Use of the GERG-2008 Equation of State for Hydrocarbon Dew Point Calculation Andrew Laughton, DNV GL (Oil & Gas), Loughborough UK andrew.laughton@dnvgl.com American Gas Association Operations Conference, Grapevine, Texas, May 19-22, 2015 Abstract This paper describes how to use the GERG-2008 equation of state (ISO 20765 parts 2 & 3) to calculate the hydrocarbon dew point of natural gas mixtures. Introduction The hydrocarbon dew point of a natural gas is the temperature at which a hydrocarbon liquid mixture first forms from the gas phase mixture (at the specified pressure) on cooling. It is an important property of the gas to know, and in the UK there is a network entry specification that it should be no more than -2 C (at any pressure). There are two basic methods to obtain this property. One is to use a dewscope instrument to measure the temperature at which liquid forms. The other is to analyse the composition of the gas with a gas chromatograph and then calculate the dew point using an equation of state. ISO 23874 (Natural gas gas chromatographic requirements for hydrocarbon dew point calculation, 2006) gives details of how this can be done using any equation of state that can use userdefined fraction input. This is the method routinely used for UK network entry. GERG Equation of State The GERG-2008 equation of state is a recently developed method for the calculation of all thermophysical properties of natural gas mixtures. Example properties that can be calculated are density, compression factor (Z), Joule-Thomson coefficient, isentropic exponent; as well as phase equilibria (vapor-liquid equilibria, VLE). It is applicable to gas, vapor, dense fluid and liquid phases. It is a general purpose, very accurate equation of state. References :- O.Kunz, R.Klimeck, W.Wagner & M.Jaeschke, GERG Technical Monograph 15, (2007) O.Kunz & W.Wagner, Journal of Chemical & Engineering Data, vol.57, pp.3032-3091, (2012) ISO 20765 part 2, Natural gas Calculation of thermodynamic properties Single-phase properties (gas, liquid, and dense fluids) for extended ranges of application, (2015) However, it can only be used for 21 components. Namely : CH 4, C 2 H 6, C 3 H 8, nc 4, ic 4, nc 5, ic 5, nc 6, nc 7, nc 8, nc 9, nc 10, N 2, CO 2, H 2, O 2, CO, H 2 O, H 2 S, He, Ar. It cannot be used for mixtures containing other alkane isomers, benzene, toluene, cyclohexane, methylcylohexane, which are known to occur in natural. These components are important when calculating the dew point from the composition. The GERG equation of state doesn t have a means to specify user-defined components ( fractions ).
Dew Points of Synthetic Mixtures Experimentally measured dew points have been reported for synthetic natural gas mixtures composed of : N 2, CO 2, CH 4, C 2 H 6, C 3 H 8, nc 4, ic 4, nc 5, ic 5, nc 6, nc 7 & nc 8, i.e. various mixtures of 4 to 10 components. The experimental dew temperatures were fitted to the function T = a + b.ln(p) + c.p + d.p 2 + e/(f-p) This function is used in order to smooth the measurements, provide uniformly spaced data, and estimate the cricondentherm (maximum dew temperature) (where dt/dp=0). Data were fitted from the lowest pressure (around 5 bar) to within about 10 bar of the cricondenbar pressure (maximum pressure). The chart below shows the difference between the experimental cricondentherm temperature and that calculated using the GERG, PR (Peng-Robinson) & RKS (Redlich-Kwong-Soave) equations of state (as implemented in the DNV GL program GasVLe). The difference is calculated experiment ( C or K). Label A B C D E F G H I J K L M N O P Q R S T U V W X Ref. 1 2 2 2 2 2 3 3 3 3 4 4 5 5 5 5 6 7 5 8 8 8 8 8 gas no. 1 2 3 4 5 1 2 3 4 1 2 1 2 4 5 1 4 1 4 5 6 8
References :- 1. S.T.Blanco, S.Avila, I.Velasco, E.Rauzy & S.Otin Fluid Phase Equil.,vol.171,pp.233-242,(2000) 2. S.Avila, S.T.Blanco, I.Velasco, E.Rauzy & S.Otin Ind.Eng.Chem.Res.,vol.41,pp.3714-3721,(2002) 3. S.Avila, S.T.Blanco, I.Velasco, E.Rauzy & S.Otin Energy & Fuels,vol.16,pp.928-934,(2002) 4. C.Jarne, S.Avila, S.T.Blanco, E.Rauzy, S.Otin & I.Velasco Ind.Eng.Chem.Res.,vol.43,pp.209-217,(2004) 5. O.Morch, Kh.Nasrifar, O.Bolland, E.Solbraa, A.O.Fredheim &.H.Gjertsen Fluid Phase Equil.,vol.239,pp.138-145,(2006) 6. S.Avila, A.Benito, E.Rauzy, S.T.Blanco & S.Otin Natural Gas Quality Conference, Loughborough UK, 26-28 Nov.2002 7. J.S.Parikh, R.F.Bukacek, L.Graham & S.Leipziger J.Chem.Eng.Data,vol.29,pp.301-303,(1984) 8. E.Solbraa et al., Statoil, GERG WG 1.52 (2005) (V.Louli, G.Pappa, C.Boukouvalas, S.Skouras, E.Solbraa, K.Christensen & E.Voutsas, Fluid Phase Equil.,vol.334,pp.1-9, 2012) GERG & RKS perform similarly difference of around +/- 1 K; whilst PR has difference 0 to -2 K. The conclusion is that the difference between equations of state and with experiment is about 2 K. Thus, when characterizing a real natural gas, any method that shows a difference of no more than about this value (2 K) with industry standard methods can be considered to be good; i.e. this level of difference is attributable to fundamental equation of state differences, and not to the characterization method.
