1268
Ind. Eng. Chem. Res. 2008, 47, 1268-1276
New Analytical Technique for Carbon Dioxide Absorption Solvents Fatemeh Pouryousefi and Raphael O. Idem* Process System Engineering, Faculty of Engineering, UniVersity of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, Canada S4S 0A2
The densities and refractive indices of two binary systems (water + MEA and water + MDEA) and three ternary systems (water + MEA + CO2, water + MDEA + CO2, and water + MEA + MDEA) used for carbon dioxide (CO2) capture were measured over the range of compositions of the aqueous alkanolamine(s) used for CO2 absorption at temperatures from 295 to 338 K. Experimental densities were modeled empirically, while the experimental refractive indices were modeled using well-established models from the known values of their pure-component densities and refractive indices. The density and Gladstone-Dale refractive index models were then used to obtain the compositions of unknown samples of the binary and ternary systems by simultaneous solution of the density and refractive index equations. The results from this technique have been compared with HPLC (high-performance liquid chromatography) results, while a third independent technique (acid-base titration) was used to verify the results. The results show that the systems’ compositions obtained from the simple and easy-to-use refractive index/density technique were very comparable to the expensive and laborious HPLC/titration techniques, suggesting that the refractive index/density technique can be used to replace existing methods for analysis of fresh or nondegraded, CO2-loaded, single and mixed alkanolamine solutions. 1. Introduction Electric power from thermal power plants is produced from the combustion of fossil fuels such as coal and natural gas. This process accounts for a significant fraction of anthropogenic emissions of greenhouse gases (mainly carbon dioxide (CO2)), other toxic gases (such as nitrogen oxides (NOx) and sulfur dioxide (SO2)), and particulates. In order to mitigate their attendant adverse environmental and health effects, it is essential to separate these pollutants from power plant flue gases for eventual sequestration. CO2 removal from flue gas streams can also produce economic benefits if the recovered CO2 is used for enhanced oil recovery, for example. One of the most attractive methods to achieve CO2 removal from a power plant low-pressure flue gas stream is by chemical absorption using aqueous alkanolamine solutions such as monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA).1 Primary and secondary amines such as MEA and DEA, respectively, are very reactive and, thus, are able to affect a high volume of acid gas removal at a fast rate,2 but they have a limitation in their CO2 loading capacity (50% maximum), unlike tertiary amines such as MDEA, which have an equilibrium CO2 loading capacity that approaches 100%. In addition, stripping of CO2 from MEA or DEA requires a high-energy input as compared to MDEA. Blended aqueous alkanolamines such as MEA-MDEA are sometimes more desirable because they can take advantage of the good aspects of each alkanolamine in the blend (for example, higher absorption rate and CO2 absorption capacity and lower regeneration energy cost). In order to evaluate the CO2 capture efficiency as well as estimate other capture performance parameters for blended or single alkanolamines, it is necessary to know the concentrations of the components in the solution and the ratios of the alkanolamine components in blended alkanolamine solutions, as well as the CO2 loading. Existing analytical techniques are mostly based on chromatography (e.g., high-performance liquid chromatog* Corresponding author. E-mail:
[email protected]. Fax: 1(306) 585-4470.
raphy (HPLC) and gas chromatography (GC)) or acid-base titration. Chromatographic techniques are excellent for determination of the amine concentrations as well as the amine ratios in blended solutions, provided appropriate columns and operating procedures are selected. However, they are expensive, complicated, laborious, and time-consuming and could be prone to human error.3 On the other hand, the titration technique is cheap and can be used for determination of CO2 loading as well as the concentration of single amine systems. However, it cannot be extended for analysis of blended alkanolamines and still requires consumables such as hydrochloric acid. Densities, viscosities,4 thermal conductivities,5 and heat capacities6 of pure ethanolamines have been measured and reported in the literature. Specifically, the densities of amine solutions such as H2O-MEA, H2O-DEA, and H2O-triethanolamine (TEA) mixtures,7,8 as well as the viscosities of H2ODEA and H2O-MDEA mixtures,9 have been reported. However, no data are available in the literature regarding the densities and refractive indices of mixed aqueous MEA-MDEA solutions at various concentrations and temperatures. As is well-known, the density and refractive index of a solution or mixture are functions of the concentrations of the components in the mixture. They are also strong functions of temperature. GladstoneDale,10 Lorentz-Lorenz,11,12 Weiner,13 Heller,14 and AragoBiot13 relations have been widely used to evaluate the refractive indices of multicomponent systems from the known values of their pure-component indices. On the basis of these relations, Pandy et al.15 have predicted the refractive indices of three ternary systems: toluene + n-heptane + n-hexane, cyclohexane + n-heptane + n-hexane, and n-hexane + n-heptane + n-decane at 298.15 K. They obtained results that were very consistent with their experimental results. Also, Oswal et al.16 have predicted refractive indices of some haloalkanes with tetrahydrofuran that were also equally consistent with the experimental measurements. In the case of the density of the liquid mixture, the relations used are either the mole fraction average of the densities of the individual components or are determined empirically. Thus, by specifying an appropriate temperature for
10.1021/ie0709786 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/16/2008
Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1269
Figure 4. Relative index of MDEA-H2O mixture as a function of MDEA mole fraction (temperature range ) 295-333 K). Figure 1. Density of MEA-H2O mixture as a function of MEA mole fraction (temperature range ) 295-333 K).
Figure 2. Refractive index of MEA-H2O mixture as a function of MEA mole fraction (temperature range ) 295-333 K).
The purpose of this work is to develop a new, simple, inexpensive, easy-to-use, accurate analytical technique that can be employed to evaluate the concentrations of all the components in fresh or nondegraded CO2-loaded and -unloaded single and blended alkanolamine solutions based only on the thermophysical properties (namely, refractive index and density) of the system. For binary systems, the simultaneous solution of the refractive index model equation (written as a function of the components’ mole fractions x1 and x2) and the mole fraction balance equation (x1 + x2 ) 1) using the measured refractive index of the solution yields the values of the mole fractions of the components x1 and x2 of the mixture. In the case of ternary mixtures, the simultaneous solution of the density and refractive index model equations with the mole fraction balance equation (x1 + x2 + x3 )1) using the measured refractive index and density of the mixture yields the values of the mole fractions of the three components x1, x2, and x3 of the mixture. This work will also evaluate the best predictive model for refractive index for aqueous alkanolamine systems out of the five relations mentioned previously. Also, an appropriate correlation for density for aqueous alkanolamine systems will be determined. These developments, evaluations, and determinations are presented and discussed in this paper. 2. Experimental Section
Figure 3. Density of MDEA-H2O mixture as a function of MEA mole fraction (temperature range ) 295-333 K).
measurement of the solution properties, such as refractive index and density of a mixture of known components, and by using an appropriate predictive model of the property for the mixture (based on those of the pure components), it is possible to determine the compositions of the components in the mixture. This involves the solution of the predictive model equation(s) in conjunction with the mass balance equation. The number of properties needed depends on the number of components in the mixture. In a binary system (e.g., MEA-H2O and MDEAH2O), a single property, preferably refractive index, which changes monotonically with composition, is sufficient, whereas for a ternary system (e.g., MEA-H2O-CO2, MDEA-H2OCO2, and MEA-MDEA-H2O), two properties, such as refractive index and density, are required.
