The Volumetric Properties of Carbonyl Sulfide and Carbon Dioxide

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The Volumetric Properties of Carbonyl Sulfide and Carbon Dioxide Mixtures from T = 322 to 393 K and p = 2.5 to 35 MPa: Application to COS Hydrolysis in Subsurface Injectate Streams Connor E. Deering, Matthew J. Saunders, Jerry A. Commodore, and Robert A. Marriott* Department of Chemistry, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4 ABSTRACT: This work describes an exploration of high-pressure acid gas chemical equilibria in CO2 rich fluids aimed at subsurface injection for acid gas reinjection, carbon sequestration, or enhanced oil recovery. To develop the capability to calculate both physical and chemical equilibria involving COS under high-pressure injectate conditions, we have measured the density changes associated with mixing COS (1) and CO2 (2) at temperatures between T = 322.91 and 393.25 K and up to p = 35 MPa. These density differences were used to calculate apparent molar volumes for COS, which were used to calibrate binary mixing parameters for high-accuracy reduced Helmholtz energy equations-of-state (γν,12 = 1.0496 and γT,12 = 0.94085). The new mixing parameters were shown to reproduce low-temperature p−x phase behavior measurements reported in the literature. The optimized mixing parameters were then applied in a Gibbs Energy Minimization (GEM) routine to find the enthalpy of formation for COS from literature equilibrium measurements at atmospheric conditions (ΔfH298.15K,0.1 MPa (COS) = 141.744 ± 0.803 kJ mol−1). The same GEM routine was used to explore the reaction of acid gases at applicable high-pressures. Results showed a decreased reaction of H2S + CO2 at low-temperature and low-pressure, that is, COS hydrolysis is less favorable at high-pressure.

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INTRODUCTION The reinjection of carbon dioxide (CO2) into subsurface reservoirs can be a preferred carbon management technique for treated production fluids (acid gas injection, AGI), flue gas sequestration (carbon capture and sequestration, CCS) and/or enhanced oil recovery (EOR). Several chemical impurities can accompany CO2 injectate streams; thus altering the vapor− liquid equilibria and potentially allowing for extraneous chemical reactions between impurities or species in the target reservoir. To this end, models which can be used to calculate chemical activities under a wide range of temperature and pressure are useful for the design and operation of AGI, CCS, and EOR processes. Of the possible impurities, there are several sulfur containing species which can be present depending on the source of the CO2. These can include hydrogen sulfide (H2S), sulfur dioxide (SO2), carbonyl sulfide (COS), and carbon disulfide (CS2). Of particular note, COS within a wet injectate stream can undergo hydrolysis to form CO2 and H2S: COS + H 2O ⇌ H 2S + CO2

studies of COS hydrolysis within high-pressure CO2 are less common. The compositional changes experienced by a wet and impure injectate can also vary during the conditioning of the fluid, for example, compression or adsorptive dehydration. While typical fixed-bed dehydration systems operate at pressures up to p = 8 MPa and temperatures above and below ambient, regeneration of an adsorptive bed can occur between temperatures above T = 477 K. Dehydration of acid gas fluids destined for reinjection often occurs during the interstage compression, which typically can see pressures up to p = 35 MPa and any temperatures ranging from T = 313 to 423 K. These two different techniques present a large range over which knowledge about the equilibrium constant for COS hydrolysis is needed. Despite this need, the only equilibrium data available in literature were measured at ambient pressures by Terres and Wesemann (1932)1 at temperatures between T = 623 and 1173 K, and by Huffmaster and Krueger (2014)2 between T = 521 and 581 K. The paucity of experimental equilibrium data for the hydrolysis of COS is not overly concerning if equilibrium constants can be calculated using other thermodynamic data. Equilibrium predictions at low-pressures, Kp1, across changing temperature can be calculated using the van’t Hoff equation and readily available enthalpies of formation data found in reference tables

(1)

The hydrolysis equilibrium is interesting from the aspect of chemical thermodynamics, because an ideal treatment of the system will show no pressure dependence; that is, all shift in equilibrium is due to nonideal chemical activities. The COS hydrolysis reaction at low-pressures has received some attention in the literature because of the various desulfurization technologies employed in the oil and gas community;1,2 however, © XXXX American Chemical Society

Received: December 15, 2015 Accepted: January 21, 2016

A

DOI: 10.1021/acs.jced.5b01061 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Reagent purities and suppliers chemical name

source

purification method

analysis method

final purity

carbon dioxide carbonyl sulfide nitrogen water

Praxair Inc. Praxair Inc. Praxair Inc. in-house, EMD Millipore

used at specification used at specification used at specification degassed under heat and vacuum

GC-TCD/FID GC-TCD/FID GC-TCD/FID resistivity

> 99.9995 mol % > 99.9 mol % > 99.998 mol % 18 MΩ·m−1

fluid respectively, through a pressure dependent isothermal calibration constant, KT, in the relative density equation

such as the National Institute of Standards and Technology’s Joint Army Navy Air Force (NIST-JANAF) Thermochemical Tables.3 To describe the nonideal equilibrium behavior at higher pressures, Qp2, volumetric information is needed for each participating component: ln Q p

