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Home , Compressibility factor, Gas composition

Accurate Calculations of Factor for Pure and Mixtures

OBEIDA, Tawfic A, AGOCO, Libya and Mining University Leoben, Austria

HEINEMANN, Zoltán E., Mining University Leoben , Austria

KRIEBERNEGG, Michael, Mining University Leoben, Austria

Paper presented at the Sth European Conference on the Mathematics of Oil Recovery, Leoben, Austria, 3-6 Sept. 1996

ABSTRACT in non-compositional simulators. An accurate method to prediet volumetrie behavior of gas INTRODUCTION mixtures, such as in the case of underground gas storage The is an important property for where the in-situ gas is mixed with the injected gas, is gases to calculate (formation volume factor) of presented in this paper. This method accurately calculates gases and the coefficient of isothermal compressibility the compressibility (Z) factor of pure hydrocarbon, non- under given conditions (, ). hydrocarbon gases and gas mixtures. To account for the non-additive behavior of volumes of hydrocarbon and non- It is important to calculate the Z-factor more accurately, hydrocarbon gases, correction functions were developed specially for gas mixtures, in order to predict the volumetrie from correlation of data (Z-factors) generated by the Peng- gas behavior more reasonable. In compositional simulators Robinson . The correction functions are the calculations of the Z-factor are accurate, but for every function of , pressure and temperature, so condition the cubic equation of state is solved for Z-factor. the Z-factor can be calculated explicitly from gas The solution procedure involves iterations such as in composition under different reservoir conditions. Newton Raphson method. These iterations and convergence checking procedure consumes, some times, a considerable Several comparative examples are presented to compare part of CPU time for just calculating gas properties (Z- the Z-factors calculated by the correction functions with factor). The CPU time should be used more efficiently those calculated by the Peng-Robinsion equation of state and wisely in the simulator. On the other side in the (PR-EOS) and with measured data published in the non-compositional simulators, the Z-factoi values are literature. The comparison results indicated that the average tabulated for certain gas composition and and a relative deviation (ARD) is 3% for gas mixtures, 2% for linear interpolation procedure is used to calculated those pure hydrocarbon, non-hydrocarbon gases and less than Z-factor values which are not listed in the table. This 1% for pure components (, , carbon procedure leads to erroneous calculations of Z-factor dioxide). A stable method of calculating Z-factor for gases specially for gas mixtures where the linear interpolations from their composition is presented. This method is iteration are no longer accurate. The calculation procedure of Z- free so the CPU time is minimized. More accurate values factor using the correlation functions presented in this paper of Z-factor can be calculated which are much better than bas two advantages: Obtaining an accurate value of Z-factor those obtained by linear interpolations. and saving CPU time for other more important calculations The correction functions can be incorporated in any non- in the simulator. compositional simulator to calculate the Z-factor directly BACKGROUND without any iterative procedures, which occur in compositional simulators during the calculations of Z-factor Some impurities such as nitrogen and carbon dioxide are by the equation of state. These functions also eliminate often existed in appreciable amounts in natural gases. The the inaccurate linear interpolations of tabulated Z-values , Z-factor for non-hydrocarbon components of natural gas specially during calculations of Z-factor for gas mixtures, in certain corresponding states differ markedly from those of hydrocarbons. This makes the non-hydrocarbon and

