University of Southern California Dissertations and Theses

Predicting The Enthalpy Of Saturated Hydrocarbon Mixtures

(USC Thesis Other)

Predicting The Enthalpy Of Saturated Hydrocarbon Mixtures

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content PREDICTING THE ENTHALPY OF SATURATED
HYDROCARBON MIXTURES
by
Harry Kenneth Bishop
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Chemical Engineering)
September 1972
INFORMATION TO USERS
This dissertation was produced from a microfilm copy of the original document.
While the most advanced technological means to photograph and reproduce this
document have been used, the quality is heavily dependent upon the quality of
the original submitted.
The following explanation of techniques is provided to help you understand
markings or patterns which may appear on this reproduction.
1. The sign or "target" for pages apparently lacking from the document
photographed is "Missing Page(s)". If it was possible to obtain the
missing page(s) or section, they are spliced into the film along with
adjacent pages. This may have necessitated cutting thru an image and
duplicating adjacent pages to insure you complete continuity.
2. When an image on the film is obliterated w ith a large round black
mark, it is an indication that the photographer suspected that the
copy may have moved during exposure and thus cause a blurred
image. You will find a good image of the page in the adjacent frame.
3. When a map, drawing or chart, etc., was part of the material being
photographed the photographer followed a definite method in
"sectioning" the material. It is customary to begin photoing at the
upper left hand corner of a large sheet and to continue photoing from
left to right in equal sections with a small overlap. If necessary,
sectioning is continued again — beginning below the first row and
continuing on until complete.
4. The majority of users indicate that the textual content is of greatest
value, however, a somewhat higher quality reproduction could be
made from "photographs" if essential to the understanding of the
dissertation. Silver prints of "photographs" may be ordered at
additional charge by writing the Order Department, giving the catalog
number, title, author and specific pages you wish reproduced.
University Microfilms
300 North Zeeb Road
Ann Arbor, Michigan 48106
A Xerox Education Company
I
I
73-4905
BISHOP, Harry Kenneth, 1929-
PREDICTING THE ENTHALPY OF SATURATED
HYDROCARBON MIXTURES.
University of Southern California, Ph.D., 1972
Engineering, chemical
University Microfilms, A XEROX Company , Ann Arbor, Michigan
U N IVE R SITY OF SO U TH E R N CALIFO RNIA
TH E GRADUATE SCHOOL
U N IV E R S ITY PARK
LOS ANGELES. C A LIF O R N IA 9 0 0 0 7
This dissertation, written by
Harry Kenneth Bishop
under the direction of /ik§.... Dissertation Com
mittee, and approved by all its members, has
been presented to and accepted by The Graduate
School, in partial fulfillment of requirements of
the degree of
D O C T O R O F P H IL O S O P H Y
Date Septembg^ 1972
DISSERTATION COMMITTEE
PLEASE NOTE:
Some pages may have
indistinct print.
Filmed as received.
University Microfilms, A Xerox Education Company
ACKNOWLEDGMENTS
The author takes this opportunity to thank those
persons who were particularly helpful in the completion of
this work. First, I should like to thank the faculty and
staff at U.S.C. for their cooperation in making this re
search work possible.
Dr. J. M. Lenoir has been particularly helpful in
guiding and encouraging the development of this disserta
tion. Dr. F. J. Lockhart has added to the clarification
of the presentation by suggested amplification of some of
the concepts which are developed. Dr. R. C. Binder has
provided additional help and encouragement toward the
successful completion of this paper.
I also want to thank the members of my family for
their encouragement and support during the research and
preparation of this paper. In particular, I want to
acknowledge the loyal support of my wife over this entire
period.
ii
TABLE OP CONTENTS
Page
ACKNOWLEDGMENTS .......................................... ii
LIST OF FIGURES .......................................... v
LIST OF TABLES ............................................ viii
I. THE PROBLEM........................................ 1
II. PREVIOUS WORK...................................... 3
A. Sources of Enthalpy Data ..................... 3
B. Heat of Vaporization ......................... 3
C. Enthalpy of Mixed Hydrocarbons .............. 8
D. Cr icondentherm................................ 14
III. PREDICTING THE SATURATED LIQUID AND VAPOR
ENTHALPIES OF MULTICOMPONENT HYDROCARBON
MIXTURES ........................................... 17
A. Introduction ................................... 17
B. Mean Enthalpy Curves of Hydrocarbon
Mixtures ....................................... 18
C. Prediction of Mean Enthalpy Equation
Coefficients ................. 25
D. Heat of Vaporization ......................... 30
E. Prediction of Cricondentherm of Binary
Mixtures ....................................... 31
F. Prediction of Cricondentherm of Multi-
component Mixtures ........................... 36
IV. ENTHALPY PREDICTION ............................... 39
A. Enthalpy Prediction of Mixtures Containing
Aliphatic Hydrocarbons ....................... 39
Page
B. Enthalpy Prediction of Mixtures Containing
Aromatic Hydrocarbons ....................... 46
C. Enthalpies of Ternary Mixtures Containing
Aromatic Hydrocarbons ....................... 58
V. ACCURACY OF CALCULATED ENTHALPIES ............. 68
VI. CONCLUSIONS ...................................... 74
VII. REFERENCES ........................................ 76
APPENDICES ........................................... 80
A. Nomenclature ................................. 81
B. Calculated Enthalpy Values of a Pentane-
Cyclohexane-Benzene Mixture ................ 84
LIST OF FIGURES
Figure No. Page
1 Mean Enthalpy of Benzene-Pentane Mixtures . 19
2 Mean Enthalpy of Cyclohexane-Pentane
Mixtures ............................ ......... 20
3 Mean Enthalpy Curves for Mixtures of
Pentane, Cyclohexane and Benzene .......... 21
4 Mean Enthalpy Curves for Mixtures of
Methane in Propane .......................... 22
5 Mean Enthalpy Curves for Mixtures of
Saturated and Unsaturated Hydrocarbons .... 23
6 Variation of Cm/Cgc with Composition ...... 27
7 Variation of Tcc/Tsc with Composition ..... 32
8 Saturated Enthalpy Boundary for a Mixture
Containing 95 Mole % Methane in Propane ... 40
9 Saturated Enthalpy Boundary for a Mixture
Containing 23.4 Mole % Methane in Propane . 41
10 Saturated Enthalpy Boundary for a Mixture
Containing 49.4 Mole % Methane in Propane . 42
11 Saturated Enthalpy Boundary for a Mixture
Containing 58.7 Mole % Pentane in
Hexadecane ................................... 44
12 Saturated Enthalpy Boundary for a Mixture
Containing 79.4 Mole % Pentane in
Hexadecane ................................... 45
13 Saturated Enthalpy Boundary for a Mixture
Containing 43 Mole % Propane in Isopentane. 47
14 Saturated Enthalpy Boundary for a Mixture
Containing 18.6 Mole % Pentane in Benzene . 48
15 Saturated Enthalpy Boundary for a Mixture
Containing 40.0 Mole % Pentane in Benzene . 49
v
Figure No. Page
16 Saturated Enthalpy Boundary for a Mixture
Containing 59.3 Mole % Pentane in Benzene . 50
17 Saturated Enthalpy Boundary for a Mixture
Containing 80.1 Mole % Pentane in Benzene . 51
18 Saturated Enthalpy Boundary for a Mixture
Containing 7.0 Mole % Octane in Benzene ... 52
19 Saturated Enthalpy Boundary for a Mixture
Containing 14.3 Mole % Octane in Benzene .. 53
20 Saturated Enthalpy Boundary for a Mixture
Containing 22.9 Mole % Octane in Benzene .. 54
21 Saturated Enthalpy Boundary for a Mixture
Containing 32.4 Mole % Octane in Benzene .. 55
22 Saturated Enthalpy Boundary for a Mixture
Containing 55.4 Mole % Octane in Benzene .. 56
23 Saturated Enthalpy Boundary for a Mixture
Containing 72.9 Mole % Octane in Benzene .. 57
24 Saturated Enthalpy Boundary for a Mixture
Containing 18.8 Mole % Cyclohexane in
Benzene ........................................ 59
25 Saturated Enthalpy Boundary for a Mixture
Containing 38.7 Mole % Cyclohexane in
Benzene...................................... 60
26 Saturated Enthalpy Boundary for a Mixture
Containing 66.6 Mole % Cyclohexane in
Benzene ........................................ 61
27 Saturated Enthalpy Boundary for a Mixture
Containing 78.9 Mole % Cyclohexane in
Benzene ........................................ 62
28 Saturated Enthalpy Boundary for a Mixture
Containing 60.1 Mole % Pentane, 19.9 Mole %
Cyclohexane and 20.0 Mole % Benzene ........ 63
vi
Figure No. Page
29 Saturated Enthalpy Boundary for a Mixture
Containing 33.3 Mole % Pentane, 33.4 Mole %
Cyclohexane and 33.3 Mole % Benzene........ 64
30 Saturated Enthalpy Boundary for a Mixture
Containing 20.0 Mole % Pentane, 20.2 Mole %
Cyclohexane and 59.8 Mole % Benzene......... 65
31 Saturated Enthalpy Boundary for a Mixture
Containing 33.3 Mole % Benzene, 33.4 Mole %
Octane and 33.3 Mole % Tetralin.............. 66
32 Saturated Enthalpy Boundary for a Mixture
Containing 45.0 Mole % Benzene, 44.9 Mole %
Octane and 10.1 Mole % Tetralin............ 67
vii
LIST OF TABLES
Table Page
I Enthalpy Data Source ............................ 4
II Cr icondentherm Data Source ..................... 5
III Comparison of Predicted and Experimental Cri-
condentherms of Binary Mixtures ............... 35
IV Comparison of Predicted and Experimental Cri-
