cloud pictures, at a fixed IW location, a farther into the depleted Wufeng–Longmaxi shale, under variable IW–PWs distance in the horizontal direction makes more IW–PWs locations. Note that this numerical model’s thick- CH in the free phase trapped in the shale fracture and ness value is 1 m when the gas content is calculated, where matrix after 10,000 d of CS-EGR operation (Fig.  5a, b). the involved gas content indicates the content of gas in free Comparatively, when PWs are located as fixed, there are less phase. obvious changes for the free CH in the shale fracture/matrix along with the variation of the IW location. Anyhow, after 4.1 Content variation of free CH 10,000 d of CS-EGR production, the vertical heterogeneity emerges for all outputs of free CH under different IW–PWs during shale‑based CS‑EGR process relative locations (Fig. 5a, b). To further display the heterogeneous characteristics of Prior to the involvement of the injected C O , the original content of free CH both in the fracture and in the matrix free CH in the Wufeng–Longmaxi shale, the content varia- tion of free CH in each layer is concluded at different points is strongly heterogeneous in the vertical direction, where the free CH in the matrix is visibly more than that in in time during the CS-EGR process. As shown in Fig. 6, the free CH content in each layer is dramatically affected by fracture (Fig.  3). This heterogeneous tendency is similar to the vertical variation of the fracture/matrix porosity of the relative locations of IW–PWs. A shorter IW–PWs dis- tance (fixed IW location) makes the CO injection-induced the Wufeng–Longmaxi shale shown in Fig. 1, owing to the free gas content being directly determined by the free space decrement of the free CH content greater, which is more obvious for the layers near the IW. Besides, when the PWs under the depleted reservoir pressure. Once the CO injec- tion starts, the content variation of the free CH in the frac- location is fixed, a smaller decrement goes to the free CH content in the layers close to the IW. Moreover, in some ture/matrix occurs. Taking M100 as an example, it is found that the free CH in the fracture continuously varies during operating cases, the content decrement is negative for the free CH in the layers near IW (e.g., Fig. 6a–c, e, f, h, i), the CS-EGR process, intuitively ree fl cting the accumulation of free CH in the left side of the PWs and the decrease in revealing that the CO injection facilitates the increment of free CH in shale fractures at the initial CS-EGR phase. Tak- that in the right side of the PWs (Fig. 4a). For the same case, the cloud pictures qualitatively indicate an overall reduction ing H150 as an example, the free CH content in the fracture of layer 1 first increases and then decreases (Fig.  7a), while of free CH in the matrix over time after C O is injected into 4 2 the shale reservoir (Fig. 4b). These variations address the that of layer 8 decreases monotonously (Fig. 7b), after CO is injected. This phenomenon is caused by the content vari- concept that the CO injection can facilitate the migration of free CH in the depleted Wufeng–Longmaxi shale reservoir. ation of free CH in the matrix. Using the same example of 1 3 Depth, m Petroleum Science (2021) 18:530–545 535 10 8 6 4 2 60 5 4 3 2 1 1.2 1.0 0.8 0.6 0.4 .2 6 5 4 3 2 1 (a) (b) (c) (d) -2 3 -1 3 3 3 CH4 in fracture, 10 kg/cm CH4 in matrix, 10 kg/cm CO2 in fracture, kg/cm CO2 in matrix, kg/cm PW PW PW PW IW IW IW IW PW PW PW PW Fig. 4 Content variation of free gases during the CS-EGR process over time for the representative case M100 10 8 6 4 2 61 5 4 3 2 (a) (b) -2 3 -1 3 CH4 in fracture, 10 kg/m CH4 in matrix, 10 kg/m H50 H100 H150 H50H100 H150 M50 M100 M150 M50M100M150 L50 L100 L150 L50 L100 L150 1.2 1.0 0.8 0.6 0.4 0.2 6 5 4 3 2 1 (c) (d) 3 3 CO2 in fracture, kg/m CO2 in matrix, kg/m H50 H100 H150 H50H100 H150 M50 M100 M150 M50M100M150 L50 L100 L150 L50 L100 L150 Fig. 5 Free gases content after 10,000 d CS-EGR operation under different IW–PWs conditions H150, the massive accumulation of free CH in the matrix, decrease of free CH in the fracture/matrix is monotonic and 4 4 caused by the displacement of the adsorbed CH by C O mainly controlled by the release of CH pressure in the shale 4 2 4 injection, allows the release of the free CH in the matrix reservoir (Fig. 7b). into the fracture, regarding layer 1 which is close to the IW With regard to the mass of CH in the matrix, its decre- location (Fig. 7a). Comparatively, for layer 8 of H150, the ment varies in a heterogeneous way for all layers, under 1 3 10000 d 8000 d 6000 d 4000 d 2000 d 0 d 536 Petroleum Science (2021) 18:530–545 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 Decrement of CH in fracture, kg Decrement of CH in fracture, kg Decrement of CH in fracture, kg 4 4 4 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 Decrement of CH in fracture, kg Decrement of CH in fracture, kg Decrement of CH in fracture, kg 4 4 4 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 Decrement of CH in fracture, kg Decrement of CH in fracture, kg Decrement of CH in fracture, kg 4 4 4 2000 d 4000 d6000 d8000 d10000 d Fig. 6 Decrement of free CH in fracture during the CS-EGR process for different IW–PWs combos 1.13 165 1.80 210 (a) (b) CH in matrix CH in matrix 4 4 1.12 164 1.75 CH in fracture CH in fracture 206 4 4 1.11 163 204 1.70 1.10 162 1.65 1.09 161 1.08 160 1.60 1.07 159 192 1.55 1.06 158 1.50 1.05 157 186 1.45 1.04 156 Layer 1 of H150 Layer 8 of H150 1.03 155 1.40 180 0246 810 0246 810 3 3 Time, 10 d Time, 10 d Fig. 7 Content variation of free CH in different layers for H150 all IW–PWs combos (Fig. 8). Basically, the CH content the highest content of the original free CH in the matrix 4 4 in the matrix at a depth of 1275  m (layer 8) decreases (Fig.  3) and the highest permeability (Fig.  1) promotes more than that in the rest of the layers, probably because the CH release from the bottom PW in layer 8. When IW 1 3 Depth, m Depth, m Depth, m Free CH in matrix, 10 kg Depth, m Depth, m Depth, m Free CH in fracture, kg Free CH in matrix, 10 kg Depth, m Depth, m Depth, m Free CH in fracture, kg 4 Petroleum Science (2021) 18:530–545 537 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 050100 150200 250 300 050100 150200 250 300 050100 150200 250 300 Decrement of CH in matrix, kg Decrement of CH in matrix, kg Decrement of CH in matrix, kg 4 4 4 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 050100 150200 250 300 050100 150200 250 300 050100 150200 250 300 Decrement of CH in matrix, kg Decrement of CH in matrix, kg Decrement of CH in matrix, kg 4 4 4 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 050100 150200 250 300 050100 150200 250 300 050100 150200 250 300 Decrement of CH in matrix, kg Decrement of CH in matrix, kg Decrement of CH in matrix, kg 4 4 4 2000 d4000 d6000 d8000 d10000 d Fig. 8 Decrement of free CH in the matrix during the CS-EGR process for different IW–PWs combos has a fixed location, the content decrement of free CH in the matrix at a shorter horizontal distance of IW–PWs is 5.10 greater than that for a longer one. By comparison, the IW L150 location only marginally affects the performance of free M100 5.05 CH in the matrix in a fixed situation of PWs, where an IW at the bottom layer makes the decrement of CH content become slightly less than that at the upper layer (Fig. 8). 5.00 Besides, no matter where the IW and PWs are, the content of free CH in the matrix is invariably greater than that in 4.95 the fracture during the CS-EGR process, in that the matrix porosity φ is considerably higher than the fracture poros- 4.90 ity φ . This phenomenon is illustrated by the examples L150 and M100, where the ratio of CH in the matrix 4.85 relative to that in the fracture decrease rapidly, then slow by after CO involvement, which however is always greater 4.80 than 1 (Fig. 9). Figure 9 also indicates this dynamic ratio 02468 10 of CH in the matrix to CH in the fracture differs under 3 Time, 10 d 4 4 different IW–PWs patterns, in which the detailed mecha- nism will be described in future work. Fig. 9 CO injection-induced variation of the ratio of CH in the 2 4 matrix relative to that in the fracture during the CS-EGR process 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Ratio of CH in matrix to CH in fracture 4 4 Depth, m Depth, m Depth, m 538 Petroleum Science (2021) 18:530–545 During the CS-EGR process, the fracture is the first space 4.2 Content variation of free CO during shale‑based CS‑EGR process in the shale reservoir to encounter the injected CO ; there- fore, the relative locations of IW and PWs significantly affect As exhibited by the representative case M100, the mass con- the performance of free C O in the fracture, as shown by the numerical outputs of every single layer (Fig. 10). For all tent and distribution area of the free CO in the reservoir gradually become greater with time after CO is injected into IW–PWs combos, the layers close to the IW meet the C O first and tend to trap more CO in the fracture. For exam- the Wufeng–Longmaxi shale (Fig. 4c, d). Here, the variation is characterized as heterogeneous in the vertical direction, ple, a 2000 d of CS-EGR operation enables a considerable amount of free CO to be trapped in layers 8–10 but less free in which the performance of free C O in the fracture differs 2 2 from that in the matrix. This heterogeneous variation leads CO to be trapped in layers 1–3 in the case L50; furthermore, after CO is injected for 10,000 d, the content of free C O to the variable outcomes of free C O content, either in the 2 2 2 fracture or in the matrix during 10,000 d of CS-EGR opera- in the fracture of layers 8–10 is obviously more than that of rest layers, for the example of case L50 (Fig. 10g). Besides, tion, under different relative locations of IW–PWs (Fig.  5c, d). From the qualitative perspective, after 10,000 d of C O it is also noted that a longer IW–PWs distance allows more free CO to be trapped in the fracture of each layer than a injection, the free CO tends to be trapped more at a longer 2 2 IW–PWs distance with a fixed IW location, while a bot- shorter one, when the IW is fixed (Fig.  10). This is due to a longer path for the CO migration that usually corresponds tom IW location enables more CO in the free phase to be 2 2 trapped than an upper one. Herein, this phenomenon is gen- to a greater area for CO accumulation in the fracture. As for the free CO in the matrix, its content in each layer eral and is suitable for the free CO , both in the fracture and 2 2 in the matrix (Fig. 5c, d). is variable during the process of CO injection, under all 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 0100 200300 400500 600700 800 0100 200300 400500 600700 800 0100 200300 400500 600700 800 CO in fracture, kg CO in fracture, kg CO in fracture, kg 2 2 2 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 0100 200300 400500 600700 800 0100 200300 400500 600700 800 0100 200300 400500 600700 800 CO in fracture, kg CO in fracture, kg CO in fracture, kg 2 2 2 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 0100 200300 400500 600700 800 0100 200300 400500 600700 800 0100 200300 400500 600700 800 CO in fracture, kg CO in fracture, kg CO in fracture, kg 2 2 2 2000 d4000 d6000 d8000 d10000 d Fig. 10 Accumulation of free CO in the fracture during the CS-EGR process for different IW–PWs combos 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Petroleum Science (2021) 18:530–545 539 5.2 IW–PWs combos (Fig. 11). At first glance, for all IW–PWs H50 situations, the matrix of layer 8 (depth of about 1275 m) M100 5.0 performs effectively in the CO trapping among all layers (Fig. 11), a result of the significant matrix porosity φ of 4.8 layer 8 when compared with other layers (Fig. 1). In addi- tion, the IW location ae ff cts the accumulation of free CO in 4.6 the matrix at a fixed situation of PWs, where the layers near the IW are likely to trap more free CO in the matrix—simi- 4.4 lar to the effect for free CO in the fracture. While for the 4.2 situation of the x fi ed IW location, a longer IW–PWs distance makes more free C O accumulated in the matrix, which is 4.0 similar to the performance of free C O in the fracture, with similar reasoning (Fig. 11). 