8 Characterization of CO 2 flow in propped fracture s is important in defining the response to CO 2 9 injection for reservoir stimulation and CO 2 sequestration . We measure the evolution of permeability 10 in propped fractures of shale to both adsorbing CO 2 and non -adsorbing He under sub - and super - 11 critical conditions . A tripa rtite permeability -pressure evolu tion curve is obtained when supercritical , 12 consisting of a dual-U-shaped evolution first below and then exceeding critical pressure with a V- 13 shaped fluctuation spanning the phase transition . The increas ing adsorbed -phase -density and resultant 14 swelling stress may control the permeability variation around the critical point . The inorga nic 15 adsorb ent (mainly clay) may contribute to the secondary U -shaped evolution according to its sorption 16 isotherm. The secondary adsorption may be generated by increasing sorption sites ( competitive 17 adsorption between CO 2 and H 2O) or through multi -layered sorption and stronger diffusion of 18 supercritical CO 2. Further constraint is applied through observations of permeability recovery 19 between initial and repeat saturations to non-adsorptive He. An abno rmal increment of permeability 20 recovery ratio is obtained for secondary adsorptio n, which may be caused by the dehydration and 21 shrinkage of the matrix and the dissolution of minerals . Mechanisms of permeability evolution for 22 CO 2 in shale are classified between organic and inorganic fractions. The contributions of adsorption to 23 the permeability evolution are quantified by comparison s for permeation by CH 4 and He. A flat X - 24 shaped trend is apparent, in which the inorganic contribution to permeability increases with increasing 25 pressure while the organic contribution to permeability decreases with increasing pressure. The ratio 26 of inorganic contribution reaches 60–70% under supercritical conditions. 27 Keywords: propped shale fracture, adsorption, permeability, clay, supercritical CO 2 28 29 1 1 Introduction 30 CO 2 injection in reservoirs (oil, gas or coal) is a promising approach for both enhancing the 31 recovery of native hydrocarbons and for sequestering carbon emission s. These techniques include 32 CO 2 flooding (Cao & Gu, 2013) , fracturing (Hou et al., 2017) , replacement (Lan et al., 2019) and 33 storage in saline aquifers or depleted reservoirs (Bielicki et al., 2018; Buscheck, White, Carroll, 34 Bielicki, & Aines, 2016) . A typical flow path of CO 2 in a reservoir is shown in Fig. 1, where CO 2 35 flows in through a well (1), then propped fractu res (2) and finally into the porous medi um (3). This 36 injection may exert significant impact s on the stimulat ed reservoir volume (SRV) for hydro carbon (oil 37 and gas) recovery and sealing behaviour for carbon (CO 2) sequestration (Middleton et al., 2015; 38 Tayari & Blumsack, 2020) . 39 40 Fig. 1. Schematic of CO 2 injection in a shale reservoir through (1) a well, (2) propped fracture s (main and 41 branching fractures) and (3) the porous medium . 42 Abundant work has examined CO 2 flows in porous media to define interaction s between gas and 43 matrix and the corresponding effect on both permeabilities (Ao, Lu, Tang, Chen, & Li, 2017; Zhou et 44 al., 2016; Zhou et al., 2020) and the mechanic al properties of rock (Yin, Zhou, Jiang, X ian, & Liu, 45 2016; Yin et al., 2017) . Less clarity is available for CO 2 flow in propped fracture s, where additional 46 complexity is added with grain -fracture interaction s to CO 2. Previous work has focus sed on grain - 47 fracture interaction s to evaluate permeability loss by embedment under various conditions of closure 48 2 stress, mineral composition , reservoir temperature and fracturing fluid s (Arshadi, Zolfaghari, Piri, Al - 49 Muntasheri, & Sayed, 2017; Kewen Li, 2015; Tang & Ranjith, 2018) . Impacts of CO 2-matrix 50 interaction (such as swelling) are relatively less prominent , especially for shales because of their 51 lower organic content s. However, recent studies in high-organic -content Green River shale indicates 52 that swelling could consume as much as 50% of th e permeability and increase embedme nt by a factor 53 of ~2 (Hou, Elsworth, & Geng, 2020) . 