ARTICLE pubs.acs.org/JPCB
Separation of N2O and CO2 Using Room-Temperature Ionic Liquid [bmim][BF4] Mark B. Shiflett,*,† Anne Marie S. Niehaus,† and A. Yokozeki‡ †
Experimental Station, DuPont Central Research and Development, Wilmington, Delaware 19880, United States ABSTRACT: We have developed a ternary equation of state (EOS) model for the N2O/CO2/1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) system in order to understand separation of these gases using room-temperature ionic liquids (RTILs). The present model is based on a generic RK (Redlich-Kwong) EOS, with empirical interaction parameters for each binary system. The interaction parameters have been determined using our measured VLE (vapor-liquid equilibrium) data for N2O/[bmim][BF4] and CO2/[bmim][BF4] and literature data for N2O/ CO2. The binary EOS models for the N2O/[bmim][BF4] and CO2/[bmim][BF4] systems correctly predicted the liquid-liquid phase separation found in VLLE experiments. The validity of the ternary EOS model has been checked by conducting VLE experiments for the N2O/CO2/[bmim][BF4] system over a range in temperature from 296 to 315 K. With this EOS model, solubility (VLE) behavior has been calculated for various (T, P, and feed compositions) conditions. For both large and small N2O/CO2 feed ratios, the N2O/CO2 gas selectivity [RN2O/CO2 = (yN2O/xN2O)/(yCO2/xCO2)] is R = 1.4-1.5, compared with (R = 0.96-0.98) in the absence of ionic liquid. While the concentration of the ionic liquid does not affect the selectivity, the addition of an ionic liquid provides the only practical means of separating CO2 and N2O.
1. INTRODUCTION Dinitrogen monoxide (N2O) or more commonly known as nitrous oxide is an important greenhouse gas that is produced both naturally and by human sources. Most of the current focus on global warming gases is centered on carbon dioxide emissions; however, N2O has an atmospheric lifetime of about 114 years and a global warming potential (GWP) of 298 (100-year time horizon) which, when compared with CO2 (GWP = 1), makes N2O a potent greenhouse gas.1-6 The present-day atmosphere contains about 319 ppbv of N2O (2005), which is a 9% increase from preindustrial levels (285 ppbv) with an annual growth rate of about 0.2-0.3%.2-4 The primary source of N2O is from biological processes in soils and oceans which represent about two-thirds of the total emissions.2,4,7 Anthropogenic sources of N2O include agricultural activities and industries such as mobile and stationary combustion, nitric and adipic acid production, and wastewater treatment.4,7 Although N2O is not the major contributor to global warming (∼6%), it is one of six greenhouse gases (CO2, CH4, N2O, HFC, PFC, SF6) identified for reduction by the United Nations Framework on Climate Change (UNFCC).4 As a result, a number of industries have voluntarily initiated efforts to reduce N2O emissions, particularly from adipic acid production. Thermal and catalytic abatement technologies have been successfully developed for this application due to the high N2O concentration in the adipic acid tail gas (typically 25-40 vol %).4 However, these technologies are not applicable to other sources such as nitric acid plants or stationary combustion processes due to dissimilar characteristics of the tail gas (i.e., lower N2O concentrations). r 2011 American Chemical Society
Furthermore, if N2O can be efficiently separated from adipic acid tail gas containing around 20 vol % of N2O and 20 vol % NO2 (plus CO2, O2, and N2), it could be recycled to produce additional adipic acid. Therefore, there still exists the need for development of an efficient and economic technology for the removal of N2O. A possible solution is to selectively recover N2O on a sorbent and produce a concentrated stream of N2O during the desorption. Attempts to concentrate these streams by selective adsorption using metal-exchanged zeolites has led to N2O concentrations of 5 vol % which is still insufficient to satisfy practical requirements. 4,8 Recently, room-temperature ionic liquids (RTILs) have been proposed for the capture and separation of N2O. Anthony et al.9 reported the first solubility data of N2O in 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([bmim][Tf2N]) at three temperatures (283.15, 298.15, and 323.15 K) and pressures up to 1.3 MPa. They show that the solubilities of N2O and CO2 are essentially the same (mole fraction basis) in [bmim][Tf2N] and have a significantly higher solubility than other hydrocarbons (C2H4, C2H6) and oxygen. Recently, Revelli et al.10 measured the solubility of N2O in five different imidazolium-based ionic liquids with a variable volume view cell at temperatures from 293 to 373 K and pressures up to 30 MPa. They claim that 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) and 1,3-diethyloxyimidazolium bis(trifluoromethylsulfonyl)imide ([(ETO)2IM][Tf2N]) are the Received: August 19, 2010 Revised: February 12, 2011 Published: March 15, 2011 3478
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Table 1. Experimental VLE for N2O (1) þ [bmim][BF4] (2)
Figure 1. Chemical structure of [bmim][BF4].