3.8 Because the matrix porosity φ is significantly greater 02468 10 than the fracture porosity φ , for each layer, the content of Time, 10 d free CO in the matrix is higher than that in the fracture, revealed by Figs. 10 and 11. Quantitatively, the examples Fig. 12 Ratio of CO in the matrix to that in the fracture after CO 2 2 of H50 and M100 indicate that the ratio of free CO in the 2 injection during the CS-EGR process matrix relative to that in the fracture is invariably superior during the whole CS-EGR process (Fig. 12). Nonetheless, 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 01000200030004000 5000 01000200030004000 5000 01000200030004000 5000 CO in matrix, kg CO in matrix, kg CO in matrix, kg 2 2 2 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 01000200030004000 5000 01000200030004000 5000 01000200030004000 5000 CO in matrix, kg CO in matrix, kg CO in matrix, kg 2 2 2 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 01000200030004000 5000 01000200030004000 5000 01000200030004000 5000 CO in matrix, kg CO in matrix, kg CO in matrix, kg 2 2 2 2000 d4000 d6000 d8000 d10000 d Fig. 11 Accumulation of free CO in the matrix during the CS-EGR process for different IW–PWs combos 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Ratio of CO in matrix to CO in fracture 2 2 Depth, m Depth, m Depth, m 540 Petroleum Science (2021) 18:530–545 in Fig. 12, a sharp decline occurs in the very initial period of IW and PWs. Overall, the injection of CO into the of CO injection, resulting from the injected C O mainly Wufeng–Longmaxi shale allows the content of free CH and 2 2 4 staying in the fracture before arriving in the matrix pores; free CO in the reservoir to decrease and increase, respec- afterwards, this ratio has a small increase after C O enters tively (Fig.  13). Although the tendency of content varia- into the matrix pores of shale reservoir, and then tends to tion for free CH and free C O is opposite, there are some 4 2 be stable. common elements; for instance, the residual free CH and trapped free C O for case L150 are the greatest, while those 4.3 Interactive behavior of free CO –CH for H50/M50 are the lowest (Fig. 13). 2 4 during the shale‑based CS‑EGR process According to the statistics, the content fraction of free CH among all free gases both in the fracture and in the In the process of CS-EGR operation, the behavior of free matrix gets a continuous decrease with time, during the CS- gases is complex. For example, the free CH in the matrix EGR operation in the depleted Wufeng–Longmaxi shale after CO injection contains the original free CH in the (Fig. 14). Therein, the fraction of free CH content in the 2 4 4 matrix and the desorbed CH (originally in adsorbed) by fracture is consistently lower than that in the matrix, on the CO displacement. So, the interactive behavior between the basis of two representative examples (Fig. 14). This phe- free CO and the free CH is dynamic and complicated dur- nomenon possibly is due to the extracted CH from the PWs 2 4 4 ing the CS-EGR process in the shale reservoir. In Fig. 13, containing the free CH in the fracture in the right side of the the content variation of free CH and C O echoes the out- PWs (Fig. 4a), while the C H –CO displacement that partly 4 2 4 2 puts shown by Fig. 5, implicating the intensified impact on supplies the free CH in the matrix mainly exists in the left the performance of free gases from the relative locations side of PWs (Fig. 4). However, this hypothesis needs more 1.70 8.6 (a) (b) 8.4 1.65 8.2 1.60 8.0 1.55 7.8 7.6 1.50 7.4 1.45 7.2 CH in fracture CH in matrix 4 4 1.40 7.0 02468 10 0246 810 3 3 Time, 10 d Time, 10 d 5 20 (c) (d) 4 16 3 12 2 8 1 4 CO in fracture CO in matrix 2 2 0 0 02468 10 0246 810 3 3 Time, 10 d Time, 10 d H50H100 H150 M50 M100 M150 L50L100L150 Fig. 13 Content variation of free CH and CO during the whole CS-EGR process 4 2 1 3 Free gas, 10 kg Free gas, 10 kg Free gas, 10 kg Free gas, 10 kg Petroleum Science (2021) 18:530–545 541 respectively. Comparatively, it seems that a shorter IW–PWs CH4 in matrix distance (cases H50, M50 and L50) tends to enable a rela- CH4 in fracture CH in reservior tively higher proportion of free CH both in the fracture and 80 in the matrix, and thus in the whole reservoir (Fig. 15). 4.4 Location selection of IW–PWs for desired M100 performance of free CO –CH 2 4 Since different IW–PWs locations facilitate variable inter - active behavior of free C O and free CH during the shale- 2 4 L150 based CS-EGR process, it is necessary to make an appro- priate selection on the relative locations of IW and PWs to achieve the desired purpose. For this selection, a parameter 02468 10 called the recovery efficiency of free CH ( f , for short) 4 free-CH Time, 10 d is defined, C − C o r Fig. 14 Fraction of free CH among all free gases (CH and CO ) for 4 4 2 f = × 100% (1) free-CH examples L150 and M100 during the CS-EGR process where C and C are the content of the original free CH o r 4 attention. In addition, the variable fraction of free CH in the (before CO involvement) and the residual free CH (after 4 2 4 fracture and that in the matrix together form the content frac- CO involvement) in the fracture/matrix, respectively, kg. tion of free CH relative to all free gases in the whole shale Herein, a higher f value indicates that more CH 4 free-CH 4 reservoir. Herein, reflected by the slope of change curves, in the free phase is recovered from PWs, and vice versa. As the decreasing tendencies in Fig. 14 are of the “fast followed exhibited in Fig. 16, the vertical heterogeneity is shown in by slow” type, which suggests the proportion of free CH the f value under each IW–PWs combo, during the 4 free-CH among all free gases has a tendency to be constant after a CS-EGR operation in the Wufeng–Longmaxi shale, which sufficient time of CO injection. Therefore, it can be specu- is codetermined by the reservoir properties and the IW–PWs lated that the CS-EGR operation probably ends when the strategy. For all IW–PWs cases, the vertical heterogeneity fraction of free CH among all free gases changes insignifi- of f has a similar relation to that of the free CH in 4 free-CH 4 cantly with time. Furthermore, after a 10,000 d of CS-EGR the matrix; that is, the f for bottom layers is higher free-CH production, the resulting proportion of free CH and free than that for the upper layers (Fig. 16). With regard to the CO differs, under different IW–PWs combos (Fig.  15). For free CH in the fracture, the f is affected by the IW 2 4 free-CH all cases, no matter whether in the fracture or the matrix, location, and when the IW locates at the upper layers (or the content of free C O is primarily greater than that of free bottom layers), the f of bottom layers (or upper layers) 2 free-CH CH . After the CS-EGR operation runs for 10,000 d, for becomes higher (Fig. 16). all IW–PWs combos, the content proportions of free C O The performance of free CH /CO in the whole reser- 2 4 2 among all free gases in the matrix, the fracture and the voir consists of that in the fracture and in the matrix of whole reservoir are 65.8%, 69.5%, and 66.6% on average, each layer. Basically, a longer IW–PWs distance generates 100 100 100 (a) (b) (c) 80 80 80 61% 62% 62% 62% 65% 66% 66% 66% 66% 65% 65% 69% 66% 67% 66% 67% 66% 70% 69% 69% 70% 70% 71% 71% 72% 74% 75% 60 60 60 CO CH 40 40 40 20 39% 20 20 38% 38% 38% 35% 34% 34% 34% 34% 35% 35% 34% 33% 34% 34% 31% 31% 33% 30% 29% 31% 30% 30% 29% 28% 26% 25% 0 0 0 Free gases in matrix Free gases in fracture Free gases in reservior Fig. 15 Proportion of free CH and free CO in the Wufeng–Longmaxi shale after 10,000 d of CS-EGR operation 4 2 1 3 Fraction of free CH , % Mass fraction, % H50 H100 H150 M50 M100 M150 L50 L100 L150 Mass fraction, % H50 H100 H150 M50 M100 M150 L50 L100 L150 Mass fraction, % H50 H100 H150 M50 M100 M150 L50 L100 L150 542 Petroleum Science (2021) 18:530–545 1200 1200 (a) (b) 1210 1210 1220 1220 1230 1230 1240 1240 1250 1250 1260 1260 1270 1270 1280 1280 1290 1290 1300 1300 57 69 8 10 11 12 13 14 15 16 17 18 26 48 10 12 14 16 18 20 Recovery efficiency of CH in matrix, %Recovery efficiency of CH in fracture, % 4 4 H50 H100 H150 M50 M100 M150 L50 L100 L150 Fig. 16 Recovery efficiency of free CH after 10,000 d of C O injection into the Wufeng–Longmaxi shale 4 2 1400 20 (a) (b) CH in matrix CO in matrix 4 2 CH4 in fracture CO2 in fracture 0 0 H50 H100 H150 M50 M100 M150 L50 L100 L150 H50H100H150M50 M100 M150 L50L100 L150 Fig. 17 Recovered free CH and trapped free CO in the Wufeng–Longmaxi shale after 10,000 d of CS-EGR operation 4 2 a lower recovered content of free CH (Fig. 17a), accom- 5 Conclusions panied with a higher trapped content of free CO (Fig. 17b), both in the fracture and the matrix. Accord- In developing a novel THM coupling model, the perfor- ingly, an appropriate IW–PWs strategy can be selected mance of free CH and free C O during the CS-EGR pro- 4 2 for different expected targets. For example, if the CS- cess in the Wufeng–Longmaxi shale is clearly obtained. EGR operation aims to trap more CO in the free phase in The main conclusions are. the depleted Wufeng–Longmaxi shale, the IW should be Vertical heterogeneity exists in the content of free C H located in the bottom layers and have a longer horizontal or free CO in the fracture/matrix throughout the whole distance with the PWs (like L150 in this work) (Fig. 17). process of CS-EGR operation, codetermined by the res- One more example, if the CS-EGR operation is designed ervoir properties and the IW–PWs strategy. Because the to get more CH in the free phase recovered from the matrix porosity φ is significantly higher than the frac- depleted Wufeng–Longmaxi shale, the IW location is ture porosity φ , the free CH /CO in the matrix is much f 4 2 flexible and only a shorter IW–PWs distance is needed, higher than that in the fracture for either layer or the whole such as H50, M50, and L50 in this work (Fig. 17). 1 3 Recovery of free CH , kg Depth, m Depth, m Trapped free CO , 10 kg 2 Petroleum Science (2021) 18:530–545 543 reservoir. After C O involvement, the ratio of free CH / Appendix 2 4 CO in the matrix relative to that in the fracture declines and tends to be stable with time, where the change behav- Key parameters for CS-EGR in this numerical simulation. ior is different for the free CH and free CO . 