J. Chem. Thermodynamics 001, 33, 185 1308 doi:10.1006/jcht.001.0837 Available online at http://www.idealibrary.com on Experimental determination of oxygen and nitrogen solubility in organic solvents up to 10 MPa at temperatures between 98 K and 398 K Kai Fischer, a Laboratory for Thermophysical Properties LTP GmbH, Institute at the University of Oldenburg, FB9-TC, P.O. Box 503, D-6111 Oldenburg, F.R.G. and Michael Wilken University of Oldenburg, Department of Industrial Chemistry, P.O. Box 503, D-6111 Oldenburg, F.R.G. Oxygen solubility in methanol, n-propanol, dibutyl ether, toluene, and octane, and nitrogen solubility in ethanol, n-propanol and -methyltetrahydrofuran was measured at pressures up to 10 MPa in the temperature range between 98 K and 398 K using the static synthetic method. The experimental results were used to extend the range of applicability of the Soave Redlich Kwong (PSRK) model for the prediction of air solubility in organic solvents and solvent mixtures by fitting the missing gas solvent group interaction parameters. The required pressure range of gas solubility data for fitting the PSRK group interaction parameters was defined by analysing the significance of the data for the optimized parameters. The applied experimental method was analysed in detail since its use at higher pressures requires the consideration of the partial molar volumes of the dissolved gases when solving the mass and volume balance equations during the data treatment. c 001 Academic Press KEYWORDS: gas solubility; PSRK group contribution; equation of state; oxygen; nitrogen; organic solvents 1. Introduction The correlation and prediction of (vapour, or gas + liquid) equilibria is possible with cubic equations of state (EoS) combined with so-called G E mixing rules. These methods combine the advantages of the local composition concept of G E models with those of equations of state. (Vapour + liquid) equilibria at high or low pressure of multicomponent a To whom correspondence should be addressed (E-mail: fischer@tech.chem.uni-oldenburg.de). 001 9614/01/10185 + 4 $35.00/0 c 001 Academic Press
186 K. Fischer and M. Wilken systems can be predicted using only binary interaction parameters, regardless of the polarity of the components, and whether they are sub- or super-critical. Also group contribution approaches such as UNIFAC can be used, so that the applicability of methods, for example the PSRK group contribution equation of state, (1) is not restricted to systems where experimental data are available. Furthermore, an equation of state allows the calculation of other properties such as enthalpies and densities which are also required for the design of separation processes. The range of applicability was extended by the introduction of new structural groups and the fitting of the group interaction parameters between the new groups and the already existing groups. ( 6) Up to now, 31 new PSRK main groups (epoxy group and 30 gases such as CO, CO, O, N, CH 4, etc.) have been introduced. An improvement of the results for strongly asymmetric systems (mixtures with compounds different in size) was achieved by Li et al. (7) A detailed analysis of different thermodynamic properties like enthalpy and volume effects and their representation by PSRK was given for (carbon dioxide + ethane) by Horstmann et al. (8) Most of the available experimental information for gas solubility is given in terms of solubility coefficients, which are based on the approximate linearity of gas solubility with its partial pressure at low concentration and low pressure. They can be used to fit the interaction parameter for the classical mixing rules for cubic equations of state. But for the optimization of the two or three parameters required by G E mixing rules a larger composition and pressure range should be covered. Therefore, in this work gas solubility data for oxygen in n-octane, toluene, n-propanol, dibutyl ether, and methanol, and nitrogen in ethanol, -methyltetrahydrofuran (-methylthf), and n-propanol were measured using a static apparatus in the temperature range between 98 K and 398 K and at pressures up to 10 MPa. These data were used to fit the required interaction parameters for the PSRK model. The calculated results were compared with all the available experimental information stored in the Dortmund Data Bank (DDB) in terms of Henry coefficients. Since the applied experimental static synthetic method was used before only at low pressure, the treatment of raw data was carefully analysed in order to provide reliable (p, x) data..1. MATERIALS. Experimental Oxygen (mole fraction purity: 0.99995) and nitrogen (mole fraction purity: 0.99999) were purchased from Messer Griesheim. They were used without further purification. The purity and the suppliers of the different solvents are given in table 1. All the solvents were distilled and degassed after drying over molecular sieves by low-pressure distillation as described previously. (9).. APPARATUS AND PROCEDURE The apparatus used was previously described in detail by Fischer and Gmehling. (9) Since it was previously used only for the measurement of v.l.e. for subcritical systems, a few modifications were made. A schematic view of the apparatus is shown in figure 1. The
Experimental determination of oxygen and nitrogen solvents 187 TABLE 1. Suppliers, mole fraction purity x and mole fraction of water x(h O) Solvent Supplier x 10 6 x(h O) Methanol Scharlau 0.999 71 Ethanol Scharlau 0.999 30 n-propanol Aldrich 0.999 8 Toluene Fluka 0.999 73 Dibutyl ether Fluka 0.999 89 n-octane Aldrich 0.999 104 -Methyl tetrahydrofuran Aldrich 0.995 445 F A E Pressure B R Vacuum H O D K M H K Pressure balance <1 MPa Pressure balance <1 MPa N H N Gas C G FIGURE 1. Schematic diagram of the static apparatus. A, buffer volume; B, pressure regulator; C, vacuum tubes; D, gas container; E, pressure display; F, container for degassed liquids; G, pump; H, constant temperature bath; K, thermometer; M, differential pressure null indicator; N, equilibrium cell; O, piston injectors; R, pressure balance gauge.