2.1. Chemicals. Concentrated MEA and MDEA (reagent grade, 99% purity) were obtained from Fisher Scientific, Whitby, Ontario, Canada. These solvents were diluted with distilled water to the desired concentrations. 1 N hydrochloric acid, also obtained from Fischer Scientific, was used to establish the exact MEA and MDEA concentrations. Analytical-grade CO2 was used for CO2 loading where appropriate, and this was supplied by Praxair, Regina, Saskatchewan, Canada. 2.2. Equipment and Procedure. 2.2.1. Density Measurement. The mixture densities were measured using a DMA 4500/ 5000 (Anton Paar) densitometer. Acetone and distilled water were used to clean the equipment before injecting the sample. Also before injection, it was ensured that the sample tube was well-dried by using the drier installed on the equipment. The system temperature was then set to the desired temperature before injection of the sample using a 5 mL syringe. It was also ensured that no bubble was formed in the tube while readings were taken in order to ensure high accuracy of the results. The density of each sample was measured 3 times, and the average was taken as the density of the sample. The accuracy of density measurement was 0.05 kg/m3. 2.2.2. Refractive Index Measurement. Refractive indices were measured using an ATAGO-FRX-5000a refractometer.
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Table 1. Experimental Values of Densities and Refractive Indices at 22, 35, 45, and 60 °C density measurements (g/cm3) x1
22 °C
35 °C
45 °C
refractive index measurements 60 °C
0 0.015546693 0.032164772 0.050202398 0.069596288 0.090746609 0.11371736 0.138710209 0.166262995 0.196813006 0.230060923 0.267827785 0.305559241 0.35742634 0.41152204 0.472607445 0.544762547 0.627916454 0.729568276 0.850161603 0.919185291 1
0.99778 0.99967 1.00168 1.00393 1.00648 1.00914 1.01192 1.01478 1.01755 1.02026 1.02273 1.02497 1.02646 1.02772 1.02823 1.02808 1.02709 1.02497 1.02217 1.01868 1.0168 1.01474
0.99403 0.99567 0.99737 0.99931 1.00142 1.00364 1.00597 1.00837 1.01067 1.01291 1.01496 1.01678 1.01793 1.01885 1.01906 1.01866 1.01746 1.01514 1.01216 1.00853 1.00658 1.00445
(a) MEA-H2O System 0.99026 0.98085 0.9917 0.98453 0.99323 0.98583 0.99495 0.98731 0.99682 0.98891 0.99878 0.99055 1.00083 0.99227 1.00293 0.994 1.00496 0.99568 1.00689 0.99724 1.00866 0.99865 1.0102 0.99984 1.01113 1.00049 1.0118 1.00087 1.01182 1.00063 1.01126 0.99987 1.00992 0.99836 1.00746 0.99574 1.00437 0.99252 1.00064 0.98866 0.99865 0.98662 0.99648 0.98441
0 0.01717 0.02708 0.037819 0.049908 0.063025 0.078004 0.095026 0.113978 0.136037 0.160258 0.191299 0.219337 0.265515 0.320422 0.385541 0.472801 0.586401 0.65757 0.747724 0.858842 0.937638 1.000
0.99778 1.0065 1.01134 1.01622 1.02129 1.02668 1.03161 1.0365 1.04092 1.04496 1.0484 1.05143 1.05315 1.05457 1.05478 1.05382 1.05162 1.04833 1.04624 1.04386 1.04126 1.03962 1.040
0.99403 1.00243 1.00689 1.01136 1.01597 1.02043 1.02482 1.02917 1.03307 1.0366 1.03968 1.04232 1.04381 1.04499 1.04503 1.044 1.04179 1.03852 1.03643 1.03406 1.03146 1.02981 1.030
(b) MDEA-H2O System 0.99026 0.98085 0.99823 0.99072 1.00243 0.99459 1.0064 0.9984 1.01089 1.00228 1.01502 1.006 1.01907 1.0096 1.02305 1.01313 1.02662 1.01628 1.02989 1.01914 1.03264 1.02152 1.03502 1.02358 1.03635 1.0247 1.03737 1.02551 1.03731 1.02534 1.03624 1.02425 1.03404 1.02211 1.0308 1.01898 1.02874 1.01698 1.02639 1.01471 1.02382 1.01221 1.02217 1.0106 1.021 1.00929
Table 2. Average Absolute Deviations (AADs) between the Predicted and Experimental Refractive Indices
22 °C
35 °C
45 °C
60 °C
1.33343 1.33906 1.3454 1.35167 1.3581 1.36481 1.37145 1.37811 1.38483 1.39172 1.3984 1.40516 1.41099 1.41793 1.42411 1.42982 1.43539 1.44056 1.44554 1.45005 1.45193 1.45428
1.33197 1.33752 1.34418 1.34985 1.35632 1.36286 1.36931 1.37625 1.38319 1.38907 1.3954 1.40176 1.409 1.41495 1.42069 1.42595 1.43193 1.43625 1.44136 1.44541 1.44737 1.44948
1.33054 1.33599 1.34267 1.34883 1.35431 1.36215 1.36786 1.37333 1.38065 1.38734 1.39311 1.39958 1.40669 1.41247 1.41803 1.42331 1.42892 1.43408 1.4379 1.44185 1.44466 1.44545
1.32794 1.33354 1.34212 1.34768 1.35328 1.35805 1.36586 1.37181 1.37818 1.38655 1.39015 1.39628 1.40438 1.41142 1.41394 1.41891 1.42403 1.42861 1.43266 1.43638 1.43939 1.43967
1.33343 1.34805 1.35549 1.36301 1.37117 1.37873 1.38629 1.3943 1.40188 1.40962 1.41682 1.42448 1.43051 1.43806 1.44481 1.4506 1.45592 1.46076 1.46306 1.46525 1.4673 1.46847 1.46928
1.33197 1.3463 1.35462 1.36142 1.36917 1.37651 1.384 1.39195 1.39995 1.40624 1.41322 1.42107 1.42654 1.4339 1.4405 1.44634 1.45162 1.45637 1.45864 1.46079 1.46277 1.4639 1.4647
1.33054 1.34538 1.35216 1.36038 1.36775 1.3748 1.38317 1.39053 1.39844 1.40462 1.41034 1.41928 1.42356 1.43063 1.43715 1.44291 1.44818 1.4529 1.45516 1.45727 1.45923 1.46033 1.46112
1.32794 1.34454 1.35124 1.35992 1.36694 1.37437 1.38267 1.3897 1.39568 1.40189 1.4078 1.4162 1.41835 1.42558 1.43201 1.43767 1.44286 1.44754 1.44976 1.45158 1.45379 1.45487 1.45553
Table 3. Refractive Index-Density Constant as a Function of Temperature for MEA
average absolute deviation (AAD), % model
295 K
308 K
318 K
333 K
Gladstone-Dale Arago-Biot Weiner Lorentz-Lorenz Heller
(a) MEA-H2O System 0.05 0.03 0.24 0.27 5.33 5.15 17.50 17.40 18.11 18.10
0.03 0.29 5.00 17.30 17.99