2

1 − ln K p = − ·( 1 RT −

∫p

1

p2

∫p

p2

VCO ̅ 2 dp +

1

Vcos ̅ dp −

∫p

p2

ρ − ρo = KT (τ 2 − τo 2)

A low-pressure nitrogen (N2), 0.2 Pa, was used in all cases as the reference fluid and 18 MΩ·cm−1 degassed H2O was used to determine the pressure dependence of KT isothermally using densities calculated by the Span et al.11 and the Wagner and Pruß12 equations-of-state, respectively. This calibration procedure was described previously8 and was completed before and after sample measurements to monitor for any instrument drift (reproducibility was found to be better than 0.04%). After obtaining KT for the experimental conditions, densities of both pure CO2 and a subsaturated mixture of CO2 solvent with 0.027376 mole fraction COS (m = 0.63956 mol·kg−1) were measured at temperatures of T = 322.914, 346.591, 369.926, and 393.25 K for pressures between p = 2.5 to 35 MPa at intervals of 2.5 MPa. The mixture was made gravimetrically inside an evacuated 316L stainless steel Swagelok 500 cm3 vessel using a Mettler Toledo XP26003L mass comparator with 1 mg resolution before being periodically agitated for 2 weeks to achieve homogeneity. The purity and supplier for each reagent used in this study is provided in Table 1, along with any additional purification that was performed.

VH̅ 2S dp

1

∫p

1

p2

VH̅ 2O dp)

(3)

(2)

The pressure dependence of each partial molar volume, V̅ i, can be readily calculated using high-accuracy reference equations-of-state for the pure components of a given mixture combined with the appropriate mixing rules; provided that the mixing rules used have been properly calibrated using experimental data. In this work we report some of the first literature density data for the COS + CO2 system at pressures up to p = 35 MPa and temperatures between T = 322.91 and 393.25 K at a subsaturated COS concentration of m = 0.63956 mol·kg−1. These relative density measurements were combined with pure CO2 density measurements, at the same conditions, to calculate apparent molar volumes of the COS in the solvent which were then, in turn, used to optimize two symmetric binary mixing parameters4 for the reduced Helmholtz energy reference equations-of-state for COS and CO2.5,6 Comparison of the equation-of-state using the optimized binary mixing parameters to an available vapor−liquid equilibrium study7 showed a significant improvement in accuracy over the previously estimated parameters, highlighting the need for experimental data for robust calibration. Finally, high-pressure equilibria for the COS hydrolysis reaction were calculated by way of a Gibbs energy minimization procedure, using the optimized binary mixing parameters of COS + CO2 from this work, the previously optimized H2O + CO28 system, and the existing optimized parameters for the H2S + CO2 system.4

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RESULTS AND DISCUSSION Experimental Density Data. The measured density values for the subsaturated COS (component 1) + CO2 (component 2) mixture along with the mixture’s difference in density from pure CO2 are reported in Table 2. Pure CO2 densities were found to be in good agreement with calculated densities from the National Institute of Standards and Technology (NIST) recommended Span and Wagner6 equation-of-state for CO2 which had been calibrated with previous literature data. As was the case with previously measured CO2 densities on this instrument,8 a larger difference (up to 1 kg·m−3) was observed in the region where CO2 goes through a density inflection and a maximum in isothermal compressibility. Expanded uncertainties in the density, U(ρ), were estimated by combining the uncertainty, U(T + p), in the temperature, U(T), and pressure, U(p), measurements with the propagated uncertainty in the density measurement itself, U(meas), from eq 4, (all levels of confidence = 0.95):

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EXPERIMENTAL SECTION The construction and specifications of the custom built vibrating tube densimeter used in this work were previously described in detail by Deering et al.8 Density measurements carried out in this work had an average estimated, expanded uncertainty of 0.07 kg·m−3 with temperature and pressure measurements being calibrated to an expanded uncertainty of U(T) = 0.005 K by the ITS-90 standard9 and (p) = 0.000052·p by dead weight piston,10 respectively, at a 95% confidence level. The density of a sample fluid contained inside the vibrating tube of the densimeter, ρ for the mixture or ρ2 for the pure CO2 solvent, can be related to the density of a reference fluid, ρo, by measuring the time periods of the vibrating tube’s oscillation, τ/τ2 and τo for the sample/solvent and reference

U (ρ)/(kg·m−3) = [U (meas)2 + U (T + p)2 ]0.5

(4)

where U (meas) takes into account the uncertainties in the calibration constant, U(KT), the vibrating tube’s time period of oscillation while containing the sample fluid, U(τ2), and the time period while containing the reference fluid, U(τ2o by U (meas)/(kg ·m−3) = {[U (KT)(τ 2 − τo 2)]2 + [2KTU (τ 2)]2 + [2KTU (τo 2)]2 }0.5 B

(5)

