Experimental Measurements and Molecular Modeling of the Hydrate


Experimental Measurements and Molecular Modeling of the Hydrate...

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Experimental Measurements and Molecular Modeling of the Hydrate Equilibrium as a Function of Water Content for Pressures up to 40 MPa Wael A. Fouad, Kyoo Y. Song, and Walter G. Chapman* Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States S Supporting Information *

ABSTRACT: Accurate determination of hydrate formation conditions and water content of natural gas systems is critical for cryogenic processes used in the production of natural gas liquids (NGL), liquefied natural gas (LNG) processing, and carbon dioxide (CO2) capture. Water content of three natural gas mixtures was measured in this work using a Panametrics moisture analyzer at low temperatures and pressures up to 40 MPa. The statistical associating fluid theory (PC-SAFT) combined with a modified van der Waals and Platteeuw (vdWP) theory was used to model the system phase behavior. The theory was found to be in good agreement with experimental data, thus exhibiting the predictive ability of the proposed model.



INTRODUCTION Natural gas dehydration using glycol solvents or molecular sieves is considered to be an important process in any natural gas plant to avoid gas hydrate formation. Also, to avoid ice or hydrate plugging issues, solvents such as methanol and glycol are injected in oil and gas transmission lines.1,2 Unless done, liquid water, ice, or hydrates can form causing a significant pressure drop in production pipelines as well as possible corrosion problems. Further, cryogenic processes for natural gas liquids (NGL) production, liquefied natural gas (LNG) processing, and carbon dioxide (CO2) capture3 require accurate knowledge of phase equilibria involving water. In these processes, traces of moisture need to be eliminated prior to cooling down the gas to very low temperatures where hydrate can easily be formed in distillation columns. As a result, hydrate formation conditions and water content of natural gas streams need to be accurately determined for better process design and operation. The hydrate dissociation temperature has been commonly measured to determine the thermodynamic equilibrium temperature for hydrate with excess water. However, this data is not useful for gas dehydration. Rather than measure the temperature at which the last crystal of hydrate disappears, we measure the water content of the hydrocarbon phase in equilibrium with gas hydrate at fixed temperature and pressure. The relationship between hydrate equilibrium (or dissociation) temperature and water content can be found by plotting the water content versus the temperature at fixed pressure. It has been found that the logarithm of water content is nearly linear with the reciprocal of temperature over a wide range of temperatures as shown in measurements from the Rice University gas hydrate laboratories.4,5 A change in the slope of the curve is indicative of a phase change (e.g., liquid water to hydrate). For any water content on the ordinate, the equilibrium hydrate temperature can be determined from the abscissa. Water content in light hydrocarbons has been measured at temperatures above the hydrate region and in equilibrium with © 2015 American Chemical Society

hydrate by several laboratories besides our own. Most recently, Fouad et al.6 reviewed and examined the consistency of data found in the literature on water content of light and heavy alkanes above the hydrate region. Among the earlier studies, water content data for the propane-rich phase above the hydrate region were reported along the gas/liquid water/liquid hydrocarbon three-phase envelope by Poettmann and Dean.7 Comprehensive investigations along the three-phase envelope as well as the two-phase regions for propane and water were reported by Kobayashi and Katz.8 Parrish et al.9 checked the earlier data in the propane-rich liquid phase and carried their measurements into the hydrate region. Similar studies were reported for water content in liquid and gaseous ethane. Coan and King10 reported data on the water content in the ethane-rich phase, while Parrish et al.9 reported water solubility in the liquid ethane-rich phase above and below the quadruple point condition. Parrish et al.9 further reported water content values of three ethane−propane mixtures containing 25, 50, and 75 mol % ethane, respectively, for temperatures above and below the hydrate conditions. Sparks and Sloan11 reported the water content of the binary systems ethane−water and propane−water below their respective initial hydrate formation temperatures. Later, Sloan et al.12,13 reported water content data for three ethane− propane mixtures whose compositions were 10.2, 64.6, and 91.5 mol % ethane, respectively, and two data points measured on the binary systems to confirm the results of the earlier report by Sparks and Sloan11 and two measurements of a five component system. All of their data reported on the binary and multicomponent systems were in the hydrate region. Equilibrium water content measurements in the hydrocarbon-rich or non-hydrocarbon-rich phase at equilibrium with either a hydrate phase or liquid water phase have been Received: Revised: Accepted: Published: 9637