condentherms of Multicomponent Mixtures ...... 37
V Comparison of Predicted and Experimental Cri-
condentherms of Multicomponent Mixtures*
(Using Method of Etter and Kay and This Work). 38
VI Deviation of Calculated Enthalpies of Binary
Mixtures of Aliphatic Hydrocarbons ......... 70
VII Deviation of Calculated Enthalpies of Binary
Mixtures of Aliphatic, Naphthenic and
Aromatic Hydrocarbons .......................... 71
VIII Deviation of Calculated Enthalpies of Ternary
Mixtures of Aliphatic, Naphthenic and
Aromatic Hydrocarbons .......................... 73
viii
I. THE PROBLEM
The design of a modern plant employing chemical pro
cesses requires knowledge of the enthalpy of the materials
used. Processes involving hydrocarbons usually are con
cerned with saturated fluids. For example, in distillation
columns, absorbers and strippers, saturated fluids are al
ways encountered, and customarily, reboilers and condensers
deal only with bubble and dew point mixtures. Such pro
cesses require accurate enthalpy data along the locus of
the saturated vapor and liquid. This is especially im
portant with saturated liquids close to the critical point
where difficulty is often encountered in making enthalpy
predictions, particularly for mixtures where one or more
components may exist as a liquid above the critical condi
tions of the pure component.
Modern methods for evaluating enthalpy values em
ploy a complex equation of state (9,11,15,42,48,51,54,55,
53), requiring large amounts of computer time for program
evaluation. These equation of state methods predict en
thalpies at all conditions, and do not particularly identi
fy the circumstances where the dew and bubble points occur.
It is the purpose of this dissertation to develop
a procedure that will result: 1) in more simple, less
time consuming equations for evaluating the enthalpy of
2
mixtures of hydrocarbons either as saturated vapors or
saturated liquids, 2) be suitable for use in plant design,
and 3) be able to predict the enthalpy of saturated liquid
mixtures near the critical point. This procedure is re
stricted to the usually encountered saturated fluid states.
It is this restriction that will allow the simplification.
Ghormley (12) has already presented the essence of
such a restricted procedure, but his work was limited to
binary paraffinic mixtures. It is the purpose of this work
to extend the procedure to all kinds of hydrocarbons and
to multicomponent mixtures.
The generalized procedure developed in this paper
allows prediction of the saturated liquid and vapor enthal
py of any mixture of hydrocarbons based on knowledge of
the critical temperature, molecular weight, normal boiling
point and degree of aromaticity of the pure components.
As noted above, a unique feature of this work is that data
are defined for the saturated conditions only, and the
method of prediction deliberately avoids the use of an
equation of state.
II. PREVIOUS WORK
A. Sources of Enthalpy Data
Considerable work has been expended in the experi
mental measurement of enthalpy of chemical components.
Most of this effort has been applied to the development of
enthalpy data for pure substances. The American Petroleum
Institute has supported research in this field, and has
published comprehensive tables of enthalpy data for the
pure hydrocarbon compounds (1) .
A limited amount of data is available which accu
rately defines the enthalpy of a mixture of two or more
substances. The major investigators in this fields are
Powers (3,42,65,66,67), and Lenoir (12,24,25,26,27,28,29,
30,31,32,33), who studied the enthalpy of various hydrocar
bon mixtures extensively, and Smith (35,58) who measured
the enthalpy of various mixtures of polar and non-polar
compounds. Table I summarizes the enthalpy data sources
that were used in the preparation of this dissertation.
Table II includes sources of cricondentherm information
that were needed in this development.
B. Heat of Vaporization
A method of predicting the heat of vaporization of
pure compounds was first described by Thiesen in 1897 (59)
3
4
Table I
Enthalpy Data Source
System References
Methane-propane 3,34
Propane-2 methylbutane 25
Pentane-hexadecane 31
Pentane-benzene 32
Benzene-cyclohexane 30
Benzene-octane 29
Pentane-cyclohexane-benzene 32
Benzene-octane-tetralin 32
5
Table II
Cricondentherm Data Source
System References
Methane-propane 3,34,47
Methane-2 methylpropane 39
Methane-butane 49
Methane-2 methylbutane 2
Methane-pentane 50
Methane-hexane 41
Methane-heptane 46
Methane-decane 43
Ethane-butane 18
Ethane-heptane 17
Propane-butane 21,26,38
Fropane-2 methylbutane 25,60
Propane-pentane 21,26
Propane-hexane 22
Propane-heptane 22
Propane-decane 45
Butane-heptane 19
Butane-decane 44
Pentane-octane 33
Pentane-hexadecane 31
Ethane-heptane 20
6
Table II (con't.)
System References
Ethane-propane 15
Ethane-propane 36
Ethane-cyclohexane 23
Ethane-benzene 24
Propane-benzene 13
Pentane-benzene 32
Hexane-toluene 62
Benzene-cyclohexane 30
Benzene-octane 29
Benzene-hexadecane 28
Tetralin-pentane 27
Ethane-propane-pentane 10
Propane-butane-pentane 10,37
Butane-pentane-hexane 10
Pentane-cyclohexane-benzene 32
Ethane-propane-butane-pentane 10
Propane-butane-pentane-hexane 10
Methane-ethane-propane-butane-pentane 10
Ethane-propane-butane-pentane-hexane 10
Methane-ethane-propane-butane-pentane-hexane 10
Benzene-octane-tetralin 32
7
and is shown in Equation 1. Subsequently, other authors
investigated this correlation and further defined the con
stants predicted.
X = K(TC - T)* (1)
where K and = constants,
T = absolute temperature,
Tc = critical temperature,
X = heat of vaporization of the
material at temperature T.
The constant oc has been shown to have a value of
about 0.38 for most hydrocarbons (4,61). For other materi
als it can vary from about 0.3 to 0.4 (52).
If the variable T in Equation 1 is allowed to ap
proach zero,
A 0 - k t* (2)
where X Q = the heat of vaporization of the
material at T = 0°R
Dividing Equation 1 by Equation 2 eliminates K and
expresses temperature as a generalized reduced temperature,
Tr; thus
X = XG(1 - Tr)**- (3)
where Tr represents the ratio T/Tc.
This equation has been modified by Ghormley and
Lenoir (12) to predict the isothermal heat of vaporization
8
of hydrocarbon mixtures as shown in Equation 4:
The term Xo for the mixture is related to the molal
average value of \ Q for the pure components by the expres
sion,
(4)
where Xoi = ^eat vaporization of the pure
component "i" at T = 0°R
= mole fraction of pure component "i"
Tc. = critical temperature at pure component
i i ^ i t
Tcc = cricondentherm of mixture
Xo = heat of vaporization of mixture at
T = 0°R
oC = 0.38, constant in heat of vaporization
equation.
C. Enthalpy of Mixed Hydrocarbons
The customary standard established method for com
puting enthalpies of gas mixtures evaluates the ideal gas
enthalpy state as a weight average (molal average if re
sults are in units of Btu/mole) of the pure component
ideal gas enthalpy and then corrects using a Tr, Pr chart
and Kay's procedure for getting pseudo critical values
(6,64). The difficulty with this procedure lies in poor
accuracy near the critical region. Also, the Tr, Pr chart
is inconvenient for computer programing. For liquids the
situation is poorer. At temperatures considerably below
9
the critical temperatures of all components the use of a
weight average retains reasonable accuracy. But at high
er temperatures, the situation becomes more complex and
the evaluation of liquid phase enthalpies close to the
critical, especially for saturated liquids, has remained
a difficult matter for prediction with confidence.
Stein and Martin (56) have outlined a simplified
procedure to predict the isobaric heat of vaporization of
a mixture by a stepwise summation in which the components
of the mixture are treated individually. The use of this
procedure generally requires that the dew point envelope
be fully defined, and that the P-V-T properties of the
mixture be known.
Often the dew point envelope is not completely de
fined and the P-V-T properties of the mixture is often
now known. Thus, this procedure is generally limited to
well defined mixtures whose P-V-T properties have been
experimentally defined.
Stevens and Thodos (57) have estimated the saturat
ed liquid and vapor enthalpy of hydrocarbon mixtures by
first calculating the vapor enthalpy at zero pressure
using the molal average of the enthalpies of the pure com
ponents. An enthalpy correction to the standard vapor
state and saturated liquid state was then calculated. A
number of constants which are functions of the critical
10
compressibility of the mixture must be determined. The
authors showed that the method could be used to predict
the enthalpy of several hydrocarbon mixtures with an error .
of from two to five percent.
Measured critical compressibility of mixtures are
not usually available. Estimation of this parameter will
introduce more error into the results which already ex
hibit an error higher than desirable.
Orentlicher and Prausnitz (40) utilized statistical
thermodynamic theory to predict the enthalpy of simple
dense fluid mixtures. This method does not define the
saturated or mixed phase region and requires a sophisti
cated computer program.
Edmister (8) used the equilibrium (K) charts to
evaluate heats of vaporization of individual components
with an equation derived by Dodge (7) for ideal solutions
where A h is independent of temperature. These assump
tions preclude the use of the equation in the critical re
