Iteratoal Joural of Chemcal geerg ad Applcatos, Vol., o., Jue ISS: - Computg Thermal Propertes of atural as by Utlzg AA8 quato of State Mahmood Farzaeh-ord, Azad hamforoush, Shahram Hashem ad Hosse Pourhadem am Abstract I curret study, a attempt has bee made to deelop a umercal method ad a computer program to calculate the thermal propertes of atural gas mxture such as ethalpy ad teral eergy addto of the compressblty factor usg AA8 state equato. The method has bee appled to a typcal Iraa atural gas mxture to calculate the thermal propertes of the gas. Fally, the deeloped program has bee utlzed to model sgle reseror fast fllg process of a typcal atural gas ehcle o-board cylder. The computed results hae bee compared wth smulato results of same process (fast fllg whch the pure methae was acted as worg flud. The results show the smlar treds ad good agreemets. Idex Terms atural as, AA8 equato of state, Thermal propertes, umercal method I. ITRODUCTIO e the curret surge the petrochemcal ad atural gas busesses, trustworthy estmates of thermodyamc propertes are ecessary to desg egeerg processes. Accurate predcto of thermodyamcs propertes for hydrocarbo fluds s a essetal requremet optmum desg ad operato of most process equpmet oled petrochemcal producto, trasportato, ad processg. Accurate alue of atural gas compressblty factors s crucal custody trasfer operatos. Other thermodyamc propertes, e.g., ethalpy ad teral eergy of the gas, are used the desg of processes ad storage facltes; Joule Thomso coeffcets are used throttlg processes ad dew pots are used ppele desg. A quato of State (os ca descrbe the thermodyamc state of a flud or flud mxture ad also ts apor-lqud phase equlbrum behaor. A deal os should predct thermodyamc propertes of ay flud accurately oer a wde rage of temperature, pressure ad composto for apor ad lqud phases. The AA8-DC9 os [] ad ISO-- [] s curretly the dustry stadard to predct the desty or compressblty factor of atural gas wth a acceptable accuracy. There are other correlatos/equatos of state (os for calculatg atural gas propertes []-[4]. Peg ad Robso (PR os are ofte used the gas dustry for predctg atural gas equlbrum propertes. Mauscrpt receed October 9, 9. Ths wor was supported by the Sema gas compay. Dr. M. Farzaeh-ord s wth the Shahrood Uersty of Techology, Shahrood, Ira(98-7-94- ext64; fax: 98-7-944; e-mal: mahmood.farzaeh@yahoo.co.u. Farzaeh et al. [] hae obtaed a PR style expresso for a typcal Iraa atural gas based o mxture compoets of PR os. Mc Carty [6] reported a accurate exteded correspodg states (CS model for L systems, Usg CS models. stela-urbe ad Trusler [] ad stela- Urbe et al. [4] predcted the compressblty factors, destes, speeds of soud ad bubble pot pressures of atural gas mxtures qute accurately. Marc [7] descrbes the procedure for the calculato of the atural gas setropc expoet based o the Redlch wog approach ad the AA8/98 equato of state. Marc et al. [8] dered a umercal procedure for the calculato of the setropc expoet of atural gas o the bass of the exteded ral type characterzato equato specfed AA8/99[9]. Marc [9] has also used the smlar method to calculate Joule-Thompso coeffcet of atural gas. asrfar ad Bolad [] used equatos of state to predct the thermo-physcal propertes of atural gas mxtures. They proposed two-costat cubc os. Ths os s obtaed by matchg the crtcal fugacty coeffcet of the os to the crtcal fugacty coeffcet of methae. Specal atteto s ge to the supercrtcal behaor of methae as t s the maor compoet of atural gas mxtures ad almost always supercrtcal at reseror ad surface codtos. As a result, the proposed os accurately predcts the supercrtcal fugacty of methae for wde rages of temperature ad pressure. Usg the a der Waals mxg rules wth zero bary teracto parameters, the proposed os predcts the compressblty factors ad speeds of soud data of atural gas mxtures wth best accuracy amog the other oses. The aerage absolute error was foud to be.47% for predctg the compressblty factors ad.7% for the speeds of soud data. Although, the AA8 os has bee used to calculate some propertes of the atural gas, o attempted yet has bee made to calculate thermal propertes of atural gas such as teral eergy ad ethalpy. I ths study, a computer program has bee deeloped to calculate the thermal propertes of atural gas mxture addto of the compressblty factor based o the AA8 os. The method has bee appled to a typcal Iraa atural gas mxture to calculate the propertes of the atural gas. Fally, the deeloped program has bee utlzed to model sgle reseror fast fllg process of atural gas ehcle atural gas cylder. II. TH UMRICAL MTHOD The commo equato of state for a real gas ca be ge
