Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 1287-1293 Cousins, W. J. New Zealand J . Sci. 1983b, 2 6 , 277-281. Dannenberg, E. M. I n “Kirk-Othmer Encyclopedia of Chemical Technology”, 3rd ed.; Wiley: New York, 1978; Voi. 4, pp 631-666. Klass, D.L. “Energy from Biomass and Wastes VI”; Institute of Gas Technolwy: Chicaao, 1982. Kollmain, F. F. PI: Kuenzi, W.; Stamm, A. J. “Principles of Wood Science and Technology”: Springer-Verlag: Berlin, Heidelberg, New York, 1975; Vol. 11, Chapter 5. Palmer, E. R.; Lauder, B.; Jones, S.; Cousins, W. J.; Garner, K. Report No.
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IPDITSCI6006. Industrial Processlng Division, DSIR, Petone, New Zealand, 1982. Reed, T. B. Report No. TR-33-239. Solar Energy Research Institute, Golden, CO, 1980.
Received f o r review July 18, 1984 Revised manuscript received January 22, 1985 Accepted March 19, 1985
Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions Chorng H. Twu Process Simulation International, Affiliate of Simulation Sciences, Inc., Fullerton, California 92633
This paper describes a simple, reliable, accurate, and internally consistent method for the calculation of iiquid viscositiis of petroleum fractions. The correlation uses n-alkanes as a reference fluid instead of spherical molecules which are traditionally used and employs normal boiling point and specific gravity. The new correlation is capable of predicting liquid viscosity for petroleum fractions with normal boiling points up to 1800 O R and API gravity up to -30. This covers the entire range of practical interest. The prediction of the viscosity shows significant improvement over published correlations.
Although many methods have been published to suggest ways to estimate liquid viscosity when no experimental data are available, most are limited to narrow ranges of temperature and pressure and often to pure fluids. A review of these methods is given by Reid et al. (1977). It presents the best and most general methods and concludes that none are particularly reliable and that all are empirical. Methods with a more theoretical foundation include those of Pederson et al. (1984), Ely and Hanley (1981),Haile et al. (1976), Hanley (1976),Mo and Gubbins (1976), and Tham and Gubbins (1970). These methods, however, require the critical constants, molecular weight, and acentric factor of each mixture component which are usually not readily available for petroleum fractions. The method of Ely and Hanley (1981) has been applied by Baltatu (1982) to estimate the viscosities of petroleum fractions. However, the application is restricted to petroleum fractions with low boiling points. In light of the complex nature of petroleum fractions and the difficulty of even identifying the components present in such a mixture, the standard methods generally used for estimating liquid viscosities from pure component data are not applicable. Yet some prediction method is necessary since fluid flow and heat-transfer calculations depend on accurate viscosity estimates. For petroleum fractions, useful viscosity prediction methods are most conveniently based on parameters such as boiling point and specific gravity which are commonly used to characterize each fraction. Watson et al. (1935) presented figures relating kinematic viscosity as a function of API gravity and the Watson characterization factor ( K ) . These figures were obtained by plotting the data collected and drawing the best average curves by cross interpolation. Recently, the API Technical Data Book (1978) replotted these data as a nomograph. From the values of API gravity and Watson characterization factor, one reads kinematic vis0196-4305/85/1124-1287$01.50/0
cosity at 210 OF and at 100 OF. Although the API nomograph is generally useful for hand calculations, the form is not suitable for computer applications. In addition, the correlation has a more serious deficiency, namely, that the valid ranges of API and the Watson characterization factor ( K )are only from -5 to +55 and from 10.0 to 12.5, respectively. Viscosities at 210 O F range from 1.0 to 100 cs and at 100 O F from 1.4 to 1000 cs. It is evident that much of the region of interest lies beyond the range of this nomograph. A final deficiency is the relatively large errors in predicted viscosities. The average error is approximately 21 ‘70(API Technical Data Book, 1978). To increase the accuracy of the API Data Book nomograph (1966), expand its range of usefulness, and provide an analytical expression for computer applications, Abbott et al. (1970, 1971) developed correlations to predict viscosities at 210 and 100 OF. The results from these correlations are superior to those obtained from the API Data Book nomograph (1966) when compared over the same validity range. However, while the correlations of Abbott et al. are more accurate and extend the range of application, they suffer from some serious shortcomings. The first is inconsistency. There is an interrelationship between viscosities at 210 and 100 OF. However, Abbott et al. derived their correlations for the viscosities at these temperatures independently. This creates an inconsistency of predicted viscosities between these two temperatures. The second is irregularity. For example, at the same value of the Watson characterization factor, ( K ) , the calculated viscosities vary irregularly with the API gravity. The third and most serious is singularity. There is a region where the calculated viscosity tends to infinity and then drops to essentially zero with a small change of specific gravity. This rapid change in the viscosity will certainly create major disturbances in any process simulation. This 0 1985 American Chemical Society
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shortcoming also reveals that the mathematical model of Abbott et al. is inadequate to describe the viscosity behavior over the entire range of practical interest. Finally, the correlations are unable to extrapolate smoothly into the regions where no experimental data are available. Smooth extrapolation is an important consideration in process simulation. In this paper, the scheme of developing an internally consistent correlation to improve accuracy and to cover the entire range of practical interest in terms of measurable properties of petroleum fractions will be presented.