gion where A h is not independent of temperature. This is
a severe limitation and greatly reduces the reliability
of this procedure.
Ghormley and Lenoir (12) have developed a simple
procedure to predict the saturated liquid and vapor en
thalpy of binary aliphatic mixtures. This procedure is
based upon the hypothesis of Cailletet and Mathias (5)
11
that the mean of the vapor and liquid densities of a com
pound could be correlated with temperature as a linear
function. Subsequent investigations have shown that the
mean density is more accurately represented by a quadratic
equation of the form:
hi Pg + P L) = A + BT + CT2 (5)
where pg = density of vapor
= density of liquid
T = temperature
A,B,C = constants
This correlation provides an accurate method of predicting
the mean vapor-liquid density up to the critical tempera
ture.
Ghormley and Lenoir have shown that a similar re
lationship exists for the enthalpy of saturated liquid and
vapor and that the mean enthalpy may be expressed as
h(Hv + Hx) = A + BT + CT2 (6)
where = enthalpy of the saturated vapor,
H-^ = enthalpy of the bubble point liquid,
A, B, and C are polynomial coefficients.
This equation may be combined with an expression
for the heat of vaporization to yield a definition of the
saturated liquid and vapor enthalpy as follows:
12
If the base level enthalpy is chosen as zero at the
saturated liquid condition, for this particular tempera
ture, = 0, and
Hy + Hi = Xb (7)
The API Data Book lists many hydrocarbon enthalpy
values using as a base level -200°F and the saturated pure
liquid state.
Using a base level of -200°F (260°R) and combining
Equations 6 and 7 yields the following expression:
l5Xb = A + B (260) + C (260) 2 (8)
Subtracting Equation 8 from Equation 6
^(Hv + Hx - Xb) = B (T - 260) + C (T2 - 2602) (9)
Combining Equation 9 with Equation 3 yields the general
working expressions of the mean enthalpy method.
Hv = ^ X b + B(T - 260) + C (T2- 2602) + ^Xd(1 - Tr)06
... (10)
H1 = ^Xb + B( T " 26°) + C(T2- 2602) - " Tr)OC
...(11)
where B = 0.221
C = 2.16 x 10"4
oC = 0.38
13
384
^A0 = M0*28
235
% A26O = M0*2
The authors applied this method to pure compounds
and found the standard deviation of calculated from experi
mental values of saturated liquid and vapor enthalpies to
be 1.7 to 2.7 BTU/lb.
For binary mixtures of aliphatic compounds where
subscripts m and he denote mixture and heavy component,
respectively
Bm = 0.221
Cm/Chc = ^ ^hc/\^
f$ = 7350(Mhc)-2*2 (13)
k = ^m/^hc when Mjlc/Mm = 1
Using this procedure, the authors found the stand
ard deviation of calculated from experimental values of
saturated liquid and vapor enthalpies to be 1.3 to 2.87
BTU/lb.
This definition of Cm suffers from two disadvan
tages :
1) It cannot be extended to multicomponent mix
tures .
2) It does not consider the concentration of the
pure components present in the mixture.
14
The latter is a more serious deficiency and limits the
use of this definition to low and intermediate concentra
tions of the light component. A dimensionless definition
of Cm will be developed in this work that will overcome
these limitations.
D. Cr icondentherm
The maximum temperature of the vapor-liquid enthal
py envelope of a mixture of hydrocarbons is called the
cricondentherm. This maximum temperature needs to be
known in order to predict the saturated enthalpy. For a
pure component, the cricondentherm and the critical tem
perature are identical, but with mixed components the cri-
condentherm can exceed the critical temperature signifi
cantly.
There are some methods available for the predic
tion of cricondentherm temperatures. Etter and Kay (7)
have developed empirical equations to predict the cricon
dentherm of a mixture of aliphatic hydrocarbons. Differ
ent equations are presented for various mixtures of light
hydrocarbons. Each equation is limited to a specific sys
tem, and is not applicable to other systems.
This generally limits the application of this pro
cedure to systems studied by the authors.
Silverman and Thodos (36) have developed an empiri
cal method of calculating the cricondentherm of binary
15
hydrocarbon mixtures. These authors used statistical
techniques to correlate the characteristic properties of
the systems. The resulting correlation is a complex poly
nomial in which the coefficients must be calculated from
other polynomial equations involving the ratio of atmos
pheric boiling points of the constituents. It shows ex
cessive error with systems containing methane.
Grieves and Thodos (8) present a group of empiri
cal equations for calculating the maximum temperature and
maximum pressure of hydrocarbon mixtures. The method re
quires a knowledge of the molal average boiling point, the
molal average critical temperature, the atmospheric boil
ing point, and the mole fraction of the light component.
Where multicomponent mixtures are to be investigated, a
stepwise calculation procedure is recommended to obtain
the maximum temperature and pressure of the liquid mixture.
The accuracy of the procedure is considerably reduced for
multicomponent mixtures.
Ghormley and Lenoir (12) developed a method for
predicting the cricondentherm temperatures for binary mix
tures of aliphatic hydrocarbons. The authors observed
that the ratio of the cricondentherm to the mole average
of the critical temperature could be represented by the
equation:
7 = 1 + bx + cx^ - dx* (14)
1sc
16
where x = mole fraction of the light component, and the
coefficients, b, c, and d are functions of the ratio of
the two critical temperatures.
Tcc = cricondentherm
Tsc = pseudo critical temperature (Zx^T^)
This method is limited to binary mixtures of aliphatic
hydrocarbons.
III. PREDICTING THE SATURATED LIQUID AND VAPOR ENTHALPIES
OF MULTICOMPONENT HYDROCARBON MIXTURES
A. Introduction
The procedures developed by Ghormley and Lenoir for
predicting the saturated liquid and vapor enthalpies apply
only to pure compounds and binary mixtures of aliphatic
hydrocarbons. This dissertation extends the range of the
mean enthalpy method to include multicomponent mixtures
and mixtures of all kinds of hydrocarbons.
The basic equations of the mean enthalpy method
were found to be valid for multicomponent mixtures of ali
phatic, naphthenic and aromatic hydrocarbons. Thus, the
saturated liquid and vapor enthalpy of most non-polar hy
drocarbon mixtures can be predicted by -the equations
Hvm = ^ m + Bm(T - 26°) + Cm (T2 - 2602) + ^ ( 1 - ^ ) *
Hi = + Bm (T - 260) + Cm (T2 - 2602) -
m m f..(ll')
where all symbols have same meaning as for the pure com
ponents (Equations 10 and 11), and subscript m refers to
mixtures of hydrocarbojns.
I
Tr = reduced temperature based on cricondentherm
= T/Tcc
17
18
B. Mean Enthalpy Curves of Hydrocarbon Mixtures
The mean enthalpy curves of saturated mixtures of
aliphatic hydrocarbons have been found to exhibit similar
slopes (12). The mean enthalpy curves of binary and ter
nary mixtures containing aromatic, naphthenic and aliphatic
hydrocarbons also exhibit similar slopes, as shown in
Figures 1, 2 and 3. Thus, the mean enthalpy curves of
all saturated hydrocarbons may be described by Equation 6
and the saturated liquid and vapor enthalpy curves for
all hydrocarbons by Equations 10' and 11'.
Ghormley (12) showed that mixtures of methane with
aliphatics produced changes in the slope of the mean en
thalpy curve. Similarly, the introduction of an aromatic
hydrocarbon into mixtures of aliphatic hydrocarbons was
found to modify the enthalpy curve. These changes are il
lustrated in Figures 4 and 5. With increasing amounts of
the lighter molecular weight hydrocarbon the mean enthalpy
curve for mixtures of aliphatic hydrocarbons is displaced
to the left. The mean enthalpy for mixtures of paraffinic,
aliphatic and aromatic hydrocarbons are shown in Figure
5. Curves 1 and 2 of Figure 5 demonstrate the increase
in saturated enthalpy of a mixture of aliphatic com
pounds with increasing amounts of the low molecular
weight component. Curves 3 and 4, and 5 and 6 show that
the addition of an aromatic will always decrease the
Mean Saturated Enthalpy - BTU/lb
400
350
' Mole %
Benzene 81.4
300
800
900
Temperature °R
Fig. 1 Mean Enthalpy of
Benzene-Pentane Mixtures
Mean Saturated Enthalpy - BTU/ib
20
400
Mole % Cyclohexane
20.7
61.
80.3
300
200
900
800 700
Temperature °R
Fig. 2 Mean Enthalpy of Cyclohexane-
Pentane Mixtures
Mean Saturated Enthalpy - BTU/lb
' ’ 21
(1) 60.1/19,9/20.0 mole % Pentane/Cyclohexane/Benzene
(2) 33.3/33.A/33.3 " " " " "
(3) 20.0/20.2/59.8 " " " " "
400
350
300
800 900
Temperature °R
Fig. 3 Mean Enthalpy Curves for
Mixtures of Pentane, Cyclohexane
and Benzene
Mean Enthalpy, BTU/lb
22
400
300
23.4% C
49.4% C
89% C.
95% C
200
100
0
300 400 500 600 700
Temperature °R
Fig. 4 Mean Enthalpy Curves for Mixtures
of Methane in Propane
Mean Saturated Enthalpy - BTU/lb
440
400
300
(1) 0.494/0.504 C. /C
200
(4) 0.407/0.593 Benz/C
(6) 0.446/0.554 Benz/C
600 500 700 800 900 1000
Temperature °R
Fig. 5 Mean Enthalpy Curves for
Mixtures of Saturated and
Unsaturated Hydrocarbons
24
saturated enthalpy of a mixture. That is, the change in
saturated enthalpy for mixtures of aliphatic and aromatic
compounds is not dependent on the respective molecular
weights of the pure compounds. For mixtures of pentane
and benzene, curves 3 and 4, benzene is the heavier mole
cular weight component. For mixtures of octane and ben
zene, curves 5 and 6, benzene is the lighter molecular
weight component. In both cases, the saturated enthalpy
decreases with increasing concentrations of benzene.
