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1 Available online at International Journal of Coal Geology 73 (2008) Predictions of the adsorption equilibrium of methane/carbon dioxide binary gas on coals using Langmuir and ideal adsorbed solution theory under feed gas conditions Hongguan Yu, Lili Zhou, Weijia Guo, Jiulong Cheng, Qianting Hu Key Laboratory of Mine Disaster Prevention and Control, Shandong University of Science and Technology, 579 Qianwangang Road, Qingdao Economic and Technical Development Zone, Qingdao, Shandong Province, , China Received 10 August 2006; received in revised form 1 March 2007; accepted 7 March 2007 Available online 28 March 2007 Abstract Presently many research projects focus on the adsorption and predictions of methane, nitrogen, carbon dioxide and their mixtures on coals under equilibrium gas conditions. It is highly important to develop a method for prediction of CO 2 /CH 4 adsorption on coal under feed (source) gas conditions in the fields of enhanced coal bed methane recovery and CO 2 sequestration in coal bed with CO 2 injection. The objective is to develop reliable models to predict the adsorption behavior of mixtures on coals under feed gas conditions. In this context, the adsorption and predictions of methane, carbon dioxide and three binary mixtures of these gases on two China coals under feed gas conditions have been performed on the experimental data and derived equation. Firstly, the experimental measurements of CH 4,CO 2 and their binary gas adsorption isotherms to investigate the adsorption behavior and use for prediction of adsorption equilibrium were conducted at 301 K at pressures up to 10 MPa. Secondly, a calculation formula of adsorbed amount of total gas was derived from relation between adsorbed amount and feed gas composition at standard state on condition of unknown equilibrium gas concentration during adsorption. Thirdly, the extended Langmuir, ideal adsorbed solution (IAS) theory in conjunction with Langmuir were used to predict the experimental data of binary gas adsorption based on an iterative algorithm. Finally, the prediction accuracy for experimental data of total and adsorbed amount of component gas and free gas compositions were analyzed. Experimental data indicate adsorbed amounts of the total gas and single-component CO 2 increase, but adsorbed amounts of CH 4 increase at low equilibrium pressure and decrease at high pressure with increase of CO 2 concentration in feed gas. Model predictions based on single-component isotherms and the calculation formula show that the quantitative formula obtained can be used to predict adsorption equilibrium of CH 4 /CO 2 binary gas under feed gas conditions. The binary gas prediction data are quite variable and depend upon the feed gas composition. The IAS Langmuir provides, on average, a better fit to total gas adsorption but is variable for the single-component adsorption with the feed gas composition. The predictions of total and component gas adsorption and equilibrium gas compositions illustrate similar trends with their experimental data Published by Elsevier B.V. Keywords: Coal bed methane; Gas mixtures; Carbon dioxide; Prediction; Feed gas; Ideal adsorbed solution theory 1. Introduction Corresponding author. Tel.: ; fax: , address: yuhongguan65@163.com (H. Yu). Coal bed gas generally consists of a mixture of CH 4 (95 98%), CO 2,N 2 and higher hydrocarbons (C2 C5), /$ - see front matter 2007 Published by Elsevier B.V. doi: /j.coal

2 116 H. Yu et al. / International Journal of Coal Geology 73 (2008) although methane is often the primary component. The injection of CO 2 in coal beds may be used to increase methane gas recovery and to sequestrate CO 2 during production, either by lowering the methane partial pressure in the free gas or by competitive adsorption (Mavor et al., 2002). Accurately knowing CH 4 /CO 2 binary gas adsorption characteristics on coals is necessary for economic forecasting of coal bed gas production and the accurate assessment of enhanced CBM recovery operations (Scott, 2003). The adsorptions of gaseous mixture on coals may depend on the coal composition, moisture content, pressure and temperature conditions, gas compositions of in free phase (Clarkson and Bustin, 2000; Ceglarska- Stefańska and Zarębska, 2002; Busch et al., 2003; Ceglarska-Stefańska and Zarębska, 2005). Laboratory measurements of coal bed gas adsorption isotherms are commonly used to know the adsorption characteristics of mixtures on coals (Goodman et al., 2004; Busch et al., 2006). The predictions of mixture gas equilibrium commonly are complementary to the laboratory measurements to know adsorption characteristics. Many models have been used to predict the experimentally determined isotherms of pure CO 2 and CH 4. These include the BET, Langmuir, Dubinin Radushkevich (D R) and Dubinin Astakhov (D A) models (Clarkson et al., 1997; Clarkson and Bustin, 1999; Laxminarayana and Crosdale, 1999). These models have been applied alone and in combination with ideal adsorbed solution (IAS) theory for adsorption of CO 2 /CH 4 binary gas mixtures on coals (Stevenson et al., 1991; DeGance, 1992; Hall et al., 1994; Clarkson and Bustin, 2000; Özgen Karacan and Okandan, 2000). Extended Langmuir is the simplest method used to predict CO 2 /CH 4 binary gas mixtures on coals (Arri et al., 1992; Harpalani and Pariti, 1993). Other models that are based on two-dimensional equations of state, the simplified local density (SLD), introduction of twodimensional analogs of activity coefficients used in vapor liquid equilibrium calculations and treating adsorption as a constrained form of vapor liquid equilibrium (VLE), have also been evaluated (Fitzgerald et al., 2003, 2005). The IAS theory and the extended Langmuir models differ significantly in their ability to predict the behavior of binary gas mixtures. IAS theory was found to be adequate for predicting binary gas adsorption on dry coal (Stevenson et al., 1991). The IAS theory model was more accurate than the extended Langmuir model for mixed gas adsorption (Hall et al., 1994). IAS predictions, however, are strongly dependent upon choice of the pure gas isotherm equation. The IAS theory, in conjunction with D A single-component isotherm is more accurate for the prediction of mixed gas desorption isotherms than the extended Langmuir (Clarkson and Bustin, 2000). The free gas (unadsorbed) mole fraction of component gas should be known for the experimental measurement and theoretical prediction of adsorption characteristics on coals. The equilibrium gas