DOI: 10.1021/acs.jced.5b01061 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Relative Density Measurements of COS(1) in CO2(2), ρ, with Their Respective Difference in Density from Pure CO2, Δρ = ρ − ρ2, and Apparent Molar Volumes, V̅ ϕ,1, at a Molality of m1 = 0.63956 (x1 = 0.02737).a Temperatures Were Between T = 322 to 393 K and Pressures Were up to p = 35 MPa at Intervals of Approximately 2.5 MPab p MPa 2.4551 ± 0.0001 2.4729 ± 0.0001 4.9758 ± 0.0003 4.9917 ± 0.0003 7.4612 ± 0.0004 7.5725 ± 0.0004 10.0319 ± 0.0005 10.0382 ± 0.0005 10.6503 ± 0.0006 10.6538 ± 0.0006 12.4302 ± 0.0006 14.9466 ± 0.0008 14.9822 ± 0.0008 17.4635 ± 0.0009 17.4815 ± 0.0009 19.9791 ± 0.0010 19.9808 ± 0.0010 22.4700 ± 0.0012 22.5025 ± 0.0012 24.9735 ± 0.0013 25.0150 ± 0.0013 27.4857 ± 0.0014 27.5147 ± 0.0014 29.9814 ± 0.0016 30.0110 ± 0.0016 32.4953 ± 0.0017 32.5227 ± 0.0017 35.0126 ± 0.0018 35.0382 ± 0.0018 2.4798 ± 0.0001 2.4933 ± 0.0001 4.9910 ± 0.0003 4.9934 ± 0.0003 7.4785 ± 0.0004 7.5324 ± 0.0004 10.0075 ± 0.0005 10.0089 ± 0.0005 12.4987 ± 0.0006 12.5156 ± 0.0007 14.9952 ± 0.0008 15.0124 ± 0.0008 17.4672 ± 0.0009 17.4936 ± 0.0009 19.9853 ± 0.0010 19.9900 ± 0.0010 22.4943 ± 0.0012 22.4975 ± 0.0012 25.0041 ± 0.0013 25.0163 ± 0.0013 27.5115 ± 0.0014 27.5274 ± 0.0014 30.0056 ± 0.0016 30.0273 ± 0.0016 32.5068 ± 0.0017

ρ kg·m

Δρ −3

T = 322.914 45.52 ± 0.04 45.98 ± 0.03 105.73 ± 0.04 106.28 ± 0.04 196.64 ± 0.05 202.93 ± 0.06 414.68 ± 0.20 415.80 ± 0.20 492.55 ± 0.18 492.86 ± 0.18 625.76 ± 0.12 707.61 ± 0.08 708.34 ± 0.07 755.04 ± 0.06 755.20 ± 0.06 788.85 ± 0.06 788.81 ± 0.06 815.25 ± 0.06 815.60 ± 0.05 837.26 ± 0.05 837.69 ± 0.05 856.18 ± 0.05 856.50 ± 0.05 872.68 ± 0.05 872.99 ± 0.05 887.56 ± 0.05 887.84 ± 0.05 901.09 ± 0.05 901.32 ± 0.05 T = 346.591 41.68 ± 0.03 41.88 ± 0.03 92.35 ± 0.08 92.43 ± 0.03 156.18 ± 0.04 156.36 ± 0.05 243.48 ± 0.06 244.17 ± 0.05 361.92 ± 0.10 362.86 ± 0.09 488.69 ± 0.09 489.50 ± 0.10 581.16 ± 0.08 582.01 ± 0.08 644.70 ± 0.07 644.82 ± 0.07 690.20 ± 0.07 690.16 ± 0.07 725.34 ± 0.07 725.41 ± 0.07 753.91 ± 0.07 754.03 ± 0.06 777.82 ± 0.07 778.01 ± 0.07 798.57 ± 0.07

kg·m

−3

V̅ ϕ,1

p −1

cm ·mol 3

MPa

K 0.79 0.89 1.36 1.52 4.13 4.40 23.74 24.25 40.95 40.92 17.54 7.45 7.29 4.56 4.44 3.48 3.42 2.92 2.96 2.41 2.50 1.95 2.06 1.62 1.74 1.54 1.66 1.75 1.85

711.47 ± 391.66 639.02 ± 385.28 374.90 ± 71.94 351.52 ± 71.40 134.87 ± 12.82 125.07 ± 12.11 −84.09 ± 3.55 −88.37 ± 3.54 −165.90 ± 2.55 −165.36 ± 2.54 23.96 ± 1.35 61.40 ± 0.98 61.87 ± 0.98 66.97 ± 0.85 67.31 ± 0.85 67.37 ± 0.77 67.52 ± 0.77 66.78 ± 0.72 66.68 ± 0.72 66.35 ± 0.68 66.12 ± 0.68 66.00 ± 0.65 65.74 ± 0.65 65.51 ± 0.63 65.24 ± 0.63 64.62 ± 0.61 64.37 ± 0.60 63.29 ± 0.59 63.09 ± 0.59

3.44 3.60 4.15 4.86 5.58 6.58 8.33 10.98 13.35 11.18 5.53 3.20 1.37 0.73 3.42 3.60 4.17 4.90 5.68 6.68 8.35 10.99 13.35 11.27 6.16

730.39 ± 281.49 768.80 ± 278.17 401.95 ± 58.19 395.71 ± 56.82 175.43 ± 40.16 265.23 ± 39.39 97.49 ± 16.63 80.21 ± 16.62 28.29 ± 3.99 27.41 ± 3.92 33.09 ± 2.16 33.16 ± 2.16 51.57 ± 1.49 51.50 ± 1.49 61.43 ± 1.19 61.34 ± 1.19 64.91 ± 1.03 65.22 ± 1.03 65.81 ± 0.93 66.09 ± 0.93 66.11 ± 0.86 66.22 ± 0.85 66.41 ± 0.80 66.44 ± 0.80 66.36 ± 0.76