Perturbation Expansion for Viscosity The properties of a real system can be expanded about the values for a reference system. In this work, the property of interest is kinematic viscosity. The real system is petroleum fractions, and the reference system is chosen as n-alkanes. Expanding the property g in the form of a Taylor series gives g = go + g1 + gz + ...
(1)
where gois the reference system values, g, is the first-order perturbation term, and so on. For the purpose of correlating properties, various forms of eq 1can be used. One of the best known rearrangements of perturbation expansion for Helmholtz free energy is the Pade approximant (Stell et al., 1972,1974). The Pade approximant has been found to be accurate and rapidly convergent even for strong intermolecular forces (Gubbins and Twu, 1978; Twu and Gubbins, 1978). At this juncture, we select a simple form of the perturbation expansion to suit our needs for correlating viscosities of petroleum fractions. To ensure that all correlated viscosities predicted will be positive under extreme conditions, in addition to the consideration of fast convergence, a special resummation of eq 1 is proposed 1+2f g=go(l-2f) where f is defined such that when g equals go,f is equal to zero. Since 210 and 100 O F are two standard temperatures for assay inspection data and are also commonly used as temperatures for viscosity specifications on petroleum products, the viscosities at these two temperatures are selected and correlated as a function of boiling point and specific gravity. The correlations for viscosities at 210 and 100 OF of real systems are viscosity a t 210
O F
viscosity a t 100 O
F
For petroleum fractions ASG = SG - SG"
For pure components ASG = 6( 1 + 2 h 1 - 2h
-)
h = (-21.6364
+ 844.687/Tb1l2)6(458.199 - 7543.00/Tb'/2)62 (10)
6 = (SG - SG0)(1.49546- SG)
(11)
where v2 and v1 are kinematic viscosities of the petroleum fraction or pure component in centistokes at 210 and 100 OF, respectively. Tband SG are the average boiling point in degrees Rankine and the specific gravity of the petroleum fraction or pure component, respectively. u Z o , vlo, and SGO are evaluated from hypothetical n-alkanes of the same average boiling point as the system of interest. The numeric value of 450 is assigned in eq 3 and 6 to ensure that the argument of the logarithmic function is always greater than unity so that the calculated viscosity after taking the logarithmic function is always greater than zero. x in eq 5 indicates that the absolute value of x is taken (the reason will be explained later). The average boiling point is used here for petroleum fractions. From a practical point of view, the precise definition of the type of boiling point (mean average, molar average, etc.) used in the calculation is not important for narrow boiling cuts, since all boiling points become equal as the boiling range approaches a single temperature. Due to the complex nature of petroleum fractions, their viscosities behave differently from those of pure components. To take this difference into account, ASG appearing in eq 4 and 7 for petroleum fractions is treated differently from that for pure components. ASG in eq 9 is for pure components. However, a simpler equation of ASG in eq 8 is sufficient for petroleum fractions. It is worth noting that not all the constants used in correlations for predicting viscosities at 210 and 100 OF are independent. Although there are six constants used in eq 4 and 7, only four of them are independent. For example, only one constant is required to represent the behavior of viscosity a t 100 O F after knowing the viscosity at 210 OF. Wright (1956) showed the kinematic viscosities at 210 OF are related to kinematic viscosities at 100 OF by a simple equation involving only one constant. Although Wright's equation is too simple to cover the entire range of viscosity, his conclusion is confirmed by the correlation in this work. Correlation of the Viscosity of Normal Alkanes It is advantageous to choose the family of n-alkanes as a reference for correlating the properties of petroleum fractions rather than spherical molecules because the convergence of any perturbation expansion depends on the choice of the reference system. The closer the system of interest is to the reference system, the more rapidly convergent the expansion will be. For this reason, the n-alkanes are chosen as the reference system in this work. Careful analysis of the kinematic viscosity data given in API Technical Data Book (1978) and API 42 (1962) indicates that the kinematic viscosity at 210 and 100 OF for normal paraffins can be correlated to a high degree of accuracy as a function of the normal boiling point as follows: In (vzo + 1.5) = 4.73227 - 27.0975~~ + 4 9 . 