Lei Chen, 1,2,3 Zhenxue Jiang, 1,2 Keyu Liu, 4 Wenming Ji, 1,2 Pengfei Wang, 1,2 Fenglin Gao 1,2 and Tao Hu 1,5. Original Article

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1 Original Article Application of Langmuir and Dubinin Radushkevich models to estimate methane sorption capacity on two shale samples from the Upper Triassic Chang 7 Member in the southeastern Ordos Basin, China Energy Exploration & Exploitation 217, Vol. 35(1) ! The Author(s) 216 DOI: / journals.sagepub.com/home/eea Lei Chen, 1,2,3 Zhenxue Jiang, 1,2 Keyu Liu, 4 Wenming Ji, 1,2 engfei Wang, 1,2 Fenglin Gao 1,2 and Tao Hu 1,5 Abstract A series of methane sorption isotherms were measured at 33 K, 313 K, 323 K, 333 K, and 343 K at pressures up to 12. Ma for two shale samples from the Upper Triassic Chang 7 Member in the southeastern Ordos Basin with total organic carbon content values of 5.15% and 4.76%, respectively. Both the Langmuir- and Dubinin Radushkevich-based excess sorption models were found to well represent the excess sorption isotherms within the experimental pressure range. The maxima of absolute methane sorption capacity fitted by both models are not significantly different. In the current study, the effects of temperature and pressure on methane sorption capacity support the findings that under isothermal condition, methane sorption capacity of organic shale goes up with increasing pressure and under isobaric condition, while it goes down with increasing temperature. Good negative linear relationships between temperature and maximum sorption capacity exist both in the Langmuir and the Dubinin Radushkevich models. In addition, a good positive linear relation exists between the reciprocal of temperature and the natural logarithm of Langmuir pressure, which indicate that temperature and pressure are really important for methane sorption capacity. The extended Langmuir and Dubinin Radushkevich 1 State Key Laboratory of etroleum Resources and rospecting, China University of etroleum, Beijing, China 2 Unconventional Natural Gas Institute, China University of etroleum, Beijing, China 3 Unconventional Oil & Gas Cooperative Innovation Center, China University of etroleum, Beijing, China 4 CSIRO Earth Science and Resource Engineering, Bentley, WA, Australia 5 College of Geosciences, China University of etroleum, Beijing, China Corresponding author: Zhenxue Jiang, Unconventional Natural Gas Institute, China University of etroleum, Beijing 12249, China. jzxuecup@126.com Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3. License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (

2 Chen et al. 123 models have been improved to calculate the methane sorption capacity of shales, which can be described as a function of temperature and pressure. By means of using the two estimation algorithms established in this study, we may draw the conclusion methane sorption capacity can be obtained as a function of depth under geological reservoir. Due to the dominant effect of pressure, methane sorption capacity increases with depth initially, till it reaches a maximum value, and then decrease as a result of the influence of increasing temperature at a greater depth. Approximately, the maximum sorption capacity ranges from 4 m to 8 m. Keywords Shale gas, methane sorption capacity, Langmuir model, Dubinin Radushkevich model, Ordos Basin Introduction Facing a situation of severe energy shortage, shale gas exploration has drawn more and more attention worldwide. A global astounding shale gas green revolution has been booming in the past few years. Shale gas resource has already become a natural gas production target with great potential and significance (Chen et al., 211, 214; Guo et al., 214; Yang et al., 214, 215, 216). With the development of hydraulic fracturing and horizontal drilling technologies (Hao et al., 213; Rexer et al., 213, 214), shale gas exploration from organic-rich shales now can be economically viable. China Government announced in 211 to the public that shale gas will be a new type of mineral resource. The purpose is to encourage and speed up its exploration. Shales are important unconventional gas reservoirs in which the natural gas is stored in three different types of geological environment (Tan et al., 214; Wang et al., 213, 215; Yuan et al., 214; Zhou et al., 214). They are (1) free gas in pores and fractures, (2) adsorbed gas in organic matters and clay minerals, and (3) dissolved gas in residual oil and water (Curtis, 22; Gasparik et al., 212, 214; Guo, 213; Ross and Bustin, 28, 29). It is extremely important to quantify each type of gas storage not only because we need to figure out the potentiality of shales to store gas, but also to understand the rates and mechanisms by which gas transports from shale source rock to the production well. Unlike the conventional gas reservoirs that are characterized with free gas, the range of contribution of adsorbed gas to total gas capacity is usually between 2% and 85% in shale gas reservoirs (Curtis, 22; Liu et al., 216; Montgomery et al., 25; Wu et al., 215; Yang et al., 215). Many experiments on methane sorption capacity of shale samples have been carried out around the world. It is now quite clear that organic matter exerts main control on adsorbed gas content (Li and Wu, 215; Merkel et al., 215; Qajar et al., 215; Tian et al., 216; Xiong et al., 216). Organic matter is the source of hydrocarbon gas (Hill et al., 27; Rodriguez and aul, 21; Wang et al., 213) and determines the intensity of gas generation. Furthermore, it can generally provide more adsorption sites and larger specific surface areas than other minerals (Tan et al., 214). Meanwhile, the type of organic matter and their thermal maturity can greatly affect the methane sorption capacity (Bowker, 27; Chalmers and Bustin, 27, 28; Lu et al., 1995; Zhang et al., 212). The sequence of methane sorption capacity of different types of organic matter can be described as type I < type II < type III. This is mainly because of (1) higher sorption capacity of vitrinite

