Thermal and catalytic processes in petroleum refining

Thermal and
Catalytic Processes in
Petroleum Refining

Serge Raseev
Consultant for UNESCO, Paris, France and
former Professor, Institute of Petroleum and Gases,
Bucharest-Ploiesti, Romania
Technical editor for the
English-language version

G. Dan Suciu

MARCEL DEKKER, INC.

Copyright © 2003 by Taylor & Francis Group, LLC

NEW YORK • BASEL


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A catalog record for this book is available from the Library of Congress.

Originally published in Romanian as Conversia Hidrocarburilor in 3 volumes, 1996–1997.
ISBN: 0-8247-0952-7
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To my dear wife Irena

Copyright © 2003 by Taylor & Francis Group, LLC


Preface

This book is considered to be a completely new version of the original book published in 3 volumes in Romania, in 1996–1997 under the title Conversia
Hidrocarburilor (‘‘the conversion of hydrocarbons’’).
Recent developments in petroleum processing required the complete revision
of some of the chapters, the elimination of outdated material and bringing up to

date the processes in which the technology was significantly improved.
Furthermore, the presentation of theoretical aspects has been somewhat expanded
and deepened.
The processes discussed in this book involve the conversion of hydrocarbons
by methods that do not introduce other elements (heteroatoms) into hydrocarbon
molecules. The first part is devoted to thermal conversion processes (pyrolysis, visbreaking, coking). The second part studies catalytic processes on acidic catalysts
(catalytic cracking, alkylation of isoalkanes, oligomerization). The third and fourth
parts analyze catalytic processes on metal oxides (hydrofining, hydrotreating) and on
bifunctional catalysts (hydroisomerization, hydrocracking, catalytic reforming),
respectively.
The importance of all these processes resides in the fact that, when required,
they allow large variations in the proportion of the finished products as well as
improvement of their quality, as required by increasingly stringent market demands.
The products of primary distillation are further processed by means of secondary
operations, some fractions being subjected to several processing steps in series.
Consequently, the total capacity of the conversion processes is larger than that of
the primary distillation.
The development of petroleum refining processes has made it possible to produce products, especially gasoline, of improved quality and also to produce synthetic
chemical feedstocks for the industry. The petrochemical branch of the refining industry generates products of much higher value than does the original refining industry
from which the feedstocks were derived.
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One should not overlook the fact that the two branches are of quite different
volume. A few percentage points of the crude oil processed in the refineries are
sufficient to cover the needs for feeds of the whole petrochemical and synthetic
organic industry and of a large portion of the needs of the inorganic chemicals
industry. The continuous development of new products will result in a larger fraction
of the crude oil than the approximately 10% used presently being consumed as
feedstocks for the chemical industry.

Hydrocarbons conversion processes supply hydrocarbons to the petrochemical
industry, but mainly they produce fuels, especially motor fuels and quality lubricating oils. The same basic processes are used in all these different applications. The
specific properties of the feedstocks and the operating parameters are controlled in
order to regulate the properties of the product for each application. In this book, the
processes are grouped by these properties, in order to simplify the presentation and
to avoid repetitions.
The presentation of each group of processes begins with the fundamentals
common to all the processes: thermodynamics, reaction mechanisms (including catalysis when applicable), and, finally, process kinetics. In this manner, operating
parameters practiced in commercial units result as a logical consequence of earlier
theoretical discussion. This gives the reader a well-founded understanding of each
type of process and supplies the basis on which improvements of the process may be
achieved.
The presentation of commercial implementation is followed by a discussion of
specific issues pertaining to the design of the reaction equipment, which results in the
unity of the theoretical bases with the design solutions adopted for commercial
equipment and the quantitative aspects of implementation.
My warmest thanks to Prof. Sarina Feyer-Ionescu, to my son Prof. George
Raseev, and especially to my technical editor Dr. G. Dan Suciu, for their support in
preparing the English-language version of this book.
Serge Raseev

Copyright © 2003 by Taylor & Francis Group, LLC


Preface to the Romanian Edition

This book is the fruit of many years of work in the petrochemical industry, and in
research, and of university teaching. It sums up my technical and scientific background and reflects the concepts that I developed over the years, of the manner in
which the existing knowledge on chemical process technology—and especially on the
processing of hydrocarbons and petroleum fractions—should be treated and conveyed to others.