Differentiation of Equation 6 with respect to temp
erature gives the slope of the mean enthalpy curve
d H, (Hv + Hi) , v
-----^ = B + 2CT (15)
Values of B and C used to describe one curve can be
used for the entire family of curves. For mixtures of
aliphatic hydrocarbons, Ghormley (12) found the coeffici
ents B and C to be constant with a value of 0.221 and 2.16
-4 . . .
x 10 , respectively. However, for mixtures containing
aromatic hydrocarbons the slope of the mean enthalpy curve
varies with aromaticity of the pure component, and for
mixtures of aliphatic and aromatic hydrocarbons, the per
cent of the aromatic hydrocarbon present in the mixture.
The coefficient B was found to have the same value for
both aliphatic and aromatic mixtures. This means that B
can be considered a constant for all hydrocarbon mixtures.
25
This discovery is very important in that it greatly simpli
fies the analytical procedure for predicting the saturated
enthalpy. The coefficient C for mixtures containing aro
matic hydrocarbons can be correlated with the Watson fac
tor .
C. Prediction of Mean Enthalpy Equation Coefficients
In order to predict the saturated liquid and vapor
enthalpies of all hydrocarbon mixtures, it is necessary to
allow for the aromaticity of the pure components. This is
done by defining the coefficient C (Equations 10 and 11)
in terms of the Watson characterization factor, K^, and the
molecular weight M.
The coefficient C for pure components was derived
from the physical properties of the pure components and a
form of the mean enthalpy equation:
h(Hv + He) = ^ \ b + Bi(T - 260) + Ci(T2 - 2602) (16)
or may be estimated by the equation:
Ci = 1.06 x 10"7 (17)
As noted above, the Watson characterization factor, Kw, is
used to allow for the aromaticity of the pure components.
The Watson factor has a meaningful value between 9.6 and
12.65. Thus, Kw values of 12.65 or above are completely
paraffinic, and hydrocarbons with computed values above
26
this number were assigned a value of 12.65. For paraffins
Equation 17 reduces to
ci paraffin = 2,16 x 10 4 (18)
The entire aromaticity effect on the saturated
liquid and vapor enthalpy is defined by Equation 17 for the
pure component, C^. The coefficient B for all kinds of
hydrocarbons was found to be a constant with a value of
0.221.
For convenience, the mixture coefficient, Cm, was
put into a dimensionless form by dividing by the molal
average of values of C for the pure components, Csc
(Csc = 21, X^C^) . For binary mixtures, this dimensionless
Cm
ratio, ■ J -, was plotted against the mole fraction of the
'-sc
light component (Figure 6). With the exception of com
pounds containing methane, the curves of Figure 6 are es
sentially linear and can be described by a general equa
tion of the form:
Cm i . * 9 /1o\
= i + qix - qix (19)
where q- = quantity that depends on the identity
of the pure component,
x = mole fraction of the light component,
* denotes that for methane x must be
raised to the 2.6 power.
For all other hydrocarbons, x is
raised to the 1st pov/er.
Cm/Csc
27
4.0
Cyclohexane
.0
2.0
1.0
1.0 0.4 0.6 0.8 0.2 0
Mole Fraction Light Component
Fig. 6 Variation of Cm/Csc. with Composition
28
If 0 is a large number, then the third term of the
equation disappears when X is small, and the initial sec
tion of the curve is described by:
- = 1 + qix* (20)
'-sc x
The assumption that 9 is a large number can now be
proved by differentiating Equation 19 and evaluating at
the maximum point where X = Xmax. Values of 0 were found
to vary as a function of the molecular weight of the light
component in accordance with the equation:
8 = - 57^ (21 )
Mic
In order to extend Equation 19 to multicomponent
mixtures, it is necessary to define Cm in terms of con
centration of the pure components. Thus, for any hydro
carbon mixture with any number of compounds, Cm/Csc is
defined as:
^ = 1 + S.qi 4 - X q i x?1 (22)
where Csc = 2- ^i ci
q^ = a quantity based on molecular weight
and Watson factor of the pure
component,
0^ = a quantity based on the molecular
weight of the pure component,
and the * denotes tha; for methane Xr must be
1
29
raised to the 2.6 power.
For all other hydrocarbons x^ is raised to
the 1st power.
The values of for aliphatic hydrocarbons corre
late with the molecular weight of the pure component by
the following equation:
maticity of the pure component by introducing the Watson
characterization factor, 1^. However, there is an inter
action between the aromatic and aliphatic components of the
mixture that requires the introduction of the average mole
cular weight of the mixture to define the contribution of
the pure aromatic component. Thus, for aromatic hydro
carbons, the coefficient q^ is expressed as:
As before, all hydrocarbons with values of 12.65 or
above were assigned a value of 12.65.
Equation 24 is a general definition of q^ and re
duces to Equation 23 for all aliphatic hydrocarbons.
The exponent 0 for each component was correlated
13
(23)
(0.1 M.)2,8
As before, it is necessary to allow for the aro-
w
(24)
where w w = (12.65 - Kw)2
Mavg = average molecular weight of the
hydrocarbon mixture.
30
with the molecular weight of the pure component by:
350
ei = ~ "2/3 (25)
1 M/
i
where = molecular weight of the pure
component.
D. Heat of Vaporization
The value of the isothermal heat of vaporization
for the pure components at the base temperature, anc^
at 0°R, \ 0, are required for solution of Equations 10' and
11'. For both saturated and unsaturated hydrocarbons,
these values are related to the molecular weight and the
Watson characterization factor by the equation:
The isothermal heat of vaporization at the base tempera
ture, Xj-,/ may also be calculated from Equation 3.
(For T = 0°R)
(For a base temperature of 260°R)
no-) t
(26)
t
(27)
where M = molecular weight,
= Watson characterization factor,
t (28)
From Ghormley (12), for mixtures, the isothermal
31
heat of vaporization may be predicted by the equation:
E. Prediction of Cricondentherm of Binary Mixtures
Ghormley and Lenoir have studied the variation of
the cricondentherm (maximum temperature of the saturated
enthalpy envelope) for binary mixtures of aliphatic com
pounds, and have derived an expression for predicting the
cricondentherm of these mixtures. This study has been ex
tended to mixtures of unsaturated compounds and an expres
sion derived for predicting the cricondentherm for binary
mixtures of most non-polar hydrocarbons.
critical temperature (Tsc) can be related to mixture com
position, as shown in Figure 7, for a number of saturated
and unsaturated binary mixtures. It is interesting to
(4)
. I
where \ 0 ~ isothermal heat of vaporization of
the mixture,
\oi = isothermal heat of vaporization of
the pure component "i" at T = °R,
= mole fraction of component "i",
Tcj _ = critical temperature of pure com
ponent "i",
Tcc = maximum temperature (cricondentherm)
of mixture,
OL -
constant = 0.38 for most hydrocarbon
mixtures.
The ratio of the cricondentherm (Tcc) to the pseudo
cc' sc
32
C2 - Cyclohexane
1.5 -
(10
(11
(12
B - Cyclohexane
0.6 1.0
0.4 0.8 0.2 0
Mole Fraction Light Component
Fig. 7 Variation of Tcc/Tgc with Composition
note that the ratio of Tcc/Tsc becomes less than one for
mixtures containing aromatic compounds. The presence of
aromatic compounds tends to depress the maximum tempera
ture of the saturated enthalpy envelope as illustrated in
Figure 5.
The maximum temperature of each curve in Figure 7
has been correlated with the ratio of critical temperatures
of pure components such that
where Tc- ^ > Tc2.
The curves of Figure 7 can be described by a general
fourth term of the equation disappears when X is small,
and the initial section of the curve is described by
= 1 + bXa + cX3 (31)
Tsc
In order to apply this equation to all kinds of hydrocar
bon binary mixtures, it is necessary to use a somewhat
max.
1.32 - .28(1^1
TC2
1
(29)
equation of the form
. ^ , va , „3 _ JT
1 + bX + cX - dX (30)
where d = (b + c) when X = 1,
X = mol fraction of the light component,
a and If are constants for each mixture.
The exponent If was found to be large, so that the
34
more complex expression for the coefficient b. One gener
al expression for b was determined as:
m u j _ u j l u n « u w u u u m u u u i i u d — - - ......................■ —
BP2 - FP2
such that BPX - PP1 > BP2 - FP2.
For values of Mr greater than 1.5, Equation 32
reduces to:
and the exponent a, in terms of the ratio of molecular
weights, Mr, as
For values of £ below 1.5 (Mr < 4), the curves are
linear so that c = 0 and a = 1. For values of € greater
than 1.5 (Mr > 4), the curve is not linear, as noted
above, and a and c are defined by Equations 34 and 35.
The coefficient was found to be a function of
Mr and € such that
b = -0.670 + 0.568 €Mr^ 2'5+
Mr3^BF
0.2
(32)
ratio of the molecular weights of the
two components = M-^/M2 such that
where M
ABF = ratio of the difference between the
atmosphere boiling point and freezing
r p , - PP
b = -0.670 + 0.568 €Mr
1/2.5€
(33)
The coefficient c is expressed in terms of b as:
c 0.12b (34)
0.1
(35) a
Data from the binary mixtures, listed in Table II,
were analyzed using the above expression, Equations 29 to
37, for predicting the cricondentherm. These predicted
values were compared with the experimental values, and the
results tabulated in Table III.
Table III
Comparison of Predicted and Experimental
Cricondentherms of Binary Mixtures
Arithmetic Deviation: 2.7°F
Standard Deviation: 4.6°F
% Error: 0.34
Although this procedure using A bf as a correlating