Iteratoal Joural of Chemcal geerg ad Applcatos, Vol., o., Jue ISS: - as follow: ZRT P = ( I whch compressblty factor ca be calculated usg arous equato of states. Accordg to AA8/99 ad ISO--/997,the equato for the compressblty factor of atural gas s: [],[] 8 DB u Z = D C T = ( 8 = C T u ( b c D D b exp( c D Where D s reduced desty, B s secod ral coeffcet, s mxture sze coeffcet ad { C } are the temperature depedet coeffcets, Whle { b }, {} c ad { } are the equato of state parameters ge ISO--/997. The gas molar desty d ad reduced desty D are defed as D = d ( P d = (4 ZRT The secod ral coeffcet ad the mxture sze coeffcet are calculated usg the followg equatos: B = = = / 8 u at = = = = = ( ( / ( u / ( B (6 Where the coeffcets{ B }, { } ad { } are defed by the followg formulas: B = ( g ( SS s s g.( WW w w.( QQ q q ( F / F / f f. / =.( (8 J ( = (9 Where T s temperature, s the total umber of gas mxture compoets, s the molar fracto of the compoet, { a }, { f }, { g }, { q }, { s }, { u } ad { w } are the equato of state parameters, { }, { F }, { }, { }, { Q }, { S } ad { W } are the correspodg characterzato parameters whle { } ad { } are the correspodg bary teracto parameters. The temperature depedet coeffcets { C, =,,8} are defed by the followg relato: g q f u C = a ( g ( Q q ( F f U ( ad the mxture parameters U,, Q ad F are calculated usg the followg equatos: (7 / / U = ( U ( ( = = = = = Q = = F = = Q F = = ( ( ( ( (4 Where { U } s the bary teracto parameter for mxture eergy The aboe equatos hae bee dscussed more AA8/99 ad ISO--/997 ad ca be utlzed to calculate the atural gas compressblty factor [],[]. I ths study, the am was to calculate the thermodyamcs propertes of atural gas mxture such as teral eergy ad ethalpy. To calculate the teral eergy of the gas mxture, the fudametal thermodyamcs relato has bee the startg pot as follow: u u du = dt d ( T Accordg to Maxwell relatos the equato ( ca also be expressed as below: u du = cdt d (6 T The equato (6 ca be tegrated to ealuate the teral eergy of atural gas at ay posto f a erece alue s ge as follow: T p u u = cdt T p T d (7 To be able to ealuate the aboe tegral, the alue of P has to be ow. Here, the alue was dered usg T geeral state equato ( as below: p Z. R Z R. T = (8 Fally, by replacg equato ( ad (8 to equato (7, the followg equato could be obtaed: T R. T Z u u = c dt T d (9 I whch, the frst derate of the compressblty factor wth respect to temperature ( Z s: 8 Z D ( u u =. u ( a T B T = = = 8 8 ( u ( u b D u C T u C T ( b c D D = = exp( c D ( The deal molar heat capacty C s also eeded equato (9 for ealuatg teral eergy. By owg the
Iteratoal Joural of Chemcal geerg ad Applcatos, Vol., o., Jue ISS: - deal heat capacty ad mole fracto of each compoet, the deal molar heat capacty of atural gas (mxture may be calculated as below: C = C ( = Oce the teral eergy of the atural gas s calculated by umercal tegrato of equato 9, the ethalpy of the gas could be calculated by usg the followg equato: h h = u u ( p p ( ( Z.9.9.8.8.7.7.6 Shaol as Feld T=( T=( T=( T=( T=9( T=8( T=7( T=6( III. CHMICAL COMPOSITIO OF ATURAL AS atural gas composto (mxture ares wth locato, clmate ad other factors ad may cota up to compoets. The prmary compoet s Methae (CH 4 wth about 9% the mxture. It also cotas heaer hydrocarbos such as thae (C H 6, Propae (C H 8 ad Butae (C 4 H. Table shows a expermetal aalyss of atural gas composto of Shaol gas feld whch s based for the aalyss ths research wor []. Table - xpermetal aalyss of atural gas composto of Shaol gas feld summer Compoet Chemcal formula xpermetal Aalyss (mole Fracto % water H O. Carbo doxde CO. troge.88 Methae CH 4 9.86 thae C H 6.89 Propae C H 8.8 Iso butae C 4 H. -Butae C 4 H.9 Iso-Petae C H. Z.9.9.8.8.7.7 4 6 8 Pressure(Mpa Fgure - ffects of pressure o compressblty P=(Mpa P=(Mpa P=(Mpa P=7(Mpa P=9(Mpa P=(Mpa Shaol as Feld.6 6 7 8 9 4 Temperature( Fgure - ffects temperature o compressblty factor Fgure shows the effects of pressure ad temperature o atural gas specfc teral eergy for Shaol gas fled. It ca be see that temperature ad pressure growth causes the teral eergy to crease. It ca be also see that the arato of teral eergy at costat pressure follow a le. Ths s the case for arous pressures. Fgure 4 shows the effects of pressure ad temperature o atural gas specfc ethalpy. The same behaor as teral eergy ca be see ths fgure too.. x Shaol gas feld PseudoC 6 PseudoC 6. PseudoC 7 PseudoC 7. PseudoC 8 PseudoC 8.4 Iteral ergy (J/g. -. P=MPa PseudoC 9 PseudoC 9. P=MPa PseudoC PseudoC. - PseudoC PseudoC. -. 