4 4 9 1 ~- ~5 ~0 . 4 7 0 6 ~(12) ~~ In (vl0) = 0.801621 + 1.37179 In (vzo) (13) CY = 1 - Tb/Tco (14) Tco = T b (0.533272 + 0.191017 x w 3 T b + 0.779681 x 10-7Tb2- 0.284376 X lO-loTb3+ 0.959468 X1028/Tb13)-1 (15)
Ind. Eng. Cham. Process Des. Dev., Vol. 24, No. 4, 1985
where v20 and vl0 are the kinematic viscosities of n-alkanes in centistokes at 210 and 100 OF, respectively. Tbis the normal boiling point in degrees Rankine and superscript O denotes correlations specific to the n-alkanes. Equation 15 represents the critical temperature of the C1-Cloo normal alkanes as given by Twu (1983, 1984). Since v20 and ul0 are interrelated by eq 12 and 13, the kinematic viscosity data of n-alkanes at 210 and 100 OF are used simultaneously in multiproperty regression analysis to derive the optimum constants shown in eq 12 and 13. The uncertainties of the data in the tabulations in the API Technical Data Book (1978) and API 42 (1962) can only be assessed from the number of significant figures reported. An assignment of about 3% to the accuracy of the data for n-alkanes is reasonable. Equations 12 and 13 give u20 and vl0 values that are very close to the literature data (API Technical Data Book, 1978; API 42, 1962) up to n-tetratetracontane (n-C,,HSO). No experimental viscosity data are available for n-alkanes beyond n-tetratetracontane. A modification is introduced to extend the correlation to n-hectane (C1,H202). The extrapolation is not based on experimental evidence. Rather, an attempt is made to extrapolate from the plot of In In (vo + 0.7) against the reciprocal of absolute boiling point temperature as suggested by Rumpf (1967). The smooth viscosity curves of n-alkanes are plotted in Figures 1and 2. The average absolute deviations between the calculated and experimental viscosities for the n-alkanes are 0.45% for vZ0 and 0.62% for vl0. The specific gravity of n-alkanes, SGO, is a useful property and will be used in this work. The analytic expression for the specific gravity of n-alkanes is given by Twu (1983, 1984): SGo = 0.843593 - 0.128624~~ - 3 . 3 6 1 5 9 ~-~13749.5~~'~ ~ (16) Viscosity at Any Desired Temperature The ASTM viscosity-temperature chart (1981) is presently accepted as an industrywide standard for representing petroleum-fraction viscosity-temperature behavior. Viscosities at any two temperatures can be plotted on the ASTM chart to interpolate or extrapolate to other temperatures. These charts allow linear representation of the variation of petroleum fraction viscosity with temperature. The generalized relationship has been developed by Wright (1969) and is given as In In Z = A + B In T (17) Z =v v =Z
+ 0.7 + exp(-1.47
- 1 . 8 4 ~- 0 . 5 1 ~ ~ ) (18)
- 0.7 - exp[-0.7487 - 3.295(2 - 0.7) + 0.6119(2 - 0.7)' - 0.3193(2 - 0.7)3] (19)
where T i s the absolute temperature in degrees Rankine and v is kinematic viscosity in centistokes at temperature T. If the kinematic viscosity exceeds 2 cSt, the exponential terms of eq 18 and 19 become insignificant and Z = v 0.7 (20) The constants A and B can be evaluated from viscosity data at two known temperature points. The kinematic viscosities at other temperatures are then readily calculated. If the viscosities at two temperatures, v1 at Tland u2 at T2, are known, there are two equations to be solved for B to give B = (In In Z1 - In In Z,)/(ln T1- In T2) (21)
+
Then, the viscosity v at any other temperature T can be determined by In In Z = In In Z1 + B(ln T - In T I ) (22)
1289
where Z1 and Z 2 are obtained from eq 18 by replacing v with v1 and v2, respectively. After obtaining Z at T from eq 22, v can be calculated from eq 19.