32.5279 ± 0.0017 35.0063 ± 0.0018 35.0302 ± 0.0018 2.5031 ± 0.0001 4.9800 ± 0.0003 7.4966 ± 0.0004 10.014 ± 0.0005 12.4815 ± 0.0006 15.0316 ± 0.0008 17.4779 ± 0.0009 17.4887 ± 0.0009 19.9919 ± 0.0010 20.0030 ± 0.0010 22.5060 ± 0.0012 22.5158 ± 0.0012 25.0125 ± 0.0013 25.0227 ± 0.0013 27.5189 ± 0.0014 27.5308 ± 0.0014 30.0276 ± 0.0016 30.0349 ± 0.0016 32.5281 ± 0.0017 32.5393 ± 0.0017 35.0222 ± 0.0018 35.0297 ± 0.0018 2.4868 ± 0.0001 2.4908 ± 0.0001 4.9583 ± 0.0003 4.9689 ± 0.0003 7.5000 ± 0.0004 7.5195 ± 0.0004 10.2071 ± 0.0005 10.2071 ± 0.0005 12.5135 ± 0.0007 12.5150 ± 0.0007 15.1001 ± 0.0008 15.1404 ± 0.0008 17.5870 ± 0.0009 17.5894 ± 0.0009 20.0825 ± 0.0010 20.0849 ± 0.0010 22.5702 ± 0.0012 22.5720 ± 0.0012 25.0535 ± 0.0013 25.0541 ± 0.0013 27.5338 ± 0.0014 27.5358 ± 0.0014 30.1103 ± 0.0016 30.1118 ± 0.0016 32.5745 ± 0.0017 32.5756 ± 0.0017 35.0270 ± 0.0018 35.0278 ± 0.0018

K

ρ kg·m

Δρ −3

kg·m

−3

T = 346.591 K 798.74 ± 0.06 1.84 816.89 ± 0.04 1.34 817.07 ± 0.06 0.78 T = 369.926 K 38.46 ± 0.02 4.97 82.32 ± 0.02 5.03 133.97 ± 0.02 5.95 196.59 ± 0.03 6.69 268.67 ± 0.04 7.26 352.24 ± 0.08 8.14 432.90 ± 0.07 9.38 433.22 ± 0.07 9.57 505.37 ± 0.07 4.86 505.60 ± 0.07 4.95 564.22 ± 0.07 5.87 564.32 ± 0.07 6.67 611.24 ± 0.07 7.22 611.37 ± 0.07 8.04 649.51 ± 0.07 9.32 649.65 ± 0.07 9.56 681.47 ± 0.07 7.53 681.49 ± 0.07 5.41 708.65 ± 0.07 3.71 708.69 ± 0.07 1.95 732.17 ± 0.07 0.97 732.34 ± 0.07 0.59 T = 393.250 K 35.67 ± 0.03 5.93 35.62 ± 0.03 6.55 74.90 ± 0.03 6.80 75.22 ± 0.03 7.21 119.67 ± 0.04 7.80 120.17 ± 0.04 8.10 173.62 ± 0.04 7.75 173.42 ± 0.04 6.58 226.32 ± 0.04 5.23 226.09 ± 0.05 3.89 287.94 ± 0.06 3.11 289.14 ± 0.29 1.50 349.93 ± 0.06 1.13 349.77 ± 0.06 0.68 410.19 ± 0.07 5.65 410.01 ± 0.07 6.29 465.29 ± 0.07 6.56 465.06 ± 0.07 6.97 513.85 ± 0.07 7.53 513.59 ± 0.07 7.84 555.77 ± 0.07 7.51 555.55 ± 0.07 6.36 593.07 ± 0.08 5.00 593.33 ± 0.07 3.63 624.51 ± 0.07 2.91 624.26 ± 0.08 1.35 651.77 ± 0.07 0.99 651.50 ± 0.07 0.58

V̅ ϕ,1 cm ·mol−1 3

66.35 ± 0.76 65.50 ± 0.71 65.44 ± 0.72 926.69 ± 218.69 502.32 ± 47.42 275.85 ± 26.98 152.60 ± 12.66 104.00 ± 6.83 73.59 ± 4.06 57.14 ± 2.68 57.27 ± 2.67 60.34 ± 1.95 60.74 ± 1.95 65.90 ± 1.55 66.43 ± 1.55 67.56 ± 1.32 67.72 ± 1.32 67.43 ± 1.16 67.52 ± 1.16 67.96 ± 1.05 68.21 ± 1.05 69.01 ± 0.97 69.25 ± 0.97 67.79 ± 0.91 67.45 ± 0.91 829.52 ± 258.51 965.72 ± 257.69 523.43 ± 57.97 482.69 ± 57.69 353.00 ± 22.65 335.68 ± 22.53 181.82 ± 10.95 192.34 ± 10.93 144.53 ± 6.45 152.83 ± 6.46 112.71 ± 5.95 108.22 ± 7.81 86.00 ± 4.05 88.96 ± 4.04 73.03 ± 2.96 75.34 ± 2.96 69.57 ± 2.30 71.56 ± 2.29 70.01 ± 1.87 71.66 ± 1.88 71.09 ± 1.60 72.39 ± 1.60 71.82 ± 1.40 70.71 ± 1.40 69.66 ± 1.26 70.73 ± 1.27 70.16 ± 1.15 71.21 ± 1.15

a m1 is the molality of COS dissolved into CO2 solvent. bThe unlisted expanded uncertainties, U, are U(m1) = 0.00015 mol·kg−1, and U(T) = 0.005 K (level of confidence = 0.95). Using the average value for U(ρ), U(Δρ) = 0.21 kg·m−3. The listed expanded uncertainties U(p), U(ρ), and U(V̅ ϕ,1) are at a confidence level of 95%.

