386
Xnd. Eng. Chem. Process Des. Dev. 1980, 19, 386-393
tivity is a common observation in petroleum hydrotreating operations. Thus, the simple coal liquid hydrogenation catalyst screening test developed for screening potential catalytic coal liquefaction catalysts appears to have predictive value in determining relative catalyst ranking for both hydrogenation and hydrocracking in catalytic coal liquefaction. Conclusions A simple coal liquid hydrogenation screening test was developed for evaluation of potential catalytic coal liquefaction catalysts. Relative ranking of catalyst activity for hydrogenation of coal liquid in the screening test correranking Observed in 'POnded to the liquefaction. In addition, a tentative hypothesis is adthat the Of a to remove nitrogen from the coal liquid corresponds with the hydrocracking activity observed in catalytic coal liquefaction. Additional experimentation is required to quantify these relations.
Literature Cited Consolidation Coal Co., "Research on Zinc Chloride Catalyst for Converting Coal to Gasoline: Phase I-Hydrocracking of Coal and Extract With Zinc Chloride", R&D Report No. 39, OCR Contract No. 14-01-0001-310, Vol. 111, Books 1 and 2, 1969. ERDA-48, US. Energy Research and Development Administration, "A National Plan for Energy Research, Development, and Demonstration: Creating Cholces for the Future: Vol. I, the Plan", Government Printing Office, Washington, D.C., 1975. Hawk, C. O., Hiteshue. R. W., U . S . Bur. Mines Bull., No. 822(3) (1965). Katzman, H., "A Research and Development Program for Catalysis in Coal Conversion Processes", Report No. EPRI 207-0-0 for Electric Power Research Institute (1974). Kawa, W., Friedman, S., WU, W. R. K., Frank, L. U., 'favorsky, P. M., Presented at the 167th National Meetlng of the American Chemical Society, Division of Fuel Chemistry, Los Angeles, Callf., April 1974. Qader, S. A., Duraiswamy, K., Wood, R. E.,Hili, G. R., AICM Symp. Ser., 69(127), 102-104 (1973). Qader, S. A., HIII, G. R., Hydrocarbon Process, 48(3), 141-146 (1969). shah, Y. T., Cromuer, D. c., M C I KH.~G., , Paraskos, J. H., I&. ~ n g chem. . process D ~ S .DW., 17, 288-301 (1978). Stanulonis, J. J., Gates, 6. C., Olson, J. H., AIChE J., 22(3), 576 (1976).
Received for review May 16, 1979 Accepted J a n u a r y 9, 1980
Prediction of Vapor-Liquid Equilibria of Undefined Mixtures William J. Sim and Thomas E. Daubert Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
The purpose of this work was to evaluate the procedures for predicting the vapor-liquid equilibria of undefined mixtures including light fractions, whole crudes, and heavy residua in order to determine which approach would be most satisfactory for all petroleum fractions. As a resutf of this investigation, it was concluded that the unmodified Soave (1972) procedure was the most accurate and reliable method for flash calculations, having an average error of 12.8% as compared to 15.9% for the Chao-Seader (1961) method and 24.6% for the Maxwell (1950) graphical procedure. While the unmodified Soave procedure was satisfactory for simulating flash data in the 25 to 90 vol YO range, it predicts low flash volume behavior less accurately. A modification of the Soave vapor pressure function and the a function helped to reduce the overall error in the low flash volume data. Improvement was limited by inaccuracies in the experimental data (TBP curve) and characterizing parameters (T,, P,, and a).
Since virtually all phases of petroleum refining involve the separation of petroleum fractions into liquid and vapor phases, a reliable estimate of the equilibrium flash vaporization curve is an essential prerequisite for the efficient design and operation of petroleum processing equipment. The methods currently available for flash calculations are empirical correlations which are not very reliable, especially at low flash volumes. Furthermore, the subatmospheric flash curves are calculated directly from the atmospheric flash curve which means that any error involved in computing the atmospheric data is compounded in going to other pressures. Computer methods, based on several equations of state have been proposed to replace the graphical procedures for flash calculations but none of these methods have been systematically evaluated for petroleum fractions. The purpose of the present work was twofold. First, the various computer and graphical procedures were tested to decide which approach showed the greatest promise. Secondly, various methods for improving existing techniques were investigated. Literature Survey and Analysis The methods presented in the literature for flash calculations are of two general types-graphical correlations and computer methods based on an equation of state. Graphical correlations were developed by Piroomov and Beiswenger (1929), Nelson and Souders (19311, Packie 0196-4305/80/1119-0386$01.00/0
(1941), Nelson and Harvey (1948), Edmister and Pollock (1948), Maxwell (1950), and Edmister and Okamoto (1959a). All of these methods convert an ASTM D86 or T B P distillation into an equilibrium flash vaporization (EFV) curve. House et al. (1966) evaluated the above mentioned flash methods using the same data base as that used to develop the original correlations. The evaluation indicated that for TBP data, the Maxwell correlation gave the best results, with an average error of 14.970,while the errors of the other procedures all exceeded 20%. For this reason, only the Maxwell correlation was considered in the present work for comparison with the computer methods proposed. Computer methods for making vapor-liquid equilibria calculations on petroleum fractions were developed by Chao and Seader (1961), Grayson and Streed (1963), Hoffman (1968), Soave (1972), Starling and Han (19721, Lee et al. (1973), and Peng and Robinson (1976). All of the methods, with the exception of Hoffman's, begin by assuming an initial set of K values and performing a flash calculation to find x i , yi, and V, based on the material balances