Results Equations 3-11 and 17-22 are used to regress the viscosity data of both pure components and petroleum fractions simultaneously. The kinematic viscosity data of pure components with carbon number from C5 to Cu are taken from API Technical Data Book (1978) and API 42 (1962). The component types include n-paraffins, monoolefins. n-Alkylcyclopentanes,n-alkylcyclohexanes,n-alkylbenzenes, and alkylnaphthalenes. Although a large quantity of petroleum fraction viscosity data is available in the literature, only a few of these sources report average boiling point and specific gravity with the viscosity data. The following papers are selected for this study: Watson et al. (1935) who reported a wide variety of petroleum fractions including typical distillates, a reduced crude, Pennsylvanialube oil, and cracked residue; FitzSimons and Thiele (1935) who presented cuts from pressure distillate, cycle stock, pressure tar, gas oil, Virgin Midcontinent naphtha cut, kerosene cut, and paraffin distillate; Mithoff et al. (1941) who reported cuts from California crude oil; Cauley and Delgass (1946) who reported catalytically cracked fuel oil; Watkins (1979) who reported Tia Juana Light crude assay data, and Amin and Maddox (1980) who reported many kinds of crudes including Pennsylvania, California, Wyoming, Oklahoma,Minas, Safaniya, Arabian crude, Boscan, Brass River, Waxy, Light Valley, and Midway Special. A total of 563 data points of pure components and petroleum fractions are used in the regression. The boiling points and specific gravities of these data vary from 580 to 1778 OR and from 0.63 to 1.11, respectively, while the viscosities at 210 O F range from 0.25 to 290 cSt and at 100 OF from 0.33 to 1750 cSt. One should point out that, in general, the accuracy and the internal consistency of the data assembled are not entirely satisfactory. A realistic estimate of the accuracy of the data quoted is 5-15% and probably much worse for the very heavy fractions. Only a minimum number of constants are required to give an accurate representation of viscosity property. For example, only 4 constants are required for predicting viscosities of petroleum fractions in this work compared with 20 constants used in the correlations of Abbott et al. (1970, 1971). As stated previously, one of the major shortcomings of the API nomograph is its limited range of applicability and the graph-reading errors from the nomograph. We cannot make a point-by-point comparison between the correlation in this work and the API nomograph. However, Abbott et al. (1970, 1971) have proved that their correlations are superior to the API Data Book nomograph (1966). For this reason, the correlation of Abbott et al. (1970, 1971) is selected for comparison. Table I gives a comparison between this work and Abbott et al. (1970, 1971) for the calculation of kinematic viscosity. During the comparison, the shortcomings of the Abbott correlations become evident. For example, one of the data points from Watson et al. (1935) is Tb= 1219.67 O R , SG = 1.1124, v2 = 29 cSt, and vl = 1750 cSt. The calculated values from Abbott are v2 = 8.98 and v1 = 0.484 x lo4' cSt. Since the calculated value of v1 from Abbott approaches infinity, the deviation in viscosity is extremely large. This is a good example to show the singularity, inconsistency, and irregularity of the Abbott correlations. If this point is excluded from the calculation, the average absolute deviation percent (AAD% ) in viscosity from Abbott is only 11.98% for petroleum fractions which is
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Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Figure
superior to that of the API nomograph. The AAD% between the experimental and calculated viscosities of petroleum fractions is 8.53% for the new correlation in this work. The agreement is excellent overall, especially when the data themselves can only be considered accurate to within about 5 1 5 % . The result also shows that errors in predictions at 210 O F are generally of the same magnitude and sign as errors at 100 O F on the same data point. This is also desirable when employing a two data point ex-
trapolation procedure such as the ASTM charts, as gross magnification of errors is less likely to occur. Equations 3-11 presume that Tband SG are known. However, in many cases, SG may not be available, but kinematic viscosity is. In such cases, eq 3 or 6 may be solved for SG by using the viscosity data. Subsequently, SG may be used to calculate viscosities at other temperatures. It is worth emphasizing that the correlations developed here are designed such that they can be solved for
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 1291
API GRAVITY
Figure 2. Kinematic viscosity a t 100 O F as a function of API gravity and Watson characterization factor K.