While initially the discipline of process technology was taught mainly by
describing the empirical information, it soon changed to a quantitative discipline
that considers the totality of phenomena that occur in the processes of chemical
conversion of industrial interest.
The objective of process technology as a discipline is to find methods for the
continual improvement of commercial processes. To this purpose it uses the latest
advances in chemistry, including catalysis, and applies the tools of thermodynamics
and kinetics toward the quantitative description of the processes. In this manner it
became possible to progress from the quantitative description provided by the reaction mechanisms to the mathematic formulation for the evolution in time of the
processes.
In order to implement the chemical process on a commercial scale, a series of
additional issues need to be addressed: the effect of the operating parameters and the
selection of the optimal operating conditions, selection of the reactor type, the design
of the reaction equipment and of the other processing steps, the limitations due to
the heat and mass transfer, and the limitations imposed by the materials of construction.
Process technology thus becomes the convergence point of several theoretical
and applicative disciplines called upon to solve in an optimal manner the complex
interrelations among quite different sciences and phenomena (chemistry, hydraulics,
heat transfer, etc.). This situation requires a multifaceted competence and the full
understanding and control of the entire complex phenomenon that is the implemenCopyright © 2003 by Taylor & Francis Group, LLC


tation of chemical conversions in the conditions of the commercial units. Without it,
one cannot address the two basic questions about process technology: first, why the
commercial processes have been developed in the manner they are presently implemented and second, how they can be continually improved.
In this manner, by mastering the complex phenomena involved, the process
engineer is fully equipped to answer the ‘‘why’’ and ‘‘how’’ questions, and will be
able to become one of the important driving forces of technical progress. This is the
concept that has guided me during my entire professional activity.
This book treats the conversion of hydrocarbons and petroleum fractions by

thermal and catalytic methods, while attempting to answer the ‘‘why’’ and ‘‘how’’
questions at the level of the current technical knowledge. In this manner, I hope to
contribute to the education of specialists who will advance continuing developments
in processing methods.
I am thankful to Mr. Gavril Musca and Dr. Grigore Pop for their help in
creating this book. My special gratitude goes to Prof. Sarina Feyer-Ionescu, for her
special contributions.
Serge Raseev

Copyright © 2003 by Taylor & Francis Group, LLC


Contents

Preface
Preface to the Romanian Edition

PART I

THERMAL CONVERSION PROCESSES

1

Thermodynamic Analysis of Technological Processes
1.1 Calculation of the Overall Thermal Effect
1.2 Equilibrium Calculations for a Wide Range of Process Conditions
References

2

Theoretical Background of Thermal Processes
2.1 Thermodynamics of Thermal Processes
2.2 Reaction Mechanisms
2.3 Kinetics of Thermal Processes
2.4 Influence of Operating Conditions
References

3

Reaction Systems
3.1 Selection of Reactor Type
3.2 Reaction Systems
References

4

Industrial Implementation of Thermal Processes
4.1 Thermal Cracking at High Pressures and Moderate Temperatures
4.2 Coking
4.3 Pyrolysis
References

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Contents

5

Elements of Reactor Design

5.1 Design of the Reaction Section of Tubular Furnaces
5.2 Design of Soakers, Coke Drums, and Reaction Chambers
5.3 Systems Using Solid Heat Carrier
References

PART II

PROCESSES ON ACID CATALYSTS

6

Theoretical Basis of Catalytic Cracking
6.1 Process Thermodynamics
6.2 Cracking Catalysts
6.3 Reaction Mechanisms
6.4 Kinetics of Catalytic Cracking
6.5 Effect of Process Conditions
6.6 Catalyst Regeneration
References

7

Industrial Catalytic Cracking
7.1 Feed Selection and Pretreatment
7.2 Process History, Types of Units
7.3 Characteristic Equipment
7.4 Operation Aspects
7.5 Catalyst Demetallation
7.6 Yield Estimation
7.7 Economic Data