concentration is often determined using gas chromatography (GC), which is complicated and time consuming. In addition, mixture gas adsorption isotherm, determined using realistic reservoir gas concentration, is required for accurate predictions of adsorbed gas content during primary coal bed methane production or enhanced coal bed methane with CO 2 injection (White et al., 2005). The free gas concentration of component is difficult to measure for whole coal bed during production. Hence, the predictions of mixture gases adsorption isotherms on coals under conditions of feed gas are of important role to know the adsorption characteristics to experimenter and producer. All studies of multicomponent adsorptions on coals have focused on the accurate modeling of equilibrium gas adsorption with known free gas equilibrium concentration, measured with GC methods. To the authors' knowledge, no studies have been performed to predict the total and single-component adsorptions under unknown free gas equilibrium concentration of component, i.e. only known initial gas (feed gas or source gas) concentration, condition. Although D A and BET were good models fitting gases adsorptions on some coals, they were not be used in this study as more parameter need to be introduced for D A model and saturated vapor pressure is difficult to obtain in supercritical state of CH 4 for BET and D A models. Langmuir was used in this study as its simplifying calculation and abundant adsorption data from literature. Firstly, a computation expression of adsorbed amount of total gas was derived based on relation between adsorbed amount and the amount of free gas under unknown free equilibrium concentration of component during adsorption. Secondly, the adsorption isotherms of pure CH 4, CO 2 and their binary gas mixture on two china's coal were measured and fitted with Langmuir. Then, the extended Langmuir, ideal adsorbed solution theory in conjunction with Langmuir single-component isotherm (Langmuir IAS theory), were used to predict the adsorption of CO 2 /CH 4 mixtures on two coals using an iterative algorithm. Finally, the predicted data of total and component gas adsorption and free gas equilibrium concentration were analyzed.

3 H. Yu et al. / International Journal of Coal Geology 73 (2008) Experimental 2.1. Samples Two coal samples from Qinshui basin in China were selected for this study. The Qinshui basin was selected for small-sized pilot, the Sino-Canada cooperative project on CBM technology development/co 2 sequestration in China. The samples were crushed to pass through a 60 mesh sieve, which were used for isotherm analysis, proximate analysis and petrographic analysis. The 60 mesh coals were equilibrated with moisture at 301 K prior to adsorption isotherm analysis. Equilibrium moisture coal samples were achieved using a procedure similar to that described by Levy et al. (1997). Proximate analysis, equilibrium moisture content measurement and petrographic analysis, including random reflectance measurements, of the coals were carried out. Proximate analysis and petrographic analysis for the coals are given in Table Experimental set-up Fig. 1 shows a simplified scheme of the experimental set-up for volumetric gas adsorption experiments. The device is kept in a temperature-controlled oven, the temperature of which is constant to ±0.1 K of the set point. The feed gas is stored in a gas cylinder for pure CH 4,CO 2 and their binary gas. The set-up consists of a stainless-steel sample cell (max. volume 150 cm 3 ) and reference cell (max. volume 60 cm 3 ), a set of actuator-driven shut-off valves and two high-precision pressure transducers (max. pressure 35 MPa, with precision of 0.05%). The volume between valve 1 and valve 2, including the void volume of the pressure transducer and the tube, is used as reference volume (V ref ). The volume between valve 2 and valve 3 is used as sample cell volume (V sample cell ). The adsorption measurements with CO 2 /CH 4 mixtures require an additional analysis step to determine the relative concentrations of the two compounds in the free (non-adsorbing) gas phase. A Shanghai 1102G gas chromatograph (GC) equipped with a micro thermal conductivity detector (TCD) was used for quantitative analysis of CO 2 and CH 4 concentration. A gas-tight syringe was used to extract small gas samples (1 ml at STP) for GC determination during a sorption step Experimental procedure Volumetric gas adsorption experiments were conducted in a programmed mode. An m g (about 100 g) portion of the powdered and moisture-equilibrated coal samples were placed into the sample cell (SC), which was then inserted into the set-up and tested for leaks. At the beginning of the experiment, the whole system was evacuated using vacuum pump to establish a defined starting condition. Before the start of an adsorption experiment, the V ref and V sample cell were determined volumetrically using a non-adsorbing gas (helium) and calculated with standard Boyle's law methodology. Pure CH 4 or CO 2 adsorption isotherms were collected for the 60 mesh, moisture-equilibrated coal using the following procedure. The reference cell (RC) was charged with gas (CH 4 or CO 2 ) to a pressure greater than the anticipated sample cell starting pressure. Gas was then dosed from the reference cell to the sample cell for a few seconds and then the valve (V 2 in Fig. 1) between the two cells closed (Clarkson and Bustin, 2000). Pressure in the sample cell dropped as gas was adsorbed to the equilibrium value. Equilibrium was considered reached when the pressure in the sample cell (SC) remained constant over a period of 1 h. A mass balance calculation was used in conjunction with the real-gas law to calculate the amounts of pure gas excess (Gibbs) sorption (Zhou and Guo, 1999). After the equilibrium for the current pressure step, pure CH 4 or CO 2 was charged to a higher pressure again for the next step. Six data points were obtained for each coal gas pair. For gas mixtures studies, a similar procedure to the pure gas isotherms was used, except that small gas samples were taken for gas chromatographic (GC) analysis during adsorption step. A gas sample (about 1 ml at STP) was extracted using a gas-tight syringe Table 1 Coal samples used for adsorption experiments Sample Proximate analysis and total Sulfur (%) Moisture Petrological analysis (vol.%) Ash VM FC S (%) Vitrinite Inertinite Liptinite MM VR r Jincheng Luan Ash and total sulfur were calculated on a dry basis. Volatile matter (VM) and fixed carbon (FC) were calculated on a dried, ash-free basis.

