CHEMICAL PROCESS SIMULATION OF HEXANE 11111:.

ISOMERIZATION IN A FIXED-BED AND

A 9~:!'<2~ REACTOR .. ----

By

TAl-CHANG KAO II

Bachelor of Science

Tunghai University

Taiwan, Republic of China

1986

Submitted to the Faculty of the Graduate College of the

Oklahoma State University in partial fulfillment of

the requirements for the Degree of

MASTER OF SCIENCE May, 1991

~ . '' l •, '·····

r,

i :

Oklahoma State Univ. Library

CHEMICAL PROCESS SIMULATION OF HEXANE

ISOMERIZATION IN A FIXED-BED AND

A CSTCR REACTOR

Thesis Approved:

Dean of the Graduate College

ii

1393133

PREFACE

In recent years, Chemical Reaction Engineering has

developed to a science that uses complicated theoretical

apparatus and sophisticated mathematical models to describe

the behavior of reacting system. It is not simple to find a

realistic approach to the application of the theory in

practical technological research. The main purpose of this

study is to develop a more reliable model to simulate

chemical reactions which proceed in reactors. For this

research work, the ideal plug flow reactor and CSTCR are

chosen.

Many people have aided me in this research work, and it

is impossible to adequately acknowledge their efforts except

in a general way. I am deeply indebted to Dr. Arland H.

Johannes who offered me numerous valuable suggestions and,

who was the main promoter of this study. Also, Dr. Robert

L. Robinson, Jr. and Dr. Khaled A. M. Gasem are most

generous in the encouragement and cooperation. Financial

support from the School of Chemical Engineering is appreci

ated.

Finally, I should like to acknowledge the help of my

parents, Mr. Kao, Ming-Pan and Mrs. Kao, Cheng Su-Chu for

their moral encouragement and constant support throughout

iii

this endeavor. All these are gratefully acknowledged.

iv

TABLE OF CONTENTS

Chapter Page

I. INTRODUCTION 1

II. LITERATURE REVIEW ........ ..... ... ... .. . . . .. . . . . . 3

Importance of Isomerization................ 3 Hexane Isomerization Kinetics . .. .. . . . . ..... 7 Catalytic Reactors . . . . . . . . . . . . . . . . . . . . . . . . . 10 LHSV and Hydrogen-to-Hydrocarbon Ratio ..... 15

LHSV ....... •. . . . . . . . . . . . . . . . . . . . . . . . . . 15 Hydrogen-to-Hydrocarbon Ratio ......... 15

Process Descriptions ....................... 16 Penex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 I s orne rat e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 BP . ................... I • • • • • • • • • • • • • • • • 17

Catalysts .. ·................................ 17 Deactivation . . . . . . . . . . . . . . . . . . . . . . . . . . 19

III. FIXED-BED REACTOR AND CSTCR DESIGN PRINCIPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Fixed-Bed Reactors ......................... 21 Derivation of Mass Balance

Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Derivation of Energy Balance

Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Pressure Drop Prediction . . . . . . . . . . . . . . 26 Model Simulation . . . . . . . . . . . . . . . . . . . . . . 27 Numerical Approach . . . . . . . . . . . . . . . . . . . . 28

Design Equations for a CSTCR ............... 28 Derivation of Mass Balance

Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 Derivation of Energy Balance

Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Model Simulation . . . . . . . . . . . . . . . . . . . . . . 32 Numeri ca 1 Approach . . . . . . . . . . . . . . . . . . . . 3 2

IV. PROGRAM DESCRIPTIONS AND TESTING ................ 33

Software Applied 33

v

Chapter Page

Program Organization and Subroutine Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

fixed-bed reactor ..................... 34 DATAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ARRAY ... ·- ... I •••••••••• I • • • • • • • • • 3 4 FNC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 PROP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 EQCON . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 SLTRES . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 RXN . • . . . . . . . . . • . . . . • . . . . . . . . . . . . . 4 5 LINPAC. ~ ...... I • • • • • • • • • • • • • • • • • • • 46

ester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 NEWTN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4'6 ENGBALS . . . . . . . . . . . . . . . . . . . . . . . . . . 48 THEQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Testing and Results ........................ 50 Overview ............................ -. . SO

Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Optimized Model.............. 52 Fixed-Length Model .......... 55 HEXCR . . . . . . . . . . . . . . . . . . . . . . . 68

