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Enthalpy of solution of carbon dioxide in (water + monoethanolamine, or diethanolamine, orN-methyldiethanolamine) and (water + monoethanolamine + N-methyldiethanolamine) atT = 298.15 K
J. Chem. Thermodynamics 2000, 32, 1285–1296 doi:10.1006/jcht.2000.0680 Available online at http://www.idealibrary.com on
Enthalpy of solution of carbon dioxide in (water + monoethanolamine, or diethanolamine, or N-methyldiethanolamine) and (water + monoethanolamine + N-methyldiethanolamine) at T = 298.15 Ka James K. Carson, Kenneth N. Marsh, Department of Chemical and Process Engineering, University of Canterbury, Christchurch, New Zealand
and Alan E. Mather Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada
Measurements of the enthalpy of solution for carbon dioxide in (water + monoethanolamine, or diethanolamine, or N -methyldiethanolamine) and in (water + monoethanolamine + N -methyldiethanolamine) at T = 298.15 K have been made by isothermal displacement calorimetry. The estimated uncertainty is between ±1 and 2 per cent. The results are compared with previous measurements made by isothermal flow calorimetry, isoperibol calorimetry and values derived from solubility measurements. c 2000 Academic Press
KEYWORDS: enthalpy of solution; calorimetry; carbon dioxide; alkanolamines
1. Introduction The removal of acidic gases (in particular carbon dioxide and hydrogen sulfide) from hydrocarbon gas streams is an area of industrial importance.(1) Due to their chemically active nature, acidic gases may be absorbed from a gas stream by a number of different chemical or physical absorbents. When both carbon dioxide and hydrogen sulfide are present in a gas stream the most commonly used absorbents are aqueous solutions of a single or mixed alkanolamine. Initially, monoethanolamine and diethanolamine were the most commonly used amines. In recent times, N -methyldiethanolamine has become a preferred absorbent due to the lower enthalpy of solution of carbon dioxide, its lower a Dedicated in memory of Prof. M. L. McGlashan, founding editor.
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corrosivity, and most significantly, its selectivity towards hydrogen sulfide over carbon dioxide. In addition, aqueous mixed amine solvents based on N -methyldiethanolamine have been tailored for specific use in individual applications. The partial molar enthalpy of solution is a molar property that is related to the measured enthalpy of solution by the equation 1sol Hm (CO2 ) = (∂1H/∂n 1 )T, p,n 2 .
(1)
where 1sol Hm (CO2 ) is the partial molar enthalpy of solution of carbon dioxide, 1H is the measured total enthalpy change on adding n 1 moles of carbon dioxide, n 2 is the number of moles of the aqueous alkanolamine solvent, T is the temperature, and p is the pressure. Along with the solubility of the acid gases in aqueous alkanolamines, the enthalpy of solution is one of the most important properties required in the design of acidic gas removal plants. It is directly related to the steam requirements of the amine regeneration stage of an acidic gas removal plant. As the steam cost accounts for over half the running cost of the plant it is desirable that the enthalpy of solution data be as accurate as possible in order to avoid overdesign and hence unnecessary costs. The enthalpy of solution can be derived from solubility measurements by using the Gibbs–Helmholtz equation. Enthalpy of solution values have been derived from solubility data for carbon dioxide in aqueous monoethanolamine by Jou et al.,(2) carbon dioxide in aqueous diethanolamine by Lee et al.(3) and carbon dioxide in aqueous N -methyldiethanolamine by Jou et al.(4) The enthalpy of solution of both carbon dioxide and hydrogen sulfide has been measured in aqueous diethanolamine at T = (298.15 K, 323.15 K, and 348.15 K) by Kahrim(5) using an isoperibol calorimeter. At Brigham Young University measurements have been made using isothermal flow calorimetry of carbon dioxide in aqueous 2[2-aminoethoxy]ethanol (diglycolamine),(6) aqueous diethanolamine(6) and aqueous N methyldiethanolamine.(7) Mathonat et al.(8, 9) have used isothermal flow calorimetry to make enthalpy of solution measurements of carbon dioxide in aqueous monoethanolamine, aqueous N -methyldiethanolamine and an aqueous mixture of monoethanolamine and N methyldiethanolamine. The uncertainties associated with all the above measurements are generally not better than ±4 per cent and in some cases are closer to ±10 per cent. Isothermal displacement calorimetry was chosen as the measurement technique for this work because it does not suffer from the limitations encountered by the techniques mentioned above.(10) However, the present apparatus has limits in the range of temperatures and pressures over which measurements may be made.
2. Experimental MATERIALS
The carbon dioxide from BOC gases had a mass fraction purity >0.9998. The alkanolamines from British Drug House, were specified by the manufacturer to have a mass fraction purity >0.98. Solvents were prepared to the desired mass fractions by mass from the alkanolamines and distilled water, both of which were degassed by boiling prior to mixing.
Enthalpy of CO2 in alkanolamines
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i k
h
g b
c e f
a d
j FIGURE 1. Isothermal displacement calorimeter; a, annular heater; b, Peltier cooling unit; c, inlet valve; d, injection tube; e, stirrer; f, thermistor; g, stirrer gland; h, solution outlet; i, inlet valve control; j, outlet to pipette; k, by-pass outlet. APPARATUS
The calorimeter is constructed from stainless steel and has been described previously by Stokes et al.(11, 12) Schematic diagrams of the calorimeter and the entire setup are shown in figures 1 and 2. Displacement calorimeters have been used primarily for measurements involving binary liquid mixtures where the solute is injected into the calorimeter from a burette. Battino and Marsh(13) used a modified burette arrangement to measure the enthalpies of solution of various gases in organic solvents. While this method proved to be effective for these particular systems where the solubilities were small, it was impractical for the high solubility of carbon dioxide in alkanolamines because of the large volumes of gas required. A diagram of the gas injection device that was used in place of the burette is shown in figure 2. The device, constructed from stainless steel, was immersed in the same
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V2 To pressure transducer
FIGURE 2. Gas injection device.
thermostatted bath as the calorimeter except for a short length connected to the pressure gauge. The volume between the two needle valves (including the pressure transducer) was 12.25 cm3 . The number of moles of carbon dioxide injected into the calorimeter was calculated from the pressure changes before and after the injection and the known temperature (assumed to be the same as the temperature of the bath). The pressure was measured to an accuracy of ±0.01 kPa with a Paroscientific digiquartz pressure transducer which was calibrated against a precision mercury manometer. From these measurements the amountof-substance density ρ of carbon dioxide was determined using data from the NIST website† from the relevant temperature and pressure. The number of moles added 1n 1 is the product of the change in density 1ρ of carbon dioxide and the volume of the device V : 1n 1 = V 1ρ.