4 118 H. Yu et al. / International Journal of Coal Geology 73 (2008) Fig. 1. Simplified scheme of the experimental set-up for gas adsorption measurement. from the sample cell following pressure stabilization for GC analysis to determine the compositions of the mixture gas. Composition (mole fraction) of component as well as pressure is required for an equilibrium component isotherm (Zhou et al., 1996). High-pressure (for CH 4 up to 10 MPa) and 301 K isotherms were obtained using a volumetric adsorption apparatus shown in Fig. 1. The experimental gases include pure CH 4,CO 2 and mixtures of CO 2 /CH 4. Three feed gas compositions (76.11% CH 4 /23.89% CO 2, 36.12% CH 4 /63.88% CO 2 and 25.96% CH 4 /74.04% CO 2 ) were used to obtain and predict excess sorption isotherms of binary gas in this study. 3. Theory 3.1. Relationship between adsorbed amount of CO 2 / CH 4 and feed gas composition The void volume mass (Vm v ) is defined as the ratio of the void volume of the sample cell (V void ) to the mass (m) of coal used adsorption isotherms experiments and expressed in units of cm 3 per gram (cm 3 /g) coal at experimental conditions. The Vm v is a key term for explain relationship between CO 2 /CH 4 adsorption and component concentration in feed gas. The Vm v is constant during adsorption experiment if the coal having constant porosity and void volume. The void volume mass can be used express the free gas volume at STP (T= K, P= MPa) for each injected feed-gas step. Using state equation for real gas, the void volume mass (Vm v ) at experimental temperature (T) and pressure (P) conditions can be converted to amount of free gas (n free ) injected into sample cell, 273:15PVm v n free ¼ 0:101325Td zd 22:414 ¼ 120:27 PVm v Td z ; ð1þ where n free is expressed in units of mmol per gram (mmol/g) coal; z represents the compressibility factor, obtained with universal expression of SRK equation just as described in Section 2.2. Hence, the amount of injected feed gas can be obtained with Eq. (1) using Vm v determined using helium expansion and standard Boyle's law methodology, at experimental temperature (301 K) and equilibrium pressure (P). Fig. 2 shows schematic diagram of adsorbed space model, which is used to show the basic principle and changes of gas composition and substance amounts in free and adsorbed phase. To be convenient to illuminate the basic prediction method of CO 2 /CH 4 adsorption on coals with adsorbed model, the adsorbed phase was concentrated on bottom of cube (sample cell) shown in Fig. 2. For simplifying the establishment of relationship between adsorbed amount of CO 2 /CH 4 and feed gas concentration, the following approximations were made: (1) independent adsorption among experimental point (six data points) for each injected feed gas step. All experimentally injected feed-gas, including the formerly adsorbed and unadsorbed mixtures, will reapportion between adsorbed and free phase. (2) Constant adsorbed and free phase amounts, only happening to the exchange of gas compositions (CO 2 and CH 4 ) between adsorbed and non-adsorbing phase for each equilibrium pressure. Fig. 2. Schematic diagram of adsorption space model.