4 2 Parameter Value For the free CH in the fracture/matrix, its recovery is lower at a longer IW–PWs distance (fixed IW location) and Langmuir strain coefficient of CH ε 8.1e−4 4 L1 is insignificantly affected by the variation of IW location at Langmuir strain coefficient of CO ε 3.6e−3 2 L2 a PW location during the CS-EGR operation. For the free Dynamic viscosity of CH μ , Pa s 1.34e−5 4 g1 CO in the fracture/matrix, it is trapped more at a longer Dynamic viscosity of CO μ , Pa s 1.84e−5 2 g2 IW–PWs distance (fixed IW location) and tends to be more Dynamic viscosity of water μ , Pa s 8.9e−4 trapped when the IW locates at bottom layers (fixed location Diffusion coefficient of CH D, m /s 3.6e−12 4 1 of PWs). After CO is injected into the Wufeng–Longmaxi Diffusion coefficient of CO D, m /s 5.8e−12 2 2 shale, the free CH content in the fracture/matrix of the lay- Thermal coefficient of gas sorption c , 1/K 0.021 ers near the IW location increases first and decreases later, Thermal coefficient of gas sorption c , 1/MPa 0.071 while that of the layers far away from the IW location suffers Capillary pressure p , MPa 0.035 cgw a monotonic decrease. Initial density of saturated vapor ρ , kg/m 0.13 fv0 During the CS-EGR operation in the Wufeng–Longmaxi Latent heat of vapor R , J/(K·kg) 461.51 shale, the content of free CH among all free gases in the Klinkenberg factor b , MPa 0.76 fracture/matrix has a continuous decline with time—in a Desorption time of CH τ , d 0.221 4 1 “fast followed by slow” way. A 10,000 d of CO injection Desorption time of CO τ , d 0.334 2 2 enables the content of free CO to be greater than that of Henry’s coefficient of CH H 0.0014 4 g1 free CH in the fracture/matrix, in which a shorter IW–PWs Henry’s coefficient of CO H 0.0347 2 g2 distance results in a relatively higher proportion of free CH . Residual gas saturation s 0.05 gr In addition, when the IW locates at the bottom layers and Irreducible water saturation s 0.42 wr has a farther distance to PWs, more CO in the free phase Reference temperature for test T , K 300 ref tends to be trapped in the depleted Wufeng–Longmaxi shale; Endpoint relative permeability of gas k 0.875 rg0 furthermore, no matter where the IW is, a shorter IW–PWs Endpoint relative permeability of water k 1.0 rw0 distance is helpful for getting more CH in the free phase Biot coefficient of matrix α 0.8 recovered from the depleted Wufeng–Longmaxi shale. Biot coefficient of fracture α 0.1 Density of the shale skeleton ρ , kg/m 2470 Acknowledgements This study was financially supported by the Initial fracture width b, m 5e−4 National Natural Science Foundation of China (Grant Nos. 51704197 and 11872258). Initial fracture stiffness K , GPa/m 10 nj Maximum fracture aperture Δv , m 0.001 max Thermal expansion coefficient α , 1/K 2.4e−5 Compliance with ethical standards Specific heat capacities of shale C , J/(kg K) 1380 Conflict of interest The authors declare that they have no known con- Specific heat capacities of CH C , J/(kg K) 2220 4 g1 flict of interest or personal relationships that could influence the work Specific heat capacities of CO C , J/(kg K) 844 2 g2 reported in this paper. Specific heat capacities of water C , J/(kg K) 4187 Specific heat capacities of vapor C , J/(kg K) 1996 Open Access This article is licensed under a Creative Commons Attri- v bution 4.0 International License, which permits use, sharing, adapta- Thermal conduction coefficient of shale λ , W/(m K) 0.1913 tion, distribution and reproduction in any medium or format, as long Thermal conduction coefficient of CH λ , W/(m K) 0.0301 4 g1 as you give appropriate credit to the original author(s) and the source, Thermal conduction coefficient of CO λ , W/(m K) 0.0137 2 g2 provide a link to the Creative Commons licence, and indicate if changes Thermal conduction coefficient of water λ , W/(m K) 0.5985 were made. The images or other third party material in this article are w included in the article’s Creative Commons licence, unless indicated Isosteric heat of CH adsorption q , kJ/mol 16.4 4 st1 otherwise in a credit line to the material. If material is not included in Isosteric heat of C O adsorption q , kJ/mol 19.2 2 st2 the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will 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/. References Abidoye LK, Khudaida KJ, Das DB. Geological carbon sequestra- tion in the context of two-phase flow in porous media: a review. 1 3 544 Petroleum Science (2021) 18:530–545 Crit Rev Environ Sci Technol. 2015;45(11):1105–47. https ://doi. Li X, Elsworth D. Geomechanics of CO enhanced shale gas recovery. org/10.1080/10643 389.2014.92418 4. J Nat Gas Sci Eng. 2015;26:1607–19. https ://doi.org/10.1016/j. Ajayi T, Gomes JS, Bera A. A review of C O storage in geological jngse .2014.08.010. formations emphasizing modeling, monitoring and capacity Li Z, Elsworth D. Controls of CO –N gas flood ratios on enhanced 2 2 estimation approaches. Pet Sci. 2019;16:1028–63. h t t p s : / / d o i . shale gas recovery and ultimate C O sequestration. J Pet Sci Eng. org/10.1007/s1218 2-019-0340-8. 2019;179:1037–45. https://doi.or g/10.1016/j.petrol.2019.04.098 . Bandis SC, Lumsden AC, Barton NR. Fundamentals of rock Liu J, Yao Y, Zhu Z, et al. Experimental investigation of reservoir joint deformation. Int J Rock Mech Min Sci Geomech Abstr. characteristics of the upper Ordovician Wufeng Formation shale 1983;20(6):249–68. https://doi.or g/10.1016/0148-9062(83)90595 in middle–upper Yangtze region, China. Energy Explor Exploit. -8. 2016a;34(4):527–42. https: //doi.org/10.1177/014459 87166 50553 . Chen B, Harp DR, Lu Z, et al. Reducing uncertainty in geologic C O Liu J, Yao Y, Elsworth D, et al. Vertical heterogeneity of the shale sequestration risk assessment by assimilating monitoring data. Int reservoir in the Lower Silurian Longmaxi Formation: analogy J Greenh Gas Control. 2020;94:102926. https://doi.or g/10.1016/j. between the southeastern and northeastern Sichuan Basin, SW ijggc .2019.10292 6. China. Minerals. 2017a;7(8):151. https://doi.or g/10.3390/min70 Chi J, Ju B, Lv G, et al. A computational method of critical well spac- 80151 . ing of CO miscible and immiscible concurrent flooding. Pet Liu J, Yao Y, Liu D, et  al. Experimental evaluation of C O 2 2 Explor Dev. 2017;44(5):771–8. https ://doi.or g/10.1016/s1876 enhanced recovery of adsorbed-gas from shale. Int J Coal Geol. -3804(17)30092 -7. 2017b;179:211–8. https ://doi.org/10.1016/j.coal.2017.06.006. Dahaghi AK. Numerical simulation and modeling of enhanced gas Liu J, Xie L, Elsworth D, et  al. C O /CH competitive adsorp- 2 4 recovery and CO sequestration in shale gas reservoirs: a feasi- tion in shale: implications for enhancement in gas produc- bility study. In: SPE international conference on C O capture, tion and reduction in carbon emissions. Environ Sci Technol. storage, and utilization, 10–12 November, New Orleans, Loui- 2019a;53(15):9328–36. https ://doi.org/10.1021/acs.est.9b024 siana, USA. Society of Petroleum Engineers. 2010. https ://doi. 32. org/10.2118/13970 1-MS. Liu J, Xie L, Yao Y, et al. Preliminary study of influence factors and Du X, Gu M, Hou Z, et al. Experimental study on kinetics of adsorp- estimation model of the enhanced gas recovery stimulated by tion of CO and CH in gas-bearing shale reservoirs. Energy Fuel. carbon dioxide utilization in shale. ACS Sustain Chem Eng. 2 4 2019;33(12):12587–600. https ://doi.org/10.1021/acs.energ yfuel 2019b;7(24):20114–25. https ://doi.or g/10.1021/acssu sc hem s.9b031 76.eng.9b060 05. Fan C, Elsworth D, Li S, et al. Thermo-hydro-mechanical–chemical Liu J, Xie H, Wang Q, et al. Influence of pore structure on shale couplings controlling CH production and CO sequestration in gas recovery with CO sequestration: insight into molecular 4 2 2 enhanced coalbed methane recovery. Energy. 2019a;173:1054–77. mechanisms. Energy Fuel. 2020;34(2):1240–50. https ://doi. https ://doi.org/10.1016/j.energ y.2019.02.126.org/10.1021/acs.energ yfuel s.9b026 43. Fan C, Li S, Elsworth D, et al. Experimental investigation on dynamic Liu Y, Zhang J, Tang X. Predicting the proportion of free and adsorbed strength and energy dissipation characteristics of gas outburst- gas by isotopic geochemical data: a case study from lower Permian prone coal. Energy Sci Eng. 2019b;8(4):1015–28. https ://doi. shale in the southern North China basin (SNCB). Int J Coal Geol. org/10.1002/ese3.565. 2016b;156:25–35. https ://doi.org/10.1016/j.coal.2016.01.011. Fan C, Luo M, Li S, et  al. A thermo-hydro-mechanical–chemical Ma D, Duan H, Zhang Q, et al. A numerical gas fracturing model of coupling model and its application in acid fracturing enhanced coupled thermal, flowing and mechanical effects. CMC Comput coalbed methane recovery simulation. Energies. 2019c;12(4):626. Mater Continua. 2020;65(3):2123–41. https: //doi.org/10.32604 https ://doi.org/10.3390/en120 40626 ./cmc.2020.01143 0. Fathi E, Akkutlu IY. Multi-component gas transport and adsorption Meng Q, Zhang G. Geologic framework and tectonic evolution of effects during CO injection and enhanced shale gas recovery. the Qinling orogen, central China. Tectonophysics. 2000;323(3– Int J Coal Geol. 2014;123:52–61. https ://doi.or g/10.1016/j. 4):183–96. https ://doi.org/10.1016/s0040 -1951(00)00106 -2. coal.2013.07.021. Mohagheghian E, Hassanzadeh H, Chen Z. C O sequestration Iddphonce R, Wang J, Zhao L. Review of C O injection techniques coupled with enhanced gas recovery in shale gas reservoirs. for enhanced shale gas recovery: Prospect and challenges. J Nat J CO2 Util. 2019;34:646–55. https ://doi.or g/10.1016/j. Gas Sci Eng. 2020;77:103240. https ://doi.or g/10.1016/j.jngse jcou.2019.08.016. .2020.10324 0. Nassir M, Settari A, Wan RG. Prediction of stimulated reservoir vol- Ji W, Song Y, Jiang Z, et  al. Estimation of marine shale methane ume and optimization of fracturing in tight gas and shale with adsorption capacity based on experimental investigations of a fully elasto-plastic coupled geomechanical model. SPE J. Lower Silurian Longmaxi formation in the Upper Yangtze Plat- 2014;19(5):771–85. https ://doi.org/10.2118/16381 4-PA. form, south China. Mar Pet Geol. 2015;68:94–106. https ://doi. Pan Y, Hui D, Luo P, et al. Experimental investigation of the geo- org/10.1016/j.marpe tgeo.2015.08.012. chemical interactions between supercritical CO and shale: impli- Kalra S, Tian W, Wu X. A numerical simulation study of C O injection cations for CO storage in gas-bearing shale formations. Energy 2 2 for enhancing hydrocarbon recovery and sequestration in liquid- Fuel. 2018;32(2):1963–78. https://doi.or g/10.1021/acs.energyfuel rich shales. Pet Sci. 2018;15:103–15. https ://doi.org/10.1007/s.7b030 74. s1218 2-017-0199-5. Rani S, Prusty BK, Pal SK. Characterization of shales from Damodar Li D, He Y, Zhang H, et  al. A numerical study of the impurity valley coalfields for CH recovery and C O sequestration. Envi- 4 2 effects on CO geological storage in layered formation. Appl ron Technol Innov. 2020;18:100739. https ://doi.org/10.1016/j. Energy. 2017;199:107–20. https ://doi.or g/10.1016/j.apene eti.2020.10073 9. rgy.2017.04.059. Řimnáčová D, Weishauptová Z, Přibyl O, et al. Effect of shale prop- Li R, Dong S, Dan L, et al. Tectonically driven organic fluid migra- erties on CH and CO sorption capacity in Czech Silurian 4 2 tion in the Dabashan Foreland Belt: evidenced by geochemistry shales. J Nat Gas Sci Eng. 2020. https ://doi.org/10.1016/j.jngse and geothermometry of vein-filling fibrous calcite with organic .2020.10337 7. inclusions. J Asian Earth Sci. 2013;75(8):202–12. https ://doi. org/10.1016/j.jseae s.2013.07.026. 1 3 Petroleum Science (2021) 18:530–545 545 Shi W, Zhang Y, Dong S, et  al. Intra-continental Dabashan oro- Ye YH, Liu SG, Ran B, et al. Characteristics of black shale in the cline, southwestern Qinling, Central China. J Asian Earth Sci. Upper Ordovician Wufeng and lower Silurian Longmaxi for- 2012;46:20–38. https ://doi.org/10.1016/j.jseae s.2011.10.005. mations in the Sichuan Basin and its periphery, China. Aust J Sun H, Yao J, Gao SH, et al. Numerical study of CO enhanced natu- Earth Sci. 2017;64:667–87. https ://doi.or g/10.1080/08120 ral gas recovery and sequestration in shale gas reservoirs. Int J 099.2017.13215 81. Greenh Gas Control. 2013;19:406–19. https ://doi.org/10.1016/j. Zhang G, Zhou W, Ji S, et al. Experimental study on CO replacement ijggc .2013.09.011. method used in shale gas exploration. J Chengdu Univ Technol. Tang X, Jiang Z, Jiang S, et al. Heterogeneous nanoporosity of the 2015;42(3):366–71 (in Chinses). Silurian Longmaxi Formation shale gas reservoir in the Sichuan Zhang K, Jiang H, Qin G. Utilization of zeolite as a potential multi- Basin using the QEMSCAN, FIB-SEM, and nano-CT methods. functional proppant for CO enhanced shale gas recovery and CO 2 2 Mar Pet Geol. 2016;78:99–109. https ://doi.org/10.1016/j.marpe sequestration: a molecular simulation study on the competitive tgeo.2016.09.010. adsorption of CH and CO in zeolite and organic matter. Fuel. 4 2 Tao Z, Bielicki JM, Clarens AF. Physicochemical factors impacting 2019;249(1):119–29. https ://doi.org/10.1016/j.fuel.2019.03.061. CO sequestration in depleted shale formations: the case of the Zhang H, Diao R, Mostofi M, et al. Monte Carlo simulation of the Utica shale. Energy Procedia. 