(2)
Due to the cooling and heating effects that accompany the passage of a gas through a partially open valve, the pressure of the carbon dioxide in the gas injection device took a considerable time to reach thermal equilibrium with the bath. Instead of waiting for the time required to obtain a steady pressure reading, a reading was taken 5 min after the valve was closed and a correction was applied to the readings to compensate for the remaining small pressure changes. The correction was determined by observing the pressure–time characteristics of the gas injection device as it was filled and emptied. A correction of 1.4 kPa was subtracted from the pressure reading taken after the device had been filled (to approximately 265 kPa) and added to the pressure reading taken after the device had been emptied (to approximately 125 kPa). PROCEDURE
The calorimeter was run according to the exothermic mode, in which the thermoelectric cooling module was run on high power and the energy removed from the calorimeter was balanced by continuous addition of sufficient electrical energy to keep the calorimeter isothermal. A known volume of about 8 cm3 of mercury was added to the calorimeter volume from a pipette. After (alkanolamine + water) was introduced into the calorimeter via a syringe the gas inlet valve of the calorimeter, c, (figure 1) was closed. Carbon dioxide †http://webbook.nist.gov
Enthalpy of CO2 in alkanolamines
e
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a d
b c
FIGURE 3. Entire setup; a, pressure transducer; b, gas injection system; c, calorimeter; d, pipette; e, carbon dioxide cylinder.
was used to flush the gas injection device, the calorimeter bypass tube and valve k to remove air and residual solvent from the injection line. The calorimeter was allowed to reach thermal equilibrium overnight. Once the temperature of the calorimeter was constant to ±5 · 10−3 K, the calorimeter heater (R = 103.6 ) was turned on with a current of approximately 50 mA. At the same time the current in the thermoelectric cooler was adjusted so that the calorimeter temperature remained constant and equal to within ±3 · 10−3 K to the bath temperature. After the calorimeter temperature remained constant to within ±2 · 10−3 K for approximately 30 min the gas injection was started. To start a run, needle valve V1 (figure 2) was opened and the gas injection device was pressurized to a known pressure of approximately 265 kPa. After V1 was closed, needle valve V2 and the inlet valve c were opened and gas was allowed to enter the calorimeter. As soon as a temperature increase was noticed on the chart recorder, the heater was switched off. The calorimeter temperature was kept as close as possible to the equilibrium temperature by adjusting the flow of gas with the needle valve V2. After an addition of approximately n = 6 · 10−4 mol of carbon dioxide, the inlet valve c was closed and the calorimeter was brought back to the initial temperature to within ±2 · 10−3 K by addition of electrical energy or more carbon dioxide. Both the time the heater was off and the pressure in the reference volume were noted. A further 20 additions of carbon dioxide were made in a similar manner to give a final mole fraction of carbon dioxide of approximately 4 · 10−3 . For a solvent with an amine mass fraction of 0.1, the final acidic gas loading {n(carbon dioxide)/n(alkanolamine)} was approximately 0.2, for a solvent with an amine mass fraction of 0.2 the final loading was approximately 0.1 and for a solvent with an amine mass fraction of 0.3 the final loading was approximately 0.067.
3. Results and discussions Tables 1 to 4 present the amounts of substance of carbon dioxide added, the associated enthalpy and the derived enthalpies of solution of carbon dioxide in the various aqueous
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J. K. Carson et al. TABLE 1. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + monoethanolamine(3)} at T = 298.15 K: n 1 denotes the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 is the amine mass fraction n 1 /mol
x1
0.00493 0.00633 0.00702 0.00843 0.00915 0.01056 0.01126 0.01268 0.01341 0.01482
0.00132 0.00169 0.00187 0.00225 0.00244 0.00282 0.00300 0.00338 0.00357 0.00395
0.00423 0.00564 0.00634 0.00704 0.00846 0.00917 0.01060 0.01130 0.01270 0.01409
0.00121 0.00161 0.00181 0.00201 0.00242 0.00262 0.00303 0.00320 0.00363 0.00402
0.00488 0.00628 0.00768 0.00840 0.00979 0.01120 0.01261 0.01332 0.01402 0.01543
0.00151 0.00195 0.00238 0.00260 0.00303 0.00347 0.00390 0.00412 0.00434 0.00477
0.00489 0.00628 0.00770 0.00910 0.01054 0.01124 0.01268 0.01339 0.01410 0.01551
0.00152 0.00195 0.00239 0.00282 0.00326 0.00348 0.00392 0.00414 0.00436 0.00480
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.1 −391.5 −507.9 −562.9 −678.7 −737.3 −856.0 −914.9 −1033.9 −1092.5 −1211.7 w3 = 0.20 −345.6 −462.3 −519.9 −580.1 −699.8 −759.0 −876.9 −936.2 −1051.4 −1168.6 w3 = 0.30 −396.7 −513.1 −631.9 −692.5 −811.0 −929.5 −1046.2 −1107.0 −1165.3 −1283.0 w3 = 0.30 (Run 2) −392.5 −509.4 −627.5 −744.2 −861.9 −921.2 −1040.4 −1099.1 −1158.1 −1276.5