3 124 Energy Exploration & Exploitation 35(1) compared with other macerals and (2) stronger methane sorption capacity on aromatic structures than aliphatic structures (Chalmers and Bustin, 28; Zhang et al., 212). The influence of thermal maturity on methane sorption capacity is quite complex. When normalized to organic matter content and type, shale samples generally show higher sorption capacity with increasing maturity (Chalmers and Bustin, 28; Gasparik et al., 214; Jarvie et al., 27; Ross and Bustin, 29). This may be caused by the formation of additional micropores in the organic matter during the process of hydrocarbon generation (Cao et al., 215; Curtis et al., 212; Mastalerz et al., 213; an et al., 215; Ross and Bustin, 29; Valenza et al., 213). In addition to organic matter, methane sorption capacity is also affected by (1) constituents of inorganic mineral (especially clay minerals, e.g., montmorillonite and kaolinite), (2) moisture content, (3) microscopic pore structure, and (4) experimental conditions, e.g. temperature and pressure (Chalmers and Bustin, 27, 28; Gasparik et al., 212, 214; Ji et al., 212; Wang et al., 213; Zhang et al., 212). The surface excess amount is usually measured in adsorption experiments. However, the actual adsorbed layer is represented by the absolute amount. Therefore we should focus on the absolute sorption quantity while not the surface excess. If the pressure goes larger than 1 Ma, the difference cannot be ignored between surface excess and absolute amount adsorbed. Therefore, the conclusion can be drawn as that the absolute amount adsorbed is more relevant than the surface excess to estimate and evaluate the potential gas resources in shale gas reservoirs (Rexer et al., 213). On the other hand, in the process of shale gas production, the amount of gas desorbed is also related to the absolute desorption isotherm, which cannot be directly estimated from the surface excess adsorption. Above all, absolute isotherms are of key performance in the context of shale gas exploitation. In high pressure adsorption measurements, only the surface excess can be obtained. As a result, proper methods are required to calculate the absolute isotherm from the surface excess. In order to access absolute sorption characteristics from high pressure adsorption isotherms, we can use the models such as the Langmuir model and the Dubinin Radushkevich (DR) model. The Langmuir model and DR model are based on different theory and originally established for the purpose of subcritical adsorption (Rexer et al., 213; Wang et al., 216). The surface excess isotherms can be directly measured in the experiments. Nevertheless, as discussed above, it is the absolute isotherms that represent the actual adsorbed layer and accurately describe the gas present in shale. As a result, they are required for the assessment and exploitation of methane in shales. In this paper, methane surface excess isotherms were measured at 33 K, 313 K, 323 K, 333 K, 343 K and pressures up to 12 Ma on two organicrich, moisture-equilibrated shale samples. In the experiment, the obtained data were used to predict the absolute isotherms for the purpose of testing the applicability of the Langmuir and DR models. The effect of temperature on sorption capacity was also studied based on multiple-temperature sorption isotherms of the shale samples. Finally, the evolution of methane sorption capacity as a function of depth was analyzed. Samples and experiments Geological setting and samples The Ordos Basin, located in the northern-central of China (Figure 1), is the second largest sedimentary basin with vast oil and gas reserves (Dai et al., 25; Duan et al., 28). It is an intracratonic depression basin with an area of more than 25, km 2. It is also well-known

