Methane Adsorption on Shale: Insights from Experiments and a Simplified Local Density Model

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1 535 Methane Adsorption on Shale: Insights from Experiments and a Simplified Local Density Model Luo Zuo 1,2,3, *, Yupu Wang 4, Wei Guo 2, Wei Xiong 1,2, Shusheng Gao 1,2, Zhiming Hu 1,2 and Shen Rui 1,2 (1) Institute of Porous Flow and Fluid Mechanics, CNPC and Chinese Academy of Sciences, Langfang 657, Hebei, China. (2) Research Institute of Petroleum Exploration and Development-Langfang, Langfang 657, Hebei, China. (3) University of Chinese Academy of Sciences, Haidian, Beijing 119, China. (4) Chinese Academy of Engineering, Xicheng, Beijing 188, China. (Received date: 22 April 214; Accepted date: 6 June 214) ABSTRACT: We herein present a method for predicting adsorption isotherms of methane on shale using the simplified local density (SLD) theory: First, the adsorption isotherms of methane on shale samples were measured and then its adsorption on illite, illite/smectite mixed layer, chlorite, type I, type II and type III kerogen was described with the SLD theory. Second, based on the SLD parameters obtained from adsorption data on kerogen, clay minerals and the composition of the studied shale, we predicted adsorption capacity of the shale using a linear combination of the adsorption capacities of the pure substances weighted by their relative abundance. 1. INTRODUCTION Increasing consumption of natural gas has immediately stimulated the development of unconventional natural gases, especially shale gas. Consequently, research in shale gas production has also been increasing substantially. Both gas in place and flow mechanisms of shale gas aect well productivity, well production performance and development plan. Gas adsorption and desorption can directly aect gas reserves and flow. Many researchers have focussed their attention on investigating gas adsorption on shale. Early research in this area mainly focused on the adsorption capacity of shale and on its composition, both of which play a key role in adsorption. However, modelling of gas adsorption on shale was rarely developed and most researchers used Langmuir model and computer simulation to study the adsorption capacity of shale. Schettler and Parmoly (199) investigated the adsorption of methane on shale, and their experimental results indicated that the gas adsorbed was mainly deposited in the illite layers and stored in the kerogen layers; both illite and kerogen are important components of shale. Schettler et al. (1991) found that dierent clay minerals have dierent specific surface area and adsorption capacity. Large amounts of gas molecules are adsorbed on illite owing to its bigger specific surface area. The adsorption capacity of clays in Devonian shales is unequal. The adsorption capacity of some types of Devonian shale is closely related to its clay content, whereas some have a positive correlation with total organic carbon (i.e. organic matter composition). *Author to whom all correspondence should be addressed. zuoluoxingfeng@163.com (L. Zuo).

2 536 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Lu et al. (1995) found that the adsorption capacity of illite plays an important role in determining the total adsorption on shale when the composition of shale includes lesser amounts of organic matter. In addition, the adsorption on these shales decreases with an increase in temperature. The authors proposed an adsorption model called the bi-langmuir model, which is essentially the same as that of the Langmuir model. The model considers that the adsorption of shale includes two parts, which are described by the Langmuir model with the weight percentage method. Although the percentage of clay mineral in shale is an important factor that determines the adsorption capacity of shale (Schettler and Parmoly 199; Schettler et al. 1991; Lu et al. 1995), some researchers concluded that organic matter in shale contains more adsorbed gas (CH 4 and CO 2 ) than clay minerals and that organic matter greatly aects the amount of adsorption (Li et al. 21; Nuttall et al. 25). Besides clay minerals and organic matter, vitrinite reflectance and micropore volume of shale also have an impact on the adsorption of gas on shale (Wang et al. 29; Strąpoć et al. 21). Hartman et al. (211) concluded that the total gas content of shale has nothing to do with its multi-component adsorbing capacity and that monolayer adsorption cannot be used to accurately estimate the total gas content of shale. In general, adsorptions on both organic matter and clay minerals are key factors to be considered in determining the overall adsorption capacity of shale. Previous studies have already combined experimental evaluation and adsorption modelling while evaluating shale gas adsorption. However, predicting the isothermal adsorption through some theories and methods is rare. Although predicting the adsorption capacity of shale is feasible, the fitting of adsorption data to specific adsorption model is low (Dantas et al. 211). Consequently, adsorption theories included the evaluation of adsorption gas content of shale. Over the last few decades, some adsorption theories have been developed to study the adsorption property of materials, such as the molecular simulation theory, density functional theory (DFT) and simplified local density (SLD) theory (Gubbins and Fraissard 1997). Although both molecular simulation and DFT can more accurately imitate the adsorption characteristics of a material than SLD, the former is more computationally complex and time consuming (Gubbins and Fraissard 1997). Rangarajan et al. (1995) developed an SLD model to study the adsorption isotherms of a pure component on a flat surface over a large pressure range. Their results provided evidence that the SLD model can better reflect the characteristics of material adsorption, and is less computationally intensive and time consuming than molecular simulation and DFT methods (Rangarajan et al. 1995; Subramanan et al. 1995; Chen et al. 1997; Yang and Lira 26). Therefore, the SLD model can serve as an engineering method to simulate the adsorption of materials. Generally, in shale gas reservoirs the percentage of organic matter is lower than that of clay minerals, but the capacity of organic matter to adsorb gas is higher than that of clay minerals (Hartman et al. 211; Ji et al. 212; Zhang et al. 212). Therefore, the compositions of both the organic material and the clay minerals should be considered when studying shale adsorption capacity. There is also a type of shale that lacks micropores and its adsorption ability is found to be much weaker than clay minerals and organic matter of other shale types (Chen et al. 212; Ji et al. 212; Jiao et al. 212; Yang et al. 213). However, the contribution of this type of shale to total gas adsorption is ignored in this study. In this paper, we investigated the adsorption isotherm on shale through experimental analysis and modelling of adsorption. We modelled the organic matter and clay mineral adsorption isotherms with the SLD model and obtained regression parameters. We then predicted the isothermal adsorption capacity of organic material and clay minerals at a given temperature using the regressed parameters. The paper is divided into five sections as follows: The Measurement

