Solubility of Nitrous Oxide in Aqueous Methyldiethanolamine Solutions

Article pubs.acs.org/jced

Solubility of Nitrous Oxide in Aqueous Methyldiethanolamine Solutions Fang-Yuan Jou,† Alan E. Mather,† and Kurt A. G. Schmidt*,‡ †

Department of Chemical and Materials Engineering, University of Alberta, Donadeo Innovation Centre for Engineering, Edmonton, AB T6G 1H9, Canada ‡ Schlumberger, Abingdon Technology Centre, Lambourn Court, Wyndyke Furlong, Abingdon OX14 1UJ, United Kingdom ABSTRACT: The solubility of nitrous oxide in a 20 mass % aqueous solution of methyldiethanolamine (MDEA) was measured at the temperatures of (283.15, 298.15, 323.15, 348.15, 373.15, and 398.15) K at pressures up to 20.37 MPa. In addition, the solubility of nitrous oxide in a 40 mass % aqueous solution of MDEA was measured at temperatures of (274.15, 283.15, 298.15, 323.15, 348.15, 373.15, and 398.15) K at pressures up to 20.57 MPa. The individual data sets were correlated with the Peng−Robinson equation of state with temperature-dependent binary interaction parameters. The correlation approach reproduced the experimental data to within an overall average percent deviation in the N2O liquid-phase mole fraction of 3.5% and 4.5% in the 20 mass % and 40 mass % MDEA solutions, respectively. The Peng−Robinson equation of state combined with the Krichevsky−Ilinskaya equation were used to obtain Henry’s law constants, partial molar volumes at infinite dilution, and Margules parameters for these systems. The new Henry’s law constants were correlated with the Li−Mather model. The new binary (N2O + MDEA) interaction energy parameters correlated the Henry’s law constants of N2O in both of the aqueous MDEA solutions to within 1.2%. As part of the solubility and Henry’s law constant model development, new models for the density of pure MDEA and (MDEA + H2O) solutions were developed. These models could reproduce the literature density data of pure MDEA and aqueous MDEA solutions to within 0.10% and 0.13%, respectively.

1. INTRODUCTION Methyldiethanolamine (MDEA) is widely used for the removal of the acid gases hydrogen sulfide (H2S) and carbon dioxide (CO2) from gas streams. MDEA is a tertiary amine and has the advantage of being more selective for H2S removal compared with conventional amines such as monoethanolamine (MEA) and diethanolamine (DEA). One disadvantage of MDEA is its higher cost compared with conventional amines. When used in gas treatment, MDEA is normally employed as an aqueous solution with a concentration of between (30 and 50) mass %. The design of suitable gas−liquid contactors requires the physical solubility of CO2. However, this solubility is difficult to determine from direct experimental measurements since the gas undergoes a chemical reaction with the solvent. Often, the physical solubility of CO2 is determined from the solubility of nitrous oxide (N2O) via the N2O analogy.1 In the present work, new solubility data were obtained that can be used to verify the N2O analogy at low and high temperatures. The new experimental data are part of an ongoing project to provide experimental data that are useful for the design of plants for the hydrocarbon-processing industry. Previous studies from this laboratory included the solubility of hydrogen sulfide,2 carbon dioxide,2 methane,3 ethane,3,4 propane,5 nbutane,6 methanethiol,2 ethanethiol,7 and propylene8 in aqueous MDEA solutions. © 2017 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Apparatus Description. The apparatus and experimental technique that were used are similar to those described by Jou et al.9 The equilibrium cell was mounted in a temperature-controlled air bath. The temperature in the cell was measured using a type J thermocouple that was calibrated against a platinum resistance thermometer. The pressure in the cell was measured by (0 to 10, 0 to 35) MPa digital Heise gauges. The pressure gauges were calibrated by comparison to a dead-weight gauge. The standard uncertainty in the temperature was u(T) = 0.1 K, and the relative standard uncertainty in the pressure was ur(P) = 0.001. Further details of the experimental apparatus can be found in Roberts.10 2.2. Experimental Procedures. Prior to the introduction of the fluids, the cell was evacuated. About 120 cm3 of the MDEA solution was drawn into the cell. The nitrous oxide was added to the cell by the cylinder pressure or by means of a spindle press. The circulation pump was started, and the vapor was bubbled through the solvent for at least 4 h to ensure that Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 31, 2017 Accepted: June 7, 2017 Published: June 26, 2017 2761