−79.37 −80.18 −80.18 −80.52 −80.62 −81.08 −81.23 −81.51 −81.49 −81.77 −81.71 −81.95 −82.00 −82.43 −82.72 −82.73 −82.73 −82.83 −82.77 −82.91 −81.29 −81.76 −82.24 −82.48 −82.83 −82.96 −82.98 −83.11 −83.10 −83.15 −80.33 −81.08 −81.48 −81.74 −81.82 −81.93 −82.03 −82.08 −82.14 −82.29
Enthalpy of CO2 in alkanolamines TABLE 2. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + diethanolamine(3)} at T = 298.15 K: n 1 is the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 is the amine mass fraction n 1 /mol
x1
61H/J
1sol H (CO2 )/kJ · mol−1
0.00502 0.00646 0.00716 0.00861 0.00931 0.01002 0.01145 0.01286 0.01357 0.01500
0.00134 0.00173 0.00191 0.00230 0.00249 0.00268 0.00306 0.00343 0.00362 0.00400
0.00422 0.00547 0.00673 0.00739 0.00864 0.00926 0.01055 0.01117 0.01245 0.01378
0.00124 0.00161 0.00198 0.00217 0.00254 0.00272 0.00310 0.00328 0.00365 0.00404
w3 = 0.20 (Run 1) −291.1 −380.3 −470.5 −518.0 −606.4 −650.6 −743.0 −786.6 −877.7 −970.7
−69.02 −69.50 −69.90 −70.08 −70.18 −70.28 −70.40 −70.43 −70.51 −70.47
0.00465 0.00596 0.00662 0.00727 0.00860 0.00989 0.01186 0.01251 0.01379 0.01445
0.00137 0.00175 0.00195 0.00214 0.00253 0.00290 0.00348 0.00367 0.00404 0.00424
w3 = 0.20 (Run 2) −312.1 −405.3 −451.6 −497.5 −591.1 −685.1 −824.9 −871.7 −964.7 −1012.2
−67.13 −67.98 −68.17 −68.39 −68.71 −69.30 −69.53 −69.68 −69.95 −70.03
0.00478 0.00618 0.00757 0.00828 0.00964 0.01036 0.01173 0.01242 0.01386 0.01527
0.00154 0.00199 0.00244 0.00267 0.00310 0.00334 0.00378 0.00400 0.00446 0.00491
w1 = 0.30 (Run 1) −334.3 −434.9 −534.0 −585.6 −683.4 −735.1 −834.8 −881.3 −981.1 −1081.8
−69.92 −70.39 −70.56 −70.74 −70.88 −70.97 −71.15 −70.93 −70.79 −70.86
w3 = 0.10 −342.0 −444.1 −493.1 −593.6 −642.7 −692.0 −791.0 −888.0 −936.8 −1035.2
−68.17 −68.79 −68.85 −68.96 −69.01 −69.08 −69.06 −69.04 −69.04 −69.03
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J. K. Carson et al. TABLE 2—continued n 1 /mol
x1
0.00492 0.00633 0.00703 0.00845 0.00914 0.01055 0.01123 0.01263 0.01333 0.01477
0.00159 0.00204 0.00227 0.00272 0.00295 0.00340 0.00362 0.00406 0.00429 0.00475
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.30 (Run 2) −341.2 −442.0 −492.0 −592.8 −643.8 −746.1 −796.2 −895.9 −945.7 −1035.0
−69.30 −69.80 −69.96 −70.19 −70.41 −70.75 −70.87 −70.92 −70.94 −70.07
alkanolamine solvents for a selection of carbon dioxide mole fractions. Table 5 presents the partial molar enthalpy of CO2 at infinite dilution in the various mixtures. There does not appear to be a significant dependence of the enthalpy of solution on the mass fraction of the alkanolamine or the carbon dioxide loading (below the saturation point). This behaviour is consistent with the observations made by Kahrim(5, 14) and by the BYU group.(6, 7) Table 6 gives a comparison with previous measurements along with their estimated uncertainties. Since the kinetics of the reaction of carbon dioxide with some alkanolamines is not rapid, it is possible that in flow calorimetry, the reaction may not be complete by the time the mixed sample leaves the calorimeter. This would lead to flow rate dependency, low values of the enthalpy of solution and more scatter in the results. During the course of each experiment a vapour space which did not disappear was formed in the calorimeter. The size of the bubble varied with the solvent, being largest with aqueous N -methyldiethanolamine (approximately 4 cm3 to 8 cm3 ) and smallest with aqueous monoethanolamine (approximately 1 cm3 to 2 cm3 ). The formation of a vapour space caused some solvent evaporation which would have made a small contribution to the measured enthalpy. It also meant that not all the carbon dioxide which entered the calorimeter had dissolved and so the calculated amount of substance of dissolved carbon dioxide would be incorrect. The effects on the measured enthalpy of both the solvent evaporation and non-dissolving carbon dioxide were estimated for a range of vapour space sizes. It was concluded that, at T = 298.15 K, from a knowledge of the vapour pressures of the components the effects resulting from evaporation could be neglected. However, the effect of the non-dissolving carbon dioxide was significant. It was observed that the bubble growth was most rapid at the start of a run and reduced after the fifth or sixth addition of carbon dioxide. A corresponding observation was that the 1H/1n 1 value for the first addition was low and the values gradually rose until the fifth or sixth addition before they remained essentially constant. It was concluded that once the bubble reached a certain size, it stopped growing and all the subsequently added carbon dioxide was therefore dissolved. This suggested that
Enthalpy of CO2 in alkanolamines TABLE 3. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + N -methyldiethanolamine(3)} at T = 298.15 K: n 1 is the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 is the amine mass fraction n 1 /mol
x1
0.00500 0.00644 0.00786 0.00930 0.01073 0.01147 0.01218 0.01363 0.01434 0.01504
0.00136 0.00175 0.00214 0.00253 0.00292 0.00312 0.00331 0.00370 0.00389 0.00408