parameter is accurate, the introduction of freezing points
for the pure component introduces an additional complica
tion. A general simplification at the cost of some ac
curacy shows.
1/2 5P
b = -0.62 + 0.55 €Mr / c (38)
All other coefficients have the same values as before.
This equation is suggested for general use unless very
36
high accuracy is needed.
F. Prediction of Cricondentherm of Multicomponent Mixtures
Prediction of the saturated enthalpy of multicompo
nent mixtures substantially increases the usefulness of the
mean enthalpy method. However, in order to predict the
saturated enthalpy, it is necessary to first determine the
value of the cricondentherm for these mixtures. In this
study, a number of multicomponent mixtures were analyzed
and an expression for prediction of the cricondentherm
der ived.
Cr icondentherms
An examination of multicomponent mixtures showed
that: 1) the cricondentherm could be expressed, as with
binary mixtures, as a ratio of the actual cricondentherm,
Tcc, to the pseudo critical temperature of the mixture,
Tsc; and 2) the deviation of the actual cricondentherm from
the pseudo critical temperature is a function of the physi
cal properties of the pure components. The contribution
of each component is proportional to its mole fraction
presence in the mixture. Based on these observations, the
cricondentherm of a multicomponent mixture has been related
by the equation
T 9'
7=^ = 1 + Lni X± - ^ni (39)
1sc
37
The coefficient n is related to the properties of the pure
component as
■ i p
where BP = atmospheric boiling point of pure
component;
BPa = average atmospheric boiling point of
mixture = 2,BPjL X^;
and Si = 1.1 + 0.01 (41)
where = molecular weight of pure component;
= Watson characterization factor with a
maximum value of 12.65;
350
and Of = 2/3 <42)
The above expressions are perfectly general and
apply to all non-polar hydrocarbon mixtures. This analy
sis has been applied to multicomponent mixtures of the
hydrcarbon compounds listed in Table II with the following
results.
Table IV
Comparison of Predicted and Experimental
Cricondentherms of Multicomponent Mixtures
Arithmetic Deviation: 1.80°F
Standard Deviation: 2.3°F
% Error: 0.24
38
Etter and Kay (10) have also developed a procedure
for predicting the cricondentherms of multicomponent mix
tures. They present different equations for each of the
light hydrocarbons which limits the use of this procedure
to the systems evaluted. A comparison of the accuracy of
Etter and Kay and Equations 39-42 is presented below.
Table V
Comparison of Predicted and Experimental Cricondentherms
of Multicomponent Mixtures* (Using Method of
Etter and Kav and This Work)
Etter and Kay This Work
Arithmetic Deviation: 3.4°P 2.2°P
Standard Deviation: 4.1°F 2.6°P
% Error: 0.48 0.29
Experimental data from Etter and Kay.
IV. ENTHALPY PREDICTION
The saturated liquid and vapor enthalpies of multi-
component mixtures of aliphatic, naphthenic and aromatic
hydrocarbons were calculated using the procedure developed
in this work. The results are plotted and tabulated, and
compared to the experimentally measured values.
A. Enthalpy Prediction of Mixtures Containing Aliphatic
Hydrocarbons_____________________________________________
1. Methane-Propane
The procedures outlined permit the ready
calculation of enthalpies of mixtures of methane
with other aliphatic hydrocarbons. To demonstrate
the effectiveness of this method of calculation,
three examples of methane mixed with 5%, 51% and
75% propane have been calculated and plotted in
Figures 8, 9 and 10. Experimental data points
are superimposed on the curves to demonstrate the
accuracy of the procedure.
2. Pentane-Hexadecane
The enthalpies of several mixtures of pentane
and hexadecane have been reported (21) . The en
thalpy data for these aliphatic hydrocarbon mix
tures have been investigated for comparison with
39
Saturated Enthalpy - BTU/lb
40
200
100
300 400
Temperature °R
Fig. 8 Saturated Enthalpy Boundary for a Mixture
Containing 95 Mole % Methane in Propane
Saturated Enthalpy - BTU/lb
41
300
200
100
600 500
Temperature #R
Pig. 9 Saturated Enthalpy Boundary for a Mixture
Containing 23.4 Mole % Methane in Propane
Saturated Enthalpy - BTU/lb
42
300
200 -
100
400 500 600
Temperature °R
Fig. 10 Saturated Enthalpy Boundary for a Mixture
Containing 49.4 Mole % Methane in Propane
43
other hydrocarbon systems. The mean enthalpy
curves for these mixtures show a divergence of the
more volatile hydrocarbon mixtures, similar to
that found in the methane-propane mixtures. Val
ues of C for these mixtures can be predicted in the
same way as that outlined for methane-propane
mixtures using Equation 22.
To demonstrate the effectiveness of this cal
culation procedure, the enthalpy envelopes of two
binary mixtures of pentane and hexadecane were
calculated. The mixtures contained 0.587 and
0.794 mole fraction pentane. The results of these
calculations are plotted in Figures 11 and 12.
Experimentally measured enthalpy points are
plotted on the curves to show how closely the cal
culated curve approximates the actual data.
3. Propane-Isopentane
Enthalpy data have been reported for a single
mixture of propane and isopentane (25,60). The
mixture contained 0.43 mole fraction propane. The
enthalpy data showed the same type of divergence
exhibited by the previous examples. The value of
C for the mixture was calculated using Equation
22. The calculated enthalpy envelope for this
Saturated Enthalpy - BTU/lb
44
600
500
400
1000 1100 1200
Temperature °R
Fig. 11 Saturated Enthalpy Boundary for a Mixture
Containing 58.7 Mole % Pentane in Hexadecane
Saturated Enthalpy - BTU/lb
45
500
300
1100 1000
900
Temperature °R
Fig. 12 Saturated Enthalpy Boundary for a Mixture
Containing 79.4 Mole % Pentane in Hexadecane
mixture is shown in Figure 13.
Enthalpy Prediction of Mixtures Containing Aromatic
Hydrocarbons___________________________________________
1. Benzene-Pentane
The enthalpies of several mixtures of ben
zene and pentane have been reported (32). The
saturated enthalpy envelope for mixtures contain
ing 19.9, 40.7, 60.0 and 81.4 mole percent benzene
have been calculated and are compared with the
experimental results in Figures 14, 15, 16 and 17.
2. Benzene-Octane
The enthalpies of several mixtures of ben
zene and octane have been reported (29). The
saturated enthalpy envelope for mixtures contain
ing 93.0, 85.7, 77.1, 67.6, 44.6 and 27.1 mole
percent benzene have been calculated and are com
pared with the experimental results in Figures
18, 19, 20, 21, 22 and 23.
3. Benzene-Cyclohexane
The enthalpies of several mixtures of ben
zene and cyclohexane have been reported (30). The
saturated enthalpy envlope for mixtures containing
81.2, 61.3, 33.4 and 21.1 mole percent benzene
have been calculated and are compared with the
Saturated Enthalpy - BTU/lb
47
300
200
100
600 700 800
Temperature °R
Fig. 13 Saturated Enthalpy Boundary for a Mixture
Containing 43 Mole % Propane in Isopentane
Saturated Enthalpy - BTU/lb
48
400
300
200
1000 900
800
Temperature °R
Fig. 14 Saturated Enthalpy Boundary for a Mixture
Containing 18.6 Mole % Pentane in Benzene
Saturated Enthalpy - BTU/lb
49
400
300
200
800 900 1000
Temperature °R
Fig. 15 Saturated Enthalpy Boundary for a Mixture
Containing 40.0 Mole % Pentane in Benzene
Saturated Enthalpy - BTU/lb
50
400
300
200
800 900
Temperature °R
Fig. 16 Saturated Enthalpy Boundary for a Mixture
Containing 59.3 Mole % Pentane in Benzene
51
400
e
p q
•U
0)
•u
n )
t - j
3
S 300
200
800 900
Temperature °R
Fig. 17 Saturated Enthalpy Boundary for a Mixture
Containing 80.1 Mole % Pentane in Benzene
Saturated Enthalpy - BTU/lb
52
400
300
200
900 1000
Temperature °R
Fig. 18 Saturated Enthalpy Boundary for a Mixture
Containing 7.0 Mole % Octane in Benzene
Saturated Enthalpy - BTU/lb
53
400
300
200
900
1000
Temperature °R
Fig. 19 Saturated Enthalpy Boundary for a Mixture
Containing 14.3 Mole % Octane in Benzene
Saturated Enthalpy - BTU/lb
54
400
300
2001
1000
900
Temperature °R
Fig. 20 Saturated Enthalpy Boundary for a Mixture
Containing 22.9 Mole % Octane in Benzene
Saturated Enthalpy - BTU/lb
55
400
300
200
900 1000
Temperature °R
Fig. 21 Saturated Enthalpy Boundary for a Mixture
Containing 32.4 Mole % Octane in Benzene
Saturated Enthalpy - BTU/lb
56
400
300
200
900 1000
Temperature °R
Fig. 22 Saturated Enthalpy Boundary for a Mixture
Containing 55.4 Mole % Octane in Benzene
Saturated Enthalpy - BTU/lb
57
400
300 -
200
1000
900
Temperature °R
Fig. 23 Saturated Enthalpy Boundary for a Mixture
Containing 72.9 Mole % Octane in Benzene
experimental results in Figures 24, 25, 26 and 27.
Enthalpies of Ternary Mixtures Containing Aromatic
Hydrocarbons___________________________________________
1. Pentane-Cyclohexane-Benzene
The enthalpies of three mixtures of pentane,
cyclohexane and benzene have been reported (32).
The saturated enthalpy envelope for mixtures con
taining 60.1/19.9/20.0, 33.3/33.4/33.3, and
20.0/20.2/59.8 mole percent, respectively, of
pentane, cyclohexane and benzene have been calcu
lated and are compared with experimental results
in Figures 28, 29 and 30.
2. Benzene-Octane-Tetralin
The enthalpies of two mixtures of benzene,
octane and tetralin have been reported (32). The
saturated enthalpy envelope for mixtures contain
ing 33.3/33.4/33.3 and 45.0/44.9/10.1 mole per
cent, respectively, of benzene, octane and tetra
lin have been calculated and are compared with the
experimental results in Figures 31 and 32.
Saturated Enthalpy - BTU/lb
59
400
o
300
200
1000 900
Temperature °R
