Water Solubility in Supercritical Methane, Nitrogen ... - ACS Publications

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Water Solubility in Supercritical Methane, Nitrogen, and Carbon Dioxide: Measurement and Modeling from 422 to 483 K and Pressures from 3.6 to 134 MPa Farshad Tabasinejad,* R. Gordon Moore, Sudarshan A. Mehta, Kees C. Van Fraassen, and Yalda Barzin Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4

Jay A. Rushing Apache Corporation, Midland, Texas 79705, United States

Kent E. Newsham Apache Corporation, Houston, Texas 77056, United States ABSTRACT: A series of experiments to measure the water solubility in supercritical nitrogen and carbon dioxide have been conducted at experimental conditions up to 483 K and 134 MPa. The accuracy of the experimental procedure is verified by comparing the water content data of methane in the literature and our experimental data for the methane-water system. In addition, a fugacity-fugacity approach including the cubic-plus-association equation of state (CPA EoS) and a fugacity-activity approach based on the Peng-Robinson EoS and the Henry’s law model are incorporated to predict the water content data of methane, nitrogen, and carbon dioxide. A comparison between our experimental data, literature data, and the results of the fugacity-activity approach shows the reliability of the PR-Henry’s law model for the phase behavior studies of the nitrogen-water system over a wide range of pressure and temperature conditions. However, the CPA equation is not capable of reproducing the high pressure vapor and liquid phase compositions of the water-nitrogen system. The concept of cross-association satisfactorily improves the performance of the CPA equation of state in predicting the water content data of supercritical methane. On the basis of the literature and new measured data in this study, it has been found that the CPA equation better represents the phase behavior of the water-carbon dioxide system if carbon dioxide is considered as a self- and cross-associating molecule.

1. INTRODUCTION The increasing global demand for fuel and energy has pushed the oil and gas industry to look for new resources which are mostly located at deep subsurface and characterized as high pressure and high temperature gas reservoirs. The majority of deep hydrocarbon gas reservoirs produce huge amounts of water during their production periods. Equilibrated water vapor in gas reservoirs constitutes a part of this produced water. Water can strongly affect the phase behavior of hydrocarbon fluids under certain conditions due to its unique chemical structure. Therefore, many studies have been done on water-hydrocarbon mixtures to better understand the thermodynamic behavior of this system. Experimental modeling of water-hydrocarbon systems has been investigated for many years mostly for simple binary mixtures of water and pure hydrocarbons. Most of the research has been conducted in a low-to-moderate range of pressure and temperature conditions. Among all hydrocarbon constituents, most studies are devoted to methane since it is the dominant component of hydrocarbon gas reservoirs. The experimental data of water solubility in methane reported by Olds et al.1 are the most accurate data generated at high pressure and high temperature conditions. Most recently, Yarrison et al.2,3 published a new set of data at higher pressures up to 110 MPa. r 2011 American Chemical Society

A literature study on the nitrogen-water system shows that there are gaps for high pressure experimental data. Sidorov et al.4 published a series of water content data for nitrogen at 373.15 K up to 40.53 MPa. Bukacek5 has reported the solubility of water in nitrogen up to 68.27 MPa at 378 K. Water content data of nitrogen for pressures up to 13.78 MPa and a temperature range from 310.93 to 588.71 K have been generated by Gillespie and Wilson.6 Maslennikova et al.7 have measured the solubility of water in nitrogen at temperature and pressure conditions up to 623.15 K and 50.66 MPa. Many experimental studies have been done in the past on the phase behavior of the water-CO2 system. Most of these studies are devoted to low pressure and temperature conditions.8-10 Only a few studies have been performed at higher pressure and temperature conditions. However, the reported experimental data are not consistent.11,12 A comprehensive list of experimental data for the water-methane, water-nitrogen, and watercarbon dioxide systems is provided by Mohammadi et al.13 Received: June 3, 2010 Accepted: February 7, 2011 Revised: February 4, 2011 Published: March 03, 2011 4029

dx.doi.org/10.1021/ie101218k | Ind. Eng. Chem. Res. 2011, 50, 4029–4041

Industrial & Engineering Chemistry Research The phase behavior of water-methane, water-nitrogen, and water-carbon dioxide systems has been extensively studied using different thermodynamic approaches and models.13-16 Association of water molecules in the presence of other compounds in a mixture can significantly affect the phase behavior of that mixture under certain conditions. Such behavior cannot be easily captured by simple thermodynamic models that only consider the physical interactions between molecules. Many modifications have been applied to the physical models to improve the phase behavior calculations of the water-containing mixtures.14,15,17 These modifications do not necessarily lead to accurate predictions at all experimental conditions. In a recent study, Yarrison et al.2 used the combination of the Peng-Robinson equation (PR EoS)18 and Henry’s law model and accurately correlated the vapor phase compositions of the water-methane system up to 110 MPa and 510 K. However, they did not investigate the accuracy of their model in generating the liquid phase compositions. The same approach has been applied to correlate the phase behavior of the water-nitrogen system.16,19 The ability of this approach to predict the high pressure experimental data has not been validated due to a lack of accurate solubility data at elevated pressures. By incorporating the concept of association into the equations of state, many improvements have been obtained in the phase behavior studies of mixtures containing associating components such as water during the past two decades. The cubic-plusassociation equation of state (CPA EoS)20 has been used in the phase behavior studies of water-hydrocarbon and water-nitrogen systems.21,22 The predicted solubility data of the model are in good agreement with the experimental data. Recently, Li and Firoozabadi23 improved the predictions of the CPA equation for the water-methane system by applying the concept of crossassociation in the equilibrium calculations. Many attempts have been made to correlate the phase behavior of the water-carbon dioxide system. Evelein et al.17 used the Soave-Redlich-Kwong equation of state (SRK EoS)24 and accurately reproduced the water content of carbon dioxide up to intermediate pressures by adjusting the energy parameter of water calculated from Soave’s correlation.24 The authors have mentioned that the accuracy of their model in predicting the liquid phase compositions was sacrificed in order to match the water content of the carbon dioxide rich phase at elevated temperatures as reported by T€odheide and Franck.11 Later, Li and Nghiem14 correlated composition of both liquid and vapor phases by applying a cubic EoS to the vapor phase and handling the solubility in the liquid phase by Henry’s law. The model underestimates the water solubility in the vapor phase at high pressures; however, it adequately predicts the composition of both phases at lower pressure conditions over a wide range of temperatures. The system of water-carbon dioxide has also been studied by incorporating the concept of association into the equations of state. Ji et al.25 applied the SAFT1-RPM model (statistical associating fluid theory coupled with restricted primitive model) to the water-carbon dioxide system and accurately represented the densities of the liquid and vapor phases alongside the compositions up to intermediate pressures. In a recent study, Li and Firoozabadi23 incorporated the concept of cross-association into the CPA equation and assumed that cross-association occurs between molecules of water and CO2 in addition to selfassociation between water molecules. Satisfactory results were obtained for equilibrium compositions for pressures up to 20 MPa