0.0050 0.0064 0.0078 0.0086 0.0093 0.0100 0.0114 0.0121 0.0135 0.0142
0.00149 0.00191 0.00233 0.00254 0.00275 0.00296 0.00337 0.00358 0.00399 0.00420
0.00497 0.00567 0.00709 0.00851 0.00921 0.01062 0.01132 0.01273 0.01345 0.01487
0.00163 0.00186 0.00232 0.00279 0.00301 0.00347 0.00370 0.00416 0.00439 0.00486
0.00495 0.00640 0.00782 0.00855 0.00997 0.01069 0.01140 0.0180 0.01351 0.01562
0.00162 0.00209 0.00256 0.00280 0.00326 0.00350 0.00373 0.00418 0.00442 0.00510
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.10 −248.5 −320.1 −395.4 −468.8 −540.3 −576.7 −613.5 −688.9 −725.6 −759.3 w3 = 0.20 −244.2 −313.7 −383.6 −418.3 −453.3 −488.6 −558.1 −590.6 −659.2 −694.2 w3 = 0.30 (Run 1) −248.8 −285.3 −357.2 −426.6 −460.9 −527.1 −561.7 −626.9 −661.8 −730.5 w3 = 0.30 (Run 2) −234.6 −305.6 −376.1 −410.1 −480.6 −516.3 −551.8 −622.0 −657.3 −761.8
−49.70 −49.71 −50.32 −50.39 −50.36 −50.28 −50.36 −50.56 −50.60 −50.49 −48.66 −48.73 −48.94 −48.88 −48.97 −48.98 −49.04 −48.93 −48.92 −48.92 −50.07 −50.30 −50.40 −50.14 −50.04 −49.64 −49.64 −49.26 −49.22 −49.14 −47.42 −47.78 −48.08 −48.00 −48.18 −48.30 −48.41 −48.59 −48.64 −48.77
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J. K. Carson et al. TABLE 4. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + monoethanolamine(3) + N -methyldiethanolamine(4)} at T = 298.15 K: n 1 is the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 and w4 are the amine mass fractions n 1 /mol 0.00495 0.00637 0.00777 0.00847 0.00986 0.01057 0.01126 0.01269 0.01480 0.01549 0.00491 0.00631 0.00774 0.00834 0.00973 0.01046 0.01186 0.01257 0.01395 0.01464
x1
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.07, w4 = 0.27 (Run 1) 0.00161 −371.2 −75.00 0.00208 −480.5 −75.39 0.00253 −588.3 −75.73 0.00276 −639.9 −75.59 0.00321 −744.7 −75.49 0.00344 −796.4 −75.31 0.00366 −847.1 −75.21 0.00412 −950.6 −74.93 0.00481 −1100.9 −74.38 0.00503 −1151.3 −74.34 w3 = 0.07, w4 = 0.27 (Run 2) 0.00160 −358.3 −73.03 0.00206 −463.8 −73.45 0.00252 −567.4 −73.32 0.00271 −618.8 −74.21 0.00317 −719.1 −73.89 0.00340 −771.3 −73.71 0.00385 −870.8 −73.44 0.00409 −922.2 −73.34 0.00453 −1019.8 −73.09 0.00476 −1068.0 −72.93
the effect of non-dissolving carbon dioxide was only significant during the first five or six additions. For this reason, the results of the first five additions of each run were rejected rather than corrected and retained. The rejection of these first five points greatly reduced the scatter in the results. Table 6 shows that the estimated uncertainties in the results obtained from this work are considerably less than those of previous workers. However, this method suffers from some of the limitations that previous workers had encountered. In particular the measurement of the amount of carbon dioxide injected remains the greatest contributor to the uncertainty. Due to temperature changes caused by the Joule–Thomson effect that occur during the filling and emptying of the gas injection device, it is recommended that an alternative method of determining the amount of substance of gas added be developed. The use of an isothermal displacement calorimeter to measure the enthalpies of solution of gases in liquid has been successfully demonstrated and the method gives results which
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TABLE 5. Partial molar enthalpies of solution at infinite dilution 1sol H ∞ (CO2 ) of carbon dioxide in aqueous alkanolamines at T = 298.15 K for aqueous monoethanolamine (MEA), diethanolamine (DEA), N -methyldiethanolamine (MDEA) and aqueous (monoethanolamine + N -methyldiethanolamine) at various mass fractions of alkanolamine w3
MEA
DEA
MDEA
(MEA + MDEA)
w3
1sol H ∞ (CO2 )/kJ · mol−1
102 · δ a /1sol H
0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.03 + 0.27
−81.0 −82.6 −82.0 −68.8 −69.2 −70.3 −50.3 −48.8 −48.7 −73.7
0.8 0.4 1 0.6 2 1 0.6 0.5 2 2
a δ is the standard deviation of the individual experimental values.
TABLE 6. Comparison of the partial molar enthalpies of solution at infinite dilution 1sol H ∞ (CO2 ) with literature values: w3 is the amine mass fraction and δ1sol H (CO2 )∞ is the estimated relative uncertainty 1sol H ∞ /kJ · mol−1 MEA DEA MDEA (MEA + MDEA) 102 · δ{1sol H (CO2 )∞ } Reference Solubility (w3 = 0.2 to 0.5) −85 −67 Isoperibol calorimetry −75 (298.15 K) BYU flow calorimetry −69 (300 K) Mathonat’s flow calorimetry −77 (extrapolated to T = 298 K) This work (298.15 K) −82 −69
10 5
2, 15, 3, 4, 2 5, 14
−49
5
6, 7
−48
4 to 7
8, 9
−60
−49
−74
−73.7
1 to 2
are more accurate than those of flow calorimetry. However, the method is limited in the range of temperatures and pressures over which measurements may be made. REFERENCES 1. Kohl, A. L.; Nielsen, R. B. Gas Purification: 5th edition. Gulf Publishing Company: Houston, TX. 1997. 2. Jou, F.-Y.; Otto, F. D.; Mather, A. E. Ind. Eng. Chem. Res. 1994, 33, 2002–2005. 3. Lee, J. I.; Otto, F. D.; Mather, A. E. J. Chem. Eng. Data 1972, 17, 465–468. 4. Jou, F. -Y.; Mather, A. E.; Otto, F. D. Ind. Eng. Chem. Process Design and Development 1982, 21, 539–544.