Fig. 24 Saturated Enthalpy Boundary for a Mixture
Containing 18.8 Mole % Cyclohexane in Benzene
Saturated Enthalpy - BTU/lb
60
400
300
200
1000 900
Temperature °R
Fig. 25 Saturated Enthalpy Boundary for a Mixture
Containing 38.7 Mole % Cyclohexane in Benzene
Saturated Enthalpy - BTU/lb
61
400
300
200
900 1000
Temperature °R
Fig. 26 Saturated Enthalpy Boundary for a Mixture
Containing 66.6 Mole % Cyclohexane in Benzene
Saturated Enthalpy - BTU/lb
62
400
300
200
900 1000
Temperature °R
Fig. 27 Saturated Enthalpy Boundary for a Mixture
Containing 78.9 Mole % Cyclohexane in Benzene
Saturated Enthalpy - BTU/lb
63
400
300
200
800
900
Temperature °R
Pig. 28 Saturated Enthalpy Boundary for a Mixture
Containing 60.1 Mole % Pentane, 19.9 Mole %
Cyclohexane and 20 Mole % Benzene
Saturated Enthalpy - BTU/lb
64
400
300
200
800 1000 900
Temperature °R
Fig. 29 Saturated Enthalpy Boundary for a Mixture
Containing 33.3 Mole % Pentane, 33.4 Mole %
Cyclohexane and 33.3 Mole % Benzene
Saturated Enthalpy - BTU/lb
65
400
300
200
1000 900 800
Temperature °R
Fig. 30 Saturated Enthalpy Boundary for a Mixture
Containing 20.0 Mole % Pentane, 20.2 Mole %
Cyclohexane and 59.8 Mole % Benzene
Saturated Enthalpy - BTU/lb
66
400
300
220
740 800 900 1000 1100
Temperature °R
Fig. 31 Saturated Enthalpy Boundary for a Mixture
Containing 33.3 Mole % Benzene, 33.4 Mole %
Octane and 3 3. 3% Tetralin
Saturated Enthalpy - BTU/lb
Fig
67
400
300
210
700 800 900 1000 1100
Temperature °R
32 Saturated Enthalpy Boundary for a Mixture
Containing 45.0 Mole % Benzene, 44.9 Mole %
Octane and 10.1 Mole % Tetralin
V. ACCURACY OF CALCULATED ENTHALPIES
A procedure has been developed to predict the vapor-
liquid enthalpy envelope for multicomponent mixtures of all
kinds of hydrocarbons. To demonstrate the accuracy of the
procedure, it is necessary to determine the dispersion or
deviation of the method. The deviation, e, is defined by
the equation
e = (Hc - H) (43)
where H = the calculated enthalpy value,
Hc = the mean enthalpy value established
by experimental measurement.
Values of H obtained from literature sources were
correlated by plotting on a smooth curve to yield the best
average value of the enthalpy at any given temperature.
Individual experimental errors which may vary up to 10%
are averaged in the correlated value. Based on reported
measurement accuracies, the correlated data may be assumed
to have an average accuracy of +1.5%. These reported data
values have been used to establish the deviation of the
calculated enthalpy values.
One measure of the accuracy of the procedure is the
arithmetic average of the error of a number of points
taken along the same curve. The arithmetic mean error of
68
69
the procedure can be obtained by dividing the sum of the
errors by the number of readings.
Z. I e \ ,AA
e = — -— (44
A more useful way of representing the data is by
the use of the standard deviation, or the root mean
square deviation (S).
The units of this deviation are the same as for the indi
vidual measurements. However, the value of S is the stand
ard deviation of the entire population of data points.
The accuracy of the general procedure developed in
this work was evaluated first for binary mixtures of ali
phatic hydrocarbons. Values were taken at 10 degree
intervals in the critical temperature region and at 40
degree intervals at lower temperatures down to a tempera
ture approximately 200°R below the critical point. Table
VI summarizes the accuracy of these calculations. The
average divergence of all the calculations was less than
0.94 which is within the accuracy of the original
measurements.
Extending the general procedure to other hydrocarbon
mixtures, the enthalpy boundaries of aliphatic, aromatic
and naphthenic hydrocarbons were evaluated. Table VII
shows the arithmetic deviation and the standard deviation
S (45)
70
Table VI
Deviation of Calculated Enthalpies of Binary Mixtures
of Aliphatic Hydrocarbons
Average Deviation
Arithmetic Standard
Deviation Deviation Percent
Molal Composition BTU/lb BTU/lb Error
0.95 Methane, 0.05 Propane 1.90 2.60 1.10
0.49 Methane, 0.51 Propane 2.30 2.85 1.00
0.24 Methane, 0.76 Propane 2.65 3.61 1.13
0.794 Pentane, 0.206 Hexadecane 1.92 2.20 0.50
0.587 Pentane, 0.413 Hexadecane 2.40 2.89 1.01
0.43 Propane, 0.57 Pentane 2.20 2.70 0.73
Average 2.22 3.37 1.13
71
Table VII
Deviation of Calculated Enthalpies of Binary Mixtures of
Aliphatic, Naphthenic and Aromatic Hydrocarbons
Average Deviation
Arithmetic Standard
Deviation Deviation Percent
Molal Composition BTU/lb BTU/lb Error
0.186 Pentane, 0.814 Benzene 1.94 2.83 0.56
0.400 Pentane, 0.600 Benzene 0.81 1.50 0.25
0.597 Pentane, 0.403 Benzene 1.44 2.10 0.40
0.801 Pentane, 0.199 Benzene 0.81 1.20 0.24
0.070 Octane, 0.930 Benzene 0.87 1.17 0.27
0.143 Octane, 0.857 Benzene 0.94 1.09 0.27
0.229 Octane, 0.771 Benzene 1.69 2.04 0.44
0.324 Octane, 0.676 Benzene 1.88 1.90 0.41
0.554 Octane, 0.446 Benzene 0.69 1.06 0.16
0.729 Octane, 0.271 Benzene 1.00 1.66 0.22
0.188 Cyclohexane, 0.812 Benzene 1.38 2.06 0.40
0.387 Cyclohexane, 0.613 Benzene 1.57 1.89 0.45
0.666 Cyclohexane, 0.334 Benzene 0.92 1.63 0.26
0.789 Cyclohexane, 0.211 Benzene 1.14 1.60 0.32
Average 1.22 1.69 0.33
72
for each of the mixtures studied, and the average devia
tion for all the cases. The percent error based on the
average enthalpy of each system is shown along with the
average percent error for all the cases. The average per
cent error for these examples is 0.33 which represents a
significant improvement over available methods of enthalpy
prediction.
The general procedure was next applied to ternary
mixtures of aliphatic, aromatic and naphthenic hydrocar
bons. Enthalpy boundaries were evaluated as before.
Table VIII shows the arithmetic and standard deviation as
well as well as the percent error. The average percent
error is 0.34, comparable to that of the binary systems.
73
Table VIII
Deviation of Calculated Enthalpies of Ternary Mixtures of
Aliphatic, Naphthenic and Aromatic Hydrocarbons'
Molal Composition
0.601 Pentane, 0.199 Cyclo
hexane, 0.200 Benzene
0.333 Pentane, 0.334 Cyclo
hexane, 0.333 Benzene
0.200 Pentane, 0.202 Cyclo
hexane, 0.598 Benzene
0.333 Benzene, 0.334 Octane,
0.333 Tetralin
0.450 Benzene, 0.449 Octane,
0.101 Tetralin
Average Deviation
Arithmetic Standard
Deviation Deviation Percent
BTU/lb BTU/lb Error
0.68 1.09 0.20
1.06 1.64 0.3 2
0.68 0.97 0.20
1.25 1.65 0.32
2.56 2.92 0.68
Average 1.24 1.66 0.34
VI. CONCLUSIONS
1. The two phase enthalpy boundaries of any multicompo
nent hydrocarbon mixture can be correlated by a poly
nomial equation of the form
k(Kv + Hx) = A + BT + CT2
2. The mean enthalpy curves of hydrocarbon mixtures has
been examined and the change of enthalpy of these
curves as a function of temperature is predicted
by the equation
6H (Hv + HL)/dT + B + 2CT
For mixtures of aliphatic hydrocarbons the values of
B and C are constant. For mixtures containing aro
matic B remains constant, but the value of C is a
function of the Watson Factor.
3. The difference between the mean enthalpy curves for
various hydrocarbons is established by the difference
in the heat of vaporization of the individual hydro
carbons at the temperature of the enthalpy base.
4. Mixtures of aliphatic hydrocarbons exhibit a mean
enthalpy curve with a slope which tends to be greater
than the slope of the pure components, and which in
creases with the percentage of light component in the
74
75
mixture. Mixtures containing an aromatic hydrocarbon
exhibit a mean enthalpy curve with a slope which tends
to be less than the slope of the pure components and
which decreases with increasing percentage of aromatic
component in the mixture. The slope for all mixtures
can be related to the slope of the pure components
using the ratio Cm/Csc.
5. The cricondentherm of any multicomponent mixture of
hydrocarbons can be predicted using only the critical
temperatures and the normal boiling point of the pure
components and the molecular composition of the mix
ture.
6. The two phase enthalpy boundary of any multicomponent
hydrocarbon can be predicted using only the pure com
ponent critical temperatures, the molecular weights,
Watson factor, and the heats of vaporization of the
components at the enthalpy base.
VII. REFERENCES
1. American Petroleum Institute, Technical Data Book -
Petroleum Refining, Port City Press, Baltimore, Md.
(1966).
2. Amick, E. H., Johnson, W. B.’and Dodge, B. F., Chem.
Engr. Progr. Symposium Ser. 48 (3), 65 (1952).
3. Bhirud, V. L. and Powers, J. E., Ph.D. Thesis, Uni
versity of Michigan, August 1969.
4. Bradford, M. L. and Thodos, G., J. Chem. Eng. Data,
12, 373 (1967).
5. Cailletet, L. and Mathias, E. 0. J., Compt. Rend.,
104, 1563 (1887) .
6. Curl, R. F. and Pitzer, K. S., Ind. Eng. Chem., SD,
265 (1958).
7. Dodge, B. F., Chemical Engineering Thermodynamics,
McGraw Hill, N. Y. (1944).
8. Edmister, W. C., A.I.Ch.E. J., JL, 38 (1955).
9. Edmister, W. C., Pearson, C. L. and Erbar, J. H.,
Proc. 42nd NGPA Ann. Conv., pg. 50 (1963).
10. Etter, D. 0. and Kay, W. B., J. Chem. Eng. Data, 6_,
409 (1961).
11. Fisher, G. D., Chappellear, P. S. and Leland, K. W.,
Proc. 47th NGPA Ann. Conv., pg. 76 (1968).
12. Ghormley, E. L. and Lenoir, J. M., Cana. J. Chem. E.,
J50, 89 (1972).
13. Glanville, J. W., Sage, B. H. and Lacey, W. W.,
Ind. Eng. Chem. 4j2, 508 (1950) .
14. Grieves, R. B. and Thodos, G., Soc. Petrol. Engr. J.,
3., 287 (1963).
15. Haselden, G. G., et.al., Proc. Roy. Soc. A240, JL,
(1957).
76
77
16. Johnson, P. W. and Colver, L. P., Proc. 49th NGPA
Ann. Conv., pg. 19 (1970).