most efficient ionic liquids for capturing N2O and also show that the type of fluid phase behavior is type III according to the classification of Scott and van Konynenburg.11,12 This work motivated us to study the global phase behavior of N2O in a variety of ionic liquids13 and evaluate whether an ionic liquid could separate N2O and CO2 which is a binary system considered to be quasi-azeotropic over the full range of composition.14 Separation of N2O and CO2 using distillation is practically impossible; therefore, this is an interesting case to study using an ionic liquid absorbent. In the present study, we measure for the first time the ternary phase behavior of N2O/CO2/[bmim][BF4] and model the behavior using our well established cubic equation-of-state (EOS) method.15-20 The ternary EOS is based on interaction parameters of each binary system. The interaction parameter for N2O/[bmim][BF4] was calculated from VLE measured in the present work. The interaction parameters for CO2/[bmim][BF4] and CO2/N2O were taken from our previous work17 and literature data,14 respectively. In order to check the validity of the ternary EOS, VLE experiments for the N2O/CO2/[bmim][BF4] system were performed under various T, P, and feed compositions, and the EOS validity was satisfactorily confirmed. Then, the N2O/CO2 selectivities with and without RTIL [bmim][BF4] were calculated at several feed, T, and P conditions. The selectivity advantage using this RTIL is discussed based on the present ternary phase calculations.
2. EXPERIMENTAL SECTION Materials. Nitrous oxide (mole fraction purity >0.99998, CAS no. 10024-97-2) and carbon dioxide (mole fraction purity >0.9999, CAS no. 124-38-9) were purchased from GTS-Welco, Inc. (Allentown, PA) and MG Industries (Philadelphia, PA), respectively. Three samples of [bmim][BF4] (C8H15BF4N2, mole fraction purity >0.97, CAS no. 174501-65-6, Lot and Filling Codes: 1142017 31205158, 1291367 13206164, and 1128375 44104293) were obtained from Fluka (St. Louis, MO). Figure 1 provides the chemical structure. The three samples of [bmim][BF4] were combined in a nitrogen-purged drybox and the initial water content was measured by Karl Fischer (KF) titration (Aqua-Star C3000, solutions AquaStar Coulomat C and A), and contained approximately 850 ( 50 ppm of water (mass basis). The [bmim][BF4] ionic liquid sample was dried and degassed by first placing the sample in a borosilicate glass tube and pulling a vacuum on the sample with a diaphragm pump (Pfeiffer, model MVP055-3) for about 3 h. Next, the sample was fully evacuated using a turbo pump (Pfeiffer, model TSH-071) to a pressure of about 5 10-3 kPa while simultaneously heating and stirring the ionic liquid at a temperature of about 348 K for 2 days. The final water content was again measured using KF titration, and the drying procedure reduced the water
T/K
P/MPa
100x1
T/K
P/MPa
100x1
298.1
0.0262
0.4
323.1
0.0258
0.2
298.1
0.0514
0.7
323.1
0.0517
0.4
298.1
0.0767
1.0
323.2
0.0768
0.5
298.1
0.1027
1.3
323.1
0.1025
0.7
298.1
0.1279
1.6
323.2
0.1291
1.0
298.1
0.1547
2.0
323.1
0.1544
1.2
298.1
0.2567
3.1
323.1
0.2562
2.1
298.1 298.1
0.5126 0.7701
6.0 8.8
323.1 323.2
0.5121 0.7703
4.1 5.9
298.1
1.0268
11.5
323.1
1.0275
7.8
298.1
1.2832
14.0
323.2
1.2836
9.6
298.1
1.5407
16.4
323.2
1.5403
11.2
298.1
1.7976
18.7
323.1
1.7964
12.8
298.1
2.0527
20.8
323.2
2.0532
14.4
348.1
0.0261
0.1
348.1 348.1
0.0515 0.0771
0.2 0.3
348.2
0.1028
0.6
348.2
0.1285
0.8
348.2
0.1541
0.9
348.0
0.2567
1.6
348.0
0.5137
3.1
347.9
0.7700
4.6
347.7 347.7
1.0270 1.2835
5.8 7.1
347.7
1.5403
8.3
347.7
1.7965
9.6
347.6
2.0527
10.7
