. 1049-1055 Ind. Eng. Chem. Process Des. D ~ v1985,24, Ledakowicz, S.; Nettelhoff, H.; Deckwer, W.-0. Ind. Eng. Chem. Fundam. 1984, 23, 510. Nettelhoff, H. Ph.D. Dissertation, Universltat Oldenburg, Oldenburg, Federal Republic of Germany, 1985. Nettelhoff, H.; Kokuun, R.; Ledakowicz, S.; Deckwer, W.-D. Chem . - I S . Tech. 1904, 56, 638. Newsome. D. S . Catal. Rev.-Sci. Eng. 1980, 21, 275. Peter, S.; Weinert, M. 2.Phys. Chem. (frankfurt am Main) 1955, 5 , 114. Pichler, H.; Schulz, H. Chem . - I S . - T e c h . 1970, 42, 1162. Rofer-DePoorter, C. K. Chem. Rev. 1901, 8 1 , 447. Satterfield, C. N.; Huff, G. A. Chem. Eng. Sci. 1980, 35, 195.
1049
Satterfield, C. N.; Huff, G. A. Can. J . Chem. Eng. 1982, 6 0 , 159. Sudheimer, G.; Gaube, J. Chem.-Ing.-Tech. 1983, 55, 644. Thompson, G. H.; Riekena, M. L.; Vickers, A. G., Final Report, DOE Contract DE-AC01-78 ET 10159, 1981 (UOP Inc. and System Development Corp.). Thomson, W. J.; Arndt, J. M.; Wright, K. L. Prepr. Fuel Chem. Div., Am. Chem. SOC. 1980, 25, 101.
Received for review April 16, 1984 Revised manuscript received December 17, 1984 Accepted January 21, 1985
Equilibrium Vaporization of a Coal Liquid from a Kentucky No. 9 Coal Ho-Mu Lln, Hwayong Kim, Tianmln Guo,+ and Kwang-Chu Chao' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
Vapor-liquid equilibrium (VLE) has been experimentally determined for a coal liquid obtained from a Kentucky No. 9 coal at the Wilsonville plant of Catalytic, Inc. The measurements, including VLE of the coal liquid in mixtures with hydrogen, were performed at temperatures up to 7 10 K and pressures to 25 MPa. Inspections are reported for the normal bolllng point, molecular weight, and specific gravity of the vaporized overhead and bottom fractions as well as for the true boiling point (TBP) fractions of the total coal liquid. Experimental data are correlated with several equations of state.
Knowledge of vapor-liquid equilibrium (VLE) of coal liquid by itself and in mixture with hydrogen is needed in the technology of fuels and oils. Experimental measurements of VLE of mixtures of hydrogen and model compounds have been reported by Simnick, Sebastian, Lin, Kim, and co-workers. The literature sources are summed up in Sebastian et al. (1981a-c) and Radosz et al. (1982). These data have been used to develop and test correlation methods (El-Twaty and Prausnitz, 1980; Sebastian et al., 1981a-c; Wilson et al., 1981; Radosz et al., 1982; Watanasiri et al., 1982; Gray et al., 1983). Experimental VLE data on coal liquids are scarce and limited to reports by Henry (1980), Lin et al. (1981), Sung (1981), and Wilson et al. (1981). We report here experimental results of VLE for a coal liquid and its mixtures with compressed hydrogen a t elevated temperatures. The coal liquid studied in this work was supplied by Catalytic, Inc., from processing of a Kentucky No. 9 Fies mine coal a t the Advanced Coal Liquefaction R&D Facility in Wilsonville, AL. The process is a combination of three units: (1) a solvent-refined coal (SRC) unit in which a slurry of coal and recycled solvent is reacted with hydrogen at elevated temperature and pressure; (2) a critical solvent deashing unit; and (3) an H-oil ebulated bed hydrotreater to raise the hydrogen content of the oil. The coal liquid was labeled sample No. 74-534 from run No. 234. A detailed description of the process, operating conditions, and the physical properties of this oil was reported by Lewis (1981). The VLE measurements were made in a flow apparatus with sapphire windows for visual observation of the liquid level. All condensate samples from cell effluents were collected and inspected for the boiling point, molecular weight, and density. The coal liquid was fractionated by Graduate Division, East China Institute of Petroleum Technology, Beijing, China. 0 196-430518511124-1049$01.50/0