V. CONCLUSIONS AND RECOMMENDATIONS ................. 72

LITERATURE

APPENDIXES

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Recommenda t i ens . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3

CITED ................................. · · · · · · 75

77

APPENDIX A- COMPUTER PROGRAM FOR HEXFI ......... 78 APPENDIX B- COMPUTER PROGRAM FOR HEXCR ......... 99 APPENDIX C- LISTING OF CONTROL PANELS .......... 120 APPENDIX D - EFFECT OF PRESSURE UPON

EQUILIBRIUM CONSTANT ............... 131

vi

LIST OF TABLES

Table Page

I. Isomerization Catalysts .......................... 5

II. Octane Numbers of Selected Hydrocarbons and Refinery Blend Stocks ....................... 8

III. Heat Capacities of Hexane Isomers ................ 39

IV. Gibbs Energy of Formation of Hexane Isomers ...... 40

v. Results of the Comparison of Experimental Data with Model Predictions for an Isothermal Fixed-Bed Reactor ................... 54

VI. Results of the Comparison of Isothermal and Adiabatic Operation of a CSTCR ............. 71

vii

LIST OF FIGURES

Figure Page

1. Sketch of Fixed-Bed Reactor ....................... 12

2 . Sketch of CSTCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 . Typical Isomerization Process 18

4. Program Organization of HEXFI 35

Sa. Program Organization of CSTCR 36

5b. Program Organization of Energy Balance ............ 37

5c. Program Organization of Newton's Method

6.

7.

8.

9.

10.

11.

12.

13.

Mole Fraction Distributions of Hexane Isomerization (35 ATM, 408 K, Isothermal)

Mole Fraction Distributions of Hexane Isomerization (61 ATM, 408 K, Isothermal)

Mole Fraction Distributions of Hexane Isomerization (35 ATM, 366 K, Isothermal)

Mole Fraction Distributions of Hexane Isomerization (61 ATM, 366 K, Isothermal)

Mole Fraction Distributions of Hexane Isomerization (35 ATM, 366 K, Adiabatic)

Mole Fraction Distributions of Hexane Isomerization {61 ATM, 366 K, Adiabatic)

Mole Fraction Distributions of Hexane Isomerization {35 ATM, 408 K, Adiabatic)

Mole Fraction Distributions of Hexane. Isomerization {61 ATM, 408 K, Adiabatic)

14. Temperature Profile vs Reactor Length of

38

56

57

58

59

60

61

62

63

Hexane Isomerization {35 ATM, 366 K) ............ 64

viii

Figure Page

15. Temperature Profile vs Reactor Length of Hexane Isomerization (61 ATM, 366 K) ............ 65

16. Temperature Profile vs Reactor Length of Hexane Isomerization (35 ATM, 408 K) ............ 66

17. Temperature Profile vs Reactor Length of Hexane Isomerization (61 ATM, 408 K) ............ 67

18. Control Panel 1 for Fixed-Bed Reactor Initial Parameter Settings ...................... 121

19. Control Panel 2 for Fixed-Bed Reactor Initial Parameter Settings ...................... 122

20. Control Panel 1 for Fixed-Bed Reactor Optimized Model, Isothermal Reaction ............ 123

21. Control Panel 2 for Fixed-Bed Reactor Optimized Model, Isothermal Reaction ............ 124

22. Control Panel 1 for Fixed-Bed Reactor Fixed-Length Model, Isothermal Reaction ......... 125

23. Control Panel 2 for Fixed-Bed Reactor Fixed-Length Model, Isothermal Reaction ......... 126

24. Control Panel 1 for CSTCR Initial Parameter Settings ...................... 127

25. Control Panel 2 for CSTCR Initial Parameter Settings ...................... 128

26. Control Panel 1 for CSTCR Isothermal Reaction ............................. 129

27. Control Panel 2 for CSTCR Isothermal Reaction ............................. 130

ix

CHAPTER I

INTRODUCTION

Present isomerization applications in petroleum

refining are used to provide additional feedstock for

alkylation units or high-octane fractions for gasoline

blending. Straight chain paraffins, such as n-butane,

n-pentane or n-hexane can be converted to isomers by

continuous, catalytic (aluminum chloride, antimony

trichloride, etc.) processes.