References

8

Design Elements for the Reactor–Regenerator System
8.1 Some Fluidization Problems
8.2 Fluidization with Solids Circulation
8.3 Reaction Systems
8.4 Catalyst Regeneration
8.5 Catalyst Entrainment
8.6 Catalyst Circulation, Transport Lines
References

9

Other Processes on Acid Catalysts
9.1 Oligomerization
9.2 Isoparaffin-Olefin Alkylation
References

PART III

PROCESSES ON METALLIC CATALYSTS

10 Hydrofining and Hydrotreating
10.1 Process Thermodynamics
10.2 Catalysts
10.3 Reaction Mechanisms
10.4 Process Kinetics

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Contents

10.5 Effect of Process Parameters
10.6 Industrial Hydrofining
10.7 Industrial Hydrotreating
10.8 Design Elements for the Reactor System
References
PART IV

PROCESSES USING BIFUNCTIONAL CATALYSTS

11 Hydroisomerization of Alkanes
11.1 Thermodynamics of Hydroisomerization
11.2 Hydroisomerization Catalysts
11.3 Reaction Mechanism
11.4 Kinetics of Isomerization
11.5 Influence of Operating Parameters
11.6 Industrial Hydroisomerization of Lower Alkanes
11.7 Hydroisomerization of Lube Oils and Medium Fractions
References
12 Hydrocracking
12.1 Thermodynamics of Hydrocracking
12.2 Catalysts
12.3 Reaction Mechanisms
12.4 Kinetics of Hydrocracking
12.5 Effect of Process Parameters
12.6 Commercial Hydrocracking of Distillates

12.7 Residue Hydrocracking
12.8 Processes Using Slurry Phase Reactors
12.9 Production of High Grade Oils by Hydrocracking
References
13 Catalytic Reforming
13.1 Thermodynamics
13.2 Catalysts
13.3 Reaction Mechanisms
13.4 The Kinetics of Catalytic Reforming
13.5 The Effect of Process Parameters
13.6 Catalyst Regeneration
13.7 Commercial Processes
13.8 Elements of Design and Modeling
13.9 Production of Aromatics
13.10 Dehydropolymerization of Lower Alkanes
References
14 Process Combinations and Complex Processing Schemes
14.1 Definition of Objectives
14.2 Evolution of the Range and Specifications of Products
14.3 Additional Resources
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Contents

14.4 Initial Data for the Selection of Refinery Configuration
14.5 Approach for Establishing the Configuration of a Modern
Refinery
References
Appendix Influence of the n=i-Alkanes Ratio in the Pyrolysis Feed

on the Ethene/Propene Ratio in the Products

Copyright © 2003 by Taylor & Francis Group, LLC


Appendix
Influence of the n/i-Alkanes Ratio in
the Pyrolysis Feed on the Ethene/
Propene Ratio in the Products

In order to evaluate the influence of the n/i-alkanes ratio in the feed on the ethene/
propene ratio in the pyrolysis effluent, three representative hydrocarbons were
selected: n-octane, 4-methyl-heptane and 2,5-dimethyl-hexane.
For these hydrocarbons, the product’s composition was calculated using the
F.O. Rice method at a temperature of 1100 K, which is typical for those used in
pyrolysis.
For n-octane, the complete decomposition of the radicals formed by different
substitution reactions gives:
ðaÞ

ðbÞ

ðcÞ
ðdÞ

ðeÞ
ðfÞ
The dissociation energies admitted by Rice for the bonds between hydrogen
and the primary, secondary, and tertiary carbons atoms (92.0, 90.8, and 88.0 kcal/
mol), give for 1100 K, according to Eq. (2.4):

rsec
¼ 1:7
rprim

rtert
¼ 5:7
rprim

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Each of the two last reactions have two possible paths for the decomposition of
the initial radicals (c,d and e,f). The relative rates of these may be calculated using
the dissociation energies given in Table 2.4. It results:
138;000À113;000
rd
1100ÁR
¼e
¼ 15:6
rc
130;000À121;000
rf
1100ÁR
¼e
¼ 2:5
re

The relative rates of the reactions (a)-(f) will be:
Reactions
(a)

Relative rate
1Â6¼6

Conversion per mol n-octane
0.22

(b)

1:7 Â 4 ¼ 6:8

0.26

(c)