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Figure 1. Schematic of experimental apparatus. A, densitometer; B, gas mixing vessel; C, demister vessel; D, pycnometer; E, equilibrium flash separator; F, desiccant; G, gasometer; H, chiller; J, gas booster; K, Quizix pump; L, pressure transducer.

over a wide range of temperatures. The authors did not compare the results with the experimental data at higher pressures. Recently, Perakis et al.26 and Pappa et al.27 used the cubic-plusassociation equation of state (CPA EoS)20 and considered carbon dioxide as an associating component which can selfand cross-associate in the presence of water in the water-carbon dioxide mixture. To better represent the liquid and vapor phase compositions, the authors used two different sets of interaction coefficients over a wide range of temperatures. They reported that the above approach generates better results than an approach which does not consider the self-association between the molecules of carbon dioxide in the system. In order to provide novel experimental data on water solubility in nitrogen and carbon dioxide at high pressure and temperature conditions, a series of experiments have been conducted from 3.6 to 134 MPa and temperatures from 422 to 483 K. The accuracy of the experimental procedure is verified by comparing the water content data of methane in the literature and our experimental data. New experimental data are generated in this study at higher pressures up to 134 MPa for the water-methane system. In section 2, the experimental procedure is explained, followed by a theoretical section (section 3) including two thermodynamic models utilized to predict the experimental results. Finally, in section 4 the measured data in the current study and some literature data are compared to the predicted results to test the reliability of the models for water content estimations.

2. EXPERIMENTAL SECTION 2.1. Materials. Pure methane, nitrogen, and carbon dioxide each with a certified purity of 99.99% were purchased from Praxair Canada Inc. Anhydrous calcium sulfate crystals (97% CaSO4 and 3% CoCl2), which are used as the desiccant, were purchased from W. A. Hammond Drierite Co. Ltd. A Barnstead Mega-Pure Water Still MP-1 distillation unit is used to produce distilled water. 2.2. Apparatus. Figure 1 shows a schematic diagram of the experimental setup. The BLUE M high temperature oven used in this study operates up to 616.15 K. The oven contains a gas mixing vessel, a demister, and a pycnometer which are made from 4030

dx.doi.org/10.1021/ie101218k |Ind. Eng. Chem. Res. 2011, 50, 4029–4041

Industrial & Engineering Chemistry Research Hastelloy C276. These vessels are designed to operate at pressures up to 137 MPa and temperatures up to 505.15 K. The gas mixing vessel, demister, and pycnometer with connecting lines have volumes of 150 ( 1, 35 ( 1, and 123 ( 1 cm3, respectively. The demister, filled with 5 mm diameter glass beads, is designed to remove any entrained liquid water from the gas mixture. A Ruska equilibrium flash separator with a maximum pressure of 4.14 MPa is used to separate as much of the water vapor as possible from the gas. A Chandler Engineering gasometer with a total capacity of 3000 cm3 is used to measure the gas volume at each pressure drop step. A Crycool chiller is used to confirm that no water remains in the gas stream coming out of the gasometer. Autoclave Engineers valves tested at 137.90 MPa and room temperature are used to control the gas streams at different points of the setup. Two gas booster pumps, connected in series, and a Quizix pump are used to boost the pressure of gas and water respectively up to the desired pressures. Gas booster pumps specifications include an Autoclave Engineering Model DLB 75-1 (68.95 MPa) and a Haskel AGT Model 62/152 twostage pump (pressure range 68.95-137.90 MPa). The positive displacement Quizix pump has minimum and maximum flow rates of 0.001 and 100 mL/min, respectively, with a volume resolution of 0.10 μL. Pressure is monitored with a Sensotec inline strain gauge transducer accurate to 0.25% of the full scale range. An Omega Engineering digital panel temperature indicator, DP 462, with a resolution of 0.1 F is used to measure the temperature of the gas mixing vessel, demister, and pycnometer. A TP-3102 Timberline Series Denver Instrument scale with a readability of 0.01 mg is used to weigh the desiccant before and after each test. 2.3. Experimental Procedure. The experiments are performed at four constant temperatures between 422.44 and 483.15 K over a wide range of pressure from 3.60 to 134.00 MPa. The experimental procedure is to first inject 10-20 cm3 of distilled water into the previously evacuated gas mixing vessel using the Quizix pump at 3.45 MPa. This volume of water is sufficient to capture the objectives of the experiments based on our experience. Next, the pressure of the gas mixing vessel is reduced to the vapor pressure of distilled water at the same temperature as the mixing vessel, which allows the water to vaporize and completely fill the gas mixing vessel. Then, the pure gas is injected, by means of the Haskel gas booster, into the gas mixing vessel to establish the desired pressure. Afterward the system is put on soak for 1 h to ensure that two equilibrated vapor and liquid phases are formed in the mixing vessel. The same experimental results have been obtained for different soak periods of 1, 3, and 16 h. Later, while the equilibrium pressure of the system is supported by the Quizix pump, the gas mixture is transferred to the evacuated pycnometer through the demister. The flow rate of the pump is continually controlled to ensure that the equilibrium pressure is maintained. Once the desired pressure in the pycnometer is stabilized, the connection between the demister and pycnometer is closed by means of an Autoclave Engineers valve. Next, the gas mixture in the pycnometer is released into the Ruska equilibrium flash separator. The maximum separator pressure is adjusted to 1.66 MPa in order to better measure the gas volume. Once the separator pressure reaches 1.66 MPa the gas flow path between the pycnometer and flash separator is isolated by an Autoclave Engineers valve. Afterward, the gas mixture in the separator is passed through a desiccant that captures the whole amount of water existing in the gas stream.

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Then, the dehydrated gas mixture is confined in the gasometer and its volume is measured at the separator temperature. Next, the gas mixture passes a chiller to ensure that the total amount of dissolved water in the gas has been captured. However, no water has been observed in the chiller in all experiments. The entire gas mixture in the pycnometer is released step by step, and its volume at each step is recorded by the gasometer. The total volume of released gas in each experiment is the sum of the collected gasometer volumes for each step and the volume of pycnometer with connecting lines. The initial and final pressures in the pycnometer and the separator temperature for each step are recorded as well. Finally, to capture the remaining droplets of water in the system by the desiccant, the pycnometer and separator are put on vacuum for 1 h. The vacuum draws the water-containing gas stream through the desiccant. Once the test is completed, the difference between desiccant weights before and after the experiment is recorded as the total mass of water absorbed by the desiccant which is then converted to the composition of water in the gas phase in mole percent as follows: ngas ¼

sep

ð1Þ

mw MW w

ð2Þ

nw nw ¼ ngas þ nw nvapor

ð3Þ

nw ¼

yw ¼

sep Plab Vgas

RTgas

where subscripts “lab” and “w” denote the laboratory condition and water phase, respectively, and superscript “sep” denotes separator condition. Calculations are done based on the ideal behavior of gas mixtures at standard conditions.