5 H. Yu et al. / International Journal of Coal Geology 73 (2008) The experimentally injected feed-gas amounts can be divided into adsorbed and free gas amount, in which component composition will reapportion. (3) Constant coal porosity and void volume in relation to helium expansion. During adsorption processes, with increase of gas loading, the porosity and void volume of the system may change due to adsorption swelling and adding of adsorbed gases (Karacan, 2003) and resulting in significant errors in measurements of CO 2 adsorption on coals (Romanov et al., 2006). However, in present adsorption experiment, the void volume determination using helium expansion was based on the changes ignore as accurate measurements of gas sorption by coals are not possible without knowing the swelling amount. On the other hand, The volume change steeply as a function of pressure for the lower-rank coals, but little or no effect is seen for the low-volatile bituminous coal (Ozdemir et al., 2003) used in this study. (4) A small quantity of gas used GC is neglected and does not affect the volume of free phase. Only 1 ml gas volume at STP was too small to effect on non-adsorbing and adsorbed amount at high pressure. (5) The CH 4 equilibrium concentration in free phase is more than initial concentration in feed gas, or the CO 2 concentration in free phase is less than that in feed gas. In adsorption curves, the CO 2 equilibrium concentration in free phase lower than the CO 2 value in feed gas represent preferential adsorption of CO 2 from the feed gas mixture (Busch et al., 2006). (6) The gas remaining in the reference cell keeps its original composition. The gaseous concentration diffusion is limited as length of the tube (about 50 cm) between valve 1 and valve 3, the constriction of the valve (V 2 ) opening start and the volumes of reference cell and sample cell (about 160 cm 3 ). The diffusive gas exchange through the tube and the valve (V 2 in Fig. 1) is ignored as the very slow concentration diffusion. Hence, the adsorbed space shown in Fig. 2 only express the sample cell, in which its volume includes the volume occupied by coal (V sample ), the void volume of the sample cell (V void ) and adsorbed phase volume (V sorbed phase ). The sample cell is charged with a given quantity of CO 2 /CH 4 feed gas, in which the molar fraction of CH 4 concentration (y 1 0 ) is known. The amount of charged mixture gas is divided into non-adsorbing and adsorbed portion. The non-adsorbing amount is n free and its molar fraction of CH 4 is y 1 0, the adsorbed amount is n ads and its molar fraction of CH 4 is y 1 0 all the same. After equilibrium is reached in the sample cell at the pressure P, the experimentally injected gas still was divided into two parts, non-adsorbing and adsorbed portion. The former amount and equilibrium concentration of CH 4 is n free and y 1, respectively, the latter amount and concentration of CH 4 is n ads and x 1, respectively. The molar fraction of CH 4 and mole amounts of mixture gas in free and adsorbed phase before and after equilibrium are denoted as follows. Phase state Before equilibrium After equilibrium Free phase y 0 1, n free y 1, n free Adsorbed phase y 0 1, n ads x 1, n ads Based on the sum of adsorbed and non-adsorbing amount of component CH 4 is constant during adsorption, the following mass balance equation is obtained: y 0 1 n free þ y 0 1 n ads ¼ y 1 n free þ x 1 n ads : ð2þ Hence, the adsorbed amount of gas mixture is n ads ¼ y0 1 y 1 x 1 y 0 n free : Langmuir and extended Langmuir ð3þ The Langmuir isotherm equation (Eq. (4)) was fitted to single-component isotherm. The simplest model used for prediction of multicomponent adsorption isotherms is the extended Langmuir equation (Eq. (5)). The Langmuir equation and extended Langmuir (Clarkson and Bustin, 2000) are: P n ¼ n L P L þ P ; ð4þ n EL;i ¼ðn L Þ i ðp L Þ i ð1 þ P P j =ðp L Þ j Þ y i ¼ðn L Þ i ðp L Þ i ð1 þ P y j P=ðP L Þ j Þ ; P i ð5þ where (n L ) i and (P L ) i are Langmuir isotherm adsorption constants of the pure gas i. Partial pressure of the component gas i in the free gas phase is determined using the following equation: P i ¼ Py i : ð6þ Langmuir parameters for pure component isotherms are used to predict adsorbed amounts of component for gas mixtures at any total gas pressure (P) and free gas composition (y i ) Ideal adsorbed solution theory The equilibrium between the ideal gas or vapor phase and an adsorbed phase can be expressed similar as for vapor liquid equilibria (VLE): x i Pi 0 ðpþg iðpþ ¼Py i : ð7þ Where y i and x i is the mole fraction of component i in the gas phase and the adsorbed phase, respectively,