188 K. Fischer and M. Wilken Input V cell V Gas tank T Cell T Gas tank v 1 p s B ii p Cell p Gas tank Solvent Calculation of the injected masses n a e 1 V B 11 V B 11 pv RT B 11 n1 T n a 1 n e 1 n T v M Starting values: x 1 y 1 1 p p s n T n l n T v V l V V V Cell V l Mass balance of solvent, calculation of n V V V B V V B V n p V V n l n T n V RT B Volume calculation Calculation of the V L n l l partial pressures v { 1 p p } v1n1 L V V V Cell V L p x p s p 1 p p Mass balance of gas, calculation of V n 1 n V 1 V V B 11 V V B 11 p 1 V V RT B 11 n L 1 n T 1 n V 1 Calculation of x i no p i,v L const? yes Output: x i y i V L p FIGURE. Flow diagram of the raw data treatment by the first procedure.
Experimental determination of oxygen and nitrogen solvents 189 GLEFLASH Input: Pure component data, starting values of mixing rule parameters, feed masses, T, p Estimating unknown Péneloux-corrections Flash calculation with starting values of mixing rule parameters Optimization of mixing rule parameters Flash calculation Flash calculation with optimized mixing rule parameters Conversion of saturation vapour pressures to average temperature Output: x i y i V L V V p END FIGURE 3. Flow diagram of the raw data treatment by the second procedure, main loop.
190 K. Fischer and M. Wilken FLASH for constant mixing rule parameters Input : z i T p Starting values: x i, y i 1. Iteration? K i y i x i Calculation with equation of state : V L i K i V V i L i L i V i L i One phase? V L = V V yes no Mass balance : calculation of x i, y i from K i, z i STOP x i new x i x i y i new y i y i no x i, y i = const yes Output : x i, y i, V L, V V FIGURE 4. Flow diagram of the raw data treatment by the second procedure, flash loop.
Experimental determination of oxygen and nitrogen solvents 191 TABLE. Critical temperatures T 1,c, critical pressure p 1,c and parameters A and B of equation (1) T 1,c /K p 1,c /MPa A B Oxygen 154.6 5.043 0.055 3.808 Nitrogen 16. 3.39 0.0411 4.71 TABLE 3. Isothermal compressibility β T, isobaric thermal expansion α, calculated partial molar volumes of oxygen in the solvents used v 1, and values of the internal pressure p in {equation (1)} at temperature T T/K β T /(10 3 MPa 1 ) α p /(10 3 K 1 ) p in /MPa v 1 /cm 3 Methanol 98.15 1.18 1.17 95.6 45.3 33.15 1.40 1.18 77.1 50.3 348.15 1.730 1.31 65.7 54.9 n-propanol 98.15 0.964 0.98 303.8 44.5 33.15 1.118 1.059 305.9 46.8 348.15 1.37 1.136 97.8 50.4 n-octane 98.15 1.07 1.147 83.4 46.7 33.15 1.475 1.33 69.9 51.3 348.15 1.81 1.318 53. 56.9 Toluene 98.15 0.908 1.105 36.8 39.4 33.15 1.107 1.13 330.4 44.3 348.15 1.375 1.184 99.9 50.1 principle of the synthetic measurement is to inject precisely known amounts of the pure components into a thermoregulated equilibrium chamber, and to measure the system pressure as a function of composition in the (gas, or vapour + liquid) system. The degassed pure liquid solvents were injected at the beginning of each experimental run into the evacuated equilibrium cell using displacement pumps. Then, the gases were injected stepwise from a gas container with constant volume (about 1 dm 3 ) filled directly from gas bottles to a pressure greater than the pressure in the equilibrium cell. The temperature and pressure in the gas container at ambient temperature were monitored by using a Pt 100 resistance thermometer (model 1560, Hart Scientific), and a calibrated piezoelectric pressure sensor (model PDCR 911, Druck). The total volumes of the gas injection system, and of the equilibrium cell were determined by displacing the complete volume under reduced pressure with pure compressed water. The estimated accuracy of the volumes determined with this procedure was better than ±0.05 per cent. After recording the initial pressure in the gas injection system, the valve to the equilibrium chamber was opened