517 2 Accurate CalcuJations of Compressibility ECMOR V, 1996 Factor for Pure Gases and Gas Mixtures hydrocarbon components not quit additive. Eilerts, Muller T = Temperature, and Carlson I studied the compressibility of natural gas p = Pressure. and nitrogen mixtures. They proposed a method to calcuJate the Z-factor for the gas mixture by introducing a correction The additive volume correction function (Fa) is a function factor into the additive foon in Eq. l. of temperature, pressure, fraction of the non- hydrocarbon gas in the mixture and the mole fraction of z, =c{nZn+(l-n)Zh} (1) carbon dioxide in the non-hydrocarbon gas. The function Where: actual Z-factor for gas mixture, z". = Fa. is symmetrical with respect to xm and equals to one at X Zn = Z-factor of the nitrogen in the mixture, m equals to zero (pure hydrocarbon gas) also at xm equals ~ = Z-factor of hydrocarbon gas, to one (pure non-hydrocarbon gas) as shown in Fig. l. n = mole fraction of nitrogen in the mixture Since the function Fa. is symmetrical with respect to ~ ' it was calcuJated only for 0 < xm < 0.5 as following: Where c is an arbitrary factor to account for the fact that 2 volumes of hydrocarbon and non-hydrocarbon are not quit Fav =aO+alP+~p (3) additive. The values of the factor c were presented in Where ao' ~ and ~ are parameters function of xm which charts for different mixtures at certain pressures and can be calcuJated from Eq. 4: . ao(xm) = bo + qXm } Olds, Sage and Lacey 4 studied the effects of carbon dioxide al(xm)=CO+ClXm ; (4) on the compressibility of methane. They computed the additive-volume correction factors for few methane-carbon a2(xm) = do +d1xm dioxide mixtures at different pressures and temperatures. If~ is grater than 0.5, then ~ in Eq. 4 should be substituted To obtained the full range of mixture compositions , by (l-xJ. The parameters bo, bI' co' cl' <10 and dl are interpolations were used. function of the mole fraction of carbon dioxide in the non-hydrocarbon gas (XcOO>and they can be calculated The main disadvantages of the above method are that the from Eq. 5 to Eq. 7 as following: values of the correction factor (c) were computed for a few and limited gas mixtures using pure components such as nitrogen or carbon dioxide to be mixed withthe 1.0 1 5,...... ~~,....~~"T'""~~""T""~~....,.~~..., hydrocarbon gas and to obtained a fuIl range of mixtures, interpolations were the only option left to be used. In this paper a more comprehensive method is proposed to eliminate the above mentioned limitations . We propose ~ . a similar method to calculate the Z-factor for any gas ~ 1.01 ················r· ··T······...... ···· mixture, but instead of a constant c, a function was ~ Ol introduced to repJace the constant c as shown by Eq. 2. § ..Q METHODOLOGY ~Ol ~ 1.005 . In this section we like to present the calculation methods "Cl of the Z-factor for gas mixtures, pure hydrocarbon gases < and pure non-hydrocarbon gases. Z~factor of Gas Mixtures To calculate the Z-factor for a mixture of hydrocarbon 1~--~--~------L-~----~ o o.z 0.4 0.6 0.8 and non-hydrocarbon gases, we propose the following equation: Mole Fraction Flue gas (Xm)

Zm = Fav(T.p,Xm,xcCY).)X {ZHc(1-Xm)+ ZNHcXm} Figure 1: Additive volume correction function of methane (2) and fIue gas (87%N2) at 60T Where: Fa. = Additive volume correction function, ~c = Z- factor for the non-hydrocarbon gas bO(XC02) bOl + b02XCO + bfJ3X:o + b04X: } ~c = Z-factor for the hydrocarbon gas, = , a , Mole fraction of the non-hydrocarbon ~ = bI (XC02) = bil + bl2Xco ,+ b13X:o , gas in the mixture, (5) Xco2 = Mole fraction of CO in the non- 2 Co(Xco2) =cOl +c02Xco2 +C03X';02} hydrocarbon gas, (6) Cl (Xco2)=