6 120 H. Yu et al. / International Journal of Coal Geology 73 (2008) γ i (π) is the activity coefficient of the adsorbed phase and P i 0 (π) is the equilibrium gas phase pressure corresponding to the solution temperature (T) and solution spreading pressure (π) for the adsorption of pure component i. Inthecaseofanidealsolution,the activity coefficient is equal to unity for all values of temperature, spreading pressure and adsorbed phase mole fraction (x i ) of component i. In the case of an ideal adsorbed solution, Eq. (6) simplifies to Pd y i ¼ x i d P 0 i ðpþ: ð8þ The universal expression of SRK equation (Zhu and Xu, 1991) is: z ¼ 1 4:934Fh 1 h 1 þ h ; ð13þ where F and h can be determined from three parameters of the gas, critical pressure (P C ), critical temperature (T C ) and the acentric factor (ω): S ¼ 0:48 þ 1:574x 0:176x 2 ; ð14þ The spreading pressure (π) itself cannot be measured, but the reduced spreading pressure of the component i at standard states, Π i, defined as F ¼ 1 1 þ S 1 Tr 0:5 Þ 2 ; T r ð15þ P i ¼ p ia RT ¼ Z P 0 i ðpþ 0 n i ðp i Þ P i dp i ; ð9þ where n i (P i ) is the local adsorption isotherm (Langmuir) of component i. Π i is equal to the reduced spreading pressure (Π ) of adsorbed mixture. The relation between the mole fraction in the gaseous phase, y i, and the mole fraction in the adsorbed phase, x i, is described by Rault's law for ideal solutions X X xi ¼ 1; yi ¼ 1: ð10þ The total adsorbed amount, n, depends on the adsorbed amount of component i, n i. If an ideal behavior is assumed, the following equation can be obtained: 1 n ¼ X j x j n j ðp 0 j Þ : The adsorbed amount of component i is n i ¼ nx i : 4. Methods 4.1. Gas compressibility factor ð11þ ð12þ As indicated by Eq. (1), accurate gas-phase compressibility factors (z) are required for CH 4,CO 2 and their mixtures to properly predict the experimental adsorption data. The compressibility factors for pure CH 4 and CO 2, z 1 and z 2 are determined from highly accurate Soave Redlich Kwong (SRK) equations of state SRK using program obtained with an iterative algorithm. h ¼ 0:08664P r zt r ; ð16þ T r ¼ T T C ; P r ¼ P P C : ð17þ The simplest method for establishment a compressibility factor for the mixture is Aagat's law (Zhu and Xu, 1991), z m ¼ X y i z i : ð18þ Since z is an implicit function of h, Eq. (16) does not permit an explicit solution for h and an iterative technique is required for the solution. Fig. 3 shows the block diagram of compressibility factor computation of pure gas with SRK equation using an iterative algorithm Extended Langmuir An iterative procedure was used to obtain y 1, in which the initial value and final value (y 1,EL )isy 1 0 and 1.00, respectively, and step is The extended Langmuir adsorbed amount of CH 4 and CO 2 (n 1,EL, n 2, EL) can be obtained with Eq. (5) at a given equilibrium pressure (P) condition, the mole fraction of adsorbed CH 4 and CO 2 (x 1,EL, x 2,EL ) also be calculated with n 1,EL and n 2,EL. The actual adsorbed phase mole fraction of CH 4 (x R,1 ) can be calculated with Eqs. (3) and (2) at a given adsorbed amount (n R =n 1,EL +n 2,EL ), feed gas composition of CH 4 (y 1 0 ) and n free in each iterative algorithm. Hence, the value of x 1,EL or x R,1, corresponding to minimal difference value between x 1,EL and x R,1, is the

7 H. Yu et al. / International Journal of Coal Geology 73 (2008) Based on n L IAS =n ads and Eq. (3), Eq. (20) can be written as 1 n free ðy 0 1 y 1Þ x y n free ðy 0 1 y 1Þ ¼ ðp LÞ 1 x1 2 y 1 Pðn L Þ 1 Let þ ðp LÞ 2 y 2 Pðn L Þ 2 x 2 2 þ x 1 ðn L Þ 1 þ x 2 ðn L Þ 2 : ð21þ Fig. 3. Block diagram of compressibility factor computation using SRK. adsorbed phase concentration of CH 4 (x 1 ). The adsorbed amount (n, n 1 and n 2 ), free phase concentration (y 1 and y 2 ) can also obtained. A block diagram of gas mixtures predictions using extended Langmuir is shown in Fig Langmuir IAS theory Applications of the Langmuir equation to binary gas adsorption predictions require integration of pure component (CH 4 and CO 2 ) isotherms in the spreading pressure equation (Eq. (9)). The equilibrium gas phase pressure of the pure adsorbed component i, P 0 i (π) (abbreviation, P 0 i ), was calculated using an analytical equation for the Langmuir isotherm. The Langmuir isotherm equations of CH 4 and CO 2 in mixture at equilibrium pressure (P 0 1 and P 0 2 ) have been described as: n 1 P1 0 P 0 1 ¼ðnL Þ 1 P1 0 þðp ; n 2 P 0 2 LÞ 1 P2 0 ¼ðn L Þ 2 P2 0 þðp : ð19þ LÞ 2 The following equation can be obtained using Eqs. (8), (11) and (19): 1 n L IAS ¼ ðp LÞ 1 y 1 Pðn L Þ 1 x 2 1 þ ðp LÞ 2 y 2 Pðn L Þ 2 x 2 2 þ x 1 ðn L Þ 1 þ x 2 ðn L Þ 2 : ð20þ a 1 ¼ ðp LÞ 1 y 1 Pðn L Þ 1 ; a 2 ¼ ðp LÞ 2 y 2 Pðn L Þ 2 ; a 3 ¼ 1 ðn L Þ 1 ; a 4 ¼ 1 ðn L Þ 2 ; a 5 ¼ 1 ðy 0 1 y 1Þn free and a 6 ¼ y 0 1 ðy 0 1 y 1Þn free ; ð22þ the Eq. (21) can be written as a 1 x1 2 þ a 2x2 2 þ a 3x 1 þ a 4 x 2 ¼ a 5 x 1 a 6 : ð23þ Substituting x 2 =1 x 1 into the Eq. (23), the following equation can be obtained: ða 1 þ a 2 Þx1 2 þða 3 a 4 a 5 2a 2 Þx 1 þða 6 þ a 4 þ a 2 Þ¼0: ð24þ Let a=a 1 +a 2, b=a 3 a 4 a 5 2a 2 and c=a 6 +a 4 +a 2, quadratic equation in x 1 can be obtained, ax 2 1 þ bx 1 þ c ¼ 0: ð25þ The mole fraction of CH 4 in adsorbed phase, x 1, can be obtained with known y 1, P, the Langmuir parameters for pure component isotherms ((n L ) 1, (n L ) 2, (P L ) 1, (P L ) 2 ), n free and y 1 0. A solution of y 1 and P i 0 is the key to predict the adsorption equilibrium of binary gas using Langmuir IAS theory. An iterative algorithm was used to obtain y 1, in which the initial value and final value (y 1,L IAS )isy 1 0 and 1, respectively. P 1 0 and P 2 0 can be calculated with Eq. (8) in the iterative algorithm. The reduced spreading pressure (Π i 0 ) equation of component i can be obtained by integration of Eq. (9) with Langmuir isotherm equation (Eq. (4)), P i ¼ðn L Þ i ln P0 i þðp L Þ i ðp L Þ i : ð26þ Because the reduced spreading pressure of CH 4 (Π 1 0 ) in the mixtures is identical to that of CO 2 (Π 1 0 ), the difference value ( P) between Π 1 0 and Π 2 0 is zero. The y 1 value corresponding to the minimum absolute value of P in the iterative algorithm is the real mole fraction of