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5. Kahrim, A.; Mather, A. E. Can. J. Chem. Eng. 1980, 58, 660–662. 6. Oscarson, J. L.; Van Dam, R. H.; Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1989, 146, 107–114. 7. Merkley, K. E.; Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1987, 121, 437–446. 8. Mathonat, C.; Mayer, V.; Mather, A. E.; Grolier, J-P. E. Fluid Phase Equilibria 1997, 140, 171–182. 9. Mathonat, C.; Mayer, V.; Mather, A. E.; Grolier, J-P. E. Ind. Eng. Chem. Res. 1988, 37, 4136– 4141. 10. Carson, J. K. ME Thesis, University of Canterbury, New Zealand. 1998. 11. Stokes, R. H. Solution Calorimetry. Marsh, K. N.; O’Hare, P. A. G.: editors. Blackwell Scientific Publications: Oxford. 1994. 12. Stokes, R. H.; Marsh, K. N.; Tomlins, R. P. J. Chem. Thermodynamics 1969, 1, 211–221. 13. Battino, R.; Marsh, K. N. Austr. J. Chem. 1980, 33, 1997–2003. 14. Kahrim, A. M.Sc. Thesis, University of Alberta, Canada. 1976. 15. Lee, J. I.; Otto, F. D.; Mather, A. E. Can. J. Chem. Eng. 1974, 52, 125–127. (Received 25 May 1999; in final form 6 March 2000)
WA99/028
Enthalpy of solution of carbon dioxide in (water + monoethanolamine, or diethanolamine, or N-methyldiethanolamine) and (water + monoethanolamine + N-methyldiethanolamine) at T = 298.15 Ka James K. Carson, Kenneth N. Marsh, Department of Chemical and Process Engineering, University of Canterbury, Christchurch, New Zealand
and Alan E. Mather Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada
Measurements of the enthalpy of solution for carbon dioxide in (water + monoethanolamine, or diethanolamine, or N -methyldiethanolamine) and in (water + monoethanolamine + N -methyldiethanolamine) at T = 298.15 K have been made by isothermal displacement calorimetry. The estimated uncertainty is between ±1 and 2 per cent. The results are compared with previous measurements made by isothermal flow calorimetry, isoperibol calorimetry and values derived from solubility measurements. c 2000 Academic Press
KEYWORDS: enthalpy of solution; calorimetry; carbon dioxide; alkanolamines
1. Introduction The removal of acidic gases (in particular carbon dioxide and hydrogen sulfide) from hydrocarbon gas streams is an area of industrial importance.(1) Due to their chemically active nature, acidic gases may be absorbed from a gas stream by a number of different chemical or physical absorbents. When both carbon dioxide and hydrogen sulfide are present in a gas stream the most commonly used absorbents are aqueous solutions of a single or mixed alkanolamine. Initially, monoethanolamine and diethanolamine were the most commonly used amines. In recent times, N -methyldiethanolamine has become a preferred absorbent due to the lower enthalpy of solution of carbon dioxide, its lower a Dedicated in memory of Prof. M. L. McGlashan, founding editor.
0021–9614/00/091285 + 12
$35.00/0
c 2000 Academic Press
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corrosivity, and most significantly, its selectivity towards hydrogen sulfide over carbon dioxide. In addition, aqueous mixed amine solvents based on N -methyldiethanolamine have been tailored for specific use in individual applications. The partial molar enthalpy of solution is a molar property that is related to the measured enthalpy of solution by the equation 1sol Hm (CO2 ) = (∂1H/∂n 1 )T, p,n 2 .
(1)
where 1sol Hm (CO2 ) is the partial molar enthalpy of solution of carbon dioxide, 1H is the measured total enthalpy change on adding n 1 moles of carbon dioxide, n 2 is the number of moles of the aqueous alkanolamine solvent, T is the temperature, and p is the pressure. Along with the solubility of the acid gases in aqueous alkanolamines, the enthalpy of solution is one of the most important properties required in the design of acidic gas removal plants. It is directly related to the steam requirements of the amine regeneration stage of an acidic gas removal plant. As the steam cost accounts for over half the running cost of the plant it is desirable that the enthalpy of solution data be as accurate as possible in order to avoid overdesign and hence unnecessary costs. The enthalpy of solution can be derived from solubility measurements by using the Gibbs–Helmholtz equation. Enthalpy of solution values have been derived from solubility data for carbon dioxide in aqueous monoethanolamine by Jou et al.,(2) carbon dioxide in aqueous diethanolamine by Lee et al.(3) and carbon dioxide in aqueous N -methyldiethanolamine by Jou et al.(4) The enthalpy of solution of both carbon dioxide and hydrogen sulfide has been measured in aqueous diethanolamine at T = (298.15 K, 323.15 K, and 348.15 K) by Kahrim(5) using an isoperibol calorimeter. At Brigham Young University measurements have been made using isothermal flow calorimetry of carbon dioxide in aqueous 2[2-aminoethoxy]ethanol (diglycolamine),(6) aqueous diethanolamine(6) and aqueous N methyldiethanolamine.(7) Mathonat et al.(8, 9) have used isothermal flow calorimetry to make enthalpy of solution measurements of carbon dioxide in aqueous monoethanolamine, aqueous N -methyldiethanolamine and an aqueous mixture of monoethanolamine and N methyldiethanolamine. The uncertainties associated with all the above measurements are generally not better than ±4 per cent and in some cases are closer to ±10 per cent. Isothermal displacement calorimetry was chosen as the measurement technique for this work because it does not suffer from the limitations encountered by the techniques mentioned above.(10) However, the present apparatus has limits in the range of temperatures and pressures over which measurements may be made.
2. Experimental MATERIALS
The carbon dioxide from BOC gases had a mass fraction purity >0.9998. The alkanolamines from British Drug House, were specified by the manufacturer to have a mass fraction purity >0.98. Solvents were prepared to the desired mass fractions by mass from the alkanolamines and distilled water, both of which were degassed by boiling prior to mixing.
Enthalpy of CO2 in alkanolamines
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i k
h
g b
c e f
a d
j FIGURE 1. Isothermal displacement calorimeter; a, annular heater; b, Peltier cooling unit; c, inlet valve; d, injection tube; e, stirrer; f, thermistor; g, stirrer gland; h, solution outlet; i, inlet valve control; j, outlet to pipette; k, by-pass outlet. APPARATUS
The calorimeter is constructed from stainless steel and has been described previously by Stokes et al.(11, 12) Schematic diagrams of the calorimeter and the entire setup are shown in figures 1 and 2. Displacement calorimeters have been used primarily for measurements involving binary liquid mixtures where the solute is injected into the calorimeter from a burette. Battino and Marsh(13) used a modified burette arrangement to measure the enthalpies of solution of various gases in organic solvents. While this method proved to be effective for these particular systems where the solubilities were small, it was impractical for the high solubility of carbon dioxide in alkanolamines because of the large volumes of gas required. A diagram of the gas injection device that was used in place of the burette is shown in figure 2. The device, constructed from stainless steel, was immersed in the same
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J. K. Carson et al. V1
V2 To pressure transducer
FIGURE 2. Gas injection device.
thermostatted bath as the calorimeter except for a short length connected to the pressure gauge. The volume between the two needle valves (including the pressure transducer) was 12.25 cm3 . The number of moles of carbon dioxide injected into the calorimeter was calculated from the pressure changes before and after the injection and the known temperature (assumed to be the same as the temperature of the bath). The pressure was measured to an accuracy of ±0.01 kPa with a Paroscientific digiquartz pressure transducer which was calibrated against a precision mercury manometer. From these measurements the amountof-substance density ρ of carbon dioxide was determined using data from the NIST website† from the relevant temperature and pressure. The number of moles added 1n 1 is the product of the change in density 1ρ of carbon dioxide and the volume of the device V : 1n 1 = V 1ρ.