concentration to approximately 300 ( 30 ppm (mass basis). Proper personal protective equipment was worn when preparing and handling samples, and all materials were disposed of by incineration. Special care should be taken when handling N2O. N2O is classified as an oxidizing gas and contact with combustible material should be avoided. Sufficient ventilation should always be used when handling N2O. Binary VLE Measurements. In this work, we measured the gas solubility of N2O in [bmim][BF4] using a gravimetric microbalance (Hiden Isochema Ltd., IGA 003). Detailed descriptions of the experimental equipment and procedures for the VLE measurements are provided in our previous reports.17,20,21 The N2O/[bmim][BF4] VLE was measured at 298, 323, and 348 K, and mass measurements were made at pressures up to 2 MPa as shown in Table 1. The CO2/[bmim][BF4] VLE was previously reported at 283, 298, 323, and 348 K and pressures up to 2 MPa.17 The CO2/[bmim][BF4] results are provided in Table 2 as a convenience to the reader. The instrumental uncertainties in T and P are within (0.1 K and (0.8 kPa, respectively.17,20,21 The total uncertainties in the solubility data due to both random and systematic errors have been estimated to be less than 0.006 mole fraction at given T and P.17,20,21 Initial experiments with an empty sample container were conducted successfully at each temperature over the given range in pressure to properly account for the buoyancy effects.17,20,21 CO2/ N2O data were taken from Nicola et al.14 Binary VLLE Measurements. Four high-pressure sample containers were filled with dried [bmim][BF4] following the 3479
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procedures outlined in our previous publications.22,23 N2O was added to two tubes (mole fractions of 71.3 and 97.6% N2O), and CO2 was added to the remaining two tubes (mole fractions of 72.8 and 98.2% CO2). All four tubes showed two liquid phases at both 283 and 293 K. VLLE experiments have been made with these samples at constant temperatures from about 283 to 298 K using the volumetric method.22,23 The VLLE determined by this method required only mass and volume measurements without any analytical method for molar composition or molar volume analysis. Special attention must be given to ensure no leaks occur from the sample containers after being filled with the highpressure gas. Weights of sample containers were checked several times before starting and after completing the VLLE experiments to quantify whether any gas had escaped from the sample container. The samples were placed inside a constant temperature water bath and were mechanically mixed while immersed in the tank.22 The bath temperature was calibrated using a standard platinum resistance thermometer (SPRT model 5699, Hart Scientific, range 73-933 K) and readout (Blackstack model 1560 with SPRT module 2560). The Blackstack instrument and SPRT are a certified secondary temperature standard with a Table 2. Experimental VLE for CO2 (1) þ [bmim][BF4] (2)a
a
T/K
P/MPa
100x1
T/K
P/MPa
100x1
282.8
0.0102
0.2
323.3
0.0102
0.3
283.0 283.1
0.0502 0.1001
1.3 2.6
323.2 323.2
0.0501 0.1001
0.6 1.2
283.1
0.4001
9.6
323.2
0.3997
4.4
283.3
0.6996
15.9
323.2
0.6996
7.3
283.1
0.9997
21.6
323.2
1.0002
10.0
283.1
1.3002
26.5
323.2
1.2997
12.7
283.2
1.5001
29.5
323.2
1.5001
14.3
283.1
2.0002
36.4
323.2
2.0000
18.2
298.0 298.2
0.0097 0.0500
0.2 1.0
348.2 348.2
0.0102 0.0501
0.2 0.3
298.1
0.1001
1.9
348.1
0.1002
0.7
298.2
0.3996
6.9
348.1
0.4002
3.0
298.2
0.7002
11.5
348.2
0.6996
5.1
298.0
0.9997
15.8
348.0
1.0003
7.1
298.2
1.3002
19.7
348.2
1.3000
8.9
298.0
1.5001
22.1
348.2
1.5002
10.3
298.1
2.0002
27.7
348.1
1.9999
13.3
Reference 17.