3 Adsorption of Methane on Shale 537 of Methane Adsorption on Shale section describes the experimental analysis carried out. The SLD Model introduces the SLD model and the modelling of organic matter and clay mineral adsorption isotherms. The Methodology section describes the methods applied to study the adsorption capacity of shale. The Results and Discussion section presents the experimental results and discusses related topics. Finally, the Conclusions section presents the concluding remarks from the study. 2. MEASUREMENT OF METHANE ADSORPTION ON SHALE 2.1. Materials The core samples of shale used in our experiments were collected from Longmaxi Formation in the southern Sichuan Basin (China). The samples were retrieved at m below the surface. The Longmaxi shale belongs to the Silurian period and is the most commonly available exploration stratum in the southern Sichuan Basin. The thickness of Longmaxi shale ranges from 5 to 6 m, including black shale whose thickness is 2 26 m. Pure methane and helium used in the study were acquired from Beijing Chengxin Shunxing Gas Company (purity %; processing standard based on GB/T ). The core samples were crushed into particle sizes of.2.3 mm (diameter) for isothermal adsorption experiments, and then dried until their weight becomes constant (drying temperature 1 C and normal atmospheric pressure). The mineralogical composition of samples was determined by X-ray diraction (XRD; D8-DISCOVER apparatus) and the SY/T criterion was used to quantitatively interpret the results of XRD for sample compositions. Table 1 presents the mineral composition of the Longmaxi shale samples. In general, the clay content of samples is the highest, and it ranges from 18% to 46% (average, 36%). The content of quartz has the next highest composition, ranging from 24% to 41% (32.8%). The average calcite content is 1.7%. The sum of average clay content, quartz and calcite accounts for 79.5% of the total composition of shale. Brittle minerals, such as quartz and calcite, account for more than 43% of the total mineral content. Other minerals such as plagioclase and pyrite content are usually less than 7%. Among the various clays, illite is the most common clay with a high composition, ranging from 39% to 6% (average, 46.7%). The samples also had the illite/smectite mixed layer, ranging in composition from 31% to 43% (average, 38.5%). The average chlorite content of the samples is 14.8%. The average organic matter content of the samples is 1.75%. TABLE 1. Mineral Weight Composition of Samples of Shale from Longmaxi Formation, Southern Sichuan Basin Organic Clay composition (%) Other minerals composition (%) matter Illite Total clay Potassium Sample (%) Chlorite Illite /smectite content Quartz feldspar Plagioclase Calcite Dolomite Pyrite