v = F(2i - X i ) / X i ( K I
- 1.0)
(1)
and c x i = 1.0
0 1980
American Chemical Society
(2)
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 387 Table I. Literature Sources and Characterization of Flash Data type of pet. fraction Colombian crude Ranger crude Hendricks crude Santa Fe Springs crude Luling crude furnace oil + naphtha light fraction
exptl flash vol range, vol %
5-70
overall SP gr 0.891
101.35
5
5-70
Chu, Staffel ( 1 9 5 5 )
5-1 0 b-7 0 5-70
0.838 0.863 0.863
101.35 101.35 101.35
5 5 5
5-70 5-70 5-70
Chu, Staffel (1955) Chu, Staffel ( 1 9 5 5 ) Chu, Staffel (1955)
51-70 0-100
0.850 variable
101.35 814-47 1 6
5 13
5-10 49-51
Chu, Staffel ( 1 9 5 5 ) White, Brown ( 1 9 4 2 )
0-100
not given
15
14-81
Okamoto, Van Winkle (1949)
range of TBP dist., vol ?A
flash pressure range, kPa
no. of TBP fractions
13.34-101.35
ref
Table 11. Characterization of Industrial Flash Data
source Kuwait crude oil A Kuwait crude oil B Kirkuk residuum Venezuelan crude oil Abu Dhabi crude oil Sumatran crude oil A Sumatran crude oil B Iranian crude oil A Iranian crude oil B Iranian crude oil C Iraq crude oil A Iraq crude oil B Qatar crude oil Saudi Arabian crude oil A Saudi Arabian crude oil B
kip rang: of crude, C
vol % distilled a t end bp
sp gr range of crude
mol wt range of crude
no. of TBP fractions
range of flash vol data, vol %
40-1150
100.0
0.6285-1.100
77-1668
0.67-13.33
66
5.15-64.26
50-570
80.2
0.6309-0.9581
82-548
0.40-0.67
43
22.4-68.1
3 15 -7 7 5 91-278
100.0 36.0
0.8489-1.046 0.746-0.9593
260-843 195-353
4.00 6.67-101.3
9 20
45 .O-80.0 4.0-30.0
40-500
87.0
0.6285-0.9465
77-450
0.67-6.67
56
7.0-85.4
45-458
42.0
0.7200-0.9147
10-407
101.3
24
11.3-31.0
37-501
73.7
0.685-0.892
70-477
101.3
38
2.2-5 1.0
34-550
78.4
0.645-0.9285
71-532
101.3
40
10.7-67.4
40-1 100
100.0
0.6285-1.100
77-1532
4.00
42
19.8-76.8
40-1000
100.0
0.6285-1.080
77-1302
4.00
56
12.1-59.3
88.4
0.657-1.006
74-568
0.67-13.33
38
3.11-68.8
40-1100
100.0
0.628-1.100
77-1532
1.3 3-4.00
57
4.58-75.1
40-900 27-462
100.0 69.1
0.6285-1.054 0.645-0.9254
7 7-1 097 68-408
1.33-4.00 1.33-101.3
55 36
13.7-90.4 2.9-51.7
26-517
80.0
0.645-0.9254
68-484
45
10.6-65.5
40-600
Using the calculated values of x L ,y I , and V , the various equations of state (Soave, Peng-Robinson, and StarlingHan) can be solved for the fugacity of the liquid (f:) and vapor (f,”) phases. If the fugacities are not equal for all components in both phases, the K values are readjusted and the procedure is repeated. Otherwise, the K values and the calculated number of moles in the vapor phase (V) are correct. The Chao-Seader, Grayson-Streed, and Lee-Erbar-Edmister methods differ from the above procedure in that an activity coefficient correlation is used for the liquid state, while an equation of state is retained for the vapor phase only. The Chao-Seader and Grayson-Streed methods rely on the Redlich-Kwong equation of state for the vapor phase, while Lee, Erbar, and Edmister develop their own equation of state for use with their procedure. Hoffman’s method, which assumes ideal solutions (Raoult’s law) and an ideal vapor phase (Dalton’s law), was not evaluated. Daubert et al. (1978) tested the Soave, Peng-Robinson, and Starling-Han procedures on hydrocarbon mixtures and found that the Soave and Peng-Robinson equations give nearly equivalent results, while the Starling-Han procedure is considerably less accurate for predicting flash volumes. Lion and Edmister (1975) evaluated the LeeErbar-Edmister method and found it to be inferior to the
flash pressure range, kPa
101.1-101.5
Grayson-Streed method for calculating flash volumes of petroleum fractions. In summary, on the basis of the literature survey, the flash procedures which were evaluated are the ChaoSeader, the Grayson-Streed, the Soave, and the graphic procedure of Maxwell. Data Sources and Calculational Methods Flash Data. The flash data examined in this work come from two sources-chemical engineering literature and industrial data. The data which were obtained from the literature are characterized in Table I. Most of these petroleum stocks are presented with incomplete T B P curves or ASTM distillations, an overall specific gravity, and limited EFV data. The industrial data, presented in Table 11, contain more complete T B P distillations (generally ranging from 0 to 80% distilled). These petroleum stocks also have specific gravities for each of the T B P fractions. Calculational Methods. 1. Maxwell’s (1950) Procedure. For atmospheric flash data, Maxwell’s procedure was used directly, without modification. For predicting subatmospheric flash points, two approaches were considered. The procedure of Edmister and Okamoto (1959b) may be used to calculate the 50% subatmospheric EFV
388
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
Table 111. Error Analysis for Heavy Residua Data % deviations
flash procedure Maxwell Maxwell Chao-Seader Grayson-Streed Soave Soave
eq for acentric factor
-
procedure for subatmospheric flash Maxwell-Bonnell Edmister- Okamoto
-
Edmister Edmister Edmister Lee-Kesler
-
no. of points
flash volumes below 25%
flash volumes above 25%
error
bias
error
bias
error
bias
36.17 55.26 47.82 46.74 31.20 52.06
27.29 55.26 47.82 46.74 30.94 52.06
12.87 17.82 7.22 6.92 4.91 10.07
12.24 17.67 6.82 6.54 3.73 10.02
17.24 24.84 14.83 14.39 9.84 17.94
15.06 24.72 14.51 14.08 8.83 17.90
18