3. THEORETICAL SECTION: THERMODYNAMIC MODELING A closed system is in thermodynamic equilibrium if each component of the system has an identical chemical potential throughout all fluid phases. Equivalently, the fugacity of each component must be the same in all phases. fiV ¼ fiL

ð4Þ

According to eq 4, thermodynamic models can be employed to predict the phase behavior of equilibrium systems at experimental conditions. Two different approaches are incorporated in this paper to predict the water content of methane, nitrogen, and carbon dioxide at desired conditions. 3.1. O-O Approach. The cubic-plus-association equation of state20 is used to predict the equilibrium compositions of the binary systems experimentally studied in this work. The CPA EoS in an explicit form in pressure is RT aðTÞ v - b vðv þ bÞ þ bðv - bÞ RT D ln g 1þF xi ð1 - XAi Þ 2v DF i Ai

P ¼

∑ ∑

ð5Þ

The physical part of the CPA equation is represented by the Peng-Robinson equation of state (PR EoS):18 4031


Industrial & Engineering Chemistry Research

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R 2 Tci 2 ai ðTÞ ¼ 0:457235 ½1 þ mi ð1 - Tri 0:5 Þ2 P ci

ð6Þ

mi ¼ 0:37464 þ 1:54226ωi - 0:26992ωi 2

ð7Þ

aij ¼

pffiffiffiffiffiffiffi ai aj ð1 - Kij Þ

ð8Þ

∑i ∑j xi xj aij

ð9Þ

RTci P ci

ð10Þ

aðTÞ ¼

bi ¼ 0:077796 b¼

∑i xi bi

XA i ¼ ð1 þ F

∑j xj ∑B XB ΔA B Þ-1 j

i j

ð13Þ

j

εA i Bj ΔAi Bj ¼ gðFÞ exp - 1 bij βA i Bj RT gðFÞ ¼

1 - 0:5η ð1 - ηÞ3

η¼

b 4v

εA i B j ¼

ð14Þ ð15Þ

ð16Þ

where F and g are density and the radial distribution function, respectively. ΔAiBj, βAiBj, and εAiBj are association strength, association volume, and association energy between site A of molecule i and site B of molecule j, respectively. The dependency of the association term on the number and types of the association sites (association scheme) is evident in eq 13. In this work the association scheme 4C described by Huang and Radosz28 is considered for water. For mixtures containing two or more associating components, combining rules should be applied to the association volume and association energy terms.

ð17Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εA i Bi εAj Bj ð1 - Lij Þ

ð18Þ

where Lij is the binary interaction coefficient for the association energy between associating components i and j in the mixture. The fugacity coefficient for each component in any phase is calculated from the following thermodynamic relation by using the CPA EoS: ! r, assoc DAr, phys DA þ RT ln φi ¼ Dni Dni T , V , nj T , V , nj - RT ln Z

ð11Þ

where P is the pressure, T is the temperature, v is the molar volume, R is the universal gas constant, and xi, ai, bi, and ωi are mole fraction, energy parameter, volume parameter, and acentric factor of component i, respectively. Kij is the binary interaction coefficient between components i and j, and subscripts “r” and “c” denote the reduced and critical properties, respectively. It should be noted that in the CPA equation the physical parameters a and b for associating components are generated by fitting the saturated liquid density and vapor pressure data rather than from the critical temperature, critical pressure, and acentric factor data. Li and Firoozabadi23 correlated the energy parameter a (J 3 m3/mol2) for water as follows: pffiffiffiffiffiffiffi pffiffiffiffiffiffiffi aw ¼ 0:09627½1 þ 1:7557ð1 - Trw Þ þ 0:003518ð1 - Trw Þ2 pffiffiffiffiffiffiffi - 0:2746ð1 - Trw Þ3 2 ð12Þ The association term of the CPA equation is developed based on the thermodynamic perturbation theory and is equal to zero for nonassociating compounds. In this term XAi is the mole fraction of molecule i not bonded at site A and is defined as

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi βA i Bi βA j Bj

βA i B j ¼

ði ¼ 1, 2, :::, NÞ

fi ¼ xi Pφi

ð19Þ ð20Þ

where Ar is the residual Helmholtz free energy and superscripts “phys” and “assoc” denote the physical and association terms. A procedure recommended by Michelsen and Mollerup29 for the residual Helmholtz free energy calculations is used in this study for the physical part of eq 19. The association part of eq 19 is calculated based on an approach suggested by Michelsen and Hendriks.30 The nonlinear CPA equation of state is numerically solved in terms of volume by an efficient method developed by Michelsen,31 where the fractions of free sites are calculated at a fixed volume in an inner loop, with volume being modified by Newton’s method in the outer loop to match a specific pressure. The fractions of free sites in the inner loop are calculated based on the generalized calculation procedure developed by Tan et al.32 In a recent study, Li and Firoozabadi23 have shown that crossassociation between molecules of water and methane should be considered for the water-methane system at very high pressure conditions in addition to the self-association between water molecules. They treated methane as a pseudoassociating component which has association sites similar to those of water. They considered four association sites belonging to two different types R and β for water (4C) and four association sites belonging to two different types R0 i and β0 i for methane (4C). They also assumed that 0 no0 self-association occurs between molecules of 0 0 methane (ΔR iR i =0 ΔR iβ j0 = 0), and the cross-associations are symmetrical (ΔRβ i = ΔβR i). Furthermore, they related the cross-association strength between the molecules of water and methane to the self-association strength of the water molecules by a temperature-dependent cross-association factor si: 0

ΔRβ i ¼ si ΔRβ

ð21Þ

The above procedure has also been applied to the water-carbon dioxide system by Li and Firoozabadi,23 and similar to methane, carbon dioxide has been treated as a pseudo-associating molecule that only cross-associates and has four association sites (4C). Carbon dioxide has also been modeled by Perakis et al.26 and Pappa et al.27 as an associating molecule with four association sites (4C) which can self- and cross-associate in the presence of water in the water-carbon dioxide system. Therefore, in addition to the physical parameters, association volume and energy parameters have to be generated for carbon dioxide in this approach. 4032