Real Natural Gas Real natural gas contains nitrogen, carbon dioxide and a large number of hydrocarbon compounds. The table below lists the number of possible hydrocarbons :- No. of C atoms Alkanes C n H 2n+2 Cycloalkanes C n H 2n Aromatics C n H 2n-6 1 1 0 0 2 1 0 0 3 1 0 0 4 2 0 0 5 3 1 0 6 5 2 1 7 9 7 1 8 18 23 4 9 35 76 8 10 75 22 (Cycloalkanes are alkyl-cyclopentanes & alkyl-cyclohexanes. Aromatics are alkyl-benzenes) Thus, there are potentially a large number of hydrocarbon components in natural gas. (The table ignores differences due to chirality, e.g. 3-methylhexane (hydrogen, methyl, ethyl & propyl groups attached to a central C atom) and 2,3-dimethylpentane (hydrogen, methyl, ethyl & isopropyl groups) ) Natural gas does not contain unsaturated hydrocarbons (alkenes etc.) A gas chromatogram of typical natural gas is shown below, with many component peaks identified, but many not identified. The heavy n-alkanes are shown in red. In general, above nc6 only the n- alkane peaks can be reliable identified in a routine analysis.
Generally, the gas chromatograph retention time (RT) is proportional to the boiling point of the compound; and generally, the boiling point increases with the number of carbon atoms. However, note that the C9 isomers 2,2,4,4-tetramethylpentane & 2,2,5-trimethylhexane have boiling points lower than n-octane (nc8). Examples of real natural gas mol% composition (from A.Brown, M.Milton, G.Vargha, R.Mounce, C.Cowper, A.Stokes, A.Benton, D.Lander, A.Ridge & A.Laughton, Energy & Fuels, vol.23, pp.1640-1650, (2009)) (n-alkanes in red) :- mol% GasA GasB GasC GasD GasE GasX GasY He 0.0319 0.047 0.042 0.0329 0.008 0.003 0.012 H2 0.0078 0.0007 0.0008 0.01 0.0011 0.0062 0.0004 O2 0.0269 0.004 0.006 0.016 0.005 0.003 0.004 N2 6.112 4.188 2.46 7.156 0.8111 0.445 0.26 CO2 0.0569 1.002 0.4775 0.4713 2.173 1.729 0.673 C1 83.50776 89.28657 93.31329 85.9473 88.06319 88.31612 98.68833 C2 5.76 3.911 2.814 4.358 6.294 7.315 0.336 C3 2.399 0.979 0.5024 1.065 2.037 1.783 0.013 ic4 0.4863 0.1597 0.0874 0.2253 0.1801 0.1625 0.003 nc4 0.8909 0.2048 0.1113 0.3273 0.312 0.1968 0.0027 neoc5 0.0094 0.0049 0.0031 0.0101 0 0 0 ic5 0.2816 0.0565 0.0356 0.124 0.042 0.0216 0.00075 nc5 0.2314 0.0528 0.0331 0.104 0.043 0.0143 0.00073 22dmb 0.0085 0.0042 0.0039 0.0105 0.00058 0.00015 0.00018 23dmb 0.0121 0.0034 0.0029 0.0066 0.0023 0.00055 0.00034 2mC5 0.0546 0.0124 0.01 0.0307 0.0057 0.0011 0.00022 3mC5 0.0309 0.0063 0.0057 0.0173 0.0027 0.00053 0.00012 nc6 0.0327 0.0161 0.0144 0.0399 0.0069 0.001 0.00039 benzene 0.00025 0.025 0.0226 0.00039 0.0028 0.00034 0.000021 Cyc6 0.0171 0.0072 0.0075 0.0077 0.0023 0.00019 0.0032 toluene 0.000031 0.0032 0.0053 0.00008 0.00069 0.000051 0.000015 MeCyc6 0.0056 0.0056 0.0077 0.0046 0.001 0.000061 0.0003 nc7 0.0339 0.0148 0.02 0.0304 0.0049 0.00049 0.00067 C8 0.0022 0.0035 0.0088 0.004 0.00049 0.000017 0.00031 C9 0.00026 0.0012 0.0042 0.00059 0.00014 0.000003 0.0002 C10 0.000003 0.00012 0.00048 0.000035 0.000009 0 0.000083 C11 0 0.000008 0.000031 0.000002 0 0 0.00003 C12 0 0.0000007 0 0 0 0.000013 ppm C10 0.03 1.2 4.8 0.35 0.09 0 0.83 C11 0 0.08 0.31 0.02 0 0 0.3 C12 0 0 0.007 0 0 0 0.13
P/bar Below is an example where the heavy components have been identified in a natural gas sample. It shows the presence of alkane isomers, alkyl-cyclopentanes, alkyl-cyclohexanes and alkyl-benzenes. RT (min) component ppm (mol) RT (min) component ppm (mol RT (min) component ppm (mol) 6.1 ic5 1338.9 9.7 11DMCyc5 17.1 14.0 34DMC6 1.4 6.3 nc5 1059.1 10.0 1c3DMCyc5 20.9 14.6 1t4DMCyc6 19.7 6.5 Cyc5 1.3 10.1 1t3DMCyc5 16.4 14.7 1c3DMCyc6 8.5 6.7 22DMB 81.4 10.2 1t2DMCyc5 26.8 15.2 113TMCyc5 5.2 7.2 2MC5 359.0 10.3 nc7 99.0 15.6 nc8 18.6 7.4 3MC5 143.7 11.3 22DMC6 1.6 16.1 1t2DMCyc6 6.0 7.7 nc6 331.5 11.5 1c2DMCyc5 2.6 16.5 