6 7 8 9 4 Temperature ( Fgure - ffects of temperature ad pressure o specfc teral eergy x Shaol as Feld IV. RSULTS AD DISCUSSIOS I ths study based o umercal method dscussed secto, a computer program has bee deeloped to predct the atural gas teral eergy ad ethalpy addto of compressblty factor. Fgure ad fgure show effects of pressure ad temperature o atural gas compressblty factor for Shaol gas fled atural gas. As expected, the compressblty factor decreases as pressure creases ad creases as temperature creases. The alue of compressblty factor approaches as pressure decreases for all temperatures. thalpy (J/g T=4... T=6 -. 4 6 7 8 9 Pressure (Pa x 6 Fgure 4- ffects of temperature ad pressure o specfc ethalpy
Iteratoal Joural of Chemcal geerg ad Applcatos, Vol., o., Jue ISS: - I addto to calculate the thermodyamcs propertes of atural gas as show aboe, the deeloped program has bee used to smulate the fllg process of a oboard atural ehcle cylder (V. A schematc dagram of the thermodyamc model has bee show fgure. The same system has bee smulated ad modeled Farzaeh [] whe worg flud assumed to be pure methae. For the thermodyamc system as show fgure, the goerg equatos are coserato of mass ad frst law of thermodyamc as: dme = m ( dt due u m e me = m h (4 dt Where ue s specfc teral eergy of V cylder, h s specfc ethalpy of reseror tha ad m s let mass flow rate. I the fllg smulato, equatos ( ad (4 hae bee soled umercally to fd specfc olume ad teral eergy. The the deeloped program was used to fd temperature ad pressure of the gas. Farzaeh [] utlzed methae thermodyamcs table to fd temperature ad pressure. For more formato about the fast fllg process ad the thermodyamcs model whch utlzed here see Farzaeh []. mxture wth heaer hydrocarbos (atural gas comparg wth pure methae. ote from the fgure, the treds for both profles are smlar. Temperature ( 8 6 4 Methae atural gas 8 4 6 7 8 Tme (secods Fgure 6- Varato of V cylder temperature durg fllg process Pressure (Mpa Methae atural gas 4 6 7 8 Tme (secods Fgure 7- Varato of V cylder pressure durg fllg process Fgure 7 shows dyamc pressure profles V cylder durg fllg process for pure methae ad atural gas. It ca be see that both profle hae smlar treds ad are good agreemet. It s worth metog that the dffereces betwee the two profles are expected as the thermodyamc propertes of two worg fluds are ot the same. Fgure - A schematc dagram of the thermodyamc model Here to aldate the umercal method of calculatg thermodyamcs propertes of the atural gas, a comparso has bee made betwee pure methae ad atural gas dyamc propertes for fllg process of a V cylder. Fgure 6 shows dyamc temperature profles V cylder durg fllg process for pure methae ad atural gas. As show Fgure 6, early fllg tme, the cylder gas temperature dps sgfcatly, before rsg to a fal alue. The reaso for the dp temperature profle, the early part of the fllg of a early empty cylder s result of the Joule-Thompso coolg effect, whch the gas udergoes the sethalpc expaso through the orfce, from the bar supply pressure to the tally low bar cylder pressure. Ths cold gas mxes wth ad compresses the gas orgally the ta, wth the result that the combed mxed gas temperature tally reduces. It ca be see that the dp for atural gas profle s hgher tha for pure methae case. Ths shows that the Joule-Thompso effects are hgher atural gas tha pure methae. Ths behaor s expected for a V. COCLUSIO e the curret surge the petrochemcal ad atural gas busesses, trustworthy estmates of thermodyamc propertes are ecessary to desg egeerg processes. Accurate predcto of thermodyamcs propertes for hydrocarbo fluds s a essetal requremet optmum desg ad operato of most process equpmet oled petrochemcal producto, trasportato, ad processg. I