4 538 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Measuring Procedure Void Volume The experimental technique used in this study is based on the volumetric method of measuring adsorption. A schematic of the experimental apparatus is shown in Figure 1. The apparatus (AST-2) was developed by China University of Petroleum (Beijing, China) and Xi an University of Technology (Shaanxi, China). The working pressure of the set up ranges from to 1 MPa with an accuracy of.1 MPa. The working temperature range of the instrument is 5 C, with an accuracy of.1 C. Before starting the experiments, the system was housed in a constant-temperature air bath. The sample cell and reference cell were kept in a constanttemperature-stability water bath. Because the adsorption capacity of shale is much less than that of activated carbon (Zhou et al. 2; Guo et al. 213), precise measurement of the gas adsorbed on the crushed samples weighing more than 3 g was possible for each experiment. The experimental procedure can be described as follows: The sample cell (Figure 1) is filled with the crushed adsorbent. The void volume in the cell, V, is determined by the helium expansion method. The helium void volume includes all the volume of the cell section except for the adsorbent volume (as it is impenetrable for helium gas). Because helium is not significantly adsorbed by materials (Malbrunot et al. 1997), the void volume can be accurately determined from measured values of temperature and pressure. The detailed procedure of measuring V is as follows: (i) Set the system temperature first and open the valves 1, 2 and 4 to vacuum the system including the reference cell, sample cell and connecting lines for 12 minutes until no significant change in pressure is observed. Then close the valves 2 and 4, and record the reference cell and sample cell pressure p 1 ; (ii) open the valves 3 and 6 to let a certain amount of helium gas flow into the reference cell, and then close the valves 1, 3 and 6. When the pressure and temperature of the reference cell become stable, the reference cylinder pressure p 2 is recorded to calculate the amount Vacuum pump Valve 4 Valve 5 To air Computer Gas compressor Valve 6 Valve 6 Pressure pump Pressure transduser Multipass valve 1 Valve 2 Multipass valve 1 CH 4 He Gas purifier Valve 3 P Pressure gauge Valve 1 Multipass valve 2 Air bath system Reference cell Sample cell Figure 1. Schematic of the isothermal adsorption experimental apparatus.

5 Adsorption of Methane on Shale 539 of helium in the reference cell. Open valve 2 to let the helium gas expand into the sample cell and record the equilibrium pressure p 1. The V can be calculated from the material balance equation pzz pzz V Vr pzz pzz (1) where V r is the volume of reference cell with connection lines; Z i (i 1, 2, 3) is the compressibility factor. In our experiments, we measured void volumes at four dierent pressures with a constant temperature of 15 C and took the average void volume as the void volume of the experiment Adsorption Measurement The volumetric (in this case manometric) method of adsorption measurement is well established and described in literature (Keller and Staudt 25). In brief, the steps involved in the measurement process are as follows: (i) After calculating the sample cell void-volume measurements, valves 1, 2, 3 and 4 are opened and the system is vacuumed for 12 minutes, following which valves 2 and 4 are closed. (ii) Open valves 3 and 7 to let methane flow into the reference cell, and then close valves 1 and 7; the reference-cell pressure is recorded after equilibrium and the amount of CH 4 in the reference cell is calculated using the gas equation of state (EOS) n pvr ZRT (2) (iii) Open valve 2 slowly, the reference cell and the sample cell are connected and methane expands from the reference cell to the sample cell. (iv) To ensure complete adsorption of methane on shale, the equilibrium time should be longer than 12 minutes before recording the final equilibrium pressure P 1. The amount of free methane in the system n 1, the excess adsorption amount N 1 and the excess adsorption amount of methane on per gram of shale Q 1 can be calculated as follows: n 1 p(v 1 r+ V) ZRT 1 pv 1 r p(v 1 r + V) N1 n1 n1 RT Z1 Z1 Q N 1 1 G 1 (3) (4) (5) where Z 1 is the compressibility factor of methane at temperature T and pressure P 1 ; G is mass of shale sample. (v) Repeat Steps (ii) (iv) and increase the experimental pressure until it reaches the required pressure. The excess adsorption amount of methane on shale and the excess adsorption amount of methane on per gram of shale can be calculated as follows: 1 pv + i r pi 1V p(v i r V) Ni Ni 1+ + RT Z Z Z i i 1 i (6)

6 54 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Q N i i G (7) where p i is the reference-cell filling pressure for the injection at time i; p i is the equibirium pressure for the injection at time i; Z i is the compressibility factor of methane at temperature T and pressure p i ; Z i is the compressibility factor of methane at temperature T and pressure p i Gas Compressibility Factor Compressibility factor of pure gas (methane in our case) is important for accurate analysis of data using the aforementioned equations. In this study, the EOS was used to calculate the compressibility factor and the compressibility factor was compared using two EOSs. Soave et al. (1972) introduced the acentric factor as a third parameter of the R K EOS for non-polar compounds. The value of Z calculated using the Soave Redlich Kwong equation is as follows: Z 3 Z 2 + Z(A B B 2 ) AB (8) T r T/T c (9) p r p/p c (1) α A p z T B.8664p T r r r r (11) (12) a[1 + ( w.176w 2 )(1 T.5 r )] (13) where T is the absolute temperature; p is pressure; T c is critical temperature; P c is critical pressure; w is the acentric factor of gas molecules. The values for methane are as follows: T c 19.56; p c MPa; w.113 (Gasem et al. 21; Mohammad et al. 211). Peng et al. (1975) proposed the Peng Robinson (PR) EOS based on the Redlich Kwong equation RT a(t) p V b V(V+ b) + b(v b) (14) a(t) a a(t) (.45724R 2 T 2 c/p c ) a(t) (15) b.77796rt c /p c (16) a(t) [1 + k(1 T.5 r )] 2 (17) k w.26992w 2 (18) The PR equation can be rewritten as a form of compressibility factor as follows: Z 3 (1 D)Z 2 + (C 2D 3D 2 )Z (CD D 2 D 3 ) (19) C ap/(r 2 T 2 ) (2) D bp/(rt) (21) Figures 2 and 3 are methane compressibility factor calculated using equations (8) and (19) at and K, respectively, together with experiment data obtained from literature (Tiab and Donaldson 211). It is found that the data obtained from the PR equation better match with