C

DOI: 10.1021/acs.jced.5b01061 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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U(T + p) was estimated using calculated CO2 densities, ρEOS,2(T, p):6 U (T + p)/(kg·m−3) = 0.5{ρEOS,2 [T − U (T ), p + U (p)] − ρEOS,2 [T + U (T ), p − U (p)]}

(6)

The expanded uncertainties for the pure CO2 and the COS(1) + CO2(2) mixture densities were found to be, on average, u(ρ2) = 0.06 kg·m−3 and u(ρ) = 0.07 kg·m−3, respectively, where these values were similar to previously published uncertainties for the H2O + CO2 system.8 Apparent Molar Volumes. As with our previous studies, we prefer to calibrate mixing parameters with apparent molar volumes, because these values only show the effect of the solute−solvent interaction and do not include small errors in the pure component equations-of-state, that is, these are excess properties rather than bulk densities or volumes. These calculations of apparent molar volumes for COS require the density difference between the pure CO2 solvent and the COS + CO2 mixture, Δρ = ρ − ρ2, which are reported in Table 2. To provide a self-consistent comparison and to compensate for slightly different pressures, the pure CO2 densities were interpolated using a Wagner-type equation for density and reduced pressure with an estimated expanded uncertainty of 0.20 kg·m−3. These smoothed CO2 densities can be recalculated using ρ2 = ρ − Δρ for the values found within Table 2. From the density measurements, the apparent molar volumes of COS (1) dissolved in CO2 (2), V̅ ϕ,1, were calculated using Vϕ̅ ,1/(cm 3·mol−1) = M1/ρ − 1000Δρ /(m1ρρ2 )

Figure 1. Apparent molar volumes of COS (1) dissolved in CO2 (2), V̅ ϕ,1, at T = 322 to 394 K and up to p = 35 MPa: ○, experimental measurement of this work; , calculated apparent molar volumes using reduced Helmholtz reference equations-of-state5,6 with (a) estimated mixing parameters4 and (b) optimized mixing parameters.

(7)

where xi are the mole ratios for component i. In eqs 9 and 10, γT,ij and γv,ij are binary mixing parameters which can be optimized using experimental mixture properties or estimated. Note that more flexible asymmetric functions can only be optimized when experimental data with multiple concentrations are available. The differences shown in Figure 1a were not unexpected, because there were no previous mixture literature data available for the COS + CO2 system to calibrate the binary mixing parameters. The estimated mixing parameters for this system are used with current reference quality programs, such as REFPROP14 or TREND 2.0.15 Optimization of Binary Mixing Parameters. For increased confidence in the calculation of mixture properties, the apparent molar volumes from this work were used to optimize the symmetric binary mixing parameters (γT,ij and γT,ij) for use with high-accuracy reduced Helmholtz equations-of-state. γν,12 = 1.0496 and γT,12 = 0.94085 were found by minimizing the sum of the squared apparent molar volume deviation objective function which was weighted by the reciprocal squared uncertainties from our measurements. Figure 1b shows the apparent molar volumes with calculations performed using the optimized parameters at T = 322.914, 346.914, 369.926, and 393.250 K. The plot can be compared to Figure 1a to show a better agreement with these apparent molar volume data. Because of the large range for molar volume in Figures 1a and 1b, it is more convenient and comprehensible to show the relative differences in density. Figure 2 shows the relative percent difference between density measurements and values calculated using the optimized mixing parameters, where agreement between the experimental densities is within 0.1% at the higher pressures or in the dense phase region. Also shown in Figure 2 are the differences for densities calculated using the

where M1 is the molar mass of COS and m1 is the molality of the mixture. The 95% confidence level expanded uncertainties reported with the apparent molar volumes found in Table 2 were calculated using U (Vϕ̅ ,1)/(cm 3·mol−1) = {([M1 − 1000/m1][U (ρ)/ρ2 ])2 + ([1000/m1][U (ρ2 )/ρ22 ])2 + ([1000Δρ/ρρ2 ][U (m1)/m12])2 }0.5

(8)

and were found to be better than ±0.04·V̅ ϕ,1 at larger densities (above the CO2 critical density6 of 467.6 kg·m−3) but were significantly greater at lower densities. As shown in Figure 1a, significant differences were found between the experimental V̅ ϕ,1 values when compared to those calculated using a combination of the pure component equations-of-state with the estimated GERG-2008 mixing parameters provided by Kunz and Wagner.4,13 We note that only estimated parameters through corresponding states were available prior to this work. The symmetrical mixing parameters for the reduced corresponding state density, ρr, and reduced corresponding state temperature, Tr, for any mixture is given by n

