Ind. Eng. Chem. Res. 1988,27, 523-527
Literature Cited Beggs, J. D.; Robinson, J. R. J. Pet. Technol. 1975, 27, 1140. Jha, K. N. J. Can. Pet. Technol. 1986,25, 54. Jha, K.N.; Verma, A, Paper presented at the 11 International Conference on Heavy Crude and Tar Sands, Caracas, Venezuala, 1982. Mehrotra, A. K.; Svrcek, W. Y. J. Can. Pet. Technol. 1982,21, 95. Miller, J. S.; Jones, R. A. Paper presented at the Second SPE/DOE Joint Symposium on Enhanced Oil Recovery, Tulsa, OK, April 1981.
523
Peng, D.-Y.; Wu, R. S.; Batycky, J. P. AOSTRA J. Res. 1987,3, 113. Quail, B., unpublished data, University of Saskatchewan, Saskatoon, Saskatchewan, 1985. G*G*Canada-Venezuda Oil Sands Symposium Proceedings 1977, Edmonton, p 284.
Received for review March 23, 1987 Revised manuscript received Octqber 20, 1987 Accepted November 2, 1987
Consistency and Extension of Experimental Vapor Pressure and Heat of Vaporization Data Judith Nyerick Dickson and Thomas E. Daubert* Department of Chemical Engineering, 133 Fenske Lab, The Pennsylvania State University, University Park, Pennsylvania 16802
Rigid demands for increased accuracy in physical and thermodynamic property data have led to a method by which experimental data can be compared with other members of the same family for consistency. By regression of experimental vapor pressure data from the normal members of a family, a generalized equation, based only on temperature and carbon number, can be used at the normal boiling point to determine an effective carbon number for each family member. The ECN so derived can be used for prediction of vapor pressure a t other temperatures and for other thermodynamic properties using a regression equation developed for the property from normal members. Vapor pressure and heat of vaporization have been studied extensively. Aliphatic hydrocarbons, alcohols, aliphatic acids, and acetates have been used as example families. The method has also been applied to ideal gas and liquid heat capacity, viscosity, and thermal conductivity. The main objective of this research (Nyerick, 1986) was to evaluate the effective carbon number (ECN) as a unifying parameter for data qualification. The effective carbon number is a nonintegral number assigned to unsaturated and branched members of a particular family. The theory behind the effective carbon number is based on the fact that a curvilinear relationship exists between the normal boiling point (NBP) and the straight-chain members of a homologous series. From this relationship, an effective carbon number can be determined for branched and unsaturated members of a family of compounds (Ambrose and Sprake, 1970). Chase (1984) showed the utility of ECN for a variety of property analyses. Willman and Teja (1985)used effective carbon number in a Wagner-type equation for predicting vapor pressure for hydrocarbons. The effective carbon number unifies the members of a particular family, tends to eliminate the contributions of various functional group contributions to physical properties, and focuses on the effect of branching or unsaturated bonds. By applying this approach, the correspondence between molecular structure and physical properties can, therefore, be more closely examined. The intent of this study was to continue to expand the work of Ambrose and Sprake (1970) to other families of compounds and other temperature-dependent properties using the effective carbon number determined from vapor pressure data as the qualifying parameter. The aim was not to develop new predictive equations but to qualify homologous series data and gain insight into the structural relationships within a family. Statistical regression was used to determine the effective carbon number for each member of four chosen families from vapor pressure data. The selected families are by no means exclusive; they have been selected to study and to demonstrate the method of correlating generalized property equations. In much the same manner as the gener0888-5885/88/2627-0523$01.50/0
alized vapor pressure equation was determined, a regression equation for heat of vaporization was recommended, derived, and evaluated.