DOI: 10.1021/acs.jced.7b00112 J. Chem. Eng. Data 2017, 62, 2761−2769

Journal of Chemical & Engineering Data

Article

Table 2. Experimental Solubilitya Data for Temperature (T), Pressure (P), and Aqueous-Phase Nitrous Oxide Mole Fraction (x2) for the System Nitrous Oxide (2) + 20 mass % Aqueous Solution of Methyldiethanolamine (1)b

equilibrium was reached. At high pressures, a sample of the liquid phase, (2 to 20) g depending on the solubility, was withdrawn from the cell into a 50 cm3 sample bomb that had previously been evacuated and weighed. The bomb contained a magnetic stirring bar to help in degassing the sample. The sample bomb was reweighed to determine the mass of the sample and then attached to a vacuum rack. The rack consisted of 6.35 mm o.d. stainless steel tubing connected to a calibrated Digigauge (range (0 to 1.0) MPa) and a 50 cm3 buret. The rack was evacuated, and the gas was allowed to evolve from the sample bomb into the buret, which was maintained at the local atmospheric pressure and room temperature. The amount collected was calculated from the P−V−T data assuming ideal gas behavior. A correction was made for the residual nitrous oxide left in the sample at atmospheric pressure by injection of an aliquot into a gas chromatograph.11 At low pressures, a 10 μL sample of liquid was taken from the liquid sample outlet and injected directly into the gas chromatograph. The relative standard uncertainty in the liquid-phase compositional (mole fraction) analyses was ur(x2) = 0.03. 2.3. Experimental Materials. The provenances and purities of nitrous oxide (CAS no. 10024-97-2), water (CAS no. 7732-18-5), and MDEA (CAS no. 105-59-9) used in the experiments are given in Table 1. Table 1. Sample Information

a

chemical name

source

stated minimum purity

MDEAa nitrous oxide water

Aldrich Union Carbide Canada University of Alberta

99%b 99.8%b deionized and distilledb

N-Methyldiethanolamine. bNo further purification was attempted.

a(T ) RT − V−b V (V + b) + b(V − b)

P/MPa

x2·103

T = 283.15 K 2.20 13.39 0.946 6.52 0.401 2.89 0.103 0.78

T = 298.15 K 20.37e 19.24 17.19e 19.04 12.92e 18.95 8.83e 18.04 5.82c 17.75 3.35 12.51 1.28 5.47 0.486 2.25 0.220 1.034 0.106d 0.503 0.055d 0.252

T = 348.15 K 19.29 16.77 15.60 15.86 11.18 14.36 6.81 10.63 3.05 5.60 2.01 3.80 1.31 2.52 0.827 1.56 0.417 0.793 0.212 0.372 0.148d 0.237 0.112d 0.158

T = 373.15 K 18.60 17.00 14.77 15.43 9.90 12.20 6.02 8.410 3.07 4.754 2.00 3.164 1.28 1.934 0.880 1.335 0.516 0.700 0.325 0.387 0.211d 0.194 0.181d 0.145 0.154d 0.096

P/MPa

x2·103

T = 323.15 K 19.75 17.00 16.07 16.98 12.70 16.03 9.44 15.27 5.32 11.37 2.90 7.094 1.15 3.066 0.363 0.984 0.174 0.468 0.113d 0.299 0.111d 0.283 0.069d 0.171 T = 398.15 K 18.82 17.99 15.26 16.10 10.73 12.76 6.95 9.133 3.65 4.983 2.31 3.133 1.33 1.627 0.600 0.550 0.409 0.287 0.371d 0.214 0.309d 0.116 0.286d 0.100

a Vapor−liquid equilibrium unless otherwise indicated. bThe standard uncertainty u and relative standard uncertainties ur are u(T) = 0.1 K, ur(P) = 0.001, and ur(x2) = 0.03. cLiquid−liquid−vapor equilibrium. d By gas chromatography. eLiquid−liquid equilibrium.

3. RESULTS AND DISCUSSION The solubility of nitrous oxide in a 20 mass % aqueous solution of MDEA was measured at the temperatures of (283.15, 298.15, 323.15, 348.15, 373.15, and 398.15) K at pressures up to 20.37 MPa. The experimental data are presented in Table 2. Table 3 presents the results on the solubility of nitrous oxide in a 40 mass % aqueous solution of MDEA, which was measured at temperatures of (274.15, 283.15, 298.15, 323.15, 348.15, 373.15, and 398.15) K at pressures up to 20.57 MPa. Threephase equilibria were observed in the nitrous oxide + aqueous solutions of MDEA. The points labeled “dew” are where a nitrous oxide-rich liquid begins to form, which is in equilibrium with an aqueous liquid and a vapor. Those marked “bubble” are where a vapor forms, which is in equilibrium with two liquids. No compositional analysis was performed on the third phase that appeared under these conditions. In addition, the N2O + 40 mass % aqueous solution of MDEA formed a hydrate at 247.15 K and 8.34 MPa. 3.1. Fluid Phase Equilibrium Model. The solubility data were correlated with the Peng−Robinson equation of state12 by a procedure similar to that described in Jou et al.11 The Peng− Robinson equation of state is shown in eq 1: P=

x2·103

P/MPa

NC NC

a=

∑ ∑ xixj i=1 j=1

aiiajj (1 − kij) (2)