SG by giving Tb and viscosity. Equations 3 or 6 may be reduced to quadratic equations in terms of ASG. aASG2 + bASG + c = 0 (23) Then
ASG =
-b f (b2- 4ac)lI2 2a
(24)
Equation 24 possesses two ASG roots. To have physical significance,the value of b in eq 24 must be always positive or always negative over the entire range of boiling point temperatures. It is for this reason that eq 5 must take the absolute value. By means of this procedure, the developed correlations between Viscosity, Tb,and SG are also justified. Another necessary test of the correlations is to plot dependent variables as a function of independent variables over the entire range of conditions to ensure that all curves
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Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table I. Comparisons between Actual and Calculated Kinematic Viscosities AAD 9c Abbott et system temp, O F no. of pts al. this work pure component 210 107 18.01 5.63 112 20.99 7.87 100 tot 219 19.53 6.77 petroleum fraction 210 83 12.78 10.14 100 138 16.70 10.66 others 123 6.15 5.06 tot 344 11.98 8.53 pure component + 210 190 15.72 7.60 petroleum fraction 18.62 9.41 100 250 others 123 6.15 5.06 7.85 563 14.92 tot
are smooth with no irregularity. The correlations of Abbott et al. (1970, 1971) fail this test. The new correlations for viscosities of petroleum fractions at 210 and 100 O F are plotted in Figures 1 and 2. These figures give kinematic viscosity a t 210 and 100 OF as a function of API gravity and the Watson characterization factor ( K ) . The value of Watson K ranges from 8 to 14 in intervals of 0.5 and the API gravity from -30 to 110. The dash-dot-dashed lines are the values of n-alkanes, and the dashed lines are the values of constant boiling point a t 600 or 1800 OR as marked in the figures. The units used for kinematic viscosity are centistokes. These figures show that all curves are smooth functions of Watson K and API gravity. They also reveal that the slope of viscosity at constant Watson K increases with API gravity. It is interesting to note that the kinematic viscosity of petroleum fractions with the same boiling point increases and then decreases with API gravity. It has long been recognized that for hydrocarbons of the same boiling point, the specific gravity increases in the order of paraffins, naphthenes, and aromatics. However, the viscosity a t the same boiling point increases in the order of aromatics, paraffins, and naphthenes. The accuracy given in Table I and the plots with no irregularity over the entire range of interest shown in the figures demonstrate that the new correlation not only extends substantially the range of applicability but improves significantly the accuracy of predicting viscosity of petroleum fractions. The correlation gives the best overall accuracy for the cuts of typical petroleum fractions. The usual viscosity range of these petroleum fractions is given in the example that follows. For the region where no data are available, a reasonable viscosity should be obtained because the predicted variation of viscosity with API and Watson K is qualitatively correct. Example. To further clarify the method, we now present a sample calculation for the kinematic viscosities of a petroleum fraction. The calculation requires only average boiling point and specific gravity of this petroleum fraction as input. One data point at Tb = 1210.17 OR and SG = 0.8964 from Watkins (1979) is chosen for calculation in the example. The viscosities and specific gravity of the reference system are evaluated at the same boiling point as the petroleum fraction. From eq 12-16 SGo = 0.8044 v20