(2)
Due to the cooling and heating effects that accompany the passage of a gas through a partially open valve, the pressure of the carbon dioxide in the gas injection device took a considerable time to reach thermal equilibrium with the bath. Instead of waiting for the time required to obtain a steady pressure reading, a reading was taken 5 min after the valve was closed and a correction was applied to the readings to compensate for the remaining small pressure changes. The correction was determined by observing the pressure–time characteristics of the gas injection device as it was filled and emptied. A correction of 1.4 kPa was subtracted from the pressure reading taken after the device had been filled (to approximately 265 kPa) and added to the pressure reading taken after the device had been emptied (to approximately 125 kPa). PROCEDURE
The calorimeter was run according to the exothermic mode, in which the thermoelectric cooling module was run on high power and the energy removed from the calorimeter was balanced by continuous addition of sufficient electrical energy to keep the calorimeter isothermal. A known volume of about 8 cm3 of mercury was added to the calorimeter volume from a pipette. After (alkanolamine + water) was introduced into the calorimeter via a syringe the gas inlet valve of the calorimeter, c, (figure 1) was closed. Carbon dioxide †http://webbook.nist.gov
Enthalpy of CO2 in alkanolamines
e
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a d
b c
FIGURE 3. Entire setup; a, pressure transducer; b, gas injection system; c, calorimeter; d, pipette; e, carbon dioxide cylinder.
was used to flush the gas injection device, the calorimeter bypass tube and valve k to remove air and residual solvent from the injection line. The calorimeter was allowed to reach thermal equilibrium overnight. Once the temperature of the calorimeter was constant to ±5 · 10−3 K, the calorimeter heater (R = 103.6 ) was turned on with a current of approximately 50 mA. At the same time the current in the thermoelectric cooler was adjusted so that the calorimeter temperature remained constant and equal to within ±3 · 10−3 K to the bath temperature. After the calorimeter temperature remained constant to within ±2 · 10−3 K for approximately 30 min the gas injection was started. To start a run, needle valve V1 (figure 2) was opened and the gas injection device was pressurized to a known pressure of approximately 265 kPa. After V1 was closed, needle valve V2 and the inlet valve c were opened and gas was allowed to enter the calorimeter. As soon as a temperature increase was noticed on the chart recorder, the heater was switched off. The calorimeter temperature was kept as close as possible to the equilibrium temperature by adjusting the flow of gas with the needle valve V2. After an addition of approximately n = 6 · 10−4 mol of carbon dioxide, the inlet valve c was closed and the calorimeter was brought back to the initial temperature to within ±2 · 10−3 K by addition of electrical energy or more carbon dioxide. Both the time the heater was off and the pressure in the reference volume were noted. A further 20 additions of carbon dioxide were made in a similar manner to give a final mole fraction of carbon dioxide of approximately 4 · 10−3 . For a solvent with an amine mass fraction of 0.1, the final acidic gas loading {n(carbon dioxide)/n(alkanolamine)} was approximately 0.2, for a solvent with an amine mass fraction of 0.2 the final loading was approximately 0.1 and for a solvent with an amine mass fraction of 0.3 the final loading was approximately 0.067.
3. Results and discussions Tables 1 to 4 present the amounts of substance of carbon dioxide added, the associated enthalpy and the derived enthalpies of solution of carbon dioxide in the various aqueous
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J. K. Carson et al. TABLE 1. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + monoethanolamine(3)} at T = 298.15 K: n 1 denotes the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 is the amine mass fraction n 1 /mol
x1
0.00493 0.00633 0.00702 0.00843 0.00915 0.01056 0.01126 0.01268 0.01341 0.01482
0.00132 0.00169 0.00187 0.00225 0.00244 0.00282 0.00300 0.00338 0.00357 0.00395
0.00423 0.00564 0.00634 0.00704 0.00846 0.00917 0.01060 0.01130 0.01270 0.01409
0.00121 0.00161 0.00181 0.00201 0.00242 0.00262 0.00303 0.00320 0.00363 0.00402
0.00488 0.00628 0.00768 0.00840 0.00979 0.01120 0.01261 0.01332 0.01402 0.01543
0.00151 0.00195 0.00238 0.00260 0.00303 0.00347 0.00390 0.00412 0.00434 0.00477
0.00489 0.00628 0.00770 0.00910 0.01054 0.01124 0.01268 0.01339 0.01410 0.01551
0.00152 0.00195 0.00239 0.00282 0.00326 0.00348 0.00392 0.00414 0.00436 0.00480
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.1 −391.5 −507.9 −562.9 −678.7 −737.3 −856.0 −914.9 −1033.9 −1092.5 −1211.7 w3 = 0.20 −345.6 −462.3 −519.9 −580.1 −699.8 −759.0 −876.9 −936.2 −1051.4 −1168.6 w3 = 0.30 −396.7 −513.1 −631.9 −692.5 −811.0 −929.5 −1046.2 −1107.0 −1165.3 −1283.0 w3 = 0.30 (Run 2) −392.5 −509.4 −627.5 −744.2 −861.9 −921.2 −1040.4 −1099.1 −1158.1 −1276.5
−79.37 −80.18 −80.18 −80.52 −80.62 −81.08 −81.23 −81.51 −81.49 −81.77 −81.71 −81.95 −82.00 −82.43 −82.72 −82.73 −82.73 −82.83 −82.77 −82.91 −81.29 −81.76 −82.24 −82.48 −82.83 −82.96 −82.98 −83.11 −83.10 −83.15 −80.33 −81.08 −81.48 −81.74 −81.82 −81.93 −82.03 −82.08 −82.14 −82.29