518 ECMOR V, 1996 OBEIDA, T. A.; HEINEMANN, Z.E.; KRIEBERNEGG, M. 3

Z-factor of hydrocarbon gases do(Xco2) = dOl + d02Xco2 + d03Xco2 The Z-factor of any hydrocarbon gas (dry gas or rich 2 } (7) gas) can be calculated in two steps. First, the Z-factor of dl (Xco2) = dll + d12Xco2 + d13X;o2 pure methane is calculated, then the Z-factor of the richer The parameters bOl' b02, b03' bw bil' b12, b13, cOl' c02' coo' gas can be calculated second. cII' C12' cl3' dOl' d02, <103' dil. d12, and dl3 are function of Z-Factor of pure Methane temperature and they can be calculated from Eq. 8 to Eq. The compressibility factor of pure methane can be 13 as following : 2 calculated directly by the correlation in Eq. 14 as bOl = aOl + /301 T +801T following. 2 b02 = a02 + /302 T + 802T Zet = llo + alP + ~p2 (14) (8) Where: ZCI = Z-factor of pure methane. b03 = a03 +/303T +803T2 30, al and ~ are parameters function of temperature which b04 = a04 +/304T +804T2 can be calculated from Eq. 15: 2 ao(T) = bo +b1T+b2T bll = al1 + /311T} T (9) 2 b12 = a12 +/312 ~(T)=co +c1T+c2T (15) b13 = a13 + /3l3T 2 ~(T)=do +d1T+d2T

2 bo, b., ....., d2 are constants obtained from regression. COl =

)X ZCl T T2 ZHC = Fhc(p,T,KCI (16) Cll =

2 Where: Fhc (p,T'~I) and ZHCare the correction function C12

519 4 ACcurate Calculations of Compressibility ECMOR V, 1996 Factor for Pure Gases and Gas Mixtures

Table I: Natnral Gas Composition and values of I Methane Deviation Foctor (KcI) I Comp. Dg (1) Wgl (2) Wg2 (3) GC (4) N2 0.690 0.00 0.32 0.00

(19) C02 0.000 0.00 1.67 0.00 Cl 87.710 82.28 71.02 75.27 C2 6.490 9.52 15.74 7.66

C3 3.220 4.64 7.51 4.41

I-C4 0.760 0.64 0.89 0.00 n-C4 0.580 0.96 1.94 3.09

I-CS 0.210 0.35 0.34 0.00

n-CS 0.120 0.29 0.27 2.21 C6 0.106 0.29 0.27 2.06 cO(T) = cOl +c02T+ c03T2 C7+ 0.114 1.03 0.03 5.30 cl (T) =cll +c12T+c13T2 (21) c2(T) = c21 +c22T+ c23T2 Kc1 1.18 1.86 2.59 3.86

c3(T) =c31 +c32T+c33T2 (1) Dry gas (separator gas), Eilerts2 (2) Wet gas, McCain3 (p-200). (3) Wet gas, McCain3 (p-216). (4) Gascondensate,Standing5 (p-71). dO(T) = dOl +d02T+d03T2

dl (T) = dll + d:t2T+dl3T2 (22) T2 d2(T)=d21 +d22T+dz3

d3(T) = d31 +d32T+d33T2 eO(T)=eOI +e02T+ e03T2 ~'·'1 . T2 el(T) = ell +eI2T+e13 ~ 0.6 j-" ( i······· (23) _ 2 e2(T)-e21 +e22T+ e23T ~ i i i l ~ 1 _ 2 = J------i.' -...... : : ~(T)-e31 +e32T+e33T ~ 0.7 -+-- 50 bar ~ The parameters (bOl' bQ2' , e33) are fixed constants I: obtained from regression, 8 For illustration purposes, the correction function of different . 0.6 --0-- 200 ba( hydrocarbon gases, listed in Table 1, was plotted versus ~250bar methane deviation factor to see the relationship between .~300bar Fhe and ~I' Figure 2 indicates that if the hydrocarbon gas O.s ... _-_ ...... i...~~-..L~~--L....~...... J is pure methane (~I= 0), the correction function equals .0 2 3 4 5 to one. If the gas becomes richer (with increasing KCI values), the correction function becomes smaller and less Methane Deviation factor (KCt) than one. The flow chart in Figure A-2 illustrates the calculation procedure of Z-factor for hydrocarbon gases. Figure 2: Correction function of hydrocarbon gas versus methane deviation factor at 60'C.