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It should be mentioned that, in the original CPA equation developed by Kontogeorgis et al.,20 the physical part of the equation is represented by the SRK equation (Soave-RedlichKwong).24 However, in this work, the physical part of the CPA equation is represented by the PR equation.18 Therefore, the following terminologies as defined by Perakis et al.26 are used in this work to distinguish between different models and approaches: • CPA-SRK is the simplified CPA equation developed by Kontogeorgis et al.20,33 and uses the SRK equation for the physical part. • CPA-PR is the CPA equation which uses the PR equation for the physical term and is used in this work. • nCPA-PR is the CPA-PR equation which only considers the self-association for the molecules of water with four associating sites (4C). The other component of the binary system is treated as a nonassociating substance. • sCPA-PR is the CPA-PR equation which considers the association for the molecules of water with four associating sites (4C) and also considers the cross-association between molecules of water and the molecules of methane (or carbon dioxide) with four associating sites (4C) in a binary system. • aCPA-PR is the CPA-PR equation which considers the association for both water and carbon dioxide molecules with four associating sites (4C) and also the cross-association between molecules of water and carbon dioxide in a binary system. 3.2. γ-O Approach. The gamma-phi approach is the second thermodynamic approach incorporated in this study for the phase behavior studies. This approach has been successfully applied in phase behavior studies of gas mixtures containing water2,34 up to intermediate pressures. The PR equation of state is used to model the vapor phase of the equilibrium system, while the liquid phase is represented by Henry’s law. The fugacity of components in the vapor phase is related to the fugacity coefficient by the following definition: ð22Þ fiV ¼ yi PφVi By use of the PR equation of state, the fugacity coefficient of each component in the vapor phase is calculated from bi ln φi ¼ ðZ - 1Þ - lnðZ - BÞ b 3 2 N

∑

pffiffiffi ! yi aij Þ 7 6ð2 7 A 6 b Z þ ð1 2ÞB j¼1 i pffiffiffi ln - 7 þ pffiffiffi 6 ð23Þ 7 6 a b 2 2B4 Z þ ð1 þ 2ÞB 5

for activity coefficient (limxsolutef0 γsolute = 1). L ¼ xLsolute Hsolute fsolute

p - psat 0 w ¼ xLsolute Hsolute exp v¥solute RT

ð27Þ

In eq 27 H0solute is Henry’s constant as correlated by Harvey.35 Lyckman et al.36 suggested a correlation to predict the partial molar volume of nitrogen and methane at infinite dilution 37 in (v¥ solute) which is reported by Heidemann and Prausnitz the following form: ! TPc, i RTc, i ¥ ð28Þ vi ¼ 0:095 þ 2:35 0 c water Tc, i Pc, i where vi¥ is in m3/kgmol, T is the temperature in K, P is the pressure in MPa, and c0 water is the cohesive energy for water in MJ/m3: c0 water ¼

vap

ΔHwater - RT vsat w

ð29Þ

Saul and Wagner38 have correlated the specific enthalpy of the saturated water (ΔHvap water), vapor pressure of water, and its density. By considering the symmetric convention for activity coefficient of water in the liquid phase (limxwaterf1 γwater = 1), the fugacity of water in the liquid phase is calculated by sat sat L p - pw P exp v fwL ¼ xLw φsat ð30Þ w w w RT where xLw is the mole fraction of water in the liquid phase and vLw is the molar volume of pure water. The fugacity coefficient of water 2 at saturation pressure (φsat w ) is correlated by Yarrison et al. based on the data of the 1995 steam tables. 274 sat φw ¼ 1 - 0:00134092747753865 exp 9:7 1 T þ 0:00195670 ð31Þ where T is in K. It must be mentioned that in section 4, unless expressed, all the physical and association parameters of pure compounds, physical and association binary interaction coefficients, and cross-association factors as reported in Tables 2-5 have been used in the phase behavior calculations.

4. RESULTS AND DISCUSSION where the compressibility factor Z is derived from the following equation: Z3 - ð1 - BÞZ2 þ ðA - 2B - 3B2 ÞZ - ðAB - B2 - B3 Þ ¼ 0

ð24Þ A¼

aP ðRTÞ2

ð25Þ

bP ð26Þ RT The fugacity of solute in the liquid phase is evaluated by the concept of Henry’s law, while asymmetric convention is assumed B¼

4.1. Methane-Water System. Water content data of methane at experimental conditions are reported in Table 1. New experimental data are generated in this study at higher pressures compared to the literature. The water solubility data in methane reported in this study and literature data are shown in Figure 2 over a wide range of experimental conditions. A comparison between the new measured data and those reported by Yarrison et al.2,3 at the same temperature condition, i.e., 422 K, indicates that our experimental data at very low pressure and high pressure conditions report higher values for the solubility of water in methane while the reported solubility data at intermediate pressures are approximately identical. A qualitative study by different thermodynamic models2,15,22 shows that our low 4033



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Table 1. Measured Solubility of Water in Methane, Nitrogen, and Carbon Dioxide (mol %)a T (K)

P (MPa)

measured data

T (K)

P (MPa)

Water-Methane System measured data T (K) P (MPa)

measured data

T (K)

P (MPa)

measured data

422.70

3.67

13.87 ( 1.07

444.10

3.87

23.04 ( 1.61

461.60

4.10

33.57 ( 2.21

483.15

7.40

30.37 ( 1.17

422.70

7.18

7.56 ( 0.35

444.10

7.31

13.04 ( 0.52

461.60

7.65

19.21 ( 0.74

483.15

7.78

29.43 ( 1.08

422.70

14.24

4.16 ( 0.13

444.10

14.60

7.30 ( 0.17

461.60

14.66

11.07 ( 0.25

483.15

14.85

17.21 ( 0.36

422.70

21.26

3.13 ( 0.08

444.10

19.83

5.65 ( 0.11

461.60

21.62

8.15 ( 0.14

483.15

21.17

13.41 ( 0.21

422.70 422.70

27.91 35.32

2.63 ( 0.06 2.26 ( 0.05

444.10 444.10

27.86 34.53

4.37 ( 0.08 3.81 ( 0.06

461.60 461.60

29.29 36.62

6.44 ( 0.09 5.49 ( 0.07

483.15 483.15

29.47 37.06

10.40 ( 0.13 9.13 ( 0.10

422.70

41.62

2.08 ( 0.04

444.10

40.36

3.47 ( 0.05

461.60

42.33

5.09 ( 0.06

483.15

45.66

7.67 ( 0.07

422.70

68.66

1.67 ( 0.03

444.10

69.29

2.69 ( 0.03

461.60

68.37

4.02 ( 0.04

483.15

73.30

5.68 ( 0.05

422.70

107.03

1.26 ( 0.03

444.10

96.24

2.44 ( 0.03

461.60

102.15

3.57 ( 0.03

483.15

104.08

-

-

444.10

133.39

2.19 ( 0.02

461.60

121.13

3.30 ( 0.03

-

-

T (K)

P (MPa)

T (K)

P (MPa)

measured data

T (K)

P (MPa)

-

measured data

Water-Nitrogen System measured data T (K) P (MPa)