1t3DMCyc6 4.0 8.1 23DMC5 0.2 11.6 MeCyc6 235.3 18.1 22DMC7 1.4 8.2 22DMC5 11.5 11.8 24DMC6 3.0 18.6 EtCyc6 0.9 8.3 24DMC5 10.6 12.0 EtCyc5 7.7 18.7 225TMC6 1.3 8.4 MeCyc5 219.8 12.4 1t2c4TMCyc5 4.5 18.9 1c2DMCyc6 5.4 8.6 223TMC4 3.9 12.6 33DMC6 1.3 19.4 113TMCyc6 0.9 8.9 3EC5 0.4 12.7 1c2t4TMCyc5 2.4 20.9 135TMCyc6 1.2 9.0 Benzene 10.9 13.2 Toluene 9.5 21.3 mxylene 2.5 9.1 33DMC5 6.3 13.4 2MC7 13.2 26.0 nc9 3.3 9.3 2MC6 54.0 13.5 4MC7 3.7 29.3 C10 0.4 9.4 Cyc6 334.7 13.7 3EC6 1.2 33.2 nc10 0.4 9.6 3MC6 47.4 13.9 3MC7 9.3 The above tables show that for processed natural gas it is not necessary to components in above C10. All these components affect the dew line. This is shown in the diagram below :- 100 90 80 70 60 50 40 30 20 10 0-20 -15-10 -5 0 5 10 15 20 T/C Full N-Cn SCN ISO ISO(AN)
The Full (blue) line is calculated using the full component description, with the RKS equation. The magenta line (right hand line) is calculate when all components with the same number of carbon atoms are lumped together and treated as the n-alkane. This gives a dew line substantially higher. The next line (red) is calculated when the components with the same number of carbon atoms are treated as a generic single-carbon-number (SCN) component (C.H.Whitson, Soc. Petr. Eng. J., pp.683-694, Aug. 1983). The next line uses the ISO 23874 method to characterize the same carbon number components. This is similar to the SCN method, but in this case the SCN component is tailored to the components in the actual mixture. This method gives a much better dew line. The best method uses the ISO method but with the major aromatic and naphthene (cycloalkane) components treated separately (i.e. benzene, toluene, cyclohexane and methylcylcohexane are treated as components in the mixture). Because of the large number of components (peaks) above C7, the method in ISO 23874 is to estimate the boiling point of the components in a peak from the retention time based on the bracketing n- alkanes, and to average these boiling points for all the peaks (including the n-alkane) in that range. Thus, to use the GERG equation there needs to be a method of converting this boiling point information into some GERG components. Commingling Model Consider a simple binary mixture. Assume that the vapor phase is an ideal gas mixture and that the liquid is an ideal mixture that obeys Raoult s law. Then the condition of equal fugacity in each phase for each component gives the following equations : P.y=P 1.x P.(1-y)=P 2.(1-x) where P is the total system pressure, y is the vapor mole fraction of component 1 and x is the liquid mole fraction of component 1 (hence, (1-y) is the mole fraction of component 2 in the vapor and (1-x) the mole fraction of component 2 in the liquid). P 1 is the vapor pressure of component 1 (at the system temperature, T) and P 2 is the vapor pressure of component 2 (at T). Eliminating x from the pair of equations above gives the condition for vapor-liquid equilibrium to be : 1/P = y/p 1 + (1-y)/P 2 Assume that the temperature dependence of P 1 and P 2 is given by the Clausius-Clapeyron equation, then : P 1 = A 1.exp(B 1 /T) P 2 = A 2.exp(B 2 /T) where A 1, B 1, A 2 & B 2 are component specific parameters. B 1 & B 2 are related to the enthalpy of evaporation. If component 1 has a dew temperature of T 1 at pressure P and component 2 a dew temperature of T 2 at P, then parameters A 1 and A 2 can be eliminated. If it is further assumed that B 1 = B 2 = H (a universal enthalpy of evaporation, then P 1 = P.exp(H/T-H/T 1 ) P 2 = P.exp(H/T-H/T 2 ) Thus, the condition for a dew point becomes exp(h/t) = y.exp(h/t 1 ) + (1-y).exp(H/T 2 ) To get a mixture (of 1 & 2) with a dew point temperature of T (kelvin) (at pressure P), the amount of component 1, y, is given by y = [exp(h/t) exp(h/t 2 )]/[exp(h/t 1 ) exp(h/t 2 )] where T 1 is the dew temperature (the same as the boiling point for a pure substance) at pressure P, and T 2 is that for component 2 at P. In order to optimize the value of H, normal boiling points for a range of hydrocarbons were considered (i.e. P = 1.01325 bar). At this low pressure the assumption of ideal vapor phase is reasonable, and since components 1 & 2 will be adjacent alkanes the assumption of an ideal liquid