NC

b=

∑ xibi i=1

(3)

where NC is the number of components and the kij are the binary interaction parameters. In this case, the ternary mixtures were treated as pseudobinary mixtures, similar to the approach described by Carroll et al.13 The a22 and b2 parameters for nitrous oxide were obtained from the critical constants presented in Jou et al.9 The a11 and b1 parameters for the aqueous MDEA solutions were obtained from the vapor pressure and the liquid density of the solutions. The vapor pressures of the solutions were obtained from the equations and the parameters presented in Schmidt et al.14 3.2. Solution Density Correlation. A new correlation for the (MDEA + H2O) solution density was developed in this investigation. A comprehensive review of the literature data was performed, and a list of all of the data available in the open literature is presented in Table 4. A total of 1081 individual data points have been reported in the literature with an MDEA mole fraction range of 0.0021741 to 0.98130 and a temperature range of (283.15 to 373.15) K. A modification of the method of

(1)

The mixture parameters a and b were obtained from the solute and solvent component properties via the van der Waals mixing rules: 2762



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Table 3. Experimental Solubilitya Data for Temperature (T), Pressure (P), and Aqueous-Phase Nitrous Oxide Mole Fraction (x2) for the System Nitrous Oxide (2) + 40 mass % Aqueous Solution of Methyldiethanolamine (1)b P/MPa

x2·103

P/MPa

x2·103

T = 274.15 K 8.34c 22.21 5.90h 22.03 3.24d,f 21.56 3.20e,f 21.40 1.21 9.995 0.365 3.263 0.101 0.965

T = 283.15 K 8.76h 20.9 6.36h 21.1 4.06d,f 21.0 3.99e,f 20.1 2.00 12.3 0.886 5.93 0.390 2.77 0.104 0.773

T = 323.15 K 19.56 21.46 15.25 20.71 10.33 19.48 5.890 15.32 4.080 11.96 2.920 8.65 1.870 6.01 1.030 3.35 0.406 1.33 0.193 0.651 0.114 0.362 0.102g 0.321

T = 348.15 K 19.28 23.09 14.61 21.38 10.63 19.03 6.19 13.44 3.04 7.335 1.51 3.812 0.701 1.756 0.267 0.657 0.176g 0.392 0.159g 0.340 0.149g 0.305 0.127g 0.255 0.111g 0.214

P/MPa

Table 4. Summary of the Available Literature Data for the Density of (MDEA + H2O) Solutions

x2·103

T = 298.15 K 20.57h 21.5 17.17h 21.2 13.17h 21.2 9.37h 20.8 5.77f 19.5 4.42 16.7 2.04 9.19 0.98 4.77 0.38 1.97 0.186 0.958 0.108g 0.544 T = 373.15 K 18.71 24.99 14.43 22.39 9.45 17.41 6.19 12.39 3.04 6.517 1.67 3.595 1.00 2.097 0.754 1.556 0.545 1.055 0.365 0.674 0.217 0.310 0.174g 0.199 0.155g 0.156

T = 398.15 K 18.63 26.87 15.74 24.22 12.71 21.67 9.00 16.26 6.03 11.39 3.32 6.573 1.49 2.863 1.24 2.349 0.789 1.303 0.685 1.036 0.325 0.260 0.320g 0.222 0.289g 0.174 0.266g 0.124

Vapor−liquid equilibrium unless otherwise indicated. bThe standard uncertainty u and relative standard uncertainties ur are u(T) = 0.1 K, ur(P) = 0.001, and ur(x2) = 0.03. cHydrate. dBubble. eDew. fLiquid− liquid−vapor equilibrium. gBy gas chromatography. hLiquid−liquid equilibrium.