curret study, a computer program has bee deeloped to calculate the thermal propertes of atural gas mxture such as ethalpy ad teral eergy addto of the compressblty factor. The method has bee appled to a typcal Iraa atural gas mxture to calculate the propertes of the atural gas. To aldate the method, the deeloped program has bee utlzed to model fast fllg process of atural gas ehcle atural gas cylder. The computed results hae bee compared wth smulato results of same process whch the pure methae was acted as worg flud. The results show the smlar treds ad good agreemets. VI. ACOWLDMTS The authors would le to tha offcals Sema as Compay for prodg facal support for ths research. VII. OMCLATUR Symbol Descrpto uts
Iteratoal Joural of Chemcal geerg ad Applcatos, Vol., o., Jue ISS: - B Secod ral coeffcet - Mxture teracto coeffcet - B Temperature ad composto depedet - C coeffcet c p Molar heat capacty at costat pressure J/(mol Α Coeffcet - Β Coeffcet - C 6 All hydrocarbo compouds wth more tha - carbo ther chemcal formula c Molar heat capacty at costat olume J/(mol D Reduced desty - d Molar desty mol/m Bary eergy teracto parameter for secod - ral coeffcet Characterzato eergy parameter for -th compoet Bary eergy parameter for secod ral coeffcet F Mxture hgh-temperature parameter - F hgh-temperature parameter for -th compoet - Mxture oretato parameter - Bary teracto parameter for oretato - oretato parameter for -th compoet - Bary oretato parameter - h Specfc ethalpy /g Sze parameter - Sze parameter for -th compoet - Bary teracto parameter for sze - M Mxture molar mass g/(mol M Molar mass of -th compoet g/(mol Mass flow rate g/s m the total umber of gas mxture compoets - P pressure Mpa or pa Q Quadrupole parameter - Q Quadrupole parameter for -th compoet - R Uersal molar gas costat J/(mol S Dpole parameter for -th compoet - T Temperature U Mxture eergy parameter u Specfc teral eergy /g Bary teracto parameter for mxture eergy - U Specfc olume m /g V Volume m W Assocato parameter for -th compoet - Molar fracto of -th compoet gas mxture - Z Compressblty factor - ρ Desty g/m [6] McCarty, R.D., 98. Mathematcal models for the predcto of lquefed-atural-gas destes. J. Chem. Thermody. 4, 87 84. [7] Marc I., 997, Derato of atural gas setropc expoet from AA-8 equato of state, Stroarsto 9, 7. [8] Marc I., Atu alo cb, Tomsla Šmuca,, Calculato of atural gas setropc expoet, Flow Measuremet ad Istrumetato 6,. [9] Marc I.,,The Joule Thomso effect atural gas flow-rate measuremets, Flow Measuremet ad Istrumetato 6 87 9. [] asrfar, h., Bollad O., 6,Predcto of thermodyamc propertes of atural gas mxtures usg equatos of state cludg a ew cubc two-costat equato of state, do:.6/.petrol.6..4 [] Shaol gas feld codtos,, atoal Iraa as Compay (IC Iteral report. [] Farzaeh-ord, M., 8, Compressed atural gas Sgle reseror fllg process, as teratoal geerg ad Maagemet, Volume 48, Issue 6, July/August, pp 6-8. Dr. Mahmood Farzaeh-ord s curretly a assocate professor Faculty of mechacal egeerg Shahrood Uersty of Techology. Hs ma teachg cotrbuto for udergraduate studets s egeerg thermodyamc ad for postgraduate studets s Adaced egeerg thermodyamc. He obtaed a PhD degree from Bath Uersty Bath, U wth subect of gas turbe coolg system. He graduated from Ferdows Uersty of Mashhad, Mashhad, Ira wth a MSc degree wth Frst class Hoours wth ergy coersato subect 997. He s curretly oled eergy optmzato proect ad software deelopmet for Ira ol ad gas dustry. VIII. RFRCS [] AA 8, 99, Compressblty ad super compressblty for atural gas ad other hydrocarbo gases, Trasmsso Measuremet Commttee Report o. 8, AA Catalog o. Q 8, Arlgto, VA. [] ISO--, 997, atural gas Calculato of compresso factor Part : Calculato usg molar-composto aalyss, ISO, Ref. o. ISO- -:997(. [] stela-urbe, J.F., Trusler, J.P..,. xteded correspodg states equato of state for atural gas systems. Flud Phase qulb. 8 84, 9. [4] stela-urbe, J.F., De Modoza, A., Trusler, J.P.., 4. xteded correspodg states model for fluds ad flud mxtures II. Applcato to mxtures ad atural gas systems. Flud Phase qulb. 6, 9 84. [] Farzaeh ord M.,, Morad., Mohebb R., Maghreb M.J., Hashem S., 8, Smulato of atural as OS (quato of State Iestgato Usg P-ROBISO OS, The frst Iteratoal coferece o mergg techologes ad applcatos geerg, Techology ad Sceces, -4 Jauary 8, Raot uarat (Ida. 4