0.07 0.37 5.00 17.20 17.81
Gladstone-Dale Arago-Biot Weiner Lorentz-Lorenz Heller
(b) MDEA-H2O System 0.05 0.04 0.42 0.42 5.00 4.90 18.21 18.09 17.40 17.40
0.04 0.44 5.00 18.00 17.30
0.10 0.51 5.00 17.90 17.00
Acetone and distilled water were used to clean the equipment prior to each measurement. Temperature was adjusted to the desired value before the injection of 2-3 drops of the sample with the help of a pipet. The refractive index of each sample was measured at the wavelength (λ) of the yellow light of the sodium D line of 589.3 nm for 4-5 times. The average of these
temperature property refractive index (n) density (F), g/m3 (n - 1)/F
22 °C
35 °C
45 °C
60 °C
1.45359
1.44875
1.44524
1.43963
1.0147
1.00445
0.99648
0.98441
0.447018823
0.44676191
0.446812781
0.446592375
readings was taken as the refractive index of the sample. The accuracy of the refractive index measurement was 0.000 04. 2.2.3. Carbon Dioxide Loading. CO2 loading experiments were conducted in a semibatch mode using a 6 × 10-4 m3 stainless steel reactor (model 4560, Parr Instrument Co., Moline, IL) equipped with an insulating jacket, a bourdon-type pressure gauge, a variable-speed stirrer, and ports for introducing and withdrawing liquid and gas samples. The operating temperature was the room temperature. For loading of CO2 into any solvent, about 4.5 × 10-4 m3 of aqueous single or mixed alkanolamine solvent of the desired concentration was loaded into the reactor. The solvent was stirred at 500 rpm, and CO2 was then fed into
Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1271 Table 4. Refractive Index-Density Constant as a Function of Temperature for MDEA temperature property
22 °C
35 °C
45 °C
60 °C
refractive 1.46819 1.46362 1.46004 1.45459 index (n) density (F), 1.04 1.03 1.021 1.00929 g/m3 (n - 1)/F 0.450182692 0.450116505 0.450577865 0.450405731 Table 5. Index-Density Constant as a Function of Temperature for H2O temperature property
22 °C
35 °C
45 °C
60 °C
refractive index (n) density (F), g/m3 (n - 1)/F
1.33287 0.99778 0.333610616
1.33139 0.99403 0.33338
1.32993 0.99026 0.333175
1.3273 0.98085 0.33369
the vessel up to the desired pressure by opening the CO2 gas inlet valve of the CO2 cylinder tank set at a predetermined value. The gas inlet valve was left open for ∼12 h, after which ∼3 × 10-6 m3 sample of the loaded mixture was withdrawn through the liquid sampling port of the reactor in order to determine the CO2 loading in the sample. The CO2 loading in the sample was measured by titration using a Chittick CO2 analyzer. 2.2.4. HPLC Technique for Measurement of MEA and MDEA Concentrations. The MEA and MDEA concentrations in the samples were measured using a high-performance liquid chromatograph (HPLC series 1100 supplied by Agilent Technologies Canada Inc., Mississauga, Ontario, Canada). Shodex IC YK-421 column (length ) 1.25 × 10-4 m, internal diameter ) 4.6 × 10-3 m, theoretical plates ) 2500 minimun) packed with silica gel bonded with carboxylic group and Shodex IC YK-G guard column (length ) 1 × 10-2 m, internal diameter ) 10-2 m) were used in the HPLC for the separation of components. The mobile phase used with the column was 5 mM tartaric acid + 1 mM dipicolinic acid + 1.5 kg/m3 boric acid dissolved in ultrapure water with the aid of an ultrasonic vibrator. The solvent (mobile phase) was passed through 0.45 µm cellulose membrane filter prior to use in the column. The components in each sample (mostly MEA and MDEA) were identified by their retention time (based on an earlier calibration) using a refractive index (RI) detector. Prior to HPLC analysis, each sample was diluted with the mobile phase to 10× its original volume to avoid column overload and to improve separation of the components. Several trials were conducted to
Figure 6. Parity chart showing predicted density against experimental density for MEA-MDEA-H2O system.
select the optimum operating conditions for the HPLC, which are summarized as follows: an autoinjector (series 1100 supplied by Agilent Technologies Canada Inc., Mississauga, Ontario, Canada) containing a 100 µL syringe was used to automatically introduce samples into the HPLC column to give better reproducibility. A standard injection with an injection volume of 1 µL was used. The column maximum and minimum pressures were 400 and 0 bar, respectively, while the flow rate and the temperature were 1 mL/min and 318 K, respectively. For the refractive index detector (RID), an optical unit temperature of 318 K and a positive polarity were used. Each sample analysis took 15 min. MEA and MDEA concentrations were based on calibrations using standard MEA and MDEA. The error of the HPLC was less than (2%. 3. Results and Discussion 3.1. Evaluation of Correlation Models for Refractive Index and Density. The Gladstone-Dale, Lorentz-Lorenz, Heller, Weiner, and Arago-Biot models were all employed to correlate the experimentally obtained mixture refractive index of each sample mixture with those of the pure components constituting the mixture at desired temperatures. These relations are given in eqs 1-5 for Gladstone-Dale, Lorentz-Lorenz, Heller, Weiner, and Arago-Biot models, respectively.
nm - 1 ) F nm2 - 1 nm + 2 2
r ∑i)1
)
nm2 - 2n12
)
nm ) Figure 5. Three-dimentional plot of the density of MEA-MDEA-H2O system.