distillation under vacuum and the resulting fractions were inspected. The experimental VLE data are correlated with the Cubic Chain-of-Rotators (CCOR) equation of state (Kim et al., 1983), the Grayson-Streed correlation (1963), the Soave equation (1972), and the modified Soave equation of Radosz et al. (1982). Experimental Section A flow apparatus was used in this work to measure VLE while minimizing thermal decomposition of the coal liquid at high temperature. The heart of the apparatus is a new equilibrium cell equipped with transparent sapphire windows to permit visual observation of the liquid level in the cell. The old cell described by Simnick and co-workers (1977)which was used extensively in this laboratory proved useless for coal liquids. Detection of the liquid level in the old cell was by means of an electric capacitor which did not function for coal liquids because of their high electric conductivity a t the higher temperatures of interest. The new cell and apparatus have been described by Lin and co-workers (1985). The residence time of the coal liquid in the equilibrium cell depends on the volume of liquid maintained in the cell and on the flow rate. At normal operating conditions, there is a holdup of about 5 mL of liquid in the cell. The normal flow rate of the liquid feed is 500-1000 mL/h, giving a plug flow residence time of approximately 18-36 s. Condensates from the cell effluents were collected for inspection of the boiling point (Tb), molecular weight (MW), and density ( p ) at 298.2 K by procedures that are commonly used for heavy petroleum fractions. Normal boiling point was determined by simulated distillation on a Varian 3700 gas chromatograph with a flame ionization detector. The calibration was prepared from 50 model coal liquid compounds, and the Tb of an oil fraction was calculated as the area average from the gas chromatograph. A Mechrolab 301A vapor pressure osmometer was used to 0 1985 American Chemical Society
1050
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table I. Inspection of 14 TBP Cuts of Coal Liquid ( T b= 564 K, p = 0.9793, MW = 214) cut w t % distilled Tb, K p (298.2 K), g/mL MW 1 2.91 470 0.8709 2 3.12 487 0.9015 3 3.81 505 0.9082 167 4 5.29 524 0.9190 5 5.54 543 0.9292 190 6 5.19 559 0.9423 7 5.80 566 0.9546 198 8 5.30 586 0.9616 9 6.03 600 0.9736 207 10 6.63 608 0.9839 11 3.58 621 0.9894 12 3.83 0.9924 623 13 6.31 652 0.9992 239 residue 36.66 674 1.0334 278 Table 11. Inspection of 28 TBP Cuts of Coal 564 K. D = 0.9793. MW = 214) p (298.2 cut w t % distilled Tb, K K), g/mL 1 0.91 443 0.8494 2 1.47 469 0.8672 3 1.03 478 0.8892 4 1.82 486 0.9018 5 1.69 0.9019 494 6 2.02 0.9076 501 7 2.50 508 0.9123 8 1.23 514 0.9155 9 1.72 520 0.9193 10 2.34 0.9224 524 2.47 11 532 0.9270 12 2.77 54 1 0.9336 13 547 2.70 0.9412 2.45 14 554 0.9457 15 3.60 0.9548 562 16 571 3.65 0.9592 17 579 2.70 0.9644 0.9725 18 588 3.60 19 596 3.33 0.9772 20 2.55 0.9817 603 21 610 3.56 0.9842 22 619 3.56 0.9874 23 626 2.80 0.9903 24 633 2.82 0.9936 25 639 2.31 0.9986 26 644 2.06 1.0034 27 1.0054 650 3.98 residue 32.36 672 1.0371
C
C
C
a
=. c Q
Liquid (Tb= 0
MW
OH %
130 142 150 155 161 168 173 177 181 184 188 191 194 196 199 202 205 208 212 215 219 224 228 234 239 242 247 285
1.01 1.58 1.22 0.95 0.51 0.42 0.67 0.76 0.25 0.38 0.35 0.26 0.39 0.38 0.39 0.71 0.31 0.33 0.36 0.43 0.40
0
0
1
10
20
30
50
40
GO
70
80
90
W t % Vaporizotlon
Figure 1. VLE of the coal liquid.