temperature and the rest of the curve may be assumed identical in curvature with the atmospheric curve. It is also possible to convert a subatmospheric temperature into an atmospheric equivalent through the Maxwell-Bonnell (1955) charts. Then the atmospheric flash curve could be used directly. Since neither of the above procedures for dealing with subatmospheric flash data have been adequately tested, both procedures were evaluated in the present work. 2. Chao-Seader (1961), Grayson-Streed (1963),and Soave (1972) Methods. In order to use either the Soave (1972), the Chao-Seader (1961), or the Grayson-Streed method, the petroleum stock must first be divided into approximately 15 TBP fractions each with a boiling range of approximately 25 “C. Using a narrow boiling range is essential to ensure that each component can be accurately represented by an average molecular weight, critical temperature, and critical pressure. Since values for the molecular weight and critical properties of petroleum fractions are not presented, they must be estimated. Various methods for characterizing hydrocarbon and petroleum fractions were evaluated by Jeter et al. (1965) and by Daubert (1978). On the basis of their investigations they concluded that the Winn (1957) nomograph is the most accurate method for characterizing petroleum fractions. For this reason, the Winn nomograph, which is represented analytically by eq 3-5, was chosen to evaluate the molecular weights and critical properties of the experimental flash data.
MW = 5.805 X
[ ~0.93711 ~b2.3776
p , = 6.1483 x 10127’ b-2.3177s2.4853
(3) (4)
exp [ ~ . ~ ~ ~ ~ ~ ~ o ~ 0 8 6 115 ~ 0 4 0 4 6 1 4 (5) 1.8 where Tb = molal average boiling point (K), S = specific gravity 15 C/15 C, P, = pseudocritical pressure (Pa), T , = pseudocritical temperature (K), and MW = molecular weight. Clearly, the use of these equations for multicomponent systems requires specific gravity data for each component in addition to the T B P curve. Once the specific gravities are known, the feed composition in terms of the mole fractions ( z i ) of each component can be calculated. The acentric factor, wi, may be determined from either the Edmister (1958) equation or the Lee-Kesler (1975) equation. Since both equations are in current use, an evaluation of the two equations was undertaken to determine which is more appropriate for petroleum fractions. The Chao-Seader and Grayson-Streed procedures were used without modification. Values for the solubility parameters of petroleum fractions were obtained from Figure
T, =
all flash volumes
78
96
8B1.6 of Chapter 8 of the “API Technical Data BookPetroleum Refining” (1977). The Soave procedure was used as supplemented by Graboski and Daubert (1978a,b, 1979). All binary interaction coefficients (“Cij” in eq 11) were assumed zero. With respect to the results presented in the tables, the following nomenclature is used. All flash volumes have units of volume percent. The errors given in the tables are defined as 1 experimental - calculated error = n experimental
- XI
I
-‘
1 experimental - calculated bias = n experimental
where n = number of data points. Analysis of Results and Developmental Methods The petroleum fractions examined in this work fall into three broad categories. The largest category in terms of the number of points examined is the heavy residua data. Heavy residua are crude oils in which the lighter boiling components have been removed. All of the heavy residua data examined have initial TBP temperatures above 300 “C. The second category consists of whole crude data. The initial T B P temperature of a typical whole crude is approximately 30 OC and the TBP distillation generally encompasses a temperature range of approximately 1100 “C. The third category consists of light fractions or narrow boiling petroleum stocks. The TBP distillation of a narrow boiling fraction usually covers a temperature range of less than 300 OC. Heavy Residua. A summary of the results for the heavy residua data is presented in Table 111. As the table indicates, the Soave (1972) procedure, in conjunction with the Edmister (1958) equation for acentric factors, is the most accurate method for calculating flash volumes over the entire range from 0 to 90 vol %. Among the graphical procedures, the use of the atmospheric flash temperature results in a substantial improvement over the EdmisterOkamoto (195910)correlation for predicting subatmospheric flashes. Finally, in comparing the Chao-Seader (1961) and Grayson-Streed (1963) methods, it appears that both procedures give identical results. This was expected since all of the data conformed to the limitations of the ChaoSeader method and the Grayson-Streed method reproduces the Chao-Seader results for TRi less than 1.0. The results have been divided into three categories to illustrate the fact that while nearly all of the procedures can adequately predict the flash curve in the region from 25 to 9070, none of the methods is very reliable at low flash volumes. It would certainly be possible to modify all of the procedures listed in Table I11 to more accurately simulate low flash volume data. However, since the Soave
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 389
Table IV. Error Analysis for Heavy Residua Using Modified Soave Procedure % deviations
eq for acentric factor modification
procedure Soave Soave Soave Soave
Edrnister Edrnister Lee-Kesler Lee-Kesler
none eq 14 none eq 15
flash volumes below 25%
bias
error
bias
error
31.20 23.72 52.06 25.22
30.94 15.27 52.06 6.28
4.91 4.30 10.07 5.27
3.73 1.36 10.02 1.97
9.84 7.94 17.94 9.01
v - 6 V ( V +6 )
where ai = 0.42747R2T,i2/P~
bi = 0.08664RTci/Pci n
6 = ExiNbi i=l
,]
(1 - Cij)(aiai(Yjaj)”2
+ SLi(l.0 - T,i1’2)]2 SLi = 0.485081+ 1.55171wj - 0.15613~: CY(
= [I