June 20, 2015 August 27, 2015 September 16, 2015 September 16, 2015 DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

Article

Industrial & Engineering Chemistry Research performed since 1976 at Rice University. Sloan et al.14 presented the equilibrium water content of methane gas in equilibrium with hydrate for 6.89 and 10.34 MPa for temperatures greater than 249.8 K. Aoyagi et al.4 reported the experimental measurements of water content in methane gas in equilibrium with hydrate at 3.45−10.34 MPa for temperatures ranging from 234 to 269.8 K. Song and Kobayashi15−19 also reported the water content of methane− propane−water, carbon dioxide−water, and carbon dioxide− methane−water systems in the nonaqueous phases in equilibrium with hydrate or liquid water. Subsequently, Song and Kobayashi20 presented the water content of pure ethane, pure propane, and their mixtures in equilibrium with liquid water or hydrates. Song et al.5,21 have presented the water content in gaseous methane, liquid ethane, liquid propane, methane−ethane mixtures, and methane−ethane−propane mixtures. These measurements have covered the temperature range from 283 to 201 K where water content is on the order of 10 ppb. Folas et al.22 measured the water content of methane in equilibrium with an aqueous phase, ice, and a hydrate phase at pressures up to 180 bar using dew point mirror technology. Finally, Chapoy et al.23 and Zhang et al.24 used tunable diode laser absorption spectroscopy (TDLAS) technology to measure the water content of pure methane and natural gas mixtures at pressures up to 13.79 and 40 MPa, respectively. Although the hydrate dissociation temperature can be measured in a closed system, measuring the water content in such a system is suspect due to adsorption of water, for example, on gas chromatographic tubing. Our experience is that more accurate results relating equilibrium hydrate temperature to water content can be obtained in a flowing system. This approach avoids errors associated with water adsorption since water adsorption reaches a steady state in the system and the approach allows measurement of equilibrium water content at any condition.

Figure 1. Schematic of the hydrate (or water or ice)−hydrocarbon contactor to determine the equilibrium concentration of moisture in the hydrocarbon-rich stream.

each water content data at a fixed condition were sufficient with excellent repeatability of better than 1 or 2%. The flow rate of the eluting stream of 0.60−0.36 cm/s, as a superficial linear velocity based on the inside diameter of the empty contact column with gaseous mixture expanded to atmospheric pressure, produced the aforementioned repeatability. The major components of the experimental equipment are discussed in detail below. Experimental Apparatus. Cryostat. The cryostat bath is an 8.5 in. in diameter and 20.5 in. in depth cylindrical glass Dewar. The entire equilibrium apparatus, including lines, refrigeration coils, equilibrium cell, presaturator, stirrer, etc. was mounted in the glass Dewar under a rectangular horizontal plate supported at four corners by vertical iron braces. The glass Dewar was filled with a liquid bath to cover all components. Silicon oil was used as the bath fluid at 253 K. Carrier Gas Metering Pump. The Ruska piston pump with a 500 cm3 capacity is capable of operating up to 86.18 MPa, and its driving speed can be varied from 0.08 to 4.48 cm3/min. The uncertainty in the displaced volume is ±0.18%. The entire pump is kept in an air bath with its temperature controlled at a value slightly higher than the room temperature. Presaturator. A 1/4 in. diameter stainless steel tubing of 3 ft long is half-full of water which is to be converted to ice at the cryostat temperature and is laid horizontally to provide a contacting surface for the nonaqueous stream without blocking its flow, as shown in Figure 1. Pressure Measurement. The pressure in the equilibrium cell is measured by a set of three Heise gauges with ranges of 0− 1.38, 0−3.45, 0−13.79, and 0−68.95 MPa, respectively, with an accuracy of 0.1% of full scale. Also two pressure transducers were employed to measure the system pressure and sample outlet pressure with ranges of 0−1.72, 0−20.68, and 0−68.95 MPa, respectively, with an accuracy of 0.07% of full scale. Saturator. The vertically installed metallic saturator, shown in Figure 1, is loosely packed with water-coated inert particles to provide an intimate contact between ice and hydrocarbon