1:7 Â 4 Â

1
¼ 0:436
15:6

0.02

(d)

1:7 Â 4 Â

14:6
¼ 6:364
15:6

0.24

(e)

1:7 Â 4 Â

1
¼ 2:72
2:5

0.10

(f)

1:7 Â 4 Â

1:5
¼ 4:08
2:5

0.16

Taking into account the number of molecules of ethene and propene formed in
the reactions (a)-(f), it results that for 1 mol of reacted n-octane the following
amounts of ethene and propene will be obtained:
— 2.14 mol ethene and
0.22 4 + 0.26 2 + 0.24 2 + 0.10 + 0.16 —
0.26 mol propene
The molar ratio ethene/propene = 8.23

For 4-methyl-heptane the different substitution reactions give:
ðaÞ
ðbÞ
ðcÞ

ðdÞ
ðeÞ
ðfÞ

ðgÞ

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ðhÞ
Estimating the relative rates of the reactions (a)/(b), (d)/(e), and (f)/(e) as in the
pyrolysis of n-octane, it results:
Reactions

Relative rate

Conversion per mol
4-methyl-heptane

(a)

1 Â 6 Â 13 ¼ 2

0.07

(b)

1 Â 6 Â 23 ¼ 4

0.14

(c)

1:7 Â 4 ¼ 6:8

0.24

(d)

1:7 Â 4 Â

1
¼ 0:436
15:6

0.02

(e)

1:7 Â 4 Â

13:6
¼ 5:928
15:6

0.21

(f)

1:7 Â 4 Â

1
¼ 0:436
15:6

0.02

(g)

5:7 Â 1 ¼ 5:7

0.20

(h)

1Â3¼3

0.10

The number of moles of ethene and propene formed from one mole of 4methyl-heptane decomposed will be:
0.07 + 0.14 2 + 0.24 + 0.21 + 0.20 + 0.10 = 1.10 moles ethene and
0.14 + 2 0.24 = 0.62 moles of propene
The molar ratio ethene/propene = 1.77
For 2,5-dimethyl-hexane, a similar reasoning gives:
ðaÞ

ðbÞ

ðcÞ

ðdÞ
ðeÞ
In the reactions (b) and (c) it is considered that the propyl radical decomposes
to propene and atomic hydrogen, since in this case the dissociation energy is only 167
kJ/mol. Analogously, in this example it was considered that the ethyl radical is
decomposed completely to ethene and atomic hydrogen. Both of these considerations correspond to the temperature and pressure conditions that are specific to
pyrolysis.
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The relative rates of the reactions (a)-(e) will be:
Reactions

1
¼ 0:77
15:6

0.04

14:6
¼ 11:23
15:6

0.52

(a)

1 Â 12 Â

(b)

1 Â 12 Â

(c)

Conversion per mol
2,5-dimethyl-hexane

Relative rate

1 5.7 = 5.7

0.26

(d)

1Â4Â

1
¼ 0:26
15:6

0.01

(e)

1Â4Â

14:6
¼ 3:74
15:6

0.17

The number of moles of ethene and propene formed from a mol of 2,5dimethyl-hexane will be:
0.52 moles ethene and
0.52 + 2 + 0.26 + 0.17 = 1.47 moles propene
The molar ratio ethene/propene = 0.35
Finally, it results:
Feed
C2H4/C3H8
n-C8H18
2-C7H15CH3
2,5-C6H12(CH3)2

ratio in the effluent
8.23
1.77
0.35

Copyright © 2003 by Taylor & Francis Group, LLC


1
Thermodynamic Analysis of
Technological Processes

The thermodynamic study of technological processes has two objectives:
Determination of the overall thermal effect of chemical transformations that
take place in the industrial process
Determination of the equilibrium composition for a broad range of temperatures and pressures in order to deduce optimum working conditions and
performances
The manner in which the two objectives are approached within the conditions of
chemical technology is different from the classical approach and requires the use of
the specific methodology outlined in this chapter.

