Evaluation of the Cubic-Plus-Association Equation ... - ACS Publications

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Evaluation of the Cubic-Plus-Association Equation of State for Ternary, Quaternary, and Multicomponent Systems in the Presence of Monoethylene Glycol Fragkiskos Tzirakis,*,† Eirini Karakatsani,‡ and Georgios M. Kontogeorgis† †

Center for Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering, Technical University of Denmark, Kgs. Lyngby, DK2800, Denmark ‡ Haldor Topsøe A/S, Nymøllevej 55, Kgs. Lyngby DK2800, Denmark S Supporting Information *

ABSTRACT: Dew point specifications are of high interest in the natural gas industry. The CPA equation of state (EoS) was previously validated against both water content and phase equilibrium data. Moreover, solid model parameters were estimated for four natural gas main components (methane, ethane, propane, and carbon dioxide). In this study we have extended the use of CPA EoS to perform equilibrium temperature calculations for natural gas main components with (mono-)ethylene glycol (MEG) as an inhibitor. The ternary systems with aqueous MEG solution include methane, ethane, propane, carbon dioxide, and hydrogen sulfide. The quaternary systems with aqueous MEG solution include methane + ethane, methane + propane, methane + n-heptane, and methane + n-octane. Three multicomponent systems (>4 components) were also studied. The temperature range of the literature data is between 241.25−333.15 K, and the pressure range is between 0.1−24.8 MPa. The results in all cases are compared against experimental data, and very good agreement with experimental data is obtained.

1. INTRODUCTION

water content of several binary and multicomponent hydrate mixtures with alcohols. The phase equilibrium of low molar mass alkanes (CH4, C2H6, C3H8, etc.) and MEG has been reported by some authors.5−11 The CH4 solubility has been measured by Zheng et al.6 using a rocking equilibrium cell from 323 to 398 K, up to 40 MPa. They compared their solubility data with Jou et al.7 who reported solubility of CH4 in MEG and DEG from 298 to 408 K up to 20 MPa. The agreement between both data sets is generally good. Jou et al.8 reported ethane solubility in MEG from 298 to 398 K up to 20 MPa. Phase equilibrium of C3H8 + MEG system is also reported9 at 298−398 K and up to 20 MPa. The Gas Processors Association (GPA) has published solubility data on CO2, H2S, and their mixtures with methane in MEG aqueous solutions.10,11 The solubility of CO2 in MEG has been reported12,13 in the temperature range from 298 to 408 K at elevated pressures using a previously described14 experimental setup. Union Carbide15 presented limited CO2 solubility data in MEG at 298 K and pressures up to 1.14 MPa. Hayduk and Malik16 reported CO2 solubility at ambient conditions. Vapor phase concentrations of

Gas hydrates are semicrystalline compounds consisting of water and light gases. Formation of gas hydrates may plug the pipelines which will cause flow stoppage until the gas hydrates are dissociated again. Hydrate dissociation may take place by depressurization or heating of the pipeline but the use of inhibitors is the most efficient and common approach. The most commonly used hydrate inhibitors are methanol and (mono)ethylene glycol (MEG). Other glycols also have important applications where physicochemical data are required, e.g., triethylene glycol (TEG) is used in ∼95% of the glycol dehydration units for natural gas streams because of its chemical stability, low cost, and high affinity to water.1 In this context, solid−liquid equilibria are relevant to the transportation and processing of natural gas. Calculation of the amount of MEG needed and the influence of this component on the phase behavior calls for a thermodynamic model and for phase equilibrium algorithms capable of handling mixtures of gas, oil, water and hydrate inhibitors. CPA EoS (cubic-plus-association equation of state2) is a model that can be applied to complex multicomponent, multiphase equilibria for systems with associating fluids.3 The CPA EoS in combination with the van der Waals−Platteeuw (vdW-P) model4 for hydrates can be used for calculating the © XXXX American Chemical Society

Received: July 12, 2016 Revised: October 6, 2016 Accepted: October 11, 2016

A

DOI: 10.1021/acs.iecr.6b02642 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

molecules while A and B indicate the bonding sites on a given molecule. The key element of the association term is XAi, which represents the mole fraction of site A on molecule i not bonded at other sites, while xi is the mole fraction of component i. XAi is related to the association strength ΔAiBj between two sites belonging to two different molecules, e.g. site A on molecule i and site B on molecule J, determined from

MEG in CO2 are also reported in a limited range of temperature and pressure.17−19 The latter are in a good agreement with data from Union Carbide.15 Zheng et al.6 measured CO2 solubility in MEG from 323 to 398 K up to 38 MPa. Abdi et al.20 presented few CO2 solubility data in MEG aqueous solutions at elevated pressures. Takahashi et al.19 reported only limited data. This work is continuation of previous studies of CPA modeling with glycols. Previously results were reported21 for CO2 with aqueous MEG, diethylene glycol (DEG), and triethylene glycol (TEG). The best results for multicomponent mixtures are obtained assuming that CO2 is a self-associating fluid and wherever possible they recommended using experimental values for the cross association energy and optimizing two interaction parameters (kij and cross association volume) to binary data. In addition, the CPA EoS has been applied successfully for mutual solubility of MEG and condensate-122 and for liquid−liquild− equilibria (LLE) data of MEG and condensate-2 at the range of 275.15−323.15 K and atmospheric pressure.23 Finally, good agreement is shown for vdW-P theory parameters of four main NG components (methane, ethane, propane, and carbon dioxide) with CPA.24 The parameters were extensively tested and in most cases the agreement among experimental data and model calculations was satisfactory. The Perturbed-Chain Statistical Association Fluid Theory (PC SAFT) EoS has been recently used for MEG + water systems.25−27 Using a 4C association scheme PC SAFT predicted accurately vapor pressure, saturated liquid density data and heats of vaporization data.28 In addition, satisfactory results of mutual solubility were produced for petroleum fluid + MEG and petroleum fluid + MEG + water.29 The authors suggested fitting approach to liquid data as a general method for LLE modeling of the systems of petroleum fluid + MEG with or without water. The purpose of this work is to evaluate CPA correlation results of mixtures of natural gas components (methane, ethane, propane, and carbon dioxide) hydrates with MEG as glycol inhibitor. CPA dew points for all possible equilibria (vapor− liquid equilibria (VLE), vapor−hydrate equilibria (VHE), vapor−ice equilibria (VIE)) are being calculated and the equilibrium with the highest equilibrium temperature is taken as the stable equilibrium. The article is organized as follows. At first, in section 2, the hydrate model is described. Then, in section 3 the parameters used are presented. In section 4, MEG results are presented for different NG compounds. In the end, conclusion summarizes the results in section 5.