EXPERIMENTAL DETAILS Experimental Procedure. We have measured the water content in the hydrocarbon-rich mixture in equilibrium with gas hydrate using a flow scheme as shown in Figure 1. A dried hydrocarbon stream is flown into a presaturator and subsequently to a contact column (saturator). The saturator is a column loosely packed with hydrate (or water or ice) coated particles. For example, at hydrate forming conditions, water-coated particles are carefully converted to hydrate-coated particles by filling the column with gas and then temperature cycling to form hydrate, melt, and then re-form hydrate. After at least three cycles of hydrate forming and re-forming, the system pressure is raised by adding more gas and the bath is cooled to a desired lower temperature. At the desired pressure and temperature, the flow of hydrocarbon is initiated. The effluent gas from the saturator contact zone is sent to a detector to measure the moisture concentration in the hydrocarbon-rich phase. The detector, probe holder, and tubing outside the cryogenic bath are heated to about 313 K to prevent any possible moisture condensation along the tubing and adsorption of water molecules onto the metal wall. Because the apparatus uses a constant gas flow, the effect of water adsorption or moisture condensation in the tubing on moisture content measurement is eliminated. Depending on the state point, water content readings for the effluent stabilize in 5−10 min. In all cases measurements are taken for at least 10 min beyond the stabilization. In general, three measurements for 9638

DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

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Industrial & Engineering Chemistry Research

model for predicting water content of acid gas containing natural gas systems in equilibrium with an aqueous phase (liquid water), ice, and a hydrate phase. The hydrocarbon phase was modeled using the statistical associating fluid theory27,28 (SAFT) which goes beyond bulk properties by using a coarsegrained atomic model based on Wertheim’s first order perturbation theory (TPT1).29−33 In reference to eq 1, the perturbed chain form of the SAFT equation of state (PCSAFT)34,35 used here includes an ideal contribution (id), a hard sphere (hs) contribution by Boublik36 and Mansoori et al.,37 a chain formation (hc) contribution as proposed by Chapman et al.,27,28 a dispersion (disp) contribution using a square well potential from Gross and Sadowski,34,35,38 and an association contribution (assoc) based on the work of Wertheim:

molecules. Thus, the effluent from the saturator column is fully saturated with moisture and subsequently advances to a heated zone. The warm sample is sent to a moisture analyzer. Temperature Control and Measurement. The cryostat temperature is controlled by balancing a small amount of cooling with a refrigeration unit versus a controlled heater and a base heater, both electric. An Omega type of heater controller in conjunction with a platinum resistance thermometer (PRT) is employed to control the temperatures to ±0.02 °F. The bath temperature is measured by a 10-junction chromel−constantan thermopile. The equilibrium cell temperature is measured with a Leeds and Northrup Model 8163 platinum resistance thermometer which is calibrated with an NIST standard-traced PRT, and the accuracy of the measured temperature should be better than ±0.01 °F Analytical Equipment. Moisture Analyzer. The Panametrics moisture analyzer is a NIST traceable, microprocessor based unit designed to measure the water content of gases and nonaqueous liquids at moisture content levels of a few parts per billion. The analyzer uses a Panametrics aluminum oxide sensor to generate an impedance measurement based upon the quantity of water absorbed on the oxide sensor. This signal is functionally related to the dew point of the gas stream. Accuracy of Data. The temperature measured in these experiments is estimated to be accurate within ±0.3 K, and the pressure is estimated to be accurate within ±0.3% of the measured values. The uncertainty in the gas composition is ±2% of the target composition as given in Table 1, based on

A Aid Ahs Ahc Adisp Aassoc = + + + + NkT NkT NkT NkT NkT NkT

where A is Helmholtz free energy, N is the total number of molecules, k is the Boltzmann constant, and T is the temperature of the system. In reference to Table 2, water parameters used within the SAFT framework were taken from our previous publications6,26 while other parameters for hydrocarbons, nitrogen, and carbon dioxide were taken as proposed by Gross and Sadowski.34 Only self-association among water molecules was allowed, and all interaction parameters (kij) were set to zero in this work. Furthermore, a modification of the van der Waals and Platteeuw39 (vdWP) solid solution theory as proposed by Klauda and Sandler40−42 was used to model the hydrate phase. Intermolecular potential parameters used within the vdWP framework were obtained through ab initio quantum mechanical calculations as performed by Klauda and Sandler.40−42 The latter offers advantages over the classical vdWP theory in the sense that guest−host interactions beyond the first water cavity and the effect of lattice distortion by guests can be taken into account. The fugacity of water in the hydrate phase is

Table 1. Compositions of Gas Mixtures by mol %a gas mixture CH4 C2H6 C3H8 n-C4H10 CO2 total a

1

2

3

90.97 3.00

95.0 3.00 2.00

86.02 5.00 5.98 3.00

100.00

100.00

6.03 100.00

(1)

⎛ V β(T , P)(P − P sat, β(T )) ⎞ w ⎟⎟ f wH (T , P) = Pwsat, β(T ) exp⎜⎜ m RT ⎝ ⎠

Analytical uncertainty is ±2% of the target composition.

the certificates of analysis by the gas supplier, Air Liquide Co., La Porte, TX. The water solubility being reported, all the factors considered (pressure, temperature, moisture sensor), is estimated to be accurate within ±5−6%.

exp(∑ vm ln(1 − m



∑ θml)) (2)

j

where vm is the number of cages of type m per water molecule in the hydrate lattice, Psat,β w (T) is the vapor pressure of the empty hydrate, Vβm(T,P) is the temperature and pressure dependence of the empty hydrate lattice molar volume, and θml is the hydrate cage occupancy of guest l in cavity m. The

MOLECULAR MODELING The thermodynamic framework followed in this work is an extension of previous efforts6,25,26 in developing a generalized

Table 2. Pure Component PC-SAFT Parameters Used in This Work AAD % −1

water methane ethane propane n-butane isobutane nitrogen carbon dioxide

molar mass (g mol )

scheme

m

σ (Å)

ε/k (K)

ε /k (K)

18.015 16.043 30.07 44.096 58.123 58.123 28.01 44.01

4C

1.00 1.0000 1.6069 2.0020 2.3316 2.2616 1.2053 2.0729

3.04 3.7039 3.5206 3.6184 3.7086 3.7574 3.3130 2.7852

204.7 150.03 191.42 208.11 222.88 216.53 90.96 169.21

1920.02

9639

AiBi

κ

AiBi

0.0425

p

ρsat

2.69 0.36 0.3 1.29 0.75 0.55 2.21 2.78

5.92 0.67 0.57 0.77 1.59 1.47 1.38 2.73

sat

DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

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Industrial & Engineering Chemistry Research Table 3. Structure I (sI) Parameters for Calculating the Langmuir Constant in eq 4 512

51262

guest

Ac

Bc

Dc

Ac

Bc

Dc

methane ethane propane nitrogen carbon dioxide

−23.6453 −23.1806 − −23.0646 −24.9824

2714.5643 13.7469 − 2475.8673 2743.7375

− 65 052.4158 − − 31 948.6496

−22.0651 −23.7290 − −21.8424 −22.4037

2760.1604 3843.2773 − 2337.1765 3171.7604

− 8882.4254 − − −

Table 4. Structure II (sII) Parameters for Calculating the Langmuir Constant in eq 4 512

51262

guest

Ac

Bc

Dc

Ac

Bc

Dc

methane ethane propane nitrogen carbon dioxide

−23.5746 −24.8378 − −22.9726 −25.1752

2708.8070 926.9897 − 2499.2232 3089.4741

− 43 614.8526 − − 48 259.6778

−22.6991 −22.2291 −23.1307 −20.6160 −21.0917

2147.6899 3534.8896 4176.1979 2033.6043 2405.3662

−12 013.6211 −3 371.3000 45 939.4593 −12 672.192 28 783.0000

Table 5. Parameters for Calculating the Vapor Pressure of the Empty Hydrate Lattice in eq 5 sI

sII

guest

Aβi

Bβi

Cβi

Aβi

Bβi

Cβi

methane ethane propane nitrogen carbon dioxide

4.641 30 4.761 52 − 4.732 8 4.590 71

−5366.10 −5419.38 − −5400.61 −5345.28

−0.008 332 −0.009 774 − −0.009 500 −0.007 522

4.608 93 4.715 91 4.707 96 4.690 09 4.842 22

−5397.85 −5492.66 −5449.89 −5354.38 −5621.08

−0.007 776 −0.008 997 −0.009 233 −0.009 346 −0.009 199

hydrate cage occupancy is calculated using eq 3 assuming Langmuir type absorption: θml =

Vmβ ,I(T , P) = (11.835 + (2.217 × 10−5)T + (2.242 × 10−6)T 2)3

Cml(T ) fl (T , P) 1 + ∑guests Cml(T ) fl (T , P)

10−30NA Nwβ

(3)

(7)

where f l is the fugacity of component l and Cml(T) is the Langmuir constant calculated using the temperature dependent correlation found in eq 4. Coefficients needed for eq 4 are given in Tables 3 and 4. B D ln Cml(T ) = Ac + c + c2 T T

Vmβ ,II(T , P) = (17.13 + (2.429 × 10−4)T + (2.013 × 10−6)T 2 3

− (1.009 × 10−9)T 3) 10−30NA

(4)

Nwβ

The vapor pressure of the empty hydrate lattice, Psat,β w (T), is calculated using the temperature dependent correlation found in eq 5: ln

Pwsat, β

=

β A mix

Bβ β ln(T ) + mix + C β + Dmix T T



RESULTS AND DISCUSSION Experimental Results. Water content of three natural gas mixtures was measured using the Panametrics moisture analyzer, and results are illustrated in Tables S1−S3 in the Supporting Information. At each isotherm, the system pressure was increased from 5 to 40 MPa in an increment of 5 MPa and the water content was recorded at every increment. In terms of mixture 1, which contains about 6.03 mol % CO2, measurements were carried out at isotherms ranging from 294.1 to 263 K. On the other hand, the sweet natural gas mixtures 2 and 3 were measured at isotherms ranging from 283 to 253 K at an increment of 10 K. The equilibrium phases listed in Tables S1− S3 in the Supporting Information were estimated using CPAMultiflash software (version 4.4) by KBC Advanced Technologies.

(5)

no.guests

∑ i=1

ziXi

− (8.006 × 10−9)P + (5.448 × 10−12)P 2 (8)

The mixture constants Aβmix, Bβmix, and Dβmix in eq 5 are obtained using the following mixing rule:

X mix =

− (8.006 × 10−9)P + (5.448 × 10−12)P 2

(6)

where zi is the overall composition of guest i in the hydrate and Xi is each of the vapor pressure constants. The coefficients needed for eq 5 are given in Table 5. The vapor pressure of the empty hydrate, Vβm(T,P), is calculated using the following correlations: 9640

DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

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Industrial & Engineering Chemistry Research

TDLAS, as used by Zhang et al.,24 in measuring low water content levels (below 10 ppm) at high pressures. Experimental data shown in Figure 2d was measured at varies pressures ranging from 0.772 to 1.1 MPa. Unlike vapor−hydrate equilibrium, water content exhibits weak pressure dependence along the liquid−hydrate coexistence curve. Good agreement is shown between the theory and the experimental data down to very low temperatures found in the literature. Figure 3 exhibits

Model Validation Using Previously Published Experimental Data. In order to examine the performance of the proposed model, we first attempt to predict water content of systems measured previously. Table 6 summarizes experimental Table 6. Summary of Experimental Water Content Data Used in Validating the Model system C1 C2, C3 C1 C1, C2, C3 C1, C2, C3 C1 + C3 C1 + C2 C1 + CO2 C1, NG mixture C1, NG mixture

experimental technique Tracor ultrasonic detector dielectric cell Tracor ultrasonic detector Tracor ultrasonic detector Panametrics moisture analyzer Tracor ultrasonic detector tunable diode laser absorption tunable diode laser absorption tunable diode laser absorption tunable diode laser absorption

equilibrium phase

ref

H−G

Sloan et al.14

H−L H−G

Sloan et al.12,13 Aoyagi et al.4

H−G and H−L

Song and Kobayashi20

H−G and H−L

Song et al.5

H−G

Song and Kobayashi15

H−G

Burgass et al.43

H−G

Burgass et al.43

H−G

Chapoy et al.

23

H−G

Zhang et al.24

Figure 3. Water content of 5.31 mol % propane in methane at hydrate conditions. (○, △, □) Experimental data by Song and Kobayashi;15 () model predictions.

results obtained for 5.31 mol % propane in methane at temperatures ranging from 234 to 277 K and pressures up to 6.89 MPa. In general, the model demonstrates good agreement with the experimental data with an absolute average deviation (AAD) of 13%. Experimental data by Burgass et al.,43 Chapoy et al.,23 and Zhang et al.24 offers the advantage of examining the effect of acid and/or inert gases on the proposed model performance. Figures 4 and 5 exhibit water content data, measured by

data used for this purpose. The validation section can serve also as a comparison among different technologies used in the literature for measuring trace moisture. Figure 2 demonstrates predictions made for pure hydrate systems across a wide range of temperatures and up to moderate pressures. Figure 2b demonstrates the limitations of

Figure 4. Water content of methane−carbon dioxide mixture in equilibrium with hydrate. (○, □, △, ◊) Experimental data by Burgass et al.;43 () model predictions.

Burgass et al.,43 for the binary systems of methane−carbon dioxide and methane−ethane, respectively. The model agreement with the experimental data is satisfactory with AADs of 13.9 and 7.21%, respectively. Burgass et al.43 reported AADs of 14 and 6% using the cubic plus association (CPA) equation of state.44 In the methane−carbon dioxide mixture, both models (PC-SAFT and CPA) tend to predict slightly stronger pressure dependence than that measured experimentally. Figure 6 shows the model predictions in comparison to data by Chapoy et al.23 on low acid gas content natural gas mixtures and experimental conditions very similar to the ones used in

Figure 2. Water content of pure (a, b) methane, (c) ethane and (d) propane hydrates. () Model predictions. (a, b) (□) Song et al.;5 (○) Aoyagi et al.;4 (△) Sloan et al.;14 (◊) Chapoy et al.;23 (×) Zhang et al.24 (c, d) (△) Song et al.;5 (□) Song et al.;20 (○) Sloan et al.12,13 9641

DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

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Industrial & Engineering Chemistry Research

Figure 5. Water content of methane−ethane mixture in equilibrium with hydrate. (○, □, △, ◊) Experimental data by Burgass et al.;43 () model predictions.

Figure 7. Water content of synthetic natural gas mixture in equilibrium with hydrate. Gas composition can be found in ref 24. (○) Experimental data by Zhang et al.24 at (a) 3.45, (b) 6.89, (c) 10.34, and (d) 13.79 MPa; () model predictions.

Figure 6. Water content of CO2 containing natural gas mixtures in equilibrium with hydrate. (○, □, △, ×) Experimental data by Chapoy et al.;23 () model predictions.

this work. Again, the model was able to accurately predict the experimental data with an AAD of 7.67%. As a final step in the validation process, we study an interesting set of experimental data by Zhang et al.24 carried out using the same experimental setup as that by Chapoy et al.24 It is worth noting that the synthetic gas composition used in their experiment was heavier in terms of hydrocarbons (including nbutane and isobutane) and sweeter in terms of CO2 than the one prepared by Chapoy et al.23 Figure 7 demonstrates results obtained at different isobars. The experimental data tends to deviate from the theory predictions at low water concentrations, typically less than 10 ppm. The overall AAD was calculated to be about 13.7%. Model Predictions of Experimental Data Measured in This Work. Figure 8a exhibits the good agreement between the experimental data measured for mixture 1 and predicted values. The AAD calculated for this set of measurements was found to be 5.81%. However, data by Burgass et al.43 showed a weaker pressure dependence at isotherms of 263 and 253 K. Furthermore, studying the phase behavior of mixture 1 is of great interest for a couple of reasons. First, the prepared synthetic gas contained a considerable amount of CO2 (6.03 mol %). Second, and in reference to Table S1 in the Supporting Information, the hydrate phase undergoes a structure transition from structure II to structure I at the lowest three measured isotherms (274.5, 268, and 263 K) and at a pressure of about 15 MPa. Figure 8b exhibits software predictions against experimental data at four isotherms. In general, all models overpredicted the experimental data measured in this work and in that by Burgass et al.43 This raises questions about the accuracy of current

Figure 8. (a) Water content isotherms for gas mixture 1 as a function of pressure. Symbols in black represent experimental data by this work at various temperatures, and symbols in blue represent data by Burgass et al.43 () Model predictions. (b) Water content isotherms for gas mixture 1 as a function of pressure. Symbols in black represent experimental data by this work at various temperatures, and symbols in blue represent data by Burgass et al.43 (purple − −) CPA-Multiflash software (version 4.4) by KBC Advanced Technologies; (green − −) CSMGem software;45,46 (black − −) PVTsim software (version 18) by Calsep International Consultants. 9642

DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

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Industrial & Engineering Chemistry Research

predict the phase behavior. The experimental data appears to be in good agreement with both the model predictions and other experimental data published in the literature.

classical and associating models in predicting acid gas hydrates phase behavior. Figures 9 and 10 depict water content of the nonpolar hydrocarbon mixtures 2 and 3 in equilibrium with hydrate. The



ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b02240. Measured water contents in mixture-1-rich phase, mixture-2-rich phase, and mixture-3-rich phase (PDF)



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 713-348-4900. Fax: 713-3485478. Notes

The authors declare no competing financial interest.



Figure 9. Water content isotherms for gas mixture 2 as a function of pressure. Symbols represent experimental data by this work at various temperatures. () Model predictions; (red − −) CSMGem software;45,46 (black − −) CPA-Multiflash software (version 4.4) by KBC Advanced Technologies.

ACKNOWLEDGMENTS The authors thank the sponsoring consortium comprised of Total, Chevron, BP, Exxon-Mobil, and Sonangol for sponsoring this work. W.A.F. gratefully acknowledges the Abu Dhabi National Oil Co. (ADNOC) for financial support through a Ph.D. scholarship. The authors gratefully acknowledge the Robert A. Welch Foundation (Grant C-1241). The authors gratefully acknowledge Dr. Jefferson L. Creek for helpful discussions and calculations.