2014;63:5153–63. https ://doi. adsorption and displacement of CH by CO Injection in shale 4 2 org/10.1016/j.egypr o.2014.11.545. organic carbon slit micropores for C O enhanced shale gas recov- Wan T, Liu HX. Exploitation of fractured shale oil resources by ery. Energy Fuel. 2020;34(1):150–63. https://doi.or g/10.1021/acs. cyclic CO injection. Pet Sci. 2018;15(3):552–63. https ://doi.energ yfuel s.9b033 49. org/10.1007/s1218 2-018-0226-1. Zhao P, Xie L, He B, et al. Strategy optimization on industrial CO Wang G, Long S, Ju Y, et al. Application of horizontal wells in three- sequestration in the depleted Wufeng–Longmaxi formation shale dimensional shale reservoir modeling: a case study of Longmaxi- in the northeastern Sichuan basin, SW China: from the per- Wufeng shale in Fuling gas field, Sichuan Basin. AAPG Bull. spective of environment and energy. ACS Sustain Chem Eng. 2018;102(11):2333–54. https ://doi.org/10.1306/05111 81714 4. 2020;8:11435–45. https://doi.or g/10.1021/acssusc hemeng.0c041 Wang T, Tian S, Li G, et al. Molecular simulation of CO /CH com- 14. 2 4 petitive adsorption on shale kerogen for C O sequestration and Zhou L, Su X, Lu Y, et al. A new three-dimensional numerical model enhanced gas recovery. J Phys Chem C. 2018;120(30):17009–18. based on the equivalent continuum method to simulate hydraulic https ://doi.org/10.1021/acs.jpcc.8b020 61. fracture propagation in an underground coal mine. Rock Mech Yao Y, Liu J, Liu D, et al. A new application of NMR in characteri- Rock Eng. 2018;52(8):213–33. https ://doi.or g/10.1007/s0060 zation of multiphase methane and adsorption capacity of shale. 3-018-1684-x. Int J Coal Geol. 2019;201:76–85. https ://doi.or g/10.1016/j. Zhou J, Jin Z, Luo K. Effects of moisture contents on shale gas recov - coal.2018.11.018. ery and C O sequestration. Langmuir. 2019;35(26):8716–25. https Yang ZL, Yu HY, Chen ZW, et al. A compositional model for CO ://doi.org/10.1021/acs.langm uir.9b008 62. flooding including CO equilibria between water and oil using Zhu Y, Wang X, Feng M, et al. Lithofacies classification and its rela- the Peng–Robinson equation of state with the Wong–Sandler mix- tionship with reservoir of the Lower Paleozoic Wufeng–Long- ing rule. Pet Sci. 2019;16:874–89. https ://doi.org/10.1007/s1218 maxi Formation in the eastern Sichuan Basin. Lithol Reserv. 2-018-0294-2. 2016;28(5):59–66 (in Chinses). 1 3 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

Performance of free gases during the recovery enhancement of shale gas by CO2 injection: a case study on the depleted Wufeng–Longmaxi shale in northeastern Sichuan Basin, China

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Copyright © The Author(s) 2020
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1672-5107
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10.1007/s12182-020-00533-y
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Abstract

In this work, a novel thermal–hydraulic–mechanical (THM) coupling model is developed, where the real geological param- eters of the reservoir properties are embedded. Accordingly, nine schemes of C O injection well (IW) and CH production 2 4 well (PW) are established, aiming to explore the behavior of free gases after C O is injected into the depleted Wufeng–Long- maxi shale. The results indicate the free CH or C O content in the shale fractures/matrix is invariably heterogeneous. The 4 2 CO involvement facilitates the ratio of free CH /CO in the matrix to that in the fractures declines and tends to be stable 2 4 2 with time. Different combinations of IW–PWs induce a difference in the ratio of the free CH to the free C O , in the ratio 4 2 of the free CH /CO in the matrix to that in the fractures, in the content of the recovered free CH , and in the content of the 4 2 4 trapped free CO . Basically, when the IW locates at the bottom Wufeng–Longmaxi shale, a farther IW–PWs distance allows more CO in the free phase to be trapped; furthermore, no matter where the IW is, a shorter IW–PWs distance benefits by getting more CH in the free phase recovered from the depleted Wufeng–Longmaxi shale. Hopefully, this work is helpful in gaining knowledge about the shale-based CO injection technique. Keywords CO geological sequestration · Enhanced shale gas recovery · Free gas · Wufeng–Longmaxi Formation · THM coupled modeling 1 Introduction reservoirs is becoming increasingly attractive and has been lauded as a win–win solution for meeting geological C O Current knowledge strongly supports CO sequestration in storage and simultaneous enhanced gas recovery (CS-EGR) geological formations (e.g., shale and coalbed) as a promis- from shales (Liu et al. 2017b, 2019a, b; Kalra et al. 2018; ing approach to respond to the issue of excessive anthropo- Pan et al. 2018; Yang et al. 2019; Zhang et al. 2020). How- genic CO emissions into the atmosphere, which is treated ever, understanding of shale-based CS-EGR is limited, with as carbon-negative technology and thus has been receiv- only few pilot field studies undertaken, in which strategy ing growing attention (Abidoye et al. 2015; Zhang et al. optimization, site characterization/monitoring, and hazard 2015; Wan and Liu 2018; Liu et al. 2020; Rani et al. 2020; assessment & management need to be taken into account Řimnáčová et al. 2020). Therein, injecting CO into shale in a comprehensive manner (Chi et al. 2017; Ajayi et al. 2019; Zhang et al. 2019; Chen et al. 2020; Iddphonce et al. 2020). In other words, despite being proven to be a feasible Edited by Yan-Hua Sun technique, CS-EGR in the shale is not yet mature enough for * Peng Zhao full national or worldwide deployment. scu_zhaopeng@163.com To promote the development of the shale-based CS-EGR 1 technique, considerable work has been organized, in which State Key Laboratory of Hydraulics and Mountain River significant achievements have been drawn (Iddphonce et al. Engineering, Institute of New Energy and Low-Carbon Technology, Sichuan University, Chengdu 610065, China 2020). For example, it has been proven that the CO –CH 2 4 displacement behavior differs in the shales from different College of Architecture and Environment, Sichuan University, Chengdu 610065, China sedimentary environments (Du et al. 2019). Another exam- ple is that the CS-EGR efficiency is considerably affected by Liaohe Oilfield Company, PetroChina, Panjin 124010, China Vol:.(1234567890) 1 3 Petroleum Science (2021) 18:530–545 531 the CO proportion in the injected CO –N mixture (Li and to several hundred meters, where vertical heterogeneity 2 2 2 Elsworth 2019). In one other example, NMR-based investi- emerges in many reservoir parameters, such as the porosity/ gation indicated that the properties (e.g., mineral composi- permeability, the Langmuir volume, and Young’s modulus tion) of shale reservoir can interfere with the CS-EGR out- (Tang et al. 2016; Liu et al. 2017a). Clearly, the development puts (Liu et al. 2019b). However, the examples mentioned of a comprehensive model that contains as many realistic above mainly pay attention to the gases (CO /CH ) in the conditions as possible is, therefore, the need of the hour, 2 4 adsorbed phase during the CO –CH interaction, in which aiming to enhance understanding of the free gases behavior 2 4 the performance of the free gases (CO /CH ) tends to be during the CS-EGR process in shales. 2 4 ignored. Unfortunately, neglecting the free gases in the pro- In this work, because the Wufeng–Longmaxi Forma- cess of shale-based CS-EGR does not exist in isolation and tion in the northeastern Sichuan Basin (SW China) has even is a common phenomenon reported in many literatures huge potential resources of shale gas (Liu et al. 2017a), it (Liu et al. 2017b; Zhou et al. 2019; Řimnáčová et al. 2020). is selected for simulation where the CS-EGR technique has Although the competitive adsorption of CO /CH is the the opportunity to be implemented. Accordingly, a ther- 2 4 primary element enabling CS-EGR in shales (Wang et al. mal–hydraulic–mechanical (THM) coupled model is devel- 2018b; Liu et al. 2019a), the gases in free phase inevitably oped using the COMSOL Multiphysics software, attempting appear to the spaces of the pores and fractures in shale res- to simulate the depleted condition of the Wufeng–Longmaxi ervoirs during the C O –CH interaction (Fathi and Akkutlu, shale. Herein, this integrated model not only contains the 2 4 2014). Basically, free gas is crucial for shale gas explora- responses of the rock deformation, competitive CH /CO 4 2 tion/exploitation and even occupies over 50% of in situ gas sorption, gas/water two-phase flow, and thermal expansion content in shales (Liu et al. 2016b). To separately study in the dual-porosity system but also involves the real hetero- the multiphase (free/adsorbed) gas in shales, experimental geneity of the reservoir properties of the Wufeng–Longmaxi approaches have been conducted, and sound achievements shale. Using a mathematical approach, this work focuses on have been made. For instance, isotopic geochemistry (Liu the dynamic interaction of free CO and free CH during the 2 4 et al. 2016b) and low-field NMR (Yao et al. 2019) were suc-continuous CO injection into the depleted Wufeng–Long- cessfully introduced to quantitatively identify the CH in the maxi shale, with a run time of roughly 30 years (10,000 free and adsorbed phase. Nevertheless, it was found that a d). Accordingly, in a quantitative manner, a series of simu- single experimental methodology was usually performed at lations are set to clarify the anisotropic content variation a restricted scale, and could hardly recognize the free CO of free gases (CO and CH ) in the modeling reservoir, 2 2 4 and free CH from the C O –CH mixture at the same time under different relative locations of the CO injection well 4 2 4 2 during the dynamic CO –CH interaction in shales. Given (IW) and the CH production well (PW). Furthermore, the 2 4 4 this situation, physics-based numerical simulations can be strengths and weaknesses of each IW–PWs combo are also employed to address concerns about the free gases during discussed, in terms of the different desired objectives. Hope- the shale-based CS-EGR process, in which multi-factors can fully, the peculiar perspectives from the gases in the free be investigated in a clear and transparent manner. phase during the CO –CH interaction in shales will help to 2 4 Up to a point, numerical attempts have given rise to deepen awareness on the potential field deployment of the knowledge improvement on the performance of free gases CS-EGR project in the shale reservoir. during the CS-EGR operation in shales. There are two exam- ples; one is that numerical work advocated that the portion of free gas is always less than that of adsorbed gas in the pro-2 Geological background cess of C O –CH interplay in shales, under variable reser- 2 4 voir permeability and temperature/pressure (Mohagheghian In this work, the case Wufeng–Longmaxi shale is from the et al. 2019). Another modeling study has suggested that an Well-WQ2 that is a shale gas exploration well and is located increase in the ratio of the free CH to adsorbed CH would in the northeastern Sichuan Basin, Southwest (SW) China 4 4 decrease the CO sequestration potential of the Utica shale (Fig. 1a). In this region, an arc tectonic belt system with a formation (Tao et al. 2014). Unfortunately, current simula- thrust belt trending to the southwest was formed by a series tions about free C H /CO in shales are usually run with a of tectonic activities, in which the Chengkou-Fangxian and 4 2 plain mathematical model with only a single layer or/and Shashi Buried fault zones are quintessential examples (Li isotropic conditions being simulated, which is contrary to et al. 2013; Ji et al. 2015; Liu et al. 2017a). field fact that multilayer and heterogeneous characteristics Figure 1b shows the continuous sedimentary succession exist extensively in shale reservoirs (Tang et al. 2016; Liu in the study area from the late Sinian to the Cenozoic Era, et  al. 2017a). For this reason, limited existing numerical except for the missing strata from the Devonian to the Car- achievements can be directly generalized and carried out boniferous period (Meng and Zhang 2000; Shi et al. 2012; in a real shale formation that usually has a thickness of tens Li et al. 2013). Under this sedimentary background, previous 1 3 Dabashan Epiplatform Sag Shashi Buried Fault Zone 532 Petroleum Science (2021) 18:530–545 (a) (b) Stratigraphy HC Lithology System system Formation Shaanxi Province 0 30 km ... ... ... ... Sandstone, mudstone . . . . Baitianba Jurassic . . . . basal conglomerate . . . Zhenping Mudstone Chengkou Xujiahe coal beds ... ... ... ... . . . . sandstone . . . . Chengkou-Fangxian Fault Zone Gypsum, halite Leikoupo Sichuan Province limestone Triassic Gypsum, halite Hubei Province Jialingjiang dolomite . . Tongjiezi Oolitic limestone . . . WQ2 . . . . Bioclastic limestone . . . Feixianguang dolostone Wuxi . . . . Changxing . . . Bioclastic limestone Wushan Mudstone, coal beds Wujiaping limestone Permian Wanzhou Sag Fold Belts Chert-bearing Chengdu Maokou limestone Chongqing Limestone Qixia mudstone Wa ... ... ... ... Sichuan Basin Cuijiagou ... ... ... ... Siltstone, shale Silurian Longmaxi Shale (c) -18 2 3 ... ... ... ... φ, % V , m /t P , MPa k, 10 m L L Wufeng Mudstone, siltstone -1 Layer No. Depth, m E, GPa v, 10 φ φ m f k k V V P P Ordovician . . . h v L-CH4 L-CO2 L-CH4 L-CO2 . . . . Baota Limestone 1 1200-1210 44.4 2.27 3.54 0.51 4.20 4.12 4.12 10.68 4.12 10.68 . . . . . . 