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Computing Thermal Properties of Natural Gas by Utilizing AGA8 Equation of State International Journal of Chemical Engineering and Applications, Vol. 1, No. 1, June 2010 ISSN: 2010-0221 Computing Thermal Properties of Natural Gas by Utilizing AGA8 Equation of State Mahmood Farzaneh-Gord, Azad Khamforoush, Shahram Hashemi and Hossein Pourkhadem Namin Farzaneh et al. [5] have obtained a PR style expression for a Abstract— In current study, an attempt has been made to typical Iranian natural gas based on mixture components of develop a numerical method and a computer program to PR EoS. calculate the thermal properties of natural gas mixture such as Mc Carty [6] reported an accurate extended corresponding enthalpy and internal energy in addition of the compressibility factor using AGA8 state equation. The method has been applied states (ECS) model for LNG systems, Using ECS models. to a typical Iranian natural gas mixture to calculate the thermal Estela-Uribe and Trusler [3] and Estela- Uribe et al. [4] properties of the gas. Finally, the developed program has been predicted the compressibility factors, densities, speeds of utilized to model single reservoir fast filling process of a typical sound and bubble point pressures of natural gas mixtures natural gas vehicle on-board cylinder. The computed results quite accurately. have been compared with simulation results of same process Maric [7] describes the procedure for the calculation of the (fast filling) in which the pure methane was acted as working fluid. The results show the similar trends and good agreements. natural gas isentropic exponent based on the Redlich–Kwong approach and the AGA8/1985 equation of state. Maric et al. Index Terms—Natural Gas, AGA8 equation of state, [8] derived a numerical procedure for the calculation of the Thermal properties, numerical method isentropic exponent of natural gas on the basis of the extended virial type characterization equation specified in AGA8/1992[9]. Maric [9] has also used the similar method to I. INTRODUCTION calculate Joule-Thompson coefficient of natural gas. Given the current surge in the petrochemical and natural Nasrifar and Boland [10] used 10 equations of state to gas businesses, trustworthy estimates of thermodynamic predict the thermo-physical properties of natural gas properties are necessary to design engineering processes. mixtures. They proposed two-constant cubic EoS. This EoS Accurate prediction of thermodynamics properties for is obtained by matching the critical fugacity coefficient of the hydrocarbon fluids is an essential requirement in optimum EoS to the critical fugacity coefficient of methane. Special design and operation of most process equipment involved in attention is given to the supercritical behavior of methane as petrochemical production, transportation, and processing. it is the major component of natural gas mixtures and almost Accurate value of natural gas compressibility factors is always supercritical at reservoir and surface conditions. As a crucial in custody transfer operations. Other thermodynamic result, the proposed EoS accurately predicts the supercritical properties, e.g., enthalpy and internal energy of the gas, are fugacity of methane for wide ranges of temperature and used in the design of processes and storage facilities; pressure. Using the van der Waals mixing rules with zero Joule–Thomson coefficients are used in throttling processes binary interaction parameters, the proposed EoS predicts the and dew points are used in pipeline design. compressibility factors and speeds of sound data of natural An Equation of State (EoS) can describe the gas mixtures with best accuracy among the other EoSes. The thermodynamic state of a fluid or fluid mixture and also its average absolute error was found to be 0.47% for predicting vapor-liquid phase equilibrium behavior. An ideal EoS the compressibility factors and 0.70% for the speeds of sound should predict thermodynamic properties of any fluid data. accurately over a wide range of temperature, pressure and Although, the AGA8 EoS has been used to calculate some composition for vapor and liquid phases. The AGA8-DC92 properties of the natural gas, no attempted yet has been made EoS [1] and ISO-12213-2 [2] is currently the industry to calculate thermal properties of natural gas such as internal standard to predict the density or compressibility factor of energy and enthalpy. In this study, a computer program has natural gas with an acceptable accuracy. There are other been developed to calculate the thermal properties of natural correlations/equations of state (EoS) for calculating natural gas mixture in addition of the compressibility factor based on gas