(1)
ni - 1
r φi ∑i)1 n2 + 2
(2)
i
n m - n1 ) n1 nm2 - n12
ni - 1 $i Fi
∑
r i)1
∑
r i)1
ni2 - 1 ni2 + 2
ni2 - n12 ni2 + 2n12
r niφi ∑i)1
(3)
φi
φi
(4) (5)
where n, F, ω, φ, and r are the refractive index, density, weight fraction, volume fraction, and number of components in the
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Table 6. Experimental Values of Densities and Refractive Indices of MEA-MDEA-H2O System at 22, 35, 45, and 60 °C density measurements (g/cm3)
MEA
refractive index measurements
x1 (MEA)
x2 (MDEA)
22 °C
35 °C
45 °C
60 °C
22 °C
35 °C
45 °C
60 °C
0.035416 0.039336 0.044231 0.050518 0.058888 0.070583 0.088073 0.117087 0.077229 0.086643 0.098669 0.114573 0.136588 0.169076 0.221842 0.127345 0.144617 0.167309 0.198448 0.243828 0.316116 0.188508 0.217324 0.25654 0.313025 0.401407 0.264824 0.311199 0.377264 0.47894 0.362721 0.437061 0.549727 0.492859 0.614614 0.674307
0.018602 0.041321 0.069695 0.106134 0.154649 0.222433 0.32381 0.491982 0.020282 0.045507 0.077736 0.120354 0.179351 0.266412 0.407814 0.022295 0.050638 0.087876 0.138974 0.213443 0.332068 0.024753 0.057073 0.101057 0.16441 0.263539 0.027819 0.065381 0.118891 0.201243 0.031752 0.076519 0.144367 0.036981 0.092233 0.044271
1.01167 1.02192 1.03173 1.0407 1.04733 1.05089 1.05051 1.04584 1.01628 1.027 1.03608 1.0432 1.04733 1.04757 1.04377 1.02236 1.03171 1.0392 1.0438 1.04463 1.04278 1.02745 1.03529 1.0406 1.04251 1.04079 1.02689 1.03607 1.03758 1.03501 1.0326 1.0343 1.03177 1.03076 1.02906 1.02623
1.00653 1.01577 1.02454 1.03249 1.03834 1.04137 1.04074 1.03604 1.01031 1.01992 1.02804 1.03434 1.03794 1.0379 1.03398 1.01543 1.0238 1.03046 1.03449 1.03498 1.03302 1.01975 1.02675 1.03145 1.03296 1.03104 1.01832 1.02683 1.02795 1.02518 1.02343 1.02469 1.0219 1.02113 1.01916 1.0163
1.00185 1.01044 1.01853 1.02582 1.03114 1.03383 1.03304 1.02833 1.00513 1.01403 1.0215 1.02726 1.03047 1.03024 1.02629 1.00966 1.01736 1.02348 1.02711 1.0274 1.02536 1.01349 1.01991 1.02419 1.02544 1.02341 1.01151 1.01954 1.0204 1.01749 1.01617 1.01716 1.01419 1.0136 1.01142 1.00857
0.99378 1.00158 1.00879 1.01521 1.01986 1.0221 1.02117 1.01655 0.99649 1.00446 1.0111 1.1615 1.01888 1.01847 1.01456 1.0029 1.00717 1.01252 1.01566 1.0157 1.01364 1.0035 1.00921 1.01292 1.01385 1.01173 1.00086 1.00826 1.00879 1.00577 1.00496 1.00557 1.00246 1.00203 0.99967 0.99676
1.36031 1.37766 1.39109 1.42595 1.43167 1.44184 1.44885 1.46001 1.38512 1.40644 1.43868 1.42882 1.44016 1.44885 1.45866 1.40415 1.42062 1.42561 1.43925 1.45198 1.45671 1.41602 1.42942 1.43594 1.44625 1.45553 1.42407 1.43508 1.44531 1.45329 1.43305 1.44503 1.45154 1.44204 1.45119 1.45003
1.35961 1.3732 1.38929 1.418 1.42602 1.43166 1.4441 1.4551 1.37967 1.39754 1.42695 1.424 1.43479 1.44331 1.45262 1.39716 1.41515 1.42069 1.4325 1.44525 1.4505 1.40853 1.42383 1.42888 1.43962 1.44994 1.41906 1.43005 1.44043 1.44868 1.42785 1.44034 1.44651 1.43704 1.44673 1.44579
1.35844 1.37214 1.38858 1.41266 1.4225 1.42831 1.43052 1.45138 1.37462 1.39121 1.41989 1.4198 1.43065 1.4393 1.44883 1.39116 1.41017 1.4164 1.42824 1.44007 1.4462 1.40263 1.41899 1.4241 1.43518 1.44596 1.4142 1.42546 1.43475 1.44429 1.42355 1.43605 1.44258 1.43314 1.44218 1.44204
1.35757 1.37072 1.38419 1.40382 1.41401 1.42324 1.43517 1.44554 1.36689 1.3836 1.4056 1.41098 1.42095 1.43309 1.44324 1.38269 1.40107 1.40853 1.4212 1.43252 1.44005 1.39388 1.41147 1.4172 1.42768 1.43998 1.4062 1.4171 1.42805 1.43862 1.41465 1.4271 1.43696 1.4262 1.43573 1.43596
Table 7. Average Absolute Deviations (AADs) between the Predicted and Experimental Refractive Indices for MEA-MDEA-H2O System average absolute deviation (AAD), % model
295 K
308 K
318 K
333 K
Gladstone-Dale Arago-Biot Weiner Lorentz-Lorenz Heller
0.46 1.00 2.40 18.94 27.00
0.34 1.00 2.00 18.69 16.92
0.28 1.00 2.00 18.48 6.87
0.25 1.00 3.00 18.18 26.74
mixture, respectively, and subscripts i and m denote the ith component and the mixture, respectively. In the case of density, two density models (additive and nonadditive in terms of volume), represented in eqs 6 and 7, respectively, were considered for correlating the experimentally determined mixture density with their components’ pure component densities for all binary and ternary systems. These models generally provide for reasonably good predictions for cases in which the mixture density changes monotonically with the concentration of each component, but they fail if a nonmonotonic pattern is the case. Our experimental results showed that a nonmonotonic pattern existed for aqueous alkanolamine systems. Consequently, we decided to fit our density data at different temperatures empirically using the software (Matlab, Statistica, and Excel).