7 Adsorption of Methane on Shale 541 the experiment data of Tiab and Donaldson (211). We choose the PR EOS to calculate the compressibility factor of CH 4. The compressibility factor of helium was calculated using an expression based on experimental data from the National Bureau of Standards Technical Note 631 for helium (McCarty 1972) Tiab et al. 211 SRK EOS PR EOS Compressibility factor Z Figure 2. Compression factor for CH 4 calculated using the Soave Redlich Kwong equation, the PR equation and that obtained from the literature at K Tiab et al., 211 PR EOS SRK EOS Compressibility factor Z Figure 3. Compression factor for CH 4 calculated using the Soave Redlich Kwong equation, the PR equation and that obtained from the literature at K.

8 542 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Experiment Results We obtained the adsorption isotherms for all the test samples at 25, 35 and 45 C, respectively, by applying the aforementioned method. In this study, we predicted adsorption isotherms for only two shale samples (Sample 1 and Sample 2). Figures 4 and 5 show the isothermal adsorption of 2. Sample 1 25 C test Sample 1 35 C test Sample 1 45 C test 1.5 Excess adsorption (m 3 /t) Figure 4. Adsorption isotherm of methane on Sample Sample 2 25 C test Sample 2 35 C test Sample 2 45 C test Excess adsorption (m 3 /t) Figure 5. Adsorption isotherm of methane on Sample 2.

9 Adsorption of Methane on Shale 543 Samples 1 and 2. We then applied our method to obtain the respective adsorption isotherms that perfectly represent the test adsorption of these two samples with the SLD model at 25, 35 and 45 C, respectively. 3. SLD MODEL The SLD model was developed by Rangarajan et al. (1995). The model describes the adsorption isotherms of a pure component on a flat surface over a large pressure range. This method is not computationally intensive and can be an engineering supplement to other available models. The SLD model assumes that the adsorbent consists of a rectangular slit pore and the adsorbate molecules reside in this slit pore, as shown in Figure 6. The distance between the two slit surfaces is L, and a molecule s position is Z in the slit pore, perpendicular to the surface of the slit pore. Any adsorbate molecule will be aected by the surfaces of the slit pore. When the interaction between adsorbent molecules and adsorbate molecules reaches the adsorption equilibrium, the chemical potential at Z position is the sum of fluid fluid and fluid slit Adsorbent Molecule Adsorbate Molecular z L-Z Figure 6. SLD slit-pore model.

10 544 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No potentials and is equal to the fluid chemical potential (Rangarajan et al. 1995). In this work, we investigated only the methane adsorption on shale, and therefore the equilibrium equation is expressed as follows: m(z) m gg (z) + m gs (z) m (22) The chemical potential can be calculated by fugacity (T) RTIn μ f μ + f μ (z) μ (T) + RTIn f (z) gg gg f o (23) (24) where R is gas constant; T is absolute temperature in Kelvin; m is chemical potential of gas; m gg (z) is chemical potential of gas gas at Z position; m gs (z) is chemical potential of gas wall at Z position; f is fugacity at reference state; m (T) is chemical potential at reference state; f is fugacity of gas; f gg (z) is fugacity of gas gas at the Z position. The chemical interaction between gas molecules and adsorbent molecule is given as follows: m gs (z) N a [Y gs (z) + Y gs (L z)] (25) where N a is Avogadro s number; Y gs (z) and Y gs (L z) are the potential between gas molecules and molecules of the slit surface at position Z. The potential of gas solid interaction, Y gs (z), can be calculated using the following equation (Chen et al. 1997; Chareonsuppanimit et al. 212): ( z) gs ψ 4πεσ n gs 1 σ 5z ss /2 2 gs gs 1 ( + σ ) i 1 ss ( ) where n is the number of adsorbent plane atoms per unit area; e gs is the gas solid interaction energy parameter; s ss s the absorbent interplanar distance; s gs is the interaction distance between the adsorbate and adsorbent molecules; in general, s gs (s gg + s ss )/2, where s gg is the molecular diameter of gas. By substituting equations (23) (25) into equation (22), the equilibrium equation of adsorption is obtained gs ( z) ( L z) ( ) ψ gs f + ψ gg z f exp kt σ gs 4 2 (z + σ /2+ i 1 σ ) ss where k is Boltzmann constant (k J/K). The PR EOS is more appropriate to reflect the repulsive force of gas molecules (Peng and Robinson 1976), and therefore we used it to calculate the fugacity of adsorbate in the slit pore. (26) (27) ρ P RT 1 ( 1 ρ b) ( ) a T ρ RT 1+ ( 1 2) ρ b 1+ ( 1+ 2) ρ b (28)