where x , =~ mole fraction of component i in phase N
it becomes apparent that a questionable assumption is being made in the applilcation of the original vapor pressure function (eq 13) to petroleum fractions. Since the coefficients of eq 13 were developed by regressing vapor pressure data of low molecular weight hydrocarbons, it is unlikely that this equation will suffice for high molecular weight petroleum fractions. There are several ways of rectifying this situation. The simplest approach is to modify the vapor presswe function by regressing the heavy residua data to accurately predict the experimental flash volumes. However, since the acentric factors for petroleum fractions are calculated from an equation such as the Edmister (1958) or Lee-Kesler (1975) equation, the actual form of the vapor pressure modification depends upon which equation was initially used for the acentric factor. With the Edmister equation for w , the modified vapor pressure function becomes SL,’(Edmister) -- 0.431
all flash volumes bias
error
procedure is far superior to any of the other methods and since it has the greatlest potential for industrial and engineering applications, all modifications and development work were restricted to the Soave equation. In carefully examini:ngthe equations which comprise the Soave procedure ET p = - RT -
(Y..a.. ,] =
flash volumes above 25%
+ 1 . 5 7 -~ 0~ . 1 6 1 ~ , ~(14)
Using the Lee-Kesler equation for w , the SL modification takes the form SL,’(Lee-Kesler) = 0.315 + 1 . 6 0 -~ 0.166w,2 ~ (15) Another method for dealing with the vapor pressure problem is to modify the (Y function (eq 12) by incorporating possible effects of the flash pressure and flash temperature. However, this method worked no better than the vapor pressure modification. Table IV presents a comparison between the errors obtained using the original Soave equation and those ob-
8.83 3.97 17.90 2.78
tained using the modified vapor pressure function. The modified results are clearly superior to the original Soave predictions, particularly for the Lee-Kesler acentric factors. It is also apparent that a considerable error (-25%) persists in the low flash volume predictions and the question arises as to whether any further improvement can be attained. In order to answer this question, it is first necessary to ensure that the accuracy of the Soave equation is not limited by errors in the measured or calculated parameters (i.e., errors in the TBP curve, flash temperature, calculated T,, P,, w etc.). For petroleum fractions it is not possible to evaluate the error introduced through the use of the Winn (1957) nomograph and the Edmister or Lee-Kesler equations since experimental values for the molecular weight and critical properties are unknown. It is, however, possible to estimate the error involved in measuring the experimental parameters-flash temperature, flash pressure, and the TBP curve. According to the ASTM Standards Part 18, (1971) the uncertainty in the thermocouple measurement is approximately h0.5 “C while the error in the recorded pressure *1.070. What is more significant, however is that the reproducibility of the T B P curve (according to the estimate provided in the industrial data) is k5.0 “C. The sensitivity of the Soave procedure to slight errors in the input parameters was evaluated and the results indicate that at low flash volumes a 0.5 “C error in the flash temperature can alter the Soave predicted flash volume by 15.0% while a 1.0% error in pressure alters the predicted flash volume by 11.0%. The major source of error is the TBP curve. For flash volumes below 1070,a 5 “C error in the TBP curve will result in a 100% error in the predicted flash volume. The results of the error analysis given above take on a greater significance when it is realized that each source of error contributes independently to the totalerror in a flash measurement so that the overall error in the predicted Soave flash volume might well exceed 150% (for low flash volume data). The above analysis only holds for flash volumes in the 0 to 10% range since the error estimates were made using experimental flash data in that range. For flash volumes above 25%, the error introduced through the use of the Winn nomograph and Edmister acentric factors is approximately 7.0%,and the error resulting from inaccuracies in the T B P curve is approximately 8.0%. The effects of errors in the flash temperature and flash pressure are negligible at high flash volumes. While it is not possible to demonstrate conclusively that the inconsistencies in the Soave results (Table IV) are due to experimental error, it is at least reasonable to conclude that errors in the characterizing parameters and experimental parameters are capable of fully explaining the Soave results. No justification exists for developing a more sophisticated explanation or interpretation with the limited data available. Whole Crude Data. A summary of the results for the whole crude data is presented in Table V. Since all of the data were collected at atmospheric pressure, there was no
390
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
Table V. Error Analysis for Whole Crude Data ~~
~
~
-
~~~~
% deviations
flash procedure
eq for acentric factor
Maxwell Ch ao-Se ader Soave Soave
Edmister Edmister Lee-Kesler
-
flash volumes below 25%
flash volumes above 25%
all flash volumes
error
bias
error
bias
error
bias
31.77 32.65 34.30 33.68
-8.28 -5.65 -5.67 -5.90
6.63 10.05 10.27 8.07
-3.49 -9.80 -10.11 -7.62
19.48 21.60 22.55 21.16
-5.94 -7.68 -7.84 -6.74
23
no. of points
40
45
Table VII. Effect of Errors in Input Parameters on Soave Flash Volumes
Table VI. Comparison between Chu-Staffel and Modern Industrial Data % deviations