54 The measurement of permeability is one principal methodology characterizing the evolution of 55 CO 2 fracture flow , which reflects the effects of both swelling and embedment (S. Wang, Elsworth, & 56 Liu, 2011, 2013) . A sorbing permeant (CO 2, CH 4 or N2) swell s the rock matrix and forms a typical U - 57 shaped curve for permeability evolution with pressure due to the competition between adsorption and 58 effective stress (Kumar, Elsworth, Liu, Pone, & Mathews, 2015; X. Li et al., 2017) . Nonetheless, t he 59 underlying mechani sms of adsorption -permeability response for CO 2 permeation in propped fracture s 60 remain unclear , due to a variety of factors, including: 61 (1) Clues to the behaviour may be found in the response to CO 2 adsorption , although the common 62 use of powder ed rocks rather than the intact s ample s (Klewiah, Berawala, Alexander Walker, 63 Andersen, & Nadeau, 2020) limits the applicability of observations to fracture flow . The cubic 64 depe ndence of permeability on fracture aperture magnif ies the effect of swelling, thus leading to the 65 appearance that the swelling of a trace content of organics may significant ly impact permeability. A 66 similar response is reported in the study of CO 2-clay interaction s, where the stiffness of an intact 67 simple may develop higher swelling stress than pure clay could under the same conditions (Zhang, de 68 Jong, Spiers, Busch, & Wentinck , 2018) . 69 (2) Swelling of clay minerals is another controll ing mechanism . An increasing number of studies 70 reveal a strong positive correlation of shale clay content to sorption capacity of CO 2 (Chalmers & 71 Bustin, 2008; M. Gasparik et al., 2012; Luo et al., 2015; L. Wang & Yu, 2016) . CO 2 sorption capacity 72 of powder ed montmorillonite is comparable to that of coal (Romanov, 2013) . However, excess 73 exposure to supercritical CO 2 may conversely lead to shrinkage of clay by interlayer dehydration 74 (Akono et al., 2019; Lu et al., 2016; Pan & Connell, 2007) . More experiments are needed to constrain 75 the effect of such swelling -shrinking response on permeability evolution. 76 3 (3) The CO 2 phase transition is observed to dramatically change permea bility in simple powder s 77 (Jia, Tsau, & Barati, 2018) , intact coal (Zhi, Elsworth, & Liu, 2019) and propped fractures in shale 78 (Hou et al., 2020; X. Li et al., 2017) . A sudden increase in density and kinetic energy may enhance the 79 sorption capacity and plastic ize the solid material to generate a precipitous drop in permeability 80 around the critical point . However, m ore studies are required to constrain this permeability evolution 81 under higher injection pressure s where the CO 2 is in a supercritical state and for longer ex posure . 82 Towards resolving these impacts , we explore CO 2-shale interaction s across the sub - to super - 83 critical phase transition in artificial (proxy -fluid -driven ) fractur es. We measure permeability evolution 84 with the injection of both non -adsorptive helium (He) and adsorptive carbon dioxide ( CO 2) on 85 samples of G reen River shale to (i) fully rev eal the interaction process from sub- to super -critical 86 pressure, (ii) define the d ifferent controlling mechanisms for permeability evolution in different stages 87 of gas injection , and (iii) quantitatively analy ze the contributions of each mechanism to provide a 88 mechanistic understanding of characteri stics of CO 2 fracture -flow towards improv ing the practice of 89 oil/gas production and CO 2 sequestration . 90 2 Methodology 91 We measure permeability evolution to CO 2 and He in propped fracture s in shale via pressure 92 transient (pulse ) method s. The apparatus (core holder and reservoirs) is immersed within a 93 temperature -controlled water bath to control the state of CO 2, as either sub - or super-critical. We 94 measure permeability to CO 2 and He alternately in the same sample to reveal the influence of 95 adsorption and deso rption behaviour . 