Ind. Eng. Chetn. Process Des. Dev. 1883, 22,49-53 T
= dead time
w = frequency w, = ultimate frequency - = Laplace transformation
-= deviation variable
Literature Cited Brlstol. E. “Recent Results On Interactions In Mukivarieble Process Control”; A I C M 71st Annual Meeting, Mlaml. FL, Nov 1978. Gagnepalgn, J.; Seborg, D. Ind. Eng. Chem. Process Des. Dev. 1982, 27, 5. Jensen. N.; Fisher, D. G.; Shah, S. L., submltted for publication in AIChE J . , 1982. Kim, Y. S.; McAvoy, 1.J. Ind. Eng. Chem. Fundam. 1981, 20, 381. Klm, Y. S.; McAvoy. 1. J. “Computing The Relethe @In for Pressure and Composition Control of a Single lower”; Proceedings of Automatic Con-
49
trol Conference, Arlington, VA, June 1982. McAvoy, T. J. “Process Dynamics and Control”; Adlo Course, American Chemical Society: Washington, DC, 1978 Unk 4. McAvoy, 1.J.; Welschedel, K. “A Dynamic Comparison Of Materiel Balance vs. Conventbnal Control Of Dlstlktbn Columns”; Paper 107.2, International Federation of Automatic Control Congress, Kyoto, Japan, Aug 1981. Shinskey, F. G. “Distlliatlon Control for Productivity and Energy Conservation”; McQraw-Hill: New York, 1077; Chapters 1.2. Shlnskey, F. 0. “Process Control Systems”. 2nd ed.; McGraw-Hill: New York, 1970; Chapter 8. Tung, L.; Edgar, 1.AIChEJ. 1981, 27, 690. lyreus. B. Ind. Eng. Chem. Process Des. Dew. 1979, 78, 177. Wkcher, M.; McAvoy. 1.J. ISA Trans. 1977, 18, 35. Woolverton, P. Intech. 1980. 27(9), 63.
Receiued for review August 10, 1981 Accepted June 18,1982
Representation of Petroleum Fractions by Group Contribution Vlastlmll RuilEka, Jr.,’ Aage Fredendund,’ and Peter Rasmwsen Instkuttet for Kemlteknik, Danmerks Tekniske H0)skok, DK-2800 Lyngby, Denmark
Most oil and gas processing operations require estimation of phase equilibria. Proper characterization of the complex mixtures encountered in petroleum fractions is a major problem. I n this work, the UNIFAC groupcontribution methcd for predicting vapor-liquid equilibria has been used as a basis for describing complex petroleum fractions in terms of model compounds. Standard procedures may be used to estimate critical properties, acentric factors, and molecular weights for the model compounds. This allows the inclusion of complex petroleum fractions in already available, generalized methods for phase equillbrlum calculations, based on equations of state or the UNIFAC group-contribution method. Good results are obtained for lower and medium molecular weight petroleum fractions at temperatures up to 600 K. At higher temperatures, the method may fail due to present limitations of the UNIFAC method.
Reservoir oil and gas fluids are complex mixtures of mainly paraffins, naphthenes, and aromatic compounds. For oil fractions of molecular weight higher than about 100, it is unpractical to list all of the compounds present. Hence one of the major problems in phase equilibrium calculations involving such fractions is the representation of the many different hydrocarbons in terms of a few properly averaged characteristic parameters. This work describes a new method of characterizing heavy petroleum fractions. The method is based on the UNIFAC group-contribution model for predicting vaporliquid equilibria (see, e.g., Fredenslund et al., 1977) and purecomponent vapor pressures (Jensen et al., 1981). The model is described in the Appendix. In additidn, a true boiling point analysis (TBP) and, if available, paraffinnaphthene-aromatic (PNA) analysis are used. A TBP curve for a complex petroleum mixture (here a lean absorber oil) is shown in Figure 1. The method suggested in this work entails the following steps: (1) division of the TBP curve into a number of subfractions; (2) definition of model components for each subfraction in terms of UNIFAC groups such as -CH3, -CH2-, and ACH (aromatic hydrocarbon group); (3) adjustment of the number of groups in each model compound so as to match the midvolume boiling point for each subfraction. The result of this procedure is a set of well-defined model compounds which represent the complex petroleum ‘Onleave from Prague Institute of Chemical Technology, 166