procedure Maxwell Chao-Seader Soave Soave no. of points
e q for acentric factor
Edmister Edmister Lee-Kesler
Soave calcd flash vol
Chu-Staffel data
modern industrial data
error
error
bias
5.0
20.11 23.20 24.64 22.89
-10.42 -23.20 -14.65 -12.92
10.0
bias
18.98 -2.36 20.32 4.73 20.88 -2.39 19.78 -1.80 25
20
need to use the Edmister-Okamoto (195913) correlation with the Maxwell graphical procedure. Also, since all of the points were within the limits of the Chao-Seader (1961) correlation, it was not necessary to consider the GraysonStreed (1963) modification. Table V indicates that all of the methods are nearly equivalent although the Maxwell (1950) and Chao-Seader methods are slightly better than the Soave. In order to understand these results, it is first necessary to point out that two types of data were used in constructing this table. Approximately 50% of the whole crude data were taken from the work of Chu and Staffel (1955), who presented TBP curves only from 5 to 70% distilled, which means that the initial and final segments of the TBP curve, which are the least predictable, had to be estimated. Since the missing portions of the TBP curve would be expected to exert a large influence on the flash volumes in the range of 0 to 10% and 70 to loo%, it is not surprising that the Soave method is at a disadvantage with respect to the Maxwell method which utilizes TBP slopes instead of TBP fractions. Table VI presents a comparison between the various flash methods separating the Chu-Staffel data from the modern industrial data. As expected, the Maxwell procedure works slightly better for the Chu-Staffel data. What is difficult to explain is why both the Soave and Chao-Seader methods do so poorly for the modern industrial data. While the exact reasons are not clear, it is certainly true that both methods display a serious bias, indicating that the correlations are not properly centered about the experimental data. The bias would be relatively easy to correct were it not for the fact that it only appears in the modern industrial data. This means that any method proposed to correct the problem must first be able to distinguish whether or not a particular crude will exhibit the bias. One method developed for this purpose is based on the 20% T B P temperature. It may be concluded from an examination of the whole crude data that the 20% TBP temperature is approximately equal to the 10% flash temperature. Furthermore, when the 20% TBP temperature is used as the flash temperature in the Soave procedure, those crudes which predict a flash volume greater than 10% tend to overpredict the experimental flash data,
20.0
error in exptl parameter
resultant % change in Soave flash vol
0.5 "C in T expt 1.0% in P expt 2.5 "C in TBP curve 5.0 " C in TBP curve 0.5 "C in T expt 1.0% in P expt 2.5 "C in TBP curve 5.0 " C in TBP curve 0.5 " C in T expt 1.0%in P expt 2.5 "C in TBP curve 5.0 " C in TBP curve
30.0 30.0 >>100.0 >> 100.0 15.0 13.0 130.0 >>100.0 6.0 6.0 25.0 50.0
while those crudes which predict flash volumes less than 10% show no consistent bias. On the basis of these observations, the Soave CY function was modified according to the equation CY^ =
0.0147
+ 0.993c~jO- O.OlO(TMFP)
(16)
where aio = original ai from eq 12, and (TMFP) = 10.0 the calculated flash volume when the 20% TBP temperature is used as the flash temperature. The a modification is only applicable if (TMFP) (as defined above) is negative, and it may be used regardless of which equation is used to calculate the acentric factor. The use of the CY modification scheme improves the accuracy of the Soave method to the extent that the average error in the predicted flash volumes is approximately 25% (for flash volumes in the 0 to 25% range). This surpasses the accuracy of the Chao-Seader and Maxwell procedures (see Table V) and is comparable to the results obtained for heavy residua (see Table IV). It is unlikely that any further improvement can be achieved since the sensitivity of the Soave predictions to slight errors in the T B P data and flash parameters is similar for both the heavy residua and whole crude data. Furthermore, the whole crude data constitute a much less reliable basis for evaluating and modifying the Soave procedure because of the deficiencies in the TBP curves of the Chu-Staffel data (see Table I). Narrow Boiling Fractions. The data on narrow boiling fractions is of two basic types. There is a large amount of data from Okamoto and Van Winkle (1953) and Edmister and Pollock (1948) which contain only ASTM D86 distillations and overall specific gravities while there are two pieces of data which present complete TBP curves and specific gravities. These latter data are taken from the papers of White and Brown (1942) and Okamoto and Van Winkle (1949). In order to use the ASTM data with the Soave procedure it is first necessary to convert the ASTM distillation into a TBP distillation. Procedures for
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980 391
Table VIII. White and Brown Data Using Recalculated Feed Compositiona calcd flash volumes flashotemp, C
flash pressure, kPa
exptl flash vol
Soave IEdmisterl w
Soave (Lee-Keslerl
347.3 371.2 371.2 311.7 304.5 350.0 387.8 348.9 372.3
1489.2 4481.5 2371.7 2344.1 2426.9 2344.1 4122.9 3564.5 1323.8
50.04 50.89 49.81 50.02 50.30 50.11 49.73 50.36 51.17
56.17 49.94 57.53 54.58 53.01 55.84 49.90 55.89 58.76
55.17 49.34 56.44 53.94 52.45 54.90 49.86 54.22 57.40
9.10 -8.7 9
7.6 -6.9 6
w
Chao-Seader Grayson-Streed (Edmisterl w (Edmisterl w 53.17
55.65 72.17 60.11 54.48 53.26 57.79 84.27 65.37 59.03
-
48.79 47.12 45.31
-
55.64
% deviations
error bias no. of points a
6.7 0.7 5
24.3 -24.3 9
Missing values outside range of method.