8 122 H. Yu et al. / International Journal of Coal Geology 73 (2008) CO 2 isotherm on Jincheng coal is generally better than that to CH 4 isotherm. The curve-fit to CH 4 isotherm on Luan coal is better than that to CO 2 isotherm. As can be seen in Fig. 6, the Langmuir fits to CH 4 adsorption is lower in the pressure range of 6 to 10 MPa and is higher in pressures outside this range on Jincheng coal. The Langmuir model similarly overestimates adsorbed amounts of CO 2 at high pressures for Jincheng coal, while underestimates adsorbed amounts of CO 2 at high pressure for Luan coal. The Langmuir parameters fitting to pure CH 4 and CO 2 can affect the prediction of total adsorption and component prediction for binary gas of CH 4 and CO Binary gas predictions using extended Langmuir and Langmuir IAS theory Binary gas adsorption equilibrium data were measured at 301 K and total adsorptive pressures between 0.3 MPa and 10 MPa on Jincheng and Luan coal. The extended Langmuir and Langmuir IAST theory Fig. 4. Block diagram of binary gas adsorption prediction using extended Langmuir. CH 4 in free phase. Finally, the adsorbed amount (n, n 1 and n 2 ), adsorbed phase concentration (x 1 and x 2 ) can also obtained. A block diagram of gas mixtures predictions using Langmuir IAS theory is shown in Fig Results and discussion 5.1. Pure component isotherms Adsorption isotherms of pure CH 4 and CO 2 at high pressure are summarized in Fig. 6. As can be seen in Fig. 6, measured isotherms of pure gases can be classified as Type I. Therefore, the experimental data can be correlated successfully using a Langmuir isotherm. The experimental data and Langmuir curvefits are shown in Fig. 6, fitted Langmuir parameters for the two coals and average relative errors estimates for experimental data are listed in Table 2. The Langmuir fits are much better to Luan coal adsorption than that to Jincheng coal. The curve-fit to Fig. 5. Block diagram of binary gas adsorption prediction using Langmuir IAS theory.

9 H. Yu et al. / International Journal of Coal Geology 73 (2008) Fig. 6. Comparison between experimental adsorption of CH 4 ( ), CO 2 ( ) and their Langmuir isotherms fits (dotted line for CH 4 and solid line for CO 2 ) on Jincheng and Luan coal at 301 K. predictions were accomplished by using the singlecomponent isotherm parameter of Langmuir (see Table 2). Figs show the experimental data (circle) and the results of extended Langmuir (cross) and Langmuir IAST theory (triangle) predictions. The extended Langmuir and Langmuir IAST theory were used to predict of total gas adsorption (Fig. 7), CH 4 adsorption (Fig. 8), CO 2 adsorption (Fig. 9) and free phase composition of CH 4 (Fig. 10). Table 3 contains the relative error estimates of extended Langmuir and IAS Langmuir for total gas, CH 4,CO 2 adsorption and mole fraction of CH 4 in free phase on Jincheng and Luan coal sample. The Vm v values for experimental feed compositions are also shown in Table Predictions of total gas adsorption Total gas adsorption predictions using extended Langmuir and Langmuir IAS theory under feed gas conditions are shown in Fig. 7. With the increase of CO 2 concentration for three feed gas compositions, the adsorbed amounts of the total gas increase for Jincheng coal and increase for Luan coal at low pressure but is constant basically for Luan coal at high pressure. The above adsorption isotherms of total gas depend on the Table 2 The Langmuir constants of gasses adsorption on coals and relative error a calculation for isotherms fits Gas name Jincheng coal V L (mmol/g) P L (MPa) ARE a (%) Luan coal V L (mmol/g) P L (MPa) ARE a (%) CH CO a ARE is average relative error, ARE ¼ 100 P n j¼1 jv calc V exp j=n, where N=number of data points. adsorption isotherms of components (CH 4 and CO 2 ) mentioned in Section 5.1. Langmuir IAS theory provides a better fits to total gas adsorption on two coals than that of extended Langmuir, particularly on Jincheng coal. The possible cause of the poorer curve-fits of the extended Langmuir to total gas adsorption are that the seeking aim of the iterative algorithm was the minimal difference value of adsorbed phase mole fraction of CH 4 between true data (x R,1, obtained with Eq. (2)) and extended Langmuir prediction (x 1,EL ) shown in Fig. 4, and the IAS theory model is more accurate than the extended Langmuir model for mixed gas adsorption (Hall et al., 1994). The extended Langmuir basically gives lower predictions to total gas adsorption. Its estimates for the total gas data are quite variable and depend upon the feed gas composition. With the decrease of CH 4 concentration in feed gas, the relative error estimates of extended Langmuir for total gas adsorption increase. The Langmuir IAS theory gives lower total adsorption estimates in a small degree at higher pressure. The relative error estimate of Langmuir IAS theory for total gas adsorption depends upon the feed gas composition and rank, in which it will increase for Luan coal and decrease for Jincheng coal with the decrease of CH 4 concentration in feed gas Predictions of CH 4 adsorption The CH 4 experimental data and its adsorption predictions in binary gas mixtures are shown in Fig. 8. The experimental data for adsorbed amount of component CH 4 on both coals increase at lower equilibrium pressure (up to 2 MPa) with the pressure increase and decrease at higher pressure with pressure increase. With the decrease of CH 4 concentration in feed gas, the decreasing magnitude of CH 4 adsorbed amount increase.