4 Chen et al. 125 Figure 1. Schematic map showing sampling location (modified from Ji et al., 214). by the world as one of the most tectonically stable basins in China (Dai et al., 25). As a typical cratonic basin, it was developed on the base of Archean granulites and the lower roterozoic greenschists of the North China block, and experienced four evolutionary stages. They belong to the Early alaeozoic shallow marine platform, the Late alaeozoic offshore plain, the Mesozoic intracontinental basin and the Cenozoic faulting and subsidence (Yang et al., 25). During the Mesozoic, its structural framework of the basin was largely developed. While during the Late Triassic, the widespread intra-continental lacustrine shales developed (Liu et al., 29). From the stage of Late Cretaceous there happened five reformation events in the Ordos Basin (Zhao et al., 211). And after the stage of Cenozoic basin general subsidence, the present tectonic situation was formed ever since (Han et al., 214; Tang et al., 214). The Yanchang Formation is part of the upper Triassic strata which lies in the middle of the Lower Jurassic Fuxian Formation above and the Middle Triassic Zhifang Formation below (Gao et al., 215). It can be subdivided into 1 members, Namely Chang 1 through Chang 1 from top to bottom. All members are composed of mudstones, shales, and sandstones. And among all those 1 members, Member Chang 9, Chang 7, and Chang 4 þ 5 consist mainly of dark shale. Other intervals of the Yanchang Formation are composed of sandstones and silt sandstone primarily interbedded with greyish-green mudstones (Tang et al., 214). In the present study, two shale samples from the Chang 7 member were collected from two wells drilled in the southeastern Ordos Basin. The sample locations are shown in Figure 1. Both the shale samples were collected from fresh core materials, with the weight up to 12 2 g. Each of them was then crushed to 6 mesh particle size below and got sufficiently mixed. Sample information such as ID, total organic carbon content (TOC), and other geological parameters are listed in Table 1, denoted by A and B shale samples for the convenience of discussion in this context. Geochemical analysis Geochemical analysis of the shale samples were performed at State Key Laboratory of etroleum Resources and rospecting in China University of etroleum (Beijing). To remove carbonates, the samples were placed in a crucible with 5% HCl at the temperature

5 126 Energy Exploration & Exploitation 35(1) Table 1. Geochemical characteristics and mineralogical composition of two shale samples. Mineral composition (wt.%) ore structure parameters ( nm) Sample Well Depth (m) TOC (wt.%) S 1 (mg/g) S 2 (mg/g) T max ( C) Quartz Feldspar Carbonates Total clays BET specific surface area (m 2 /g) ore volume Average pore diameter (nm) A YY B YY of 8 C. A carbon analyzer with the model of Leco CS-23 was used to measure the TOC (in Table 1). The type, maturity, and hydrocarbon generation potential of the organic matter were obtained by an OGE-II rock pyrolyze from a sample of about 7 mg. During this process, the parameters were measured as following: (1) the amount of free hydrocarbons in the sample (S 1 ); (2) the amount of hydrocarbons which was generated through thermal cracking of nonvolatile organic matter (S 2 ); (3) the maximum temperature released from cracked hydrocarbons (T max ), which is an indicator of the maturity of the sample (Rexer et al., 214). X-ray diffraction Quantitative X-ray diffraction (XRD) analysis of randomly oriented powders was used for the mineralogy of the shale samples at Experimental Research Center of East China Branch, SINOEC. The measurements were performed on Ultima IV diffractometer using Cu Ka-radiation ( ¼ nm) produced at a voltage of 4 kv and a current of 4 ma. A scan rate of 4 (2y)/min was used in the range of 5 45 for recording the XRD traces. In the beginning, the bulk mineral composition of the powder sample was determined, but at this stage only the total clay content was included. Then moving to the next stage, the individual mineral content of clay fractions, which was separated from the rock powder sample was determined. lease be noted that in this experiment both the bulk and individual contents were measured under exactly the same conditions. Low-pressure N 2 sorption By using a Micromeritics Õ Tristar II 32 surface area analyzer, we performed low-pressure (<.127 Ma, K) N 2 sorption analyses at State Key Laboratory of Heavy Oil rocessing in China University of etroleum, Beijing. Shale sample aliquots weighing 1 to 2 g were analyzed with N 2 to obtain information about microscopic pore characteristics within the range of nm. Samples were automatically degassed at about 11 C under vacuum for about 14 h to remove adsorbed moisture and volatile matter before analyzing with N 2. The sample was kept at the temperature of liquid nitrogen (77.35 K at 11.3 ka) in order to quantify nitrogen gas adsorption. The equilibrium interval (time over which the pressure must remain stable within a very small range) was set at 3 s, and the pressure tolerance was set at.6666 ka (5 mm Hg). The adsorption isotherms and calculated