1.1

CALCULATION OF THE OVERALL THERMAL EFFECT

In practical conditions under which technological processes operate, the main reaction may be accompanied by secondary reactions. In many cases the transformation
is of such complexity that it cannot be expressed by a reasonable number of chemical
reactions.
When calculating the heat of reaction in such situations, in order to avoid the
difficulties resulting from taking into account all reactions many times in the calculation, simplified approaches are taken. Thus, one may resort to the approximation
of limiting the number of the reactions taken into consideration, or to take account
only the main reaction. Such approximations may lead to significant errors.
Actually, the exact value of the thermal effect can be calculated without having
to resort to such approximations. Since the thermal effect depends only on the initial
and the final state of the system (the independence of path, as stipulated by the
second principle of thermodynamics), it may be calculated based on the initial and
final compositions of the system, without having to take in account the reactions that
take place.
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Accordingly, the classic equations, which give the thermal effect of a chemical
reaction:
X
X
0
0
0
¼
p ÁHfT
À
r ÁHfT
ð1:1Þ
ÁHrT
0
¼
ÁHrT

X

X

0
p ÁHcT

ð1:2Þ

may be written under the form:
X
X
ne ÁHfT À

ni ÁHfT
ÁHrT ¼

ð1:3Þ

ÁHrT ¼

X

0
r ÁHcT
À

ni ÁHcT À

X

ne ÁHcT

ð1:4Þ

The heats of formation ÁHf and of combustion ÁHc for hydrocarbons and
organic compounds, which are of interest in studying petrochemical processes, are
given in thermodynamic data books [1,2]. The values are usually given for temperature intervals of 100 K, within which linear interpolation is accurate. Thus, the
calculations that use the heat capacities may be avoided.
Example 1.1 shows how to perform the calculations by means of relations (1.3)
and (1.4).
Example 1.1. Compute the overall thermal effect of an industrial dehydrogenation process of isopentane to isoprene at 6008C.
The composition of the streams at the inlet and outlet of the reactor is given in
Table 1.1. The coke composition by weight, is 95% carbon and 5% hydrogen.

The calculations of the heat of formation at the inlet and the outlet of the
reactor at 6008C are collected in Table 1.2.
Table 1.1
Component
H2
CH4
C2H6
C2H4
C3H8
C3H6
C4H10
C4H8
C4 H6
i-C5H12
i-C5H10
C5H8
n-C5H12
n-C5H10
1,3-C5H8
coke

Reactor inlet feed + recycle
(wt %)

Reactor Outlet
(wt %)

0.3
79.3
16.6

0.8
1.8
1.7
-

1.0
0.6
0.7
0.7
0.7
1.4
1.2
2.2
0.2
55.8
17.1
12.1
0.8
1.7
2.0
1.8

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Table 1.2
Heat of formation
ÁHf0 (kcal/mol) [2]
Component
H2

CH4
C2H6
C2H4
C3H8
C3H6
C4H10
C4H8
C4H6
i-C5H12
i-C5H10
C5H8
n-C5H12
n-C5H10
1,3-C5H8
C

800
(K)

900
(K)

0
À20.82
À24.54
9.77
À30.11
0.77
À36.41
À6.32

23.25
À44.13
À13.45
14.16
À42.28
À12.23
14.17
0

0
À21.15
À24.97
9.45
À30.58
0.35
À36.93
À6.84
22.95
À44.65
À13.93
13.82
À42.85
À12.78
13.73
0

873=600
(K) (8C)

0

À21.05
À24.85
9.54
À30.45
0.46
À36.79
À6.70
23.03
À44.61
À13.80
13.91
À42.70
À12.63
13.85
0
&
kcal/kg
Total
kJ/kg

Inlet

Outlet

ni
(mol/kg)

ni ÁHf0873
(kcal/kg)

ne
(mol/kg)

ne ÁHf0873
(kcal/kg)

0.05
10.99
2.37
0.12
0.25
0.24
-

À1.84
À489.16
À32.71
1.67
À10.68
À3.03
-

9.92
0.37
0.23
0.25
0.16
0.33
0.21
0.39

0.04
7.73
2.44
1.78
0.11
0.24
0.29
-

0
À7.79
À5.72
2.39
À4.87
0.15
À7.73
À2.61
0.92
À344.06
À33.67
24.76
À4.70
À3.03
4.02
-

-

À535.75
À2243.1

-

À381.94
À1599.1

According to Eq. (1.3), the overall thermal effect per unit mass (kg) of feed will
be:
ÁHr;873 ¼