11 Adsorption of Methane on Shale 545 ln f p bρ 1 bρ a T RT 1 2b b ( ) ρ p pb a( T) 2 2 ( + ρ ρ ) ln RTρ ( ) ( ) + + ρ RT 2 2bRT ln b ρ b (29) α(t)r Tc a(t) P c (3) b.77796rt C /p C (31) where p is pressure; r is density of gas; p c is critical pressure; T c is critical temperature (K). The method of calculating a(t) has been developed previously; in this study, we chose the method suggested by Gasem et al. (21) C+ Dω+ Eω ( T) exp( ( A BTr)( 1 Tr )) 2 α + (32) where A, B, C, D and E are coeicients and their values are 2.,.8145,.134,.58 and.467, respectively. The value of acentric factor w is.113 (Gasem et al. 21). The density r and energy parameter a of the adsorbed gas are position dependent, meaning that these parameters vary with coordinate Z; the fugacity of the adsorbed gas phase can be calculated using the following equation (Hasanzadeh et al. 21; Chareonsuppanimit et al. 212): ln f gg ( z ) bρ( z) 1 bρ( z) p ( ) ρ( ) p ln ( ) ( ) RTρ( z) aads z z RT 1 2b z b z 2 2 ( + ρ ρ ) ( ) ( ) ( ) ( ) + + ρ pb a z RT 2 2bRT ln z b ρ( z) b According to Fitzgerald et al. (23), the covolume b in the PR EOS needs to be adjusted in order to more accurately describe the repulsive interaction of adsorbed fluid at high pressures. The covolume is corrected using the parameter L b. Equation (33) then becomes ( z ) ln f gg p badsρ 1 b z ads ( z) a ( ) ρ ( ) ads z z p ln ρ( ) RT 1 2b ( z) b ( z) RTρ ( z) ( z) + + ρ ( ) ( adsρ ads ρ ) ( ) ads ( ) ( ) ads a 2 2b RT ln z b ads ads ρ z b pb ads RT (33) (34) ( ) b b 1+Λ ads b (35) For the energy parameter a ads (z), the expression introduced by Chen et al. (1997) was used When L/s 3

12 546 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No a(z) 3 z σ z.5 a 8 6 σ 3 L z 3.5 σ 1.5 (36) a(z) z L 1.5 a 8 3 σ σ σ 3 z L z σ a(z) 3 L z a 8 σ 6 3 L z.5 σ When 2 < L/s < 3 a(z) 3 z σ a L z.5 σ a(z) 3 L σ 1 a 8 a(z) 3 L z a 8 σ 6 3 L z.5 σ 3 L σ z σ L 1.5 σ.5 3 z L.5.5 σ σ 3 z L σ σ (37) (38) (39) (4) (41) When 1.5 L/s 2 a(z) 3 L σ 1 a 8 (42) When 1 L/s < 1.5 a(z) 3 (43) a 16 where L is the width of the slit pore; s is the molecular diameter of gas; a (27/64)(R 2 T 2 c/p c ). By combining equations (22) (35), the density profile r(z) of the slit pore can be computed. Based on the definition of excess adsorption (Rangarajan et al. 1995), the adsorption capacity of the material containing slit pores can be calculated as follows: n ex A ρ ρ x 2 x1 ( ( z) ) dz (44)