X Ai =

where the association strength ΔAiBj in CPA is expressed as ⎤ ⎡ ⎛ ε A iBj ⎞ ΔA iBj = g (ρ)⎢exp⎜ ⎟ − 1⎥bijβ A iBj ⎦ ⎣ ⎝ RT ⎠

g (ρ ) =

n=

bij =

1 1 − 1.9n

(4)

1 bρ 4

(5)

bi + bj (6)

2

Finally, the energy parameter of CPA is given by a Soave-type temperature dependency, while b is temperature independent: ai(T ) = a0, i[1 + c1, i(1 −

where Tr =

T and Tc

Tr )]2

(7)

Tc is the critical temperature.

In the expression for the association strength ΔAiBj, the parameters εAiBj and βAiBj are called the association energy and the association volume, respectively. These two parameters are only used for associating components, and together with the three additional parameters of the SRK term (a0, b, c1), they are the five pure compound parameters of the model. They are usually obtained by fitting vapor pressure and liquid density data. For inert components e.g. hydrocarbons, only the three parameters of the SRK term are required, which can be obtained either from vapor pressures and liquid densities or calculated in the conventional manner (critical data, acentric factor). When the CPA EoS is used for mixtures, the conventional mixing rules are employed in the physical term (SRK) for the energy and covolume parameters. The geometric mean rule is used for the energy parameter aij. The interaction parameter kij is usually fitted to experimental data: a(T ) =

∑ ∑ xixjaij(T ), i

∑ xi ∑ (1 − X A )

j

where aij(T ) =

i

Ai

(3)

and the radial distribution function

∂ln g ⎞ α (T ) RT 1 RT ⎛ − − ⎜1 + ρ ⎟ Vm − b Vm(Vm + b) 2 Vm ⎝ ∂ρ ⎠ i

(2)

j

2. HYDRATE MODELING 2.1. CPA Theory. The CPA EoS can be expressed for mixtures in terms of pressure P, as30−32 P=

1 1 + ρ ∑j xj ∑ B X BjΔA iBj

(1)

b=

where R is the gas constant, T is the temperature, Vm is the molar volume, α(T) is the energy parameter, and b is the covolume parameter, ρ is the molar density of the mixture, g is the radial distribution function, XAi is the fraction of A-sites on molecule i that do not form bonds with other active sites, and xi is the mole fraction of component i. The letters i and j are used to index the

∑ xibi i

ai(T )aj(T ) (1 − kij)

(8)

(9)

In case of cross-associating systems, e.g. water−alcohol or water−glycol systems, combining rules for the association energy and volume parameters are needed in order to calculate the value of the association strength in eq 3. B


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Industrial & Engineering Chemistry Research Table 1. Pure Component Parameters of CPA EoS

a

compound

ass. schemea

Tc (K)

methane ethane propane n-butane i-butane n-pentane n-hexane n-heptane n-octane CO2 water MEG nitrogen i-pentane

na na na na na na na na na na 4C 4C na na

190.56 305.32 369.83 425.12 407.80 469.70 507.60 540.20 568.70 304.21 647.29 720.00

αo (L2bar/mol2)

b (L/mol)

ε (bar L/mol)

c1

2.3203 0.0291 0.44718 5.5093 0.0429 0.58463 9.15391 0.0587 0.66719 13.14274 0.072081 0.70771 12.9094 0.074700 0.70210 18.198 0.091008 0.79858 23.681 0.107890 0.83130 29.178 0.12535 0.91370 34.875 0.14244 0.99415 3.5079 0.072 0.76020 1.2277 0.0145 0.6736 166.55 10.819 0.0514 0.6744 197.52 Tc = 126.20 K, Pc = 33.555 bar, ω = 0.0377 Tc = 460.40K, Pc = 33.8 bar, ω = 0.337875

β

ref

0.0692 0.0141

Tsivintzelis et al.1 Tsivintzelis et al.1 Tsivintzelis et al.1 Folas et al.32 Folas et al.32 Folas et al.32 Folas et al.32 Kontogeorgis et al.37 Folas et al.32 Tsivintzelis et al.38 Folas et al.32 Tsivintzelis et al.1 from SRK parameters39 from SRK parameters39

na, nonassociating.

where R is the universal gas constant, νi is the number of type i cavities per water molecule (which are ν1 = 1/23 and ν2 = 3/23 for structure I hydrate and ν1 = 2/17 and ν2 = 1/17 for type II hydrates) and the summation is over all cavity types (both 1 and 2). The occupancy of cavity m by a component i, Θmi, is calculated as follows:

Previous investigations31,32 have identified two choices which proved to be very successful in various cases; the so-called CR-1 rule: ε A iBj =

ε A iBi + ε AjBj 2

(10)

β A iBj =

β A iBi β AjBj

(11)