6 Chen et al. 127 surface areas, pore volumes, and pore distributions were obtained based on multiple adsorption theories, namely, Langmuir, Brunauer Emmett Teller (BET), Barrett Joyner Halenda, DR, and Dubinin Astakhov, among others (Mastalerz et al., 212, 213). A detailed description of these theories and techniques can be found in Gregg and Sing (1982). High-pressure methane sorption isotherm Experimental setup and procedure. The methane sorption isotherms ( K; up to 12 Ma) were measured on HVA-2 high-pressure gas sorption/desorption instrument adopting GB/T (China national standard) testing standard at Experimental Research Center of East China Branch, SINOEC. The measurements were carried out based on a manometric method, which has been described in detail in a series of publications (Gasparik et al., 214; Guo et al., 214; Weniger et al., 21). arameterization of excess sorption isotherms. The experimentally measured excess adsorption isotherms were expressed by the following function n exc ¼ n abs 1 gas ð1þ ads where n exc is the surface excess sorption amount, n abs is the absolute sorption amount. gas and ads are densities of the free gas phase and the adsorbed gas phase, respectively, and both expressed in the same units (e.g., kg/m 3 ). And gas is calculated from the National Institute of Standards and Technology Webbook ( All the conventional isotherm equations were originally derived for absolute adsorption amount (n abs,cm 3 /g), therefore modified models should be used to parameterize the measured excess sorption data (Gasparik et al., 212, 214). Langmuir model. The Langmuir model is based on a homogeneous distribution of sorption sites and monolayer formation on an open surface and it is used as a standard model to describe vapor isotherms on shales (Rexer et al., 213). The original Langmuir equation is n abs ¼ n L ð2þ þ L where n L is the Langmuir maximum sorption capacity, is the pressure (Ma), L is the Langmuir pressure (Ma). Combining equation (2) and equation (1), the experimentally measured excess adsorption isotherms used herein is expressed as n exc ¼ n L þ L 1 gas ads ð3þ DR model. The DR model is based on the olanyi potential theory and applies when the adsorption process follows a pore filling mechanism, e.g. sorption in micropores

7 128 Energy Exploration & Exploitation 35(1) (Rexer et al., 213). The original DR equation is ( n abs ¼ n exp D ln ) 2 R T ð4þ where n is the maximum absolute amount adsorbed, is the saturation pressure (Ma), is the pressure (Ma), R is the ideal gas constant (.8314 kj/(molk)), and T is the temperature (K). D is an interaction constant, which equals to 1/(E ) 2 where and E are adsorbate characteristic parameters (Rexer et al., 213; White et al., 25). Since the critical temperature for methane is 19.6 K, methane is in the supercritical state in all shale gas reservoirs. Methane does not exhibit a saturated vapor pressure under supercritical conditions. Therefore, the original DR equation, which uses relative pressure as a parameter, cannot be used in this case. For the purpose of applying the DR equation to supercritical sorption processes, Sakurovs et al. (27) proposed the replacement of the pressure term / with ads / gas, where ads and gas represent maximum adsorbed and free gas phase densities, respectively ( n abs ¼ n exp D ln ) 2 ads R T ð5þ gas As a result, the experimentally measured excess adsorption isotherms used herein can be written as ( n exc ¼ n exp D ln ) 2 ads R T 1 gas ð6þ gas ads In order to calculate the absolute sorption from the surface excess sorption, we must try to get the value of the adsorbed gas density ( ads ). Considering that direct measurement of the adsorbed phase density is difficult, empirical methods are regularly used to calculate it (Sudibandriyo et al., 23; Tian et al., 216). In this study, we regarded the adsorbed phase density ( ads ) as the liquid density at boiling temperature and ambient pressure (421 kg/m 3 is used for CH 4 ) (Dreisbach et al., 1999; Yang et al., 214, 215). Results Geochemical parameters and mineralogical composition The results of geochemical parameters and mineralogical composition are listed in Table 1. The TOC tests obtained value of 5.15% for sample A, and 4.76% for sample B. Based on the measured TOC content, two samples were categorized as organic-rich shales. From their Rock-Eval T max values, we could infer that the thermal maturity of the organic matter is at a stage of mature oil-gas generation. XRD results confirmed the dominant minerals in the samples are clay minerals and quartz. For example, in sample A, total clay minerals account for 51%, quartz account for 22%, feldspar account for 14%, and carbonates account for 13%.