19 K. Fischer and M. Wilken TABLE 4. Calculated partial molar volumes of nitrogen in the solvents used, and values of the internal pressure p in {equation (1)} T/K β/(10 3 MPa 1 ) α/(10 3 K 1 ) p in /MPa v 1 /cm 3 n-propanol 98.15 0.964 0.98 303.8 51. 348.15 1.37 1.136 97.8 58.5 398.15 1.909 1.89 68.7 70.7 Ethanol 98.15 1.117 1.074 86.6 46.3 348.15 1.675 1.077 3.8 6.6 398.15.866 1.531 1.5 7.7 for several seconds so that the pressure in the equilibrium chamber became equal to the pressure in the gas injection system. Then the valve was closed, and the pressure of the gas injection system was measured again. From the (p, V, T ) data before and after injection, the amount of the gaseous compound injected can be calculated using suitable equations of state, which are available for most of the common gases. We have used the virial equation with the second virial coefficients recommended by DIPPR. (10) Liquid densities of the pure solvents were required to calculate the solvent loading from the volume displaced during injection. From the volume change with pressure in the displacement pumps, the liquid compressibility could be determined and taken into account, since the injection of the compressed pure liquids was performed at about MPa. The amount of solvent initially injected into the equilibrium chamber was chosen to be large enough to fill the major part of the equilibrium chamber because most of the gas injected would be in the liquid phase. For each loading of the equilibrium cell the temperature and pressure were monitored while stirring the mixture. After about (30 to 45) min equilibrium was indicated by stable readings of temperature and pressure. Then the next gas injection could be made..3. TREATMENT OF RAW DATA Since only temperature, pressure, total loadings n T i, and the total volume V T are measured, the composition of the coexisting phases must be determined by an isothermal and isochoric flash calculation. The following balance equations must be fulfilled: n T i = n l i + nv i, (1) V T = V l + V V. () We have compared two different methods for treating the raw data: In the first procedure (a), the liquid phase volume V l is calculated from the solvent density at a given temperature. The remaining gas phase volume V V is given by equation (), and allows the calculation of the amount of gas in the gas phase n V 1 at given pressure and temperature. Then equation (1) allows the calculation of the amount of gas in the liquid phase n l 1. It is necessary to consider the following effects in this procedure: the amount of solvent in the liquid phase must be reduced because a certain amount evaporates;
Experimental determination of oxygen and nitrogen solvents 193 10 a 10 b 8 8 p / MPa 6 4 p / MPa 6 4 0 0 0.1 x 0 0. 0 0.1 0. x FIGURE 5. Pressure against the mole fraction of oxygen x for (oxygen+n-octane) at T = 348.15 K: a, without consideration of v 1 and β T ; b, with consideration of v 1 and β T ;, first procedure;, second procedure. 1 10 a 1 10 b 8 8 p / MPa 6 4 p / MPa 6 4 0 0 0.05 x 0 0.05 0 0.05 x 0.05 FIGURE 6. Pressure against mole fraction of nitrogen x for (nitrogen + ethanol) at T = 348.15 K: a, without consideration of v 1 and β T ; b, with consideration of v 1 and β T ;, first procedure;, second procedure. the liquid volume is reduced at high pressures due to the compressibility of the solvent; the total pressure p is not equal to the partial pressure of the gas p 1 because the solvent has a significant partial pressure p which can be estimated from the vapour pressure p s ; the liquid phase volume increases when a gas is dissolved due to the partial molar volume of dissolution. These effects become important when either the solubility or the pressure is high, or the solvent is volatile or compressible. When the solvent activity coefficient is assumed to be equal to unity (solvent mole fraction x 1), equation (3) can be used to estimate the