2 1210-1220 45.6 2.70 2.78 0.32 1.82 3.84 3.84 8.75 3.84 8.75 Oolitic dolostone Sanyoudong . . . 3 1220-1230 51.5 2.52 2.07 0.43 3.20 3.58 3.58 8.69 3.58 8.69 . . . Qinjiamiao Limestone 4 1230-1240 63.8 2.08 2.84 0.66 4.60 3.04 3.04 9.50 3.04 9.50 Cambrian Shipai Dolostone 5 1240-1250 62.4 2.13 1.36 0.44 1.68 2.28 2.28 11.75 2.28 11.75 ... ... ... ... Carbonaceous 8.79 6 1250-1260 60.7 2.19 2.88 0.42 6.40 3.16 3.16 3.16 8.79 Guojiaba mudstone 5.00 2.60 2.60 13.99 2.60 13.99 7 1260-1270 60.9 2.18 1.72 0.53 HC-hydrocarbon system; E-Young's modulus; v-Poisson's ratio; 8 1270-1280 61.3 2.17 5.54 0.66 8.10 3.21 3.21 10.09 3.21 10.09 φ-Porosity; φ -Fracture porosity; φ -Matrix porosity; k-Permeability; f m 9 1280-1290 58.6 2.26 1.26 0.51 3.80 2.87 2.87 9.11 2.87 9.11 k -Horizontal permeability; k -Vertical permeability; V -Langmuir volume h v L 10 1290-1300 57.8 2.29 2.59 0.78 3.60 4.01 4.01 6.01 4.01 6.01 P -Langmuir pressure Fig. 1 Geological background of Well-WQ2 and the vertical heterogeneous reservoir characteristics (Shi et al. 2012; Li et al. 2013; Zhu et al. 2016; Liu et al. 2017a; Zhao et al. 2020). a Geological information of the Northeastern Sichuan Basin. b Integrated stratigraphic column of the Northeastern Sichuan Basin. c Vertical heterogeneity of the Wufeng–LongMaxi shales in the WQ2 shale well studies have identified two conventional hydrocarbon source which also has anisotropic characteristics in the reservoir systems (Fig. 1b): the bottom one (from the Cambrian Guo- properties (e.g., porosity/permeability) (Liu et al. 2016a, jiaba Formation to the Silurian Cuijiagou Formation) and the 2017a) (Fig. 1c). In addition, the well logs of Well-WQ2 upper one (from the Permian Qixia Formation to the Trias- indicate the temperature of the Wufeng–Longmaxi shale is sic Leikoupo Formation) (Li et al. 2013; Liu et al. 2017a). 36 °C (310 K), the water saturation is 0.3, and the in-situ Therein, during the shale gas exploration and exploitation, stresses in the horizontal and vertical directions are 30 MPa the Wufeng–Longmaxi shale is usually treated as a close and 36 MPa, respectively (Zhao et al. 2020). Such field data combination due to the conformable contact relationship provide a basis for the model development in this numerical between the upper Ordovician Wufeng Formation and the work, ensuring this model is as close to the real formation lower Silurian Longmaxi Formation (Zhu et al. 2016; Ye conditions as possible. et al. 2017; Wang et al. 2018a). The Wufeng–Longmaxi shale in the Well-WQ2 has a thickness of roughly 100  m with a buried depth of 3 Development of the mathematical model 1200–1300  m, where the bottom section (about 10  m) belongs to the Wufeng shale (Liu et  al. 2016a, 2017a). 3.1 Model description for the Wufeng–Longmaxi At such a buried depth, the depleted pressure of the shale Wufeng–Longmaxi shale is estimated at about 1.7  MPa (Zhang et al. 2015). Statistics suggest that the vertical het- Figure 2a exhibits the schematic of the simulation model in erogeneity is strong in the involved Wufeng–Longmaxi shale this work, which is treated as a typical pattern and contains 1 3 Huayingshan Mountain Convex Fold Belts Qiyaoshan Mountain Convex Fold Belts Reservoir beds Seal beds Source rocks Reservoir beds Seal beds Lower hydrocarbon system Upper hydrocarbon system Petroleum Science (2021) 18:530–545 533 300 m Layer 1 (a) (b) PWs candidate Layer 2 Layer 3 Layer 4 50 m Layer 5 100 m Layer 6 Layer 7 Layer 8 Layer 9 150 m Layer 10 (c) CO2 injection well (IW) CH4 production well (PW) CH4 CO2 Water Fractures Matrix pores Gas and water Mass exchange at Gas diffusion and flow in fracture matrix surface adsorption/desorption Shale skeleton Fig. 2 Schematic diagram of the process of CS-EGR in a shale reservoir (Zhao et al. 2020). All involved wells have a radius of 0.1 m. a Typical pattern of IW–PWs. b Relative locations of IW–PWs. c Mass transport of multi-fluids in the shale one injection well (IW) in the center and four production combos, when the IW is located at the lower section and is wells (PWs) in the corners (Li and Elsworth 2019). This pat- 50 m far away from the PWs in the horizontal direction, the tern is axisymmetric, so a two-dimensional representative is modeling case is labeled as L50. In a similar fashion, the selected for the numerical simulation (Fig. 2b). According to rest of the cases are marked as L100, L150, M50, M100, the geological parameters, the model height is determined as M150, H50, H100, and H150, respectively (Fig. 2). Herein, 100 m and is equally divided into ten sections to reveal the the layer 3, interface of layers 5–6, and layer 8, where the vertical heterogeneity of the reservoir properties. The model IW candidate is set, represent the upper, middle, and lower width is set 300 m to avoid possible influence of the right sections of the simulative shale reservoir, respectively. boundary condition (e.g., formation overpressure) (Li et al. 2017). Accordingly, the simulation area of 100 m × 300 m is divided into 5085 elements, and all boundaries are air- 3.2 THM coupling process and governing equations tight for flux, except for the right boundary with the initial gas pressure being set. As the CS-EGR operation is con- Since many parameters are involved in this simulation work ducted in the depleted conditions of the Wufeng–Longmaxi (see "Appendix"), CS-EGR in shales is identified as a com- shale, the initial pressure of the simulative reservoir is set as plicated process and involves integral feedback in the THM 2 MPa (that is, 0.3 MPa for C O and 1.7 MPa for CH ). In coupling phenomenon. Basically, the hydraulic field contains 2 4 this modeling process, under a temperature of 305 K, con- complex mass transport of binary gases (CO /CH ) with the 2 4 stant pressures of 0.1 MPa and 7 MPa are applied to the gas–water represented as two-phase flows superposed on PWs and IW during the CS-EGR process, respectively. To competitive non-isothermal adsorption (Fig. 2c). Once the develop the mathematical model, the primary parameters shale reservoir captures the nonthermally equilibrated C O , (see "Appendix") are obtained from the existing literatures heat transfer, such as thermal conduction/convection, occurs (Dahaghi 2010; Sun et al. 2013; Fathi and Akkutlu 2014; Li among the CH, CO , water, and shale skeleton, which is 4 2 and Elsworth 2015, 2019; Fan et al. 2019a, b, c; Ma et al. accompanied by energy release/adsorption associated with 2020; Zhao et al. 2020), while the key heterogeneous infor- gas adsorption/desorption, in turn impacting on the thermal mation on the Wufeng–Longmaxi shale is derived from real field (Fan et al. 2019a). Furthermore, the dynamic variation fieldwork (Fig.  1). in the hydraulic and thermal fields can interfere with the As shown in Fig. 2b, three IW candidates and three PWs mechanical field (e.g., shrink/swelling of the shale matrix), candidates are organized to investigate how the relative influencing the anisotropic porosity/permeability and thus locations of IW and PWs affect the free gas behavior of the affecting the convective fluxes of the water, gas, and energy CS-EGR operation in shales. Among these nine IW–PWs (Fan et al. 2019a). 1 3 Wufeng-Longmaxi Formation IW candidate a b a 100 m 534 Petroleum Science (2021) 18:530–545 The shale reservoir in this work is described as a dual- porosity media (Fig. 2c), which is used extensively in previ- ous numerical works (Bandis et al. 1983; Nassir et al. 2014; CH in matrix Li and Elsworth 2015, 2019; Zhou et al. 2018; Zhao et al. CH in fracture 2020). According to these works above, a series of govern- ing equations representing rock deformation, competitive CH /CO sorption, gas/water two-phase flow, and thermal 4 2 expansion are used for the CS-EGR model development in this work. 4 Results and discussion 0 200 400 600 80010001200140016001800 In the dual-porosity media, fractures and matrix pores are Free CH , kg the internal spaces of shale for trapping free gases ( CO / CH ). In this work, four types of free gases are classified Fig. 3 Original free CH content in modeling reservoir of the to investigate the behavior of free C O /CH during the CS- 2 4 depleted Wufeng–Longmaxi shale EGR process in the depleted Wufeng–Longmaxi shale— CH in the fracture, CO in the fracture, CH in the matrix 4 2 4 and CO in the matrix. Accordingly, this work separately After a production period of 10,000 d, the CS-EGR studies the performance of free CH or free CO , and then 4 2 operation enables the content difference of free CH in the the dynamic interaction between free CH and free C O dur- 4 2 fracture/matrix under variable IW–PWs combos. Accord- ing the recovery enhancement of shale gas by C O injection ing to the cloud pictures, at a fixed IW location, a farther into the depleted Wufeng–Longmaxi shale, under variable IW–PWs distance in the horizontal direction makes more IW–PWs locations. Note that this numerical model’s thick- CH in the free phase trapped in the shale fracture and ness value is 1 m when the gas content is calculated, where matrix after 10,000 d of CS-EGR operation (Fig.  5a, b). the involved gas content indicates the content of gas in free Comparatively, when PWs are located as fixed, there are less phase. obvious changes for the free CH in the shale fracture/matrix along with the variation of the IW location. Anyhow, after 4.1 Content variation of free CH 10,000 d of CS-EGR production, the vertical heterogeneity emerges for all outputs of free CH under different IW–PWs during shale‑based CS‑EGR process relative locations (Fig. 5a, b). To further display the heterogeneous characteristics of Prior to the involvement of the injected C O , the original content of free CH both in the fracture and in the matrix free CH in the Wufeng–Longmaxi shale, the content varia- tion of free CH in each layer is concluded at different points is strongly heterogeneous in the vertical direction, where the free CH in the matrix is visibly more than that in in time during the CS-EGR process. As shown in Fig. 6, the free CH content in each layer is dramatically affected by fracture (Fig.  3). This heterogeneous tendency is similar to the vertical variation of the fracture/matrix porosity of the relative locations of IW–PWs. A shorter IW–PWs dis- tance (fixed IW location) makes the CO injection-induced the Wufeng–Longmaxi shale shown in Fig. 1, owing to the free gas content being directly determined by the free space decrement of the free CH content greater, which is more obvious for the layers near the IW. Besides, when the PWs under the depleted reservoir pressure. Once the CO injec- tion starts, the content variation of the free CH in the frac- location is fixed, a smaller decrement goes to the free CH content in the layers close to the IW. Moreover, in some ture/matrix occurs. Taking M100 as an example, it is found that the free CH in the fracture continuously varies during operating cases, the content decrement is negative for the free CH