8 Chen et al. 129 Adsorbed volume, cm 3 /g (ST) Adsorption Desorption Sample A Adsorbed volume, cm 3 /g (ST) Relative pressure (/ ) 2 Adsorption Sample B 16 Desorption Relative pressure (/ ) Figure 2. Low-pressure N 2 adsorption desorption isotherms for two shale samples. ore structure characterization by low-pressure nitrogen sorption According to the International Union of ure and Applied Chemistry (IUAC) classification (Figure 2; Gregg and Sing, 1982), both the low-pressure nitrogen adsorption isotherms of the two samples studied belong to type IV. This type of isotherms are caused by micropore filling at low pressures, multilayer sorption at moderate pressures, and capillary condensation evaporation at high pressures, which suggests that mesopores developed well in two shale samples. The hysteresis loops, formed by the adsorption and desorption branches, are of type H3, which always result from slit-shaped pores (Gregg and Sing, 1982). Figure 2 shows that the higher TOC content (sample A), the wider the hysteresis loops. The pore structure parameters of two shale samples are reported in Table 1. The BET specific surface area of sample A is 3.26 m 2 /g, while sample B is 6.48 m 2 /g; the pore volume of sample A is.148 cm 3 /g, while sample B is.37 cm 3 /g; average pore diameter is 18.2 nm for sample A and 18.9 nm for sample B. For pore volume distribution, dv/dw versus W, which is commonly regarded as the differential distribution plot and the pore volume in any pore width range is given by the area under the curve. With logarithmically compressed of the W-axis, dv/d log(w) versus W is frequently used to display the pore size distribution (Clarkson et al., 213; Kuila and rasad, 213; Tian et al., 213, 215). As illustrated in Figure 3(a) and (b), dv/d log(w)

9 13 Energy Exploration & Exploitation 35(1) (a).18 dv/dlog(w), cm 3 /g (c) 2 ds/dlog(w), m 2 /g Sample A ore width, W (nm) Sample A (b).3 dv/dlog(w), cm 3 /g ore width, W (nm) (d) 25 ds/dlog(w), m 2 /g Sample B Sample B ore width, W (nm) ore width, W (nm) Figure 3. ore volume distribution with pore size (a, b) and specific surface area distribution with pore size (c, d) derived from the N 2 adsorption branch for the isotherms of two shale samples. versus W clearly reveals that the mesopores and part of macropores significantly contribute to the total pore volume. The reason lies in that that one large pore does have a volume correspondent to many small pores. Meanwhile, for the distributions of specific surface area with respect to pore size, the results are displayed in Figure 3(c) and (d). The pore volumes are mainly connected with larger pores, while the specific surface areas are primarily controlled by smaller pores. Methane sorption isotherms Methane excess sorption isotherms measured at 33, 313, 323, 333 and 343 K on two shale samples are shown in Figure 4, Tables 2, and 3. As shown in Figures 4 and 5, methane excess sorption amount can be well fitted by the modified Langmuir and DR models. The sorption isotherms show the typical trend of decreasing excess sorption capacity with increasing temperature. Moreover, when temperature keeps rising, the shape of the isotherms will be largely affected. At five different temperatures, essentially no maxima are evident in the excess sorption isotherms within the experimental pressure range. Isothermal adsorption quantity will surely decrease after it reached the maximum if the experimental pressure increased further (Gasparik et al., 212, 214; Rexer et al., 213, 214; Tan et al., 214; Tian et al., 216; Yang et al., 215). This is due to the fact that at elevated pressures the density difference between the adsorbed phase ads and the free gas phase gas diminishes, decreasing the term inside the brackets in equation (1). The Langmuir model parameters (n L and L ) and DR model parameters (n and D) for the excess sorption isotherms are listed in Tables 4 and 5. The Langmuir sorption capacities (n L ) vary from 5.21 cm 3 /g to 7.9 cm 3 /g for sample A and from 3.47 cm 3 /g to 7.29 cm 3 /g for sample B. Langmuir pressures ( L ) vary from 2.2 Ma to 3.95 Ma for sample A and from

10 Chen et al. 131 Excess sorption Sample A 33K measured 313K measured 323K measured 333K measured 343K measured 33K fitted 313K fitted 323K fitted 333K fitted 343K fitted Excess sorption ressure (Ma) Sample B 33K measured 313K measured 323K measured 333K measured 343K measured 33K fitted 313K fitted 323K fitted 333K fitted 343K fitted ressure (Ma) Figure 4. Methane excess sorption isotherms of two shale samples measured at different temperatures (lines represent the fitted Langmuir-based excess sorption function, equation (3)). Table 2. Excess adsorption data of sample A at different temperatures. 33 K 313 K 323 K 333 K 343 K (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4