28 Prague 6,Czechoslovakia.
mixture. Molecular weights, acentric factors, and critical properties of the model compounds may be readily established by use of standard procedures. As indicated in Figure 1, usually 5-10 subfractions are required, each containing three model compounds: one paraffinic, one naphthenic, and one aromatic. The approach has been found to yield reliable results for temperatures up to 600
K. Data Requirements The method requires the following data: a complete TBP-analysis (boiling point temperature vs. liquid volume percent boil-off), a PNA (paraffin-naphthene-aromatic) analysis, preferably for each subfraction, and density, preferably for each subfraction. Often, all of these data are not available for complex hydrocarbon mixtures. Various procedures for transforming incomplete information on C,+ fractions into satisfactory TBP analyses are outlined by Erbar (1977). Although primarily developed for absorber oil C6+ fractions, the procedures can also be used for other petroleum fractions. A review of different categories of basic data available for C,+ fractions is given by Wilson et al. (1978). Procedure The TBP curve is broken into five to ten subfractions as indicated in Figure 1. The number of subfractions must be kept as low as possible so as to keep the computer requirements reasonably low. For the PNA analysis, no distinction is made between volume, weight, or mole percent. This is a reasonable 0 1982 American Chemical Society
50
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 I
I
Table I group
3AO
CH, CH, CH
c
P 2 + n 4 + 3n n
model compounds N
l + n 2n
n
1
0 0
0
4
0
2
5
ACCH,
0
A 2 + n n n
Table I1 0
group
20 40 60 80 100 L l q u t d volume per c e n t " B O I L - O F F "
CH, CH, CH CH2,CYC CHCYC ACH ACCH,
Figure 1. TBP curve for a lean oil fraction. 'CH,
=
VCH2
= 2
H2
CH Z
VCH*.cyc = 5
I
CH / \ CH2
CH2
I
'CH,
='
cyc
I
'CH3
I
'
c H2
CH3
Figure 2. Sample group assignments.
approximation since the PNA analysis most often is highly uncertain and does not take into account the presence of paraffinic CH3- and CH2- groups in naphthenic and aromatic molecules. In this work we use mole percent. The structure of the model compounds of the subfractions is defined in terms of the UNIFAC Uk(i) matrix (Uk(i) is the number of groups k in molecule i). In contrast to real molecules, the model molecules may be described by noninteger values of Vkcn. Sample group assignments are shown in Figure 2. For the pure-component vapor pressure calculations it was necessary to distinguish between "chain" and "cyclic" groups, i.e., between CH2and CH2 The molecular weight of the model compounds is termined by the number of groups, which is adjusted so that the boiling point of the mixture of model compounds matches the midvolume boiling point of the real subfraction. If the pure-component vapor pressures of the three model compounds for a given subfraction are found to differ greatly, the structure of the model components is changed so 89 to bring the vapor pressures closer together. An example of this procedure is given below. Example. Identifieation of Model Compounds. It is desired to establish the model compounds for the heaviest subfraction of a highly naphthenic absorber oil (Erbar, 1977). The observed midvolume boiling point is 433.2 K at 0.101 MPa, and the following PNA analysis is
model compounds P N
A 1
2 t n 3 t 3n n 0
l + n 2n n
4
0
0
1 0 0
0 5
0 0
n 0
1
given: 36% P, 55% N and 9% A. As our first set of model compounds we try those listed in Table I. The number n is established so that the bubble point of the mixture of model compounds matched the observed midvolume boiling point &kr