Table IX. Summary of Okamoto and Van Winkle Analysis ~
~
~
~
~
_
_
_
_
Maxwell Maxwell procedure procedure with EdmisterATM Okamoto flash temp procedure
flash temp, "C
flash pressure, kPa
exptl flash vol
Soave flash vol
Chao-Seader flash vol
GraysonStreed flash vol
-1.1 4.5 10.0 20.0 46.1 51.7 60.0 66.7 65.6 71.1 76.7 80.0 93.4 100.0 105.0 110.0 110.0 115.0 120.0
1.33 1.33 1.33 1.33 13.33 13.33 13.33 13.33 26.67 26.67 26.67 26.67 66.67 66.67 66.67 66.67 101.35 101.35 101.35
15.40 34.50 53.80 81.10 14.20 34.70 63.00 83.80 20.00 40.60 60.20 70.70 18.30 45.50 63.50 80.00 28.00 46.60 65.80
16.41 35.06 52.62 79.79 13.87 33.95 62.02 82.58 18.90 39.25 58.65 69.76 18.66 44.27 62.67 80.48 27.08 46.72 65.81
29.83 48.86 65.98 93.85 17.58 37.76 65.66 86.16 18.16 38.64 58.05 69.14 11.54 37.35 56.01 73.72 17.19 36.96 56.26
40.23 58.07 74.12 100.0 20.60 40.61 68.17 88.54 19.66 40.08 59.39 70.43 12.20 37.95 56.58 74.22 17.99 37.68 56.93
U
b
48.4 63.6 94.0 100.0 53.0 70.8 88.8 100.0 56.0 74.0 90.0 100.0 63.6 78.8 96.0
33.0 50.0 73.4 96.0 42.0 57.6 72.4 82.0 58.0 75.6 94.0 100.0 63.6 78.8 96.0
2.2 1.1 19
20.1 -2.4 19
26.7 -86.6 19
86.6 -86.6 15
66.3 -66.3 15
% deviations
error bias no. of points
a Missing values were outside the range of Maxwell-Bonnell charts. Okamoto correlation.
accomplishing this conversion (see House et al., 1966) involve errors of *5 "C, thus rendering such methods unsuitable for use with the Soave procedure. The effects of slight errors in the flash temperature, flash pressure, and T B P curve on the ,Soave predicted flash volumes for narrow boiling fractions are presented in Table VII. Therefore, only the White and Brown (1942) data and the Okamoto and Van Winkle (1949) data were evaluated. A representative number of points from the White and Brown data were evaluated by the Soave and Chao-Seader methods with both methods giving erratic results. It was subsequently discovered that the feed composition as calculated from Tables I and I1 of White and Brown's paper did not agree with that calculated from the flash vaporization data (Table VI of White and Brown's paper). The feed composition (as calculated from Table VI) was used with the Soave, Chao-Seader, and Grayson-Streed methods with the results shown in Table VIII. Because the flash pressures used by White and Brown (ranging from 1380 to 4480 kPa) generally exceed the limits of the
Missing values were outside the range of Edmister-
Chao-Seader method (i.e., >0.8Pc),many of the data points failed to converge with this method. The Soave results show excellent agreement with the experimental data. The Okamoto and Van Winkle data consists of EFV curves for a mixture of 15 low molecular weight compounds, all of whose critical properties and acentric factors are known. The feed composition stipulated in the Okamot0 and Van Winkle paper was used without modification or recalculation. The results for all flash methods are shown in Table IX. The Soave method shows excellent agreement with the experimental results and there is no sign of underprediction at low flash volumes. As the Chao-Seader and Grayson-Streed methods both predict very poorly, an inherent weakness in the methods probably exists since the bias is not significant, particularly for the Chao-Seader method. The Maxwell procedure also predicts very poorly regardless of whether one uses atmospheric flash temperatures or the Edmister-Okamoto (1959b) procedure for subatmospheric flash points.
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_
392
Ind. Eng. Chem. Process Des. Dev., Vol. 19, No. 3, 1980
Since the Soave method worked reasonably well for both the White and Brown data and the Okamoto and Van Winkle data and since there are not enough data on narrow boiling fractions to conduct a meaningful evaluation, no attempt was made to modify the Soave procedure. The Okamoto and Van Winkle data were also run using calculated T,,P,, and w values in an attempt to estimate the error introduced into the Soave procedure from the Winn nomograph and Edmister and Lee-Kesler equations. The results show that the Lee-Kesler method for acentric factor should be used and that the error is not significant at higher flash volumes. The use of the calculated critical properties and acentric factors can result in a 30% error in the Soave predictions of flash volume below 20%. For all points of Table IX the average percent deviation is 7.3% with a bias deviation of 1.4%. Conclusions On the basis of all data available, the Soave (1972) procedure is the most reliable and accurate method for f h h calculations involving undefined mixtures, regardless of the specific nature of the mixture. The results for 156 data points, including heavy residua, whole crudes, and light fractions, indicate that the average error in prediction of flash volumes is 12.8% for the unmodified Soave procedure, 15.9% for the Chao-Seader (1961) method and 24.6% for the Maxwell (1950) procedure using atmospheric flash temperatures. Only 111 of the 156 points were at subatmospheric pressures and the use of the EdmisterOkamoto (1959b) procedure in conjunction with the Maxwell procedure for these data resulted in an average error of 30.4%. The use of atmospheric flash temperatures from the Maxwell-Bonnell (1955) charts in conjunction with the Maxwell correlation is a far better technique for handling subatmospheric flash data than the EdmisterOkamoto correlation although neither method is comparable to the Soave procedure. Although the unmodified Soave procedure is adequate for predicting flashes in the range of 25 to 90%, it predicts low flash volumes rather poorly, with an average error of 31.2% for heavy residua and 42.7% for modern whole crude data. It was concluded that a modification of