properties [3]-[4]. the AGA8 EoS. The method has been applied to a typical Peng and Robinson (PR) EoS are often used in the gas Iranian natural gas mixture to calculate the properties of the industry for predicting natural gas equilibrium properties. natural gas. Finally, the developed program has been utilized to model single reservoir fast filling process of natural gas vehicle natural gas cylinder. Manuscript received October 9, 2009. This work was supported by the Semnan gas company. Dr. M. Farzaneh-Gord is with the Shahrood University of Technology, Shahrood, Iran(+98-273-3392204- ext2642; fax: +98-273-3395440; e-mail: II. THE NUMERICAL METHOD [email protected]). The common equation of state for a real gas can be given 20 International Journal of Chemical Engineering and Applications, Vol. 1, No. 1, June 2010 ISSN: 2010-0221 2 as follow: ⎡ N ⎤ N −1 N U 5 = X E 5/ 2 + 2 X X (U 5 −1)(E E )5/ 2 (11) = ZRT ⎢∑ i i ⎥ ∑∑ i j ij i j P ⎣ i=1 ⎦ i=1 j=i+1 v (1) N N −1 N In which compressibility factor can be calculated using = + * − + (12) G ∑∑∑X iGi X i X j (Gij 1)(Gi G j ) various equation of states. According to AGA8/1992 and i=1 i=+11j=i ISO-12213-2/1997,the equation for the compressibility N factor of natural gas is: [1],[2] = Q ∑ X iQi (13) 18 = DB − i 1 Z = 1+ − D C *T un + 3 ∑ n N K = 2 n 13 (2) F = X F (14) 58 ∑ i i − i=1 * un − kn bn − kn ∑ CnT (bn cn K n D )D exp( cn D ) n=13 Where {}Uij is the binary interaction parameter for mixture Where D is reduced density, B is second virial energy * coefficient, K is mixture size coefficient and {}Cn are the The above equations have been discussed more in AGA8/1992 and ISO-12213-2/1997 and can be utilized to temperature dependent coefficients, While {}b , and n {}cn calculate the natural gas compressibility factor [1],[2]. In this {}kn are the equation of state parameters given in study, the aim was to calculate the thermodynamics ISO-12213-2/1997. The gas molar density d and reduced properties of natural gas mixture such as internal energy and enthalpy. To calculate the internal energy of the gas mixture, density D are defined as the fundamental thermodynamics relation has been the = 3 D K d (3) starting point as follow: = P ⎛ ∂u ⎞ ⎛ ∂u ⎞ d (4) du = dT + dv (15) ZRT ⎜ ∂ ⎟ ⎜ ∂ ⎟ ⎝ T ⎠v ⎝ v ⎠T The second virial coefficient and the mixture size According to Maxwell relations the equation (15) can also be coefficient are calculated using the following equations: 2 expressed as below: ⎡ N ⎤ N −1 N ∂ K 5 = X K 5 / 2 + 2 X X (K 5 −1)(K K )5 / 2 = + ⎛ u ⎞ ⎢∑ i i ⎥ ∑∑ i j ij i j du cvdT ⎜ ⎟ dv (16) i=1 i=+11j=i ∂ ⎣ ⎦ ⎝ v ⎠T (5) The equation (16) can be integrated to evaluate the internal 18 N N − energy of natural gas at any position if a reference value is B = a T un X X Eun (K K )3/ 2 B* (6) ∑∑∑n i j ij i j nij given as follow: n===111i j * T2 v 2 ⎡ ⎛ ∂p ⎞ ⎤ Where the coefficients , and are defined by − = + − (17) {}Bnij {}Eij {}Gij u u ref cv dT ⎢T ⎜ ⎟ p ⎥ dv ∫Tref ∫vref ⎝ ∂T ⎠ the following formulas: ⎣ v ⎦ To be able to evaluate the above integral, the value of * = + − gn + − qn 1/2 1/2 + − fn Bnij (Gij 1 gn) .(QiQj 1 qn) (Fi Fj 1 fn) . ∂P ⎞ (7) ⎟ has to be known. Here, the value was derived using s w ∂T (SS +1−s ) n.(WW +1−w ) n ⎠v i j n i j n general state equation (1) as below: = * 1/ 2 Eij Eij .(Ei E j ) (8) ⎛ ∂p ⎞ Z .R ⎛ ∂Z ⎞ R.T ⎜ ⎟ = + ⎜ ⎟ × (18) * ∂ ∂ G (G + G ) ⎝ T ⎠ v v ⎝ T ⎠ v v = iJ i j Gij (9) Finally, by replacing equation (1) and (18) into equation 2 (17), the following equation could be obtained: Where T is temperature, N is the total number of gas 2 T2 v 2 ⎡ R.T ∂Z ⎤ − = + × ⎛ ⎞ (19) mixture components, X is the molar fraction of the u u ref c v dT ⎜ ⎟ dv i ∫Tref ∫vref ⎢ ∂ ⎥ ⎣ v ⎝ T ⎠ v ⎦ component i , {}an , {}f n , {}gn , {}qn , {}sn , {}un and {}wn In which, the first derivative of the compressibility factor ⎛ ∂Z ⎞ are the equation of state parameters, {}Ei , {}Fi , {}Gi , {}Ki , with respect to temperature (⎜ ⎟ ) is: ⎝ ∂T ⎠ , and are the corresponding characterization v {}Qi {}Si {}Wi 18 N N 3 ⎛ ∂Z ⎞ D ⎛ ( − u −1) u ⎞ ⎜ ⎟ = .⎜ − u a T n X X E n (k k ) 2 B * ⎟ + * * 3 ⎜ ∑∑∑n n i j ij i j n ij ⎟ ∂T k === parameters while {}Eij and {}Gij are the corresponding ⎝ ⎠ v ⎝ n 111i j ⎠ 18 58 ⎛ − − ⎞ ⎛ − − ⎞ binary interaction parameters. The temperature dependent * ( u n 1) − * ( u n 1) − k n bn ⎜ D ∑ u n C n T ⎟ ⎜ ∑ u n C n T (b n c n k n D ) D ⎟ * ⎝ n =13 ⎠ ⎝ n =13 ⎠ coefficients {,Cn= 1,,58}" are defined by the following n × − k n exp( c n D ) relation: (20) * = + − g n 2 + − qn + − f n un Cn an (G 1 g n ) (Q 1 qn ) (F 1 f n ) U (10) The ideal molar heat capacity Cv is also needed in and the mixture parameters U, G, Q and F are calculated equation (19) for evaluating internal energy.
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