11 132 Energy Exploration & Exploitation 35(1) Table 3. Excess adsorption data of sample B at different temperatures. 33 K 313 K 323 K 333 K 343 K (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 (Ma) q gas (kg/m 3 ) CH 4 Excess sorption Sample A 33K measured 313K measured 323K measured 333K measured 343K measured 33K fitted 313K fitted 323K fitted 333K fitted 343K fitted Excess sorption ressure (Ma) Sample B 33K measured 313K measured 323K measured 333K measured 343K measured 33K fitted 313K fitted 323K fitted 333K fitted 343K fitted ressure (Ma) Figure 5. Methane excess sorption isotherms of two shale samples measured at different temperatures (lines represent the fitted Dubinin Radushkevich (DR)-based excess sorption function, equation (6)).

12 Chen et al. 133 Table 4. Fitted temperature-dependent parameters of the Langmuir- and DR-based excess sorption models (equations (3) and (6)) for methane on sample A. Langmuir-based excess sorption model DR-based excess sorption model Temperature (K) n L L (Ma) n D (mol 2 /kj 2 ) DR: Dubinin Radushkevich. Table 5. Fitted temperature-dependent parameters of the Langmuir- and DR-based excess sorption models (equations (3) and (6)) for methane on sample B. Langmuir-based excess sorption model DR-based excess sorption model Temperature (K) n L L (Ma) n D (mol 2 /kj 2 ) DR: Dubinin Radushkevich Ma to 2.98 Ma for sample B. The DR maximum absolute sorption capacities (n ) vary from 5.41 cm 3 /g to 8.48 cm 3 /g for sample A and from 3.95 cm 3 /g to 7.9 cm 3 /g for sample B. The interaction constants (D) are.112 mol 2 /kj 2 for sample A and.15 mol 2 /kj 2 for sample B. Discussion Effect of temperature on methane sorption capacity The effect of temperature on methane sorption capacity of shales has been extensively studied around the world (Gasparik et al., 214; Guo, 213; Ji et al., 214, 215; Rexer et al., 213; Yang et al., 215). Higher temperature favors gas in the free state more than in the adsorbed state. Gas sorption is an exothermic process in which sorption capacity of organic shales decrease with increasing temperature (Hao et al., 213; Hildenbrand et al., 26; Ross and Bustin, 28). As shown in Figure 4, when temperature keeps increasing, methane sorption capacity will decrease very fast. In order to determine the Langmuir maximum sorption capacity (n L ), Langmuir pressure ( L ), DR maximum sorption capacity

13 134 Energy Exploration & Exploitation 35(1) Langmuir maximum sorption capacity Langmuir maximum sorption capacity y = -.697x R² = Temperature (K) y = -.972x R² =.976 Sample A Sample B Temperature (K) Figure 6. Langmuir maximum sorption capacity (n L ) as a function of temperature for two shale samples. (n ), and interaction constant (D), a least squares fit was applied based on measured methane excess sorption isotherms. A good negative linear relationship between Langmuir maximum sorption capacity and temperature is obtained and shown in Figure 6 (R 2 ¼.9876,.976, respectively). Such result was also reported by Ji et al. (215) and Rexer et al. (213). Similarly, a good negative linear relationship between the DR maximum sorption capacity and temperature is obtained and shown in Figure 7 (R 2 ¼.9866,.9733, respectively), which was also reported by Rexer et al. (213) and Tian et al. (216). Effect of pressure on methane sorption capacity ressure has important influence on shale gas adsorption capacity (Gasparik et al., 212, 214; Guo, 213; Ji et al., 214, 215; Zhang et al., 212). In general, prior to reaching the maximum adsorption, as pressure rises, the adsorption rate is greater than the desorption rate, represented by an increase in adsorbed gas content. Similar trends were also observed in shale samples from other places using high-pressure methane sorption (to 2 25 Ma) (Gasparik et al., 212, 214). Note the maxima cannot be observed in many sorption isotherms because they were conducted in relatively lower pressure conditions (to 6 15 Ma) (Ross and Bustin, 29; Wang et al, 213; Zhang et al., 212). Figure 8 shows a clear linear