8/ρr (x) =

n

+1/ρc,1/3 )3 ∑ ∑ xixjγv ,ij(1/ρc,1/3 i j i=1 j=1

(9)

and n

1/Tr(x) =

n

∑ ∑ xixjγT ,ij(Tc,iTc,j)0.5 i=1 j=1

(10) D

DOI: 10.1021/acs.jced.5b01061 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Figure 2. Percent relative deviations, 100·(ρ − ρcalc,opt)/ρcalc,opt, for COS (1) + CO2 (2) densities calculated using the optimized mixing rules, ρcalc,opt, as a function of pressure from ○, experimental mixture densities of this work, and , calculated mixture densities using estimated mixing parameters4 and Helmholtz reference equations-ofstate.5,6 ρ(calc) is calculated with Helmholtz reference equations-ofstate5,6 and the optimized mixing parameters from this work.

Figure 3. P−x diagram for COS (1) + CO2 (2) at T = 248 and 273 K. ○, McDougal et al. at measured loading pressure;7 ●, McDougal et al. at calculated equilibrium pressures;7 ---, estimated binary mixing parameters4 combined with high-accuracy equations-of-state;5,6 , binary mixing parameters from this work.

estimated, or nonoptimized, parameters of Kunz and Wagner.4 The density difference plot shows a more explicit improvement in the mixing parameters, in which the same dense phase region shows ca. 1% differences from the nonoptimized parameters in the dense phase region and up to 6% near the critical density. For many engineering applications, a 1 to 4% improved agreement is rarely important; however, the improvement is important when using the same equations to calculate p−V−T properties and/or fugacities for reaction equilibria. In particular, a better fit in the density inflection region, near the supercritical region of the solvent (CO2), provides for more consistent calculation of other thermodynamic properties. Again, optimizing to density alone was not as successful as optimization to apparent molar volumes for reasons provided earlier. External Validation through p−T−x Calculations. The newly optimized mixing parameters were used to calculate dew and bubble point pressures for comparison to a recent vapor− liquid equilibrium study by McDougal et al. (2014)7 who used the Wilson Equation16 to model the equilibrium compositions of each phase at T = 248 and 273 K (see Figure 3). Although the optimization of the mixing parameters resulted in a density adjustment of only 0.2% from the estimated parameters across the pressure range studied by McDougal, there was a substantial improvement in calculating the phase behavior as the dew/bubble point pressures were shifted upward of Δp = 0.3 and 0.6 MPa for T = 248 and 273 K, respectively. This illustrates the need for accurate density measurements and robust calibration for the mixing parameters employed within high-accuracy reference equations. In some cases, less precise density measurements may not have the required precision, where small deviations in the density measurement can have a large impact when it comes to calculating other thermodynamic properties. We note that the comparison in Figure 3 is for much cooler temperatures than our experimental calibration data which also was measured at only one low concentration (0.02737 mole fraction COS). Again, this highlights the effectiveness of calibrating in a region close to the supercritical conditions as was also the case for the H2O + CO2 system studied previously. Gibbs Energy Minimization for the COS Hydrolysis Equilibrium. The calculation of COS hydrolysis equilibria has

received some attention in the literature, owing to the impact of historically incorrect enthalpies of formation, where recent thermodynamic databases have been corrected.2 Thermodynamic data from sources, such as the JANAF tables3 are often used for simulator calculations involving COS destruction within low-pressure surface processing facilities.2 These same Gibbs energy minimization (GEM) calculations can be applied at high-pressure for multiple species using the fugacity coefficient of each species, ϕi: n

G (T , p) =

∑ yi [Δf Gi1Pa + RT ln(yi ϕip)] i=1

(11)

By iteratively minimizing eq 11, the concentrations of all species, yi, can be obtained. Although there are more elegant closedform solutions for a single reaction in a single phase, we intend to continue this work for multiple reactive species; therefore, we chose the GEM technique because it is more general for complex systems. Our minimization routine was as follows: (1) iteratively minimize the G(T,p) for ϕi = 1 and p = 1 Pa; (2) use the concentrations, yi, appropriate mixing parameters, and the reference equations-of-state to calculate fugacity coefficients for all species in a mixture at T and p of interest; (3) reminimize eq 11 for new concentrations, yi; (4) repeat steps 2 and 3 until concentrations have fractionally changed by δyi /yi < 0.00001. At each step, the generalized reduced gradient nonlinear optimization routine within MS Excel was used to find the minimum for eq 11. The reduced Helmholtz energy reference equations-of-state for fugacity coefficient calculations were Wagner and Pruß for H2O;12 Span and Wagner for CO2;6 and Lemmon and Span for COS and for H2S,5 that is, those implemented in NIST’s REFPROP.14 Mixing coefficients were as follows: H2S-CO2, as optimized by Kunz and Wagner;4 H2O−CO2, as optimized by Deering et al.;8 and COSCO2, as reported in this study. Note that fugacity coefficients for H2O + CO2 were treated separately from the COS + H2S + CO2 phase, due to the lack of H2O−COS mixing coefficients. The latter simplification is only robust for low concentrations of H2O. To be consistent with the current JANAF tables, the enthalpy and entropy reference states for the reduced Helmholtz energy E