96 2.1 Materials and preparation 97 Axially -split core samples (25mm diameter 50mm length) of Green River shale are packed with 98 tape then placed in a pressurized core holder with monolayer proppant (40/80 mesh , Carbo -Lite 99 ceramic proppant) sandwiched within the fracture. We explore the behaviour of a monolayer since the 100 branch fracture s or micro -fracture s (usually monolayer -propped) compose a crucial component of the 101 total stimulated reservoir volume (Gale, Laubach, Olson, Eichhuble, & Fall, 2014; Hoek & Martin, 102 2014; Weng, 2015) . Besides, similar permeating behaviour of CO 2 has been observed for both multi - 103 4 and mono -layer propped samples, in which the monolayered sample exhibits an amplified swelling 104 effect (X. Li et al., 2017) . We use sorbing CO 2 (purity of 99.995 %) and effectively - non-sorbing He 105 (99.999 %) as contrasting permeants for the permeability measurement s. 106 2.2 Apparatus 107 A standard triaxial apparatus, as shown in Fig. 2, is used as the pressurized core holder (Temco) . 108 Both confining and axial stresses to 25 MPa are applied by syringe pump s (ISCO 500D) to a 109 resolution of ± 0.007MPa . A Viton rubber jacket is applied to seal and isolate the sample from the 110 confining fluid in the core holder. Reservoir volumes are 26.7 ml fo r the upstream and 16.8 ml for the 111 downstream with reservoir pressures measured by transducer s (Omega PX302 -2KGV and Omega 112 PX302 -5KGV) to resolutions of ± 0.03 MPa. Each transducer is calibrated for each new sample with 113 National Instruments Labview used fo r data acquisition and pump control. The tests are performed at 114 both room temperature ( 23°C ) and supercritical temperature (45 °C for a supercritical transition at 115 31°C) in a water bath with the core holder and reservoirs immersed, as shown in Fig. 2. Interior g as 116 pressure s in the range 2 to 13 MPa access the various phase states of CO 2. 117 118 Fig. 2. Schematic of the experimental apparatus and water bath system (Hou et al., 2020; S. Wang et al., 2011) . 119 2.3 Procedure 120 We use standard pressure transient (pulse ) method s for permeability measurements. A pressure 121 difference (pulse) is applied between upstream and downstream and its upstream decay and 122 5 downstream build -up behaviour is recorded and analysed to obtain the permeability that is calculated 123 as (Brace, Walsh, & Frangos, 1968) , 124 ()up dn up dnLV VkA V V=+ (1) 125 where α is the slope of pressure decay against the logarithm of time ; µ and β are the viscosity and 126 compressibility of the fluid, respectively; L is the length of the sample; Vup and Vdn are volumes of the 127 upstream and downstream reservoirs, respectively; and A is the fluid flow cross -section al area in 128 fracture (permeation through the rock matrix is ignored ). 129 The compressibility of the fluid β is calculated from the bulk modulus 130 211 MB== (2) 131 where BM is the bulk modulus of the fluid ; υ is the speed of sound in the fluid; ρ is the fluid density. 132 The values of υ and ρ are recovered from standard characterizations ( National Institute of Standards 133 and Technology (NIST) ). The values of compressibility are calculated and plotted in Fig. 3. 134 135 Fig. 3. Compressibility of CO 2 and He (based on NIST database) . 136 3 Results 137 Four groups of permeability measurements are conducted and summarized in Table 1. Five rounds 138 of experiments are carried out in Group 1 for He and CO 2 as gaseou s, liquid then supercritical state . 139 The first four rounds are c ompleted at room temperature (23 °C) with the final performed at a 140 temperature of 45°C beginning at a supercritical pressure. In particular, the permeability to non- 141 sorbing He is repetitively measured in the same sample before and after the permeation of CO 2 to 142 compare the impact of CO 2 adsorption and desorption. Each round of e xperiments involved in Group 143 6 2 is conducted continuously at 45 °C. Control G roup 3 and 4 repeat sub- and super -critical pressure 144 measurements with non -sorbing He. 145 Table 1 . Matrix of e xperiment s defining samples and conditions . 