13 Adsorption of Methane on Shale 547 where A is specific surface area; x and x 1 are respectively limits of the integral. In this paper, x s gg /2 and x 1 L s gg /2 because it was considered that gas molecules can infinitely be close to the wall of the slit pore. In summary, there are six variables in the SLD PR model: the slit pore width L, the specific surface area A, the gas solid interaction energy parameter e gs, the absorbent interplanar distance s ss, the molecular diameter of gas s gg and the number of adsorbent plane atoms per unit area n. In general, s ss, s gg and n are fixed for molecular structure considerations (Rangarajan et al. 1995; Subramanan et al. 1995; Chareonsuppanimit et al. 212). The variables L, A and e gs are modified to match the experiment data. Therefore, we could model the adsorption isotherm of materials by varying these parameters. 4. METHODOLOGY In this work, we attempted to predict the adsorption isotherms of shale at dierent temperatures with the acquired adsorption isotherms of clay minerals and organic matter in shale and the SLD model. The adsorption capacities of the other materials in shale are ignored in this study because it is feeble (Chen et al. 212; Ji et al. 212; Jiao et al. 212; Yang et al. 213). It has been recognized that shale must be crushed into small particles before conducting the experiments to evaluate its adsorption isotherms. As a result, clay minerals, kerogen and the other substances in shale are mixed together in the crushed samples. The clay minerals and the organic matter, which are the main materials responsible for adsorption, are also dispersed at the same time. Although crushed shale loses many macropores, almost all mesopores and micropores still remain in these small particles, because the diameter of the particles (.2.3 mm) is far greater than the diameter of the mesopores and micropores. Because the adsorption on shale is related to some mesopores and all micropores (Keller and Staudt 25), the adsorption capacities of both clay minerals and organic matter will remain the same even when they are scattered everywhere in the crushed shale particles. We assume that the adsorption of clay minerals and organic is noninterfering. In other words, the total adsorption of each shale sample is equal to the sum of the individual adsorption of clay minerals and organic matter particles dispersed in smashed shale. Therefore, if we obtain the individual adsorption capacity of clay minerals and organic matter at the same pressure and temperature, the total adsorption isotherm of shale can be predicted by summing up the individual adsorption capacities of clay minerals and organic matter by calculating their weight percentages. If we want to predict the adsorption isotherm of shale at a specific temperature, we need the individual adsorption isotherms of clay minerals and organic matter at that particular temperature. In fact, it is not possible to obtain the adsorption isotherms of clay minerals and organic matter at all temperatures desired, because we usually only measure the adsorption isotherms of one material at several temperatures. As a result, when predicting the isotherms of shale at a particular temperature, one finds that the adsorption isotherms of clay minerals and organic matter were not measured at the same temperature. Therefore, there is a need to find a solution to obtain the adsorption isotherms of clay minerals and organic material at any temperature. According to the SLD Model section, the parameters s ss, s gg, n, L, A and e gs are varied to fit the isotherms of adsorption for one material at a specified temperature. Because the value of s ss, n, L and A are constant for one material at any given temperature (these parameters reflect the structural characteristics of that particular material), the value of s gs also remains unchanged. Therefore, as long as s ss, n, L and A are determined by fitting the data for the material at a given

14 548 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No temperature, the same values for s ss, n, L and A can be used at other temperatures for the same material. Only the value of e gs changes with temperature during the whole process. If we can find a correlation between e gs and temperature, the value of e gs can be computed at any given temperature for the material. The adsorption isotherm of the material can then be determined by the SLD model using the six aforementioned parameters at any temperature. Using the SLD model and the adsorption isotherms of clay minerals and organic material at a few temperatures, we can calculate the adsorption isotherms of clay minerals and organic matter at any temperature. 5. RESULTS AND DISCUSSION 5.1. Organic Matter and Clay Minerals Content of Samples To calculate the adsorption isotherms of shale we need the weight percentage of the main adsorption materials in shale (i.e. clay minerals and organic matter). The detailed compositions of organic matter and clay minerals in each shale sample studied are presented in Table 1. The organic matter of the two samples mainly includes type II kerogen, which is identified based on a chemical analysis by applying the test criterion GB/T We therefore assumed that the organic matter of samples mainly consists of type II kerogen and the adsorption isotherms of organic matter of Sample 1 and Sample 2 and type II kerogen are almost equal SLD PR Model Represents the Gas Adsorption on Clay Minerals and Kerogen According to the previous analysis, clay and organic materials are mainly responsible for the gas adsorption on shale. It has also been known that the total amount of adsorbed methane is directly proportional to the organic matter content and the kerogen type of the shale (Jenkins and Boyer 28; Prasad et al. 29; Chen et al. 211; Elgmati et al. 211; Zhang et al. 212). In this study, kerogen types I, II and III were modelled with the SLD PR model. In order to predict the adsorption property of shale, the regression parameters of the SLD PR model are needed, which were obtained by fitting the adsorption curves of clay minerals as listed in Table 1. Methane is the major constituent of shale gas, and the molecular diameter of gas (s gg ) in the SLD PR model is.38 nm. The adsorption of methane on clay minerals and kerogen was then presented using the acquired regression parameters. The adsorption data of kerogen and clay minerals were available from the literature (Hartman et al. 211; Ji et al. 212; Zhang et al. 212); all these adsorption data are obtained from adsorption experiments on drying samples. The regression parameters are listed in Table 2. Fitting curves are presented in Figures Figures 8 1 show that the adsorption capacity of kerogen declines from type III to type I. Table 2 shows that the energy parameter of type III kerogen is the largest; energy parameter of type II kerogen is the second largest and that of type I is the lowest at the same temperature. These results reveal that the adsorption capacity of kerogen types is closely related to their energy parameter values (the higher the value, the larger the adsorption capacity). It can also be noted that only the energy parameter e gs varies with changing temperature, and that the remaining parameters remain unchanged with respect to change in temperature for the same material. In addition, the value of e gs increases with decrease in temperature. The illite/smectite mixed layer has the maximum adsorption capacity, specific surface area and energy parameter; by contrast, these properties for illite are lesser. Chlorite has the lowest value compared with these two clay minerals.