14 Chen et al. 135 DR maximum sorption capacity Sample A y = -.812x R² =.9866 DR maximum sorption capacity Temperature (K) Sample B y = -.124x R² = Temperature (K) Figure 7. Dubinin Radushkevich (DR) maximum sorption capacity (n ) as a function of temperature for two shale samples. relationship between the natural logarithm of the Langmuir pressure (ln L ) and the reciprocal of temperature (1/T) for each sample (R 2 ¼.911,.7243, respectively). In previous studies, we found out a similar exponential relationship between the Langmuir pressure and temperature (Gasparik et al., 214; Ji et al., 215; Rexer et al., 213; Zhang et al., 212). Estimation algorithms of methane sorption capacity Extended Langmuir model. As outlined above, temperature greatly affects the Langmuir maximum sorption capacity in two shale samples (Figure 6). Their relation can be well represented by the standard form of linear regression n L ¼ a T þ b ð7þ where n L is the Langmuir maximum sorption capacity and T is temperature (K). Coefficients a and b can be adjusted through the regression fitting procedure.

15 136 Energy Exploration & Exploitation 35(1) ln L (Ma) Sample A y = x R² = /Temperature (K -1 ) ln L (Ma) Sample B y = x R² = /Temperature (K -1 ) Figure 8. Linear relation between the natural logarithm of the Langmuir pressure (ln L ) and the reciprocal of temperature (1/T). In addition, the Langmuir pressure is greatly controlled by temperature (Gasparik et al., 214; Ji et al., 215). Based on the notable linear relationship between the natural logarithm of the Langmuir pressure (ln L ) and the reciprocal of temperature (1/T) (Figure 8), their relation can be indicated by the following equation lnð L Þ¼ c T þ d ð8þ where L is the Langmuir pressure and T is the temperature (K). Coefficients c and d can be adjusted through the regression fitting procedure. Substituting equations (7) and (8) into the Langmuir equation (2), we can obtain an extended Langmuir model for methane sorption capacity under geological conditions ða T þ bþ n abs ¼ exp T c þ d ð9þ þ

16 Chen et al. 137 Based on the experimentally measured excess adsorption isotherms data of sample A (Table 2), an algorithm for methane sorption capacity estimation was determined ð :697 T þ 28:968Þ n abs ¼ exp 167:5 ð1þ T þ 6:2341 þ where n abs is the methane sorption capacity at a given temperature T (K) and pressure (Ma). In order to elaborate the effects which are caused by depth-variant temperature and pressure on methane sorption capacity of organic shale, this empirical formula can be applied. Similarly, an algorithm for methane sorption capacity estimation of sample B was determined ð :972 T þ 36:523Þ n abs ¼ exp 133:3 ð11þ T þ 4:8971 þ Extended DR model. As discussed previously, the DR maximum sorption capacity in two shale samples is greatly affected by temperature (Figure 7). Their relation can be well described by the standard form of linear regression n ¼ a T þ b ð12þ where n is the DR maximum sorption capacity and T is temperature (K). Coefficients a and b can be adjusted through the regression fitting procedure. In addition, to calculate the methane sorption capacity by DR model, it is necessary to find out the effect of temperature and pressure on the free gas phase density ( gas ). As illustrated in Figure 9, the free gas phase density of the two shale samples both show good linear relationships with temperature and pressure. Therefore, a multiple regression approach was used to relate the free gas phase density to the combined effects of the independent variables (temperature and pressure). The free gas phase density was expressed using the standard form of multiple linear regressions gas ¼ c T þ d þ e ð13þ where gas is the free gas phase density (kg/m 3 ), T is temperature (K), and is pressure (Ma). To adjust the coefficients c, d and e, a multiple regression fitting procedure was performed. Substituting equations (12) and (13) into the DR equation (5), we can obtain an extended DR model for methane sorption capacity under geological conditions as shown below ( ) 2 ads n abs ¼ðaTþbÞexp D ln R T c T þ d þ e ð14þ

17 138 Energy Exploration & Exploitation 35(1) (a) Density of free gas phase (kg/m 3 ) (b) Density of free gas phase (kg/m 3 ) y = -.26x R² = Temperature (K) y = x R² = ressure (Ma) Figure 9. Density of free gas phase as a function of temperature (a) and pressure (b). Based on the experimentally measured excess adsorption isotherms data of sample A (Table 2), an algorithm for methane sorption capacity estimation was determined n abs ¼ð :812 ( T þ 33:1Þ ) exp :112 ln :8314 T :1391 T þ 6:7667 þ 43:8535 ð15þ where n abs is the methane sorption capacity at given temperature T (K) and pressure (Ma). Elucidating the effects of depth-variant temperature and pressure on methane sorption capacity of organic shale can be reached via this empirical formula. Similarly, an algorithm for methane sorption capacity estimation of sample B was determined n abs ¼ð :124 ( T þ 38:729Þ ) exp :15 ln :8314 T :1391 T þ 6:7667 þ 43:8535 ð16þ