10 124 H. Yu et al. / International Journal of Coal Geology 73 (2008) Fig. 7. Comparison between adsorption predictions of CO 2 /CH 4 binary mixture using extended Langmuir ( ), Langmuir IAS theory ( ) and experimental data ( ) on Jincheng and Luan coal at 301 K. Fig. 8. Comparison between adsorption predictions of CH 4 in CO 2 /CH 4 binary mixture using extended Langmuir ( ), Langmuir IAS theory ( ) and experimental data ( ) on Jincheng and Luan coal at 301 K.

11 H. Yu et al. / International Journal of Coal Geology 73 (2008) Fig. 9. Comparison between adsorption predictions of CO 2 in CO 2 /CH 4 binary mixture using extended Langmuir ( ), Langmuir IAS theory ( ) and experimental data ( ) on Jincheng and Luan coal at 301 K. Fig. 10. Comparison between predicted mole fraction of free phase component (CH 4 ) using extended Langmuir ( ), Langmuir IAS theory ( ) and experimental data ( ) on Jincheng and Luan coal at 301 K under various feed gas conditions ( ). Regression line ( ), regression equation (y i =a+ bp) and squared correlation coefficient (R 2 =1 Σ((y 1 ) j (ŷ 1 ) j ) 2 /(Σ(y 1 2 ) j Σ(y 1 ) j 2 /N)) from experimental data of y 1.

12 126 H. Yu et al. / International Journal of Coal Geology 73 (2008) Table 3 Relative error a calculations of extended Langmuir and Langmuir IAS theory prediction for binary gas CH 4 (1)/CO 2 (2) adsorbed amount (n), singlecomponents adsorbed amount (n 1 for CH 4, n 2 for CO 2, mmol/g) and CH 4 equilibrium concentration (y 1, %) in free phase Sample Feed gas Vm v Extended Langmuir Langmuir IAS theory (cm 3 /g) n n 1 n 2 y 1 n n 1 n 2 y 1 Jincheng b 76.11% CH b 36.12% CH b 25.96% CH All feed gas c Luan b 76.11% CH b 36.12% CH b 25.96% CH All feed gas c a ARE is average relative error, ARE ¼ð100=NÞ P N j¼1 absðn calc n exp Þ j =n exp, where N=number of data points. b Six data points. c Eighteen data points, including 79.11%, 36.12% and 25.96% CH 4 feed gas isotherms. The extended Langmuir and Langmuir IAS theory provide better fits to experimental data for the 76.11% CH 4 feed gas composition than that for other feed gas composition and give better CH 4 adsorption on Jincheng coal than that on Luan coal. With the decrease of CH 4 concentration in feed gas, the relative errors of CH 4 adsorption predictions increase. Langmuir IAS theory provides a better fits to CH 4 adsorption on two coals than that of extended Langmuir, particularly on Luan coal. The reduced trend of CH 4 adsorption at high pressure can be fitted with the extended Langmuir and Langmuir IAS theory. Except for the 76.11% CH 4 feed gas composition, the extended Langmuir and Langmuir IAS theory give CH 4 significantly lower predicted value than its experimental data. The extended Langmuir basically provides lower predictions than that of Langmuir IAS theory for Luan coal Predictions of CO 2 adsorption The experimental data and adsorption predictions of CO 2 in binary gas mixtures are shown in Fig. 9. The experimental data for component CO 2 adsorption on both coals increase at the experimental pressure range. Adsorbed amount of CO 2 increases as its concentration in feed gas increase. CO 2 adsorption isotherms for three feed gas compositions illustrate similar trends with binary gas as found with pure CO 2 isotherms. Except for 76.11% CH 4 feed gas, the extended Langmuir and Langmuir IAS theory provide better fits to CO 2 adsorption than that to CH 4 adsorption, especially on Luan coal and give a better prediction at low pressure than that at high pressure. The IAS theory predictions of CO 2 are higher than its experimental data on Jincheng coal for 36.12% and 25.96% CH 4 feed gas composition and lower than that on Jincheng coal for 76.11% CH 4 feed gas. The extended Langmuir gives CO 2 lower predictions than its experimental data on Jincheng coal. To Luan coal, the extended Langmuir and Langmuir IAS theory provide CO 2 higher predictions for 36.12% CH 4 feed gas at all experimental pressure, 76.11% CH 4 feed gas composition at lower pressure and 25.96% CH 4 feed gas composition at higher pressure. The extended Langmuir and IAST Langmuir model predict characteristics and the experimental trend to single-component CO 2 adsorption, which is consistent with the experimental data Predictions of CH 4 free gas concentration The experimental data and predictions of CH 4 free phase concentrations (y 1 ) for three feed gas compositions are shown in Fig. 10. In the diagrams, the mole fractions of feed gases used, y 0 1, are shown as dotted lines. Generally, y 1 values are higher than those of the feed gases. The decrease trend with pressure increase is identical with the assumption of Eq. (5) in Section 3.1 for predictions. With increase of pressure for all feed gasses on two coals, the y 1 values decrease. The relation between y 1 value and equilibrium pressure (P) was examined with linear regression again. The linear regression equations for y 1 and P show that P provides negative effect on y 1 on two coals, and the decreasing magnitude of y 1 is increase with decrease of CH 4 concentration in feed gas (see slope of equation in Fig. 10). The regression equations provide 36.12% CH 4 feed gas composition with the lowest error estimates of y 1 (see squared correlation coefficient, R 2, in Fig. 10) and 76.11% CH 4 feed gas composition with the highest error estimates of y 1.