=
Ak,i/T
4-
4
2
+ A k J T + A k , 4 In T
(12A)
or 0.36ypPpO + 0.55yNPN0 + 0.09y~P~O = 0.101
As shown in the Appendix, both the activity coefficients y i and pure-component vapor pressures Piomay be obtained from UNIFAC. The unknown in the above equation is n. For T = 433.2 K we get: n = 0.582. This corresponds to M,= 132 (observed value: 139), Pp" = 0.138, P N o = 0.089, and P A o = 0.020 MPa. The vapor pressures of the model compounds differ somewhat. In order to reduce Ppo and increase the others, we now arbitrarily try the group assignments listed in Table 11. In this case we obtain: n = 0.881, Ppo= 0.110, P N o = 0.090, and P A o = 0.107 MPa. Now the vapor pressures of the model compounds are brought much closer together. The procedure shown in the above example is repeated for each of the 5-10 subfractions. Thus, for each subfraction a characteristic value of the parameter n completely defines the subfraction in terms of three model compounds. Naturally it is too cumbersome to assign the groups "by hand" for each oil mixture. "Automatic" group assignment procedures are described by Hansen (1982). For each of the, say, 3 x 5 defined model compounds one may predict the critical temperature and pressure using Lydersen's group contribution method (Lydersen, 1955), and one may calculate the acentric factor from the known vapor pressure curve using Pitzer's definition (Pitzer, 1955). Thus the model compounds may be ussed in describing thermodynamic properties of mixtures containing "undefined" petroleum fractions using any of the standard procedures. One may, for example, use the Soave-Redlich-Kwong equation of state to predict K values, enthalpies, entropies, bubble points, etc. In each case it is, however, necessary to study the sensitivity of the
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 51
Table 111. Comparisons between “Experimental” and Predicted Properties property “experimental” value
prediction on the basis of model compounds
PNA analysis density molecular weight of oil fraction critical properties of oil fraction and acentric factor
reported values reported values reported or, in some cases, predicted values by the Kesler and Lee method prediction by the Kesler and Lee method from known av boiling point and density; for two oil fractions (jet and low-boiling naphtha): reported values
the Rackett equationa direct calculation from known model compounds prediction from Lydersen’s methodC and predicted av molecular weight
ASTM distillation curve
reported values
prediction from vapor pressure curve using Pitzer’s definitiond predicted from mixture of model components using the multicomponent Rayleigh distillation equation and assuming constant relative volatility
Kesler and Lee (1976).
Rackett (1970).
Lydersen (1955).
Pitzer (1955).
Table IV. Predictions for Naphthenic and Aromatic Oil Fractions aromatic 122 mol wt absorber oil
naphthenic 113 mol wt absorber oil
pred values, % dev
pred values, % devC exptl valuesa
property overall PNA, % crit temp, K crit press., MPa acentric factor mol wt, g/mol density, g/cm3 ASTM temp, K; LV % off: 0 10 30 50 70 90 100 a Erbar (1977).
5 10 subfractions subfractions
exptl valuesasb
5 10 subfractions subfractions
33-58-9 567.8 3.06 0.365 113 0.756
-3.1 3.7 11.4 3.1 0.7
-3.2 4.7 10.3 2.4 0.8
35-32-33 606.5 2.98 0.400 122 0.789
-1.6 4.6 10.9 0.6 -0.5
-1.5 5.8 10.2 0.1 0.0
372 387 391 395 400 4 09 439
-5.1 -1.6 -1.3 -1.0 -1.0 -0.7 1.6
-5.4 -1.6 -1.5 -1.5 -1.3 -1.0 1.6
411 414 417 41 9 422 429 451
-1.9 -1.4 -1.4 -1.7 -1.7 -1.2 1.6
-2.2 -1.7 -1.4 -1.7 -1.9 -1.4 0.9
% deviation = lOO(expt1- pred)/exptl.
Wilson and Barton (1971).