17. Kay, W. B., Ind. Eng. Chem., _30, 459 (1938).
18. Kay, W. B., Ind. Eng. Chem., 32., 353 (1940).
19. Kay, W. B., Ind. Eng. Chem., 33.# 590 (1941).
20. Kay, W. B., Ind. Eng. Chem., 40, 1459 (1948).
21. Kay, W. B., J. Chem. Eng. Data, JL5, 46 (1970).
22. Kay, W. B., J. Chem. Eng. Data, JUS, 137 (1971).
23. Kay, W. B. and Albert, R. E., Ind. Eng. Chem., 48,
422 (1956).
24. Kay, W. B. and Nevens, T. D., A.I.Ch.E. Symp. Ser.
48, 108 (1952).
25. Lenoir, J. M., Hydrocarbon Processing, ,46, 161
(1967).
26. Lenoir, J. M., Hayworth, K. E. and Hipkin, H. G.,
Proc. Amer. Petrol. Inst., 5_0, 212 (1970).
27. Lenoir, J. M., Hayworth, K. E. and Hipkin, H. G.,
J. Chem. Eng. Data, JL5, 424 (1970) .
28. Lenoir, J. M., Hayworth, K. E. and Hipkin, H. G.,
J. Chem. Eng. Data, 16., 276 (1971) .
29. Lenoir, J. M., Hayworth, K. E. and Hipkin, H. G.,
J. Chem. Eng. Data, 16., 280 (1971) .
30. Lenoir, J. M., Hayworth, K. E. and Hipkin, H. G.,
J. Chem. Eng. Data, 16., 285 (1971) .
31. Lenoir, J. M. and Hipkin, H. G., J. Chem. Eng. Data,
15, 368 (1970).
32. Lenoir, J. M. and Hipkin, H. G., J. Chem. Eng. Data,
In Press.
33. Lenoir, J. M., Robinson, D. R. and Hipkin H. G., J.
Chem. Eng. Data, .15, 26 (1970) .
34. Mather, A. E., Ph.D. Thesis, University of Michigan
(1967).
78
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
McCracken, P. G. and Smith, J. M., A.I.Ch.E. J., _2,
498 (1956).
McKay, R. A., Reamer, H. H., Sage, B. H. and Lacey,
W. N., Ind. Eng. Chem. 4.3, 2112 (1951).
Nelson, J. M., and Holcomb, D. E., Chem. Eng. Progr.
Symp. Ser. No. 7, £9, 93 (1953).
Nysewander, C. N., Sage, B. H. and Lacey, W. N.,
Ind. Eng. Chem., 3_2, 118 (1940).
Olds, R. H., Sage, B. H. and Lacey, W. N. , Ind. Eng.
Chem., 34, 1008 (1942).
Orentlicher, M. and Prausnitz, J. M., Can. J. Chem.
Eng., 45, 78 (1967).
Poston, R. S. and McKetta, J. J., J. Chem. Eng. Data,
JJL, 362 (1966).
Powers, J., Furtado, A. W., Globe, J. C. and Katz,
P. L., Proc. 49th NGPA Ann. Conv., pg. 1 (1970).
Reamer, H. H., Olds, R. H., Sage, B. H. and Lacey,
W. N., Ind. Eng. Chem., 34, 1526 (1942).
Reamer, H. H. and Sage, B. H., J. Chem. Eng. Data,
9, 24 (1964).
Reamer, H. H. and Sage, B. H., J. Chem. Eng. Data,
11, 17 (1966).
Reamer, H. H., Sage, B. H. and Lacey, W. N., J. Chem.
Eng. Data, _1, 29 (1956).
Reamer, H. H., Sage, B. H. and Lacey, W. N., Ind.
Eng. Chem., 42, 534 (1950).
Reid, R. C. and Sherwood, T. K., The Properties of
Gases and Liquids, 2nd Ed., McGraw Hill, N. Y. (1966).
Sage, B. H., Hicks, B. L. and Lacey, W. N., Ind. Eng.
Chem., 32, 1085 (1940).
Sage, B. H., Reamer, H. H., Olds, R. H. and Lacey,
W. N., Ind. Eng. Chem., 34_, 1108 (1942).
Shaw, R., J. Chem. Eng. Data, jL4_, 461 (1969).
79
52. Silverberg, P. M. and Wenzel, L. A., J. Chem. Eng..
Data, 10, 363 (1965).
53. Silverman, E. D. and Thodos, G., Ind. Eng. Chem.
Fund., 1, 299 (1962).
54. Starling, K. E., Proc. 49th NGPA Ann. Conv., Pg. 9
(1970).
55. Starling, K. E., Johson, D. W. and Cohen, C. P.,
"Evaluation of Eight Enthalpy Correlations," Res.
Rept. RR-4, NGPA, Tulsa, Okla., May 1971.
56. Stein, F. P. and Martin, J. ., Chem. Eng. Progr.
Symp. Ser. No. 44, 59_ (1963) .
57. Stevens, W. F. and Thodos, G., A.I.Ch.E. J., _9, 293
(1963).
58. Storvick, T. S. and Smith, J. M., J. Chem. Eng. Data,
5_, 133 (1960) .
59. Thiesen, A., Verhl. Deut. Phys. Ges., 1_6, 80 (1897).
60. Vaughan, W. E. and Collins, F. C., Ind. Eng. Chem.,
34, 885 (1942).
61. Watson, K. M. , Ind. Eng. Chem., 3_5, 398 (1943).
62. Wilson, G. M., Advan. in Cryogenic Eng., 2_, 392
(1966).
63. Yen, L. C. and Alexander, R. E., A.I.Ch.E. J., 11,
334 (1965) .
64. Yesavage, V. F., Ph.D. Thesis, University of Michigan
(1968).
65. Yesavage, V. F., Furtado, A. W. and Powers, J. E.,
Proc. Nat'l. Gas Process. Assoc., Tech. Papers, 47,
3 (1968) .
66. Yesavage, V. F., Mather, A. E., Katz, D. L. and
Powers, J. E., Ind. Eng. Chem., _59, 35 (1967).
A P P E N D I C E S
80
APPENDIX A
NOMENCLATURE
a,b,c,d Constants in the cricondentherm equation
A, B, C Constants in the mean enthalpy equation
BP^ Atmospheric boiling point of pure component
BPavq Average atmospheric boiling point of mixture
(ZXi BP-l)
Csc Pseudo cricondentherm (2, X^ C^)
H - | _ Enthalpy of saturated liquid (BTU/lb)
Hv Enthalpy of saturated vapor (BTU/lb)
k Constant in Equation 12
K Constant in Thiesen's equation
Kw Watson characterization factor
M Molecular weight of hydrocarbon
Mavg Average molecular weight of mixture
Mr Ratio of molecular weights for binary mix
tures, M^/M2/ such that M2
M^c Molecular weight of light component
n Constant in Equation 39
q Constant in Equation 19
s Exponent in Equation 41
t Exponent in Equation 28
T Temperature (°Rankine)
Tc Critical temperature (°Rankine)
Tcc Cricondentherm temperature (°Rankine)
81
82
Tcl
Critical temperature, component 1
T c 2
Critical temperature, component 2
Tci
Critical temperature of component (i)
Tr
Reduced temperature (T/Tc)
Tr
Reduced temperature based on cricondentherm =
T/Tcc
T
sc
Pseudo critical temperature
w Exponent in Equation 24
xi
Mol fraction of component (i)
X Mole fraction of lighter component of binary
where cricondentherm occurs
£*.
Exponent in Thiesen's equation
/?
Exponent in Equation 12
T
Exponent in cricondentherm Equation 30
€
Maximum ratio of cricondentherm temperature
to pseudo critical temperature
9
X
Exponent in definition of C, Equations
Heat of vaporization (BTU/lb)
19, 22
Xb
Heat of vaporization at base-level enthalpy
x;
Latent heat of vaporization of mixture
T = 0°F
when
p v
Density of vapor
Pi.
Density of liquid
83
Subscripts:
b Base level of enthalpy where = 0
i Refers to individual component of mixtures
m Mixture
he Heavy component
lc Light component
sc Pseudo values (pseudo critical, pseudo
cr icondentherm)
APPENDIX B
CALCULATED ENTHALPY VALUES OF A PENTANE-
CYCLOHEXANE-BENZENE MIXTURE
To demonstrate the application of the equations
presented in this study for the prediction of the enthalpy
of a multicomponent mixture, the enthalpy envelope of a
mixture containing 60.1% pentane, 18.9% cyclohexane and
20.0% benzene has been calculated. The constants used in
this calculation are as follows:
Components
Mol
Fraction
Mol
Weiqht
Critical
Temp., °R
Boiling
Point, °R Kw
Pentane 0.601 72.15 84 5.7 556.6 12.65
Cyclohexane 0.199 84.16 995.3 637.0 10.99
Benzene 0.200 78.11 1011.7 635.9 9.73
Molal Average Critical Temperature
(0.601) (845.7) = 508.3
(0.199)(995.3) = 198.1
(0.200)(1011.7) = 202.3
Tsc = 908.7
84
85
Molal Average Mol Weight
(0 .6 0 1 ) (7 2 .1 5 ) = 4 3 .4
(0 .1 9 9 ) (8 4 .1 6 ) = 16.7
(0 .2 0 0 ) (7 4 .1 1 ) = 15.6
Mavg = 75.7
Molal Average Boiling Point
( 0 . 6 0 1 ) ( 5 5 6 . 6 ) = 3 3 4 .5
(0 .1 9 9 ) (6 3 7 .0 ) = 126.8
(0 .2 0 0 ) (6 3 5 .9 ) = 127.2
BPgyg = 5 88 .5
Cricondentherm
Coefficients for Pure Components
Pentane:
*1 O C C
S = 1 . 1 + (0 .0 1 ) (7 2 .1 5 ) (12:65) = 1-8215 (EcJ* 4 1 )
BPS = ( 5 5 6 . 6 ) 1 *8215 = 1 00 ,50 0
n = TooTfoo “ °-00586 (E<3- 40)
Cyclohexane:
1 0 99
S = 1 .1 + (0 .0 1 ) (8 4 .1 6 ) (■^255 ) = 1-941 6 (E q . 4 1 )
BPS = ( 6 3 7 . 0 ) 1 *9415 = 3 25 ,00 0
n = - 5 8 8 .!t5__ = 0 .0 0 1 8 1 (E q . 40)
3 2 5 ,0 0 0
Benzene:
S = 1 .1 + (0 .0 1 ) (7 3 .1 1 ) (T f ^ -) = 1 .8 8 1 1 (E q . 4 1 )
86
BPS = (635.9)1*8811 = 214,000
n = 2H 7&S0 = °-00275 (Eq- 401
0-i ^>1 so that for this mixture the contribution
Q •
of n^X^1 can be neglected.
Cricondentherm of the Mixture (Eq. 39)
T
Tsc
CC = 1 + (0.00586(0.601) + (0.00181)(0.199)
+ (0.000275)(0.200)(Eq. 30)
= 1.0044
Tcc = 912.7°R
Saturated Enthalpy
Coefficients for Pure Components
Pentane: (Eq. 24)
w = (12.65 - 12.65)2 = 0
q = 13/(0.1 x 72.15)2*8 = 13/253 = 0.051
Cyclohexane: (Eq. 24)
w = (10.99 - 12.65)2 = 2.756
q = (13) (0.015 x 75.7)2-756 = 0>0227
(0.1 x 84.16)2*8
Benzene: (Eq. 24)
w = (9.73 - 12.65)2 = 8.526
. (13) (0.015.x 7. 5.. 7 J ^ 26 = 0 _0126
(0.1 x 78.II)2-8
87
Coefficient C for Pure Component (Eq. 17)
Pentane C = 1.06(12.65)3 x 10-7 = 2.16 x 10“4
Cyclohexane C = 1.06(10.99)3 x 10”7 = 1.41 x 10~4
Benzene C = 1.06(9.73)3 x 10"7 = 0.98 x 10”4
Molal Average C for Mixture
Csc = (2.16 x 10“4) (0.601) + (1.41 x 10"4) (0.199)
+ (0.98 x 10"4)(0.200) = 1.77 x 10~4
Coefficient C for Mixture (Eq. 22)
Cm
7^“ = 1 + (0.601) (0.051) + (0.199) (0.0227)
'-sc
+ (0.200) ().0126) = 1.037
Cm = 1.80 x 10"4
Heat of Vaporization
h \ 0 = 384 m~° *28 (108/^2)t (Eq. 27)
where t = (12.65/KW)2 - 1 (Eq. 28)
For Pentane: (Eq. 27) t = (12.65/12.65)2 -1=0
h \ Q = (384)/(72.15)0*28 = 384/3.31 = 116.0
For Cyclohexane: (Eq. 27) t = (12.65/10.99)2 - 1
= 0.3249
^ X 0 = 384(84.16)"0,28 [(108/(10.99) 2J °*3249
= (384) (0.9968)/3.460 = 110.6
88
For Benzene: (Eq. 27) t = (12.65/9.73)2 - 1 = 0.S903
H \ 0 = 384 (78. II)-0*28 [l08/(9. 73)^j °-6903
= (384) (1.0945)/3.387 = 124.1
For Mixtures:
v f \ Too 0.38
^Xo = ^ xi Xoi ^Tcc^ ^E<3* ^
= (0.601) (116.0) - 1 - (0.199) (110.6)
+ (0.200) (124.1)
(|2.|.-_Z)0 '38 = (116.54) (.9981) = 116.3
^ S O ^ X o U - f ^ ) 0'38 (Eq. 3)
= (116.3) 1 - (260/912.7) °*38
= (116.3) (0.88) = 102.3
89
Saturated Enthalpy of Pentane/Cyclohexane/Benzene*
(60.1/19.9/20.0 Mole %)
T (°R) Bm (T2 — 260) Cm (T2-2602) ^(1-T^.f Hv Hx
776 114.0 96.2 56.3 368 255
800 119.3 103.0 52.2 376 272
820 123.8 109.0 48.7 383 286
840 128.2 114.8 44.1 389 301
870 134.7 123.9 36.0 396 324
892 139.7 131.0 27.3 399 344
905.5 142.7 135.4 17.4 396 361
909 143.4 136.5 14.0 395 367
As defined by:
Hv = *^260 + Bm (T-260) + Cm (T2-2602) + 3 j AoU-Tr>*
H1 = ^ 2 6 0 + Bm (T-260) + Cm (T2-2S02) - A^ <1-Tr )*
where, from previous calculations:
Bm
m
= 0.221
cm
= 1.80 x 10"4
- 0
= 116.3
x '
= 102.3
^■260
Tr
= T/Tcc = T/912