13 H. Yu et al. / International Journal of Coal Geology 73 (2008) Surprisingly, although Langmuir IAS theory is clearly superior to extended Langmuir for predicting total and single-component gas adsorption, it is inferior to extended Langmuir for predicting y 1 on Luan coal and gives better prediction than that of extended Langmuir to y 1 on Jincheng coal Except for the 76.11% CH 4 feed gas on two coal and the 36.12% CH 4 feed gas at low pressure on Luan coal, the extended Langmuir and Langmuir IAS theory give lower predicted value of CH 4 free phase concentration than experimental data. The Langmuir IAS theory provide higher y 1 predictions than that of extended Langmuir on Jincheng coal, and extended Langmuir give higher y 1 predictions than that of Langmuir IAS theory on Luan coal. Although the relative error of predicted CH 4 equilibrium concentration in free phase is lower, its absolute error of predicted value is greater as the CH 4 concentration value is greater than total and single-component adsorption. 6. Conclusions Although the volume swelling during gases adsorption was ignored as high rank coal and difficult to correct data, both the data and the isotherms are approximate, but still useful. Experimental binary gas adsorptions demonstrate that total gas adsorption are affected by coal composition and gas composition, as discussed in a previous study (Clarkson and Bustin, 2000). With increase of CO 2 concentration in feed gas, the adsorbed amounts of total gas and single-component CO 2 increase, adsorbed amounts of CH 4 increase at low equilibrium pressure and decrease at high pressure. CH 4 -adsorbed phase concentration decreases and CO 2 - adsorbed phase concentration increase with pressure increase for all feed gas compositions. The free concentrations of component CH 4 in equilibrium phase are higher than the initial concentrations in the feed gas. Varying compositions of feed gas do not affect the general trend of total gas, component gas adsorption and free gas composition and have only some influence on the magnitude of these trends. An identical equation for feed gas compositions and adsorbed amount of mixture on coal can be obtained based on the relation between adsorbed amount and free volume of void space at STP. The equation, in conjunction with extended Langmuir or Langmuir IAS theory can be used to predict adsorbed amount of component gas and mixture in binary gas on coal and equilibrium composition in free phase. Extended Langmuir and IAS theory predictions using pure component isotherm data show that the total gas adsorptions are generally superior to component adsorption in conditions of unknown free gas composition. They provide different prediction error to adsorbed amount and free phase composition of component gas for varying feed gas compositions, which depend upon the feed gas composition. Langmuir IAS theory is clearly superior to extended Langmuir for predicting total, CH 4 and CO 2 adsorption. In general, the prediction trends of total and component gas adsorption under known feed-gas composition condition, is similar to that under known equilibrium composition condition, as discussed in the previous studies (Clarkson and Bustin, 2000; Karacan and Okandan, 2000). Equilibrium concentration of free gas should be obtained based on relation between adsorbed amount and feed gas composition, additional parameter was introduced for predictions of the adsorption equilibrium under feed gas conditions. The interaction of parameters could causes higher error than that of convenient condition under known equilibrium concentration determined with GC. Nomenclature A Adsorbent surface area [cm 3 ] ARE Average relative error [%] m Mass of coal sample [g] n Amount adsorbed [mmol/g] n free Amount of free gas [mmol/g] n L Langmuir isotherm adsorption constant [mmol/g] N Number of data points P Total pressure [MPa] P i 0 P i P L Partial pressure of component i Equilibrium gas phase pressure corresponding to the solution temperature and solution spreading pressure for the adsorption of pure component i [MPa] Langmuir isotherm adsorption pressure constant [MPa] R Gas constant: [cm 3 MPa/mol K] R 2 Squared correlation coefficient T Temperature [K] Vm v Void volume mass at experimental conditions [cm 3 /g] x Adsorbed phase mole fraction [%] y Gas phase mole fraction [%] z Gas compressibility factor Subscripts ads Adsorbed C Critical condition EL Extended Langmuir

14 128 H. Yu et al. / International Journal of Coal Geology 73 (2008) i Component i, 1 for CH 4 and 2 for CO 2 L Langmuir L IAS Ideal adsorbed solution (IAS) theory in conjunction with Langmuir m Mixture r Reduced condition R Real STP Standard temperature and pressure Superscripts Standard state 0 Initial condition Greek symbols Π Reduced spreading pressure γ Activity coefficient of the adsorbed phase π Spreading pressure ω Eccentric factor Acknowledgments Financial support for this study was provided by the National Natural Science Foundation of China grant to Qianting Hu and the Open Research Fund Program of Key Laboratory of Mine Disaster Prevention and Control (Shandong University of Science and Technology) grant MDPC0607 to Hongguan Yu. The anonymous reviewers are acknowledged for helpful and careful comments and modification of this manuscript that improved the quality of this paper. 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