0'9
i
0
Interpolated f r o m Experimental Data
P
07
0.89 0.73 0.44 1.17
determine the molecular weight to an estimated accuracy of f3 % . The density was measured at 298.2 K with three glass pycnometers of 2; 5; and 10-cm3capacity, respectively. The pycnometers were calibrated with deionized distilled water. The same procedures were employed for the inspection of the true boiling point (TBP) fractions of the feed coal liquid. Hydrogen gas used in this work was purchased from Airco with a minimum purity of 99.95%. Results Two TBP distillations were made of the total coal liquid. Table I shows inspections of the 14 cuts obtained from one distillation, and Table I1 shows the 28 cuts from the other distillation. The number of cuts was varied in order to reveal possible effects on the correlation of the VLE results. Inspections of the total coal liquid are included in both tables. Information on the content of hydroxyl groups in the coal liquid fractions is of potential interest for the interpretation of the VLE results. Table I1 presents this information in terms of weight percent of the oxygen content of the hydroxyl groups determined by the acetylation method of Blom et al. (1957).
O.'t 0 1
640
660
680
700
720
T. K
Figure 2. Phase diagram of the coal liquid.
Table I11 presents VLE data of the coal liquid by itself, and Table IV presents VLE data of mixtures of the coal liquid and hydrogen. At least two samples were taken from the overhead and bottom streams each at any one condition of temperature, pressure, and flow. The reported weight percent vaporization and concentrations of hydrogen represent mean values of the multiple samples. Figure 1 shows the data of Table I11 with pressure as a function of weight percent vaporization at various temperatures for the VLE of the coal liquid itself. Figure 2 shows the phase diagram of the coal liquid that is obtained by interpolation of Figure 1. Figures 3 and 4 show the mole fractions of hydrogen in the VLE bottom and overhead streams, respectively, that are obtained from the values of grams of hydrogen per gram of oil reported in Table IV.
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table 111. Equilibrium Vaporization of Coal Liquid T,K P, MPa w t % vaporized id. no. 656.9
0.342
37.5
656.8
0.414
21.4
672.8
0.252
73.3
672.7
0.289
62.0
673.1
0.348
48.3
673.1
0.407
34.0
673.1
0.435
29.3
698.6
0.357
82.6
698.9
0.506
53.7
698.9
0.514
52.3
698.5
0.590
39.1
698.5
0.680
22.8
710.8
0.480
75.1
711.0
0.541
63.1
710.8
0.617
51.2
710.2
0.733
29.6
phase
Tb,K
vav
549 583 542 583 588
p(298.2
571 623 564 615 564 603 558 603 556 603 543 579 100
-
K), g/mL
MW
0.9475 0.9972 0.9416 0.9912 0.9647 1.0186 0.9608 1.0128 0.9560 1.0066 0.9506 1.0012 0.9467 0.9934 0.9706 1.0169 0.9601 1.0095 0.9572 1.0016 0.9516 0.9955 0.9464 0.9912 0.9700 1.0154 0.9630 1.0085 0.9587 1.0007 0.9520 0.9948
646 577 637 566 630 562 616 594 642 582 637
0.4-
1051
545K
~
188 236 179 209 210 261 192 239 204 250 199 242 185 220 213 255 209 253 209 247 192 232 199 233 203 257 199 235 200 235 181 208
=
0 951
c
O l 10
15
20
0.801
25
10
Figure 3. Solubility of hydrogen in coal liquid.
Correlation of the Data Correlation of the VLE data requires, first of all, the molecular weights of the fractions in order to make the conversion into mole fractions. We, therefore, start by examining the existing molecular weight correlations. Figure 5 shows a comparison of the Kesler-Lee correlation (1976) and the Riazi-Daubert correlation (1980) with the molecular weight of the TBP cuts of this work. Both correlations express molecular weight as a function of normal boiling point and specific gravity and were developed for petroleum fractions. The Kesler-Lee correlation appears to give consistently high values for the TBP cuts of this work. The Riazi-Daubed correlation appears to be in good agreement with data for TBP cuts in the 570-670 K boiling range but tends to be low in other
15
20
I
25
P , MPo
P. MPo
Figure 4. Mole fraction of hydrogen in saturated vapor of hydrogen coal liquid.
+
boiling ranges. The comparison indicates that experimental molecular weight is needed for the TBP cuts of a coal liquid for the purposes of correlations until such a time when a valid molecular weight correlation becomes available for coal liquids. Experimental molecular weights are used in the calculations described below. The critical temperature T,,critical pressure p c , and acentric factor o are needed for the TBP cuts in equation of state correlations of the VLE. Three methods for the estimation of these properties were tested in this work: Kesler-Lee (1976), Wilson et al. (1981)) and Lin-Chao (1984). The Kesler-Lee method was developed for petroleum fractions and that of Wilson et al. for coal liquids. Both require only Tb and p , whereas the Lin-Chao cor-
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
1052
Table IV. VLE of Coal Liquid
+ Hydrogen ~~~~~
id. no. 1
p, MPa 10.19
wt % vaporized
545.4
8.8
equilib phase V
2
545.6
15.27
12.1
V
3
545.6
20.33
5.7
4
545.5
25.37
4.3
5
625.0
24.2
V L V L V
6
625.0
14.96
34.6
V
7
624.8
20.31
16.6
8
625.4
25.61
14.6
9
704.3
10.37
17.1
10
704.6
15.51
30.6
11
704.5
20.61
36.5
V L V L V L V L V L
T,K
concn of H g(H2)/g(coalliquid)
L
9.991
L L
Tb,K
mol fract 0.9913 0.0979 0.9934 0.1435 0.9943 0.1761 0.9954 0.2173 0.9706 0.1203 0.9783 0.1672 0.9799 0.2180 0.9812 0.2758 0.8906 0.1471 0.9336 0.2166 0.9482 0.2786
509 586 506 577 497 573 494 575 511 584 551 596 522 571 521 564 529 565 550 579 553 577
~(298.2K), g/mL 0.9262 0.9850 0.9309 0.9865 0.9278 0.9850 0.9249 0.9845 0.9416 0.9922 0.9469 0.9974 0.9391 0.9908 0.9385 0.9860 0.9480 0.9889 0.9526 0.9926 0.9543 0.9927
MW 188 209 190 210 191 210 188 216 190 211 191 210 189 213 195 226 189 211 190 220 197 228
0 9-
0 8-
0
Interpolated from Experimental Data
0
Expt.(l4 T B P C u t s )
n
Expt.(24 TBPCuts) Calc
_ _ ,-
0
0 7-
0 /
--COR
P
Eq
0 6-
/
2 z a
050 40 3-
0 2-
,
0
150 500
,,
0 11
550
GOO Tb,
650
700
K
0 1 640
660
680
700
720
T,K
Figure 5. Molecular weight of TBP cuts of coal liquid-compared with correlations.
Figure 6. Comparison of the CCOR calculated result with experimental VLE data of the coal liquid.
relation additionally requires MW. For the purpose of comparing the three correlations of T,, p,, and w , VLE calculations of the coal liquid were made with the three correlations in the Cubic Chain-ofRotators equation of state (Kim et al., 1983). The calculated results are compared in Table V with the experimental data. The calculations search for the temperature that produces the experimentally observed weight percent vaporization at the experimental pressure. The calculated temperature is compared in the table with the experimental value. With the coal liquid represented a~ 28 TBP cuts, the comparison shows that the T,, pe,and w estimated by the Lin-Chao correlation give the best results in vaporization calculations. The maximum deviation of the calculated temperature from the experimental is 6.2 K; the average absolute deviation of 0.45% amounts to about 3.1 K. The table also shows that the calculated results with the coal liquid represented as 14 cuts are only slightly worse than those obtained with 28 cuts. With T,, pe, and w calculated from the Lin-Chao correlation, Table VI compares the VLE data with the calculated resulb from the Grayson-Streed (GS)correlation, the Soave equation of state, and the modified Soave
equation (M-Soave)with conformal mixing rules by Radosz et al. The coal liquid is represented as 28 cuts in the calculations. All three methods appear to give a reasonable representation of the vaporization of the coal liquid when the Lin-Chao correlation for T,, po and w is used. Figure 6 shows the good agreement of the CCOR calculated result with experimental data. The data are substantially different from those calculated from a previous petroleumbased correlation (Edmister, 1961) as shown in Figure 7. The comparison indicates that the Edmister correlation should not be used for coal liquids. On the basis of the CCOR equation, the phase diagram for this coal liquid was constructed and is shown in Figure 8. In all the CCOR, Soave, and M-Soave calculations of Table VI in the absence of hydrogen, the interaction constants are treated as zero. The calculations are, therefore, entirely of a predictive nature. No adjustment is made of the equations by making use of the experimental VLE data. For vaporization calculations of coal liquid in mixtures with hydrogen, non-zero values are required for hydrogen interaction constants ke and kbi,in the CCOR equation. Correlations for the hydrogen interaction constants are
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table V. Calculated VLE Using Various Correlations of T., pe,and w in CCOR Equation CCOR equation calculations exptl Lin-Chao Lin-Chao Wilson et al., (14 cuts) (28 cuts) (28 cuts) wt% T, K T, K (calcd) dev % T,K (calcd) dev % T, K (calcd) dev % p, MPa id. no. vaporized 658.9 0.30 661.9 0.76 665.7 1.34 656.9 0.342 37.5 1 660.6 0.57 662.2 0.82 656.8 667.2 1.58 0.414 21.4 2 -1.75 -0.92 661.0 -0.39 666.6 672.8 670.2 73.3 3 0.252 662.3 -1.55 668.2 -0.67 671.6 -0.16 672.7 0.289 62.0 4 667.1 -0.89 0.16 670.9 -0.32 673.1 674.2 48.3 5 0.348 671.2 -0.28 668.1 -0.75 674.6 0.22 673.1 0.407 34.0 6 669.9 -0.47 672.3 -0.12 676.2 0.46 7 0.435 29.3 673.1 686.7 -1.70 692.3 -0.90 695.9 -0.39 82.6 698.6 8 0.357 695.8 -0.44 0.40 699.6 0.10 698.9 702.7 53.7 9 0.506 696.2 -0.39 0.59 699.8 0.13 698.9 703.0 10 0.514 52.3 0.45 698.8 0.05 0.90 701.7 11 0.590 39.1 698.5 704.8 0.23 0.48 700.1 698.5 705.3 0.97 701.9 12 0.680 22.8 702.8 -1.13 707.6 -0.45 710.9 0.01 13 0.480 75.1 710.8 705.4 -0.79 709.5 -0.21 712.6 0.23 63.1 711.0 14 0.541 710.8 -0.26 712.3 0.21 15 0.617 51.2 710.8 715.3 0.64 0.03 715.6 0.76 712.5 0.33 710.2 29.6 710.2 16 0.733 AAD, % O 0.57 0.45 0.71 ~~~~
a
1053
Kesler-Lee (28 cuts) T, K (calcd) dev % 656.5 -0.06 656.8 0.00 661.0 -1.75 661.5 -1.67 665.2 -1.18 665.0 -1.20 666.5 -0.99 685.6 -1.87 692.6 -0.89 692.9 -0.86 694.7 -0.55 694.9 -0.51 700.2 -1.49 702.1 -1.25 704.8 -0.84 -0.72 705.1 0.99
Average absolute deviation.
Table VI. Calculated VLE of the Coal Liauid by Itself Using Various Equations wt%
id. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 AAD, %
vaporized (exptl) 37.5 21.4 73.3 62.0 48.3 34.0 29.3 82.6 53.7 52.3 39.1 22.8 75.1 63.1 51.2 29.6
P, MPa 0.342 0.414 0.252 0.289 0.348 0.407 0.435 0.357 0.506 0.514 0.590 0.680 0.480 0.541 0.617 0.733
(exptl) 656.9 656.8 672.8 672.7 673.1 673.1 673.1 698.6 698.9 698.9 698.5 698.5 710.8 711.0 710.8 710.2
Table VII. Calculated VLE of Coal Liquid wt%
id. no. 1 2 3 4 5 6 7 8 9 10 11 AAD, % a
D. MPa .,
10.19 15.27 20.33 25.37 9.99 14.96 20.31 25.61 10.37 15.51 20.61
vaporized (. e .x d, 8.8 12.1 5.7 4.3 24.2 34.6 16.6 14.6 17.1 30.6 36.5
CCOR
T, K
exDtl 545.4 545.6 545.6 545.5 625.0 625.0 624.8 625.4 704.3 704.6 704.5
M-Soave
G-S
Soave
T, K (calcd) dev % T,K (calcd) dev % T, K (calcd) dev % T,K (calcd) dev % 661.9 662.2 666.6 668.2 670.9 671.2 672.3 692.3 699.6 699.8 701.7 701.9 707.6 709.5 712.3 712.5
0.76 0.82 -0.92 -0.67 -0.32 -0.28 -0.12 -0.90 0.10 0.13 0.45 0.48 -0.45 -0.21 0.21 0.33 0.45
663.1 661.5 669.8 671.0 672.9 671.8 672.4 695.9 701.9 702.1 702.7 701.0 711.2 712.6 714.5 712.5
0.94 0.72 -0.45 -0.25 -0.03 -0.19 -0.11 -0.38 0.44 0.46 0.60 0.35 0.06 0.22 0.53 0.32 0.38
663.0 662.0 669.1 670.4 672.6 671.9 672.6 695.2 701.6 701.8 702.7 701.4 710.6 712.1 714.3 712.8
0.93 0.79 -0.56 -0.34 -0.07 -0.18 -0.07 -0.49 0.39 0.42 0.60 0.41 -0.03 0.16 0.49 0.36 0.39
666.4 664.8 673.2 673.3 676.1 674.6 675.5 698.7 704.4 704.6 705.1 703.3 713.4 714.7 716.6 714.5
1.45 1.21 0.06 0.09 0.45 0.22 0.35 0.01 0.79 0.81 0.94 0.68 0.37 0.52 0.81 0.61 0.59
+ Hydrogen Using CCOR Equation to Compare 28 and 14 Cuts" temperature, 28 cuts calcd dev % 537.4 -1.46 545.6 0.0 0.14 544.8 -0.17 544.5 1.00 618.8 0.92 630.7 0.72 629.3 1.47 634.6 -0.99 697.3 -1.19 696.2 0.00 704.5 0.73
K 14 cuts calcd dev % 548.3 0.54 556.3 1.96 1.88 555.9 1.84 555.5 0.37 627.3 2.15 638.5 2.12 638.1 2.81 643.0 0.10 705.3 -0.10 703.9 1.03 711.8 1.35
exDtl 10.12 6.90 5.65 4.58 8.07 5.85 4.49 3.56 6.05 4.31 3.40
hydrogen K Val 28 cuts 14 cuts calcd dev % calcd dev % 9.03 -10.76 9.98 -1.40 6.40 -7.23 7.05 2.21 5.17 -8.59 5.66 0.08 -3.02 4.44 4.84 5.73 7.77 -3.70 8.61 6.66 5.50 -6.02 6.07 3.72 4.39 -2.21 4.82 7.28 5.40 4.10 15.07 3.75 5.48 -9.42 6.12 1.23 4.22 -2.02 4.68 2.51 1.11 3.79 11.37 3.44 5.41 5.75
T,,p o and w of coal liquid fractions were calculated by Lin-Chao correlations.
developed by analyzing experimental binary mixture data (see Radosz et al., 1982, for sources). The results are as follows k,, = 0.408 + 2.4 X 10-4Tcj kbij =
0.225
+ 3.5 X 10-2(RT,j/pcj)
(')
(2)
where subscript i here denotes hydrogen and j the solvent. The units are kelvin for T,, and kilopascal for p , with R
= 8.3143 (kF'a.m3)/(kmo1.K). Calculations of vaporization of coal liquid in hydrogen mixtures based on these correlations are again predictive. The equation is not adjusted in any way by making use of the experimental equilibrium data on coal liquids. Table VI1 presents the calculated vaporization of coal liquid in mixtures with hydrogen from the CCOR equation. The calculations match the experimental weight percent vaporization of coal liquid a t the experimental pressure
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
1054
" 31
-
Focal Point
Calculated Dy Edmitter's Method
Critical P o i n t k
Interpolated from Experimental Data
t
a 50% A 70%
L
se 0.1 400
450
500
550
600
650
a5
700 750 eo0 e50
T, K Figure 7. Comparison of the calculated result from the Edmister's method with experimental VLE data of coal liquid.
B
3 se 5 a
"1
I
4
W t Fraction Vaporized:
B
3 se 5 p: a
8 u
0.2
600
se
I
, 625
650
675
700
725
750
775
800
>
825
T, K Figure 8. CCOR equation calculated phase diagram of the coal liquid.
and the ratio of hydrogen to coal liquid in the total feed. The calculated temperature is compared with the experimental value, and the percent deviation of the absolute temperature is reported. At each experimental condition, two calculations are made in which the coal liquid is represented either as 28 TBP cuts or 14 cuts. The Lin-Chao correlation is used for the estimation of T,, p c , and o of the cuts. The 28-cuts calculations show a maximum deviation of 9.2 K and an average deviation of 0.73% or about 4.6 K. The calculations with 14 cuts show larger deviations in temperatures, the average of 1.35% corresponding to about 8.4 K. The results indicate that significantly improved agreement with data is obtained by representing the coal liquid with narrower TBP cuts in calculations for the coal liquid + hydrogen mixtures. Table VI1 also shows the K values of hydrogen calculated at the searched temperature. This calculation is essentially for the solubility of hydrogen. The calculated results with 14 and 28 cuts are comparable. Calculations with the Grayson-Streed, the Soave, and the M-Soave for the hydrogen + coal liquid mixtures are compared with experimental data in Table VIII. Coal liquid is represented as 28 cuts for which T,,po and w are estimated with the Lin-Chao correlation. The values of the hydrogen interaction parameter k , in the M-Soave equation are given by Radosz and co-workers. Chao and co-workers (1980) showed that the interaction parameter k , of the Soave equation is approximately a constant equal to 0.7 for hydrogen in mixtures with heavier hydrocarbons. The calculations with the Soave equation are, therefore, based on a hydrogen k , of 0.7. Both the CCOR and the M-Soave equations are found to represent well the experimental vaporization of coal
se 5
a
se 5 a 'El
2 se p: v5 0 a
8
4
-8 Y
$
0
.;logg?4003
Ind. Eng. Chem. Process
Des. Dev. 1985, 24, 1055-1062
liquid in the mixture with hydrogen. The satisfactory result obtained from the M-Soave equation is no surprise; the equation is a modification of the Soave equation for asymmetric mixtures with the introduction of conformal mixing rules. The calculated results from the Soave equation are also reasonable, but not as good as those from the CCOR or the M-Soave. The Grayson-Streed correlation is found to deviate substantially from the experimental data. Acknowledgment Funds for this research were provided by the Electric Power Research Institute through research project RP-367. Catalytic, Inc., supplied the coal liquid. W. A. Leet assisted in sample inspections. R. G. Mallinson conducted the hydroxyl contents determinations. Registry No. H2, 1333-74-0.
Literature Cited Blom, L.; Delttausen, L. E.; van Kreveien, D. W. Fuel 1957, 3 6 , 135. Chao, K. C.; Lln, H. M.; Nageshwai, G. D.; Kim, H. Y.; Ollphant, J. L.; Sebastian, H. M.; Slmnlck, J. J. Phase Equilibrium in Coal Liquefaction Processes"; Electric Power Research InstRute: Paio Alto, CA, Oct, 1980; EPRI AP-1513. Edmister, W. C. "Applied Hydrocarbon Thermodynamics"; Gulf Publishing Co.: Houston, 1961; Chapter 12. El-Twaty. A. I.;Prausnitz, J. M. Chem. Eng. Sci. 1980, 3 5 , 1765. Gray, R. D.; Heldman, J. L.; Hwang, S. C.; Tsonopouios, C. Fluid Phase Equilib. 1983, 13. 59.
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Grayson. H. G.; Streed, C. W. Paper presented at the 6th World Petroleum Conference, Frankfurt am Main, Germany, June 19-26, 1963, Paper 20, Section VII. Henry, R. M. "Vapor-Liquid Equilibrium Measurements for the SRC-I I Process"; Gulf Science and Technology Co.: Pittsburgh, PA, Oct, 1980; DOEIET11004-1. Kesler, M. G.; Lee, B. I.Hydrocarbon Process. 1976, 55 (3). 153. Kim, H.; Lin, H. M.; Chao, K. C. Paper presented at the Proceedings of the 3rd Pacific Chemical Engineering Congress, Seoul, Korea, May 8-1 1, 1983, Vol. 11. p 321. Ind. Eng. Chem. Fundam., In press. Lewis, H. E., Plant Manager Quarterly Technical Progress Report, Catalytic, Inc., Wilsonvllle, AL, July-Sept 1981, Dlst. Category UC-9Od FE-10154110. Lin, H. M.; Chao, K. C. AIChE J. 1984, 3 0 , 981. Lin, H. M.; Kim, H.; Leet, W. A,; Chao, K. C. Ind. Eng. Chem. Fundam. 53. Radosz, M.; Lln, H. M.; Chao, K. C. Ind. Eng. Chem. Process Des. Dev. 1982. 2 1 .. 653. .- . -, .... Riazi, M. R.; Daubert, T. E. Hydrocarbon Process. 1980, 5 9 , No. 3, 115. Sebastian, H. M.; Lln, H. M.; Chao, K. C. AIChE J. 198la, 2 7 , 138. Sebastian, H. M.; Lin, H. M.; Chao. K. C. Ind. Eng. Chem. Fundam. 1981b, 20, 346. Sebastian, H. M.; Lln, H. M.; Chao, K. C. Ind. Eng. Chem. Process Des. Dev. 198lc, 20, 508. Simnick, J. J.; Lawson, C. C.; Lin, H. M.; Chao, K. C. AIChE J. 1977, 23, 469. Soave, G. Chem. Eng. Sci. 1972, 27, 1197. Sung, C. Ph.D. Thesis, University of Pittsburgh, PA, 1961. Watanaslri, S.; Bruie, M. R.; Starling, K. E. AIChE J. 1982, 28, 626. Wilson, G. M.; Johnston, R. H.; Hwang, S. C.; Tsonopouios, C. Ind. Eng. Chem. Process Des. Dev. 1981, 2 0 , 94.
Received for review July 30, 1984 Accepted January 28, 1985
Multiple Time Scale State Estimation Wayne S. Gaafar and W. Fred Ramlrez' Deparfment of Chemical Engineering, Universlv of Colorado, Boulder, Colorado 80309
The existing technique commonly used to estimate process states, Kalman filtering, does not normally use the knowledge that multiple time scales exist. Ignoring this information leads to stiff differential equations. This paper uses multivariable singular Perturbation theory for process identification. I t investigates a hypothetical system and a continuous stirred tank slurry reactor. The singular perturbation technique consistently required less computational effort than the traditional complete Kalman fitter or the extended Kalman fitter. The effectiveness of both estimators was studied for varying ratios of model to measurement uncertainty, changes in the level of measurement error, and the qualii of the initial conditions. The traditional and extended Kalman estimators always equaled or surpassed the singular perturbation estimators. However, the singular perturbation estimators in all cases were able to follow the different time scale dynamics. The singular perturbation technique increases in usefulness as the stiffness or the number of stiff equations increases.
Systems demonstrating multiple time scales are wellknown. Examples of such systems from the chemical industry are heat exchangers, catalytic reactors, distillation columns, and fluidized beds. Heat exchangers have separate time constants for each flowing fluid. They also have a longer time constant associated with the fouling of the heat-exchanging surfaces. Catalytic reactors can have time constants associated with the resonance time of the reactants,the thermal wave produced by the reaction and the catalyst bed, and longer time constants associated with catalyst degradation. Distillation columns show similar types of time constants as reactors, but instead of the degradation of catalyst, the fouling of trays is observed. Fluidized beds also show similar time constant behavior, but for the longer time scale, the elutriation of the particles is observed. The existing technique commonly used to estimate process states, a Kalman filter, does not normally use the 0196-4305/85/1124-1055$01.50/0
knowledge that multiple time scales exist. Ignoring this information leads to stiff differential equations for the covariance variables with complex coupling of the various time constant modes. When the number of states involved in such equations grows, so does the number and complexity of the stiff differential equations. Stiff equations pose serious problems when solved numerically (Aiken, 1983) with real-time constraints. If a method could be developed that described these systems using the knowledge that multiple time scales exist, it would uncouple the stiff equations and reduce computation times. This paper shows how a perturbation analysis can uncouple processes with widely varying time scales. Perturbation Theory for State Estimation Perturbation analysis is used to approximate solutions to a set of differential equations by defining an arbitrary scalar variable. The solution of the differential equations 0 1985 American Chemical Society