146 Sample Type Green River Shale Group No. Experimental Group 1 Experimental Group 2 Control Group 3 Control Group 4 Injection Pressure 3 ~ 13 MPa 2 ~ 1 2 MPa 2 ~ 1 3 MPa 2 ~ 9 MPa Temperature 23 °C & 45 °C 45 °C 23 °C 23 °C CO 2 Phases Gaseous, Liquid & Supercritical Supercritical Gaseous Gaseous Dimension s 25 (dia.) * 50 (length) mm Proppant Carbo-Lite Ceramisite (40/80 Mesh) Gas Helium & Carbon Dioxide Triaxial Pressure 25 MPa Observations recovered by probing with both injection (increasing gas pressure) then depletion 147 (decreasing gas pressure) are plotted in Fig. 4 . Generally, positive parallel linear relationships are 148 recovered between increasing gas pressure and increasing permeability for all cases of He and liquid 149 CO 2, indicating that deformations under changes in effective stress (confining pressure minuses 150 injection pressure) dominate the permeability evolution. This is expe cted for non-adsorptive He since 151 swelling is absent . For liquid CO 2, with permeabil ity one order -of-magnitude lower than that for He, a 152 swell ing effect may be manifest but is counteract ed by the high injection pressure. 153 7 154 155 Fig. 4. Permeability evolution versus gas pressure in propped fractures in Green River shale . The repeat He tests are 156 performed after all CO 2 tests in the same sample of each group. Group 2 is completed at 45 °C. Group 3 and 4 are at 157 23°C. Group 1 is conducted at both temperatures and for various CO 2 phases. 158 For the remainder of the CO 2 cases, typical U -shaped curve s are observed under subcritical 159 pressure s as the result of the competition between adsorption and effective stress. A new U -shaped 160 curve und er high pressure is formed for the supercritical CO 2 cases . Results from all CO 2 cases are 161 averaged and presented in Fig. 5. A tripartite permeating behaviour is apparent , consisting of ( I) a 162 typical U -shaped curve below the critical pressure, ( II) a V -shaped fluctuation around the phase 163 transition point and ( III) a secondary U -shaped curve above supercritical pressure and temperature. 164 Part III exhibits a similar parabolic trend as Part I, and reaches the minimum value around a pressure 165 of 11 –12 MPa. 166 8 167 Fig. 5. Permeability evolution versus gas pressure for all CO 2 cases presented as averaged values. 168 4 Discussion 169 The mechanism of permeability evolution in a propped fracture is described schematically in Fig. 170 6. Different from a n intact simple with pores or natural micro -fractures at the nano meter -scale, the 171 existence of proppant particles (1) provides a m acroporous flow channel that is modified by the 172 synthetic impacts of effective stress, grain embedment and matrix swelling. The gap between grains 173 (2) generates a pair of non-contact ing surface s, through which swelling magnif ies the resulting 174 fracture closure . The surface deformation of the fracture an d the crushed zone between matrix and 175 grains (3) increase s the contact area with permeant s and enhance s the sorbing capacity. In addition , 176 the mineral matter tends to be enriched in the crushed zone, which enhances permea nt diffusion and 177 sorption kinetics (Spears & Booth, 2002) . 178 179 Fig. 6. Schematic of flow mechanisms of a propped fracture in shale. 180 9 4.1 Influence of CO 2 phase transition 181 Permeability decreases precipitously at the beginning of phase transition s from gaseous to both 182 liquid and supercritical states (Fig. 5) . However, the influencing mechanisms may be different 183 between these liquid and supercritical transitions – suggested by the differences in the subsequent 184 permeability trend s at high pressure. The permeation of liquid CO 2 remains continuous for the 185 overlapping pressure from 7 –9 MPa (Group 1 L -CO 2 in Fig. 5 ). In contrast, the permeability to 186 supercritical CO 2 (SC-CO 2) emerge s as a direct climb back t o the subcritical level. The liquid case is 187 explained by the sudden volume change during the phase transition for a r elatively stable pressure (X. 188 Li et al., 2017) . For the supercritical case, the effective aperture variation may be controlled by 189 adsorbed mass and effective stress , graphically described in Fig. 7. 190 191 Fig. 7. Schematic s of effective aperture evolution (a) during the phase transition and (b) under supercritical state . 