X

ne ÁHf 873 À

X

ni ÁHf 873 ¼ À1599 À ðÀ2243:1Þ ¼ 644 kJ/kg

Since the process is performed at a temperature much above the critical point
and at low pressure, no deviations from the ideal state have to be considered.
In many cases it is convenient to express the thermal effect on the basis of the
reacted isopentane or of the formed isoprene.
For this example, according to Table 1.1, 793 À 558 ¼ 235g, isopentane reacts
and 121 À 8 ¼ 113g, isoprene is formed. In these conditions, the thermal effect
expressed per mole of reacted isopentane is:
ÁHr ¼

644
 72:15 ¼ 197:7 kJ/mole
235

and per mole of produced isoprene:
Hr ¼

644
 68:11 ¼ 388:2 kJ/mole
113

If only the main reaction:
i À C5 H12 ¼ i À C5 H8 þ 2H2
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is taken into account, then according to the Eq. (1.1) one obtains:
ÁHr ¼ ðÁHf ÞC

5 H8

À ÁHf ÞC5 H12 ¼ 13:91 À ðÀ44:51Þ ¼ 58:42 kcal=mol

¼ 244:59 kJ=mol
the value being the same whether expressed per mole of isopentane or of isoprene.
This example shows that large errors may result if the computation of the
overall thermal effect is not based on the real compositions of the inlet and outlet
streams of the reactor.
Eq. (1.4) makes it possible to compute the thermal effects by using the heats of
combustion. This is useful for the conversion of petroleum fractions of other feedstocks consisting of unknown components. In such cases it is usually more convenient to perform the calculation in weight units, by modifying the terms n and ÁH
accordingly.
For liquid petroleum fractions, the heats of combustion may be determined by
using the graph of Figure 1.1 [3], from the known values of the specific gravity and

the characterization factor.
The characterization factor of residues may be determined graphically from the
viscosity, by means of Figure 1.2 [3].
The heat of combustion of coke is determined experimentally or less precisely
on the basis of the elementary composition.
The heats of combustion of gaseous components may be found in data books
[1,2], or may be calculated from the heats of formation [2], by applying Eq. (1.1). For
hydrocarbons, this equation takes the form:
m
ð1:5Þ
ðÁHa ÞCn Hm ¼ nðÁHf ÞCO2 þ ðÁHf ÞH2 O À ðÁHf ÞCn Hm
2
This heat of combustion of gases must be brought to the same reference state as
that of liquid fractions, i.e. 158C and liquid water. For these conditions, Eq. (1.5)
becomes:
ðÁH a ÞCn Hm ¼ À393:77n À 143:02m À ðÁH f ÞCn Hm
ð1:6Þ
It must be noted that Eq. (1.6) gives the heat of combustion in thermodynamic
notation, expressed in kJ/mole. Figure 1.1 gives the heat of combustion in technical
notation, expressed in kJ/kg.
An illustration of these calculations is given in Example 1.2.
Example 1.2. Calculate the thermal effect of the processing of a vacuum residue
by visbreaking. The composition of the produced gases is given in Table 1.3. The
yields and the characterization factors, KUOP for the feed and the fuel oil were
obtained from Table 1.4.
The characterization factor and the specific gravities were used to determine
the heats of combustion for all the liquid fraction from Figure 1.1.
SOLUTION. By introducing the values of the heats of combustion from Tables
1.3 and 1.4 into Eq. (1.4), one obtains:
Qr ¼ 43,645 À ð0:0244 Â 51,319 þ 0:1166 Â 46,827 þ 0:859 Â 43,233Þ

¼ À204 kJ/kg
Calculation of the thermal effects for a specific reaction, usually a small number obtained as the difference of heats of combustion, usually larger numbers, is
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Figure 1.1 Heat of combustion of petroleum fractions. Final state: gaseous CO2 and liquid
water at 158C.

associated with large errors, unless the determination of the values of the heats of
combustion was made with high accuracy. This fact is especially valid for liquid
fractions, for which the graphical determination of the combustion heats may give
errors. In order to obtain exact results, the determination of the heats of combustion
of the liquid fractions by direct calorimetric methods is recommended.
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Figure 1.2

KUOP as function of the kinematic viscosity and density.

Graphs and empirical relations are given [4–7] for the calculation of the thermal effect in the petroleum refining processes. The values calculated by their means
and the numerical values given in the literature must be critically analyzed, taking
into account the characteristics of the feed, the operating conditions, and the conversion. Only values that refer to comparable feeds and conditions should be used in
computations.
For the process of thermal cracking, the use of equation [8] is recommended:
ÁH ¼ 117,230

Ma À Mp
Ma  Mp

Copyright © 2003 by Taylor & Francis Group, LLC

ð1:7Þ


Table 1.3
Component

Composition
(wt %)

0
ÞC
ðÁH288
(kJ/kg)

0
ÞC fraction
(ÁH283
(kJ/kg)

CH4
C2H6
C3H8
C3H6
i-C4H12
n-C4H12
i-C4H10
n-C4H10
1-C4H8

cis-2-C4H8
trans-2-C4H8
C4H6
C5+

22.32
18.84
4.57
20.56
7.97
2.20
9.20
1.85
3.50
0.55
2.37
2.01
4.06

À55,540
À51,910
À50,330
À50,380
À48,950
À49,390
À49,540
À48,170
À48,470
À48,340
À48,270

À47,020
À49,050

À12,396
À9,780
À2,300
À10,358
À3,901
À1,093
À4,558
À891
À1,696
À266
À1,144
À945
À1,991

0
ÞC fraction À51,319 kJ/kg
Total (ÁH288

The calculated ÁH is expressed in kJ/kg of feed. The sign is that used in the
thermodynamic notation.
Using the data from example 1.2 (see the Table 1.4), this equation gives:
ÁH ¼ 117,230

440 À 253
¼ 197 kJ/kg
440 Â 253

which gives the same result as the heats of combustion method.
In the literature, the thermal effect of reactions is often expressed per unit mass
of main product and not per unit mass of feed. In some cases, this way of expression is
useful, since the thermal effect thus becomes actually independent of conversion [5].
1.2

EQUILIBRIUM CALCULATIONS FOR A WIDE RANGE OF
PROCESS CONDITIONS

The computation of the equilibrium compositions for a wide range of process conditions (temperatures and pressures) has the purpose of identifying practical operating conditions that will optimize the performance of the process. Depending on the
specifics of the process, the problem may be limited to the calculation of the equilibrium of the main reaction, or may be extended also to the secondary reactions.
In all cases, the composition at equilibrium, calculated on basis of thermodynamic principles, represents the maximum conversion that is possible to achieve in
the given conditions. There is however no certainty that such performance will be
actually obtained. Nonthermodynamic factors, such as the reaction rate and the
residence time within the reactor will determine how close the actual performance
will approach the theoretical one.
The use of classical methods for computing equilibrium compositions for the
large number of temperature–pressure values needed for thermodynamic analysis of
a broad range of process conditions necessitates a large number of calculations. A
Copyright © 2003 by Taylor & Francis Group, LLC


Figure 1.3

Thermodynamic equilibrium of propene dimerization. Parameter: conversion x

as %.

method elaborated by the author many years ago [9] provides a simple method for
the calculation and graphical representation of the equilibrium. The method is outlined below.

For any chemical reaction, the standard free energy is expressed by the relation:
ÁG0T ¼ ÁH 0T À TÁS0T
Copyright © 2003 by Taylor & Francis Group, LLC

ð1:8Þ


Table 1.4

Feed
Products
gases
gasoline
fuel oil

Density

Viscosity
(cSt)

Characterization
factor
(KUOP Þ

Thermal
effect
(kJ/Kg)

1.0000

0.989

1,000

11.38

43,645

0.0244
0.1166
0.8590

0.760
1.000

630

11.9
11.1

51,319
46,827
43,233

Yields
(wt %)

and as function of the equilibrium constant, by the expression:
At equilibrium, ÁGT ¼ 0 and ÁG0T ¼ RT ln K a

(1.9)

Assuming that the substances participating in the reaction do not deviate from
the behaviour of ideal gas, the equilibrium constant may be expressed by the relation:
Ka ¼ Kp ¼