F)
xi
r ∑i)1 Fi
(6)
r xiFi ∑i)1
(7)
1 ) Fi
3.2. Correlations for Refractive Index and Density of Binary Systems. 3.2.1. MEA-H2O and MDEA-H2O Systems. Mole fractions, densities, and refractive indices of these binary systems at different temperatures (295, 308, 318, and 333 K) were measured. Figures 1 and 2, respectively, show the variation of experimental densities and refractive indices with mole fraction of MEA at the indicated temperatures for the MEA-H2O system, while Figures 3 and 4 show corresponding variations for the MDEA-H2O system. The composition variations of density (Figures 1 and 3) show a maximum value at approximately x ≈ 0.4 for MEA-H2O and at x ≈ 0.25 for MDEA-H2O systems for all temperatures. However, at any MEA or MDEA mole fraction, density decreases as the temperature is increased. The use of the density correlations (eqs 6 and 7) to predict the densities of the mixtures was unsuccessful because of the occurrence of a maximum point on the density-mole fraction curve. Hence, polynomials were used to fit the experimental density data. Figures 2 and 4 show that the refractive indices of MEA-H2O and MDEA-H2O mixtures increase monotonically with increasing MEA and MDEA mole fractions, respectively, at all temperatures. Also, at any MEA or MDEA mole fraction, the refractive index decreases as the temperature is increased. The refractive index correlations shown in eqs 1-5 were used to predict the mixture refractive indices under the same conditions as the experimental refractive indices for the two systems. The experimental results and the average absolute deviations (AADs) between the predicted and experimental refractive indices are, respectively, given in Table 1 and Table 2 for different temperatures for MEA-H2O and MDEA-H2O systems. Table 2 shows that the Gladstone-Dale model has the least deviation at all tempera-
Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1273 Table 8. Experimental Densities and Refractive Indices of MEA-H2O-CO2 System at Different Temperatures x1
x2
20 °C
25 °C
30 °C
35 °C
20 °C
25 °C
30 °C
35 °C
0.110857933 0.109883417 0.109522376 0.1091637 0.108689104 0.108218616 0.106512672 0.221298 0.214188 0.212639 0.209258 0.206663 0.282816 0.277865 0.277325 0.275644 0.274735 0.267675 0.380095 0.366177 0.362198 0.355755 0.351998 0.342358 0.47288 0.459834 0.447487 0.437694 0.428321 0.426494 0.523779 0.515676 0.50782 0.505254 0.502714 0.49771
0.863644743 0.856052724 0.853240016 0.850445731 0.846748364 0.843083006 0.829792751 0.738868472 0.715129958 0.709959753 0.698668845 0.690005505 0.629511544 0.618491641 0.617290977 0.613547626 0.611524871 0.595810634 0.543886176 0.523970333 0.518276906 0.509057922 0.503682295 0.489887137 0.394713242 0.3838231 0.373517742 0.365343414 0.35751921 0.355994413 0.308612013 0.303837701 0.299208858 0.297697094 0.296200529 0.293252091
1.0492 1.06215 1.06878 1.07644 1.08173 1.08734 1.11275 1.0758 1.11636 1.12856 1.15152 1.16937 1.12746 1.14381 1.14973 1.15821 1.1633 1.19044 1.10849 1.14377 1.15926 1.16914 1.18487 1.21072 1.15458 1.17548 1.19747 1.22184 1.24042 1.24872 1.18026 1.18653 1.19156 1.19292 1.19431 1.19666
1.04704 1.06002 1.06664 1.07422 1.07956 1.08515 1.11042 1.0731 1.11372 1.12595 1.14892 1.16672 1.12466 1.14105 1.14702 1.15551 1.16059 1.18776 1.10547 1.1409 1.15642 1.16635 1.18211 1.20802 1.15164 1.17264 1.19466 1.21905 1.23765 1.24594 1.17728 1.18359 1.18863 1.19001 1.19141 1.19375
1.04482 1.05778 1.0644 1.07195 1.07727 1.08285 1.10799 1.07032 1.11103 1.1233 1.14628 1.16404 1.12183 1.13827 1.14423 1.15275 1.15784 1.18504 1.10237 1.13797 1.15355 1.16352 1.17933 1.2053 1.14868 1.16977 1.19189 1.21623 1.23485 1.24312 1.17434 1.18061 1.18568 1.18706 1.18845 1.19084
1.0425 1.05547 1.0621 1.06959 1.0749 1.08047 1.10553 1.06749 1.10831 1.12058 1.14359 1.16134 1.11898 1.13546 1.14144 1.14996 1.15508 1.18231 1.09928 1.13502 1.15066 1.16068 1.17654 1.20255 1.14565 1.16687 1.18909 1.21346 1.23204 1.24028 1.17144 1.17776 1.18284 1.18419 1.18558 1.18793
1.38167 1.38559 1.38653 1.38838 1.38975 1.39109 1.39747 1.41202 1.42198 1.42467 1.42981 1.43429 1.43604 1.43968 1.44104 1.44287 1.44408 1.44988 1.4436 1.45128 1.45487 1.45748 1.46027 1.46601 1.46505 1.46941 1.47316 1.47862 1.48181 1.48355 1.47592 1.47776 1.47849 1.4787 1.47884 1.47923
1.38135 1.38487 1.38591 1.388 1.389 1.39058 1.39669 1.41102 1.42094 1.42398 1.42884 1.43322 1.43491 1.4386 1.43995 1.44183 1.44301 1.44876 1.4423 1.45015 1.45367 1.45658 1.45922 1.46493 1.46382 1.46825 1.47225 1.47763 1.48053 1.48255 1.47474 1.4763 1.47736 1.4773 1.47771 1.478
1.38115 1.38454 1.3848 1.38702 1.38846 1.38977 1.39588 1.41085 1.4208 1.4237 1.42827 1.43329 1.4338 1.43841 1.43892 1.44093 1.44239 1.44779 1.44103 1.44901 1.45251 1.45568 1.45816 1.46386 1.46259 1.46705 1.47122 1.4766 1.47943 1.48146 1.47353 1.4751 1.47619 1.47615 1.47653 1.47687
1.38095 1.3845 1.38465 1.38636 1.38843 1.3897 1.39544 1.4092 1.42011 1.42336 1.42803 1.43216 1.43348 1.43814 1.43828 1.44039 1.4419 1.44678 1.43992 1.44782 1.45133 1.45469 1.45709 1.46275 1.46132 1.46584 1.47018 1.4755 1.47839 1.48034 1.47228 1.47392 1.47499 1.47496 1.4753 1.47574
Table 9. Experimental Densities and Refractive Indices of MDEA-H2O-CO2 System at Different Temperatures x1 (MDEA)
x2 (water)
20 °C
25 °C
30 °C
35 °C
20 °C
25 °C
30 °C
35 °C
0.133033345 0.131407558 0.130703366 0.129972887 0.128817633 0.127927748 0.124736302 0.220561 0.218298 0.215059 0.211198 0.205639 0.202475 0.198535 0.310756401 0.309391139 0.304975248 0.299226085 0.285554813 0.277549984 0.449481 0.438253 0.436341 0.425209 0.410714 0.396544 0.56296 0.54103 0.520203 0.634749 0.604805 0.589475