192 The phase change of CO 2 near the critical point results in a sharp increase in adsorbed phase 193 density and its resultant swelling strain (Bakhshian & Hosseini, 2019) , which compresses the effective 194 aperture and induces a drop in permeability , as shown in Fig. 7(a). The severe swell ing strain may 195 consume ~80% of the effective aperture (Hou et al., 2020) . Swelling stress es of 9.6 –24.7 MPa may 196 result upon introduction of CO 2 at 10 MPa and 44 °C measured by uniaxial compaction/swelling test 197 on montmorillonite and shale (Zhang et al., 2018) . The swelling stress coverts into a free -swelling 198 strain enabled by the non-contact ing surface s (Fig. 6). With increasing swelling , the cumulative stress 199 opposes and overcomes the confining pressure then partly releases the confining -stress -compressed 200 aperture (Fig. 7 (b)) - increasing permeability at the conclusion of the phase transition . The presence 201 of an artificial fracture and g rains liberate s the swelling stress opposing the confining pressure, which 202 10 is the essential difference with the intact sample tha t retains the swelling stress within the rock 203 structure (Zhi et al., 2019) . 204 4.2 Dual -U-shaped evolution due to s econdary adsorption in clay 205 Similar concave -upwards evolutions of permeability are present in Part s I and III of the response 206 which may result from secondary adsorption of CO 2. Direct evidence is reported in studies of CO 2- 207 clay interaction s. The isotherms show dual-inverted -parabolic fluctuations at pressures above ~8–12 208 MPa in Muderong shale at the same temperature of 45 °C. This is attributed to CO 2 adsorption in clay 209 because of the consisten t pattern with the isotherm of pure clay (Kaolinite) , as shown in Fig. 8 (a) 210 (Busch et al., 2008) . At micro pore scale, the CO 2 pore density ( sum of the bulk fluid density and pore 211 volume normalized excess density ) in the clay ( montmorillonite ) pore is estimated b y combining the 212 data for excess sorption and interlayer thickness measurements. A similar evolution curve is observed 213 in Fig. 8 (b), which is induced by the entrance of supercritical CO 2 into the inter-molecular layer spac e 214 within the clay and multilayer sorption at higher fluid density (Rother et al., 2013) . More evidence is 215 apparent in experiments on T exas and Wyoming clay s (Romanov, 2013) and Utica shale (Sanguinito 216 et al., 2018) . 217 218 Fig. 8 . CO 2 adsorption in shale and clay. (a) E xcess adsorption in Muderong shale and kaolinite at 45 °C (Busch et 219 al., 2008) ; (b) CO 2 pore density in montmorillonite as a function of bulk density and co rresponding pressure (Rother 220 et al., 2013) . 221 CO 2 adsorption induces swelling strain that consumes the effective aperture in the propped 222 fracture , thus decreasing permeability with increased swelling . The M -shaped isotherms of CO 2 in 223 clay (Fig. 8) are the inverse (reflection) of the dual-U-shaped permeability curves ( Fig. 5 ). The 224 press ures corresponding to the second peak values of adsorption and CO 2 pore density are 11.7 MPa 225 11 and 12.2 MPa, respectively, which agree with the pressure (11 –12 MPa) corresponding to the trough 226 in the second v alley in permeability magnitude in Part III . The previous study of real-time X -ray CT 227 analysis indicates that clay - and inerti te-rich micro -lithotypes hold most of the CO 2 adsorption 228 increment with increasing gas pressure because of their high porosity (Karacan & Mitchell, 2003) . It 229 may infer that the CO 2 adsorption in clay dominate s the secondary permeability evolution . 230 4.3 Generation of secondary adsorption and impact on permeability recovery 231 The difference in response both with (Group 1 and 2) and without (Group 3 and 4) the secondary 232 adsorption ( Part III) is reflected in the permeability recovery between initial and repeat He cases, as 233 shown in Fig. 9 . The permeation of CO 2 swells and softens the rock matrix, which intensifies the 234 irreversible embedment of grains then restrain s the permeability recovery ratio (Hou et al., 2020) . 