520 ECMOR V, 1996 OBEIDA, T. A.; HEINEMANN, Z.E.; KRIEBERNEGG, M. 5

Z-factor of Pure Non-hydrocarbon Components P'"hc(P, T, XC02) = ao + açp + ~p2 + ~p3 (29) The compressibility factor of non-hydrocarbon components The parameters 30, al ' a2 and Il:l are function of XC02 such as pure nitrogen and carbon dioxide can he calculated which can be calculated from Eq. 30. as following: 2 ao(Xc~)=bo+blXc~ +b2Xc~ Z-Factor of Pure Nitrogen 2 The compressibility factor of pure nitrogen can he calculated ~(Xc~)=cO+clXc~ +c2XClh directly by the following correlation in Eq. 24. 2 a2(XClh )=do +dlXc~ +d2Xc~ ZN2 = ao + açp + ~p2 (24) 2 Where: ZN2 = Z-factor of pure nitrogen. a3(Xc~)=eO+elxClh +e2xClh (30) The parameters 30, al and Il:l are function of temperature which can be calculated from Eq. 25. The parameters bo, bI' b2, co. cl' c2' do, dl' a, eo' el and e2 2 are function of temperature and they can be calculated aO(T) b +'1T+b2T = O from Eqs.20 to 23. The constants (bOl' bOl' .... , e33) are 2 obtained from regression. al (T) = Co + CtT +c2T (25) Figure 3 illustrates the relationship between the correction ~(T)=dO +dtT+~T2 function (Fnhe ) and the mole fraction of carbon dioxide for different non-hydrocarbon gases at 60T. bo, b., , ~ are constants obtained from regression. The correction function (Fnhe ) equals to one for pure nitrogen Z-Factor of Pure Carbon Dioxide (XC02= 0 ) and becomes smaller (Iess than one) if the Pure carbon dioxide is much more compressibie than content of carbon dioxide increases as shown in Fig. 3. nitrogen so it is recommended to. use a fourth degree polynomial function of pressure to calculate directly the Z-factor of this gas as shown by Eq. 26. 3 4 ZC02 = ao + alP + ~p2 + a3p + a4P (26) ...... 0.9 Where: ZC02 = Z-factor of pure carbon dioxide. 30, al ' ~ ' Il:l and a, are parameters function of temperature which are calculated from Eq. 27. 0.8 ·················I··················i············ 3 aO(T) =bO +'1T+b2T2 +b3T 2 3 at(T)=cO+CtT+c2T +c3T "=:~Ir··i . 3 ~(T) =dO +dtT+d2T2 +d3T (27) ..=::111 . 2 3 ~(T) =eO +etT+e2T +e3T 0.5 a4(T) = fo + ftT+ hT2 + f3T3 o 0.18 0.36 0.54 0.72 0.9 bo, b., , f3 are constants obtained from regression. Mole fractIon of carbon dIoxIde (XC02) Figure 3: Correction function of non-hydrocarbon Z-Factor of Non-Hydrocarbon Gases gasesat 60T. The calculation method of Z-factor for non-hydrocarbon gas is similar to the method of calculating 2i.rC' but it is The flow chart in Figure A-3 illustrates the calculation based on Z-factor of pure nitrogen rather than the Z-factor procedure of Z-factor for non-hydrocarbon .gases. of pure methane, as shown by Eq. 28. EVALUATION OF RESULTS ZNHC = P'"hc(p.r, XC02) x ZN2 (28) The evaluation of results was accomplished by comparing Where: Zrmc = Z-factor of non-hydrocarbon gas, the Z-factor values calculated by the proposed method F nhe = Correction function of non-hydrocarbon and those values calculated by the Peng-Robinson equation gas. of state (PR-EOS) or measured values of Z-factor (if available). To quantify the differences, the average relative The correction function of the non-hydrocarbon gas is a deviation (ARD), which is calculated as the absolute value function of pressure, temperature and the mole fraction of of the difference between the calculated values by the carbon dioxide in the gas

521 6 Accurate Calculations of Compressibility ECMOR V, 1996 Factor for Pure Gases and Gas Mixtures measured values) divided by the PR-EOS values (or 1- Temperature range: from 40·C to 120·C, measured values), was calculated for each comparison case. 2- Pressure range; from 5000 KPa (725 psi) to 30 MPa The comparisons were done for pure components (N2' CO2, (4350 psi).