Θmi =

or alternatively, the Elliott Combining Rule (ECR) ΔA iBj =

ΔA iBi ΔAjBj

β

=

β

A i Bi

·β

A j Bj

+γ

A j Bj

Cmi(T ) =

1 NP

NP

∑i = 1

xiexp − xical xiexp

× 100 where NP is number of

data points. The average absolute error (K) is calculated as the difference of predicted hydrate dissociation temperature minus the experimental temperature. 2.2. van der Waals−Platteeuw Hydrate Model. In order to obtain the fugacity of water in the hydrate phase, an appropriate hydrate model is needed. In this work, the wellestablished vdW-P hydrate model has been used,4 which is presented by the following equation for the chemical potential of the hydrate μHW: μ WH = μ WEH + RT ∑ νi ln(1 − i

∑ guests m

(15)

A mi ⎛ Bmi ⎞ exp⎜ ⎟ ⎝T ⎠ T

(16)

where Ami and Bmi are fitted parameters (two parameters per guest molecule and structure). The second, more rigorous approach is to introduce a model potential that depends on the guest molecule in the cage, based on water-guest interactions. The Kihara potential is commonly used.35 However, if the square-well (SW) potential is used, the Langmuir constant is given by

(13)

The introduction of γAiBj parameter is to show that cross association volume, βAiBj, is fitted to experimental data and CR-1 rule is used for cross association energy εAiBj for solvating systems. The average absolute deviation (AAD %) is AAD % =

1 + ∑guests k Ckifk

where f k is the fugacity of a component k in the equilibrium vapor phase obtained from an equation of state (CPA in this work), the summation is over all hydrate-forming components, and Cmi is the Langmuir adsorption constant for guest m in i type cage (in other words, the concept of hydrate formation is considered to be similar to Langmuir adsorption). There are two main approaches for the computation of the Langmuir constants, which are the key quantities of the theory. The simplified approach, suggested by Parrish and Prausnitz (PP),34 is the one uses of the empirical equation:

(12)

Voutsas et al.33 have shown that Elliott’s rule fails to correlate satisfactorily LLE for heavy alcohol−water systems with a single binary interaction parameter. However, Elliott’s rule provides good results for the VLE correlation in alcohol−water systems.31,32 In the case of cross-association between two self-associating molecules as well as cross-association between one selfassociating and one nonself-associating molecule (solvation), γAiBj, is added in eq 11; the modified combing rule (mCR1)1 emerges: A i Bj

Cmifm

Cmi(T ) =

⎛ε ⎞ 4π Vmi exp⎜ mi ⎟ ⎝ kT ⎠ kT

(17)

where Vmi is the free volume of guest molecule i inside m type cage and εmi is the depth of the SW potential, and the resemblance between eq 17 and the “empirical” eq 16 is obvious. In addition, the “van’t Hoff-type temperature dependence” of eq 16 can be expected based on quite general thermodynamic considerations according to Bazant and Trout.35 Papadimitriou et al.36 recently obtained Langmuir-type mathematical expressions for the cavity occupancies of methane hydrate of the following type:

Θmi) (14) C


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Industrial & Engineering Chemistry Research Table 2. BIP Values Used When Calculating CPA Deviations system CH4−H2O C3H8− H2O

BIP 0.7988 − 236.5/T 0.4809 − 130.5/T (Wei) 0.0095

ref

system

BIP Values Used for Figure 10 Tsivintzelis and Maribo-Mogensen41 Yan et al.

nC4H10− H2O iC4H10− H2O MEG− H2O MEG− CH4 MEG− C2H6 MEG− C3H8 MEG− nC4H10

42

Folas5 nC7H16− H2O MEG− 0.00056295T − Haghighi et al.43 H2O 0.2313 MEG− 0.17541 Tsivintzelis and Maribo-Mogensen41 CH4 MEG− 0.110081 fitted to solubility data9 C3H8 MEG− 0.029 Afzal et al.40 nC7H16 BIP Values Used When Calculating CPA Deviations Shown in Table 3 Tsivintzelis and Maribo-Mogensen41 CH4−H2O 0.7988 − 236.5/T −0.0166 Folas5 nC8H18− H2O −0.115a MEG− Folas5 H2O MEG− 0.17541 Tsivintzelis and Maribo-Mogensen41 CH4 MEG− 0.025 Afzal et al.40 nC8H18 BIP Values Used for Figure 11 Tsivintzelis and Maribo-Mogensen41 CH4−H2O 0.7988 − 236.5/T C2H6− 0.543729 − Tsivintzelis and Maribo-Mogensen41 H2O 143.25/T 0.2828 − Yan et al.42 nC4H10− 73.73/T H2O 0.00056295T − Haghighi et al.43 MEG− 0.2313 H2O MEG− 0.17541 Tsivintzelis and Maribo-Mogensen41 CH4 MEG− −0.073 fitted to solubility data of Wang et al.44 C2H6 MEG− 0.038 extrapolated from the BIP values for MEG− nC4H10 C5H12/C6H14/C7H16/C8H18 given by Afzal et al.40 BIP Values Used in Figure 12 Tsivintzelis and Maribo-Mogensen41 CH4−H2O 0.7988 − 236.5/T 0.4497 − Yan et al.42 C2H6− 127.2/T H2O 0.4809 − Yan et al.42 C3H8− 130.5/T H2O

MEG− iC4H10 CH4−H2O C2H6− H2O C3H8− H2O nC4H10− H2O nC5H12− H2O N2−H2O MEG− H2O MEG− CH4 MEG− C2H6 MEG− C3H8 MEG− nC4H10 MEG− nC5H12 MEG−N2