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equations-of-state used to calculate Kp1 in eq 2 were chosen to reproduce the formation enthalpies and entropies from the JANAF Tables3 at T = 298.15 K and p = 0.1 MPa. These are reported in Table 3 along with the optimized enthalpy of

To test our GEM procedure and investigate the impact of high-pressure, we performed GEM for an H2S + CO2 acid gas mixture for T = 278.15 to 900 K and at p = 0.1, 15, and 30 MPa (0.045 mole fraction H2S feed). The feed and pressures were chosen to remain in the single phase or the CO2-rich phase. The resulting equilibrium quotients, Q = (yH2S·yCO2/yCOS·yH2O), have been shown in Figure 4, along with the experimental

Table 3. Reference Enthalpies and Entropies Used in the Hydrolysis Equilibrium Calculation ΔfH298 K,0.1 MPa

ΔfS298 K,0.1 MPa

−1

J·K−1·mol−1

species

kJ·mol

H2O COS CO2 H2S

−285.830 ± 0.042 −141.744 ± 0.803 −393.522 ± 0.050a −20.502 ± 0.800a

a,b

69.95 ± 0.042a 231.581a 213.795 ± 0.120a 205.757a

a

Taken directly from the current NIST-JANAF Tables.3 bFor calculation purposes, reference conditions were set at 1 Pa with the appropriate euations-of-state5,6,12 in order to reproduce the 0.1 MPa formation values, as per convention in the JANAF Tables. Other literature values for COS are ΔfH298 K,0.1 MPa = −138.41,3 −142.55,17 −142.09,12 −142.00,19 −142.04,2 −141.548,21 and −141.7 kJ mol−1.20

formation, ΔfH298.15K,0.1 MPa for COS. As discussed in the introduction, COS hydrolysis calculations have received some attention in the literature, where the reference COS formation enthalpy in the early JANAF Tables was apparently in error, ΔfH298.15K,0.1 MPa(COS) = 138.41 kJ mol−1.2,3 Other evaluations for the reference COS formation enthalpy have resulted in values close to 142 kJ mol−1.2,3,17−21 For an independent evaluation which was self-consistent with the real fluid equations-ofstate used here, we optimized the reference COS formation enthalpy by reducing the squared deviation from the GEM calculated equilibrium constants, ln(K) = ln(yH2S·yCO2/yCOS·yH2O), and experimental values reported in the literature.1,2 These literature values included those of Terres and Wesemann1 and measurements by Huffmaster and Krueger as reported by Dowling et al.2 Our new optimized value of ΔfH298.15K,0.1 MPa(COS) = 141.744 ± 0.803 kJ mol−1 is in agreement with the value reported by Gurvitch et al. We note that the Gurvitch et al.20 value has been used in other databases (DIPPR and NASA Glenn) and is listed as the reference on the current NIST Webbook. The optimization uncertainty, or uncertainty in equilibria reference data, was far less than the uncertainty in the reference formation enthalpies for the reactants. Thus, the expanded uncertainty in the optimized value was estimated using standard propagation of error with the uncertainties for the remaining three reactants. The 95% confidence uncertainty of 0.803 kJ mol−1 is quite large; however, it is largely based on the stated uncertainty for the enthalpy of H2S (0.800 kJ mol−1). As an alternative, our GEM routine could have used the same ideal gas formation enthalpies from the JANAF Tables (0.1 MPa) and simply applied them at 1 Pa within the equation-of-state reference enthalpy. The results are the same, because the JANAF tabulated data is based on ideal gas behavior, where the effect of pressure change is the same for all species. As noted in the introduction, because the stoichiometry involves the reaction of two molecules to form two molecules, any GEM routine which uses ideal gas for a symmetric reaction stoichiometry will not show a pressure effect. In this case, all changes due to pressure are a result of the real fluid properties, that is, the fugacities or chemical activities. The convergence to the stable high-pressure equilibria values required updating/ substituting real fugacities within less than four cylces.

Figure 4. Calculated reaction quotient for a H2S + CO2 mixture at p = 0.1, 15, and 30 MPa. A feed concentration of 0.045 mole fraction H2S was used for these exploratory calculations (Tc(calc) = 304.73 K and pc(calc) = 7.3393 MPa). ◊, Terres and Wesemann (1932);1 ○, Huffmaster and Krueger (2014).2

equilibrium measurements from the literature.1,2 The GEM calculations show that COS + H2O is less favored at lowtemperature and low-pressure. Although a 0.045 mole fraction H2S in CO2 is not specific to any particular acid gas injection location, the exploratory calculation shows two general results which are applicable to CCS or AGI processes, where a CO2 fluid is compressed for injection: (1) if a dry H2S + CO2 acid gas were to be injected, additional reaction to form H2O and COS can be expected upon compression to a dense phase or (2) if a wet CO2 mixture were to contain some COS impurity, there will be less hydrolysis of COS to form H2S upon compression to the dense phase. Finally, these GEM calculations demonstrate how the mixing coefficients and high-accuracy equations-of-state can be used to explore chemical reactions in real fluids which are of interest to emerging technologies involving impure CO2 fluids. This is particularly important in pressure and temperature regions where no reaction equilibrium data exist.