NIST traceable accuracy to (0.005 K. The uncertainty in the bath temperature was 0.2 K. One of the most useful aspects of the present VLLE method is the ability to obtain the molar volume of each separated liquid simultaneously with the mole fraction of each liquid at any given isothermal condition. Then, the excess0 molar volume (or volume of mixing) of each liquid solution (VE and VE) can be obtained, by use of the pure component molar volumes V01 (N2O) and V02 ([bmim][BF4]) using 0
V E ¼ Vm - x0 1 V10 - x0 2 V20 V ¼ E
Vm - x1 V10
and
- x2 V20
ð1Þ
where Vm is the measured molar volume of the mixture (Vm = V0 for the lower phase L0 or Vm = V for the upper phase L), and (x0 1, x0 2 or x1,x2) are mole fractions of (CO2 or N2O) (1) and [bmim][BF4] (2) in phase L0 and L, respectively. Saturated liquid molar volumes for CO2 and N2O were calculated using the NIST REFPROP EOS program.24 The molar volume for [bmim][BF4] was calculated from known liquid density data.25 It is important to mention that the density of the vapor phase, which contains CO2 or N2O with a negligible contribution of [bmim][BF4], must be properly accounted for in the mass balance equations. The observed liquid-phase compositions and molar volumes for N2O þ [bmim][BF4] and CO2 þ [bmim][BF4] are shown in Tables 3 and 4, respectively. Total uncertainties δxTE = (δxRE2 þ δxSE2)1/2 were estimated by calculating both the overall random (δxRE) and systematic errors (δxSE). The following experimental parameters were considered to have an effect on the random errors: sample container calibration constants, mass of components, and height of lower and upper phases. The heights had the largest overall effect. The systematic errors include properly correcting for the sample level, area expansion, meniscus, and vapor-phase moles. For additional details on estimation of total errors, see our previous work.22,23 Ternary VLE Measurements. We have also conducted VLE experiments for the present ternary system (N2O/CO2/[bmim][BF4]) at several thermodynamic conditions similar to our previous experiments with CO2/SO2/[hmim][Tf2N],26 CO2/ SO2/[bmim][MeSO4],27 CO2/H2S/[bmim][PF6],28 and CO2/ H2S/[bmim][MeSO4]29 in order to verify the present EOS model. Ten sample cells have been constructed as shown in Figure 2. Each cell was made using Swagelok fittings, two Swagelok valves (valve 1 is a stem valve, part number SS-4JB1 and valve 2 is a ball valve, part number SS-426S4), a stainless steel cylinder, and a pressure gauge (Parker Instruments, 0-0.7 MPa). The internal volume of each cell was estimated by measuring the mass of
Table 3. Experimental VLLE for N2O (1) þ [bmim][BF4] (2) T/K
a
100x0 1
100x1
V 0 a/(cm3 3 mol-1)
V a/(cm3 3 mol-1)
V 0 ex b/(cm3 3 mol-1)
V ex b/(cm3 3 mol-1)
282.7
48.0 ( 1.0
99.7 ( 0.3
116.1 ( 2.0
51.3 ( 1.0
-5.0 ( 2.0
-0.1 ( 1.0
293.6
44.5 ( 1.3
99.8 ( 0.2
121.0 ( 1.7
57.4 ( 1.5
-7.6 ( 1.7
1.0 ( 1.5
Observed molar volume. b Excess molar volume.
Table 4. Experimental VLLE for CO2 (1) þ [bmim][BF4] (2)
a
T/K
100x0 1
100x1
V 0 a/(cm3 3 mol-1)
V a/(cm3 3 mol-1)
V 0 ex b/(cm3 3 mol-1)
V ex b/(cm3 3 mol-1)
282.7 293.4
59.0 ( 0.6 56.1 ( 0.7
99.9 ( 0.1 99.9 ( 0.1
99.7 ( 2.1 104.1 ( 2.0
51.6 ( 1.0 58.4 ( 1.5
-7.2 ( 2.1 -10.3 ( 2.0
0.5 ( 1.0 1.3 ( 1.5
Observed molar volume. b Excess molar volume. 3480
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Figure 2. Schematic diagram of a sample cell.