Enthalpy of CO2 in alkanolamines TABLE 2. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + diethanolamine(3)} at T = 298.15 K: n 1 is the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 is the amine mass fraction n 1 /mol
x1
61H/J
1sol H (CO2 )/kJ · mol−1
0.00502 0.00646 0.00716 0.00861 0.00931 0.01002 0.01145 0.01286 0.01357 0.01500
0.00134 0.00173 0.00191 0.00230 0.00249 0.00268 0.00306 0.00343 0.00362 0.00400
0.00422 0.00547 0.00673 0.00739 0.00864 0.00926 0.01055 0.01117 0.01245 0.01378
0.00124 0.00161 0.00198 0.00217 0.00254 0.00272 0.00310 0.00328 0.00365 0.00404
w3 = 0.20 (Run 1) −291.1 −380.3 −470.5 −518.0 −606.4 −650.6 −743.0 −786.6 −877.7 −970.7
−69.02 −69.50 −69.90 −70.08 −70.18 −70.28 −70.40 −70.43 −70.51 −70.47
0.00465 0.00596 0.00662 0.00727 0.00860 0.00989 0.01186 0.01251 0.01379 0.01445
0.00137 0.00175 0.00195 0.00214 0.00253 0.00290 0.00348 0.00367 0.00404 0.00424
w3 = 0.20 (Run 2) −312.1 −405.3 −451.6 −497.5 −591.1 −685.1 −824.9 −871.7 −964.7 −1012.2
−67.13 −67.98 −68.17 −68.39 −68.71 −69.30 −69.53 −69.68 −69.95 −70.03
0.00478 0.00618 0.00757 0.00828 0.00964 0.01036 0.01173 0.01242 0.01386 0.01527
0.00154 0.00199 0.00244 0.00267 0.00310 0.00334 0.00378 0.00400 0.00446 0.00491
w1 = 0.30 (Run 1) −334.3 −434.9 −534.0 −585.6 −683.4 −735.1 −834.8 −881.3 −981.1 −1081.8
−69.92 −70.39 −70.56 −70.74 −70.88 −70.97 −71.15 −70.93 −70.79 −70.86
w3 = 0.10 −342.0 −444.1 −493.1 −593.6 −642.7 −692.0 −791.0 −888.0 −936.8 −1035.2
−68.17 −68.79 −68.85 −68.96 −69.01 −69.08 −69.06 −69.04 −69.04 −69.03
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J. K. Carson et al. TABLE 2—continued n 1 /mol
x1
0.00492 0.00633 0.00703 0.00845 0.00914 0.01055 0.01123 0.01263 0.01333 0.01477
0.00159 0.00204 0.00227 0.00272 0.00295 0.00340 0.00362 0.00406 0.00429 0.00475
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.30 (Run 2) −341.2 −442.0 −492.0 −592.8 −643.8 −746.1 −796.2 −895.9 −945.7 −1035.0
−69.30 −69.80 −69.96 −70.19 −70.41 −70.75 −70.87 −70.92 −70.94 −70.07
alkanolamine solvents for a selection of carbon dioxide mole fractions. Table 5 presents the partial molar enthalpy of CO2 at infinite dilution in the various mixtures. There does not appear to be a significant dependence of the enthalpy of solution on the mass fraction of the alkanolamine or the carbon dioxide loading (below the saturation point). This behaviour is consistent with the observations made by Kahrim(5, 14) and by the BYU group.(6, 7) Table 6 gives a comparison with previous measurements along with their estimated uncertainties. Since the kinetics of the reaction of carbon dioxide with some alkanolamines is not rapid, it is possible that in flow calorimetry, the reaction may not be complete by the time the mixed sample leaves the calorimeter. This would lead to flow rate dependency, low values of the enthalpy of solution and more scatter in the results. During the course of each experiment a vapour space which did not disappear was formed in the calorimeter. The size of the bubble varied with the solvent, being largest with aqueous N -methyldiethanolamine (approximately 4 cm3 to 8 cm3 ) and smallest with aqueous monoethanolamine (approximately 1 cm3 to 2 cm3 ). The formation of a vapour space caused some solvent evaporation which would have made a small contribution to the measured enthalpy. It also meant that not all the carbon dioxide which entered the calorimeter had dissolved and so the calculated amount of substance of dissolved carbon dioxide would be incorrect. The effects on the measured enthalpy of both the solvent evaporation and non-dissolving carbon dioxide were estimated for a range of vapour space sizes. It was concluded that, at T = 298.15 K, from a knowledge of the vapour pressures of the components the effects resulting from evaporation could be neglected. However, the effect of the non-dissolving carbon dioxide was significant. It was observed that the bubble growth was most rapid at the start of a run and reduced after the fifth or sixth addition of carbon dioxide. A corresponding observation was that the 1H/1n 1 value for the first addition was low and the values gradually rose until the fifth or sixth addition before they remained essentially constant. It was concluded that once the bubble reached a certain size, it stopped growing and all the subsequently added carbon dioxide was therefore dissolved. This suggested that
Enthalpy of CO2 in alkanolamines TABLE 3. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + N -methyldiethanolamine(3)} at T = 298.15 K: n 1 is the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 is the amine mass fraction n 1 /mol
x1
0.00500 0.00644 0.00786 0.00930 0.01073 0.01147 0.01218 0.01363 0.01434 0.01504
0.00136 0.00175 0.00214 0.00253 0.00292 0.00312 0.00331 0.00370 0.00389 0.00408
0.0050 0.0064 0.0078 0.0086 0.0093 0.0100 0.0114 0.0121 0.0135 0.0142
0.00149 0.00191 0.00233 0.00254 0.00275 0.00296 0.00337 0.00358 0.00399 0.00420
0.00497 0.00567 0.00709 0.00851 0.00921 0.01062 0.01132 0.01273 0.01345 0.01487
0.00163 0.00186 0.00232 0.00279 0.00301 0.00347 0.00370 0.00416 0.00439 0.00486
0.00495 0.00640 0.00782 0.00855 0.00997 0.01069 0.01140 0.0180 0.01351 0.01562
0.00162 0.00209 0.00256 0.00280 0.00326 0.00350 0.00373 0.00418 0.00442 0.00510
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.10 −248.5 −320.1 −395.4 −468.8 −540.3 −576.7 −613.5 −688.9 −725.6 −759.3 w3 = 0.20 −244.2 −313.7 −383.6 −418.3 −453.3 −488.6 −558.1 −590.6 −659.2 −694.2 w3 = 0.30 (Run 1) −248.8 −285.3 −357.2 −426.6 −460.9 −527.1 −561.7 −626.9 −661.8 −730.5 w3 = 0.30 (Run 2) −234.6 −305.6 −376.1 −410.1 −480.6 −516.3 −551.8 −622.0 −657.3 −761.8