CH4), pure gases (hydrocarbon , non-hydrocarbon gases) 3- Hydrocarbon gas composition: from pure methane and gas mixtures. (Kcl=O) to a gascondensate having Kei less than 5.0. Pure Components Only sweet hydrocarbon gases are considered in this . 1- For pure components such as nitrogen and carbon dioxide, 4- Non-hydrocarbon gas composition: from pure nitrogen the comparison between the calculated values (by the to a gas with 90% carbon dioxide content. correlation functions in Eq. 24 and Eq. 26 ) and measured 2 values published by Eilerts , indicate that ARD less than CONCLUSIONS 1% from the measured values as shown in Figures A-4 1. A stabie method of calculating Z-factor from gas andA-5. composition is presented. This method is iteration free, 2- The Z-factors calculated by the correlation function since the parameters are calculated only once, sothe CPU for pure methane (Eq. 14) were compared with calculated time is minimized. values by the Peng-Robinson equation of state (PR-EOS). 2. Better values of Z-factor than those obtained by linear The comparison results indicate no deviation from the PR- interpolation, from tabulated values, are derived. EOS values as shown in Figure A-6. 3. The correction functions are easy to program also they Pure Hydrocarbon Gases can be used in spread-sheet applications for wide range of 1- The Z-factors calculated by Eq. 16 for a dry hydrocarbon temperatures and pressures. gas (separator gas) were compared with measured data 2 published by Eilerts • The comparison results indicate that NOMENCLATURE the ARD is less than 2% as shown in Figure A-7. Symbols 2- The Z-factors calculated by Eq. 16 for rich hydrocarbon F av Additive volume correction function, 3 gases, two wet gases (Wg1, Wg2) from McCain and gas Fbe Correction function for hydrocarbon gas, condensate (Ge) from Standing , were compared with the Fuhe Correction function of non-hydrocarbon values calculated by the PR-EOS. The comparison results gas, indicate that the ARD is about 2% as shown in Figure Kei Methane deviation factor, A-8. Mi Molecular weight of the i th component Pure Non-Hydrocarbon Gases in the hydrocarbon gas The Z-factors calculated by Eq. 28, for several pure non- p Pressure; [bar] hydrocarbon gases having carbon dioxide content ranging T Temperature; [T] from 15% up to 90%, were compared with the values x.n Mole fraction of non-hydrocarbon gas, calculated by the PR-EOS. The comparison results indicate Xc02 Mole fraction of carbon dioxide, that theARD is about 1.5% as shown in Figure A-9. Yi Mole percent of the i th component in Gas Mixtures the hydrocarbon gas, 1- The Z-factors for gas mixtures calculated by Eq. 2 ZCI Z-factor of pure Methane, were compared with measured data, mixtures of separator ZC02 Z-factor of pure carbon dioxide, gas and 7.907% nitrogen and separator gas and 18.28% ~c Z-factor of hydrocarbon gas, 2 nitrogen, published by Eilerts • The comparison results ~ Z-factor of gas mixture, indicate that the ARD is less than 2% as shown in Figures ~2 Z-factor of pure nitrogen, A-1O and A-Il.o ~c Z-factor of non-hydrocarbon gas. 2-. The Z-factors for gas mixtures calculated by Eq. 2 were compared with the calculated values by the PR-EOS ACKNOWLEDGMENT for a wet hydrocarbon gas (Wg1), at 40"C, mixed one The authors are grateful to the University of Mining in time with a flue gas (85% N2 ' 15% CO~ and second Leoben (Austria) for it's support. time with a non-hydrocarbon gas (15% N2 ' 85% CO2). SI. Metric Conversion Factors The comparison results indicate that the ARD is less than psi x 6.894 757 E+OO= kPa 2% as shown in Figures A-12 and A-13. bar xJ.OOOE+2=kPa 3- Same as in point 2, but the hydrocarbon gas is richer (Wg2) at 60·C. The comparison results indicate that the REFERENCES ARD is about 2.5% as shown in Figures A-14 andA-15. 1- Eilerts, C.K., Carlson, H.A., and Muller.: "Effect of Added Nitrogen on Compressibility of Natural Gas," LIMITATIONS World Oil (June 1948), 128 (part 1), pp. 129-140. The proposed functions presented in this paper were 2- Eilerts c.x.. " Relations of Gas-Condensate developed for certain ranges of temperatures, pressures Fluids," US Bureau of Mines, (1959) Monograph 10, and composition of different gases. The followingare the volume 11,pp. 761-784. ranges of these variables :