methanol required to completely fill one of the cells and knowing the density of methanol at the fill temperature. The average internal volume of the cells (VT) was 90 ( 2.5 cm3; however, VT is not required in the ternary EOS model. This is one advantage of the model we have developed. Before the cells were filled, each was pressure tested with helium to 0.7 MPa and visually checked for leaks by submerging under water and looking for any evidence of bubble formation. The cells were dried in air before loading with ionic liquid. Ionic liquid was loaded by mass (1.11-11.40 g) inside a nitrogen-purged drybox. In order to load ionic liquid in the cell, the pressure gauge, valves, and fittings were removed and a glass pipet (10 mL) which fit through the cylinder opening was used for filling. The pressure gauge, valves, and fittings were assembled as shown in Figure 2 and the sample cell was removed from the drybox. After filling with the ionic liquid, the sample cell was always maintained in a vertical upright position when valve 1 was open to prevent ionic liquid from coming in contact with the valves and pressure gauge. If the sample cell had to be mixed or weighed in a horizontal position, valve 1 would be closed and then reopened once the cylinder was in the vertical position again. The cell was connected to a diaphragm pump, with both valves open, to remove residual nitrogen. After the cell was evacuated, the ball valve (valve 2) was closed and the
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cell was weighed on an analytical balance with a resolution of 0.01 g (Mettler Toledo PG-4002-S) to obtain the initial ionic liquid mass. The N2O/CO2 gas mixtures were loaded by mass (0.76 to 0.89 g) from a high-pressure gas cylinder. Three N2O/CO2 gas mixtures (47.4/52.6, 22.8/77.2, and 82.4/17.6 mole ratios N2O/CO2) were prepared by weight and analyzed by gas chromatography (GC) (Hewlett-Packard HP6890) using an isothermal (308 K) method (GS-Q capillary column, 30 m length, 0.530 mm i.d., model 115-3432, Agilent Technologies, inlet injector temperature 473 K, thermal conductivity detector temperature 523 K, helium carrier gas, flow rate 30 cm3 min-1 with a 10:1 split ratio, injection volume 25 μL). When the N2O/ CO2 gas mixtures were prepared, the N2O was added first since it has a slightly lower vapor pressure (N2O at 293 K is lower at 5.04 MPa) than CO2 (5.71 MPa at 293 K). The total pressures for the three gas mixtures (47.4/52.6, 22.8/77.2, and 82.4/17.6 mole ratios N2O/CO2) were 1.45, 1.38, and 0.76 MPa, respectively. The sample cells were set upright in a ventilated hood at room temperature for 48 h before any measurements were made. The sample cells were vigorously shaken periodically to assist with mixing, and the pressure levels were monitored over time until they remained constant. The final weight and pressure of each cell were recorded. The process was repeated at a higher temperature of about 315 K by placing the sample cells inside a Plexiglas tank filled with water and controlling the temperature with a heated circulator (VWR International, Model 1160S) which pumped water through a copper coil inside the tank. The bath was stirred with an agitator (Arrow Engineering Co., Inc. model 1750) and the temperature measured with a thermocouple (Fluke 52II thermometer). The sample cells were vigorously shaken to assist with mixing prior to being immersed in the tank. The water level in the tank was adjusted such that the entire cell was under water including both valves, but not the pressure gauge. To ensure the samples were at equilibrium and properly mixed, the cells were momentarily removed from the water bath and vigorously shaken. The cells were placed back in the bath and the process was repeated until no change in pressure was measured. The pressure gauges were calibrated using the Paroscientific Model 765-1K pressure transducer. The Fluke thermometer was calibrated using the standard platinum resistance thermometer (SPRT model 5699, Hart Scientific, range 73-933 K) and readout (Blackstack model 1560 with SPRT module 2560). The temperature and pressure uncertainties were (0.2 K and (0.005 MPa. After the cells had reached equilibrium at each temperature, the vapor space of each sample was analyzed by placing a rubber septum over the end of valve 2 and inserting a gastight syringe (Hamilton Company, Reno, NV) to remove a small sample (25 μL) which was analyzed by GC. When sampling at elevated temperature (315 K), the syringe was heated in an oven to about 333 K before each injection to prevent any condensation. The CO2 and N2O peaks appeared at about 6.5 and 7.1 min, respectively with a total method run time of 12.0 min.
3. THERMODYNAMIC MODEL In order to study the phase behavior of a ternary system of N2O/CO2/[bmim][BF4], we have developed thermodynamic models based on equations of state (EOS), which have been successfully applied for refrigerant/lubricant oil mixtures,15 3481
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Table 5. EOS Constants for Pure Compounds Used in the Present Study carbon dioxidea
nitrous oxide
[bmim][BF4]b
molar mass/(g 3 mol-1)
44.01
44.01
226.03
Tc/K Pc/MPa
309.58 7.254
304.13 7.377
894.90 3.019 1.0
β0
1.00032
1.00049
β1
0.38330
0.43866
0.94162
β2
-0.06299
-0.10498
-
β3
0.001538
0.06250
-
a
Developed using REFPROP24 database and ref 35. b The critical parameters for [bmim][BF4] were estimated with the method proposed by Vetere,36 using two-liquid density data and an assumed critical compressibility factor of 0.253.