Development of the Model Ambrose and Sprake (1970), noting a curvilinear relationship between the normal boiling point and carbon number and a linear relationship among the logarithm of the vapor pressure at a given temperature and carbon number for members of a homologous series, recognized the value of a generalized vapor pressure equation. On the basis of the Cragoe vapor pressure equation, l o g P = A + B / T C T + DT2 (1)
+
where P = pressure, T = temperature, and A-D = regression constants, Ambrose and Sprake (1970) modified eq 1 to incorporate carbon number as a parameter by introducing a linear dependence through the constants log P = ( A ’ + B’n) (C’+D’n)/T + (E’+ F’n) (C’+H’n)T2 ( 2 ) where P = pressure, T = temperature, n = carbon number, and A‘-H’= regression coefficients. By regressing the eight coefficientsin eq 2 using vapor preasure data for n-alcohols, Ambrose and Sprake (1970) previously regressed this equation for alcohols log P = 17.5832 0.96958~1(3175.08 + 346.908n)/T - (1.99352 X + 1.24927 X 10-3n)T + (1.02395 X 6.50235 X 10-7n)T2 (3) where P = pressure in kilopascals, T = temperature in kelvin, and n = carbon number. The n-alcohols used in the regression were assigned integral carbon numbers equivalent to the number of carbon atoms present in each molecule. An effective carbon number for branched and unsaturated alcohols could be determined by evaluating eq 3 at the normal boiling point. Once the effective carbon
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0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 3, 1988
524
Table I. Representative Families
normal members
aliph. hydrocarbons CH3(CHdnCH3
nb
0-18
other members'
RH
aliph. acids CH,(CHZ),C(=O)OH 0-17 RC(=O)OH
alcohols CH3(CHz),OH 0-19 ROH
acetates CH&(=O)O(CHz),CH, 0-4
RO(=O)CCH,
Aliph. = aliphatic. * n = the number of CH2 groups and is greater than or equal to 0. 'R = any branched alkyl chain.
'ca
c?
8
Q
8
Q
o
-L,L
-
q
2 k
c
-4 0
2
6
4
8
EFFECTIVE
10
18
16
14
12
CARBON NUMBER
Figure 3. Vapor pressure of aliphatic acids. 13
I i ,
t
L
I
,.
I
I
~
~
I
i
y3
5 L
t
7t
; e -
-
?
a
' 5
-'
I 3
1-
L r
i
I
1
0
a
I
11
t
3 Y
3 0
a
I
i i
i
I
I
Ind. Eng. Chem. Res., Vol. 27, No. 3, 1988 525
1
0 $ 0 :
0
8
0
1
8
0
0 0
0
0
0
0
IJ 430O t
w 2.1
=
IO 20
1
2
4
6 8 10 12 14 EFFECTIVE CARBON NUMBER
16
18
1
2
0
0
1
1 4
20
1 1 1 1 1 I 1 I I " ( 6 8 10 12 14 EFFECTIVE CARBON NUMBER
I
16
1
1
20
I8
Figure 6. Heat of vaporization of alcohols.
Figure 5. Heat of vaporization of paraffins.
of a methyl group in any position on a chain is approximately additive. This relationship is displayed below. ECN isobutane isopentane 2-methylpentane 2-methylhexane 2-methylheptane 3-methylheptane 4-methylheptane 2-methyloctane
!
3.710 4.784 5.768 6.765 7.773 7.822 7.775 8.788
0
0
70
The addition of a methyl group caused approximately eighbtenths of a carbon number to be added to the integral carbon number of the normal homologue. Study of the effect of the position of the methyl group on the chain has been hampered as limited experimental data are available. The addition of a methyl group and an ethyl group to a straight chain has the sum total of the effect of each group added individually as illustrated below.
i 525
ECN
(1) 3-ethylpentane 6.886 ethyl group 5.768 methyl group (2) 2-methylpentane (3) 2-methyl-3-ethylpentane 7.697 ethyl and methyl group total of (1) and (2) group contributions
-
IO L
A(ECN)
1
1.885 0.768 2.697 0
2.653
Insufficient data preclude determination of the additivity relationships of the effective carbon number for alcohols, aliphatic acids, and acetates. However, it is obvious that a more complicated relationship exists for these families due to the effect of the functional group. In a previous study, Ambrose (1976) determined the effective carbon numbers for alcohols by means of structural relationships. Although the observation of specific trends was hampered by a limited amount of published experimental data, a few generalities, common to all famiIies undertaken in this study, have been recognized. The presence of branching or of unsaturated bonds in a molecule makes the molecule more compact and therefore decreases the effective carbon number. This effect seems to diminish as the length of the normal homologue increases. This effect also seems to be more pronounced when the branching or unsaturated bond is positioned at the end of the molecule. Cyclic compounds have a larger effective carbon number relative to their normal homologues. This can be explained by the increase in steric interaction. Generalities such as these can lead to greater insight into the effects that structural relationships of molecules have on physical properties, eventually allowing better predictive qualities.
> 3
3
0 3 0
27 5
30
35
40
45
5 0 55 6 0 6 5 7 0 7 5 EFFECTIVE CARBON NUMBER
BO
8 5
90
Figure 8. Heat of vaporization of acetates.