Weiland et al.15 was used to correlate the densitometric data. The pertinent equations are: xamVam + x H2OVH2O V

V = xamVam + x H2OVH2O + xamx H2OV *

year

no. of points

AAPD/%

ref

1989 1992 1994 1994 1995 1995 1996 1997 1998 1999 2000 2000 2001 2003 2003 2006 2006 2006 2006 2008 2009 2010 2010 2011 2012 2012 2013 2013

43 8 15 10 5 112 4 15 4 117 6 72 11 7 187 15 40 27 3 153 60 6 5 4 98 32 12 10 1081

0.08 0.10 0.20 0.09 0.17 0.09 0.33 0.20 0.33 0.20 0.10 0.10 0.10 0.17 0.13 0.10 0.12 0.12 0.15 0.09 0.05 0.16 0.17 0.13 0.12 0.16 0.20 0.96 0.13

28 29 30 31 32 33 34 35 15 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

Table 5. Summary of the Available Literature Data for the Density of MDEA

a

ρ=

investigators Al-Ghawas et al. Li and Shen Rinker et al. Li and Lie Welsh and Davis Maham et al. Weiland Rinker et al. Weiland et al. Fischer et al. Rinker and Sandall Hawrylak et al. Aguila-Hernandez et al. Mandal et al. Bernal-Garcia et al. Á lvarez et al. Hawrylak et al. Paul and Mandal Rebolledo-Libreros and Trejo Muhammad et al. Chowdhury et al. Speyer et al. Zhao et al. Lu et al. Han et al. Jayarathna et al. Shojaeian and Haghtalab Yusoff et al. overall

(4) (5)

where “am” stands for “amine”. The densities of pure MDEA and H2O are both needed for this model. The density of pure MDEA was taken from a new quadratic polynomial expression 2763

investigators

year

no. of points

AAPD/%

ref

Knorr and Matthes Al-Ghawas et al. DiGuilio et al. Wang et al. Li and Shen Maham et al. Rinker et al. Noll et al. Fischer et al. Burke et al. Hawrylak et al. Henni et al. Aguila-Hernandez et al. Bernal-Garcia et al. Á lvarez et al. Paul and Mandal Rebolledo-Libreros and Trejo Muhammad et al. Chowdhury et al. Zhao et al. Han et al. Jayarathna et al. Shojaeian and Haghtalab Yusoff et al. overall

1898 1989 1992 1992 1992 1995 1997 1998 1999 2000 2000 2000 2001 2003 2006 2006 2006 2008 2009 2010 2012 2012 2013 2013

1 10 8 5 8 7 6 17 9 3 3 5 3 17 6 3 3 9 5 5 20 7 6 5 171

0.27 0.10 0.07 0.08 0.07 0.12 0.24 0.10 0.17 0.04 0.04 0.07 0.06 0.08 0.01 0.13 0.06 0.14 0.05 0.11 0.08 0.11 0.17 0.18 0.10

55 28 56 57 29 33 35 58 36 59 38 60 39 41 42 44 45 46 47 49 51 52 53 54



Article

Figure 1. Literature density data for MDEA solutions compared with correlated values. For T = 283 K: black ◆, Bernal-Garcia et al.;41 ◇, Hawrylak et al.;38 gray ◆, Welsh and Davis.32 For T = 298 K: black ●, Al-Ghawas et al.;28 ○, Alvarez et al.;42 gray ●, Bernal-Garcia et al.;41 black ◓, Hawrylak et al.;38 gray ◓, Hawrylak et al.;43 black ◑, Han et al.;51 gray ◑, Maham et al.;33 black ◒, Mandal et al.;40 gray ◒, Muhammad et al.;46 black ◐, Rinker and Sandall;37 gray ◐, Weiland;34 black top-half-shaded triangles, Weiland et al..15 For T = 323 K: black ■, Al-Ghawas et al.;28 □, Aguila-Hernandez et al.;39 gray ■, Alvarez et al.;42 black ⬒, Bernal-Garcia et al.;41 gray ⬒, Chowdhury et al.;47 black ◨, Fischer et al.;36 gray ◨, Han et al.;51 black ⬓, Jayarathna et al.;52 gray ⬓, Li and Shen;29 black ◧, Li and Lie;31 gray ◧, Maham et al.;33 black ◮, Mandal et al.;40 black bottom-halfshaded triangles, Muhammad et al.,46 black ◭, Rebolledo-Libreros and Trejo;45 black top-half-shaded diamonds, Shojaeian and Haghtalab;53 black right-half-shaded diamonds, Zhao et al.49 For T = 348 K: ▲, Bernal-Garcia et al.;41 △, Han et al.51 For T = 373 K: ×, Fischer et al.;36 +, Rinker et al.;35 *, Rinker and Sandall.37 Aqueous MDEA solution density model: brown dotted line, 283 K; brown solid line, 298 K; black dashed line, 323 K; black dotted line, 348 K; black solid line, 373 K.