mixture will be good. The assumption of the Clausius-Clapeyron equation is also reasonable around the normal boiling point. For a given substance, with boiling point T, the n-alkane with boiling point T 2 just above T (N C atoms) and the n-alkane with boiling point T 1 just below T (N-1 C atoms) are chosen. The value of H is adjusted so that the mole fraction of nc N-1 (y), using the equation above, in a mixture of nc N and nc N-1 gives a dew point calculated using the GERG equation of state of T. A large range of alkane isomers, alkyl-cycloalkanes, and alkyl-benzenes with boiling points in the range of 309 K (nc 5 boiling point) to 447 K (nc 10 boiling point) were used to establish the optimal values for H. The best approach was to use a fixed value for each C atom range in the table below :- T (K) H nc5 309.214 nc6 341.865-3949 nc7 371.533-4216 nc8 398.773-4485 nc9 423.913-5124 nc10 447.270-5481 (The above boiling point T are the actual values calculated by the GERG-2008 equation of state.) Thus, the procedure is to apportion a non-gerg component, with boiling point T, to the bracketing n- alkanes with N-1 C atoms below, and N C atoms above. For example, this could be a C N isomer, since the n-alkane always has the higher boiling point (for the same number of C atoms). The fraction of nc N-1 (y) is given by and the fraction of nc N as 1-y. (neoc5 (2-methylpropane) is apportioned as 0.752 nc4 and 0.248 ic5.) For example, benzene (bp 353.242 K) is between nc6 & nc7, so the fraction of nc6 is given by y = [ exp(-4216/353.242) - exp(-4216/371.533) ]/[ exp(-4216/341.865) - exp(-4216/371.533) ] i.e. 0.709 nc6 and 0.291 nc7. Hence, if the original mol% of benzene was 0.1, then 0.0709 is added to nc6 amount and 0.0291 added to nc7. The vapor pressures curves of benzene, n-hexane & n-heptane are shown below, with the dew point curve of the hexane/heptane mixture that matches the benzene vapor pressure curve :-
The vapor pressure of benzene (and other non-gerg components) was calculated using a Wagner vapor pressure equation (3/6 and 2.5/5 forms), generally from IHS ESDU data items. Although the fit was optimized to the (normal) boiling point (1.01325 bar), the complete vapor pressure curve is accurately modeled. Note that for a mixture there are two phase boundaries the dew line and the bubble line. For a pure substance the dew and bubble lines are identical, and called the vapor pressure curve. From the values of H specified above, it is the mixture dew line that matches the pure component vapor pressure curve. Dew Points of Natural Gas The above procedure has been implemented as an Excel function in the GasFrac.xla AddIn as part of the GasVLe package. The picture below shows an example calculation. Column A is the identified component some are GERG components, and some are not. Some of the heavy components are not identified and only a representative boiling point is given (according to the method of ISO 23874). Column B is the component mol%. Column C is the component specification for GasVLe, with some components characterized as userfractions using the column A boiling point. This input can be used for RKS & PR equations of state but not GERG. The input specific gravity (SG) and boiling point ( C) are used with the Kesler-Lee equations (M.G.Kesler & B.I.Lee, Hydrocarbon Processing, p.153, March 1976) to provide the component critical temperature (Tc), critical pressure (Pc) and acentric factor ( ) that are needed by cubic equations of state. The SG used is the SG of the corresponding n-alkane (SG is the liquid mass density at 60 F divided by the mass density of liquid water at 60 F), whilst the BP comes from the retention times of the identified peaks in the gas chromatograph. Column E is the GERG components used to model this mixture; Column F is the apportioned composition.