5.28 ( 0.04 -

measured data

422.44

3.81

13.12 ( 1.02

445.60

4.05

22.89 ( 1.59

461.60

3.87

33.85 ( 2.43

483.15

4.13

51.15 ( 3.18

422.44

7.35

7.09 ( 0.35

445.60

7.42

13.00 ( 0.55

461.60

7.50

18.77 ( 0.77

483.15

7.33

31.16 ( 1.24

422.44

14.01

3.97 ( 0.14

445.60

14.35

7.44 ( 0.20

461.60

14.29

10.97 ( 0.27

483.15

15.33

16.87 ( 0.37

422.44

21.07

2.90 ( 0.09

445.60

20.88

5.74 ( 0.12

461.60

21.15

8.05 ( 0.15

483.15

21.24

12.93 ( 0.22

422.44

28.07

2.35 ( 0.07

445.60

28.38

4.57 ( 0.08

461.60

28.22

6.90 ( 0.11

483.15

28.45

10.29 ( 0.14

422.44 422.44

34.23 35.28

1.95 ( 0.06 1.90 ( 0.06

445.60 445.60

37.02 42.28

3.80 ( 0.06 3.48 ( 0.06

461.60 461.60

34.78 41.82

5.80 ( 0.08 5.08 ( 0.07

483.15 483.15

35.39 41.78

8.91 ( 0.11 8.01 ( 0.09 5.60 ( 0.05

422.44

41.41

1.73 ( 0.05

445.60

72.98

2.64 ( 0.04

461.60

72.23

3.79 ( 0.04

483.15

73.14

422.44

70.26

1.32 ( 0.03

445.60

102.86

2.14 ( 0.03

461.60

101.64

2.89 ( 0.03

483.15

109.60

422.44

106.29

0.92 ( 0.03

445.60

134.90

1.81 ( 0.03

461.60

133.73

2.60 ( 0.03

-

-

T (K)

P (MPa)

measured data

T (K)

P (MPa)

measured data

T (K)

P (MPa)

Water-Carbon Dioxide System measured data T (K) P (MPa)

4.33 ( 0.04 -

measured data

422.98

3.91

13.85 ( 0.98

445.74

3.85

25.00 ( 1.70

461.62

3.89

34.60 ( 2.40

478.35

4.05

47.04 ( 3.24

422.98

7.29

8.22 ( 0.32

445.74

7.39

14.29 ( 0.51

461.62

7.13

21.18 ( 0.80

478.35

7.20

29.96 ( 1.10

422.98

14.39

5.57 ( 0.11

445.74

16.64

8.78 ( 0.14

461.62

14.86

12.99 ( 0.22

478.35

15.42

17.45 ( 0.29

422.98

21.98

4.59 ( 0.06

445.74

22.35

7.45 ( 0.09

461.62

21.13

10.56 ( 0.13

478.35

21.79

14.76 ( 0.17

422.98

28.49

4.47 ( 0.05

445.74

28.78

7.07 ( 0.07

461.62

28.58

9.87 ( 0.09

478.35

30.21

12.98 ( 0.12

422.98

36.03

4.47 ( 0.04

445.74

36.05

7.04 ( 0.06

461.62

35.60

9.65 ( 0.08

478.35

36.70

13.08 ( 0.10

422.98

42.91

4.58 ( 0.04

445.74

42.89

7.10 ( 0.05

461.62

43.48

9.46 ( 0.07

478.35

42.27

12.91 ( 0.09

422.98 422.98

73.19 103.32

4.82 ( 0.03 5.07 ( 0.03

445.74 445.74

70.65 110.41

7.37 ( 0.04 7.52 ( 0.04

461.62 461.62

73.21 96.57

9.67 ( 0.05 9.83 ( 0.05

478.35 478.35

71.09 99.39

13.00 ( 0.07 13.32 ( 0.06

422.98

124.26

5.18 ( 0.03

445.74

124.26

7.57 ( 0.04

461.62

124.14

10.03 ( 0.04

478.35

129.19

13.24 ( 0.05

a

Uncertainties in the measured water content data are calculated using the propagation of error analysis. The uncertainty value in measured temperatures is (0.06 K and for each measured pressure is 0.25% of its value.

pressure data at 422 K better represent the solubility of water in the vapor phase. In addition, it must be mentioned that the new measured low pressure data in the current study at 444.10 K are in good agreement with the low pressure data of Olds et al.1 at 444.26 K (Figure 3). The difference between experimental data at high pressure conditions could be related to the difference between the experimental equipment used in this study and that used in Yarrison et al.’s work2,3 to transfer the water-saturated gas to the pycnometer (this study) and the chemical absorption traps (Yarrison et al.’s work). In this study, a positive displacement Quizix pump has been used to transfer the water-saturated gas to the pycnometer at the equilibrium pressure by injecting water at a constant pressure equal to the equilibrium pressure of the mixture. However, Yarrison et al.2,3 used two positive

Table 2. Physical Properties of Pure Components component water

Pc (MPa)

Tc (K)

ω

22.055

647.13

0.3449

methane nitrogen

4.599 3.394

190.56 126.10

0.0115 0.0403

carbon dioxide

7.382

304.19

0.2276

displacement pumps to transfer the equilibrium mixture to the chemical absorption traps by injecting gas at the equilibrium pressure of the mixture. As for our procedure, the pump flow rate was manually adjusted to maintain the cell pressure throughout the experiment in Yarrison et al.’s work.2,3 Basically, the accuracy of the experimental data depends on the stability of the pump 4034



Figure 2. (a) Methane solubility in water: (O) experimental data measured by Culberson et al.40 from bottom to top at 310.93, 410.93, and 444.26 K. Black solid lines, generated results of PR-Henry; red longdash lines, results of nCPA-PR; blue dash-dot-dot lines, results of nCPA-SRK; dark green long-short-short lines, results of nCPA-SRK with Kij = 0. (b) Water solubility in methane: (0) experimental data measured by Olds et al.1 from bottom to top at 310.93, 344.26, 377.59, and 510.93 K; (O) experimental data measured by Yarrison et al.2 at 422.04 K; (4) experimental data measured in this work from bottom to top at 422.70, 444.10, 461.60, and 483.15 K. Black solid lines, generated results of PR-Henry; red medium-dash lines, results of nCPA-PR; blue dash-dot-dot lines, results of nCPA-SRK.

pressure, which is a function of water or gas compressibility, and also human error when manually adjusting the pump flow rate. Thus, the difference between the data obtained from these two works reflects the experimental error existing in the measured data and will not necessarily imply a higher accuracy level of one data set over that of another. The phase behavior of the water-methane system over a broad range of experimental conditions has been modeled by Yarrison et al.2 using the gamma-phi approach (PR-Henry’s law model) which has been explained in detail in section 3.2. The predicted data of water solubility in methane and methane solubility in water (Figure 2) show that the model represents the compositions of the equilibrium vapor phase better than those of the liquid phase. As depicted in Figure 2, at high temperatures, the model overestimates the methane solubility in water as pressure increases. Furthermore, higher values are measured in the current study for the solubility of water in methane compared to the predicted results of the PR-Henry’s law model at pressures greater than 100 MPa. The same behavior can be observed for the high

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Figure 3. (a) Methane solubility in water: (O) experimental data measured by Culberson et al.40 from bottom to top at 310.93, 410.93, and 444.26 K. Black solid lines, generated results of sCPA-PR; red medium-dash lines, results of sCPA-SRK. (b) Water solubility in methane: (0) experimental data measured by Olds et al.1 from bottom to top at 310.93, 344.26, 377.59, 444.26 and 510.93 K; (O) experimental data measured by Yarrison et al.2 at 422.04 K; (4) experimental data measured in this work from bottom to top at 422.70, 444.10, 461.60, and 483.15 K. Black solid lines, generated results of sCPA-PR; red mediumdash lines, results of sCPA-SRK.