Figure 2. Experimental data for the nitrous oxide (1) + 20 mass % MDEA aqueous solution (2) system compared with correlated values using the Peng−Robinson equation of state. Experimental data: ○, 283.15 K; ◆, 298.15 K; ◇, 323.15 K; ▲, 348.15 K; △, 373.15 K; ■, 398.15 K. Peng−Robinson equation of state: black dotted line, 283.15 K; black dashed line, 298.15 K; brown solid line, 323.15 K; brown dotted line, 348.15 K; brown dashed line, 373.15 K; solid blue line, 398.15 K.

Table 6. Equation of State Parameters MDEA solution (1) T/K

a

a11

a

283.15 298.15 323.15 348.15 373.15 398.15

0.992 0.971 0.938 0.906 0.875 0.847

274.15 283.15 298.15 323.15 348.15 373.15 398.15

1.23 1.22 1.19 1.14 1.10 1.06 1.02

b1b

nitrous oxide (2) a22a

20 mass % MDEA Solution 18.9 0.441 18.9 0.428 18.9 0.407 18.9 0.388 18.9 0.369 18.9 0.352 40 mass % MDEA Solution 23.4 0.449 23.4 0.441 23.4 0.428 23.4 0.407 23.4 0.388 23.4 0.369 23.4 0.352

b2b

k12

27.6 27.6 27.6 27.6 27.6 27.6

−0.129 −0.108 −0.076 −0.048 −0.024 −0.002

27.6 27.6 27.6 27.6 27.6 27.6 27.6

−0.028 −0.017 −0.001 0.025 0.048 0.070 0.090

Figure 3. Experimental data for the nitrous oxide (1) + 40 mass % MDEA aqueous solution (2) system compared with correlated values using the Peng−Robinson equation of state. Experimental data: ●, 274.15 K; ○, 283.15 K; ◆, 298.15 K; ◇, 323.15 K; ▲, 348.15 K; △, 373.15 K; ■, 398.15 K. Peng−Robinson equation of state: black solid line, 274.15 K; black dotted line, 283.15 K; black dashed line, 298.15 K; brown solid line, 323.15 K; brown dotted line, 348.15 K; brown dashed line, 373.15 K; blue solid line, 398.15 K.

reproduces the experimental data to within an overall average absolute percent deviation (AAPD) of 0.10%. The temperature range of the data available in the literature was (283.15−430.9) K. This expression was used to calculate the molar volume of MDEA, Vam, in eqs 4 and 5. The correlation of Wagner and Pruss16 was used to calculate the molar volume of pure water, VH2O. The optimization approach of Schmidt et al.17 was used to determine the molar volume associated with the interaction between water and the amine, V*. The objective function related the differences between the calculated solution densities and the experimental values. The V* function that best correlated the solution density data was:

The units of a are Pa·m6·mol−2. bThe units of b are cm3·mol−1.

determined from all of the pure MDEA density data available in the literature (171 points). The overall data set is summarized in Table 5. The resulting equation, ρam = 1.224 − 5.104 × 10−4(T /K) − 3.890 × 10−7(T /K)2

V * = −6.962 + 5.461xam

(6) 2764

(7) DOI: 10.1021/acs.jced.7b00112 J. Chem. Eng. Data 2017, 62, 2761−2769


Article

The new solution density model reproduces the literature density data to within an AAPD of 0.13%. A comparison of the solution density model and the experimental data for five isotherms (283.15, 298.15, 323.15, 348.15, 373.15) K is presented in Figure 1. 3.3. Equation of State Correlation. The a11 and b1 parameters of the MDEA solutions were then determined from the calculated solution properties. The resulting values of a11 and b1 for the 20 mass % and 40 mass % MDEA solutions are given in Table 6. Analysis of the results indicated that a temperature-independent covolume parameter was sufficient for both solutions. The binary interaction parameter k12, which appears in the mixing rule for the equation of state, was regressed from the experimental data following the optimization approach of Schmidt et al.17 In this case, the objective function related the differences between the calculated liquid-phase mole fractions (of the aqueous phase) and the experimental values. A twophase flash calculation was performed to obtain the compositions of the fluid phases at each experimental pressure P and temperature T. This modeling approach reproduces both the experimental vapor−liquid equilibrium data and the liquid−liquid equilibrium data (as indicated in Tables 2 and 3) satisfactorily close to the experimental uncertainty. The binary interaction parameters are for each pseudobinary mixture, i.e., (N2O + 20 mass % aqueous solution of MDEA) and (N2O + 40 mass % aqueous solution of MDEA). The modeling approach was used to correlate each data set, and no attempt was made to generalize the modeling approach to all of the MDEA aqueous solutions. Caution should be exercised if the correlation is extrapolated to other aqueous mixtures. The values of k12 were found to be dependent on the temperature, and the optimal relationships were determined to be