235 Only ~52% of the permeability , on average , recovers in Group s 3 and 4. For Group s 1 and 2, t he 236 secondary adsorption of supercritical CO 2 could prompt increased embedment that should have 237 reduced the permeability recovery . In contrast , it raises the permeability to ~79% and ~68% in Group s 238 1 and 2 , respectively . 239 240 Fig. 9. Permeability recovery of non -sorbing He both before (initial) and then after (repeat) the injection of 241 sorbing CO 2. 242 The mechanism of secondary adsorption may result in such abnormal phenomena . The phase 243 transition of CO 2 into a supercritical state increas es the binding energy , which may break the balance 244 of competitive adsorption between CO 2 and H 2O then dehydrate the clay or other water -containing 245 12 constituent s (Bowers et al., 2017) . The macropore flow -channel (Fig. 6 ) aids this effusion of fugitive 246 water . The sorption site occupied by a water molecule vacates enough space for 2.2 CO 2 molecules 247 (Gensterblum, Busch, & Krooss, 2014) . Besides, the increasing density of supercritical CO 2 generate s 248 more molecular layers attaching to the surface , thus enhancing the total absorbed mass (Klewiah et 249 al., 2020; Rother et al., 2013) . The higher diffusibility of supercritical CO 2 also increase s the 250 intera ction surfaces by diffusing into more pores and deeper into the matrix (S. Li, Li, & Dong, 2016; 251 Lv, Chi, Zhao, Zhang, & Mu, 2019) . Therefore, increasing sorption sites, enabling sorption of multi - 252 layered molecules and increased diffusion rate of supercritical CO 2 may all contribute to secondary - 253 adsorption (Fig. 5) . 254 Subsequent ly, the dehydration induces shrinkage of the rock matrix and increases the effective 255 aperture that follows a cubic law with permeability (Elsworth & Goodman, 1986; Piggott & Elsworth, 256 1993) . Moreover, the dissolution of minerals resulting from the co -existence of CO 2 in water may 257 additionally enlarge the effective aperture (Weniger, Kalkreuth, Busch, & Krooss, 2010) , particularly 258 for the Green River shale w ith a high content of carbonate s (Dolomite 39.4% and Calcite 12.4%) 259 (Fang, Elsworth, Wang, Ishibashi, & Fitts, 2017) . This may fur ther explain the different recovery 260 ratios between Group 1 and 2 experiments , where the longer CO 2 exposure leads to greater carbonate 261 dissolution and higher permeability recovery for Group 1 . The irreversible shrinkage and dissolution 262 enlarge ment after the desorption of CO 2 in the repeat -He case may contribute to the abnormal 263 increment of permeability recovery. 264 4.4 Contributions of organic and inorganic adsorptions to permeability evolution 265 The contributions of organic and inorganic adsorption s to the dual-U-shaped permeability 266 evolution are estimated based on assumptions that (1) the permeability is a sum of functions of 267 organic adsorption -f(Org ads), inorganic adsorption -f(Inorgads) and effective stress -f’(Effective Stress ), 268 in which (2) the adsorption functions ( f(Org ads), f(Inorgads)) are inversely proportional to adsorption 269 masses. Acc ording to assumption (1), the permeability of the adsorptive permeant may be calculated 270 from 271 ( , , ) ( ) ( ) ( )ads ads ads adsPerm f Org Inorg Effective Stress af Org bf Inorg cf Effective Stress=  = + + (3) 272 13 where Org ads and Inorg ads are the adsorption mass es of the permeant in the organic and inorganic 273 constituent s, respectively. a, b and c are coefficients and all assigned the value of 1 in this study. 274 The permeability evolution of CH 4 in Green River shale is utilized for a comparative analysis since 275 the adso rption occurs mainly in the organic s, as shown in Fig. 10 (Weniger et al., 2010) . As the TOC 276 content reduces , the CH 4 adsorption in shale approaches zero and yet residual CO 2 adsorption remains 277 in the inorganic constituent s under the same condition . Similar result s are reported in experiments on 278 shales from the U nited States (Matus Gasparik et al., 2014) and South China (Tan et al., 2014) . The 279 maximum sorption capacity of CH 4 commonly appears at a lower pressure than that of CO 2, even in 280 the same shale. Largmiur pressure s to CO 2 and CH 4 in a group of split tests are approximately a factor 281 of two different ( Table 2 ). The corresponding pressures of the minimum permeability in Part III (11– 282 12MPa) and I (5–6MPa) are also offset by a factor of two , as shown in Fig. 5. 