194 K. Fischer and M. Wilken TABLE 5. Comparison of the resulting mole fraction solubility data x for the procedures T/K x b x a 10 δ c V lb /cm 3 V la /cm 3 10 δ c xo + (1 x)ch 3 (CH ) 6 CH 3 98.4 0.00183 0.00179.1 93.53 93.54 0.01 0.18445 0.17956.7 98.79 98.3 0.57 33.9 0.0006 0.0006 0.1 97.01 97.0 0.01 0.18440 0.17771 3.6 10.51 10.09 0.41 348.31 0.00183 0.00179.1 100.04 100.06 0.0 0.18445 0.17956.7 105.85 105.60 0.3 xn + (1 x)ch 3 CH OH 98. 0.0006 0.0005 4.7 14.63 14.64 0.01 0.03347 0.03173 5. 145. 144.83 0.5 348.0 0.00038 0.00039 1.9 141.4 141.8 0.03 0.03949 0.03971 0.6 144.06 144.78 0.50 398.0 0.00059 0.00057 3.0 14.68 14.51 0.1 0.04364 0.04348 0.4 145.56 145.9 0.5 a First procedure; b Second procedure; c δ is the deviation per cent between experimental and calculated values. Total volume of the equilibrium cell is 167.08 cm 3. solvent partial pressure: and the partial pressure of the gas: p = x p s, (3) p 1 = p p. (4) The liquid volume is calculated from the liquid molar volume of the pure solvent v l, at a reference pressure p (usually 1 atmosphere), its compressibility β, and the partial molar volume of the dissolved gas v 1 (see Section.4). V l = n l vl, {1 β (p p )} + v 1 n l 1. (5) Since these calculations depend on the mole numbers of the components in the liquid phase, the solution for the solubility data can only be found iteratively, where the mole numbers of the compounds in the vapour phase must be calculated using suitable equations of state by the following relation: n V i = V V /[RT {( ln ϕ V i i / p i ) T + (1/p i )}]. (6) For nitrogen and oxygen we have used the virial equation, where equation (6) transformed
Experimental determination of oxygen and nitrogen solvents 195 TABLE 6. Henry coefficients H 1 derived from the experimental pressure and mole fraction at temperature T and deviation δ System T/K H1 a /MPa H 1 b /MPa 10 δ Methanol + oxygen 98.34 5.8 47.4.1 33.3 57.5 47.4 3.9 348.9 33.4 39.1.4 Toluene + oxygen 98.41 104.5 103.9 0.6 33.30 96.4 99. 3.0 348.9 89. 94.3 5.7 Octane + oxygen 98.43 45.9 46.3 0.7 33.9 46.9 46.6 0.7 348.9 46.4 46.5 0.1 Dibutylether + oxygen 98.30 47.6 47.3 0.7 n-propanol + oxygen 98.0 150. 15.4 1.5 33.56 141. 145.5 3.1 348.0 139.7 139.3 0. -Methyltetrahydrofuran + nitrogen 311.03 135.8 136.1 0. n-propanol + nitrogen 98.34 54.0 57.7 1.5 348.18 13.9 17.6 1.7 398.9 164. 168.3.5 Ethanol + nitrogen 98.0 96.5 90.8 1.9 348.0 5.3 54.9 1.0 398.0 198.3 08.3 5.0 10 δ 0.9 a SRK + Huron-Vidal mixing rules + UNIQUAC; b virial equation. to equation (7), where the second virial coefficient B ii must be known at the temperature T to calculate the fugacity coefficient φ V i. n V i = V V /B ii ± [(V V /B ii ) + {p i (V V ) /RT B ii }]. (7) This iterative treatment of the raw data is applied for each single data point. In the second procedure (b), equations of state allow the calculation of the desired auxiliary quantities given above. They even allow a further refinement of the first procedure because for the expression of the solvent activity coefficient γ i {assumed to be unity in equation (3)} and the real mixture behaviour of the gas phase (cross virial coefficients) no assumptions are required. But knowledge of the EoS mixture parameters is required and these parameters must be obtained from solubility data. Consequently, another iterative
196 K. Fischer and M. Wilken TABLE 7. Experimental pressure p and mole fraction x of oxygen for (oxygen + methanol) at temperature T T/K 98.34 33.3 348.9 x p/mpa x p/mpa x p/mpa 0.00000 0.0169 0.00000 0.0557 0.00000 0.1511 0.00041 0.1197 0.0009 0.196 0.00045 0.58 0.0007 0.1976 0.00081 0.65 0.00076 0.395 0.00098 0.644 0.0011 0.3455 0.0010 0.393 0.0018 0.3403 0.00138 0.411 0.0013 0.4616 0.00194 0.5046 0.00179 0.5173 0.00163 0.5351 0.00357 0.9113 0.0039 0.8980 0.00311 0.8843 0.0054 1.3680 0.00513 1.3613 0.00479 1.8 0.00989.4517 0.00968.484 0.00936.3578 0.0153 3.7108 0.01476 3.6939 0.01499 3.6791 0.010 5.0358 0.0048 5.0104 0.0055 4.9808 0.0714 6.3933 0.0675 6.3994 0.0648 6.364 0.03353 7.7667 0.0336 7.7863 0.0313 7.678 0.04014 9.1409 0.0408 9.55 0.03839 9.193 TABLE 8. Experimental pressure p and mole fraction x of propanol for (oxygen + propanol) at temperature T T/K 98. 