Table 7. Parameters of the Krichevsky−Ilinskaya Equation T/K 283.15 298.15 323.15 348.15 373.15 398.15 274.15 283.15 298.15 323.15 348.15 373.15 398.15

H21/MPa

3 −1 v∞ 2̅ /cm ·mol

N2O (2) + 20 mass % MDEA Solution (1) 149 33.1 225 33.8 367 35.1 495 36.6 588 38.4 637 40.7 N2O (2) + 40 mass % MDEA Solution (1) 127 33.4 157 33.8 210 34.6 295 36.0 366 37.8 413 39.8 437 42.5

A/RT 5.30 5.54 5.74 5.80 5.77 5.68 4.42 4.46 4.50 4.50 4.44 4.37 4.28

Figure 4. Temperature dependence of the Henry’s law constants for nitrous oxide (1) in 20 mass % MDEA aqueous solution: black ▲, Haimour et al.;61 □, Jou et al.26 and Tomcej;27 black ◆, Al-Ghawas et al.;28 black ■, Browning and Weiland;62 black ●, Rinker and Sandall;25 gray ●, Bishnoi and Rochelle;63 gray ◆, Jamal;64 gray ■, Kierzkowska-Pawlak and Zarzycki;65 gray ▲, this work; Li−Mather model, black dashed line.

⎡ (T / K ) ⎤ 107.1 k12 = 0.206 + 0.154⎢ ⎥− ⎣ 1000 ⎦ (T / K )

(8)

for the 20 mass % solution and ⎡ (T / K ) ⎤ 58.03 k12 = 0.068 + 0.422⎢ ⎥− ⎣ 1000 ⎦ (T / K )

(9)

for the 40 mass % solution. With this approach, the experimental solute liquid-phase mole fraction could be calculated to within 3.5% and 4.5% for the 20 mass % and 40 mass % solutions, respectively. The solubility results are compared with the experimental results in Figures 2 and 3. This modeling approach reproduces both the experimental vapor−liquid equilibrium data and the liquid−liquid equilibrium data (as indicated in Tables 2 and 3) reasonably close to the experimental uncertainty. 3.4. Krichevsky−Ilinskaya Equation. Bender et al.18 showed the connection between the Peng−Robinson equation of state, the binary interaction parameter, and the three parameters in the Krichevsky−Ilinskaya equation. The Krichevsky−Ilinskaya equation is given by

Figure 5. Temperature dependence of the Henry’s law constants for nitrous oxide (1) in 40 mass % MDEA aqueous solution: black ▲, Haimour et al.;61 □, Jou et al.26 and Tomcej;27 ◆, Al-Ghawas et al.;28 ■, Browning and Weiland;62 ●, Rinker and Sandall;25 gray ▲, this work; Li−Mather model, black dashed line.

v ∞(P − P1s) A + ln(f2̂ /x 2) = ln H21 + 2̅ (x12 − 1) RT RT (10)

where the three parameters are the Henry’s law constant, H21, the partial molar volume at infinite dilution, v∞ 2̅ , and the 2765



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Table 8. Henry’s Law Constants of Nitrous Oxide (2) in 20 mass % and 40 mass % Aqueous Solutions of MDEA investigators Haimour and Sandall Jou et al. and Tomcej Al-Ghawas et al. Browning and Weiland Rinker and Sandall Bishnoi and Rochelle Jamal Kierzkowska-Pawlak and Zarzycki Jou et al. overall Haimour et al. Jou et al. and Tomcej Al-Ghawas et al. Browning and Weiland Rinker and Sandall Jou et al. overall

year

no. of points

N2O (2) + 20 mass % MDEA Solution (1) 1984 4 1986, 1987 5 1989 7 1994 1 1996 4 2000 1 2002 8 2002 1 6 28 N2O (2) + 40 mass % MDEA Solution (1) 1984 4 1986, 1987 5 1989 7 1994 1 1996 4 7 37

AAPD/%

ref(s)