283 284 Fig. 10. Adsorp tion capacities of CH 4 and CO 2 versus TOC (in shale and CBM sample , 45°C and ~12 MPa) 285 (Weniger et al., 2010) . 286 Table 2 . Comparison of Langmuir pressure ( PL) between CO 2 and CH 4 in shale samples from Paraná Basin, 287 Brazil (Weniger et al., 2010) 288 No. Rock Type nL CH 4 mmol/g PL CH 4 MPa nL CO 2 mmol/g PL CO 2 MPa PLCO2 / PLCH4 07_114 Carbonate Shale 0.07 4.09 0.69 8.43 2.06 07_117/118 0.28 2.31 0.8 6.19 2.68 07_181 0.18 5.79 0.9 12.01 2.07 08_100 Shale 0.04 16.09 0.78 20 1.24 08_101 0.08 7.09 0.69 19.03 2.68 08_168 0.37 8.39 2.02 15 1.79 08_170 0.25 14.16 1.25 13.43 0.95 08_154 0.04 5.65 0.65 19.9 3.52 14 289 Based on assumption (2), the contribution ratio of CO 2 and CH 4 adsorption to permeability in 290 organics in the same sample is expressed as 291 2 2 4 4 4 2( ) ( ) ( ) ( )ads CO CO CH ads CH CH COf Org f Adsorption Mass Adsorption Mass f Org f Adsorption Mass Adsorption Mass== (4) 292 The adsorption mass es under various pressure s are estimated by the Langmuir model, in which the 293 maximum adsorption volume and Langmuir pressure are fitted using the measurements in anthracite 294 for its high carbon content (>90%), as shown in Fig. 11 (Merkel, Gensterblum, Krooss, & Amann, 295 2015) . 296 297 Fig. 11. Excess adsorption (45 °C) of CH 4 and CO 2 in anthracite and fitted Langmuir equations (Merkel et al., 2015) . 298 Eq. (4) is then resolv ed as 299 24 42() 52 ( ) 14 0.77ads CO CH ads CH COf Org Adsorption Mass P f Org Adsorption Mass P+==+ (5) 300 where P is the injection pressure, MPa. 301 The ratio of permeabilities under the same effective pressure in the same sample is calculated as 302 2 2 2( ) ( ) ( ) ()CO ads CO ads CO HePerm f Org f Inorg f Effective Stress Perm f Effective Stress ++= (6) 303 and 304 44( ) ( ) ()CH ads CH HePerm f Org f Effective Stress Perm f Effective Stress+= (7) 305 15 where the adsorption of CH 4 in inorganics is ignored comparing with that of CO 2 (Fig. 10) . 306 The normalization of Eqs. (6) and (7) relative to effective stress is applied to eliminate th is effect in 307 their intercomparisons . Then, 308 44 2 2 2( ) 1 ( ) ( ) 1ads CH CH He ads CO ads CO CO Hef Org Perm Perm f Org f Inorg Perm Perm−=+− (8) 309 We define the relative contribution of orga nic and inorganic adsorption to permeability evo lution for 310 the case of CO 2 as “Contribution rat io”. Combing Eqs. (5) and (8), it is estimated as 311 24 2 2 2( ) 1 52 ( ) ( ) 14 0.77 1adsads CO CH He Org ads CO ads CO CO Hef Org Perm Perm PContribution ratiof Org f Inorg P Perm Perm− +==+ + − (9) 312 1 ads ads Inorg Org Contribution ratio Contribution rate =− (10) 313 The averaged d ata from Group s 1 and 2 (Fig. 4), excluding the liquid CO 2 and He -repeat cases, are 314 employed to define the permeabilities to CO 2 and He. The permeability to CH 4 is recovered from 315 measurements using the same m aterial ( Green River shale and 40/80 Carbo -Lite proppant) and similar 316 apparatus and procedures , as shown in Fig. 12 (X. Li et al., 2017) . The approximation s for CO 2 317 permeability are reported and compar ed with those in Fig. 4. 318 319 Fig. 12. Permeability evolution in Green River shale upon injection of CO 2 and CH 4 at a temperature of 21 °C and 320 confining pressure of 20 MPa (X. Li et al., 2017) . 321 The ratios of the contribution of organic and inorganic adsorption to permeability evolution are 322 analyz ed by Eq s. (9) and (10) and plotted in Fig. 13. A flat X -shaped curve is presented, in which the 323 contribution of adsorption to the organic fraction decreases with increasing pressure , while the 324 16 inorganic contribution increases with increasing pressure. Reflected in the t ripartite permeability 325 evolution , the effect of organic adsorption is initially dominant but decreases rapidly before flatten ing 326 out in Part I. The effect of inorganic adsorption increases with increasing pressure before approaching 327 the magnitude of the effect to that of organic adsorption under subcrit ical pressure. For the secondary 328 adsorption of Part III, the inorganic constituent s (mainly clay with high porosity and high surface 329 area) provide most of the sorption sites and contribute 60–70% of the total adsorptive fraction s that 330 induce another U -shaped evolution of permeabil ity under supercritical condition s. Similarly, t he 331 previous study of real-time X -ray CT scanning on the different positions of a coal sample show s that 332 the vitrinite -liptinite -region and clay -inertinite -region adsorb ed 19% and 81% of CO 2 (4.42 MPa) , 333 respectively (Karacan & Mitchell, 2003) . 