various hydrofluorocarbons and CO 2 mixtures with ionic liquids,17-20 along with the ternary systems of CO2/SO2/ [hmim][Tf2N],26 CO2/SO2/[bmim][MeSO4],27 CO2/H2S/ [bmim][PF6],28 and CO2/H2S/[bmim][MeSO4].29 The model is based on a generic Redlich-Kwong (RK) type of cubic EOS: P¼
RT aðTÞ V - b V ðV þ bÞ
aðTÞ ¼ 0:427480
R 2 Tc 2 RðTÞ Pc
ð2Þ
ð3Þ ð4Þ
The temperature-dependent part of the a parameter in the EOS for pure compounds is modeled by the following empirical formula:15-20,26-29 e3
∑ βkð1=Tr - TrÞk, k¼0
Tr T=Tc
N
pffiffiffiffiffiffiffi ai aj fij ðTÞð1 - kij Þxi xj , ∑ i, j ¼ 1 R2 T Ri ðTÞ Pci
ð6Þ
where τij ¼ τji , and τii ¼ 0
ð7Þ
ai ¼ 0:427480 fij ðTÞ ¼ 1 þ τij =T, kij ¼
lij lji ðxi þ xj Þ , lji xi þ lij xj
where kii ¼ 0
ð8Þ
N
b¼
∑
b0i
N
¼
∑ ðbi þ bjÞð1 - mij Þxj
(
j¼1
∑
1 ðbi þ bj Þð1 - kij Þð1 - mij Þxi xj , 2 i, j ¼ 1 RTci bi ¼ 0:08664 Pci
ð9Þ
where mij = mji, mii = 0; Tci is the critical temperature of the ith species, Pci the critical pressure of the ith species, R the universal gas constant, and xi the mole fraction of the ith species.
1 - kij -
lij lji ðlij - lji Þxi xj ðlji xi þ lij xj Þ2
) -b ð12Þ
The equilibrium solubility for the ternary VLE system can be obtained by solving the following equilibrium conditions ði ¼ 1, 2, 3Þ
ð13Þ
where xi is the liquid mole fraction of the ith species (x1 þ x2 þ x3 = 1); yi is the vapor mole fraction of the ith species (y1 þ y2 þ y3 = 1); φLi is the liquid-phase fugacity coefficient of the ith species; and φVi is the vapor-phase fugacity coefficient of the ith species. In the case of three phase equilibria (VLLE), equations corresponding to eq 13 become
ð5Þ
The a and b parameters for general N-component mixtures are modeled in terms of their respective binary interaction parameters.15-26,32-35 a¼
where a0 i [(∂na)/(∂ni)]nj6¼i and b0 i [(∂nb)/(∂ni)]nj6¼i, n is total mole number, and ni the mole number of ith species (or xi = ni/n). The explicit forms of a0 i and b0 i may be useful for readers and are given as ( ) N lij lji ðlij - lji Þxi xj pffiffiffiffiffiffiffi 0 ai aj fij xj 1 - kij ai ¼ 2 - a ð11Þ j¼1 ðlji xi þ lij xj Þ2
xi φLi ¼ yi φVi ,
RTc b ¼ 0:08664 Pc
RðTÞ ¼
In the above model, there are a maximum of four binary interaction parameters, lij, lji, mij, and τij, for each binary pair. However, only two or three parameters are sufficient for most cases. The fugacity coefficient φi of the ith species for the present EOS model, which is needed for the phase equilibrium calculation, is given by RT 1 a 0 þ bi ln φi ¼ ln PðV - bÞ V - b RTbðV þ bÞ 0 a ai b0i V ð10Þ þ - þ 1 ln RTb a b V þb
L1 L2 L2 V V xL1 i φi ¼ xi φi ¼ yi φi ,
ði ¼ 1, ::, NÞ
ð14Þ
where superscripts L1 and L2 denote one liquid phase (1) and another coexisting liquid phase (2) of VLLE, respectively. Numerical solutions of eqs 13 or 14 (nonlinearly coupled equations) can be obtained by use of the TP-Flash (Rachford-Rice) method.30 EOS Model Parameters. Pure component EOS parameters for N2O and CO2 were determined based on data from the NIST REFPROP EOS database.24 The ionic liquid [bmim][BF4] critical parameters (Tc and Pc) were estimated using the method proposed by Vetere36 in eqs 3 and 4. The coefficients, βk, are determined so as to reproduce the vapor pressure of each pure compound (N2O and CO2), while those for the ionic liquid [bmim][BF4] are determined from the binary VLE data analysis.17 Table 5 shows the EOS constants for the present compounds. Binary interaction parameters, lij, lji, mij, and τij in eqs 7-9, for each binary pair were obtained using nonlinear regression analyses of experimental PTx (pressuretemperature-composition) data for N2O þ [bmim][BF4] (Table 1), CO2 þ [bmim][BF4],17 and CO2 þ N2O14 systems. Table 6 presents optimal binary interaction parameters for the present system pairs. Figure 3a is a PTx phase diagram which shows our model calculations of N2O solubilities in [bmim][BF4] with the present VLE data. The standard deviation for the P versus x1 fit is 3482
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Table 6. Optimal Binary Interaction Parameters in eqs 7-9 l12
system 1/2
m12 = m21
τ12 = τ21/K
N2O/[bmim][BF4]
0.10464
0.12049
-0.12831
34.07938
CO2/[bmim][BF4]
0.09481
0.09481
-0.08381
27.10464
CO2/N2Oa a
l21
-0.0037
-0.0037
0.0
0
Developed using ref 14.