522 ECMOR V, 1996 OBEIDA, T. A.; HEINEMANN, Z.E.; KRIEBERNEGG, M. 7

3- McCain, W. D.: The Properties of Petroleum Fluids, second edition, PennWell Books, Tulsa, Oklahoma (1990) 548, pp. 200-216. 4- Olds, R.H., Sage, B.H., and Lacey, W.N.; "Partial Volumetrie Behavior of Methane Carbon Dioxide system," API Fundamental Research on Occurrenee and Recovery of Petroleum (1943) 44. 5- Standing M.B.: Volumetrie and Phase Behavior of Oil Field Hydrocarbon Systems, SPE of AIME, Dallas, USA, (1977) 130, P 71.

APPENDIX A

[nIer Z-Hr ga. and/or End Z-NHr ga. Figure A-2: Calculation procedure of Z-factor for hydrocarbon gases

Figure A-I:: Calculation procedure of Z-factor for gas mixtures.

End Figure A-3: Calculation procedure of Z-factor for non- hydrocarbon gases.

523 8 Accurate Calculations of Compressibility ECMOR V, 1996 Factor for Pure Gases and Gas Mixtures

1.14 • 100 F-MD • 40 C-EOS --lOOF-CF --40C-CF o 130F-MD 1.12 60 C-EOS --130F-CF --60C-CF • 160F-MD • 100 C-EOS 1.1 --160F-CF --100C-CF I> 250 F-MD 1.08 --250F-CF 0 ..o ti ti ~ 1.06 :! 0.95 N N 1.04

1.02 0.9

l • o .9 8 L...I...L...I.-L..1...JL....L..JL....L..J...J....I...J....1...L..J.....L...J...J...l...L...L...L.1..J.-L...L...l...L...L..W

800 12001600200024002800320036004000 1000 1500 2000 2500 3000 3500 4000 Pressure (psia) Pressure (psl) Figure A-6: Z-factor of pure methane, calculated by Figure A-4: Z-factor of pure nitrogen, measured data! and PR-EOS and calculated by the correlation calculated by the correlation function at function at indicated temperatures. indicated temperatures.

0.9 • 130 F-MD _130F-CF o 160 F·MD 0.8 --160F-CF 0.95 • 190 F-MD _190F-CF e 220 F-MD 0.7 --220F-CF 0.9 .9 0 ~ 0.6 N 0.85

0.5 ......

0.8 ...:- ~ ...... ; ; ~ . 0.4 .. I I I I r······r··

8 0 0 '1 2 0 0 1 6 0 0 2 0 0 0 2 4 0 0 2 8 0 0 3 2 0 0 3 6 0 0 4 0 0 0 1000 1500200025003000350040004500 Pressure (psia) Pressure (psia)

Figure A-5: Z-factor of pure carbon dioxide, measured Figure A-7: Z-faftor of separator gas (dry gas), measured data 2and calculated by the correlation- data and calculated by the proposed method function at indicated temperatures. at indicated temperatures.