BIP

ref BIP Values Used in Figure 12 Yan et al.42

0.2828 − 73.73/T 0.2828 − 73.73/T 0.00056295T − 0.2313 0.17541

Tsivintzelis and Maribo-Mogensen41

−0.0733

fitted to solubility data45

0.110081


Yan et al.42 Haghighi et al.43

0.038

extrapolated from the BIP values for MEG− C5H12/C6H14/ C7H16/C8H18 given by Afzal et al.40 0.038 extrapolated from the BIP values for MEG-C5H12/ C6H14/ C7H16/C8H18 given by Afzal et al.40 BIP Values Used in Figures 13 and 14 0.7988 − Tsivintzelis and Maribo-Mogensen41 236.5/T 0.543729 − Tsivintzelis and Maribo-Mogensen41 143.5/T 0.4809 − Yan et al.42 130.5/T 0.2828 − Yan et al.42 73.73/T 0.0615 Folas5 (generalized expression) −0.2 0.00056295T − 0.2313 0.17541

fitted to solubility data45 Haghighi et al.43

−0.0733


0.110081


0.038

0.035

extrapolated from the BIP values for MEG− C5H12/ C6H14/ C7H16/ C8H18 given by Afzal et al.40 Afzal et al.40

0.194567


Tsivintzelis and Maribo-Mogensen41

The constant BIP fitted to VLE data by Folas5 was preferred for the MEG−H2O system instead of the BIP suggested by Haghighi et al.43 fitted to both SLE and VLE data because of the high temperatures of the system examined. Calculations with the BIP suggested by Haghighi et al.43 have also been performed and provided poor results. a

Table 3. Average Absolute Deviations (%) in Water Vapor Content Using Different BIPs for the system Methane−n-Octane− MEG−water Using CPA with Mathias−Copeman and Soave Expressions (See Equation 4) % AAD in composition x(CH4) Soave Mathias−Copeman Soave Mathias−Copeman

Θi(P) =

Ci(T ) ·P 1 + Ci(T ) ·P

5.12 5.14 x(CH4)aq 24.16 25.28

x(nC8H18)

x(MEG)

1.46 1.46

77.26 76.79 x(nC8H18)aq 61.60 58.73

x(H2O)

y(CH4)

y(nC8H18)

y(MEG)

y(H2O)

350.06 375.22 x(MEG)aq

0.49 0.53 x(H2O)aq

46.40 46.39

70.73 70.12

163.32 199.88

2.09 2.10

0.64 0.66

Monte Carlo simulations.36 In this work the computationally (18)

cheaper and still acceptable from a theoretical point of view PP

They obtained optimum values of Ami and Bmi by matching them to the cavities occupancies resulting from Grand Canonical

approach is used, eq 16. D


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3. CPA PARAMETERS USED The pure component parameters are presented in Table 1. The binary interaction parameters (BIPs) used in CPA are presented in this section. The notion of using only one BIP between the two associating compounds of the system, H2O and MEG, was first adopted by Riaz25 who used CPA to predict satisfactorily water content using a single temperature independent kij = −0.115 with the Elliott combining rule; see Table 2. Riaz25 mentions also that all the other kij between water−hydrocarbon and MEG−hydrocarbon can be set equal to zero. However, as it is shown in Table 3, by adopting this approach, the model considerably overpredicts the solubility of hydrocarbons; however the accuracy of the water content prediction is almost unaffected. This low performance may also be related to the MEG−CH4 and MEG−C3H8 BIP estimation, since they were both adjusted to pressure data and not to compositions. In accordance to the above observations, Afzal et al.40 applied CPA to predict the phase behavior of ternary and quaternary mixtures that contain CO2 and glycols using CO2−glycol BIPs which were fitted to both liquid and limited vapor phase composition data and CO2−glycol BIPs fitted to only liquid phase composition data. They found that using the BIPs fitted to liquid and vapor compositions in all approaches investigated for CO2 (inert, self-associating, and cross-associating) result in similar deviations against experimental data for multicomponent mixtures, which is physically more meaningful. In Table 2, the BIPs for alkanes + water and alkanes + MEG used are presented.

The suitability of a T-dependent BIP between water and MEG was also tested for the description of hydrate-dissociation curves for methane in the presence of MEG. In Figure 2, it becomes

Figure 2. Prediction of hydrate dissociation curves for methane in the presence of ethylene glycol. Symbols represent experimental data:43,47,48 CPA with a T-dependent (black lines) and a T-independent (red lines) BIP between MEG and water from Table 2.

more profound that a T-dependent BIP suggested by Haghighi et al.43 achieves better results for such calculations, especially at high MEG concentrations (it should be of course reminded that this may be due to the fact that the T-dependent BIP was fitted to both VLE and SLE data in contrast to the constant BIP suggested by Folas et al.46 and fitted experimental data). The AAD % deviations of CPA model in water vapor content for Mazloum et al.45 and Folas et al.34 data are in the order of 2.78% and 8.45%, respectively. 4.1.2. C2H6 + MEG + H2O System. The conditions of the systems used are shown in Supporting Information Table S.1. The results obtained with CPA are satisfactory and are presented in Figure 3. In general, good agreement against experimental data is obtained with a tendency to overpredict the pressure at the high concentrations.

4. MEG RESULTS 4.1. Ternary System Results. 4.1.1. CH4 + MEG + H2O System. The results of methane−MEG−water are presented in Figure 1. The data of Mazloum et al.45 correspond to 0, 5, 15, 30,

Figure 1. Prediction of water content of the system CH4−MEG−H2O with respect to pressure. Experimental data45,46 and model correlations for the system CH4−MEG−H2O: (■) 293.15 K, 22.5 mol % MEG, Mazloum et al.;45 (◆) 278.15 K, 100 bar, 22.9 mol % MEG, Folas et al.;46 (▲) 298.15 K, 100 bar, 22.8 mol % MEG, Folas et al.46 A Tdependent BIP between water and MEG was used from Table 2.

Figure 3. Prediction of ethane hydrates in equilibrium with aqueous solutions of MEG (experimental data49−51 are points and CPA results are lines). The BIP value from MEG−ethane is shown in Table 2.