the vapor pressure function to eq 14 for use with the Edmister (1958) equation for wi and to eq 15 for use with the LeeKesler (1975) equation for wi would reduce the error in the heavy residua to 23.7%. Similarly, a modification of the a function to eq 16 reduced the error for the modern whole crude data to 23.5%. The CY modification is only applicable if the calculated flash volume is greater than 10% when the 20% T B P temperature is used as the flash temperature. Both the a modification and the vapor pressure function modification are applicable to the entire range of the flash curve (0 to 100%) but the greatest improvement occurs in the low flash volume range. Even with these modifications, there were still several points which were severely underpredicted by the Soave equation which may be due to two separate factors-errors in the experimental parameters (e.g., flash temperature, flash pressure, T B P curve) and errors in the calculated parameters (Tpci, Ppci,ai). For petroleum fractions, it is not possible to determine which of the above sources of error is more important since the true critical properties of the individual species are not known and the use of aggregate pseudocritical properties is merely an approximation. However, slight changes in the experimental parameters ( f 5 OC in the T B P curve) can alter the Soave flash volume by 100% and this may be a sufficient explanation of the inconsistencies in the results. On the other hand, from the Okamoto and Van
Winkle analysis it is apparent that slight inaccuracies in the characterizing parameters can have serious consequences, particularly in the low flash volume range. For example, when the calculated values for the critical properties and acentric factors were substituted for the correct values in the Okamoto and Van Winkle calculation, the average error in the Soave flash volumes increased by 7.0% while the error for one of the low flash volume points went from 6.6 to 35.6% (an increase of 29%). From these results one can conclude that neither the Soave method nor any other equation of state based on the corresponding states principle is capable of accurately predicting flash volumes below 20% for undefined mixtures although results for higher flash volumes are acceptable. Any further developments in such vapor-liquid equilibria calculations must await a refinement of the methods used to characterize petroleum fractions or else the development of a new approach which utilizes only readily accessible fundamental properties of petroleum fractions (e.g., viscosity, specific gravity, etc.). Nomenclature a = energy constant for Soave equation ASTM = abbreviation for American Society for testing and materials b = volume constant in Soave equation EFV = abbreviation for equilibrium flash vaporization f = fugacity F = number of moles in the feed K = equilibrium vaporization ratio P = pressure S = specific gravity SL = vapor pressure function in Soave equation T = temperature TMFP = 10.0 minus the flash volume when the 20% TBP temperature is used as the flash temperature TBP = true boiling point V = number of moles in vapor state (eq 1)or volume (eq 6) VLE = vapor liquid equilibrium x = mole fraction in liquid y = mole fraction in vapor z = mole fraction in feed 2 = compressibility factor for Soave equation Greek Symbols cy = parameter in Soave equation based on reduced temperature and the acentric factor 4 = fugacity coefficient w = acentric factor Superscripts L = liquid V = vapor N = refers to phase which can be liquid or vapor s = saturated Subscripts b = boiling point ci = critical state of component i exp = experimental i = component i R = reduced state Literature Cited American Petroleum Institute, "Technical Data Bock-Petroleum Refining", 3rd ed, Washington, D.C., 1977. ASTM Standards, Part 18, "Petroleum Products-LPG, Aerospace Materials, Sulfonates, Petroleum, Wax", American Soclety for Testing and Materials, Philadelphia, Pa., 1971. Chao, K. C., Seader, J. D., AICbE J., 7, 598 (1901). Chu, J. C., Staffel, E. J., J . Inst. Pet., 41, 92 (1955). Daubert, T. E., private communication, 1978. Daubert, T. E., Graboski, M. S., Danner, R. P., "Documentation of the Basis for Selection of the Contents of Chapter 8-Vapor-Liquid Equilibrium KValues", American Petroleum Institute, Dept. of Refining, Washington, D.C., 1978. Edmister, W. C., Pet. Refiner, 37(4), 173 (1958).
Ind. Eng. Chem. Process Des. Dev. 1980, 79, Edmister, W. C., Okamoto, K. K., Pet. Refiner, 38(8), 117 (1959a). Edmister, W. C., Okamoto, K. K., Pet. Refiner, 38(9), 271 (1959b). Edmister, W. C., Pollock, D. H., Chem. Eng. Prog., 44, 905 (1948). Graboski. M. S.,Daubert, T. E., Ind. Eng. Chem. Process Des. D e v . , 17, 443 (1978a); 17, 448 (1978b); 18, 300 (1979). Grayson, H. G., Streed, C. W., Sixth World Petroleum Congress, Frankfurt am Main, 111, Paper 20-PD7, p 233, 1963. Hoffman, E. J., Chem. Eng. Sci., 23, 957 (1968). House, G. G., Braun, W. G., Thompson, W. H., Fenske, M. R., "Documentation of the Basis for the Selection of the Contents of Chapter 3-ASTM, TBP, and EFV Relationships for Petroleum Fractions", American Petroleum Institute, Dept. of Refining, Washington, D.C., 1966. Jeter, L. T., Thompson, W. H., Braun, W. G., Fenske, M. R., "Documentation of the Basis for Selection of the Contents of Chapter 2-Characterization of Hydrocarbons", American Petroleum Institute, Dept. of Refining, Washington, D.C., 1965. Lee, B. I., Erbar, J. H., Edmister, W. C., AIChE J., 18, 349 (1973). Lee, B. I., Kesier, M. G., AIChEJ., 21, 510 (1975). Lion, A. R., Edmister, W. C., Hydrocarbon Process., 54(8), 119 (1975). Maxwell, J. B., Bonneli, L. S., "Vapor Pressure Charts for Petroleum Engineers", Esso Res. and Eng. Co., Linden, N.J., 1955.