Table V. Results for Light Petroleum Fractions
jet naphthaa
crit temp, K crit press., MPa acentric factor mol wt, g/mol density, g/cm3 ASTM temp, K; LV % o f f : 0 10 30 50 70 90 100
kerosinea
fuel oil“
gas oil“
Paraho shale oil 400-650 iF product
exptl values
pred values, % devC
exptl values
pred values, 3’% dev
exptl values
pred values, % dev
exptl values
pred values, % dev
exptl values
pred values, % dev
625 3.03 0.416 144 0.798
-0.9 11.1 12.3 10.2 1.5
666q 2.22 0.522 162 0.802
6.3 -1.9 11.9 4.4 -5.4
745 1.79 0.683 228 0.855
-0.2 -2.3 10.3 8.7 -4.7
737 1.77 0.681 214 0.842
-0.1 1.7 4.6 0.0 -7.8
729 1.78 0.669 202 0.841
-0.3 -1.1 7.4 -2.4 -7.2
414 424 429 434 438 445 456
-4.1 71.9 -1.4 -0.7 -0.5 0.0 0.0
439 450 466 480 496 516 533
-5.2 -3.3 -1.1 0.2 1.4 2.3 0.4
496 528 548 559 571 591 608
-9.3 -3.2 -0.7 0.2 0.5 1.7 0.7
520 535 543 553 563 580 600
-4.8 -2.2 -1.7 -0.1 0.0 1.0 0.0
503 515 530 545 563 582 600
-5.4 -3.5 -1.3 0.7 2.1 -0.7 -6.8
Lenoir and Hipkin (1973).
Sullivan and Stangeland (1979).
calculated results with respect to the critical constants and acentric factors. Comparisons Literature data on petroleum fractions are incomplete and scarce. Descriptions of petroleum fractions in terms of all the properties of all the components do not exist in the literature. In order to test the validity of our procedure, it is therefore necessary to extend published data on petroleum fractions using standard, empirical procedures. To test our procedure we make the comparisons outlined in Table 111.
% deviation = lOO(expt1- pred)/exptl.
Results Reported values for five light and medium petroleum fractions are chosen to illustrate the validity of the suggested procedure. Complete TBP analyses are available for a highly naphthenic and highly aromatic oil fraction (Wilson and Barton, 1971). These fractions were simulated using respectively five and ten subfractions, each with three model compounds. The results are given in Table IV. It may be seen that the predicted critical properties, densities, molecular weights, and ASTM distillation curves are in
52
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983
good agreement with the corresponding experimental values. It may also be seen that for these relatively narrow cuts using 10 subfractions gives no improvement over using 5 subfractions. Results for various light and medium petroleum fractions are shown in Table V. The agreement between experimental and predicted results is good in general. The critical properties and densities are in slightly better agreement with experimental values than the acentric factors. Also, the low-temperature ends of the ASTM distillation curves exhibit somewhat larger deviations than the high-temperature ends. This is not surprising; we would expect relatively large discrepancies between "real molecules" and "model molecules" at low molecular weights. In addition, the large reflux a t the beginning of the ASTM distillation was not taken into account. It would be of interest also to test our procedure for heavy oil fractions. Howevei, it was not possible to find data in the literature which are complete enough to_hoth establish the model compounds and evaluate the results. Since UNIFAC parameters for predicting the pure component vapor pressures were fitted to experimental data in the range 275-600 K, we would expect some difficulties for heavy oil fractions due to extrapolation problems. Comparison with data for a whole Romashkino crude oil (Daroczi et al., 1960) indicates that this is the case, but the results are not conclusive. In order to properly develop and evaluate our procedure at temperatures above 600 K, we need more experimental data in this region. In addition, the UNIFAC method for predicting pure-component vapor pressures must be extended. Such work is in progress.