4.1.3. C3H8 + MEG + H2O System. The conditions of the systems used are shown in Supporting Information Table S.2. The results of propane−MEG−water are presented in Figure 4. The results are satisfactory especially for low MEG concentrations. For high concentrations there is disagreement between modeling and experimental data. More specifically, there is disagreement with the experimental data reported by Bishnoi and Mahmoodaghdam53 and Mohammadi et al.52 at 30 wt % MEG. A powerful EoS as CPA can be used as a tool for assessing the

50 wt % MEG concentration for T = 293.15 K and P = 10.345 MPa and that of Folas et al.46 to 50.5 wt % MEG concentration for T = 278.15 and 298.15 K and P = 50, 10, and 200 MPa. The two data sources are not in good agreement to each other as it is observed in Figure 1. The data point of Mazloum et al.45 at 293.15 K does not lie between the data series of Folas et al.46 at 278.15 and 298.15 K but almost coincides with a data point measured by the latter group at 298.15 K. E


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Figure 4. Prediction of propane hydrates in equilibrium with aqueous solutions of MEG (experimental data52−54 are depicted as points and CPA results are shown in straight lines). The BIP value from MEG− propane is shown in Table 2.

Figure 6. Prediction of incipient hydrate dissociation curves for carbon dioxide in the presence of MEG. Points are experimental data,49,50,55 and lines are CPA results. BIP values from MEG−CO2 and CO2−H2O are taken from the work of Tsivintzelis and Maribo-Mogensen.30

quality of different experimental data that disagree to each other, and according to Figure 5, it is the data of Mohammadi et al.52 that seem to be more reliable.

4.1.5. H2S + MEG + H2O System. The existence of very few data56−59 available for systems with a hydrate phase containing hydrogen sulfide S(II) is surprising, noting the fact that H2S has the highest critical temperature (temperature beyond which no hydrate of the compound is formed), which means that NG systems containing H2S form hydrates more readily than gases of the same density without H2S.60 Ward et al.61 stated that a paucity of data for H2S hydrates requires necessary tools like GSMGem to extrapolate predictions in applied gas field scenarios. van der Waals and Platteeuw62 examined the properties of an HIV system under MEG inhibition. The article provides only the Langmuir constants measured at −3 °C. The conditions of the systems used are shown in Supporting Information Table S.4. CPA describes with good accuracy the effect of the inhibitor on the hydrate formation in systems containing hydrogen sulfide as shown in Figure 7. BIP values for H 2 S−H 2 O and MEG−H 2 S are −0.0098 and −0.0253, respectively.1 The AAD % in hydrate forming temperature by CPA in H2S− MEG−water system for Majumdar et al.49 and Ng et al.51 data is 1.12%.

Figure 5. Prediction of water content (vapor) of the system CO2− MEG−H2O at 5 bar (80 wt % MEG). Experimental data10 and CPA model: BIP values from MEG−CO2 and CO2−H2O are taken from Tsivintzelis and Maribo-Mogensen.41

4.1.4. CO2 + MEG + H2O System. The conditions of the systems used are shown in Supporting Information Table S.3. The water content and incipient conditions for the carbon dioxide−MEG−water system are presented in Figures 5 and 6, respectively. CPA is qualitatively closer to the experimental data, especially when solvation between CO2 and H2O is taken into account at intermediate temperature and pressure conditions. The parameters for CO2−MEG are kij = 0.2253 and βcross = 0.1274 (mCR1), and for CO2−H2O, they are kij = 0.1141, βcross = 0.0162, and εcross = 142.0 bar/(L mol) (mCR1). BIP values from CO2−MEG and CO2−H2O are taken from the work of Tsivintzelis and Maribo-Mogensen.41 In Figure 5 model correlation with CPA is applied while in Figure 6 CPA is applied in hydrate forming conditions. The AAD % in water content for Davis et al.10 is 16.42% and the absolute error (K) in hydrate equilibrium conditions for CO2−MEG−H2O with CPA for Maekawa,55 Majumdar et al.,50 Mohammadi and Richon,49 is 0.58 K. In Figure 6 the same trend is observed as in Figure 4; the deviation is larger as the inhibitor concentration increases.

Figure 7. Prediction of incipient hydrate dissociation curves for hydrogen sulfide in the presence of MEG. Points are experimental data (Majumdar et al.,49 Ng et al.51) and lines are CPA results. BIP values were obtained from Tsivintzelis et al.1 F


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Industrial & Engineering Chemistry Research 4.2. Quaternary Systems. 4.2.1. CH4 + C2H6 + MEG + H2O System. The conditions of the systems used are shown in Supporting Information Table S.5. Constant BIPs have been used for the CH4−H2O and C2H6−H2O binaries (0.0098 and 0.08086 correspondingly, taken from the internal CHIGP report of Tsivintzelis and Maribo-Mogensen,41 “Water-light hydrocarbons”). The results of methane−ethane−MEG−water are presented in Figure 8.

Figure 9. Prediction of hydrate dissociation curves for a CH4−C3H8 gas mixture (88.13% CH4−11.87% C3H8) in various aqueous MEG solutions. Points are experimental data:63 CPA with a T-dependent (black lines) and a T-independent (red lines) BIP between MEG and water from Table 2.