Once the effective carbon number has been calculated for a given compound, it is postulated that this value remains constant and can then be used as the correlating parameter for other temperature-dependent properties. A linear relationship was observed between the effective carbon numbers determined from the vapor pressure correlating equation and heat of vaporization (HVP) data at a constant temperature. This relationship is shown for the four families studied in Figures 5-8. In much the same way that Ambrose and Sprake (1970) altered the equation of Cragoe to incorporate a linear dependence on carbon number, the equation HVP = A !( 1 - Tr) [B"+C"Tr+D"T,2+E"T,S] (4)
526 Ind. Eng. Chem. Res., Vol. 27, No. 3, 1988 Table IV. Evaluation of Equation 2 for Prediction of Vapor Pressure normal boiling point entire range max % av % av % max % error error error error 6.93 4.28 n-paraffins 12.76 8.46 1.79 0.44 isoparaffins 8.98 7.09 0.63 0.13 14.57 7.65 cycloparaffins 0.72 0.13 8.09 6.65 other paraffins 2.45 0.46 1-olefins 13.48 7.28 4.22 0.33 14.38 8.28 other olefins 0.59 0.16 14.04 11.31 diolefins 2.04 0.64 31.54 20.23 acetylenes all hydrocarbons 6.93 0.81 31.54 8.23 27.13 10.80 20.21 11.15 n-alcohols 3.01 0.78 21.91 10.72 other alcohols 27.13 21.91 10.88 4.62 all alcohols n-aliph. acids 16.14 8.56 28.12 14.74 3.75 1.45 25.96 13.59 other aliph. acids 16.14 5.83 28.12 14.30 all aliph. acids n-acetates 9.88 4.65 7.61 5.35 3.44 1.50 7.50 4.54 other acetates 9.88 2.81 7.61 4.91 all acetates
where TI= reduced temperature and A ‘-E’ I = regression constants, was changed to HVP = (A’’’ B%) X (1 - ~ ~ ) [ ~ C ” ’ + ~ ” ’ n ~ + ~ E ” ’ + P ” n ~ T , + ~ G ” ’ + ~ ” ’ n ~(5) T~+~I”’+S”n~T~ where T, = reduced temperature, n = carbon number, and A”‘-J“‘ = regression constants. Equation 4 is the recommended correlating equation selected by the AIChE DIPPR (Design Institute for Physical Property Data) Project to statistically regress heat of vaporization data for individual compounds. Because of the form of eq 5, a nonlinear least-squares search method is required to determine the coefficients. Only experimental heat of vaporization data for the normal members of each family were used, and again, care was taken to ensure that each member had an equal contribution to the regression. A Marquardt search method was selected to determine the coefficients of eq 5 because this search method converged most consistently. Table I11 presents the heat of vaporization correlation coefficientsfor the four families studied.
+
Results In order to evaluate the overall predictive ability of the vapor pressure and heat of vaporization general property equations, errors were calculated at the normal boiling point (NBP) and at five reduced temperatures (TI= 0.5, 0.6, 0.7, 0.8, and 0.9). The errors determined at the five reduced temperatures were averaged. The error at the normal boiling point was instrumental in evaluating the fit of the experimental data of the regression equation because the effective carbon number was determined at the normal boiling point. The errors in vapor pressure for the normal members of each family are higher than for the other members of the family as the normal members retain the integral values for the effective carbon numbers rather than being assigned the decimal numbers as determined from the regression equation for the remaining members of the family. Tables IV and V illustrate the summary of errors of vapor pressure and heat of vaporization, respectively, for the four families undertaken in this study. The generalized equations were able to predict vapor pressure with an average overall error of 8.2% for hydrocarbons, 10.9% for alcohols, 4.9% for acetates, and 14.3% for aliphatic acids. The equation for heat of vaporization was able to predict
Ind. Eng. Chem. Res. 1988,27,527-536
527
Table V. Evaluation of Equation 5 for Prediction of Heat of Vaporization normal boiling point entire range max % av % max % av 70 error error error error n-paraffins 3.41 2.85 1.34 1.19 1.10 isoparaffins 1.55 0.77 1.60 cycloparaffins 11.59 6.26 13.74 7.08 other paraffins 9.61 3.37 10.02 3.56 1-olefins 8.41 2.38 8.71 2.64 8.50 other olefins 2.32 9.88 3.02 diolefins 4.74 2.84 9.33 5.14 acetylenes 8.95 7.88 4.24 3.95 all hydrocarbons 11.59 3.15 13.74 3.67 n-alcohols 7.12 3.14 4.43 3.40 other alcohols 24.47 4.65 27.07 5.80 all alcohols 24.47 4.07 27.07 4.88 n-aliph. acids 17.98 5.47 19.52 8.19 other aliph. acids 21.40 8.39 27.28 9.98 all aliph. acids 21.40 6.52 27.28 8.83 n-acetates 0.93 0.42 1.56 0.84 other acetates 3.31 1.80 3.75 2.74 all acetates 3.31 1.23 3.75 1.95
the accuracy of data compilation sources. Large errors for individual compounds signal the need to reexamine predictive methods and to reevaluate experimental data. The equations, based only on temperature and effective carbon number, allow prediction of properties for families of compounds whose effective carbon number can be determined by structural relationships and for which experimental data are not available or predictive methods are not usable or are questionable. The effective carbon number is a unifying qualification parameter for temperature-dependent properties. Its study provides insight into the effect that changing the molecular structure of a compound has on physical thermodynamic properties. Further work has been completed on extension of the method to viscosity and thermal conductivity (Ibrahim, 1987).