Table 3. Constants Used in the aCPA-PR Equation component a

a

b (m2/kgmol) a

ε (MJ/kgmol)

water

0.014 584

14.453 75

carbon dioxide

0.028 700

4.000 06

a

β 0.123 53a 0.045 70

These values have also been used for nCPA-PR and sCPA-PR.

pressure experimental water content data of Yarrison et al. at 477.5 K. It should be mentioned that the physical parameters and binary interaction coefficients (Kij) employed in the PR-Henry’s law model in the current study for the water-methane system are identical to those used by Yarrison et al. The water-methane system has also been investigated by Li and Firoozabadi23 through implementing the nCPA-PR model. Despite the accurate predictions of the liquid phase compositions, the model underestimates the vapor phase water content of methane. Estimated compositions of the equilibrium liquid and vapor phases are compared to the literature data in Figure 2. The deficiency of the nCPA-PR model was eliminated by Li and Firoozabadi23 by applying the concept of cross-association in the 4035



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Table 4. Physical and Association Binary Interaction Coefficients and Association Factors Used in the nCPA-PR, sCPA-PR, and aCPA-PR Models Water-Methane System (310.93-483.15 K)a equation nCPA-PR

Kij = -0.2080Tr,c14 þ 1.8241Tr,c13 - 6.1843Tr,c12 þ 9.9388Tr,c1 - 6.1378

-

sCPA-PR

Kij = -0.1028Tr,c12 þ 1.1609Tr,c1 - 1.5488

si = 0.0628Tr,c12 -0.1826Tr,c1 þ 0.1315

Water-Nitrogen System (298.15-483.15 K)a equation Kij = -0.1295Tr,N22 þ 0.5935Tr,N2 - 0.195 Kij = -0.1181Tr,N22 þ 1.2355Tr,N2 - 2.3774

PR-Henry’s law nCPA-PR

-

Water-Carbon Dioxide System (304.21-533.15 K)a equation

a

sCPA-PR

Kij = 0.6478Tr,CO2 - 0.5643

aCPA-PR

Kij = 0.7272Tr,CO2 - 2.5537Tr,CO2 þ 3.3450Tr,CO2 - 1.5736 3

si = -0.2388Tr,CO3 þ 1.0272Tr,CO22 - 1.2417Tr,CO2 þ 0.4760 Lij = -1.0305Tr,CO23 þ 3.1480Tr,CO22 - 3.0480Tr,CO2 þ 1.1554

2

The temperature range that correlations are valid.

Table 5. Parameters, Binary Interaction Coefficients, and Association Factors Used in the nCPA-SRK and sCPA-SRK Models component water

a0 (J 3 m3/mol2)

b (m3/kgmol)

c

ε (MJ/kgmol)

β

0.1228

0.01452

0.67360

16.655

0.0692

Water-Methane System (310.93-483.15 K)a equation

a

nCPA-SRK

Kij = 0.0385Tr,c13 - 0.5806Tr,c12 þ 2.1167Tr,c1 - 2.0824

-

sCPA-SRK

Kij = -0.3712Tr,c12 þ 1.8514Tr,c1 - 2.0322

si = 0.0051Tr,c12 þ 0.0042Tr,c1 - 0.0197

The temperature range that correlations are valid.

phase behavior calculations of the methane-water system. They assumed methane as a pseudo-associating compound with four associating sites (4C) which only cross-associates with molecules of water. This model has been explained in section 3.1, and sCPA-PR is used as an acronym for this model in the current work. The estimated results of sCPA-PR are shown in Figure 3. As can be seen from Figures 2 and 3, effect of the cross-association on the liquid phase composition is practically negligible while it significantly improves the vapor phase compositions in the water-methane system. The physical properties of pure compounds as reported by Danesh39 are provided in Table 2. Other parameters used for water in the nCPA-PR and sCPA-PR models are provided in Table 3. The binary interaction coefficients (Kij) used for the nCPA-PR and sCPA-PR models and the cross-association factor (si) for the sCPA-PR model are correlated based on the reduced temperature of methane and are represented in Table 4. These parameters are generated in a way to minimize the average absolute deviation (AAD) between the experimental data of Olds et al.,1 Culberson and McKetta,40 and Gillespie and Wilson8 and the generated results of the models. " ! !# jyexp - ycalc j jxexp - xcalc j 1 AAD ¼ þ ð32Þ n n yexp xexp n

∑

∑

Yan et al.22 have studied the water-methane system using the simplified CPA-SRK.33 The authors treated methane as a nonassociating compound, and association was considered only for the

water molecules with four associating sites (4C). To be consistent with the defined terminologies in the current work, this model hereafter will be called nCPA-SRK. Details of nCPA-SRK are represented elsewhere.22 The physical and association parameters and the temperature-dependent Kij correlation used for nCPASRK in the current study are presented in Tables 2 and 5. The results of this model are compared to nCPA-PR generated data and the experimental solubility data in Figure 2. Both models generate acceptable liquid phase compositions. However, nCPA-SRK better predicts the vapor phase compositions compared to nCPA-PR as pressure increases. The discrepancy between predicted vapor phase water content data from nCPA-SRK and n-CPA-PR equations can be related to the fundamental differences between SRK and PR equations besides the physical and association parameters (a, b, ε, and β) used for water in both models. It is worth mentioning that acceptable water solubility data in methane can be obtained by nCPA-PR and nCPA-SRK models if we assume a zero Kij at all temperatures.22 However, this assumption leads to significantly different values for methane solubility in water which are not consistent with the literature data (Figure 2). It is depicted in Figure 2 that in spite of the better performance of nCPA-SRK than of nCPA-PR, the former still underestimates the composition of water in the vapor phase. Therefore, we applied the concept of cross-association (sCPA-SRK) and obtained better results for the vapor phase compositions while the liquid phase compositions remained nearly unchanged. The generated results are plotted in Figure 3. The physical and 4036



