An accurate empirical correlation for predicting natural gas compressibility factors

Availableonlineatwww.sciencedirect.coe Science Direct峡8ELSEVIERournal of Natural Gas Chemistry 21(2012)184-188www.elsevier.com/locate/jngcAn accurate empirical correlation for predictingnatural gas compressibility factorsEhsan Sanjari, Ebrahim Nemati LayDepartment of Chemical Engineering, Faculry of Engineering, University of Kashan, Ravand Street, Kashan, P. O. Box 87317-51167, IranI Manuscript received July 15, 2011: revised November 10, 2011 IAbstractThe compressibility factor of natural gas is an important parameter in many gas and petroleum engineering calculations. This study presentsa new empirical model for quick calculation of natural gas compressibility factors. The model was derived from 5844 experimental data ofcompressibility factors for a range of pseudo reduced pressures from 0.01 to 15 and pseudo reduced temperatures from 1 to 3. The accuracy ofhe new empirical correlation has been compared with commonly used existing methods. The comparison indicates the superiority of the newempirical model over the other methods used to calculate compressibility factor of natural gas with average absolute relative deviation percent(AARD%)of0.6535Key wordsnatural gas; compressibility factor; correlation; empirical model; equation of state1. Introductiondata and the accuracy of the model has been compared withcommonly used empirical correlations as well as classical andNatural gas is a subcategory of petroleum that is a natstatistical equations of stateurally occurring, complex mixture of hydrocarbons, with asmall amount of inorganic compounds [1 ]. Knowledge of the 2. Natural gas compressibility factorpressure-volume-temperature (PVT)behavior of natural gasesis necessary to solve many petroleum engineering problems,In the real gas equation, Z-factor can be obtained as fol-design and analyze natural gas production and processing low:PV= ZnRTIn most petroleum and natural gas engineering calcula-tions, the compressibility factor and density of fluids are nec- where, P is pressure in kPa, V is the volume in L, n is theessary to gas metering, gas compression, design of pipelines number of gas mol, R is universal gas constant, T isand surface facilities [2]. Petroleum engineers need to predict ture in K, and Z is the compressibility factor of g tempera-pressure-volume temperature(PVT) properties of petroleumThe theory of corresponding states dictates that thefluids under given conditions of temperature and pressure. Z-factor can be uniquely defined as a function of reduced pres-This can be determined through PVT analysis of fluid sample sure and reduced temperature. The pseudo reduced pressuretests or can be calculated by Equations of State(EOS)based and temperature are defined by Equations 2 and 3, respec.on computer codes if the fluid composition is known. This tively.information is often unavailable particularly at the early stageof field development or needs to be verified, supported andTpr=T/Tsupplemented during the course of field development. Then itis the task of empirical correlations to estimate the petroleumPpr=P/Ppcfluid properties as a function of the reservoir's readily avail- where, Ppr and Tpr are pseudo reduced pressure and tempera-able characteristics [3]. In this study, a simple, quick and ac- ture, Tpc is pseudo critical temperature and Ppe is pseudo crit-curate empirical model has been derived from experimental ical pressure th中国煤化工Corresponding author. Tel: +98-361-5555333: Fax: +98-361-5559930: E-mail: enema @kashiThis work was supported by the University of Kashan( Grant No. 65460)HCNMHGCopyrighto201, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. All rights reserved.doi:l0.o16s1003-9953(11)603526Joumal of Natural Gas Chemistry Vol 21 No. 2 2012pirical models to predict compressibility factorof com-F=∑Pv(4) monly used empirical correlations and equationstate forcalculating of Z-factor are presented as followTk=∑Tv(5) 2.1. Dranchuk and Abu-Kassem correlation and Heidaryani=1Salarabadi-Moghadasi (HMs)correlationwhere, Pci is critical pressure, Tci is critical temperature, andyi is the mole fraction of componentIn 1975, Dranchuk and Abu -Kassem(DA) proposedBy knowing the composition of natural gas, pseudo pres- Equation 6 with eleven-constant for calculating the gas comsure and temperature of gas can be obtained and used in em- pressibility factors [4]A2A3.A4,A5A7 Asz=A1+rPr+[A6+Tpr r lp2[+第]Ao(1+A1)p+A1n的]+1where, P is reduced density of gas.on Standing and Katz chart for rapid estimation of natural gasIn 2010, Heidaryan et al. presented a correlation based Z-factor as Equation 7[5]:A1+A2In(Ppr)+A3(npP)2+A4(In Ppr)3As A6,,八,AA1+4h(p)+4(mP+m+卫2.2. Azizi-Behbahani-Isazadeh(ABlcorrelationmedium to high pressures. Good results have been obtainedby this method for demethanizer, de-ethanizers, depropaniz-Azizi, Behbahani and Isazadeh in 2010 presented a new ers, debutanizer and wellhead processes. The compressibilitycorrelation for calculating compressibility factor of natural factors for both vapor and liquid phases can be calculated bygases based on 3038 points from Standing and Katz Z-factor the PR equation of state. The PR EOS has been presented byEquation14[小z=A⊥B+CRTPV-b V(V+b-b(V-b(14)+e2.4. Statistical association fluid theory(SAFT) equation ofA=am216+bP108+cP13-21+dln(T)05(9)sfateThe SAFT equation of state is similar to perturbed hardB=e+fr+gPl.56+hPo.124r3033 (10) chain equations, but provides competitive accuracy with UNI-QUAC, NRTL, or Wilsons equation for hydrogen bondingC=iln(T)-1.28+jIn(T-).37+kIn(P)+lIn(P)2+mIn(P)In(T)(11) mixtures. Unlike the interpolation methods, the SAFT equation is based on treating the hydrogen bonding interactionsas chemical reactions. The compressibility factor can be ob-D=1+nr5+oP0680(12) tained from SAFT EOS as Equation 15[8]E=pIn(Tr)8qIn(T)2+rIn(P)+ (13)RI1+zsg+Z+Z25soc(15)8In(P)+tIn( P)In(Tr)3. New proposed compressibility factor correlationThe tuned coefficients in equations 8 to 13 are constantThis work tried to find a rapid method to calculate com-ndependent parameters which can be calculated by curve pressibility factor based on experimental data with high accu-fitting method [6]racy compared with other emnirical methods by reduced pres-sure and redu中国煤化工ring5844 expel-2.3. Peng-Robinson equation of statemental data poCNMHGgas mfixtures andusing all of theni uf uiulupie icgicasiUl alalysis, an empiricalelf the peng-Robinson(PR)equation of state(EOS)is very correlation based on Virial equation of state is suggested to ac-ective for predicting K-values for hydrocarbon systems at curately predict natural gas compressibility factor in the rangeEhsan Sanjari et al/ Joumal of Natural Gas Chemistry Vol. 21 No. 2 2012of101≤Tpr≤30and0.01≤Pr≤150. This new correlationTable 2. Properties of different natural gas used in this studhas two dependent variables(Ppr and Tpr)and eight indepenomposition(mol%)MinimumMaximumdent variables(Al-Ag). The Z-factor from this correlationis expressed as followCarbon dioxide03.4970z=1+APpr+A2P2z+A3PEthane64.56PropaA4+1)(16)i-butane00.7550.0236A 6Ag Ppin-butaneTpa 7+I-pentane0299For further accuracy of this model, the independent vari-Hexane0.058ables in reduced pressures from 0.01 to 3.0 are different fromHeptane plus0000000430.00043.0 to 15, which are presented in Table 14.156333.750.9382Table 1. Tuned coefficients used in Equation 16Pressure(bar)0.1173.51Coefficients30