Figure 8. Experimental and predicted hydrate dissociation S(II) curves for two CH4−C2H6 systems in the presence of 70 wt % MEG aqueous solutions. Points are experimental data:48 (◆) 80% CH4−20% C2H6, (▲) 90% CH4−10% C2H6; solid lines are CPA results. BIP values were obtained from the work of Tsivintzelis and Maribo-Mogensen.41

nent parameters for water are used. The Mathias−Copeman expression is α = ac

The AAD % for hydrate forming temperature using CPA for system 1.1 and 1.2 is 0.88% and 0.87%, respectively. The results are satisfactory but there could be an area where hydrates are ignored if we trust CPA results. More data would be necessary to verify this finding. It is also important to use T-dependent BIPs at high inhibitor concentrations. 4.2.2. CH4 + C3H8 + MEG + H2O System. The BIP estimation of MEG−CH4 and MEG−C3H8 were adjusted to pressure data and not to compositions. This idea was previously adopted by Riaz25 who used one BIP between the two associating compounds of the system, H2O, and MEG, i.e. he included a single temperature independent kij = −0.115 between water and MEG using Elliott combining rule and all the other kij between water−hydrocarbon and MEG−hydrocarbon equal to zero. In accordance with the above observations, Tsivintzelis et al.38 applied CPA to predict the phase behavior of ternary and quaternary mixtures that contain CO2 and glycols using CO2− glycol BIPs which were fitted to both liquid and limited vapor phase composition data and CO2−glycol BIPs fitted to only liquid phase composition data. They found that using the BIPs fitted to liquid and vapor compositions, all approaches investigated for CO2 (inert, self-associating and cross-associating) result in similar deviations against experimental data for multicomponent mixtures. This fact is physically more meaningful. For the system (88.13% CH4−11.87% C3H8) hydrate stability conditions have been measured by Song and Kobayashi.63 CPA calculations are not in good agreement with the measured data for high MEG concentrations, as it is presented in Figure 9. For low MEG concentrations, the results are satisfactory. The BIPs used are shown in Table 2. 4.2.3. CH4 + nC8H18 + MEG + H2O System. For the system methane−n-octane−MEG−water, Mathias−Copeman compo-

[1 + C1(1 −

Tr ) + C2(1 −

Tr )2 + C3(1 −

Tr )3 ]2 (19)

and the parameters used C1, C2, and C3 are 0.789, −1.061, and 2.207, respectively.64 BIP values are shown in Table 2. The absolute deviations of methane−n-octane−MEG−water are presented in Table 3. In Table 3, the deviations for the specific system are very high regardless of the alpha-function formulation (Soave or Mathias− Copeman for water). The quality of experimental data63 is also being questioned. The experimental measurements are 30 years old, and the authors mention only the temperature accuracy (±0.02 K) without referring to the experimental pressure uncertainties. 4.2.4. CH4 + nC7H16 + MEG + H2O System. In Figure 10, the partition coefficient of methane as predicted by CPA is presented. The results are very satisfactory. 4.3. Multicomponent Systems (More than Four Components). 4.3.1. CH4 + C2H6 + nC4H10 + MEG + H2O System. The system of Chapoy et al.66 is used which is 34.02 (wt %) MEG in 94% CH4, 4% C2H6, 2% nC4H10 and the conditions are T = 268.1, 273.1, 278.1, 288.13, 293.15, and 298.15 and P = 5.98−34.5 MPa. The results are presented in Figure 11. The largest deviations are observed at the lowest temperatures as expected. The AAD% deviations of methane−ethane−n-butane− MEG−water are 17.47%. 4.3.2. CH4 + C2H6 + C3H8 + iC4H10 + nC4H10 + MEG + H2O System. Mazloum et al.45 have used 20 wt % MEG in 89.39% CH4, 5.08% C2H6, 1.45% C3H8, 0.18% iC4H10, 0.26% nC4H10, and the conditions are T = 283.15, 288.15, and 293.15 K and P = 10.58 MPa. The water content of methane−ethane−propane−ibutane−n-butane−MEG−water is presented in Figure 12. G


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content is 70 wt % (see also Figure 11). The water content of methane−ethane−propane−n-butane−n-pentane−nitrogen− MEG−water is presented in Figure 13.

Figure 10. Prediction of the partition coefficient of methane between the gas phase and the hydrocarbon phase for the CH4−nC7H16−MEG− H2O system at 283.15 and 310.95 K. Experimental data from the work of Ashcroft et al.65 BIP values are shown in Table 2.

Figure 13. Prediction of water content of the system CH4 + C2H6 + C3H8 + nC4H10 + nC5H12 + N2 + MEG + H2O at concentrations of 84.13, 4.67, 2.34, 0.93, 0.93, and 7 mol %, respectively, at different MEG concentrations. Experimental data48 (points) and modeling results (points are experimental data and solid lines are CPA results). BIP values are shown in Table 2.

The absolute deviations of methane−ethane−propane−ibutane−n-butane−MEG−water are presented in Table 4. Again the high uncertainties are at higher MEG concentrations but nonetheless all uncertainties are below 10%. Figure 11. Prediction of water content of the gas phase for the CH4− C2H6−nC4H10 system inhibited by MEG at different temperatures. Points are experimental data,66 and solid lines are CPA results. BIP values are shown in Table 2.

Table 4. Average Absolute Deviations (%) in Water Vapor Content Using Different BIPs for the System Methane− Ethane−Propane−n-Butane−n-Pentane−Nitrogen−MEG− Water Using CPA AAD % in Water Content in the Gas Phase

ref

MEG (wt %)

CPA (only kH2O−MEG = −0.115)

Chapoy et al.67

50%

9.04

70%

ref Chapoy and Tohidi48

Figure 12. Prediction of water content of the system CH4−C2H6− C3H8−iC4H10−nC4H10−MEG−H2O at 105.8 bar. Experimental data45 (points) and modeling results (solid line) are CPA results. BIP values are shown in Table 2.

Chapoy and Tohidi68

CPA (BIPs used)

CPA + Kiharaa

semiempirical approachb

1.77

2.76

4.0

10.73 7.75 6.03 10.0 average absolute error of hydrate dissociation temperature (K)

MEG (wt %)

CPA (constant BIPs used, except for MEG− H2O)

25% 50% 70% 50% 70%

0.21 0.67 1.57 1.23 (T-dependent BIP for MEG−H2O) 1.33 (T-independent BIP for MEG−H2O)

a

As mentioned in the work of Chapoy et al.68 bThe semiempirical approach of Chapoy et al.67 is given in appendix C of that article. It should be noticed that it includes 15 constants.