Figure 4. Isothermal Pxy (pressure-liquid-vapor composition) diagrams of the binary N2O (1)/CO2 (2) system. Lines: the present EOS calculations; solid lines = bubble point curves; broken lines = dew point curves. Bubble and dew point curves almost indistinguishable due to the quasi-azeotropic behavior over the entire composition range. Figure 3. Isothermal Px (pressure-liquid composition) phase diagram. (a) Px phase diagram of N2O (1) þ [bmim][BF4] (2) binary system, lines predicted by the present EOS calculations: (b) present VLE data; (9) present VLLE data. (b) Px phase diagram of CO2 (1) þ [bmim][BF4] (2) binary system, lines: the present EOS calculations: (b) VLE data;17 (9) present VLLE data.
excellent (dP = 0.017 MPa). EOS model predictions have also been compared with the observed VLLE data and are in excellent agreement with the experimental data shown in Table 3 which suggest that this binary system is probably the type V phase behavior, according to the classification of von Konynenburg and Scott.11,12 Our EOS model has predicted a LCST of about 203 K. The triple point for N2O is 182.4 K Figure 3b is a similar plot of our model calculations of the CO2 VLE in [bmim][BF4]. The standard deviation for the P versus x1 fit is good (dP = 0.023 MPa). The present EOS has also predicted the VLLE (or liquid-liquid separation) in the CO2-rich side solution, as shown in Figure 3b. In this case, the liquid-liquid equilibria will likely intersect with the solid-liquid equilibria such that no LCST can exist and may be classified as type III phase behavior. The temperature, pressure, and composition for the EOS model are valid over the ranges shown in Figure 3, a and b. Vapor liquid equilibrium (VLE) data for the N2O þ CO2 mixtures was obtained from the literature14 and correlated using the present EOS model. Figure 4 shows selected isotherms (273.15, 283.15, and 298.15 K). The VLE data were shown over the whole temperature range of the binary system to be almost ideal in terms of Raoult’s law, and because of small differences in saturated pressures of the system constituents, there are very
Figure 5. Comparison of experimental and calculated VLE data for the ternary N2O/CO2/[bmim][BF4] system. Calculated vapor-phase compositions of N2O (CO2 mole fraction = 1 - N2O mole fraction) are compared with observed N2O vapor compositions for various experimental conditions (see Table 7). Symbols: open symbols, about 296 K; solid symbols, about 315 K; circle symbols, 82.4/17.6 mole ratio N2O/ CO2 feed; square symbols, 47.4/52.6 mole ratio N2O/CO2 feed; diamond symbols, 22.8/77.2 mole ratio N2O/CO2 feed.
small differences (less than 0.1%) between the compositions of the liquid and vapor phases at equilibrium.14 Therefore, this binary system may be considered to be quasi-azeotropic over the full range of composition.14 This is an interesting challenge to study the use of an ionic liquid extractant for separation. 3483
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Table 7. Experimental VLE Data for Ternary Mixtures of CO2 (1) þ N2O (2) þ [bmim][BF4] (3)a init feed 100x1
init feed 100x3
T/K
P/MPa
calcd liq 100x1
calcd liq 100x3
calcd vapor 100y1