Isomerization found initial commercial application

during World War II for making high-octane aviation

gasoline. Atlas Processing Company of Shreveport, La., was

the first to install a hexane isomerization process (Penex)

for the production of a motor-fuel blending component (1).

Licensed by the Pure Oil Company, a division of the

Union Oil Company of California, Isomerate is another

continuous isomerization process designed to convert

pentanes and hexanes into highly branched isomers. A rugged

dual-function catalyst is used in a fixed-bed reactor system

(2). Another process licensed by British Petroleum Company,

BP is a two fixed-bed-reactor (one for Cs feed) process

using high activity Platinum catalyst and external hydrogen

(3). These processes will be described in more detail.

1

2

This study is devoted to model design and neglects

the mechanical design and stability study of hexane

isomerization reactors. To model a reactor it is necessary

to write a set of mathematical equations which express the

behavior of the reacting system under various operating

conditions. For the fixed-bed reactor model, two ordinary

differential equations (ODEs) are required to describe the

reactor system. One is a reactor mass balance and the other

is energy balance. For the perfectly mixed reactor model,

two linear equations are also required to describe the

reactor system. One is a reactor material balance and the

other is a reactor energy balance. The two ODEs describing

catalytic fixed-bed and the two linear equations describing

perfectly mixed reactors must be solved simultaneously and

can be solved by means of a computer.

There are various numerical methods which have been

developed to solve systems of simultaneous ODEs. A modified

fourth-order, Runge-Kutta algorithm will be utilized to

obtain the solution of the initial-value ODEs encountered in

fixed-bed reactor problems. Newton's method was used to

solve the linear equations in the Continuously Stirred Tank

Catalytic Reactor (CSTCR) model.

The fixed-bed reactor program is called HEXFI. The

CSTCR model is called HEXCR. Both programs are written in

the FORTRAN language and are listed in Appendix A and B.

CHAPTER II

LITERATURE REVIEW

The literature review will cover the following

subjects:

1. Importance of Isomerization

2. Hexane Isomerization Kinetics

3. Catalytic Reactors

4. Process Descriptions and Catalysts

Importance of Isomerization

The demand of today's automobiles for high-octane

gasolines has stimulated the use of catalytic reforming.

Catalytic reformate furnishes approximately 45-55\ of the

United States gasoline requirements and with the increasing

utilization of low-lead and lead-free gasolines, this can be

expected to increase (4).

Catalytic reforming is a continuous process to upgrade

low-octane virgin, or heavy catalytically cracked naphthas

into high-octane components for motor or aviation fuel

blending or petrochemical usage. The commercial processes

available for use today can be broadly classified as moving

bed, fluidized-bed or fixed-bed types. The primary reaction

mechanisms include in the followings (2):

3

(1) dehydrogenation of naphthenes

(2) dehydrocyclization of paraffins

{3) paraffin isomerization

(4) dehydroisomerization of naphthenes

(5) paraffin hydrocracking

{6} desulfurization

{7) olefin saturation

The petroleum processing industry is without doubt the

largest user of catalysts in the chemical industry. The

catalytic materials include both solids and liquids and

range all the way from common clay to precious metals.

Table I lists various catalytic processes commonly used in

petroleum processing and the materials employed.

4

To understand the significance of catalytic reforming

in refinery operations, the use of the octane number as a

standard for gasoline quality must be understood. Octane

rating has been used for years to measure the antiknock

performance of gasoline. The higher the octane number, the

less the tendency for a gasoline to produce a knocking sound

in an automobile engine.

In 1923, a standard was established for measuring the

octane number of gasoline. The straight-chain paraffin,

n-heptane, was assigned an octane number of zero, and a

branched-chain paraffin, iso-octane {2,2,4-trimethyl

pentane), was assigned an octane number of 100. The octane

number of a gasoline is determined by comparing its anti-

TABLE I

AISOMERIZATION CATALYSTS

Low-temperature processes Catalyst Selectivity

Vapor phase: Anglo-Jersey . . . . . . . . . Impreg. bauxite 95 Phi 11 ips . . . . . . . . . . . . . Impreg. bauxite 95 Shell . . . . . . . . . . . . . . . . Impreg. bauxite 95

Liquid phase: UOP . . . . . . . . . . . . . . . . . . Complex on quartz 97 Standard Oil . . . . . . . . . Liquid complex 97

High-temperature processes Catalyst Regeneration

Butamer . . . . . . . . . . . . . . . Platinum None required Iso Kel . . . . . . . . . . . . . . . Precious metal Regenerable Isomerate . . . . . . . . . . . . Nonnoble metal Infrequent Penex . . . . . . . . . . . . . . . . Platinum None required

AREFERENCE (2)

(11

knock engine performance with various blends of n-heptane

and iso-octane under specified laboratory conditions.

Automotive engineers fix compression ratios for particular

engine designs. Engines with higher compression ratios

require higher-octane-number fuel than those with lower

ratios.

6

Two methods of determining motor fuel octane number are

now in use (5):

1) the research method, ASTM D-2699, a laboratory

simulation of engine performance at low speed

(reported as RON, research octane number).

2) the motor method, ASTM D-2700, a laboratory

simulation of engine performance at high speed

(reported as MON, motor octane number).

Road testing a number of different autos under varying

conditions and gasolines have shown that the average of the

RON and MON, (R+M}/2, gives an acceptable number for rating

gasolines. This average is now a specification on gasoline

and is the octane number displayed on the pumps at service

stations. In the U.S., most service stations offer three

gasoline choices: leaded regular, unleaded regular and

unleaded premium. Leaded regular at service stations has an

octane rating of 88-89. Unleaded regular has an octane

rating of 87-88 and unleaded premium is 91-92.

A few examples of octane number of individual

hydrocarbons and some selected refinery motor fuel blend

stocks are shown in Table II. Note Cs+ reformate

7

(pentane and heavier) from a reformer is the only gasoline

stock that varies in octane number. Reformate octane number

can be varied from 1 to 25 or more. That flexibility is

what makes the catalytic reformer so useful to the petroleum

refiner.

There is one thing I would like to mention here about

tetraethyl lead (TEL) in TABLE II. First introduced in

1922, its effect in improving the octane number of motor

gasoline is well established, the response varying with the

hydrocarbon composition of the gasoline. In spite of much

research work, the exact mechanism by which TEL works to

suppress knock is not known. It is visualized that the

compound is decomposed by heat in the combustion chamber.

This gives rise to particles which then influence the

chemical reactions involved in the combustion of the fuel.

This promotes smooth combustion to the exclusion of knock.

However, TEL has certain well-recognized disadvantages such

as tending to increase deposits in the combustion chamber,

tending to inverse exhaust valve burning, and tending to

foul spark plugs (6).

Isomerization Kinetics

The isomerization of n-hexane to its isomeric forms has

been the subject of a great deal of study (7-10). Various

postulations related to the reaction paths have been made

and rate constants for the mathematical model have been

determined. There are some possible models which describe

TABLE II

OCTANE NUMBERS OF SELECTED HYDROCARBONS AND REFINERY BLEND STOCKSa

Research Motor ml TEL/galb ml TEL/gal

Octane Rating 0.0 3.0 0.0 3.0 (R + M)/2

n-Butane 94.0 104.0 89.0 104.7 91.5 i-Butane 102.0 118.0 97.0 - 99.5 n-Pentane 61.8 84.6 83.2 84.8 72.5 i-Pentane 93.0 104.9 89.7 107,. 3 91.4 n-Octane - 24.8 - 28.1 2 I 2 I 4-TMPC 100.0 115.5 100.0 115.5 100.0 Cyclohexane 84.0 96.6 77.6 87.4 80.8 Alkyl ate 93.0 104.0 92.0 106.0 91.0 Csf- reformate 90.0 98.0 81.0 89.0 85.5 Csf- reformate 95.0 101.0 85.0 93.0 90.0 Csf- reformate 100.0 104.5 90.0 94.0 95.0

a REFERENCE (5)

b To convert milliliters of tetraethyl lead per gallon(ml TEL/gal) to grams Pb/gall multiply ml TEL/gal by 1.057

c Trimethylpentane

00

9

the reaction kinetics:

Frolich (11) and Evering (9) deduced from experimental

data that the isomerization of n-hexane proceeded stepwise

according to the scheme.

Model I:

2-MP

~ ll ~DMB <---=> 2,2-DMB

3-MP

Note that for this model, they used AlCl3-HCl catalyst.

Frolich and Evering also found that the rate determining

step for isomerizing n-hexane to 2,2-dimethylbutane (2,2-

DMB) was the last step in Model I. Later on, Evering

proposed another mathematical model (9) based on graphical

analysis of his experimental data.

Model II:

2-MP

<=> J t <====> 2,3-DMB <====> 2,2-DMB

3-MP

To simplify calculation of the reaction kinetics, a

slightly different reaction mechanism was proposed by Cull

and Brenner (12). First-order reactions were assumed and

the system was described by differential equations given in

the following:

Model III:

n-C6 --- 3-MP --- 2-MP --- 2,3-DMB --- 2,2-DMB

d(n-C6)

dt

d(3-MP)

dt

ka

10

d(2-MP)

dt = k3{3-MP) + k6(2,3-DMB) - (k4+ks)(2,3-DMB)

d(2,3-DMB) = ks(2-MP) + ka(2,2-DMB) - (k6+k7)

dt {2,3-DMB)

d(2,2-DMB) = k7{2,3-DMB) - ka(2,2-DMB)

dt

To test this model, data were obtained from batch runs

and a nonlinear regression technique was applied to

determine the rate constants.

Catalytic Reactors

Choosing a suitable reactor for a gas-solid reaction is

a question of matching the characteristics of the reaction

system, especially the reaction kinetics, with the charac-

teristics of the reactors under consideration.

There is a wide choice of contacting methods and

equipment for gas-solid reaction. These reactors include

fixed-bed reactor, Carberry reactor and fluidized-bed

11

reactor. Each of these reactors has different key features

and are discussed below.

Fixed-bed reactors consist of one or more tubes packed

with catalyst particles and are typically operated in a

vertical position. The catalyst particles may be a variety

of sizes and shapes: granular, pelleted, cylinders, spheres,

etc .. Because of the necessity of removing or adding heat,

it may not be possible to use a single large-diameter tube

packed with catalyst. In this event the reactor may be

built of a number of tubes encased in a single body, such as

is illustrated in Figure 1. The energy exchange with the

surroundings is obtained by circulating, or boiling, a fluid

in the space between the tubes. For an exothermic reaction,

heat evolved due to reaction is much often greater than that

can be transferred to the cooling fluid. This leads to a

maximum temperature somewhere in the reactor, and is called

a "hot spot" (13).

The construction of this type of reactor is

straightforward. In general, unsteady operation results due

to catalyst aging. The reactor is, not very useful for

gathering kinetic data when the catalyst decays rapidly

(14). Leva {15) reported the calculation of pressure drop

along the fixed bed, and Nauman (16) suggests using the

Ergun equation to calculate the pressure drop in this type

of reactor.

The rotating-basket reactor (often known as the

Carberry reactor) has been widely used for gas-solid

Heotinq (or coo!inq) __ !-Fluid in

Tubes pocked witll coto!yst-~

--v

Product stream

t r-----r-r-

~---~--- .... ~....--

t Feed

stream

Heotinq (or coolinq)

----+- Flutd out

Figure l. Multitube Reactor, Fixed-Bed; adapted from Smith (1970).

12

13

catalytic reactions. The construction is not very

difficult, but it is more complex and expensive to build

than a batch or fixed-bed reactor. The catalyst baskets can

be attached to a stirrer or they can be used as the stirrer

paddles. The reactor is operated under transient conditions

if the catalyst decays rapidly. Otherwise, steady-state

operation is obtained. Baffles can be installed to obtain

better contact (17). Figure 2 sketches the main features of

an experimental reactor.

This type of reactor has several disadvantages.

Erosion of the catalyst may occur under sever agitation and

it can be a problem to keep powered catalyst in the baskets.

The surface temperature of the catalyst is very difficult

to measure and it is often erroneously assumed to be equal

to the bulk temperature. For these reasons, the use of very

small catalyst particle size is not recommended.

Fluidized-bed reactors are catalyst particles supported

by an upflow of gas as a fluid bed (18). A mechanical

advantage is also gained by the relative ease with which

solids may be conveyed and, because of solids mixing, the

gas in the reactor is at approximately the same temperature.

Another important advantage of the fluidized-bed reactor

over the fixed-bed type is that the catalyst can be

externally regenerated without disturbing the operation of

the reactor. A disadvantage of the fluidized-bed reactors

is that the equipment is large. To avoid the solid

particles from being blown out the top of the reactor, the

Composition is uniform at XA, out• CA. out

Four rapidly spinning wire baskets containing catalyst pellets, W

-..:::::::::::> ~

Spinning shaft

Figure 2. CSTCR; adapted from Levenspiel (1972).

Fluid out, XA, out• CA, out

14

15

gas velocity must be low. This means that we need to design

large-diameter vessels and this increases the initial cost . . There are also losses of catalyst fines from the reactor,

necessitating expensive dust-collection equipment in the

exit streams.

LHSV and Hydrogen-to-Hydrocarbon Ratio

Space velocity is an important variable in refinery

because it is interchangeable with reaction temperature.

Space velocity has to do with the length of time of contact

between the reactants and the catalyst. Refiners choose an

easily accessible parameter of residence time in either

liquid hourly space velocity (LHSV) or in weight hourly

space velocity (WHSV).

LHSV is the volume per hour of reactor charge per

volume of catalyst. The higher the LHSV, the greater the

volume of feed charge per hour over a given amount of

catalyst. Therefore, contact time with catalyst is less.

Normally, in most isomerization process, LHSVs are

controlled between 1.5- 2.5 (19).

Hydrogen-to-Hydrocarbon Ratio

The main purpose of hydrogen recycle is to increase

hydrogen partial pressure in the reactors. The hydrogen

react with co*ke precursors, removing them from the catalyst

before they can form polycyclic aromatics which ultimately

deactivate the catalyst. Also, hydrogen can inhibit side

reactions such as cracking. Most of the present processes

control the ratio between 2 - 1 (3,20).

Process Descriptions

16

Many papers have published information about their

isomerization processes and operating conditions. These

processes such as Penex, Isomerate and BP are now applied in

commercial processes.

Pen ex

Licensed by Universal Oil Products, Penex is a

nonregenerative Cs and/or C6 isomerization process. The

reaction takes place in the presence of hydrogen and a

platinum catalyst. The Penex process may be applied to many

feedstocks by varying the fractionating system. Mixed feed

may be split into pentane and hexane fractions, and

respective isofractions separated from each other. Reactor

temperatures range from 500 - 900 oF; pressures from 300 -

1000 psig. Hydrogen requirements are low-- (49 scf/bbl)

for pentane isomerization and slightly higher for hexane

isomerization (21,22,23).

Isomerate

Licensed by the Pure Oil Company, Isomerate is a

continuous isomerization process designed to convert

17

pentanes and hexanes into highly branched isomers. A rugged

dual-function catalyst is used in a fixed-bed reactor

system. Operating conditions include reactor temperatures

and pressures which are less than 750 oF and 750 psig,

respectively (24,25).

Licensed by British Petroleum Company, BP is a two

fixed-bed-reactor isomerization process. It uses very high

activity, regenerable Platinum catalyst and hydrogen.

Pentanes, hexanes or mixtures of the two from catalytic

reforming or solvent extraction may be processed. Operating

temperatures are typical less than 320 OF , pressure is

about 250 psig, LHSV is around 1 to 2 and hydrogen to

hydrocarbon mole ratio is 2:1.

A typical simplied flow diagram is shown in Figure 3

( 1 1 3 ) o

Catalysts

The platinum-based catalysts used for isomerization are

similar to those used in catalytic reforming but the

conditions are much less severe. A catalyst promoter such

as hydrogen chloride is added continuously to maintain high

catalyst activity but catalyst deactivation occurs so slowly

that catalyst regeneration is not necessary except at long

intervals (generally greater than one year). Hydrogen is

used to minimize carbon deposits on the catalyst but

DESULFURIZED FEED

ORGANIC CHLORIDE MAKEUP I (

LEAD TAIL ISOMERIZATION ISOMERIZATION

REACTOR REACTOR

MAKEUP H2

STABILIZER

PRODUCT TO STORAGE

Figure 3. Hexane Isomerization Flow Diagram

1-' (X)

19

hydrogen consumption is negligible {19). Table I lists the

catalysts used in some commercial processes. Supported

metal catalysts have been developed for use in high

temperature processes which operate in the range 700 - 900

OF and 300 to 750 psig. Aluminum chloride plus hydrogen

chloride are universally used in the low-temperature

processes.