Figure 4. (a) Nitrogen solubility in water: (O) experimental data measured by Maslennikova41 from bottom to top at 323.15, 298.15, and 423.15 K; (4) experimental data measured by Wiebe and Gaddy44,45 from bottom to top at 323.15 and 298.15 K. Black solid lines, generated results of PR-Henry’s law; red medium-dash lines, results of nCPA-PR; blue dash-dot-dot lines, results of nCPA-PR with Kij = 0. (b) Water solubility in nitrogen: (þ) measured data by Oellrich and Althaus46 from bottom to top at 273.15, 278.15, 283.15, and 293.15 K; (4) measured data by Ugrozov47 at 310.95 K; (0) measured data by Rigby and Prausnitz48 from bottom to top at 323.15 and 348.15 K. (1) measured data by Sidorov et al.4 at 373.15 K. (O) measured data in the current study from bottom to top at 422.44, 445.60, 461.60, and 483.15 K. () measured data by Maslennikova et al.7 at 423.15 K. Black solid lines, generated results of PR-Henry’s law; red medium-dash lines, results of nCPA-PR.

association parameters and the Kij and si correlations used in sCPA-SRK are reported in Tables 2 and 5. It must be noted that applying the concept of cross-association to the CPA equation causes an increase in the Kij values; i.e., the Kij values of nCPA-PR and nCPA-SRK are smaller than the Kij values of sCPA-PR and sCPA-SRK, respectively. In a temperature range from 420 to 480 K, the Kij values of nCPA-PR and sCPA-PR are around 0.4 and 0.7, respectively. The corresponding values for nCPA-SRK and sCPA-SRK are 0.18 and 0.26, respectively. The increase in the Kij value is larger for CPA-PR compared to CPASRK. This behavior may be related to the basic differences existing in the formulation of the PR and SRK equations. 4.2. Nitrogen-Water System. The measured solubility data of water in nitrogen are presented in Table 1. The PR-Henry’s law and nCPA-PR models have been applied to predict the equilibrium compositions of liquid and vapor phases of the water-nitrogen system. The Kij values used in the PR-Henry’s

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law model are correlated as a function of reduced temperature of nitrogen based on the minimization of average absolute deviation (AAD) using the experimental data of Gillespie and Wilson6 and Maslennikova.41 This correlation is reported in Table 4. New measured data and literature solubility data of both liquid and vapor phases are compared with the generated data of the PRHenry’s law model in Figure 4. The model properly represents the equilibrium compositions of the water-nitrogen system over a wide range of pressure and temperature conditions. Gillespie and Wilson6 and Maslennikova41 data points were also used to generate the optimum values of the binary interaction coefficients for the nCPA-PR model. The developed correlation is represented in Table 4. The nCPA-PR generated solubility data are shown in Figure 4. The model is able to precisely reproduce the compositions of the equilibrium phases at low pressure conditions over the entire range of temperatures considered in this study. As pressure increases, the model underestimates the nitrogen and water solubility data in the liquid and vapor phases, respectively. This is in contrast to the performance of nCPA-PR for the water-methane system. nCPA-PR (or nCPA-SRK) was able to correctly reproduce liquid phase compositions of the water-methane system. The deficiency of this model in reproducing the vapor phase compositions of the water-methane system was later improved by applying the concept of cross-association, which had a marginal effect on the liquid phase compositions. It can be concluded from this behavior that the concept of crossassociation does not improve the predictions of nCPA-PR for the water-nitrogen system. To verify the conclusion, we applied the cross-association (sCPA-PR) to the water-nitrogen system and no improvement was obtained. Although the phase behavior of the water-nitrogen system has been better represented by the PR-Henry’s law model compared to the nCPA-PR or sCPA-PR models in the current study, it must be mentioned that there are only a few experimental data for nitrogen solubility in water at pressures more than 50 MPa and, therefore, we have to cautiously speak about the accuracy of different thermodynamic models in representing the phase behavior of the water-nitrogen system at elevated pressures. Again, it should be mentioned that the vapor phase compositions of the water-nitrogen system can be approximately estimated by nCPA-PR or nCPA-SRK21 assuming a zero binary interaction coefficient. However, the assumed Kij value causes large discrepancies between measured and predicted solubility data of nitrogen in water (Figure 4). 4.3. Carbon Dioxide-Water System. The measured water solubility data in the carbon dioxide rich phase are presented in Table 1 and Figure 5. A comparison between the new measured data in the current work and those from T€odheide and Franck11 and Takenouchi and Kennedy12 show that the reported data do not agree with each other. The measured data of T€odheide and Franck11 show higher water content values at the same temperature conditions compared to the current work; however, the data trend is almost similar at the same pressure range, which is in contrast with the experimental data reported by Takenouchi and Kennedy.12 An experimental study conducted by Mather and Franck42 at elevated pressures and temperatures has shown that the measured water content data of T€odheide and Franck are better representatives of the vapor phase compositions. Therefore, we only consider the water content data of T€odheide and Franck in this work. It should be mentioned that the carbon dioxide solubility data in water reported by T€odheide and Franck11 and Takenouchi and Kennedy12 are in good agreement. 4037



Figure 5. (a) Carbon dioxide solubility in water: (0) experimental data measured by Wiebe and Gaddy49 at 304.19 K; (þ) measured data by Bamberger et al.10 at 323.20 K; (O) measured data by Gillespie and Wilson8 from top to bottom at 348.15, 366.48, and 394.26 K; (1) measured data by Takenouchi and Kennedy12 from bottom to top at 383.15, 423.15, and 473.15 K; (4) measured data by T€odheide and Franck11 from bottom to top at 523.15 and 533.15 K. Black solid lines, generated results of aCPA-PR; red medium-dash lines, results of sCPAPR. (b) Water solubility in carbon dioxide: (O) experimental data measured by Gillespie and Wilson8 from bottom to top at 304.21, 348.15, 366.48, 394.26, and 422.04 K; (0) measured data by Wiebe and Gaddy50 from bottom to top at 304.55 and 348.15 K; (þ) measured data by M€uller et al.9 from bottom to top at 413.15, 433.15, and 453.15 K; (1) measured data in the current work from bottom to top at 422.98, 445.74, 461.62, and 478.35 K; (4) measured data by T€odheide and Franck11 from bottom to top at 323.15, 423.15, 473.15, 523.15, and 533.15 K. Black solid lines, generated results of aCPA-PR; red mediumdash lines, results of sCPA-PR.