15 Adsorption of Methane on Shale 549 TABLE 2. Parameters of the SLD PR Model Representing the Adsorption Data of Clay Minerals and Kerogen Specific Temperature Slit width surface area e gs /k s ss s gg Sample (ºC) (nm) (m 2 /g) (K) nm nm n(nm 2 ) Type I kerogen Type II kerogen Type III kerogen Illite Illite/smectite Chlorite Type l kerogen 8 Excess adsorption (m 3 /t) C (Zhang et al. 212) 5.4 C (Zhang et al. 212) 65.4 C (Zhang et al. 212) 35.4 C SLD model 5.4 C SLD model 65.4 C SLD model Figure 7. SLD PR model representation for adsorption of methane on type I kerogen. Also shown for comparison are data from the literature.

16 55 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Type li kerogen 8 Excess sorption (m 3/ t) C (Zhang et al C (Zhang et al C (Zhang et al C SLD model 5.4 C SLD model 65.4 C SLD model Figure 8. SLD PR model representation for adsorption of methane on type II kerogen. Also shown for comparison are data from the literature Type lll kerogen 18 Excess adsorption (m 3 /t) C (Zhang et al C (Zhang et al C (Zhang et al C SLD model 5.4 C SLD model 65.4 C SLD model Figure 9. SLD PR model representation for adsorption of methane on type III kerogen. Also shown for comparison are data from the literature.

17 Adsorption of Methane on Shale Excess adsorption (m 3 /t) C (Hartman et al. 211) 5 C (Hartman et al. 211) 25 C SLD model 5 C SLD model Figure 1. SLD PR model representation for adsorption of methane on illite. Also shown for comparison are data from the literature. 6 5 Excess adsorption (m 3 /t) C (Zhang et al. 212) 5.4 C (Zhang et al. 212) 65.4 C (Zhang et al. 212) 35.4 C SLD model 5.4 C SLD model 65.4 C SLD model Figure 11. SLD PR model representation for adsorption of methane on illite/smectite. Also shown for comparison are data from the literature.

18 552 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Excess adsorption (m 3 /t) C (Ji et al. 212) 5 C (Ji et al. 212) 35 C SLD model 5 C SLD model Figure 12. SLD PR model representation for adsorption of methane on chlorite. Also shown for comparison are data from the literature Predicting the Adsorption Isotherm of Shale In this work we predicted the adsorption isotherms of shale at 25, 35, 45 C for Sample 1 and Sample 2. Based on the data in Table 1, the weight of organic matter and clay mineral of 1-t sample was predicted, and their details are presented in Table 3. Second, according to the details in the Methodology section, we calculated the adsorption isotherm of one material with the SLD PR model at any given temperature using the result of the modelled adsorption data, which was used to find the relation between e gs and temperature. The predicted isothermal adsorption data are found to be close to the experimental data. In this paper, we adopted the empirical formula suggested by Fitzgerald, which was developed based on experiments to find the relation between e gs and temperature (Fitzgerald 25). Based on this method, we used the acquired regression energy parameters (listed in Table 2) for each material at two temperatures to calculate the correlation coeicients, and then averaged all correlation coeicients to obtain one set of correlation coeicients that is appropriate to calculate the energy parameter of the SLD PR model for each material at 25, 35 and 45 C. Table 2 shows that all regression parameters for the SLD PR model representing the adsorption of methane on TABLE 3. Weight of TOC, Illite, Illite/Smectite and Chlorite in 1-t Sample Sample number TOC (t) Illite (t) Illite/smectite mixed layer (t) Chlorite (t)

19 Adsorption of Methane on Shale 553 clay minerals and kerogen remain constant, except for the energy parameter. We obtained the adsorption isotherms of kerogen and clay minerals at 25, 35 and 45 C using the SLD PR model, respectively. The relevant parameters are presented Table 4. Finally, using the weighted sum of the individual adsorption capacity of the clay minerals and organic matter for each pressure point at 25, 35 and 45 C, we predicted the total isothermal adsorption of shale at 25, 35 and 45 C (Figures 13 and 14). Results show that our method is able to accurately predict the adsorption isotherm of shale; however, there is a small deviation between the experimental data and the simulated results. We also predicted the adsorption isotherm of Sample 1 and Sample 2 at 65 C (Figures 13 and 14). From our experiments, it can be said that if we have the detailed data of the mineral composition for one target field and the adsorption isotherms of clay minerals and organic matter of shale at dierent temperatures, the adsorption isotherm of gas on shale can be accurately predicted. For this purpose, the composition of shale is first analyzed, and then the adsorption isotherms of clay minerals and organic matter are measured at several temperatures. In this way, the adsorption isotherms of shale for dierent target fields can be obtained using the suggested method. Although we used the empirical formula of Fitzgerald (a model for coarse-grained materials) to calculate the value of solid fluid energy e gs and its variation with changing temperature, the predicted isotherms closely approximated the isotherms obtained from our experiments. This indicates that our method can be used as a quick engineering method to obtain the adsorption isotherms of methane for the shale of interest. TABLE 4. Parameters for Predicting the Adsorption of Methane on Clay Minerals and Kerogen with the SLD PR Model Specific Temperature Slit width surface area e gs /k s ss s gg Sample (ºC) (nm) (m 2 /g) (K) (nm) (nm) n (nm 2 ) Type I kerogen Type II kerogen Type III kerogen Illite Illite/smectite Chlorite