393
393-396
Maxwell, J. R., "Data Book of Hydrocarbons", Van Nostrand. New York, N.Y., 1950. Nelson, W. L., Harvey, R. J., Oil Gas J., 47(7), 71 (1948). Nelson, W. L., Souders, M., Jr., Pet. Eng., 3(1), 131 (1931). Okamoto, K. K., Van Winkle, M., Pet. Refiner, 28(8), 113 (1949). Okamoto, K. K., Van Winkle, M., Ind. Eng. Chem., 45, 429 (1953). Packie, J. W., Trans. AIChE, 37, 51 (1941). Peng, D. Y., Robinson, D. B., Ind. Eng. Chem. Fundam., 15, 59 (1976). Piroomov, R. S.,Beiswenger, G. A., Proc. Am. Pet. Inst., 10(2), 52 (1929). Soave, G., Chem. Eng. Sci., 27, 1197 (1972). Starling, K. S.,Han, M. S., Hydrocarbon Process., 51(6), 107 (1972). Winn, F. W., Pet. Refiner, 36(2), 157 (1957). White, R. R., Brown, G. G., Ind. Eng. Chem., 34, 1162 (1942).
Received for review June 4, 1979 Accepted F e b r u a r y 4, 1980 F i n a n c i a l s u p p o r t of this work was p r o v i d e d by the Department o f R e f i n i n g o f t h e American P e t r o l e u m I n s t i t u t e .
Simulation of Low-Temperature Water-Gas Shift Reactor Chandra P. P. Singh and Deokl N. Saraf" Department of Chemical Engineering, Indian Institute of Technology, Kanpur-2080 16, India
A rate?equation for water-gas shift reaction over a low-temperature catalyst, similar to that over a high-temperature catalyst, has been used. This rate equation takes into account the effects of temperature, pressure, and age of the catalyst on the catalyst activity. It also considers the reduction in reaction rate due to diffusional resistances. Subsequently, this rate equation has been used in a mathematical model developed for design and simulation calculation of the reactor. Agreement between plant data and calculated values is generally very good.
The reformed gas in an ammonia plant contains a high percentage of carbon monoxide in addition to hydrogen and carbon dioxide. A high-temperature shift reactor (HT), using an iron oxide catalyst and operating at 35G450 "C, is used to convert most of the carbon monoxide to hydrogen and COz. Since high temperature favors high CO content even at equilibrium, the H T effluent still contains about 3% CO. This is usually treated in a lowtemperature shift reactor (LT) which uses a CuO-ZnO catalyst and operates in the temperature range 180-250 "C. The L T exit gases contain less than 0.3% CO, which is eventually removed in the methanator. The total amount of conversion that takes place in an L T reactor is small compared to that in an HT reactor. However, a slightly higher carbon monoxide content at the L T outlet can result i n heavy purge loss or/and high inert content in synthesis gas, both resulting in reduced production of ammonia. This makes the study of the behavior of an L T reactor important from the industrial point of view. Reaction Rates The first commercial application of an LT catalyst dates back to 1930 (Larson, 1931). The catalyst, however, did not find significant commercial use due to its relatively poor life of about 6 months. The catalyst has subsequently been improved and has found widespread commercial application since the early 1960's. Therefore, the studies pertaining to the preparative (Habermehl and Atwood, 1964; Lombard, 1969; Saleta et al. 1970; Ahmed et al. 1971) and kinetic (Cherednik et al., 1969; Kasaoka et al., 1970; Tsuchimoto et al. 1970; Yureva et al., 1969) aspects of L T catalysts are relatively recent and these are not as ex0196-4305/80/1119-0393$01 .OO/O
haustive as that over the H T catalyst (Ruthven, 1969; Singh and Saraf, 1977). In general, a rate equation similar to that for reaction over an H T catalyst has been found to be suitable for L T catalysts (Ahmed et al. 1971,1972; Cherednik et al., 1969; Kasaoka et al.,1970; Mahapatra et al. 1971). In the present work, the following equation has been used to represent the rate of the shift reaction over the catalyst pellets r = EffX 2.955
X
1013exp(-20960/Rgn
X
Agf X
Pf(XC0
-
x*co) (1)
where Effis the effectiveness factor which accounts for intrapellet diffusional resistance (Ahmed et al., 1972). Wheeler's (1955) method has been used to calculate Effin the same way as done for the H T catalyst (Singh and Saraf, 1977). External mass and heat transfer resistances have been neglected (Ahmed et al., 1971; Kasaoka et al., 1970; Tsuchimoto et al., 1970; Yureva et al., 1969). A , is an aging factor which accounts for loss in activity of the catalyst with usage. This has been correlated with temperature and age from the data reported for the catalyst (Mahapatra et al., 1971) as log A,f = (4.66 X - 1.6 X 10-6T) X r
Pf accounts for the effect of pressure on the rate of reaction as follows pf = p(0.5- P / 2 5 0 ) In the absence of actual data available on L T catalysts and the similarity with HT, the above expression valid for H T catalysts (Singh and Saraf, 1977) has been used here also: R, = universal gas constant and T is absolute tem0 1980 American
Chemical Society