= 2.94 cSt
vl0 = 9.827 cSt
The specific gravity correction is obtained from eq 8
ASG = 0.0920
The kinetic viscosities of the petroleum fraction are readily calculated from eq 3-7 v 2 = 4.155 cSt v 1 = 24.26 cSt
To calculate viscosity at 150 O F rather than at the usual temperature of 210 or 100 O F , 2, and Z 2 should be evaluated first from eq 17 by replacing v with the values of v l and v 2 given above respectively. Z, = 24.96 a t T I = 559.67
O R
Z2 = 4.855 at T2 = 669.67
O R
The slope of the viscosity-temperature equation can then be obtained from eq 21
B = -3.963 After obtaining B, Z at 150 O F can be calculated from eq 22 Z = 9.896 at T = 609.67 "R
Finally 2 is converted to viscosity by using eq 19 v = 9.196 cSt at T = 609.67
O R
For comparison, the values from Watkins (1979) are ~2
= 4.15 cSt
v 1 = 24.7 cSt v = 9.40 cSt at T = 609.67
O R
Watkins (1979) reported Tia Juana Light crude assay data. These assay data cover the general viscosity range of usual petroleum fractions. There are 65 data points from Watkins (1979),with viscosities from 0.54 to 27 cSt at 210 O F and from 1.17 to 245 cSt at 100 OF. The average boiling point and specific gravities vary from about 810 to 1460 O R and from 0.78 to 0.94, respectively. The average absolute deviation percent (AAD%) between the calculated and experimental viscosities is 4.28% for viscosity for these 65 points. Conclusion A correlation using n-alkanes as a reference has been developed for estimating the liquid viscosities of petroleum fractions at all practical temperatures. This new correlation provides a method for the prediction of viscositytemperature behavior of petroleum fractions from the boiling point temperature and specific gravity. The proposed correlation substantially improves on the accuracy and significantly extends the range of applicability. The correlation presented here is the most accurate and consistent method examined for liquid viscosity prediction based on the normal boiling point and specific gravity. Acknowledgment
I thank Simulation Sciences Inc. for permission to publish this work. Nomenclature a, b, c = constants in the quadratic equation in eq 23 A , B = constants in viscosity temperature function in eq 17 API gravity = 141.5/SG - 131.5 exp = exponential function fl = function of boiling point and specific gravity used in calculation of viscosity at 100 O F in eq 7
Ind. Eng. Chem. Process Des. Dev. 1905, 24, 1293-1297
f 2 = function of boiling point and specific gravity used in
calculation of viscosity at 210 O F in eq 4 g, go,g,, g? = terms in Taylor series in eq 1 h = function of boiling point and specific gravity used in calculation of specific gravity correction for pure components, eq 10 K = Watson characterization factor = Tb1I3/sG In = logarithmic function, base e SG = specific gravity at 60 O F T = absolute temperature, O R Tb = normal boiling point, OR TI = 559.67 O R T2 = 669.67 OR x = function of normal boiling point defined in eq 5 Z = function of kinematic viscosity at temperature T 2, = function of kinematic viscosity at 100 OF Z2 = function of kinematic viscosity at 210 O F Greek Letters a = reduced normal boiling point defined in eq 14
6 = function of specific gravity defined in eq 11 ASG = specific gravity correction u = kinematic viscosity at temperature T, cSt u1 = kinematic viscosity at 100 O F , cSt u2 = kinematic viscosity at 210 O F , cSt
Superscripts O = n-alkanes property Subscripts c = critical property Literature Cited Abbott, M. M.; Kaufmann, T. G.; Domash, L. Can. J. Chem. Eng. 1971, 49, 379.