The AAD % deviations of methane−ethane−propane−ibutane−n-butane−MEG−water using CPA are 3.14%. The BIP used are shown in Table 2. 4.3.3. CH4 + C2H6 + C3H8 + nC4H10 + nC5H12 + N2 + MEG + H2O System. The conditions of the systems used are shown in Supporting Information Table S.6. It is interesting to note once again that when using CPA to predict the hydrate dissociation temperature of the mixture, the error increases when the MEG content increases. However, it is kept below 2 K even when MEG

4.3.4. Other Multicomponent Systems. The conditions of the systems used are shown in Supporting Information Table S.7. The hydrate dissociation conditions for a multicomponent NG system are presented in Figure 14. The AAD% of methane−ethane−propane−i-butane−n-butane−n-pentane−nitrogen−carbon dioxide−MEG−water by H


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5. CONCLUSIONS The CPA model coupled with the vdW-P theory was initially applied to various types of phase equilibria (VHE, LHE, HIV, HLV) of binary systems containing hydrate forming NG components and water. The purpose was to evaluate the accuracy of the solid parameters previously suggested and to improve them if possible. The effect of the BIP values used in the framework of CPA has been studied in order to evaluate to what extent the use of different BIPs influences the accuracy of dew point/water content calculations. As a general conclusion, one may say that Tdependent BIPs work better at low temperature regimes where hydrates also form, while for VLE at high temperature calculations satisfactory accuracy can be obtained with Tindependent BIPs. The use of different CPA versions or CPA coupled with the Kihara potential instead of the PP approach does not show substantial difference to the model accuracy. In general, the results produced by different thermodynamic models tend to scatter more at high inhibitor concentrations and/or low temperatures and/or high pressures. The water content calculations of NG systems with chemicals were found almost insensitive to the use of T-dependent BIPs vs the use of T-independent BIPs, although a T-dependent BIP for H2O−MEG leads to overall more accurate phase composition results when it comes to NG systems inhibited by MEG. Concerning NG with acid gases, the solvation effect when using CPA has proven to improve significantly the accuracy of our calculations. At low P (373.15 K) conditions, the solvation effect between CO2−H2O does not play a significant role when calculating vapor H2O content. Nevertheless, solvation should be taken into account according to our calculations. NG systems rich in H2S are more complex and the solvation is also important. An important problem here hindering thermodynamic model development is the lack of experimental data for S(II) H2S hydrates. When solvation is taken into account, the B1 approach suggested by Tsivintzelis et al.38 where CO2 is modeled as a non-self-associating compound with two proton acceptor sites and H2S as a non-self-associating compound with two proton donor sites provides results of acceptable accuracy apart from the fact that it is physically realistic. In the T-range between 0 and −20 °C, it is difficult to predict whether the moisture will condense as dew or precipitate as ice,

Figure 14. Hydrate dissociation curve for a multicomponent NG system (CH4 + C2H6 + C3H8 + iC4H10 + nC4H10 + iC5H12 + nC5H12 + N2 + CO2 + MEG + H2O) at concentrations 88.3, 5.4, 1.5, 0.2, 0.3, 0.1, 0.09, 2.39, and 1.72 mol %, in the presence of 50% MEG aqueous solutions. Points are experimental data,43 and the line represents CPA correlations. The BIP values are shown in Table 2 and the BIP for MEG + H2O is taken from the work of Folas.5

CPA is 0.53% for 10 and 30 wt % MEG and 0.74% for 50 wt % MEG. In case of hydrate phase boundary calculations, results which are produced by different thermodynamic models tend to be more similar to each other at low inhibitor concentrations, while the scattering is more pronounced at high concentrations. In mixtures without inhibitors, the scattering is greater at high pressures and low temperatures (HPLT) where hydrates usually form. Some representative results are shown in Figure 15. 4.3.5. Discussion of Multicomponent Results. Concerning vapor and liquid compositions’ prediction, satisfactory accuracy could be obtained with CPA in most cases using a T-dependent BIP for the water−MEG binary system (∼10−20% AAD in water content for most systems and acceptable deviations for the other components’ concentrations; it should be restated that 1 K deviation corresponds to around 5−8% change in water content above 0 °C and to about 10−11% below46). However, the water vapor content calculation accuracy itself is almost insensitive to the use of either T-dependent or T-independent BIPs (there is a difference of ∼1% among them). An exception was the CH4− nC8H18−MEG−H2O water system for which VLLE data exist. The available water content data for this system do not follow the linear trends observed for many data versus the inverse temperature and/or pressure.69

Figure 15. Experimental and predicted water content (ppm mol) of a CH4 + C2H6 + C3H8 + nC4H10 + nC5H12 + N2 + MEG + H2O mixture of Chapoy et al.66 in equilibrium with a 50 wt % aqueous MEG solution (■) and in equilibrium with a 70 wt % aqueous MEG solution (◆). Solid lines: CPA results. I