The PR-Henry’s law model has been previously applied to the water-carbon dioxide system.14,43 This approach fails to correctly predict the high pressure and temperature water content of carbon dioxide rich phase. The strong quadrupole moment of carbon dioxide can cause the formation of complex bonds in the presence of other compounds at specific temperature and pressure conditions which cannot be described by equations of state that only consider the physical interactions between molecules.27 By applying nCPA-PR to the water-carbon dioxide system, Li and Firoozabadi23 correctly predicted the equilibrium liquid phase compositions. However, similar to the water-methane system, they obtained lower values for the water content of the vapor phase compared to the literature data. Accordingly, they

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applied sCPA-PR to this system and obtained accurate results for both equilibrium liquid and vapor phases. The experimental range of pressures and temperatures investigated by Li and Firoozabadi in their work was up to 20 MPa and 533.15 K. The sCPA-PR model is extended to higher pressures in the current study, and the predicted results are compared to the literature and new measured data in Figure 5. It is depicted in Figure 5 that sCPA-PR correlates the liquid phase compositions with good accuracy while it overestimates the water content of carbon dioxide as pressure increases. The binary interaction coefficients and the cross-association factors used in this work for the sCPA-PR model are correlated in terms of the reduced temperature of carbon dioxide and are reported in Table 4. These correlations are generated by minimizing the AAD between the experimental data of Gillespie and Wilson8 and the generated results of the sCPA-PR model. It was also tried to improve the performance of the sCPA-PR by adjusting the Kij and si parameters using the high pressure data measured in the current study and those reported by T€odheide and Franck in addition to the low pressure data of Gillespie and Wilson. However, success was not achieved over the entire range of pressures. To further improve the accuracy of the sCPA-PR model in predicting the high pressure water content data of carbon dioxide, as claimed by Perakis et al.26 and Pappa et al.,27 the self-association between molecules of carbon dioxide was added to sCPA-PR to form the aCPA-PR model. In this model, carbon dioxide is considered as an associating compound with four associating sites. Similar to water, the association scheme 4C is considered for carbon dioxide. To better represent the vapor pressure and saturated liquid density of carbon dioxide, the following correlation is developed for the energy parameter a (J 3 m3/mol2): pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi aCO2 ¼ 0:32936½1 þ j0 ð1 - Tr, CO2 Þ þ j1 ð1 - Tr, CO2 Þ2 pffiffiffiffiffiffiffiffiffiffiffiffi þ j2 ð1 - Tr, CO2 Þ3 2 ð33Þ where j0, j1, and j2 are 0.704 48, -0.508 80, and 1.476 74, respectively. The other parameters used for carbon dioxide in the aCPA-PR model are presented in Table 3. These parameters reproduce the reported vapor pressures and saturated liquid densities of carbon dioxide in the DIPPR 801 database over a temperature range from 217 to 302 K with average absolute deviations (%) of 0.70 and 0.54, respectively. To adjust the binary interaction coefficients of the physical and association terms of the aCPA-PR model, i.e., Kij and Lij, Pappa et al.27 used the experimental solubility data of Takenouchi and Kennedy12 for temperatures greater than 383 K. Consequently, due to the questionable accuracy of these data points as mentioned above, two different sets of temperature-dependent correlations for the physical and association interaction coefficients were generated for temperature less and greater than 373 K. Nevertheless, the model generated data are not in good agreement with the Takenouchi and Kennedy’s high pressure water content data of carbon dioxide rich phase. To eliminate the above deficiency, we used the new high pressure experimental water content data measured in this work and those reported by Gillespie and Wilson8 and developed a set of correlations for the Kij and Lij parameters. These correlations are presented in Table 4. The generated results of the aCPA-PR model using the new developed correlations for Kij and Lij parameters are shown in Figure 5. The accuracy of aCPA-PR in reproducing the low 4038


Industrial & Engineering Chemistry Research pressure data is nearly identical to that of sCPA-PR. However, aCPA-PR demonstrates a superior capability in generating the high pressure solubility data of water in carbon dioxide compared to sCPA-PR. At high pressure conditions, the solubility of water in the carbon dioxide rich phase does not significantly increase with pressure, which can be related to the self-association of carbon dioxide molecules in the vapor phase. It is interesting to compare the predicted results of aCPA-PR to the data points of T€odheide and Franck11 which were not used for tuning the physical and association binary interaction coefficients. As can be seen in Figure 5, aCPA-PR can predict the very high pressure solubility data of T€odheide and Franck at least qualitatively up to 350 MPa and 533.15 K.

5. CONCLUSIONS A series of new experimental data for water solubility in supercritical methane, nitrogen, and carbon dioxide were measured from 422 to 483 K over a wide range of pressure from 3.6 to 134 MPa. The accuracy of the experimental procedure was verified by comparing the new water content data generated for the methane-water system in the current work with literature data. Among two models used in this study for the watermethane system, the CPA equation with the concept of crossassociation (sCPA-PR or sCPA-SRK) was superior to the PRHenry’s law model in representing the phase behavior of the water-methane system over a wide range of experimental conditions. The thermodynamic behavior of the water-nitrogen system can be accurately represented by the PR-Henry’s law model. We were not able to correctly represent the phase behavior of the nitrogen-water systems with the CPA equation. The new measured solubility data of water in carbon dioxide revealed that carbon dioxide should be considered as an associating compound enabled to self- and cross-associate in the presence of water in the binary system of water-carbon dioxide. By considering the 4C association scheme for water and carbon dioxide, accurate solubility data were predicted by the aCPA-PR model over a wide range of pressures and temperatures. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The financial support of this study, provided by Anadarko Petroleum Corp., Apache Corp., and NSERC, is gratefully acknowledged. Special thanks go to Mr. D. F. Marentette for his technical support during the completion of the experimental part of this work. The authors also would like to thank the staff of the Engineering Machine Shop at the University of Calgary for their help in fabricating experimental equipment. ’ NOMENCLATURE A = Helmholtz free energy AD = absolute deviation AAD = average absolute deviation CPA = cubic-plus-association equation of state EoS = equation of state H = specific enthalpy K = physical binary interaction coefficient

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L = association binary interaction coefficient MW = molecular weight P = pressure PR = Peng-Robinson equation of state R = universal gas constant T = temperature V = volume XA = mole fraction of component not bonded at site A Z = compressibility factor a = attractive term in the PR, and CPA equations b = parameter of the equation of state c0 = cohesive energy f = fugacity g = radial distribution function m = parameter of the equation of state n = number of moles s = cross-association factor x = liquid mole fraction y = vapor mole fraction Greek Letters

Δ = association strength β = association volume γ = activity coefficient ε = association energy η = reduced fluid density ν = molar volume F = density φ = fugacity coefficient ω = acentric factor Subscripts

A = for site A on the molecule B = for site B on the molecule c = critical property calc = calculated parameter exp = experimental parameter i = component i j = component j lab = laboratory condition r = reduced parameter w = water Superscripts

L = liquid V = vapor assoc = association parameter phys = physical property r = residual property sat = property at saturation sc = standard condition sep = separator condition vap = vapor R = for type R on the molecule β = for type β on the molecule

’ REFERENCES (1) Olds, R. H.; Sage, B. H.; Lacey, W. N. Phase Equilibria in Hydrocarbon Systems. Composition of the Dew-Point Gas of the Methane-Water System. Ind. Eng. Chem. 1942, 34 (10), 1223–1227. (2) Yarrison, M.; Cox, K. R.; Chapman, W. G. Measurement and modeling of the solubility of water in supercritical methane and ethane 4039


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’ NOTE ADDED AFTER ASAP PUBLICATION After this paper was published online March 3, 2011, a correction was made to the affiliation of author Jay A. Rushing. The revised version was published March 8, 2011.

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Water Solubility in Supercritical Methane, Nitrogen ... - ACS Publications

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