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Prediction Of Enthalpy Of Saturated Paraffin Hydrocarbon Mixtures

PDF

An Experimental Investigation Of Heat Conduction Through Liquid-Liquid Phase Boundaries

PDF

The Separation Of Multicomponent Mixtures In Thermally-Coupled Distillation Systems

PDF

Thermal Conductivity Of Binary Liquid Mixtures

PDF

Phase Behavior In A Multicomponent Heteroazeotropic System

PDF

The Generation Of Predictor Equations By Recursive Linear Regression

PDF

Thermal Conductivity Of Liquids

PDF

Prediction of densities of liquid hydrocarbons

PDF

A Study Of The Behavior Of Thixotropic Fluids

PDF

Absorption And Scattering Of Thermal Radiation By A Cloud Of Small Particles

PDF

Mechanistic Study Of Air Pollution

PDF

Measurement of the enthalpy of n-pentane, n-octane, and n-pentane-n-octane mixtures

PDF

Radiative Transfer Through Plane-Parallel Clouds Of Small Particles

PDF

Vapor-Liquid Equilibria For The Benzene - N-Octane System Near The Regionof The Critical-Locus

PDF

The construction of a horizontal contactor for the study of interfacial velocities in immiscible fluid-fluid systems

PDF

A study of tack of Nordel hydrocarbon rubber

PDF

Investigations On The Flow Behavior Of Disperse Systems

PDF

The phase behavior of cyclohexane-rich mixtures with water

PDF

Dental Enamel Electrochemistry

PDF

Perovskite Structure Rare-Earth Transition-Metal-Oxide Catalysts

Asset Metadata

Creator Bishop, Harry Kenneth (author)

Core Title Predicting The Enthalpy Of Saturated Hydrocarbon Mixtures

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, chemical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Lenoir, John M. (committee chair), Binder, Raymond C. (committee member), Lockhart, Frank J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-774778

Unique identifier UC11364242

Identifier 7304905.pdf (filename),usctheses-c18-774778 (legacy record id)

Legacy Identifier 7304905

Dmrecord 774778

Document Type Dissertation

Rights Bishop, Harry Kenneth

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA