Article pubs.acs.org/jced
Experimental Determination of the Equilibrium Water Content of CO2 at High Pressure and Low Temperature Published as part of The Journal of Chemical and Engineering Data special issue “Proceedings of the 19th Symposium on Thermophysical Properties” Louis V. Jasperson,† Jeong Won Kang,‡ Chul Soo Lee,‡ Don Macklin,§ Paul M. Mathias,*,∥ Rubin J. McDougal,† Won Gu Rho,‡ and David VonNiederhausern† †
Wiltec Research Company, Inc., 488 South 500 West, Provo, Utah 84601, United States Department of Chemical and Biological Engineering, Korea University, 5-1 Anam-Dong, Sungbuk-Ku, Seoul 136-701, South Korea § Alaska Gasline Development Corporation Calais Building One 3201 C Street, Suite 200, Anchorage, Alaska 99503, United States ∥ Fluor/Worley Parsons Arctic Solutions, 3 Polaris Way, Aliso Viejo, California 92698, United States ‡
ABSTRACT: Quantitative understanding of the water content of pipeline fluids in equilibrium with hydrates is critically important to ensure pipeline flow without hindrance from solid precipitation. This paper focuses on pipelines with CO2rich fluids in cold environments (such as those in Alaska) and generally in CO2 capture. Since there is considerable question about the available data for the water solubility in CO2 at these conditions, a round-robin testing program was structured by Fluor/Worley Parsons Arctic Solutions to quantitatively establish the water solubility. The goal of the data program was to determine the water solubility in CO2-rich mixtures to estimated uncertainty. This paper presents the data program and evaluates its results through thermodynamic analysis and comparison to available literature data.
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publications.5,6 These data have been questioned by other researchers, principally because the measured water solubility exhibits unexpectedly strong pressure dependence. Seo, Kang, and Lee7 measured data at high pressure (6.1 MPa to 10.1 MPa) and relatively high temperature (274 K to 294 K), and concluded that the pressure dependence of the solubility is weak. The strong pressure dependence of the Song and Kobayashi data have also been questioned using theory and analysis by Yang et al.,8 Li Jakobsen and Stang,3 Mathias,9 and researchers from Bryan Research and Engineering, Inc.10 Since these results are critically important to the process design of the ASAP Project,4 Fluor/Worley Parsons Arctic Solutions solicited proposals for a data program to measure and confirm the equilibrium water content of CO2 at low temperatures (down to 227 K) and high pressures (17 MPa to 28 MPa). Two laboratories (Wiltec Research Company and Korea University) were chosen to independently make the measurements, and the data program may be considered to be Round Robin Testing (RRT). Guidance on how to perform RRT has been published by the British Standards Institute.11
INTRODUCTION Flow assurance is of critical importance to gas pipelines.1 Hydrate formation is the dominant problem hindering flow assurance, and here it is important to keep the water concentration below the hydrate-forming solubility limit.2 In this paper we focus on the equilibrium water concentration for hydrate formation in CO2-rich mixtures, and specifically pure CO2. These fluids are important to CO2 capture for climatechange mitigation,3 and also in purification of natural gas with excess CO2 content. Processes to reduce the CO2 content of natural gas with excess CO2 typically produce two product streams: a sales gas with low CO2 content and a CO2 product with high CO2 content. In particular, for the CO2 pipeline that is part of the ASAP Project,4 the worst-case pipeline condition for hydrate formation in the CO2 pipeline has been defined as 17−28 MPa and 227 K. If the water concentration of the CO2 product from the gas-purification plant exceeds the solubility limit, an expensive dehydration unit must be added to the process design. Song and Kobayashi measured and analyzed the equilibrium water content of natural gas and natural-gas liquids (including CO2-rich fluids) in an extensive research program for the Gas Processors Association over more than a decade, and their data for the equilibrium water content of CO2 are contained in two © XXXX American Chemical Society
Received: April 5, 2015 Accepted: July 14, 2015
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DOI: 10.1021/acs.jced.5b00320 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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the Centre for Gas Hydrate Research at Heriot-Watt University presented water-content measurements, especially at low temperatures ( vSH W . Figure 11 indicates that the Wiltec data at 268.15 K and lower temperatures support the weak decrease in solubility with increasing pressure. However, Figure 12 suggests that the experimental solubility increases with pressure for temperatures above 243.15 K, and that the water solubility may decrease with pressure for the two lowertemperature isotherms (233.15 K and 223.15 K). Figure 12 shows + 20 % error bars for the 243.15 K data, and it is now clear that establishment of the pressure dependence of the solubility data requires data with uncertainty better than 20 % for the data at 243.15 K and lower. We may thus conclude that the water solubility decreases weakly with pressure at low temperatures (< 243.15 K), but confirming this conclusion will require additional high-accuracy data. It should also be noted that we would have come to a slightly different theoretical 29 result if the values of vSH W inferred from the Hlavinka calculations had been used in this analysis. However, we can conclude that the analysis in this work, together with the data of Seo et al.,7 the new data from Wiltec and Korea University, and the data from Heriot-Watt University16,17 have established the water solubility of water as hydrate in CO2-rich mixtures to an expanded combined uncertainty of 20 % at low temperatures (< 253.15 K) and high pressures (> 5 MPa).
⎞2 ⎛ ∂x ⎞2 ⎛ ∂x ux2 = ⎜ ·un w ⎟ + ⎜⎜ ·unCO ⎟⎟ 2 ⎝ ∂n w ⎠ ⎝ ∂nCO2 ⎠ +
⎛ ∂x ⎞2 ⎛ ∂x ⎞2 ⎜ ·uT ⎟ + ⎜ ·uP ⎟ ⎝ ∂T ⎠ ⎝ ∂P ⎠
(10)
The uncertainty in temperature measurements (uT) is the sum of calibrated thermometer uncertainty (0.12 K) and that in determining the dissociation of gas hydrates. It is conservatively set to 0.2 K. The temperature derivative of the solubility is determined from data. It depends on temperature. At 257 K the value is 3.6·10−5 and (uT·∂x/∂T) becomes 7.2·10−6. The uncertainty in pressure measurement (uP) is determined in the gauge calibration and estimated to be 0.01 MPa. Pressure dependence of the solubility is very weak and estimated to be 1.1·10−5. Thus, (uP·∂x/∂P) is 1.1·10−7. CO2 moles are determined by measuring masses before and after dosing the gas. The associated uncertainty (unCO2) is thus twice the uncertainy of each measurement, which is determined from balance charateristics to give 0.0144 kg or 3.3·10−4 kmol. The associated derivative is calculated using the relation,
∂x x =− ∂nCO2 nCO2 + n w
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CONCLUSIONS Data are needed for the equilibrium water content of CO2-rich mixtures at low temperature and high pressures, in particular at 227.15 K and 28 MPa, to confirm the design decision that a dehydration unit is not required for pipeline transportation of the CO2 product from the ASAP4 natural-gas purification plant.4 These data are also generally useful in understanding flow assurance in CO 2 -rich pipelines. Since there is considerable uncertainty in the available literature data for the equilibrium water content of CO2, round robin testing (RRT) was structured by Fluor/Worley Parsons Arctic Solutions and was performed by two laboratories (Wiltec Research Company and Korea University). This data program, the complementary data from Seo7 and Heriot-Watt University16,17 and the process analysis performed in this work have established that the pressure dependence of the water content of CO2-rich mixtures is weak, and, in particular, the water solubility at 227.15 K and
(11)
The contribution (unCO2·∂x/∂nCO2)clearly depends on the solubility and the total number of moles. Its value is 6.7·10−7 at x = 1.8·10−3. The uncertainty in moles of water (unW) is dependent on dosing loop volume (VlP) which is determined by calibrated ethanol moles in the loop and properties. Vlp = nE
ME M = nW W ρE ρW
(12)
Neglecting effects of temperature and pressure on densities, uncertainty in loop volume calibration is dependent on measured peak area fraction (θE). uVlp = H
∂nE ∂n M M u θE E = W u θE W ∂θE ρE ∂θE ρW
(13)
DOI: 10.1021/acs.jced.5b00320 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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(8) Yang, S. O.; Yang, I. M.; Kim, Y. S.; Lee, C. S. Measurement and Prediction of Phase Equilibria for Water + CO2 in Hydrate Forming Conditions. Fluid Phase Equilib. 2000, 175, 75−89. (9) Mathias, P. M. Explicit and Tacit Knowledge in the Development and Use of Property Databases. The Eighteenth Symposium on Thermophysical Properties, Boulder Colorado, 24−29 June 2012. (10) Hendrick. C.; Hernandez, V.; Hlavinka, M.; McIntyre, G. An Analysis of Hydrate Conditions and Property Predictions in Acid Gas Injection Systems. GPA Convention, Austin, TX, 21−24 March 2010. (11) Guidance on How to Perform Round Robin Tests. PD CLC/TR 50619:2014; British Standards Institution (BSI) Publication: February 2014. (12) Guide to the Expression of Uncertainty in Measurement; International Organization for Standardization: Geneva, Switzerland, 1993. (13) U.S. Guide to the Expression of Uncertainty in Measurement; NCSL International: Boulder, CO, 1997; ANSI/NCSL Z540-2-1997, ISBN 1-58464-005-7. (14) Chirico, R. D.; Frenkel, M.; Diky, V. V.; Marsh, K. N.; Wilhoit, R. C. ThermoML - An XML-Based Approach for Storage and Exchange of Experimental and Critically Evaluated Thermophysical and Thermochemical Property Data. 2. Uncertainties. J. Chem. Eng. Data 2003, 48, 1344−1359. (15) Cox, K. R.; Chapman, W. G.; Song, K. S.; Dominik, A.; French, R. Water Content of Liquid CO2 in Equilibrium with Liquid Water or Hydrate; GPA Convention, San Antonio, TX, 7−10 April, 2013. (16) Chapoy, A.; Haghighi, H.; Burgass, R.; Tohidi, B. On the Phase Behaviour of the (Carbon dioxide + Water) Systems at Low Temperatures: Experimental and Modelling. J. Chem. Thermodyn. 2014, 69, 1−5. (17) Burgass, R.; Chapoy, A.; Duchet-Suchaux, P.; Tohidi, B. Experimental water content measurements of carbon dioxide in equilibrium with hydrates at (223.15 to 263.15) K and (1.0 to 10.0) MPa. J. Chem. Thermodyn. 2012, 47, 6−12. (18) NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP; version 9.1, NIST: May 7, 2013. (19) Gillespie, P. C.; Wilson, G. M. Vapor−Liquid and Liquid Equilibria: Water−Methane, Water Carbon Dioxide, Water Hydrogen Sulfide, Water−n-pentane, Water−Methane−n-Pentane. GPA Research Report, RR-48, Gas Processors Association: Tulsa, OK, 1982. (20) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice-Hall, Inc.: Upper Saddle River, NJ, 1999. (21) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135−144. (22) Hare, D. E.; Sorensen, C. M. Densities of Supercooled H2O and D2O in 25 Micro Glass Capillaries. J. Chem. Phys. 1986, 84, 5085− 5089. (23) Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Zundel, N. A. DIPPR® Data Compilation of Pure Chemical Properties; Design Institute for Physical Properties, AIChE: New York, NY, 2010. (24) Van der Waals, J. H.; Platteeuw, J. C.; Prigogine, I. Clathrate Solutions. Adv. Chem. Phys. 1959, 2, 1−57. (25) Parrish, W. R.; Prausnitz, J. M. Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures. Ind. Eng. Chem. Process Des. Dev. 1972, 11, 26−35. (26) Holder, G. D.; Corbin, G.; Papadopoulos, K. D. Thermodynamic and Molecular Properties of Gas Hydrates from Mixtures Containing Methane, Argon, and Krypton. Ind. Eng. Chem. Fundam. 1980, 19, 282−286. (27) Chapoy, A., Heriot-Watt University. Personal communication, 18 February 2015. (28) Chapoy, A.; Haghighi, H.; Burgass, R.; Tohidi, B. Hydrate and Phase Behavior Modeling in CO2-Rich Pipelines. J. Chem. Eng. Data 2015, 60, 447−453. (29) Hlavinka, M., Bryan Research and Engineering, Inc. Personal communication, 28 February 2015.
The volume of the sampling loop may be a source of error and hence its volume is determined chromatographically by first filling it with ethanol, and flushing with acetone.7 In the first step, the peak area fraction of ethanol is analyzed as a linear function of known mass fraction of ethanol (mE) to yield the calibration curve and the uncertainty of peak area fraction (uθE) that is estimated to be 0.0016.
θE = a + b·mE
(14)
The curve is used to determine the unknown mass of ethanol in the loop by measuring total mass and the peak area fraction. ⎛ ρE ⎞ ∂n ⎜ ⎟uVlp = unE = E u θE ∂θE ⎝ ME ⎠
(15)
where the partial derivative is obtained from the calibration curve. ∂nE nE = ∂θE bmEmA
un w ·
(16)
⎛ M ∂n ⎞ ρ 1−x ∂x = ⎜⎜ E E u θE⎟⎟ · W · ∂n w ρ ∂ θ M n ⎝ E E ⎠ W CO2 + n w =
x(1 − x) u θE bmEmA
(17)
Equation 17 gives 2.5·10−5 as the contribution to the uncertainty at x = 0.0018. Finally combined expanded uncertainty in solubility is obtained from all contributions by setting the coverage factor to 2: ux(combined) = 5.2·10−5 or ux(combined)/x = 0.029. It is noted that the combined uncertainty is practically dependent on that of the water quantity introduced.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Koh, C. A..; Sum, A.; Sloan, E. D. Natural Gas Hydrates in Flow Assurance; Gulf Professional Publishing: Burlington, MA, 2010. (2) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gas, 3rd ed.; CRC Press: Taylor and Francis Group: Boca Rat, FL, 2008. (3) Li, H.; Jakobsen, J. P.; Stang, J. Hydrate Formation During CO2 Transport: Predicting Water Content in the Fluid Phase in Equilibrium with the CO2-Hydrate. Int. J. Greenhouse Gas Control 2011, 5, 549−554. (4) The Alaska Stand Alone Pipeline (ASAP) is Alaska’s in-state natural gas pipeline project designed to develop an affordable, longterm energy solution for Fairbanks, South-Central, and as many other Alaskan communities as possible (http://asapgas.agdc.us/). (5) Song, K. Y.; Kobayashi, R. The Water Content of CO2-Rich Fluids in Equilibrium with Liquid Water and/or Hydrates. GPA Research Report RR-99. Gas Processers Association: June 1986. (6) Song, K. Y.; Kobayashi, R. Water Content of CO2 in Equilibrium with Liquid Water and/or Hydrates. SPE Form. Eval. 1987, 2, 500− 508. (7) Seo, M. D.; Kang, J. W.; Lee, C. S. Water Solubility Measurements of the CO2-Rich Liquid Phase in Equilibrium with Gas Hydrates Using an Indirect Method. J. Chem. Eng. Data 2011, 56, 2626−2629. I
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(30) Wiebe, R. The Binary System Carbon Dioxide-Water Under Pressure. Chem. Rev. 1941, 29, 475−481. (31) Gillespie, P. C.; Wilson, G. M. Vapor−Liquid and Liquid−Liquid Equilibria: Water−Methane/Water−Carbon Dioxide/Water−Hydrogen Sulfide/Water−n-Pentane/Water−Methane/n-Pentane, Research Report RR-48; Gas Processors Association: Tulsa, OK, 1982.
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DOI: 10.1021/acs.jced.5b00320 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