0.845681319 0.83534633 0.830869844 0.826226251 0.818882407 0.813225487 0.792937739 0.754956454 0.747210586 0.736122678 0.722907914 0.703879671 0.693048315 0.67956405 0.658478715 0.655585785 0.646228713 0.634046498 0.605077693 0.588115823 0.504221995 0.491626312 0.489481145 0.476993245 0.460732909 0.44483792 0.397632784 0.382143322 0.367432696 0.327165913 0.31173193 0.303830332
1.07106 1.0851 1.09225 1.09882 1.109 1.116 1.13802 1.07468 1.08517 1.09679 1.11265 1.13545 1.15388 1.17159 1.07307 1.08048 1.08845 1.10281 1.12732 1.15828 1.07823 1.088 1.0986 1.11069 1.13541 1.14902 1.0649 1.08854 1.1104 1.06903 1.08755 1.10494
1.06789 1.08189 1.08904 1.09561 1.10576 1.11277 1.13481 1.07118 1.0817 1.09333 1.10924 1.13206 1.15056 1.1683 1.0695 1.07693 1.08489 1.09934 1.12389 1.15496 1.07461 1.08443 1.09506 1.10714 1.13179 1.14544 1.06124 1.08491 1.10666 1.06536 1.08382 1.10113
1.06466 1.07862 1.08578 1.09233 1.10248 1.10948 1.13155 1.06764 1.07817 1.08983 1.10577 1.12864 1.1472 1.16498 1.06586 1.0733 1.08128 1.09579 1.12039 1.15156 1.07093 1.08077 1.09143 1.10352 1.12815 1.1414 1.05751 1.0812 1.1029 1.06159 1.08003 1.09725
1.06137 1.07532 1.08248 1.08901 1.09916 1.10617 1.12827 1.06405 1.07461 1.08629 1.10226 1.12518 1.14379 1.16162 1.06216 1.06961 1.07762 1.09217 1.11686 1.14809 1.06719 1.07705 1.08773 1.09979 1.12314 1.13788 1.05371 1.07738 1.09889 1.05775 1.07563 1.0899
1.41543 1.41782 1.41821 1.42029 1.42207 1.42321 1.42653 1.43577 1.43741 1.43978 1.44227 1.44616 1.15388 1.17159 1.44843 1.45028 1.45126 1.45334 1.45854 1.46224 1.46105 1.46253 1.46271 1.46559 1.46741 1.46992 1.46463 1.4685 1.47034 1.46765 1.47041 1.472
1.41417 1.41655 1.41721 1.41902 1.42082 1.42198 1.42532 1.43429 1.43605 1.43832 1.44098 1.44492 1.15056 1.1683 1.44692 1.44847 1.44974 1.45193 1.45715 1.46094 1.4595 1.46102 1.4612 1.46407 1.46624 1.46887 1.46301 1.46692 1.46887 1.466 1.46888 1.47077
1.41359 1.41531 1.41623 1.41776 1.41955 1.42076 1.42415 1.43284 1.43464 1.43692 1.43963 1.44366 1.1472 1.16498 1.44538 1.44692 1.44821 1.45051 1.45576 1.45959 1.45793 1.4595 1.45966 1.46254 1.46536 1.46787 1.46136 1.46533 1.46734 1.46434 1.46722 1.46946
1.41148 1.41428 1.41554 1.41657 1.41829 1.41953 1.4231 1.43142 1.4332 1.43548 1.43824 1.4423 1.14379 1.16162 1.4438 1.44531 1.44668 1.449 1.45431 1.45821 1.45628 1.45796 1.45937 1.46103 1.46429 1.46667 1.45964 1.46366 1.46586 1.46261 1.46552 1.46794
tures for the two systems. This can be explained on the basis that the Gladstone-Dale equation is empirical while the Lorentz-Lorenz equation is based on some theory. The aqueous
solutions used for this work are highly nonideal. Thus, the accuracy of the theoretically based models such as LorentzLorenz depends on how well the deviation from ideality is
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Figure 7. Parity chart showing predicted density against experimental density for MEA-H2O-CO2 system.
Figure 8. Parity chart showing predicted density against experimental density for MDEA-H2O-CO2 system. Table 10. Average Absolute Deviations (AADs) between the Predicted and Experimental Refractive Indices average absolute deviation (AAD), % model
295 K
308 K
318 K
333 K
Gladstone-Dale Arago-Biot Weiner Lorentz-Lorenz Heller
(a) MEA-H2O-CO2 System 0.62 0.56 0.56 30.00 30.00 30.00 7.50 2.00 2.00 30.50 30.50 30.40 2.00 2.00 2.00
0.53 30.00 2.00 30.40 2.00
Gladstone-Dale Arago-Biot Weiner Lorentz-Lorenz Heller
(b) MDEA-H2O-CO2 System 1.62 1.63 1.64 28.90 28.90 28.80 3.20 8.40 3.00 29.60 64.60 64.50 3.81 3.80 3.80
1.65 28.70 3.00 64.50 3.72
described by the model. It appears from our results that the assumptions made in deriving the theoretically based models to describe the nonideality are not suitable for these aqueous solutions. Also, we are aware that the Gladstone-Dale equation and other such equations have been used successfully to model refractive index for many other chemicals such as alcohols, ethers, esters, mixtures of alcohol with hexadecane, etc. However, this appears to be the first time the models have been used for our type of chemicals. In order to further evaluate the consistency of the Gladstone-Dale equation at different temperatures, we decided to test the Gladstone-Dale assumption, (n - 1)/F ) constant, for the pure components MEA, MDEA, and H2O as a function of temperature. The results are given in Tables 3-5 for MEA, MDEA, and H2O, respectively, which
show that the constants do not change with temperature but are different for MEA, MDEA, and H2O. 3.3. Correlations for Refractive Index and Density of Ternary Systems. Three ternary systems were evaluated. These were MEA-MDEA-H2O, MEA-H2O-CO2, and MDEAH2O-CO2 systems. 3.3.1. MEA-MDEA-H2O System. Densities and refractive indices of aqueous mixed MEA-MDEA were measured at the temperatures of 295, 308, 318, and 333 K. As in the case of binary systems, the mixture density was correlated empirically with the density of the pure components using the experimental density data with the help of a polynomial function. Statistical parameters show 94% consistency in the fitting. Figure 5 shows a typical 3-dimentional plot of this ternary mixture at 295 K, while Table 6 shows the actual experimental values. A parity chart showing the plot of the predicted density against the experimental density for the four temperatures is shown in Figure 6. Also, Gladstone-Dale, Lorentz-Lorenz, Weiner, Heller, and Arago-Biot empirical relations were used to predict the refractive indices of this ternary mixture at the desired temperatures. Gladston-Dale had the least absolute average deviation, as shown in Table 7. 