in the layers near IW (e.g., Fig. 6a–c, e, f, h, i), the CS-EGR process, intuitively ree fl cting the accumulation of free CH in the left side of the PWs and the decrease in revealing that the CO injection facilitates the increment of free CH in shale fractures at the initial CS-EGR phase. Tak- that in the right side of the PWs (Fig. 4a). For the same case, the cloud pictures qualitatively indicate an overall reduction ing H150 as an example, the free CH content in the fracture of layer 1 first increases and then decreases (Fig.  7a), while of free CH in the matrix over time after C O is injected into 4 2 the shale reservoir (Fig. 4b). These variations address the that of layer 8 decreases monotonously (Fig. 7b), after CO is injected. This phenomenon is caused by the content vari- concept that the CO injection can facilitate the migration of free CH in the depleted Wufeng–Longmaxi shale reservoir. ation of free CH in the matrix. Using the same example of 1 3 Depth, m Petroleum Science (2021) 18:530–545 535 10 8 6 4 2 60 5 4 3 2 1 1.2 1.0 0.8 0.6 0.4 .2 6 5 4 3 2 1 (a) (b) (c) (d) -2 3 -1 3 3 3 CH4 in fracture, 10 kg/cm CH4 in matrix, 10 kg/cm CO2 in fracture, kg/cm CO2 in matrix, kg/cm PW PW PW PW IW IW IW IW PW PW PW PW Fig. 4 Content variation of free gases during the CS-EGR process over time for the representative case M100 10 8 6 4 2 61 5 4 3 2 (a) (b) -2 3 -1 3 CH4 in fracture, 10 kg/m CH4 in matrix, 10 kg/m H50 H100 H150 H50H100 H150 M50 M100 M150 M50M100M150 L50 L100 L150 L50 L100 L150 1.2 1.0 0.8 0.6 0.4 0.2 6 5 4 3 2 1 (c) (d) 3 3 CO2 in fracture, kg/m CO2 in matrix, kg/m H50 H100 H150 H50H100 H150 M50 M100 M150 M50M100M150 L50 L100 L150 L50 L100 L150 Fig. 5 Free gases content after 10,000 d CS-EGR operation under different IW–PWs conditions H150, the massive accumulation of free CH in the matrix, decrease of free CH in the fracture/matrix is monotonic and 4 4 caused by the displacement of the adsorbed CH by C O mainly controlled by the release of CH pressure in the shale 4 2 4 injection, allows the release of the free CH in the matrix reservoir (Fig. 7b). into the fracture, regarding layer 1 which is close to the IW With regard to the mass of CH in the matrix, its decre- location (Fig. 7a). Comparatively, for layer 8 of H150, the ment varies in a heterogeneous way for all layers, under 1 3 10000 d 8000 d 6000 d 4000 d 2000 d 0 d 536 Petroleum Science (2021) 18:530–545 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 Decrement of CH in fracture, kg Decrement of CH in fracture, kg Decrement of CH in fracture, kg 4 4 4 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 Decrement of CH in fracture, kg Decrement of CH in fracture, kg Decrement of CH in fracture, kg 4 4 4 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 05 10 15 20 25 30 35 40 45 Decrement of CH in fracture, kg Decrement of CH in fracture, kg Decrement of CH in fracture, kg 4 4 4 2000 d 4000 d6000 d8000 d10000 d Fig. 6 Decrement of free CH in fracture during the CS-EGR process for different IW–PWs combos 1.13 165 1.80 210 (a) (b) CH in matrix CH in matrix 4 4 1.12 164 1.75 CH in fracture CH in fracture 206 4 4 1.11 163 204 1.70 1.10 162 1.65 1.09 161 1.08 160 1.60 1.07 159 192 1.55 1.06 158 1.50 1.05 157 186 1.45 1.04 156 Layer 1 of H150 Layer 8 of H150 1.03 155 1.40 180 0246 810 0246 810 3 3 Time, 10 d Time, 10 d Fig. 7 Content variation of free CH in different layers for H150 all IW–PWs combos (Fig. 8). Basically, the CH content the highest content of the original free CH in the matrix 4 4 in the matrix at a depth of 1275  m (layer 8) decreases (Fig.  3) and the highest permeability (Fig.  1) promotes more than that in the rest of the layers, probably because the CH release from the bottom PW in layer 8. When IW 1 3 Depth, m Depth, m Depth, m Free CH in matrix, 10 kg Depth, m Depth, m Depth, m Free CH in fracture, kg Free CH in matrix, 10 kg Depth, m Depth, m Depth, m Free CH in fracture, kg 4 Petroleum Science (2021) 18:530–545 537 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 050100 150200 250 300 050100 150200 250 300 050100 150200 250 300 Decrement of CH in matrix, kg Decrement of CH in matrix, kg Decrement of CH in matrix, kg 4 4 4 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 050100 150200 250 300 050100 150200 250 300 050100 150200 250 300 Decrement of CH in matrix, kg Decrement of CH in matrix, kg Decrement of CH in matrix, kg 4 4 4 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 050100 150200 250 300 050100 150200 250 300 050100 150200 250 300 Decrement of CH in matrix, kg Decrement of CH in matrix, kg Decrement of CH in matrix, kg 4 4 4 2000 d4000 d6000 d8000 d10000 d Fig. 8 Decrement of free CH in the matrix during the CS-EGR process for different IW–PWs combos has a fixed location, the content decrement of free CH in the matrix at a shorter horizontal distance of IW–PWs is 5.10 greater than that for a longer one. By comparison, the IW L150 location only marginally affects the performance of free M100 5.05 CH in the matrix in a fixed situation of PWs, where an IW at the bottom layer makes the decrement of CH content become slightly less than that at the upper layer (Fig. 8). 5.00 Besides, no matter where the IW and PWs are, the content of free CH in the matrix is invariably greater than that in 4.95 the fracture during the CS-EGR process, in that the matrix porosity φ is considerably higher than the fracture poros- 4.90 ity φ . This phenomenon is illustrated by the examples L150 and M100, where the ratio of CH in the matrix 4.85 relative to that in the fracture decrease rapidly, then slow by after CO involvement, which however is always greater 4.80 than 1 (Fig. 9). Figure 9 also indicates this dynamic ratio 02468 10 of CH in the matrix to CH in the fracture differs under 3 Time, 10 d 4 4 different IW–PWs patterns, in which the detailed mecha- nism will be described in future work. Fig. 9 CO injection-induced variation of the ratio of CH in the 2 4 matrix relative to that in the fracture during the CS-EGR process 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Ratio of CH in matrix to CH in fracture 4 4 Depth, m Depth, m Depth, m 538 Petroleum Science (2021) 18:530–545 During the CS-EGR process, the fracture is the first space 4.2 Content variation of free CO during shale‑based CS‑EGR process in the shale reservoir to encounter the injected CO ; there- fore, the relative locations of IW and PWs significantly affect As exhibited by the representative case M100, the mass con- the performance of free C O in the fracture, as shown by the numerical outputs of every single layer (Fig. 10). For all tent and distribution area of the free CO in the reservoir gradually become greater with time after CO is injected into IW–PWs combos, the layers close to the IW meet the C O first and tend to trap more CO in the fracture. For exam- the Wufeng–Longmaxi shale (Fig. 4c, d). Here, the variation is characterized as heterogeneous in the vertical direction, ple, a 2000 d of CS-EGR operation enables a considerable amount of free CO to be trapped in layers 8–10 but less free in which the performance of free C O in the fracture differs 2 2 from that in the matrix. This heterogeneous variation leads CO to be trapped in layers 1–3 in the case L50; furthermore, after CO is injected for 10,000 d, the content of free C O to the variable outcomes of free C O content, either in the 2 2 2 fracture or in the matrix during 10,000 d of CS-EGR opera- in the fracture of layers 8–10 is obviously more than that of rest layers, for the example of case L50 (Fig. 10g). Besides, tion, under different relative locations of IW–PWs (Fig.  5c, d). From the qualitative perspective, after 10,000 d of C O it is also noted that a longer IW–PWs distance allows more free CO to be trapped in the fracture of each layer than a injection, the free CO tends to be trapped more at a longer 2 2 IW–PWs distance with a fixed IW location, while a bot- shorter one, when the IW is fixed (Fig.  10). This is due to a longer path for the CO migration that usually corresponds tom IW location enables more CO in the free phase to be 2 2 trapped than an upper one. Herein, this phenomenon is gen- to a greater area for CO accumulation in the fracture. As for the free CO in the matrix, its content in each layer eral and is suitable for the free CO , both in the fracture and 2 2 in the matrix (Fig. 5c, d). is variable during the process of CO injection, under all 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 0100 200300 400500 600700 800 0100 200300 400500 600700 800 0100 200300 400500 600700 800 CO in fracture, kg CO in fracture, kg CO in fracture, kg 2 2 2 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 0100 200300 400500 600700 800 0100 200300 400500 600700 800 0100 200300 400500 600700 800 CO in fracture, kg CO in fracture, kg CO in fracture, kg 2 2 2 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 0100 200300 400500 600700 800 0100 200300 400500 600700 800 0100 200300 400500 600700 800 CO in fracture, kg CO in fracture, kg CO in fracture, kg 2 2 2 2000 d4000 d6000 d8000 d10000 d Fig. 10 Accumulation of free CO in the fracture during the CS-EGR process for different IW–PWs combos 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Petroleum Science (2021) 18:530–545 539 5.2 IW–PWs combos (Fig. 11). At first glance, for all IW–PWs H50 situations, the matrix of layer 8 (depth of about 1275 m) M100 5.0 performs effectively in the CO trapping among all layers (Fig. 11), a result of the significant matrix porosity φ of 4.8 layer 8 when compared with other layers (Fig. 1). In addi- tion, the IW location ae ff cts the accumulation of free CO in 4.6 the matrix at a fixed situation of PWs, where the layers near the IW are likely to trap more free CO in the matrix—simi- 4.4 lar to the effect for free CO in the fracture. While for the 4.2 situation of the x fi ed IW location, a longer IW–PWs distance makes more free C O accumulated in the matrix, which is 4.0 similar to the performance of free C O in the fracture, with similar reasoning (Fig. 11). 3.8 Because the matrix porosity φ is significantly greater 02468 10 than the fracture porosity φ , for each layer, the content of Time, 10 d free CO in the matrix is higher than that in the fracture, revealed by Figs. 10 and 11. Quantitatively, the examples Fig. 12 Ratio of CO in the matrix to that in the fracture after CO 2 2 of H50 and M100 indicate that the ratio of free CO in the 2 injection during the CS-EGR process matrix relative to that in the fracture is invariably superior during the whole CS-EGR process (Fig. 12). Nonetheless, 1200 1200 1200 (a) (b) (c) H50 H100 H150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 01000200030004000 5000 01000200030004000 5000 01000200030004000 5000 CO in matrix, kg CO in matrix, kg CO in matrix, kg 2 2 2 1200 1200 1200 (d) (e) (f) M50 M100 M150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 01000200030004000 5000 01000200030004000 5000 01000200030004000 5000 CO in matrix, kg CO in matrix, kg CO in matrix, kg 2 2 2 1200 1200 1200 (g) (h) (i) L50 L100 L150 1220 1220 1220 1240 1240 1240 1260 1260 1260 1280 1280 1280 1300 1300 1300 01000200030004000 5000 01000200030004000 5000 01000200030004000 5000 CO in matrix, kg CO in matrix, kg CO in matrix, kg 2 2 2 2000 d4000 d6000 d8000 d10000 d Fig. 11 Accumulation of free CO in the matrix during the CS-EGR process for different IW–PWs combos 1 3 Depth, m Depth, m Depth, m Depth, m Depth, m Depth, m Ratio of CO in matrix to CO in fracture 2 2 Depth, m Depth, m Depth, m 540 Petroleum Science (2021) 18:530–545 in Fig. 12, a sharp decline occurs in the very initial period of IW and PWs. Overall, the injection of CO into the of CO injection, resulting from the injected C O mainly Wufeng–Longmaxi shale allows the content of free CH and 2 2 4 staying in the fracture before arriving in the matrix pores; free CO in the reservoir to decrease and increase, respec- afterwards, this ratio has a small increase after C O enters tively (Fig.  13). Although the tendency of content varia- into the matrix pores of shale reservoir, and then tends to tion for free CH and free C O is opposite, there are some 4 2 be stable. common elements; for instance, the residual free CH and trapped free C O for case L150 are the greatest, while those 4.3 Interactive behavior of free CO –CH for H50/M50 are the lowest (Fig. 13). 