33.56 348. x p/mpa x p/mpa x p/mpa 0.00000 0.008 0.00000 0.015 0.00000 0.0414 0.00073 0.1117 0.0009 0.0535 0.00049 0.1100 0.0019 0.1954 0.0007 0.1151 0.00100 0.1816 0.0017 0.604 0.0011 0.1843 0.00158 0.69 0.006 0.3396 0.00171 0.54 0.0008 0.334 0.00300 0.4499 0.008 0.3361 0.0091 0.4469 0.00601 0.8909 0.00406 0.5887 0.00601 0.878 0.0095 1.3568 0.00671 0.9683 0.0101 1.4417 0.01734.4833 0.01194 1.71 0.0177.431 0.0654 3.7065 0.01884.753 0.0796 3.7316 0.0369 5.0188 0.0714 3.953 0.0405 5.08 0.04843 6.3991 0.03557 5.1 0.05030 6.3848 0.06113 7.8387 0.04341 6.411 0.06316 7.8107 0.07379 9.1978 0.0551 7.8376 0.07663 9.338
Experimental determination of oxygen and nitrogen solvents 197 TABLE 9. Experimental pressure p and mole fraction x of oxygen for (oxygen + octane) at temperature T T/K 98.43 33.9 348.9 x p/mpa x p/mpa x p/mpa 0.00000 0.000 0.00000 0.0069 0.00000 0.0198 0.000 0.1030 0.0006 0.1035 0.00183 0.1049 0.00405 0.188 0.00377 0.1838 0.00341 0.1784 0.00546 0.530 0.00519 0.508 0.00488 0.475 0.0070 0.349 0.00673 0.333 0.00633 0.3151 0.0104 0.480 0.0100 0.4778 0.00961 0.4683 0.0185 0.8570 0.01803 0.8560 0.01066 0.5173 0.0840 1.3159 0.0635 1.495 0.01773 0.8481 0.04985.301 0.04805.8 0.0664 1.668 0.07644 3.5800 0.0741 3.538 0.0473.390 0.10390 4.8984 0.1014 4.8484 0.07317 3.4741 0.13054 6.1951 0.1889 6.09 0.10114 4.8190 0.15897 7.5988 0.15640 7.5643 0.1874 6.1587 0.1869 8.9671 0.18440 8.9633 0.15651 7.50 0.18445 8.906 TABLE 10. Experimental pressure p and mole fraction x of oxygen for (oxygen + toluene) at temperature T T/K 98.41 33.3 348.9 x p/mpa x p/mpa x p/mpa 0.00000 0.0039 0.00000 0.014 0.00000 0.039 0.00101 0.1094 0.00103 0.1117 0.00090 0.1139 0.00177 0.1884 0.00191 0.1961 0.00170 0.1851 0.0044 0.589 0.0063 0.657 0.0047 0.538 0.00318 0.3359 0.00334 0.3337 0.0033 0.330 0.00473 0.4969 0.0050 0.4954 0.00507 0.4868 0.0085 0.8893 0.00916 0.8908 0.00934 0.8679 0.014 1.916 0.01370 1.37 0.01417 1.989 0.033.394 0.0501.3851 0.0604.3539 0.03603 3.6801 0.03895 3.6711 0.0409 3.6155 0.04953 5.0137 0.0546 5.089 0.05538 4.947 0.06373 6.39 0.06875 6.347 0.07081 6.938 0.0785 7.7775 0.08470 7.7304 0.08691 7.6947 0.0967 9.193 0.10156 9.1671 0.108 9.0705
198 K. Fischer and M. Wilken TABLE 11. Experimental pressure p and mole fraction x of oxygen for (oxygen + diethylether) at T = 98.3 K x p/mpa x p/mpa 0.00000 0.0007 0.019 0.599 0.0017 0.089 0.01460 0.7057 0.006 0.156 0.01900 0.95 0.00343 0.1644 0.033 1.130 0.00415 0.1991 0.0538 1.39 0.00533 0.559 0.03153 1.5488 0.00669 0.31 0.03470 1.7096 0.00806 0.3874 0.03851 1.9049 0.00948 0.4565 0.0455.119 0.01093 0.566 TABLE 1. Experimental pressure p and mole fraction x of -methyltetrahydrofuran at T = 311.03 K x p/mpa x p/mpa 0.00000 0.0 0.00743 1.0383 0.00041 0.078 0.01349 1.871 0.00089 0.1435 0.0309 3.009 0.00138 0.107 0.03646 5.0715 0.0019 0.841 0.04985 6.9650 0.0083 0.408 0.06069 8.5140 0.00480 0.6771 0.0645 9.0650 data treatment has to be applied, where in addition to the balance equations the isofugacity criterion is considered: fi l = fi V. (8) There are two important conditions which must be satisfied before applying the second procedure: the EoS model should describe the phase equilibrium and solubility behaviour reliably and especially the liquid volumes. The first condition is proved to be correct for the majority of systems when suitable mixing rules (e.g. G E mixing rules) are used. Of course, the interaction parameters must be fitted, and experimental data covering a considerable concentration or pressure range must be used to fit the two or three G E model parameters for the NRTL, UNIQUAC, or Wilson models introduced in the G E mixing rule. A significance analysis given in Section 3 demonstrates this requirement.
Experimental determination of oxygen and nitrogen solvents 199 TABLE 13. Experimental pressure p and mole fraction x of nitrogen for (nitrogen + ethanol) at temperature T T/K 98.0 348. 398.0 x p/mpa x p/mpa x p/mpa 0.00000 0.0080 0.00000 0.0894 0.00000 0.5000 0.0006 0.0849 0.00038 0.1869 0.00059 0.6195 0.0005 0.163 0.00073 0.740 0.0011 0.7464 0.00075 0.95 0.0013 0.441 0.00190 0.8878 0.00100 0.308 0.0057 0.7413 0.00313 1.1387 0.00145 0.4387 0.00407 1.137 0.0053 1.5845 0.0054 0.7589 0.00754 1.9996 0.00813.1556 0.00390 1.159 0.01 3.1767 0.0170 3.0853 0.00691.0333 0.0178 4.4395 0.01834 4.50 0.015 3.5671 0.093 5.8378 0.0455 5.4741 0.01883 5.4153 0.0835 7.1687 0.031 6.8087 0.0593 7.3565 0.03397 8.5370 0.03771 8.0977 0.03347 9.3637 0.03950 9.8705 0.04364 9.690 TABLE 14. Experimental pressure p and mole fraction x of nitrogen for (nitrogen + propanol) at temperature T T/K 98.34 348.18 398.9 x p/mpa x p/mpa x p/mpa 0.00000 0.009 0.00000 0.0415 0.00000 0.690 0.00045 0.1171 0.00037 0.119 0.00063 0.3737 0.00076 0.1953 0.00074 0.000 0.00118 0.4664 0.00104 0.671 0.00106 0.694 0.00158 0.533 0.00135 0.3445 0.00140 0.341 0.0074 0.744 0.0001 0.5136 0.0015 0.5036 0.0043 0.9865 0.00371 0.9415 0.00419 0.9376 0.00656 1.3530 0.00544 1.3761 0.00630 1.3865 0.01305.396 0.00571 1.4446 0.01148.4816 0.0131 3.674 0.01015.5481 0.01761 3.766 0.0975 4.9305 0.01567 3.9068 0.0441 5.163 0.03984 6.371 0.0087 5.1648 0.03114 6.530 0.04956 7.6988 0.0690 6.6036 0.03811 7.951 0.06040 9.1144 0.034 7.8973 0.04503 9.890 0.0670 9.968 0.03849 9.950
1300 K. Fischer and M. Wilken 10 a 10 b 8 8 p / MPa p / MPa 6 4 0 0 0.00 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.00 0.01 0.0 0.03 0.04 0.05 10.5 c 8 6 4 x p / MPa p / MPa 6 4 d.0 1.5 1.0 x 0.5 0 0.0 0.00 0.01 0.0 0.03 0.04 0.05 0.06 0.07 0.00 0.01 0.0 0.03 0.04 0.05 x x FIGURE 7. Experimental and calculated pressure p and mole fraction of nitrogen or oxygen x for: a, (nitrogen + -methyltetrahydrofuran); b, (nitrogen + ethanol); c, (nitrogen + n-propanol); d, (oxygen + dibutyl ether);, T = 98.15 K;, T = 311.03 K;, T = 348.15 K;, T = 398.15 K;, PSRK. The latter condition (liquid density representation) is known to be poorly obeyed using simple cubic equations of state, but recognizing the importance of this property when solving the volume balance equation (), the Péneloux volume translation can be used to overcome this weakness. Unfortunately, it is not possible to separate the different contributions for the various effects described in the first procedure, so that the EoS flash procedure (b) remains difficult. This is the reason why we have extensively studied the resulting solubility data in order to verify procedure (b). The iterative treatment of the raw data by procedure (b) is applied to
Experimental determination of oxygen and nitrogen solvents 1301 10 a 10 b 8 8 p / MPa 6 4 p / MPa 6 4 0 0.00 0.01 0.0 0.03 0.04 0.05 x 0 0.00 0.04 0.08 0.1 0.16 0.0 x 10 c 10 d 8 8 p / MPa 6 4 p / MPa 6 4 0 0.00 0.0 0.04 0.06 0.08 0.10 x 0 0.00 0.0 0.04 0.06 0.08 0.10 0.1 x FIGURE 8. Experimental and calculated pressure p and mole fraction x for: a, (oxygen + methanol); b, (oxygen + n-octane); c, (oxygen + n-propanol); d, (oxygen + toluene};, T = 98.15 K;, T = 33.15 K;, T = 348.15 K;, PSRK. all the data points together, which allows the use of the implied information on the mixture behavior. The flow diagrams of both data treatment procedures are shown in figures, 3, and 4..4. PARTIAL MOLAR VOLUMES OF GASES DISSOLVED IN LIQUIDS It is important that the liquid phase volume increases significantly when the gas solubility is high. Therefore, the partial molar volumes of these gases must be considered for the data treatment in procedure (a). Fortunately, there are reliable methods for estimating the partial molar volumes (11 14) from the critical data T c and p c of the gases and the internal pressure
130 K. Fischer and M. Wilken 1 0.9 0.8 0.7 0.6 F (rel) 0.5 0.4 0.3 0. 0.1 0 0 4 6 8 10 p / MPa FIGURE 9. Significance of pressure for the regression of PSRK interaction parameters fitted to solubility data of oxygen (1) in n-propanol ():, F (rel) for a 1 ;, F (rel) for a 1 ; F (rel) for a 1 and a 1 normalized by the value of F (rel) for a 1 at the pressure limit of 10 MPa. p in of the solvents defined by: or: p in = ( U/ V ) T = T ( p/ T ) V p, (9) p in = (T α P /β T ) p, (10) where β T is the isothermal compressibily coefficient, and α p is the isobaric thermal expansion. Handa et al. (1) proposed the following expression for estimating the partial molar volumes with a ±10 per cent accuracy: v 1 p 1,c /(RT 1,c ) = 0.088 +.763 T p 1,c /(T 1,c p,in ). (11) The use of specific parameters A and B for the different gases permits an increase in accuracy to about ±1 per cent (Cibulka and Heintz, 1995). (13,14) v 1 p 1,c /(R T 1,c ) = A + B T p 1,c /(T 1,c p,in ), T < T,c. (1) The parameters for oxygen and nitrogen are given in table. The partial molar volume of a gas usually decreases when the size of the solvent molecule of a certain class of substances (e.g. alcohols) increases. It increases by about 0.3 cm 3 mol 1 K 1 with temperature, as Walkley and Jenkins (1968) (15) found. This effect is caused by the solvent properties (internal pressure). The values used for the data treatment are listed in tables 3 and 4. When the first procedure is used in the data treatment, neglecting the partial molar volume of the gas leads to a significant error in the volume balance. The reason for this
Experimental determination of oxygen and nitrogen solvents 1303 TABLE 15. New PSRK group interaction parameters n m a nm /K b nm a mn /K b mn CH O 19.68 1.819 104.8 1.191 ACH O 85.6 0.0000 0.6989 0.0000 ACH O 130.37 63.33 384.98.1163 OH O 018.6 0.0000 38.59 0.0000 CH 3 OH O 1061.4 1.561 516.85 1.1696 CH O O 147.51 0.0000 1986.8 0.0000 OH N 589.0.6810 836.9 5.997 CH O N 3191.3 0.0000 66.63 0.0000 is that the vapour volume is assumed to be larger than it actually is. Thus, the amount of gas calculated for the gas phase will be too high, and the solubility in the liquid solvent too small. Furthermore, the compressibility of the solvent must be considered in order to obtain an accurate value for the liquid volume. It is important to take into account all the different effects having an influence on the liquid volume, as can be judged from figures 5 to 6, where the resulting solubility data (with and without consideration of the effects of the liquid volume) are plotted. When these results are compared with those obtained by the second procedure, a good agreement is observed. This makes the second procedure a very attractive alternative for obtaining reliable solubility data, because the effects mentioned above are automatically part of the equation of state model used for the isochoric flash calculation. Its reliability is demonstrated in table 5 for the examples of oxygen and nitrogen solubility in ethanol and n-octane. From figures 5 to 6 it can also be seen that both procedures provide almost the same results for the solubility data when they are applied correctly. The experimental data listed in tables 7 to 14 and plotted in figures 7 and 8 were obtained with the help of the second procedure..5. EXPERIMENTAL RESULTS In table 6 the Henry coefficients and their deviations for both procedures are presented. It can be seen that the results are almost identical, because at low pressure the solubility is small and thus the partial molar volume is not significant. In figures 7 and 8 the experimental and predicted (p, x) data are shown for all investigated system at pressures up to 10 MPa and over the temperature range between 98 K and 398 K. Three isothermal data sets for each system were measured. For (oxygen + n-octane) it can be seen that the solubility is nearly identical at different temperatures because the experimental solubility data are close to the maximum of the Henry coefficient at T = 35 K, as shown in figure 10(c). In tables 7 to 14 the experimental (p, x) data for the solubility of the gases in the organic solvents are listed.
1304 K. Fischer and M. Wilken H 1 / MPa H 1 / MPa 350 170 a 160 b 300 50 150 140 130 00 10 110 150 100 100 90 80 50 00 50 300 350 400 70 00 50 300 350 400 H 1 / MPa H 1 / MPa 55 140 c 50 130 10 45 110 40 100 35 90 d 30 80 5 70 00 50 300 350 400 00 50 300 350 400 FIGURE 10. Experimental and calculated Henry coefficients H 1 against temperature T for: a, (oxygen + methanol}; b, (oxygen + n-propanol); c, (oxygen + n-octane); d, (oxygen + toluene); experimental:, this work; +, literature data from DDB;, PSRK. 3. Fitting of the PSRK group interaction parameters The details of the optimization procedure for the interaction parameters are available elsewhere. (1 3) Temperature-dependent interaction parameters b i j are introduced in the UNIFAC expression ψ i j = exp{(a i j + b i j T )/T }. (13) The new PSRK group interaction parameters are listed in table 15.
Experimental determination of oxygen and nitrogen solvents 1305 50 45 a 160 150 140 b H 1 / MPa 40 35 H 1 / MPa 130 10 110 30 00 50 300 100 350 400 00 50 300 350 400 H 1 / MPa 340 340 30 c 300 80 60 40 0 00 H 1 / MPa 60 40 0 00 180 160 d 180 00 50 300 140 350 400 00 50 300 350 400 FIGURE 11. Experimental and calculated Henry coefficients H 1 against temperature T for: a, (oxygen + dibutylether); b, (nitrogen + -methyltetrahydrofuran); c, (nitrogen + ethanol}; d, (nitrogen+n-propanol}; experimental:, this work; +, literature data from DDB;, PSRK. The gradient F of the objective function F with respect to the interaction parameters a i j, F = (df/da i j ), contains information on the significance of these parameters for the correlation of experimental data. As an example, the solubility data of (oxygen + 1- propanol) were used in the following procedure: for given starting values of the interaction parameters the gradient of the objective function with respect to these parameters was calculated. This was repeated while the experimental database used in the fit was limited to different pressure values. The relative gradients of F (rel) with respect to a 1 and a 1, normalized by the value of F (rel) for a 1 at the pressure limit of 10 MPa, are plotted against this pressure limit. Figure 9 shows that for fitting reliable interaction parameters,
1306 K. Fischer and M. Wilken H 1 / MPa 160 150 140 130 10 110 100 90 80 70 60 00 50 300 a H 1 / MPa 95 b 90 85 80 75 70 350 400 00 50 300 350 400 170 100 c 160 90 150 d H 1 / MPa 140 130 H 1 / MPa 80 10 70 110 100 50 300 350 60 400 180 30 80 330 380 FIGURE 1. Experimental and calculated Henry coefficients H 1 against temperature T for: a, (nitrogen + benzene}; b, (oxygen + ethylbenzene}; c, (nitrogen + n-heptanol}; d, (nitrogen + diethyl ether); +, experimental literature data from DDB;, PSRK. solubility data up to ( to 4) MPa are required. If only solubility data at atmospheric pressure are used, the significance of the parameters is not guaranteed, because two parameters are used to represent one property, the Henry coefficient. The significance for the 1-propanol oxygen parameter (a 1 ) is lower than for the oxygen 1-propanol parameter (a 1 ), because of the limited mole fraction range (about 0.1) of (oxygen + n-propanol). To check the reliability of the PSRK method for this application, experimental values for Henry coefficients (from this work and literature data from DDB) are compared with the calculated results in figure 10 to 13. All these examples demonstrate the reliability of PSRK.
Experimental determination of oxygen and nitrogen solvents 1307 H 1 / MPa 95 50 a 90 85 H 1 / MPa 45 40 35 b 80 75 30 5 0 300 35 350 375 00 50 300 350 400 60 50 c 80 70 60 d H 1 / MPa 40 H 1 / MPa 50 30 40 30 0 0 00 50 300 350 400 00 50 300 350 400 FIGURE 13. Experimental and calculated Henry coefficients for: a, (oxygen + n-octanol); b, (oxygen +,, 4-trimethylpentane); c, (oxygen + n-hexane}; d, (oxygen + n-decane); +, experimental literature data from DDB;, PSRK. 4. Conclusion The present study was carried out in order to extend the applicability of PSRK for the prediction of air solubility in organic substances and their mixtures. The solubility of gases up to 10 MPa in the temperature range between 98 K and 398 K was measured with a static synthetic apparatus. To obtain the desired (p, x) data from the raw data two different methods were used and compared with each other. Both methods gave reliable and almost identical results. PSRK now enables the prediction of oxygen and nitrogen solubilities in organic solvents with the newly fitted interaction parameters. These solubilities find an important application in the field of storage and transportation of organic liquids where,
1308 K. Fischer and M. Wilken for example, the oxygen solubility can be decisive for the purity or stability of products, or the pressure changes with temperature in closed containers must be known. The authors thank the Bundesministerium für Wirtschaft for financial support via Arbeitsgemeinschaft industrieller Forschungsvereinigungen (AiF project 10931N). REFERENCES 1. Holderbaum, T.; Gmehling, J. Fluid Phase Equilib. 1991, 70, 51 65.. Fischer, K.; Gmehling, J. Fluid Phase Equilib. 1996, 11, 185 06. 3. Gmehling, J.; Li, J.; Fischer, K. Fluid Phase Equilib. 1997, 141, 113 17. 4. Horstmann, S.; Fischer, K.; Gmehling, J. Fluid Phase Equilib. 000, 167, 173 186. 5. Horstmann, S. Ph.D. Thesis, University of Oldenburg. 000. 6. Guilbot, P.; Théveneau, P.; Baba-ahmed, A.; Horstmann, S.; Fischer, K.; Richon, D. Fluid Phase Equilib. 000, 170, 193 0. 7. Li, J.; Fischer, K.; Gmehling, J. Fluid Phase Equilib. 1998, 143, 71 8. 8. Horstmann, S.; Fischer, K.; Gmehling, J. J. Chem. Thermodynamics 000, 3, 451 464, doi:10.1006 jcht.000.0611. 9. Fischer, K.; Gmehling, J. J. Chem. Eng. Data 1994, 39, 309 314. 10. Daubert, T. E.; Danner, R. R. Physical and Thermodynamic Properties of Pure Chemicals. Taylor & Francis: Washington D.C. 1989. 11. Handa, Y. P.; Benson, G. C. Fluid Phase Equilib. 198, 8, 161 180. 1. Handa, Y. P.; D Arcy, P. J.; Benson, G. C. Fluid Phase Equilib. 198, 8, 181 196. 13. Cibulka, I.; Heintz, A. Fluid Phase Equilib. 1995, 107, 35 55. 14. Izák, P.; Cibulka, I.; Heintz, A. Fluid Phase Equilib. 1995, 109, 7 34. 15. Walkley, J.; Jenkins, W. I. Trans. Faraday Soc. 1968, 64, 19. WA 00/039 (Received 7 July 000; in final form 4 January 001)