18 Chen et al. 139 Methane sorption capacity Sample A Methane sorption capacity Sample B Depth (m) 2 Depth (m) Langmuir model DR model 2 Langmuir model DR model Figure 1. Methane sorption capacity as a function of depth by the Langmuir and Dubinin Radushkevich (DR) models for two shale samples. Methane sorption capacity as a function of depth With a surface temperature of 12 C (i.e. 285 K), a thermal gradient of 3 K/km (Ji et al., 214) and a hydrostatic pressure gradient of 1 Ma/km for the present investigation on the southeastern Ordos Basin of China, methane sorption capacity of sample A versus depth profiles can be calculated using equation (1) and equation (15), respectively, and methane sorption capacity of sample B versus depth profiles can be calculated using equation (11) and equation (16), respectively. Considering the negative effect of increasing temperature and the positive effect of increasing pressure, methane sorption capacity varies with depth non-monotonically. As shown in Figure 1, methane sorption capacity initially increases with depth, till it reaches a maximum value, and then decreases as a result of increasing temperature at a greater depth. Approximately, the maximum sorption capacity ranges from 4 m to 8 m. The pattern explains why the shale has the highest adsorbed gas content under a certain value of T, which is quite analogous to previous studies (Hao et al., 213; Hildenbrand et al., 26; Ji et al., 214, 215). Conclusions and suggestion High-pressure methane sorption isotherms were measured on two shale samples from the Upper Triassic Chang 7 Member in the southeastern Ordos Basin, China. Supercritical adsorption was modeled using both the Langmuir and DR models, in which the effects of temperature and pressure on methane sorption capacity have been investigated. Two extended models considering the contribution of temperature and pressure have been developed to estimate the methane sorption capacity, and its evolution as a function of depth was established. The following conclusions can be drawn: (1) When pressure rises under isothermal condition, methane sorption capacity of organic shale will increase accordingly, while it will decline with increasing temperature under

19 14 Energy Exploration & Exploitation 35(1) isobaric condition. For individual shale sample, the Langmuir maximum sorption capacity and the DR maximum sorption capacity both have good negative linear relationships with temperature. In addition, a clear negative linear relation was obtained for the natural logarithm of Langmuir pressure and the reciprocal of temperature, which indicate that both temperature and pressure have significant effects on methane sorption capacity. (2) Based on the effects of temperature and pressure on methane sorption capacity of Upper Triassic Chang 7 Member shale, this article presented the extended Langmuir and DR models (equations (9) and (14)) and established the empirical formulas (equations (1) and (15)) for sample A and the empirical formulas (equations (11) and (16)) for sample B, respectively. Using these empirical formulas, methane sorption capacity as a function of depth under geological reservoir conditions can be estimated with reasonable accuracy. (3) Due to the dominant effect of pressure, methane sorption capacity increases with depth initially, till it reaches a maximum value, and then decreases as a result of the influence of increasing temperature at a greater depth. Approximately, the maximum sorption capacity ranges from 4 m to 8 m. As discussed in the previous section, both the Langmuir and DR models fitted well with the experimental data of the two shale samples. In fact, the Langmuir model is simpler, and therefore commonly used for describing the adsorption behavior of shales. Our study suggests it is adequate for most of the practical reservoir assessments since it gave quite similar results with the DR model. Other geological parameters affecting methane sorption capacity such as organic matter, mineral composition, pore structure, and moisture need to be further studied to provide better estimation algorithm and more accurate evolution pattern of methane sorption capacity. Meanwhile, more shale samples are needed to conduct relevant experiments to provide a better understanding between Langmuir model and DR model. Acknowledgment We thank the anonymous reviewers for their critical and constructive comments. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: National Science and Technology Major roject (No. 216ZX534-1) and National Natural Science Foundation of China (No ). References Bowker KA (27) Barnett shale gas production, Fort Worth Basin: Issues and discussion. AAG Bulletin 91(4): Cao Q, Zhou W, Deng HC, et al. (215) Classification and controlling factors of organic pores in continental shale gas reservoirs based on laboratory experimental results. Journal of Natural Gas Science and Engineering 27:

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