334 335 Fig. 13. Relative contribution ratio of organic and inorganic adsorptions to permeability evolution for supercritical 336 CO 2 (45°C) in the propped shale fracture . 337 5 Conclusions 338 Permeability evolution in propped shale fractures to non -adsorptive He and adsorptive CO 2 have 339 been measured across both sub - and super -critical conditions . The CO 2-matrix and grain -to-surface 340 interactions , CO 2 phase transition and their mutual effects are analysed to reveal mechanisms of 341 permeability evolution . Contributions of CO 2 adsorption to permeability evolution are classified and 342 quantified by comparing with response s to slightly -adsorptive CH 4 and non -adsorptive He . The main 343 observations of this work are as follow: 344 17 (1) A tripart ite permeability curve is apparent for supercritical CO 2, including dual-U-shaped 345 evolution s at pressures first below (I) and then exceeding (III) the critical point (pressure) with a 346 precipitous V-shaped fluctuation during the intervening case of the phase transition (II). Different 347 from the case of subcritical CO 2, the initial permeability drop at the beginning of the phase transition 348 may be induced by an increase i n the adsorbed -phase -density and the resulting swelling strain. The 349 subsequent recovery of permeability may result from the accumulative swelling stress that overcomes 350 the confining pressure and partly releases the confining -stress -compressed aperture . 351 (2) The dual-U-shaped permeability evolution is controlled by CO 2 adsorptions. The phase 352 transition of CO 2 may increase the binding energy that favors its competitive adsorption with H 2O and 353 results in more sorption si tes. Additionally, an increased diffusivity and density of supercritical CO 2 354 increase s the interaction surface area and generate s multilayer molecul ar sorption onto the surface , 355 respectively. The se synthetic factors result in a second ary-adsorption then a secondary -U-shaped 356 permeability evolution at fluid pressures in excess of the critical condition . 357 (3) The abnormal increments of permeability recovery for He-repeat cases in Group s 1 and 2 are 358 observed where secondary -adsorption occurs . Dehydration by the competitive adsorption between 359 CO 2 and H 2O shrink s the matrix, especially for the clay constituent s. The accompanying process of 360 mineral dissolution by the co -existence of CO 2 in water makes an extra contrib ution . Irreversible 361 matrix shrinkage and mineral dissolution yield larger effective aperture that results in abnormal 362 increments of permeability recovery after the desorption of CO 2. 363 (4) Mechanism s of permeability evolution for CO 2 in shale are classified between organic and 364 inorganic fractions . Each contribution to the permeability evolution is quantified by comparison 365 between CH 4 and He measurements. A flat X -shaped trend is apparent , in which the inorganic 366 contribution in creases rapidly with increasing pressure then flattens out while the organic contribution 367 decreases rapidly with increasing pressure then levels off . The inorganic constituents (mainly clay 368 with high porosity and large surface area) provide most of the sorption sites and contribute 60 –70% of 369 the total adsorptive fractions that result in the secondary -U-shaped permeability evolution under 370 supercritical condition s. 371 372 18 373 Acknowledgements 374 375 This research has received funding from the European Union's Horizon 2020 research and 376 innovation programme under the Marie Sklodowska -Curie grant agreement No 846775. 377 19