REFERENCES

(1) Kohl, A. L.; Nielson, R. Gas Purification; Gulf Publishing Co.: Houston, TX, 1997. (2) Kidnay, A. J.; Parrish, W. R. Fundamentals of Natural Gas Processing; CRC Press: Boca Raton, FL, 2006; Vol. 200. (3) Denton, R. D.; Valencia, J. A. Method and apparatus for separating carbon dioxide and other acid gases from methane by the use of distillation and a controlled freezing zone. U.S. Patent US 4533372 A, 1985. (4) Aoyagi, K.; Song, K.; Sloan, E.; Dharmawardhana, P.; Kobayashi, R. Improved measurements and correlation of the water content of methane gas in equilibrium with hydrate. Presented at the 58th Annual GPA Convention, Denver, CO, 1979. (5) Song, K. Y.; Yarrison, M.; Chapman, W. Experimental low temperature water content in gaseous methane, liquid ethane, and liquid propane in equilibrium with hydrate at cryogenic conditions. Fluid Phase Equilib. 2004, 224, 271−277. (6) Fouad, W. A.; Ballal, D.; Cox, K. R.; Chapman, W. G. Examining the Consistency of Water Content Data in Alkanes Using the Perturbed-Chain Form of the Statistical Associating Fluid Theory Equation of State. J. Chem. Eng. Data 2014, 59, 1016−1023. (7) Poettmann, F.; Dean, M. Water content of propane. Pet. Refin. 1946, 25, 125−128. (8) Kobayashi, R.; Katz, D. Vapor-liquid equilibria for binary hydrocarbon-water systems. Ind. Eng. Chem. 1953, 45, 440−446. (9) Parrish, W.; Pollin, A.; Schmidt, T. Properties of ethane-propane mixes, water solubility and liquid densities. Presented at the 61st Annual GPA Convention, Dallas, TX, 1982. (10) King, A. D., Jr.; Coan, C. Solubility of water in compressed carbon dioxide, nitrous oxide, and ethane. Evidence for hydration of carbon dioxide and nitrous oxide in the gas phase. J. Am. Chem. Soc. 1971, 93, 1857−1862. (11) Sparks, K. A.; Sloan, E. D. Water Content of NGL in Presence of Hydrates; Gas Processors Association: Tulsa, OK, 1983. (12) Sloan, E.; Bourrie, M.; Sparks, K.; Johnson, J. An experimental method for the measurement of two phase liquid hydrocarbon-hydrate equilibrium. Fluid Phase Equilib. 1986, 29, 233−240.

Figure 10. Water content isotherms for gas mixture 3 as a function of pressure. Red symbols represent experimental data by this work, while black symbols represent data by Chapoy et al.23 () Model predictions.

agreement between the experimental data and predicted values is good, with calculated AADs of 14.38 and 8.37%, respectively. In terms of Figure 9, the model appears to compare well with other commercial software available in the market. In general, PC-SAFT as well as CSMGem software tends to predict slightly higher pressure dependence than that measured in our lab and predicted by CPA-Multiflash. Moreover, Figure 10 shows how data measured in this work and that by Chapoy et al.23 almost match each other within experimental error. We continue to evaluate the pressure dependence of the theory including the different assumptions made in developing the modified van der Waals−Platteeuw solid solution theory.41 However, more experimental work is still needed to understand the effect of pressure on water content.



CONCLUSION Water content of three natural gas mixtures in equilibrium with hydrates was measured using a flow apparatus with a Panametrics moisture analyzer. Readings were taken at temperatures ranging from 294.1 to 253 K and pressures ranging from 5 to 40 MPa. A model based on the perturbed chain form of the SAFT equation of state combined with a modified form of the solid solution theory was proposed to 9643

DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644

Article

Industrial & Engineering Chemistry Research

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DOI: 10.1021/acs.iecr.5b02240 Ind. Eng. Chem. Res. 2015, 54, 9637−9644