10.5 4.0 21.8 2.3 4.2 3.1 8.6 14.8 1.7 8.9

61 26, 27 28 62 25 63 64 65 this work

7.7 2.5 15.6 4.0 5.0 0.8 6.5

61 26, 27 28 62 25 this work

Table 9. Henry’s Law Constants of Nitrous Oxide (2) in Aqueous Solutions of Methyldiethanolamine (1) investigators

year

no. of points

AAPD/%

ref(s)

Haimour et al. Versteeg et al. Jou et al. and Tomcej Versteeg and van Swaaij Al-Ghawas et al. Wang et al. Browning and Weiland Davis and Pogainis Li and Lai Rinker and Sandall Bishnoi and Rochelle Ko and Li Park and Sandall Jamal Kierzkowska-Pawlak and Zarzycki Mandal et al. Jou et al. overall

1984 1987 1986, 1987 1988 1989 1992 1994 1995 1995 1996 2000 2000 2001 2002 2002 2004

20 9 10 41 35 5 4 6 3 20 2 18 5 24 9 15 13 239

8.7 7.8 2.6 6.4 17.1 13.9 4.7 12.4 21.9 4.5 2.1 11.7 6.1 7.5 14.6 11.1 1.2 9.4

61 66 26, 27 67 28 57 62 68 69 25 63 70 71 64 65 72 this work

Margules parameter, A. These three parameters were obtained from optimized equation of state parameters via the corrected equations presented by Schmidt.19 The results for each system are presented in Table 7. The calculated partial molar volumes at infinite dilution for each of the systems are very similar to those presented by Jou et al.9 for the N2O + H2O system and the value used by Perişanu20 for the solubility of N2O in polar solvents. The calculated Henry’s law constants are consistent with those previously published in the literature (as discussed in the next section). 3.5. Henry’s Law Constant Correlation. The new Henry’s law constant results were then correlated with the Li−Mather model. Li and Mather21 proposed a model for calculating the solubility of N2O in various amine solutions based on extended scaled-particle theory and the work of Hu et al.22:

ln H21 =

1 ∂Ah 1 ∂A s + + ln(kT ∑ ρj ) kT ∂N1 kT ∂N1 j

(11)

In their approach and the approach used here, Ah was calculated from the Boublik−Mansoori−Carnahan−Starling− Leland equation23,24 and As was calculated using a first-order simplified perturbation theory, i.e., neglecting the three-particle interaction term derived by Li and Mather.21 The necessary inputs to the model are the hard-sphere diameters and molecular weights of the pure components (N2O, H2O, and MDEA), the binary interaction energy parameters for (N2O + MDEA) and (H2O + MDEA), and the solution density of the solvent. The hard-sphere diameters and molecular weights for N2O, H2O, and MDEA were taken from Li and Mather.21 The binary interaction energy parameter for (N2O + H2O) was also taken from Li and Mather.21 The solution densities were calculated with eqs 4 to 7. 2766



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Ah As b fî H21 k k12

Similar to the correlative approach used by Rinker and Sandall,25 new (N2O + MDEA) binary interaction energy parameters were obtained from a fit of the new (N2O + MDEA + H2O) solubility data. A temperature-dependent ε12 function was determined to fit the data the best: ε12 /k = 321.2 −

Helmholtz energy, hard-sphere contribution, J Helmholtz energy, soft-sphere contribution, J parameter in the Peng−Robinson equation, cm3·mol−1 fugacity of component i in a mixture, MPa Henry’s law constant of solute 2 in solvent 1 at Ps1, MPa Boltzmann’s constant, J·K−1 binary interaction parameter in the Peng−Robinson equation Ni average number of molecules NC number of components Psi vapor pressure of component i, MPa P Pressure, MPa R gas constant, J·mol−1·K−1 T absolute temperature, K u standard uncertainty ur relative standard uncertainty V molar volume of the mixture, cm3·mol−1 Vi molar volume of component i, cm3·mol−1 V* molar volume associated with the interaction between water and the amine, cm3·mol−1 v∞ partial molar volume at infinite dilution, cm3·mol−1 2̅ xi mole fraction of component i

2.850 × 104 + 1.117 × 10−4(T /K )2 (T / K ) (12)

Equation 12 could correlate the new Henry’s law constants to within an overall AAPD of 1.2% (1.7% and 0.8% for the 20 mass % and 40 mass % solutions, respectively). The results are compared with the new data and with the literature data in Figures 4 and 5 and Table 8. All of the available Henry’s law constants in the open literature (239 individual points) for the (N2O + MDEA + H2O) system were then used as an a posteriori check of the Li− Mather model and the new binary interaction parameter obtained in this investigation. The calculated values are compared with the data in Table 9. Included in this table are the Henry’s law constants at (298.15, 323.15 348.15, 373.15, and 398.15) K that were reported by Jou et al.26 and Tomcej.27 These points were determined from a partial set of the data shown in Tables 2 and 3 and a different modeling approach. The AAPD between the model and the reported results is 9.4%. As can be seen in Figures 4 and 5 and Tables 8 and 9, there is scatter in some of the existing data sets.