3.3.2. MEA-H2O-CO2 and MDEA-H2O-CO2 Systems. The densities and refractive indices of CO2-loaded aqueous MEA and MDEA systems were measured at temperatures of 293, 298, 303, and 308 K. The results are given in Tables 8 and 9. The density was modeled empirically, and the deviations between the predicted densities and the experimentally determined densities were very good. Parity charts showing the plot of the predicted density against the experimentally determined density for the four temperatures are shown in Figures 7 and 8 for the MEA-H2O-CO2 and MDEA-H2OCO2 systems, respectively. On the other hand, Gladstone-Dale, Lorentz-Lorenz, Weiner, Heller, and Arago-Biot empirical relations were used to predict the refractive indices of this ternary mixture at the desired temperatures. Gladston-Dale had the least absolute average deviation, as shown in Table 10. 4. Comparison of the Mole Fractions Obtained from Density-Refractive Index Technique with Those from HPLC-Titration Technique The practical CO2 absorption or loading in amine solutions is limited. For example, in aqueous MEA, the MEA concentration is typically up to 5 mol/L, and the maximum CO2 loading is 0.5 (mol of CO2)/(mol of MEA). In mole fraction, this would translate into maxima of 0.15 and 0.075 for MEA and CO2, respectively. Similar scenarios apply to the MDEA-H2O-CO2 and MEA-MDEA-H2O systems. On this basis, the ranges of values used for comparison of experimental results with those from the new method are limited to the ranges of concentrations used in practice. 4.1. Binary systemssMEA-H2O and MDEA-H2O Systems. Aqueous MEA and MDEA samples were separately prepared at different MEA and MDEA concentrations. The exact MEA and MDEA concentrations were established by titration using 1 N hydrochloric acid. The mole fractions of MEA in the MEA-H2O system and the mole fractions of MDEA in the MDEA-H2O system were determined with the HPLC using the procedure described earlier. Because of its monotonic relationship with mole fraction, the refractive index was used to determine the mole fractions of MEA and MDEA in the MEA-H2O and MDEA-H2O systems. The refractive indices of the samples of these systems of unknown MEA and MDEA mole fractions were measured at 308 K. The Gladstone-Dale
Ind. Eng. Chem. Res., Vol. 47, No. 4, 2008 1275 Table 11. Comparison of Experimental and Predicted Mole Fractions of MEA for MEA-H2O System mole fractions of MEA by HCl titration (standard)
experimental mole fractions of MEA by HPLC
predicted mole fractions of MEA by refractive index method
SD% (experimental standard)
SD% (predicted standard)
0.0322 0.0465 0.066 0.08 0.1334
0.0345 0.0487 0.083 0.0886 0.1439
0.03123 0.049 6.80E-02 8.70E-02 1.38E-01
6.67 4.52 20.48 9.71 7.3
3.01 5.38 3.03 8.75 3.45
9.74
4.72
average
SD% (HPLC-refractive index) 9 1 18 2 4 6.8
Table 12. Comparison of Experimental and Predicted Mole Fractions of MDEA for MDEA-H2O System standard mole fractions of MDEA
experimental mole fractions of MDEA
predicted mole fractions of MDEA
SD% (experimental standard)
SD% (refractive index standard)
0.0267 0.047 0.085 0.114 0.17
0.0278 0.0474 0.089 0.117 0.174
0.0245 0.0476 0.09 0.129 0.182
3.96 0.84 4.49 2.56 2.3
8.98 1.26 5.55 11.63 6.59
2.83
6.8
average Table 13. Comparison of Experimental and Predicted Mole Fractions MDEA in MEA-MDEA-H2O System experimental mole fraction (HPLC)
predicted mole fraction (refractive index)
0.045 0.05 0.03 0.03 0.06
0.04 0.05 0.005 0.03 0.061
r refractive index model (eq 1) together with ∑i)1 xi ) 1 was used to obtain the mole fractions of the components from the measured mixture refractive index and the refractive indices of the pure components. The results are shown in Tables 11 and 12 for MEA-H2O and MDEA-H2O systems, respectively. These tables show excellent agreement with AADs of 6.83% for HPLC-refractive index technique, 9.73% for HPLCstandard titration technique, and 4.71% for refractive indexstandard titration technique in the MEA-H2O system. Also, the AADs were 5.65% for the HPLC-refractive index technique, 2.83% for the HPLC-standard titration, and 4.8% for the refractive index-standard titration technique in the MDEAH2O system. 4.2. Ternary SystemssMEA-MDEA-H2O, MEA-H2OCO2, and MDEA-H2O-CO2 Systems. Samples of the indicated systems were prepared at different concentrations of the various components. The total amine concentrations in mole fractions in the MEA-MDEA-H2O system were determined using the hydrochloric acid titration method, whereas the mole fractions of MEA and MDEA were determined with the HPLC. The mole fractions of MEA in the MEA-H2O-CO2 system and the mole fractions of MDEA in the MDEA-H2O-CO2 system were also determined with the HPLC. The CO2 loading was determined by titration, as described earlier. In ternary systems, more than one property is required to determine the mole fractions of the three components. The properties selected for the samples, densities, and refractive indices were measured at 308 K (MEA-MDEA-H2O) and at 303 K (MEA-H2OCO2 and MDEA-H2O-CO2). Then the Gladstone-Dale refractive index model (eq 1) together with the empirical density r xi ) 1 was used to obtain the mole fractions of model and ∑i)1 the components from the measured mixture refractive index and density and those of the pure components, as described earlier. The results are given in Tables 13-15 for the MEAMDEA-H2O, MEA-H2O-CO2, and MDEA-H2O-CO2 sys-
SD% (HPLC-refractive index) 12 0 1 10 5 5.6
Table 14. Comparison of Experimental and Predicted Mole Fraction of CO2 in MEA-H2O-CO2 System
(mol of CO2)/ (mol of amine)
total mol of CO2
experimental mole fraction of CO2 by HCL titration
0.198 0.25 0.35 0.43 0.51
1.590711615 2.008474262 2.811863967 3.454575731 4.097287494
0.042 0.054 0.07 0.09 0.1