2 4 during the shale‑based CS‑EGR process According to the statistics, the content fraction of free CH among all free gases both in the fracture and in the In the process of CS-EGR operation, the behavior of free matrix gets a continuous decrease with time, during the CS- gases is complex. For example, the free CH in the matrix EGR operation in the depleted Wufeng–Longmaxi shale after CO injection contains the original free CH in the (Fig. 14). Therein, the fraction of free CH content in the 2 4 4 matrix and the desorbed CH (originally in adsorbed) by fracture is consistently lower than that in the matrix, on the CO displacement. So, the interactive behavior between the basis of two representative examples (Fig. 14). This phe- free CO and the free CH is dynamic and complicated dur- nomenon possibly is due to the extracted CH from the PWs 2 4 4 ing the CS-EGR process in the shale reservoir. In Fig. 13, containing the free CH in the fracture in the right side of the the content variation of free CH and C O echoes the out- PWs (Fig. 4a), while the C H –CO displacement that partly 4 2 4 2 puts shown by Fig. 5, implicating the intensified impact on supplies the free CH in the matrix mainly exists in the left the performance of free gases from the relative locations side of PWs (Fig. 4). However, this hypothesis needs more 1.70 8.6 (a) (b) 8.4 1.65 8.2 1.60 8.0 1.55 7.8 7.6 1.50 7.4 1.45 7.2 CH in fracture CH in matrix 4 4 1.40 7.0 02468 10 0246 810 3 3 Time, 10 d Time, 10 d 5 20 (c) (d) 4 16 3 12 2 8 1 4 CO in fracture CO in matrix 2 2 0 0 02468 10 0246 810 3 3 Time, 10 d Time, 10 d H50H100 H150 M50 M100 M150 L50L100L150 Fig. 13 Content variation of free CH and CO during the whole CS-EGR process 4 2 1 3 Free gas, 10 kg Free gas, 10 kg Free gas, 10 kg Free gas, 10 kg Petroleum Science (2021) 18:530–545 541 respectively. Comparatively, it seems that a shorter IW–PWs CH4 in matrix distance (cases H50, M50 and L50) tends to enable a rela- CH4 in fracture CH in reservior tively higher proportion of free CH both in the fracture and 80 in the matrix, and thus in the whole reservoir (Fig. 15). 4.4 Location selection of IW–PWs for desired M100 performance of free CO –CH 2 4 Since different IW–PWs locations facilitate variable inter - active behavior of free C O and free CH during the shale- 2 4 L150 based CS-EGR process, it is necessary to make an appro- priate selection on the relative locations of IW and PWs to achieve the desired purpose. For this selection, a parameter 02468 10 called the recovery efficiency of free CH ( f , for short) 4 free-CH Time, 10 d is defined, C − C o r Fig. 14 Fraction of free CH among all free gases (CH and CO ) for 4 4 2 f = × 100% (1) free-CH examples L150 and M100 during the CS-EGR process where C and C are the content of the original free CH o r 4 attention. In addition, the variable fraction of free CH in the (before CO involvement) and the residual free CH (after 4 2 4 fracture and that in the matrix together form the content frac- CO involvement) in the fracture/matrix, respectively, kg. tion of free CH relative to all free gases in the whole shale Herein, a higher f value indicates that more CH 4 free-CH 4 reservoir. Herein, reflected by the slope of change curves, in the free phase is recovered from PWs, and vice versa. As the decreasing tendencies in Fig. 14 are of the “fast followed exhibited in Fig. 16, the vertical heterogeneity is shown in by slow” type, which suggests the proportion of free CH the f value under each IW–PWs combo, during the 4 free-CH among all free gases has a tendency to be constant after a CS-EGR operation in the Wufeng–Longmaxi shale, which sufficient time of CO injection. Therefore, it can be specu- is codetermined by the reservoir properties and the IW–PWs lated that the CS-EGR operation probably ends when the strategy. For all IW–PWs cases, the vertical heterogeneity fraction of free CH among all free gases changes insignifi- of f has a similar relation to that of the free CH in 4 free-CH 4 cantly with time. Furthermore, after a 10,000 d of CS-EGR the matrix; that is, the f for bottom layers is higher free-CH production, the resulting proportion of free CH and free than that for the upper layers (Fig. 16). With regard to the CO differs, under different IW–PWs combos (Fig.  15). For free CH in the fracture, the f is affected by the IW 2 4 free-CH all cases, no matter whether in the fracture or the matrix, location, and when the IW locates at the upper layers (or the content of free C O is primarily greater than that of free bottom layers), the f of bottom layers (or upper layers) 2 free-CH CH . After the CS-EGR operation runs for 10,000 d, for becomes higher (Fig. 16). all IW–PWs combos, the content proportions of free C O The performance of free CH /CO in the whole reser- 2 4 2 among all free gases in the matrix, the fracture and the voir consists of that in the fracture and in the matrix of whole reservoir are 65.8%, 69.5%, and 66.6% on average, each layer. Basically, a longer IW–PWs distance generates 100 100 100 (a) (b) (c) 80 80 80 61% 62% 62% 62% 65% 66% 66% 66% 66% 65% 65% 69% 66% 67% 66% 67% 66% 70% 69% 69% 70% 70% 71% 71% 72% 74% 75% 60 60 60 CO CH 40 40 40 20 39% 20 20 38% 38% 38% 35% 34% 34% 34% 34% 35% 35% 34% 33% 34% 34% 31% 31% 33% 30% 29% 31% 30% 30% 29% 28% 26% 25% 0 0 0 Free gases in matrix Free gases in fracture Free gases in reservior Fig. 15 Proportion of free CH and free CO in the Wufeng–Longmaxi shale after 10,000 d of CS-EGR operation 4 2 1 3 Fraction of free CH , % Mass fraction, % H50 H100 H150 M50 M100 M150 L50 L100 L150 Mass fraction, % H50 H100 H150 M50 M100 M150 L50 L100 L150 Mass fraction, % H50 H100 H150 M50 M100 M150 L50 L100 L150 542 Petroleum Science (2021) 18:530–545 1200 1200 (a) (b) 1210 1210 1220 1220 1230 1230 1240 1240 1250 1250 1260 1260 1270 1270 1280 1280 1290 1290 1300 1300 57 69 8 10 11 12 13 14 15 16 17 18 26 48 10 12 14 16 18 20 Recovery efficiency of CH in matrix, %Recovery efficiency of CH in fracture, % 4 4 H50 H100 H150 M50 M100 M150 L50 L100 L150 Fig. 16 Recovery efficiency of free CH after 10,000 d of C O injection into the Wufeng–Longmaxi shale 4 2 1400 20 (a) (b) CH in matrix CO in matrix 4 2 CH4 in fracture CO2 in fracture 0 0 H50 H100 H150 M50 M100 M150 L50 L100 L150 H50H100H150M50 M100 M150 L50L100 L150 Fig. 17 Recovered free CH and trapped free CO in the Wufeng–Longmaxi shale after 10,000 d of CS-EGR operation 4 2 a lower recovered content of free CH (Fig. 17a), accom- 5 Conclusions panied with a higher trapped content of free CO (Fig. 17b), both in the fracture and the matrix. Accord- In developing a novel THM coupling model, the perfor- ingly, an appropriate IW–PWs strategy can be selected mance of free CH and free C O during the CS-EGR pro- 4 2 for different expected targets. For example, if the CS- cess in the Wufeng–Longmaxi shale is clearly obtained. EGR operation aims to trap more CO in the free phase in The main conclusions are. the depleted Wufeng–Longmaxi shale, the IW should be Vertical heterogeneity exists in the content of free C H located in the bottom layers and have a longer horizontal or free CO in the fracture/matrix throughout the whole distance with the PWs (like L150 in this work) (Fig. 17). process of CS-EGR operation, codetermined by the res- One more example, if the CS-EGR operation is designed ervoir properties and the IW–PWs strategy. Because the to get more CH in the free phase recovered from the matrix porosity φ is significantly higher than the frac- depleted Wufeng–Longmaxi shale, the IW location is ture porosity φ , the free CH /CO in the matrix is much f 4 2 flexible and only a shorter IW–PWs distance is needed, higher than that in the fracture for either layer or the whole such as H50, M50, and L50 in this work (Fig. 17). 1 3 Recovery of free CH , kg Depth, m Depth, m Trapped free CO , 10 kg 2 Petroleum Science (2021) 18:530–545 543 reservoir. After C O involvement, the ratio of free CH / Appendix 2 4 CO in the matrix relative to that in the fracture declines and tends to be stable with time, where the change behav- Key parameters for CS-EGR in this numerical simulation. ior is different for the free CH and free CO . 4 2 Parameter Value For the free CH in the fracture/matrix, its recovery is lower at a longer IW–PWs distance (fixed IW location) and Langmuir strain coefficient of CH ε 8.1e−4 4 L1 is insignificantly affected by the variation of IW location at Langmuir strain coefficient of CO ε 3.6e−3 2 L2 a PW location during the CS-EGR operation. For the free Dynamic viscosity of CH μ , Pa s 1.34e−5 4 g1 CO in the fracture/matrix, it is trapped more at a longer Dynamic viscosity of CO μ , Pa s 1.84e−5 2 g2 IW–PWs distance (fixed IW location) and tends to be more Dynamic viscosity of water μ , Pa s 8.9e−4 trapped when the IW locates at bottom layers (fixed location Diffusion coefficient of CH D, m /s 3.6e−12 4 1 of PWs). After CO is injected into the Wufeng–Longmaxi Diffusion coefficient of CO D, m /s 5.8e−12 2 2 shale, the free CH content in the fracture/matrix of the lay- Thermal coefficient of gas sorption c , 1/K 0.021 ers near the IW location increases first and decreases later, Thermal coefficient of gas sorption c , 1/MPa 0.071 while that of the layers far away from the IW location suffers Capillary pressure p , MPa 0.035 cgw a monotonic decrease. Initial density of saturated vapor ρ , kg/m 0.13 fv0 During the CS-EGR operation in the Wufeng–Longmaxi Latent heat of vapor R , J/(K·kg) 461.51 shale, the content of free CH among all free gases in the Klinkenberg factor b , MPa 0.76 fracture/matrix has a continuous decline with time—in a Desorption time of CH τ , d 0.221 4 1 “fast followed by slow” way. A 10,000 d of CO injection Desorption time of CO τ , d 0.334 2 2 enables the content of free CO to be greater than that of Henry’s coefficient of CH H 0.0014 4 g1 free CH in the fracture/matrix, in which a shorter IW–PWs Henry’s coefficient of CO H 0.0347 2 g2 distance results in a relatively higher proportion of free CH . Residual gas saturation s 0.05 gr In addition, when the IW locates at the bottom layers and Irreducible water saturation s 0.42 wr has a farther distance to PWs, more CO in the free phase Reference temperature for test T , K 300 ref tends to be trapped in the depleted Wufeng–Longmaxi shale; Endpoint relative permeability of gas k 0.875 rg0 furthermore, no matter where the IW is, a shorter IW–PWs Endpoint relative permeability of water k 1.0 rw0 distance is helpful for getting more CH in the free phase Biot coefficient of matrix α 0.8 recovered from the depleted Wufeng–Longmaxi shale. Biot coefficient of fracture α 0.1 Density of the shale skeleton ρ , kg/m 2470 Acknowledgements This study was financially supported by the Initial fracture width b, m 5e−4 National Natural Science Foundation of China (Grant Nos. 51704197 and 11872258). Initial fracture stiffness K , GPa/m 10 nj Maximum fracture aperture Δv , m 0.001 max Thermal expansion coefficient α , 1/K 2.4e−5 Compliance with ethical standards Specific heat capacities of shale C , J/(kg K) 1380 Conflict of interest The authors declare that they have no known con- Specific heat capacities of CH C , J/(kg K) 2220 4 g1 flict of interest or personal relationships that could influence the work Specific heat capacities of CO C , J/(kg K) 844 2 g2 reported in this paper. Specific heat capacities of water C , J/(kg K) 4187 Specific heat capacities of vapor C , J/(kg K) 1996 Open Access This article is licensed under a Creative Commons Attri- v bution 4.0 International License, which permits use, sharing, adapta- Thermal conduction coefficient of shale λ , W/(m K) 0.1913 tion, distribution and reproduction in any medium or format, as long Thermal conduction coefficient of CH λ , W/(m K) 0.0301 4 g1 as you give appropriate credit to the original author(s) and the source, Thermal conduction coefficient of CO λ , W/(m K) 0.0137 2 g2 provide a link to the Creative Commons licence, and indicate if changes Thermal conduction coefficient of water λ , W/(m K) 0.5985 were made. The images or other third party material in this article are w included in the article’s Creative Commons licence, unless indicated Isosteric heat of CH adsorption q , kJ/mol 16.4 4 st1 otherwise in a credit line to the material. If material is not included in Isosteric heat of C O adsorption q , kJ/mol 19.2 2 st2 the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will 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/. References Abidoye LK, Khudaida KJ, Das DB. Geological carbon sequestra- tion in the context of two-phase flow in porous media: a review. 