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(5) Folas, G. Modeling of Complex Mixtures Containing Hydrogen Bonding Molecules. PhD Thesis, Technical University of Denmark, 2006. (6) Zheng, D. Q.; Wei, W. D.; Guo, T. M.; Ma, W.-D. Solubility study of methane, carbon dioxide and nitrogen in ethylene glycol at elevated temperatures and pressures. Fluid Phase Equilib. 1999, 155, 277−286. (7) Jou, F. Y.; Otto, F. D.; Mather, A. E. Solubility of methane in glycols at elevated pressures. Can. J. Chem. Eng. 1994, 72, 130−133. (8) Jou, F. Y.; Schmidt, K. A. G.; Mather, A. E. Vapor−liquid equilibrium in the system ethane + ethylene glycol. Fluid Phase Equilib. 2006, 240, 220−223. (9) Jou, F. Y.; Otto, F. D.; Mather, A. E. The solubility of propane in 1,2-ethanediol at elevated pressures. J. Chem. Thermodyn. 1993, 25, 37− 40. (10) Davis, P. M.; Clark, P. D.; Fitzpatrick, E.; Lesage, K. L.; Svrcek, W. Y.; Satyro, M. A study of solubility of certain gases in glycol solutions at elevated pressures and temperatures, GPA RR-183; 2002. (11) Marriott, R. A.; Fitzpatrick, E.; Davis, P. M.; Clark, P. D.; Svrcek, W. Y.; Satyro, M. A. The impact of sulfur species on glycol dehydration - a study of the solubility of certain gases and gas mixtures in glycol solutions at elevated pressures and temperatures, GPA RR-189; 2005. (12) Jou, F.-Y.; Deshmukh, R. D.; Otto, F. D.; Mather, A. E. Vapor− liquid equilibria of H2S and CO2 and ethylene glycol at elevated pressures. Chem. Eng. Commun. 1990, 87, 223−231. (13) Jou, F.-Y.; Otto, F. D.; Mather, A. E. Solubility of H2S and CO2 in ethylene glycol at elevated pressures. Energy Progr. 1988, 8, 218−219. (14) Jou, F.-Y.; Mather, A. E.; Otto, F. D. Solubility of H2S and CO2 in aqueous methyldiethanolamine solutions. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 539−544. (15) Union Carbide Corp. Gas Treating Chemicals; 1969. (16) Hayduk, W.; Malik, V. K. Density, viscosity, and carbon dioxide solubility and diffusivity in aqueous ethylene glycol solutions. J. Chem. Eng. Data 1971, 16, 143−146. (17) Wallace, C. B. Drying supercritical CO2 demand care. Oil Gas J. 1985, 83, 98−104. (18) Adachi, Y.; Malon, P.; Yonemoto, T.; Kobayashi, R. Glycol vaporization losses in supercritical CO2, GPA RR-98; 1986. (19) Kaminishi, G. I.; Takano, S.; Yokoyama, C.; Takahashi, S.; Takeuchi, K. Concentration of triethylene glycol, diethylene glycol and ethylene glycol in supercritical carbon dioxide up to 16 MPa at 313.15 and 333.15 K. Fluid Phase Equilib. 1989, 52, 365−372. (20) Abdi, M. A.; Hussain, A.; Hawboldt, K.; Beronich, E. Experimental study of solubility of natural gas components in aqueous solutions of ethylene glycol atlow-temperature and high-pressure conditions. J. Chem. Eng. Data 2007, 52, 1741−1746. (21) Tsivintzelis, I.; Kontogeorgis, G. M. Modelling phase equilibria for acid gas mixtures using the CPA equation of state. Part VI. Multicomponent mixtures with glycols relevant to oil and gas and to liquid or supercritical CO2 transport applications. J. Chem. Thermodyn. 2016, 93, 305−319. (22) Riaz, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Haugum, T.; Christensen, K. O.; Solbraa, E.; Løkken, T. V. Mutual Solubility of MEG, Water and Reservoir Fluid: Experimental Measurements and Modeling using the CPA Equation of State. Fluid Phase Equilib. 2011, 300, 172−181. (23) Riaz, M.; Yussuf, M. A.; Frost, M.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Solbraa, E. Distribution of Gas Hydrate Inhibitor Monoethylene Glycol in Condensate and Water Systems: Experimental Measurement and Thermodynamic Modeling Using the Cubic-PlusAssociation Equation of State. Energy Fuels 2014, 28, 3530−3538. (24) Karakatsani, E.; Kontogeorgis, G. M. Thermodynamic Modeling of Natural Gas Systems Containing Water. Ind. Eng. Chem. Res. 2013, 52, 3499−3513. (25) Riaz, M. Distribution of Complex Chemicals Oil-Water Systems. PhD Thesis, Technical University of Denmark, 2011. (26) Liang, X. Thermodynamic modeling of complex systems. PhD Thesis, Technical University of Denmark, 2014.

so it is always advisible to use CPA and perform both VLE and VIE to define the dew point temperature. In the future, it would be also of interest to study closer the effect of BIPs of NG subsystems with nitrogen, for which a gap in CPA BIPs was found. The phase behavior prediction of systems containing alkanes and nitrogen is a challenging task. Except the binary system N2 + CH4 which exhibits a type I phase behavior in the classification scheme of van Konynenburg and Scott, all the other alkanes mixed with N2 exhibit a type III phase behavior. It is worth mentioning that no CPA BIPs for N2-alkanes or N2−CO2 are found in the literature, although Li and Yan69 analyzed the impacts of binary interaction parameter for CO2-mixtures and found it to have a clear effect on the calculating accuracy of an EoS in the property calculations of CO2 mixtures. According to the authors, one problem is that the determination of BIPs requires a large amount of experimental data, which are not always available. An inappropriate BIP may cause poor calculating accuracy of an EoS. As a conclusion it may be necessary to carry out more experiments to close the experimental gap and also to improve the CPA EoS accuracy. Finally, some room for improvement is believed to exist within the framework of the vdW-P theory used to describe hydrate phases. Not all assumptions of the theory are valid for all cases. The assumption of single occupancy of hydrate cavities does not hold for nitrogen, the assumption of nondistortion of the cavities by the encaged molecules does not hold for large guest molecules like carbon dioxide, the assumption of lack of interactions between encaged molecules has been questioned based on Monte Carlo simulation results by Kvamme and Førrisdahl,70 and of course the spherical symmetry assumption only works well for hydrates formed by small, monatomic gases like argon. Beside that, the “traditional” choice of the Kihara potential could also be reconsidered, especially given the recent results of Paricaud71 or Anderson et al.72 who solved for the potential directly for hydrates for which the Langmuir constants are computed, either by experimental data or by ab initio data.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b02642.

■

Tables S.1−6 as mentioned in the text (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel.: +45 45252821. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

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