’i ðxÞ
pÁn

ð1:10Þ

Here, ’iðxÞ is a function of the conversion at equilibrium x. The form of this function
depends on the stoechiometry of the reaction but is independent on the nature of the
substances that participate in the reaction.
Equating Eqs. (1.8) and (1.9), and replacing K a with the expression (1.10),
dividing the right and left sides by TÁHT0 , and effecting some elementary transformations, one obtains:
1
RÁn
ÁST0 À R ln ½’i ðxފ
¼
ln
p
þ
T ÁHT0
ÁHT0

ð1:11Þ

For a given chemical reaction and a temperature range of 200–3008C, which is
sufficient for a process analysis, ÁH 0 T and ÁS0 T can be considered constants. In

these conditions, using as coordinates log p and 1=T, the Eq. (1.11) corresponds to a
family of parallel straight lines with the equilibrium conversion x as parameter.
Simple plots are obtained, by writing:
2:3 RÁn ¼ b
and
R ln½’iðxފ ¼ d
Equation (1.11) becomes:
1
b
ÁST0 À d
¼
log
p
þ
T ÁHT0
ÁHT0

ð1:12Þ

The parameter b depends only on the stoechiometric form of the chemical
reaction. Parameter d depends both on the stoechiometry and on x, the conversion
at equilibrium. Both b and d are independent of the nature of the chemical subCopyright © 2003 by Taylor & Francis Group, LLC


stances that take part in the reaction and have been calculated [9] for chemical
reactions of various stoechiometric forms (Table 1.5).
For reactions proceeding in the opposite direction, the sign of the constants b
and d must be changed, and the meaning of the conversion x reversed (for example
x ¼ 0:95 from the table will have the meaning x ¼ 0:05 for the reverse reaction).
Since in plots of log p versus 1=T the straight lines of constant conversion are

parallel, it is enough to calculate one point of each line and to determine the slope of
all the straight lines by calculating just one point for any other pressure. Thus, the
whole family of lines may be obtained by selecting a pressure of 1 bar for the
determining one point on each straight line and a pressure of either 10 bar or 0.1
bar for which one calculates the one point needed to determine the slope of all lines.
For these values of the pressure, the relation (1.12) becomes:
p ¼ 1bar

1 ÁST0 À d
¼
T
ÁHT0

p ¼ 10 bar

1 ÁST0 À d þ b
¼
T
ÁHT0

p ¼ 0:1 bar

1 ÁST0 À d À b
¼
T
ÁHT0

ð1:13Þ

The calculation is illustrated by the Example 1.3.

Example 1.3.

For the reaction:

2C3 H6 Ð C6 H12
determine the equilibrium graph for pressures comprised between 1 and 100 bar and
temperatures between 450–8008C.
SOLUTION. The reaction corresponds to the form 2A $ B, in Table 1.5.
Using the thermodynamic constants for 900 K [2] and taking mean values for ihexenes, it results:
0
¼ À20020 À 2 Â 350 ¼ À20,720 cal/mol
ÁH900
0
¼ 143:65 À 2 Â 89:75 ¼ À35:85 cal/mol K
ÁS900

Using the Eq. (1.13) corresponding to the pressure of 1 bar and the values of the
constant d from the Table 1.5, following pairs of values are obtained:
X
ð1=TÞ Â 103

0.01 0.05 0.10 0.20 0.3 0.40 0.50 0.60 0.70 0.80 0.90 0.95 0.99
1.22 1.38 1.46 1.54 1.60 1.65 1.70 1.76 1.82 1.90 2.04 2.17 2.50

For the pressure of 10 bar and x ¼ 0:5 and using the constant b from the Table
1.5, one obtains, according to the Eq. (1.13):
1=T ¼ 1:48 Â 10À3
By using the obtained values, the equilibrium is represented in Figure 1.3.
Note that for temperature ranges of not more than 200–3008C that intervene in
the analysis of industrial processes, the variations with the temperature of ÁH 0 and

ÁS 0 may be neglected, without consequently introducing any practical errors.
Deviations from ideal conditions are important near the critical state and do
not affect the results at temperatures much higher than the critical, as used in the
Copyright © 2003 by Taylor & Francis Group, LLC