20 554 L. Zuo et al. /Adsorption Science & Technology Vol. 32 No Excess adsorption (m 3 /t) Sample 1 25 C test Sample 1 35 C test Sample 1 45 C test Sample 1 25 C model Sample 1 35 C model Sample 1 45 C model Sample 1 65 C model Figure 13. Adsorption isotherms of Sample 1 acquired by testing and modelling Excess adsorption (m 3 /t) Sample 2 25 C test Sample 2 35 C test Sample 2 45 C test Sample 2 25 C model Sample 2 35 C model Sample 2 45 C model Sample 2 65 C model Figure 14. Adsorption isotherms of Sample 2 acquired by testing and modelling.

21 Adsorption of Methane on Shale CONCLUSIONS Obtaining the adsorption isotherms of shale through experiments is often time consuming. Experimental work can also be expensive if one wants to have more adsorption isotherms of gas for one shale gas field. In this paper, we presented an engineering method to predict the adsorption isotherms of methane on shale. This method is fast and requires only limited amount of experimental data. Our research shows that the SLD theory can eectively represent the adsorption of methane on illite, illite/smectite mixed layer, chlorite, type I kerogen, type II kerogen and type III kerogen. In addition, a few regression parameters of the SLD model were obtained by fitting the adsorption curves. Among these parameters, only the energy parameter e gs varies with temperature, whereas the remaining parameters are constant at dierent temperatures for one material. It is possible to predict the adsorption isotherm of gas on one material at a given temperature with the SLD model by understanding the relationship between e gs and the temperature of the material. By fitting the adsorption of methane on the organic matter, which is mainly responsible for the adsorption capacity of shale, the appropriate SLD parameters can be acquired to calculate the adsorption capacity of materials at dierent pressures and temperatures by applying the same method. The total adsorption capacity of each shale sample is equal to the sum of the individual adsorption capacity of clay minerals and organic matter particles dispersed in smashed shale. Therefore, if we obtain the individual adsorption capacity of clay minerals and organic matter at the same pressure and temperature, the total adsorption isotherm of shale can be predicted by summing up the individual adsorption quantities of clay minerals and organic matter by calculating their weight percentages. Using our method, acquiring the adsorption isotherms of methane on shale becomes easier and faster. ACKNOWLEDGEMENTS We thank the Institute of Porous flow and Fluid Mechanics, CNPC and Chinese Academy of Sciences for providing us with conditions for this research and also appreciate all the laboratory technicians for their technical guidance. REFERENCES Chareonsuppanimit, P., Mohammad, S.A., Robinson Jr., R.L. and Gasem, K.A. (212) Int. J. Coal Geol. 95, 34. Chen, J.H., Wong, D.S.H., Tan, C.S., Subramanian, R., Lira, C.T. and Orth, M. (1997) Ind. Eng. Chem. Res. 36, 288. Chen, S., Zhu, Y., Wang, H., Liu, H., Wei, W. and Fang, J. (211) Energy. 36, 669. Chen, S.B., Zhu, Y.M., Wang, H.Y., Liu, H.L., Wei, W. and Fang, J.H. (212) J. China Coal Soc., 37, 438. Dantas, T.L.P., Luna, F.M.T., Silva, I.J., Torres, A.E.B., De Azevedo, D., Rodrigues, A.E. and Moreira, R.F. (211) Chem. Eng. J. 172, 698. Gasem, K.A.M., Gao, W., Pan, Z. and Robinson Jr., R.L. (21) Fluid Phase Equilib., 181, 113. Elgmati, M.M., Zhang, H., Bai, B., Flori, R.E. and Qu, Q. (211) Submicron-pore characterization of shale gas plays. North American Unconventional Gas Conference and Exhibition, Society of Petroleum Engineers, Richardson, TX. Fitzgerald, J.E. (25) Adsorption of pure and multi-component gases of importance to enhanced coalbed methane recovery: measurements and simplified local density modeling. Doctoral dissertation, Oklahoma State University, Stillwater, OK.

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