Greek Letters

ε12 energy parameter in the Li−Mather model, J ρi density of component i, g·cm−3

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(1) Laddha, S. S.; Diaz, J. M.; Danckwerts, P. V. The N2O analogy: The solubilities of CO2 and N2O in aqueous solutions of organic compounds. Chem. Eng. Sci. 1981, 36, 228−229. (2) Jou, F.-Y.; Mather, A. E.; Ng, H. J. Effect of CO2 and H2S on the solubility of methanethiol in an aqueous methyldiethanolamine solution. Fluid Phase Equilib. 1999, 158−160, 933−938. (3) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. Solubility of methane and ethane in aqueous solutions of methyldiethanolamine. J. Chem. Eng. Data 1998, 43, 781−784. (4) Jou, F.-Y.; Mather, A. E. Solubility of ethane in aqueous solutions of monoethanolamine and diethanolamine. J. Chem. Eng. Data 2006, 51, 1141−1143. (5) Jou, F.-Y.; Mather, A. E.; Otto, F. D.; Carroll, J. J. Experimental investigation of the phase equilibria in the carbon dioxide-propane-3 M MDEA system. Ind. Eng. Chem. Res. 1995, 34, 2526−2529. (6) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. Phase equilibria in the system n-butane-water-methyldiethanolamine. Fluid Phase Equilib. 1996, 116, 407−413. (7) Jou, F.-Y.; Mather, A. E.; Schmidt, K. A. G.; Ng, H. J. Vaporliquid equilibria in the system ethanethiol + methyldiethanolamine + water in the presence of acid gases. J. Chem. Eng. Data 1999, 44, 833− 835. (8) Jou, F.-Y.; Mather, A. E. Solubility of propylene in aqueous alkanolamine solutions. Fluid Phase Equilib. 2004, 217, 201−204. (9) Jou, F.-Y.; Carroll, J. J.; Mather, A. E.; Otto, F. D. The solubility of nitrous oxide in water at high temperatures and pressures. Z. Phys. Chem. 1992, 177, 225−239. (10) Roberts, B. E. Solubility of carbon dioxide and hydrogen sulphide in mixed and chemical solvents. M.Sc. Thesis, Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada, 1983. (11) Jou, F.-Y.; Deshmukh, R. D.; Otto, F. D.; Mather, A. E. Vapor liquid equilibria for acid gases and lower alkanes in triethylene glycol. Fluid Phase Equilib. 1987, 36, 121−140. (12) Peng, D.-Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (13) Carroll, J. J.; Jou, F.-Y.; Mather, A. E.; Otto, F. D. Phase equilibria in the system water-methyldiethanolamine-propane. AIChE J. 1992, 38, 511−520.

4. CONCLUSIONS New solubility data were obtained for the system (water + MDEA + nitrous oxide). In this investigation, the solubility of nitrous oxide in a 20 mass % aqueous solution of MDEA was measured at temperatures in the range of (283.15 to 398.15) K at pressures up to 20.37 MPa, and the solubility of nitrous oxide in a 40 mass % aqueous solution of MDEA was measured at temperatures in the range of (274.15 to 398.15) K at pressures up to 20.57 MPa. The two data sets were correlated with the Peng−Robinson equation of state to within an overall average absolute percent deviation in the N2O liquid-phase mole fraction of 3.5% and 4.5% for the 20 mass % and 40 mass % MDEA solutions, respectively. Temperature-dependent binary interaction parameters were found to satisfactorily correlate both sets of data. New Henry’s law constants for each system were determined from the equation of state correlations, and these were accurately correlated with the Li−Mather model to within 1.2%. The new binary interaction energy parameters of (N2O + H2O) in the Li−Mather model were able to reproduce all of the literature Henry’s law constant data to within 9.4%.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for financial support of this research. Notes

The authors declare no competing financial interest.

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NOMENCLATURE a parameter in the Peng−Robinson equation, Pa·m6·mol−2 A Margules parameter, J·mol−1 2767



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Solubility of Nitrous Oxide in Aqueous Methyldiethanolamine Solutions

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