524 ECMOR V, 1996 OBEIDA, T. A.; HEINEMANN, Z.E.; KRIEBERNEGG, M. 9

0.9 100 F-MD --100 F-CF 0.85 o 130 F-MD --130F-CF & 160 F-MD 0.8 0.95 --160F~F rrrTt .. 0.75 0 0 ij ij .... ( ~ ~ ;...... ~ 0.7 ~ 0.9 • i i i N N 0.65 0.85 r1 1000 1500 2000 2500 3000 3500 4000 1600 2000 2400 2800 3200 3600 4000 Pressure (psl) Pressure (psla) Figure A-8: Z-faetor of rieh hydroearbon gases, Figure A-lO: Z-faetor of separator gas and nitrogen calculated by PR-EOS and calculated by the (7.907%) mixture, measureddata' and proposed method at 40·C. calculated at indicated temperatures.

1.1 • 15%C02-EOS --15%C02-CF 100F-MD .... _ . " 40%C02-EOS· --100" F-CF -- 40%C02-CF 0.98 0 130F-MD • 60%C02-EOS -- 60%C02-CF --130 F-CF o 80%C02-EOS L 0.96 160 F-MD 0.9 -- 80%C02-CF • • 90%C02-EOS --160F-CF -- 90%C02-CF 0.94 0.8 .. 0 ti .:! 0.92 0.7 N 0.9 0.6

0.88 0.5 0.86

0.84 1000 1500 2000 2500 3000 3500 4000 Pressure (psl) 1600 2000 2400 2800 3200 3600 .4000 Figure A-9: Z-factor of non-hydroearbon gases, Pressure (ps la) calculated by PR~EOS and calculated by the proposed method at 40·C Figure A-II: Z-faetor of separator gas and nitrogen (18.28%) mixture, measured data and ealeulated at indicated temperatures.

525 10 Accurate Calculations of Compressibility ECMOR V, 1996 Factor for Pure Gases and Gas Mixtures

1.0 5 fi!=!:===:::::c:!=~...... ,....,.....-r-r-p-'-'-',....""""'T'~ Xm=.25-EOS -- Xm=.25-CF o Xm=.5-EOS --Xm=.5-CF .. Xm=.75-EOS -- Xm=.75-CF

0.95 0.95 (; Ü :! 0.9 N 0.9 0.85

\ 0.8 0.85

0.75

0.7

1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 Pressure (psl) Pressure (psl) Figure A-12: Z-factor of wet gas (Wgl) and flue gas Figure A-14: Z-factor of wet gas (Wg2) and flue gas (15%CO~ mixture, calculated by PR-EOS .(15%CO) mixture, calculated by PR-EOS and by the proposed method at 40T. and by the proposed method at 60°C.

0.9 I!t~~~~~!!""-'!I .. Xm=.25-EOS o Xm=.25-EOS -- Xm=.25-CF -- Xm=.25·CF ...., L 0 Xm=.5-EOS 0.85 • Xm=.5-EOS : : -- Xm=.5-CF i i. Xm=.75-EOS --Xm=.5-CF ...... -- Xm=.75-CF 0.85 ···T:::::·.············ . .••• ...•...... • :•.•. 0.8

(; 0.75 (; Ü Ü 1 :! :! 0.8 ...111 , i N N 1 0.7 ~ 0: : : :

0.65 ! .: ! ! : 0.75 ····f··...... · ....·ö..·+...... ·....+..·.... 0.6 I i ~

1000 1500 2000 2500 3000 3500 4000 1000 1500 2000 2500 3000 3500 4000 Pressure (psl) Pressure (psl) Figure A-13: Z-factor of wet gas (Wgl) and non- Figure A-IS: Z-factor of wet gas (Wg2) and non- hydrocarbon gas (85%CO) mixture; hydrocarbon gas (85%CO) mixture, calculated by PR-EOSand by the proposed calculated by PR-EOS andby the proposed method at 4OT. metbod at 60°C. .

-.'1'-..

526