predicted mole fraction of CO2
SD% (CO2 mole fraction)
0.05 0.06 0.08 0.1 0.1
19.00 11.00 14.00 11.00 0.00
average
11.00
Table 15. Comparison of Experimental and Predicted Mole Fraction of CO2 in MDEA-H2O-CO2 System
(mol of CO2)/ (mol of amine)
total mol of CO2
experimental mole fraction of CO2 by HCL titration
0.15 0.28 0.33 0.45 0.53
0.9 1.68 1.98 2.7 3.18
0.04 0.07 0.08 0.11 0.12 average
predicted mole fraction of CO2 0.04 0.08 0.1 0.12 0.14
SD% (CO2 mole fraction) 0 14 25 9 16 12.8
tems, respectively. These tables show excellent agreement with AADs of 6% for HPLC-refractive index/density for MEA and 19% for MDEA; 8% for HPLC-standard titration for total amine concentration. The AADs were 9% in the refractive index/ density-standard titration for total amine concentration in the MEA-MDEA-H2O system and 11% in the refractive index/ density-standard titration for CO2 in the MEA-H2O-CO2 system (8 × 103 mol/m3 amine concentration). Furthermore, the AAD was 13% in the refractive index/density-standard titration for CO2 in the MDEA-H2O-CO2 system (6 × 103 mol/m3 amine concentration). 5. Industrial Applications In field operations, quick and easy-to-use physical techniques are required to determine parameters that aid in the evaluation of the performance of a CO2 capture process by chemical absorption. Knowledge of these parameters will also help in determining whether or not the process is proceeding according to specified operating conditions, such as maintaining the amine ratios in blended or mixed amines, and the need for water or
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amine makeup for the solvent. Chromatographic techniques are not expedient in field situations. Consequently, the new physical techniques, which are very expedient in these situations, will help to achieve the indicated objectives. 6. Conclusions We have used two binary systems (MEA-H2O and MDEAH2O) and three ternary systems (MEA-MDEA-H2O, MEAH2O-CO2, and MDEA-H2O-CO2) typical of CO2-loaded and -unloaded single and blended alkanolamine systems used for CO2 capture from power plant flue gases to show that the solution of density-refractive index equations can be used as a simple and inexpensive technique to determine the mole fractions of the components of the mixture. Also, because it gives very accurate results, this technique can be used to replace chromatographic techniques such as the HPLC technique as an easier and quicker analytical technique for composition determination of fresh and nondegraded CO2 capture solvents, especially in field situations. Acknowledgment The financial support provided by the Natural Science and Engineering Research Council of Canada (NSERC) and CANMET Energy Technology Centre, Natural Resources Canada, Ottawa, is gratefully acknowledged. Literature Cited (1) Kohl, A. L.; Riesenfield, F. C. Gas Purification, 4th ed.; Gulf Publishing: Houston, TX, 1985. (2) Dawodu, O. F.; Meisen, A. Degradation of alkanolamine blends by carbon dioxide. J. Chem. Eng. 1996, 74, 960-962. (3) Supap, T.; Idem, R. O.; Tontiwachwuthikul, P.; Saiwan, C. Analysis of Monoethanolamine and its Oxidative Degradation Products during CO2 Absorption from Flue Gases: A Comparative Study of GC-MS, HPLCRID and CE-DAD Analytical Techniques and Possible Optimum Combinations. Ind. Eng. Chem. Res. 2006, 45, 2437-2451. (4) DiGuilio, R. M.; Lee, R. J.; Schaeffer, S. T.; Brasher, L. L.; Teja, A. S. Densities and Viscosities of the Ethanolamines. J. Chem. Eng. Data 1992, 37, 239-242.
(5) DiGuilio, R. M.; McGregor, W. L.; Teja, A. S. The Thermal Conductivity of the Ethanolamines. J. Chem. Eng. Data 1992, 37, 242245. (6) Maham, Y.; Hepler, L. G.; Mather, A. E.; Hakin, A. W.; Marriott, R. A. Molar Heat Capacities of Alkanolamines from 299.1 to 397.8 K. Group Additivity and Molecular Connectivity Analyses. J. Chem. Soc., Faraday Trans. 1997, 93, 1740-1750. (7) Maham, Y.; Teng, T. T.; Hepler, L. G.; Mather, A. E. Densities, Excess Molar Volumes, and Partial Molar Volumes for Binary Mixtures of Water with Monoethanolamine, Diethanolamine, and Triethanolamine from 25-80 °C. J. Solution Chem. 1994, 23, 195-205. (8) Maham, Y.; Teng, T. T.; Mather, A. E.; Hepler. L. G. Volumetric Properties of (Water + Diethanolamine) Systems. Can. J. Chem. 1993, 73, 1514-1519. (9) Teng, T. T.; Maham, Y.; Hepler, L. G.; Mather, A. E. Viscosity of Aqueous Solutions of N-Methyldiethanolamine and of Diethanolamine. J. Chem. Eng. Data 1994, 39, 290-293. (10) Dale, D.; Gladstone, F. On the influence of temperature on the refraction of light. Philos. Trans. 1858, 148, 887. (11) Lorentz, H. A. On the Lorentz-Lorenz Formula and Model of Dielectric. Ann. Phys. 1880, 9, 641-665. (12) Lorenz, L.V. On the Lorentz-Lorenz Formula and Model of Dielectric. Ann. Phys. 1880, 11, 70-103. (13) Bhatti, S. S.; Prabhakar, K. P.; Singh, D. P. Relative validity of refractive index mixing rule for ternary liquid mixtures. Indian J. Pure Appl. Phys. 1995, 33, 18-22. (14) Heller, W. J. Remarks on Refractive Index Mixture Rules. J. Phys. Chem. 1965, 69, 1123. (15) Pandy, J. D.; Vyas, V.; Jain, P.; Dubey, G. P.; Tripathi, N.; Dey, R. Speed of Sound, Viscosity and Refractive Index of Multicomponent Systems, Theoretical Predictions from the Properties of Pure Components. J. Mol. Liq. 1999, 81, 123-133. (16) Oswal, S. L.; Gardas, R. L.; Phalak, R. P. Densities, Speeds of Sound, Isentropic Compressibilities, Refractive Indexes, and Viscosities of Tetrahyrofuran with Haloalkane or Alkyl Ethanoate at T ) 303.15 K. Thermodyn. Acta 2005, 426, 199-206.
ReceiVed for reView July 18, 2007 ReVised manuscript receiVed November 16, 2007 Accepted November 16, 2007 IE0709786