−49.70 −49.71 −50.32 −50.39 −50.36 −50.28 −50.36 −50.56 −50.60 −50.49 −48.66 −48.73 −48.94 −48.88 −48.97 −48.98 −49.04 −48.93 −48.92 −48.92 −50.07 −50.30 −50.40 −50.14 −50.04 −49.64 −49.64 −49.26 −49.22 −49.14 −47.42 −47.78 −48.08 −48.00 −48.18 −48.30 −48.41 −48.59 −48.64 −48.77
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J. K. Carson et al. TABLE 4. Partial molar enthalpy of solution 1sol H (CO2 ) of carbon dioxide(1) in {water(2) + monoethanolamine(3) + N -methyldiethanolamine(4)} at T = 298.15 K: n 1 is the amount of substance of CO2 , x1 its mole fraction, 61H is the enthalpy change and w3 and w4 are the amine mass fractions n 1 /mol 0.00495 0.00637 0.00777 0.00847 0.00986 0.01057 0.01126 0.01269 0.01480 0.01549 0.00491 0.00631 0.00774 0.00834 0.00973 0.01046 0.01186 0.01257 0.01395 0.01464
x1
61H/J
1sol H (CO2 )/kJ · mol−1
w3 = 0.07, w4 = 0.27 (Run 1) 0.00161 −371.2 −75.00 0.00208 −480.5 −75.39 0.00253 −588.3 −75.73 0.00276 −639.9 −75.59 0.00321 −744.7 −75.49 0.00344 −796.4 −75.31 0.00366 −847.1 −75.21 0.00412 −950.6 −74.93 0.00481 −1100.9 −74.38 0.00503 −1151.3 −74.34 w3 = 0.07, w4 = 0.27 (Run 2) 0.00160 −358.3 −73.03 0.00206 −463.8 −73.45 0.00252 −567.4 −73.32 0.00271 −618.8 −74.21 0.00317 −719.1 −73.89 0.00340 −771.3 −73.71 0.00385 −870.8 −73.44 0.00409 −922.2 −73.34 0.00453 −1019.8 −73.09 0.00476 −1068.0 −72.93
the effect of non-dissolving carbon dioxide was only significant during the first five or six additions. For this reason, the results of the first five additions of each run were rejected rather than corrected and retained. The rejection of these first five points greatly reduced the scatter in the results. Table 6 shows that the estimated uncertainties in the results obtained from this work are considerably less than those of previous workers. However, this method suffers from some of the limitations that previous workers had encountered. In particular the measurement of the amount of carbon dioxide injected remains the greatest contributor to the uncertainty. Due to temperature changes caused by the Joule–Thomson effect that occur during the filling and emptying of the gas injection device, it is recommended that an alternative method of determining the amount of substance of gas added be developed. The use of an isothermal displacement calorimeter to measure the enthalpies of solution of gases in liquid has been successfully demonstrated and the method gives results which
Enthalpy of CO2 in alkanolamines
1295
TABLE 5. Partial molar enthalpies of solution at infinite dilution 1sol H ∞ (CO2 ) of carbon dioxide in aqueous alkanolamines at T = 298.15 K for aqueous monoethanolamine (MEA), diethanolamine (DEA), N -methyldiethanolamine (MDEA) and aqueous (monoethanolamine + N -methyldiethanolamine) at various mass fractions of alkanolamine w3
MEA
DEA
MDEA
(MEA + MDEA)
w3
1sol H ∞ (CO2 )/kJ · mol−1
102 · δ a /1sol H
0.1 0.2 0.3 0.1 0.2 0.3 0.1 0.2 0.3 0.03 + 0.27
−81.0 −82.6 −82.0 −68.8 −69.2 −70.3 −50.3 −48.8 −48.7 −73.7
0.8 0.4 1 0.6 2 1 0.6 0.5 2 2
a δ is the standard deviation of the individual experimental values.
TABLE 6. Comparison of the partial molar enthalpies of solution at infinite dilution 1sol H ∞ (CO2 ) with literature values: w3 is the amine mass fraction and δ1sol H (CO2 )∞ is the estimated relative uncertainty 1sol H ∞ /kJ · mol−1 MEA DEA MDEA (MEA + MDEA) 102 · δ{1sol H (CO2 )∞ } Reference Solubility (w3 = 0.2 to 0.5) −85 −67 Isoperibol calorimetry −75 (298.15 K) BYU flow calorimetry −69 (300 K) Mathonat’s flow calorimetry −77 (extrapolated to T = 298 K) This work (298.15 K) −82 −69
10 5
2, 15, 3, 4, 2 5, 14
−49
5
6, 7
−48
4 to 7
8, 9
−60
−49
−74
−73.7
1 to 2
are more accurate than those of flow calorimetry. However, the method is limited in the range of temperatures and pressures over which measurements may be made. REFERENCES 1. Kohl, A. L.; Nielsen, R. B. Gas Purification: 5th edition. Gulf Publishing Company: Houston, TX. 1997. 2. Jou, F.-Y.; Otto, F. D.; Mather, A. E. Ind. Eng. Chem. Res. 1994, 33, 2002–2005. 3. Lee, J. I.; Otto, F. D.; Mather, A. E. J. Chem. Eng. Data 1972, 17, 465–468. 4. Jou, F. -Y.; Mather, A. E.; Otto, F. D. Ind. Eng. Chem. Process Design and Development 1982, 21, 539–544.
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5. Kahrim, A.; Mather, A. E. Can. J. Chem. Eng. 1980, 58, 660–662. 6. Oscarson, J. L.; Van Dam, R. H.; Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1989, 146, 107–114. 7. Merkley, K. E.; Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1987, 121, 437–446. 8. Mathonat, C.; Mayer, V.; Mather, A. E.; Grolier, J-P. E. Fluid Phase Equilibria 1997, 140, 171–182. 9. Mathonat, C.; Mayer, V.; Mather, A. E.; Grolier, J-P. E. Ind. Eng. Chem. Res. 1988, 37, 4136– 4141. 10. Carson, J. K. ME Thesis, University of Canterbury, New Zealand. 1998. 11. Stokes, R. H. Solution Calorimetry. Marsh, K. N.; O’Hare, P. A. G.: editors. Blackwell Scientific Publications: Oxford. 1994. 12. Stokes, R. H.; Marsh, K. N.; Tomlins, R. P. J. Chem. Thermodynamics 1969, 1, 211–221. 13. Battino, R.; Marsh, K. N. Austr. J. Chem. 1980, 33, 1997–2003. 14. Kahrim, A. M.Sc. Thesis, University of Alberta, Canada. 1976. 15. Lee, J. I.; Otto, F. D.; Mather, A. E. Can. J. Chem. Eng. 1974, 52, 125–127. (Received 25 May 1999; in final form 6 March 2000)
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