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CONCLUSIONS This study has focused on p−V−T and reaction equilibria associated with COS as an impurity in high-pressure CO2 streams. We have reported new experimental densities for 0.027376 mole fraction of COS in CO2 from T = 322 to 394 K and up to p = 35 MPa, where these conditions are applicable to carbon management processes such as AGI, CCS, and EOR. Density differences were used to calculate apparent molar volumes, which were then used to calibrate mixing parameters for high-accuracy reference equations-of-state.5,6 The optimized mixing parameters were externally validated by reproducing p−x measurements at lower temperatures and over the complete composition range. In concluding our study, we applied these equations-of-state and optimized mixing parameters in a GEM routine for mixtures F

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of H2O, COS, H2S, and CO2 to find the enthalpy of formation for COS from experimental equilibrium measurements at atmospheric conditions and much greater temperatures. Our independently optimized value of ΔfH298.15K,0.1 MPa(COS) = 141.744 ± 0.803 kJ mol−1 agrees with the previous value reported by Gurvitch et al.20 Finally, the same GEM routine was used to explore the COS hydrolysis reaction (or reverse of the H2S reaction with CO2) at pressures applicable to CO2 injectate fluids. These results showed decreased reaction of H2S + CO2 at low-temperature and low-pressure. Our intention is to continue our studies toward further likely impurities in compressed CO2 streams, thus building a database to explore high-pressure chemical processes in CO2-rich fluids.

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Mixtures. GERG Technical Monograph 15; Fortschr.-Ber. VDI, VDIVerlag: Düsseldorf, 2007. (14) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, version 9.0; National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, MD, 2010. (15) Span, R.; Eckermann, T.; Herrig, S.; Hielscher, S.; Jäger, A.; Thol, M. TREND: Thermodynamic Reference and Engineering Data, version 2.0; Lehrstuhl fuer Thermodynamik; Ruhr-Universitaet: Bochum, Germany, 2015. (16) Wilson, G. M. Vapor−Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127−130. (17) Ferm, R. J. The Chemistry of Carbonyl Sulfide. Chem. Rev. 1957, 57, 621−640. (18) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. The NBS Tables of Chemical Thermodynmaic Properties. Selected Values for Inorganic and C1 and C2 Organic Substances. J. Phys. Chem. Ref. Data 1982, 11, Suppl 2.180710.1063/1.555845 (19) Svoronos, P. D. N.; Bruno, T. J. Carbonyl Sulfide: A Review of its Chemistry and Properties. Ind. Eng. Chem. Res. 2002, 41, 5321− 5336. (20) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of Individual Substances, 4th ed.; Hemisphere: New York, 1989−1996; Vols. 1−3. (21) Cox, J. D.; Wagman, D. D.; Medvedev, V. A. CODATA Key Values for Thermodynamics; Hemisphere: New York, 1989.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The authors are grateful for funding through the NSERC ASRL Industrial Research Chair in Applied Sulfur Chemistry and the sponsoring companies of Alberta Sulphur Research Ltd. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Terres, E.; Wesemann, H. Equilibrium measurements for the reactions involved in the transformation of carbon disulfide with water vapor at temperatures of 350° to 900°C. Angew. Chem. 1932, 45, 795− 803. (2) Dowling, N. I.; Huffmaster, M. A.; Krueger, K.; Wissbaum, R. J. Are the JANAF Thermochemical Data for Carbonyl Sulfide “Correct”?, Proceedings of the 21st Brimstone Sulfur Recovery Symposia, Vail, CO, September 8−12, 2014. (3) Chase, M. W. NIST-JANAF Thermochemical Tables, 4th edition. J. Phys. Chem. Ref. Data 1998, 9, 1−1951. (4) Kunz, O.; Wagner, W. The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG2004. J. Chem. Eng. Data 2012, 57, 3032−3091. (5) Lemmon, E. W.; Span, R. Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 2006, 51, 785−850. (6) Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509−1595. (7) McDougal, R. J.; Jasperson, L. V.; Wilson, G. M. Vapor-Liquid Equilibrium for Several Compounds Related to the Biofuels Industry Modeled with the Wilson Equation. J. Chem. Eng. Data 2014, 59, 1069−1085. (8) Deering, C. E.; Cairns, E. C.; McIsaac, J. D.; Read, A. S.; Marriott, R. A. The partial molar volumes for water dissolved in high-pressure carbon dioxide from T = (318.28 to 369.40) K and pressures up to p = 35 MPa. J. Chem. Thermodyn. 2016, 93, 337−346. (9) Preston-Thomas, H. The International Temperature Scale of 1990 (ITS-90). Metrologia 1990, 27, 3−10. (10) Tilford, C. R. Pressure and Vacuum Measurements. In Physical Methods of Chemistry; Rossiter, B. W., Baetzold, R. C., Eds.; John Wiley & Sons: New York, 1992; Vol. 6, pp 101−173. (11) Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W.; Yokozeki, A. A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000K and Pressures to 2200 MPa. J. Phys. Chem. Ref. Data 2000, 29, 1361−1433. (12) Wagner, W.; Pruß, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (13) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG2004 Wide-Range Equation of State for Natural Gases and Other G

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