Conclusions A new procedure for characterizing light to medium petroleum fractions has been established. The procedure is as follows. (1)Using the TBP analysis for a petroleum fraction, divide the fraction into approximately five subfractions. (2) Using the UNIFAC group-contribution method, fmd a paraffiic, naphthenic, and aromatic model compound for each subfraction; this is done by adjusting the predicted vapor pressure to the observed midvolume boiling point. (3) Using Lydersen's and Pitzer's methods, estimate the critical properties and acentric factors for each model compound. (4) Use the estimated constants for the model compounds in any standard correlation (e.g., the SRK equation of state) for computing thermodynamic properties ( K values, enthalpies, etc.). The procedure has been found to work well for light to medium petroleum fractions, including highly aromatic and naphthenic absorber oils. For petroleum fractions with true boiling points above about 600 K, more data and more model development are needed in order to use the procedure with confidence. Acknowledgment The authors wish to thank Professor J. H. Erbar for fruitful discussions and the Danish Ministry of Education and the Danish Council for Scientific and Technical Research for financial support. Appendix The composition of petroleum fractions in terms of pseudocomponenta is calculated by fitting the bubble point of the model subfraction to the midvolume boiling point of the actual subfraction. The bubble point is computed assuming
For activity Coefficients, yi, the UNIFAC group contribution method is used (Fredenslund et al., 1977). The activity coefficients are given by a combinatorial and a residual term
+ In yiR
In yi = In y:
(2A)
The combinatorial part is given by In yiC = (In ai/xi+ 1 - ai/xi)- l/zzqi (In ai/Oi+ 1 - ai/Oi) (3.4)
ai = x i r i / Xj x j r j ; Oi = x i g i / CJ x j g j
(44
summation over all components ?'i
= &(i)R& k
gi
(54
CVk(i)Qk k
summation over all groups; R k = volume parameter for group k;Qk = surface area parameter for group k;u k ( i ) = number of groups of type k in molecule i; xi = liquid mole fraction of component i; and z = coordination number = 10. For the residual part the following equations are used In yiR = Zuk(i)(lnrk - lnrk(i))
(6A)
k
The summation is over all groups In
rk
=
Qk[l -
In ( C o m q m k ) - C ( o m q k m / C o n q n m ) l m
n
m
(7A) qnm = exp(-anm/??;
dm
=
QmXm/EQnXn n
(8A)
am,, = group interaction parameter for the interaction between groups m and n (amn# an,,,). Equations 7A-9A
also hold for In rkm,except that the group composition variable, Ok, is now the group fraction of group k in pure fluid i. The pure component vapor pressures Pio are calculated by the UNIFAC group contribution method, in part based on the UNIFAC method for predicting activity coefticients (Jensen et al., 1981)
RT In pi" =
C V k ( ' ) &k k
+ R T C kV k " ) hl r k " )
(10A)
The group Gibbs energy functions, &, depend to some extent on the detailed structure of the molecules. The first term in eq 10A is therefore split into two expressions c V k ( i ' &Jk k
=
x U k ( i ) &k' k
+ AG,"
The structure-independent contribution, A&', depends strongly on temperature (12A) = A k , i / T + 4 2 + A k , 3 T 4- &,4 In where A h , [ are constants. The structure-dependent term, AGF, depends only weakly on temperature and was here used only for naphthenic ring groups. This is shown in detail by Jensen et al. (1981). Literature Cited &k'
Daroczi, M.; Kerenyi, E.; Mozes, Q.; Zakar, P. Publicatkm No. 203 of the Hungarian 011 and Qas Research Institute, Veszprem, Hungary, 1960. Erbar, J. H. Research Report 13. Qas Process Assoclatlon, T u b , OK, 1977. Fredenslund. Aa.; QmeMbrg, J.; Rasmussen, P. "Vapor Liquid Equlllbrie Using UNIFAC"; Elsevler: Amsterdam, 1977.
Ind. Eng. Chem. Process Des. Dev. 1083, 22, 53-58
Hansen, E. M.S. Thesis, InstihMet for Kemlteknk, The Technlcel Univerelty of Denmark, 1982. Jensen, T.; Fredenslund, Aa.; Rasmussen, P. Id.Eng. Chem. Fundam. 1981, 20,239. Kesler, M. G.; Lee, 6. I. h)&ocarbOn Process. 1976, 55, 153. Lenolr, J. M.; Hlpkln, H. G. J . f%m. €ng. Data 1973, 18, 195. Lyderasn, A. L. University of Wleconsln College of Englneerlng Experimental Statlon Report 3 Medison, WI,1955. Pitzer. K. S. J . Am. Chem. Soc.1955, 77, 3427.
53
Rackett, H. 0. J . Chem. €ng, Data 1970, 75, 514. Sullivan, R. F.; Stangeland, B. E. A&. Chem. Ser. 1979, No. 179, 25. Wilson, A.: Meddox, R. N.; Erbar, J. H. OH Ges J . Aug 21, 1978, 76. WHson, 0. M.; Barton, S.T. Research Report 2; Gas Processors Assoclatlon: Tulsa, OK,1971.