Note that the compositions in column F of N2, CO2, CH4, C2H6, C3H8 & ic4 are unchanged; nc4 & ic5 change slightly due to the neoc5; whilst nc5 to nc10 change according to the equation above. The boiling points of the named components are :- 22DMB 23DMB 2MC5 3MC5 Benz Cyc6 Tol MeCyc6 bp (K) 322.883 331.129 333.414 336.423 353.242 353.883 383.783 374.088 Each non-gerg component is individually apportioned to the neighbouring n-alkanes, i.e. the result of several components are added to the n-alkane. The alternative approach, not used, is to calculate an average boiling point of all the components, in the same n-alkane range, and then apportion that single lumped component. The difference in these methods doesn t make a large difference.
The diagram below shows the dew lines calculated using the RKS method using fractions (columns B & C above), and the GERG method (columns E & F). The dew lines are drawn only up to the cricondenbar (maximum pressure), and not to the end of the dew line at the critical point, since the main interest is around the cricondentherm (maximum temperature). The difference, at the cricondentherm (maximum temperature) is less than 1 K. This result is typical of many other mixtures tested. Generally, the GERG method is around 1 K higher than the fraction method using RKS. This mixture can also be used to demontrate the sensitivity of the dew temperature calculation to the amount of the heavy components. The mixture above has 13 ppm(mol) $fr8, 1.4 ppm $fr9 and 0.1 ppm $fr10. In order to increase the cricondentherm temperature by 1 C, $fr8 would need to increase to 36 ppm (methane adjusted to keep the total to 100 mol%), or $fr9 increased to 11 ppm, or $fr10 increased to 3 ppm.
Potential Hydrocarbon Liquid Content An alternative to the dew point specification for gas quality, is to use the potential hydrocarbon liquid content (PHLC). In this case the sample gas is cooled to a required temperature (at a specified pressure) and the amount of liquid (if any) that forms is measured. This is measured as the mass of liquid per standard volume of the gas, e.g. mg/sm 3. This is described in ISO 6570 (Natural gas determination of potential hydrocarbon liquid content gravimetric methods, 2004). The method outlined above can also be used with the GERG-2008 equation of state to calculate PHLC. In this case an isothermal flash (VLE) calculation is done (at the specified T & P), rather a dew temperature calculation. The agreement with RKS is typically around 5%. Conclusion A method has been developed so that the GERG-2008 equation of state can be used to calculate the hydrocarbon dew point of natural gases with an accuracy as good as other industry standard methods, i.e. around 2 K. Although the motivation was to find a method to enable the GERG-2008 equation of state to be used for hydrocarbon dew point calculations, the approach could be applied to any equation of state. Since the GERG components only go up nc10 it is not possible to use this method if the gas contains a significant amount of C11 or C12. The best that can be done in that case is to add that amount (or possibly an artificially increased amount) to nc10 and allow for the possibility of the calculated dew temperature being less than it should be.