1 3 544 Petroleum Science (2021) 18:530–545 Crit Rev Environ Sci Technol. 2015;45(11):1105–47. https ://doi. Li X, Elsworth D. Geomechanics of CO enhanced shale gas recovery. org/10.1080/10643 389.2014.92418 4. J Nat Gas Sci Eng. 2015;26:1607–19. https ://doi.org/10.1016/j. Ajayi T, Gomes JS, Bera A. A review of C O storage in geological jngse .2014.08.010. formations emphasizing modeling, monitoring and capacity Li Z, Elsworth D. Controls of CO –N gas flood ratios on enhanced 2 2 estimation approaches. Pet Sci. 2019;16:1028–63. h t t p s : / / d o i . shale gas recovery and ultimate C O sequestration. J Pet Sci Eng. org/10.1007/s1218 2-019-0340-8. 2019;179:1037–45. https://doi.or g/10.1016/j.petrol.2019.04.098 . Bandis SC, Lumsden AC, Barton NR. Fundamentals of rock Liu J, Yao Y, Zhu Z, et al. Experimental investigation of reservoir joint deformation. Int J Rock Mech Min Sci Geomech Abstr. characteristics of the upper Ordovician Wufeng Formation shale 1983;20(6):249–68. https://doi.or g/10.1016/0148-9062(83)90595 in middle–upper Yangtze region, China. Energy Explor Exploit. -8. 2016a;34(4):527–42. https: //doi.org/10.1177/014459 87166 50553 . Chen B, Harp DR, Lu Z, et al. Reducing uncertainty in geologic C O Liu J, Yao Y, Elsworth D, et al. Vertical heterogeneity of the shale sequestration risk assessment by assimilating monitoring data. Int reservoir in the Lower Silurian Longmaxi Formation: analogy J Greenh Gas Control. 2020;94:102926. https://doi.or g/10.1016/j. between the southeastern and northeastern Sichuan Basin, SW ijggc .2019.10292 6. China. Minerals. 2017a;7(8):151. https://doi.or g/10.3390/min70 Chi J, Ju B, Lv G, et al. A computational method of critical well spac- 80151 . ing of CO miscible and immiscible concurrent flooding. Pet Liu J, Yao Y, Liu D, et  al. Experimental evaluation of C O 2 2 Explor Dev. 2017;44(5):771–8. https ://doi.or g/10.1016/s1876 enhanced recovery of adsorbed-gas from shale. Int J Coal Geol. -3804(17)30092 -7. 2017b;179:211–8. https ://doi.org/10.1016/j.coal.2017.06.006. Dahaghi AK. Numerical simulation and modeling of enhanced gas Liu J, Xie L, Elsworth D, et  al. C O /CH competitive adsorp- 2 4 recovery and CO sequestration in shale gas reservoirs: a feasi- tion in shale: implications for enhancement in gas produc- bility study. In: SPE international conference on C O capture, tion and reduction in carbon emissions. Environ Sci Technol. storage, and utilization, 10–12 November, New Orleans, Loui- 2019a;53(15):9328–36. https ://doi.org/10.1021/acs.est.9b024 siana, USA. Society of Petroleum Engineers. 2010. https ://doi. 32. org/10.2118/13970 1-MS. Liu J, Xie L, Yao Y, et al. Preliminary study of influence factors and Du X, Gu M, Hou Z, et al. Experimental study on kinetics of adsorp- estimation model of the enhanced gas recovery stimulated by tion of CO and CH in gas-bearing shale reservoirs. Energy Fuel. carbon dioxide utilization in shale. ACS Sustain Chem Eng. 2 4 2019;33(12):12587–600. https ://doi.org/10.1021/acs.energ yfuel 2019b;7(24):20114–25. https ://doi.or g/10.1021/acssu sc hem s.9b031 76.eng.9b060 05. Fan C, Elsworth D, Li S, et al. Thermo-hydro-mechanical–chemical Liu J, Xie H, Wang Q, et al. Influence of pore structure on shale couplings controlling CH production and CO sequestration in gas recovery with CO sequestration: insight into molecular 4 2 2 enhanced coalbed methane recovery. Energy. 2019a;173:1054–77. mechanisms. Energy Fuel. 2020;34(2):1240–50. https ://doi. https ://doi.org/10.1016/j.energ y.2019.02.126.org/10.1021/acs.energ yfuel s.9b026 43. Fan C, Li S, Elsworth D, et al. Experimental investigation on dynamic Liu Y, Zhang J, Tang X. Predicting the proportion of free and adsorbed strength and energy dissipation characteristics of gas outburst- gas by isotopic geochemical data: a case study from lower Permian prone coal. Energy Sci Eng. 2019b;8(4):1015–28. https ://doi. shale in the southern North China basin (SNCB). Int J Coal Geol. org/10.1002/ese3.565. 2016b;156:25–35. https ://doi.org/10.1016/j.coal.2016.01.011. Fan C, Luo M, Li S, et  al. A thermo-hydro-mechanical–chemical Ma D, Duan H, Zhang Q, et al. A numerical gas fracturing model of coupling model and its application in acid fracturing enhanced coupled thermal, flowing and mechanical effects. CMC Comput coalbed methane recovery simulation. Energies. 2019c;12(4):626. Mater Continua. 2020;65(3):2123–41. https: //doi.org/10.32604 https ://doi.org/10.3390/en120 40626 ./cmc.2020.01143 0. Fathi E, Akkutlu IY. Multi-component gas transport and adsorption Meng Q, Zhang G. Geologic framework and tectonic evolution of effects during CO injection and enhanced shale gas recovery. the Qinling orogen, central China. Tectonophysics. 2000;323(3– Int J Coal Geol. 2014;123:52–61. https ://doi.or g/10.1016/j. 4):183–96. https ://doi.org/10.1016/s0040 -1951(00)00106 -2. coal.2013.07.021. Mohagheghian E, Hassanzadeh H, Chen Z. C O sequestration Iddphonce R, Wang J, Zhao L. Review of C O injection techniques coupled with enhanced gas recovery in shale gas reservoirs. for enhanced shale gas recovery: Prospect and challenges. J Nat J CO2 Util. 2019;34:646–55. https ://doi.or g/10.1016/j. Gas Sci Eng. 2020;77:103240. https ://doi.or g/10.1016/j.jngse jcou.2019.08.016. .2020.10324 0. Nassir M, Settari A, Wan RG. Prediction of stimulated reservoir vol- Ji W, Song Y, Jiang Z, et  al. Estimation of marine shale methane ume and optimization of fracturing in tight gas and shale with adsorption capacity based on experimental investigations of a fully elasto-plastic coupled geomechanical model. SPE J. Lower Silurian Longmaxi formation in the Upper Yangtze Plat- 2014;19(5):771–85. https ://doi.org/10.2118/16381 4-PA. form, south China. Mar Pet Geol. 2015;68:94–106. https ://doi. Pan Y, Hui D, Luo P, et al. Experimental investigation of the geo- org/10.1016/j.marpe tgeo.2015.08.012. chemical interactions between supercritical CO and shale: impli- Kalra S, Tian W, Wu X. A numerical simulation study of C O injection cations for CO storage in gas-bearing shale formations. Energy 2 2 for enhancing hydrocarbon recovery and sequestration in liquid- Fuel. 2018;32(2):1963–78. https://doi.or g/10.1021/acs.energyfuel rich shales. Pet Sci. 2018;15:103–15. https ://doi.org/10.1007/s.7b030 74. s1218 2-017-0199-5. Rani S, Prusty BK, Pal SK. Characterization of shales from Damodar Li D, He Y, Zhang H, et  al. A numerical study of the impurity valley coalfields for CH recovery and C O sequestration. Envi- 4 2 effects on CO geological storage in layered formation. Appl ron Technol Innov. 2020;18:100739. https ://doi.org/10.1016/j. Energy. 2017;199:107–20. https ://doi.or g/10.1016/j.apene eti.2020.10073 9. rgy.2017.04.059. Řimnáčová D, Weishauptová Z, Přibyl O, et al. Effect of shale prop- Li R, Dong S, Dan L, et al. Tectonically driven organic fluid migra- erties on CH and CO sorption capacity in Czech Silurian 4 2 tion in the Dabashan Foreland Belt: evidenced by geochemistry shales. J Nat Gas Sci Eng. 2020. https ://doi.org/10.1016/j.jngse and geothermometry of vein-filling fibrous calcite with organic .2020.10337 7. inclusions. J Asian Earth Sci. 2013;75(8):202–12. https ://doi. org/10.1016/j.jseae s.2013.07.026. 1 3 Petroleum Science (2021) 18:530–545 545 Shi W, Zhang Y, Dong S, et  al. Intra-continental Dabashan oro- Ye YH, Liu SG, Ran B, et al. Characteristics of black shale in the cline, southwestern Qinling, Central China. J Asian Earth Sci. Upper Ordovician Wufeng and lower Silurian Longmaxi for- 2012;46:20–38. https ://doi.org/10.1016/j.jseae s.2011.10.005. mations in the Sichuan Basin and its periphery, China. Aust J Sun H, Yao J, Gao SH, et al. Numerical study of CO enhanced natu- Earth Sci. 2017;64:667–87. https ://doi.or g/10.1080/08120 ral gas recovery and sequestration in shale gas reservoirs. Int J 099.2017.13215 81. Greenh Gas Control. 2013;19:406–19. https ://doi.org/10.1016/j. Zhang G, Zhou W, Ji S, et al. Experimental study on CO replacement ijggc .2013.09.011. method used in shale gas exploration. J Chengdu Univ Technol. Tang X, Jiang Z, Jiang S, et al. Heterogeneous nanoporosity of the 2015;42(3):366–71 (in Chinses). Silurian Longmaxi Formation shale gas reservoir in the Sichuan Zhang K, Jiang H, Qin G. Utilization of zeolite as a potential multi- Basin using the QEMSCAN, FIB-SEM, and nano-CT methods. functional proppant for CO enhanced shale gas recovery and CO 2 2 Mar Pet Geol. 2016;78:99–109. https ://doi.org/10.1016/j.marpe sequestration: a molecular simulation study on the competitive tgeo.2016.09.010. adsorption of CH and CO in zeolite and organic matter. Fuel. 4 2 Tao Z, Bielicki JM, Clarens AF. Physicochemical factors impacting 2019;249(1):119–29. https ://doi.org/10.1016/j.fuel.2019.03.061. CO sequestration in depleted shale formations: the case of the Zhang H, Diao R, Mostofi M, et al. Monte Carlo simulation of the Utica shale. Energy Procedia. 2014;63:5153–63. https ://doi. adsorption and displacement of CH by CO Injection in shale 4 2 org/10.1016/j.egypr o.2014.11.545. organic carbon slit micropores for C O enhanced shale gas recov- Wan T, Liu HX. Exploitation of fractured shale oil resources by ery. Energy Fuel. 2020;34(1):150–63. https://doi.or g/10.1021/acs. cyclic CO injection. Pet Sci. 2018;15(3):552–63. https ://doi.energ yfuel s.9b033 49. org/10.1007/s1218 2-018-0226-1. Zhao P, Xie L, He B, et al. Strategy optimization on industrial CO Wang G, Long S, Ju Y, et al. Application of horizontal wells in three- sequestration in the depleted Wufeng–Longmaxi formation shale dimensional shale reservoir modeling: a case study of Longmaxi- in the northeastern Sichuan basin, SW China: from the per- Wufeng shale in Fuling gas field, Sichuan Basin. AAPG Bull. spective of environment and energy. ACS Sustain Chem Eng. 2018;102(11):2333–54. https ://doi.org/10.1306/05111 81714 4. 2020;8:11435–45. https://doi.or g/10.1021/acssusc hemeng.0c041 Wang T, Tian S, Li G, et al. Molecular simulation of CO /CH com- 14. 2 4 petitive adsorption on shale kerogen for C O sequestration and Zhou L, Su X, Lu Y, et al. A new three-dimensional numerical model enhanced gas recovery. J Phys Chem C. 2018;120(30):17009–18. based on the equivalent continuum method to simulate hydraulic https ://doi.org/10.1021/acs.jpcc.8b020 61. fracture propagation in an underground coal mine. Rock Mech Yao Y, Liu J, Liu D, et al. A new application of NMR in characteri- Rock Eng. 2018;52(8):213–33. https ://doi.or g/10.1007/s0060 zation of multiphase methane and adsorption capacity of shale. 3-018-1684-x. Int J Coal Geol. 2019;201:76–85. https ://doi.or g/10.1016/j. Zhou J, Jin Z, Luo K. Effects of moisture contents on shale gas recov - coal.2018.11.018. ery and C O sequestration. Langmuir. 2019;35(26):8716–25. https Yang ZL, Yu HY, Chen ZW, et al. A compositional model for CO ://doi.org/10.1021/acs.langm uir.9b008 62. flooding including CO equilibria between water and oil using Zhu Y, Wang X, Feng M, et al. Lithofacies classification and its rela- the Peng–Robinson equation of state with the Wong–Sandler mix- tionship with reservoir of the Lower Paleozoic Wufeng–Long- ing rule. Pet Sci. 2019;16:874–89. https ://doi.org/10.1007/s1218 maxi Formation in the eastern Sichuan Basin. Lithol Reserv. 2-018-0294-2. 2016;28(5):59–66 (in Chinses). 1 3

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