Received for review August 28, 1981 Accepted July 14, 1982
Scale-up of Plate Efficiency from Laboratory Oldershaw Data James
R. Falr,'
Harold R. Null, and Wllllam L. Bolles
Monsanto Company, St. Louis, Missouri 63 167
Conditions for commercial-scale testing at Fractionation Research, Inc. (FRI) and other plant situations were duplicated as closely as possible in the laboratory wlth the use of glass and metal Oldershaw columns. A consistent correlation between scales was found, with the indication that point efficlencles may be measured directly with the laboratory equipment. The resutts are especially useful for complex mlxtures and/or when vapor-liquid equilibria are not well defined.
Knowledge of mass transfer efficiency is critical to the design or analysis of a plate-type distillation column. While models for predicting the theoretical stage requirements of such a column have been developed extensively to provide rigorous results, the next step toward column design, the specification of actual stages or plates, may not be taken normally with a high degree of rigor or reliability. The development of reliable predictive models for plate efficiency is still in progress and remains in a fairly primitive stage for separations involving more than two components, large and complex molecules, and highly nonideal solutions. The efficiency of a plate depends upon three sets of design parameters: (1) the system-composition and properties, (2) flow conditions-vapor and liquid flow rates, and (3) geometry-type and dimensions of contacting device. These parameters may be varied more or less independently, although the particular separation at hand will dictate the system, the ratio of vapor to liquid, pressure drop allowance, and so on. The approaches normally used to predict plate efficiency encompass one or more of the following: (1)comparison with a similar commercial installation for which efficiency data are available, (2) use of empirical correlations, and (3) use of theoretical or semitheoretical mass transfer models. The present work proposes that a fourth approach is available, which for some cases may be the most reliable approach direct scale-up from laboratory distillation data, using special tray columns for the bench scale experiments. This work was initiated in the late 1950s at the Monsanto laboratories in Dayton OH. At the time there was developing interest in bypassing expensive pilot plants and going directly from bench scale research to final commercial design. It was also at this time when the program of Fractionation Research, Inc. (FRI) had progressed to a point where efficiency tests of large-diameter sieve trays were being conducted. The results from these tests represented the first reliable and comprehensive performance
* Department of Chemical Engineering, The University of Texas, Austin, T X 78712. 0190-4305/83/1122-0053$01.50/0
data ever available on commercial scale sieve trays. Accordingly, plans were formulated for scaling down the FRI test data such that parallel laboratory test runs could be made. The program continued over a period of years, first at the Dayton laboratories and later at the St. Louis Research Center of Monsanto. During this time it was encouraging to have reports such as that of Veatch et al. (1960) stating that glass Oldershaw columns had been used successfully in scale-up studies for the Sohio acrylonitrile process or that of Martin (1964))showing that laboratory studies with glass Oldershaw equipment were in good correspondence with plant studies of a high-vacuum solvent-water fractionator. The results of the Monsanto scale-down studies were used to support the successful design of a great many large fractionators, but they could not be disclosed publicly because the FRI data were classified as confidential. Some FRI data were published from time to time, but it was not until recently that any FRI sieve-tray data were released (Sakata and Yanagi, 1979; Yanagi and Sakata, 1981). Thus it is just now possible for Monsanto to share with others its experiences in the scale-up of laboratory distillation data. In the early stages of the present work it was decided that standard, off-the-shelf distillation apparatus should be used, if at all possible. For this purpose the Oldershaw column was selected, and it will be described in the following section. Experimental Work Laboratory Equipment. All of the laboratcry work was done with Oldershaw equipment. The Oldershaw column is essentially a bench-scale sieve (perforated) tray column containing circular downcomers. The associated reflux condenser, reflux trap, feed section, and reboiler components of the total system can be easily assembled with the column through ground-glass joint connections. The column was originally described in a paper by 01dershaw (1941) and is now available from a number of laboratory supply houses. A sketch of a typical Oldershaw section is shown in Figure 1. The usual application is for 0 1982 American Chemlcal Society