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Abbott, M. M.; Kaufmann, T. 0.; Domash. L. 67th National AIChE Meeting, Atlanta, Ga, Feb 15-18, 1970. American Society for Testing and Materlal (ASTM) "1981 Annual Book of ASTM Standards"; ASTM: Philadelphia, PA, 1981; Part 23, p 205. Amin, M. B.; Maddox, R. N. Hydrocarbon Process 1980, 59 (12), 131. API "Properties of Hydrocarbons of High Molecular Weight"; American Petroleum Instltute: New York, 1962 Reserach Project 42. API "Technical Data Book-Petroleum Refining"; American Petroleum Institute: New York, 1978. API "Technical Data Book-Petroleum Refining"; American Petroleum Institute: New York, 1966. Baltatu, M. E. Ind. Eng. Chem. Process Des. D e v . 1982, 27, 192. Cauley, S. P.; Deglass, E. B. Oil Gas J. 1948, 45, 166. Ely, J. F.; Hanley, H. J. M. Ind. Eng. Chem. Fundam. 1981, 20 (4), 323. FttzSimons, 0.; Thlele, E. W. Ind. Eng. Chem. 1935, 7 (I), 11. Gubbins. K. E.; Twu, C. H. Chem. Eng. Sci. 1978, 33,863. Haile, J. M.; Mo, K. C.; Gubbins, K. E. Adw. Cryog. Eng. 1978, 27, 501. Hanley, H. J. M. Cryogenics 1978, 76 ( I l ) , 643. Mithoff, R. C.; MacPherson, 0. R.; Slpos, F. OilGas J. 1941, 40, 81. Ma, K. C.; Gubblns, K. E. Mol. Phys. 1976, 31, 825. Pederson, K. C.; Fredenslund, A.; Christensen, P. L.; Thomassen, P. Chem. Eng. Sci. 1984, 39, 1011. ReM, R. C.; Prausnttz, J. M.; Sherwood, T. K. "The Properties of Gases and LiquMs", 3rd ed.;McGraw-Hill: New York, 1977. Rumpf, V. K. K. ErdollKohle, Erdgas, Petrochem. 1987, 2 0 , 276. Stell, G.; Rasalah, J. C.; Narang, H. Mol. Phys. 1972, 23 (2), 393. Stell, G.; Rasaiah, J. C.; Narang, H. Mol. Phys. 1974, 27(5), 1393. Tham, M. J.; Gubblns, K. E. Ind. Eng. Chem. Fundam. 1970, 9 ( l ) , 63. Twu, C. H. fluid Phase Equilib. 1983, 7 7 (I), 65. Twu, C. H. fluH Phase Equilib. 1984, 76 (2), 137. Twu, C. H.; Gubblns, K. E. Chem. Eng. Sci. 1978, 33, 879. Watkins, R. N. "Petroleum Refinery Distillation"; Gulf Publishing Co.: Houston, 1979. Watson, K. M.; Nelson, E. F.; Murphy, G. 8. Ind. Eng. Chem. 1935, 27(12), 1460. Wright, W. A. J. Mater. 1969, 4(1), 19. Wright, W. A. ASTM Bull. 1956, No. 215, 84.
Received for review June 25, 1984 Revised manuscript received December 31, 1984 Accepted March 25, 1985
COMMUNICATIONS Kinetics of Formation of Triphenyl Phosphate: Phase-Transfer Catalysis in a Liquid-Liquid System Kinetics of reaction of diphenyl chlorophosphate with sodium phenolate to give triphenyl phosphate, in an organic-aqueous two-phase system, catalyzed by a variety of phase transfer catalysts, was studied. The reaction occurs in the organic phase and diffusional factors were found to be important. The reactlon was found to be first order in the concentration of diphenyl chlorophosphate and the phase-transfer catalyst (Aliquat 336). The hydrodynamic factors were found to be unimportant and the system conformed to the fast-pseubflrstader reaction regime. Aliquat 336 gave the highest rate of extraction among the catalysts studied. I t was observed that an Aliquat 336 concentration of 1.42 X mol/cm3 organic phase enhanced the rate of extraction by a factor of
90.
Introduction Triaryl phosphates, namely, triphenyl phosphate, tricresyl phosphate, etc., find a variety of industrial applications. They are widely used as plasticizers for PVC, cellulose acetate, etc., as high-pressure additives for lubricating oils and as base stocks for formulating industrial fire resistant hydraulic fluids. Commercially triaryl phosphates are manufactured by reacting stoichiometric quantities of the hydroxyaryl compound and phosphoryl chloride at 160-250 "C in the presence of catalytic amounts of anhydrous A1C13 or MgC12. This process has some inherent drawbacks, namely, corrosion in industrial reactors OI96-4305/85/1 I24-1293$01.5O/O
due to hydrogen chloride liberation, byproduct formation, and discoloration of the product due to the high temperatures employed. Recently we have reported a novel two-phase synthesis of triaryl phosphates at ambient conditions employing phase-transfer catalysis (Krishnakumar and Sharma, 1983; Krishnakumar, 1984). This process gave nearly quantitative yields of the relevant phosphates and has a number of advantages over the conventional process. This method involves reacting an aqueous solution of the sodium salt of the hydroxyaryl compound with phosphoryl chloride dissolved in an organic solvent such as chloroform in a two-phase system and uses 0 1985 American Chemical Society