the average overall errors of 3.7% for hydrocarbons, 4.9% for alcohols, 8.8% for aliphatic acids, and 2.0% for acetates.
Ambrose, D. National Physics Lab Report Chemical No. 57, Dec 1976; Middlesex, England. Ambrose, D.; Sprake, C. H. S. J. Chem. Thermodyn. 1970, 2, 631-645. Chase, J. D. Chem. Eng. Prog. 1984, 80(4), 63. Daubert, T. E.; Danner, R. P. Data Compilation: Tables of Properties of Pure Compounds; AIChE: New York, extant 1985. Ibrahim, S. M.S. Thesis, The Pennsylvania State University, University Park, 1987. Nyerick, J. A. M.S. Thesis, The Pennsylvania State University, University Park, 1986. Will", B.; Teja, A. S. Ind. Eng. Chem. Process Des. Dev. 1985,24, 1033.
Observations The method for determining general property equations can easily be extended to other temperature-dependent properties and other families of compounds as well. Nyerick (1986) successfully correlated both ideal gas heat capacity and liquid heat capacity by an effective carbon number method for the same families of compounds. Once determined, the equations can be used to check experimental data of all members in a family in order to increase
Acknowledgment Financial support for this study was provided by the sponsors of AIChE DIPPR Project 801-Data Compilation.
Literature Cited
Received for review March 26, 1987 Accepted October 15, 1987
Fluoride Distribution Coefficients in Wet Phosphoric Acid Processes Sietse van der Sluis, Annie H. M. Schrijver, Frits P. C. Baak, and Gerda M. van Rosmalen* Technical University of Delft, Faculty of Chemical Engineering, De Vries van Heystplantsoen 2,
2628 RZ Delft, The Netherlands
Phosphoric acid for use in fertilizer applications is mainly produced by digestion of phosphate ore, containing 2-4 wt % F, with sulfuric acid. During the digestion of the ore, the fluoride is released as hydrogen fluoride, which reacts with silica to produce fluorosilicic acid. Part of this acid decomposes in SiF4and HF, which on their turn partly evade into the air. These fluoride distribution coefficients were measured by saturation of a nitrogen gas stream passing through fluorosilicic acid dissolved in mixtures of distilled water, chemically pure phosphoric acid, and sulfuric acid a t various temperatures. A theoretical expression is derived, which allows calculation of the fluoride distribution coefficients between the acid and the ambient air between 70 and 95 "C, for solutions containing 30-50 wt % Pz05,up to 6 wt % H2S04,maximal 4 wt % H2SiF6,and a molar F/Si ratio of six. 1. Introduction The production of phosphoric acid is almost directly related to the world phosphate fertilizer consumption, which still tends to increase (Phosphoric Acid; Outline of the Industry, 1984). Phosphoric acid for use in fertilizer application is mainly produced by wet processes. In these processes the phosphate ore is digested by a mixture of sulfuric and phosphoric acids, and huge amounts of hydrated calcium sulfate are precipitated as a byproduct. The phosphate ore is mainly fluoroapatite (Calo(P04)6Fz) 0888-5885/88/2627-0527$01.50/0
with some additional compounds such as calcite, quarts, clay, etc. During digestion of the ore, the fluoride is released as hydrogen fluoride. The hydrogen fluoride reacts with the silica, present in the ore or added as a clay, to form fluorosilicic acid. Some of the fluorosilicic acid precipitates during the production process with sodium or potassium ions as Na2SiF6,K2SiF6,or NaKSiF, or as more complex compounds (Frazier et al., 1977). The remaining fluorosilicic acid in the phosphoric acid partly decomposes and 0 1988 American Chemical Society