measd vapor 100y1
41.1 ( 0.4
21.9 ( 0.7
296.8
0.6115
6.0 ( 0.2
90.3 ( 0.2
52.3 ( 0.5
52.4 ( 1.0b
30.3 ( 0.4
42.5 ( 0.7
296.5
0.5909
5.8 ( 0.2
90.6 ( 0.2
51.8 ( 0.6
52.0 ( 1.0b
24.1 ( 0.3
54.3 ( 0.7
296.9
0.5840
5.7 ( 0.2
90.8 ( 0.2
51.4 ( 0.7
51.8 ( 1.0b
13.4 ( 0.4
74.5 ( 0.5
296.3
0.4736
4.7 ( 0.2
92.3 ( 0.2
50.0 ( 1.4
51.0 ( 1.0b
62.0 ( 0.5
19.7 ( 0.7
296.8
0.6115
8.7 ( 0.2
89.5 ( 0.2
77.0 ( 0.4
77.1 ( 1.0c
35.7 ( 0.5
53.8 ( 0.7
296.7
0.5840
8.3 ( 0.2
89.9 ( 0.2
76.5 ( 0.6
76.7 ( 1.0c
21.2 ( 0.4
72.5 ( 0.5
297.2
0.5012
7.1 ( 0.2
91.3 ( 0.2
75.5 ( 0.7
76.2 ( 1.0c
13.4 ( 0.1 7.9 ( 0.1
23.9 ( 0.7 55.1 ( 0.7
296.4 296.7
0.5977 0.5564
2.0 ( 0.2 1.8 ( 0.2
91.8 ( 0.2 92.3 ( 0.2
17.4 ( 0.3 16.9 ( 0.4
17.3 ( 1.0d 17.0 ( 1.0d
4.7 ( 0.1
73.1 ( 0.6
296.9
0.4943
1.6 ( 0.2
93.2 ( 0.2
16.1 ( 0.6
16.6 ( 1.0d
41.1 ( 0.4
21.9 ( 0.7
314.1
0.6460
4.5 ( 0.2
92.7 ( 0.2
52.4 ( 0.5
52.7 ( 1.0b
30.3 ( 0.4
42.5 ( 0.7
314.0
0.6253
4.3 ( 0.2
92.9 ( 0.2
52.1 ( 0.6
52.2 ( 1.0b
24.1 ( 0.3
54.3 ( 0.7
314.0
0.6391
4.4 ( 0.2
92.7 ( 0.2
51.8 ( 0.7
52.0 ( 1.0b
13.4 ( 0.4
74.5 ( 0.5
314.0
0.5288
3.6 ( 0.2
93.9 ( 0.2
50.9 ( 1.4
51.4 ( 1.0b
62.0 ( 0.5
19.7 ( 0.7
313.9
0.6460
6.5 ( 0.2
92.7 ( 0.2
77.1 ( 0.4
77.2 ( 1.0c
35.7 ( 0.5 21.2 ( 0.4
53.8 ( 0.7 72.5 ( 0.5
315.3 315.3
0.6253 0.5633
6.1 ( 0.2 5.5 ( 0.2
92.5 ( 0.2 93.2 ( 0.2
76.8 ( 0.6 76.0 ( 0.7
76.9 ( 1.0c 76.5 ( 1.0c
13.4 ( 0.1
23.9 ( 0.7
315.2
0.5771
1.3 ( 0.2
94.3 ( 0.2
17.5 ( 0.3
17.4 ( 1.0d
7.9 ( 0.1
55.1 ( 0.7
315.0
0.6046
1.4 ( 0.2
94.0 ( 0.2
17.1 ( 0.4
17.1 ( 1.0d
4.7 ( 0.1
73.1 ( 0.6
315.0
0.5426
1.2 ( 0.2
94.6 ( 0.2
16.6 ( 0.6
16.8 ( 1.0d
Initial feed N2O mole fraction = (x2 = 1 - x1 - x3). Liquid N2O mole fraction = (x2 = 1 - x1 - x3). Vapor N2O mole fraction = (y2 = 1 - y1) and vapor [bmim][BF4] = 0. b N2O/CO2 gas mixture (47.4/52.6) mole ratio. c N2O/CO2 gas mixture (22.8/77.2) mole ratio. d N2O/CO2 gas mixture (82.4/17.6) mole ratio). a
Table 8. Henry’s Law Constants for N2O and CO2 in [bmim][BF4]a T/K
HN2O/MPa
HCO2/MPa
283.15
-
3.7 ( 0.1
298.15
7.8 ( 0.1
5.4 ( 0.1
323.15 348.15
11.6 ( 0.2 15.4 ( 0.3
8.9 ( 0.2 13.2 ( 0.2
a Fugacity function fitted with “second order” polynomials. Used all data points shown in Tables 1 and 2 and included the theoretical “zero” point. Errors are the standard deviation of the fugacity fitting as a function of N2O or CO2 mole fraction (“with 0” and “without 0”).
Although the solubility behavior of each binary system has been well correlated with the present EOS model as illustrated in Figures 3 and 4, the phase behavior prediction of the ternary system of N2O/CO2/[bmim][BF4] may not always be guaranteed based on the binary interaction parameters alone. Particularly for systems containing supercritical fluids and/or nonvolatile compounds such as the present case, the validity of a proposed EOS model for ternary mixtures must be checked experimentally. Figure 5 presents the comparison of observed and calculated values for CO2 mole fraction in the vapor phase (N2O mole fraction = 1 - CO2 mole fraction, and [bmim][BF4] mole fraction = 0) under various T, P, and feed composition conditions; see Table 7. The model calculations and experimental data are in excellent agreement (