Deactivation

Most often catalysts are employed to speed up

reactions that are sluggish or will not proceed at all.

They may also allow operation at a lower operating

temperature level, influence the product distributions, or

more rarely, slow down a reaction.

During the chemical process the properties of the

catalyst gradually deteriorate

reasons for this {27):

There may be several

Catalytic Poisoning Catalysts become poisoned when

feed stream contains impurities which are deleterious to the

activity of the catalyst. Particularly strong poisons are

substances whose molecular structure contains lone electron

pairs capable of forming covalent bonds with catalyst

surfaces. For instance, catalytic poisons for metals are

compounds containing sulphur, arsenic and nitrogen. Acidic

catalyst poisons are all normally basic compounds.

Catalytic poisons most often come from impurities present in

raw materials, but sometimes may be present in the material

20

used for preparation of the catalyst itself.

Catalyst Fouling Reactions involving organic compounds

are inevitably accompanied by decomposition of the materials

to carbon or possibly the formation of high-molecular weight

compounds. These gradually cover the surface of the pellets

and block access the active surface (20).

CHAPTER III

FIXED-BED REACTOR AND CSTCR

DESIGN PRINCIPLES

Fixed-Bed Reactors

Beecher, and Voorhies (28) reported that hexane

isomerization was obtained under plug flow (tubular flow)

conditions in a fixed-bed reactor. In a plug-flow reactor

specific assumptions are usually made about the extent of

mixing: no mixing in the axial direction, complete mixing in

the radial direction and uniform velocity across the radius.

The absence of longitudinal mixing is the special character

istic of this type of reactor (29).

Derivation of Mass Balance Equation

The performance equation for a steady state plug flow

reactor is:

Rp dW = F dx

where

W = mass of catalyst, kg

F = molar flow rate of reactant, kgmole/hr

x = conversion of reactant

21

(3-1)

Rp = global rate of reaction per unit mass of

catalyst, kgmole/(kg of cat -hr)

22

Equation (3-1) is based on a material balance and is derived

by several authors (29,30).

Although equation (3-1) is the general form for

tubular-flow reactor packed with catalyst pellets, it does

not meet our requirements. Therefore, it was converted into

the following form which can be utilized for this study:

I (-rij Rj} dW = Fio dXi

Rearranging,

dW

Integrating,

w

Since,

=I __ d_x1 __ I( -n jRj)

= I

F1 = Fio ( 1-Xi )

then,

dF1 = and,

dXi =

Therefore,

w

-Fio dXi

dFi

-Fio

= I ( -dFi /Fi o >

I(-rtjRj}

(3-2)

23

or,

w

1

taking derivatives of both sides, it becomes

dFi dW =

or,

(3-3)

If we assume the reactor tube has a diameter, D, then:

dZ (3-4) 4

Substituting equation (3-4) into equation (3-3) gives:

xD2 dFi = ( pb dZ) I: ( rt j Rj )

4 or,

dFi xD2 = pb t( n j Rj) (3-5)

dZ 4

This is the final mass balance equation utilized in my

design.

where

Fi = the molar flow rate of species i, kgmole/hr

rij = stoichiometric coefficient of the ith

component in the jth reaction.

Rj = reaction rate of the jth reaction,

kgmole/(kg of cat -hr)

A, = the bulk density of the bed, kgjm3

D = the diameter of the tube, m

z = the length of the reactor, m

Derivation of EnergY Balance Equation

If the enthalpy of the reaction per unit mass

above a base state is H at the entrance to an element and

H+~H at the exit, a standard energy balance can be written

as:

FtHilt- Ft(H+t1H) t + U(~Ab.)(T.-T)Llt = 0

or

24

-Ft.dH + U(ilAb)(T.-T) = 0 (3-6)

where

Ft = total molar-flow rate, kgmole/hr

u = overall heat transfer coefficient, kj/(m2-hr-K)

nH = enthalpy change due to reaction,

11 Ab = heat transfer area, m2

but,

llt = time interval, hr

T. = surrounding temperature, K

T = bulk temperature in reactor, K

ilH = Cpt6T + l: (L\Haj} Xij

Fi

Ft

kj/kgmole

25

Using this expression for fj H in equation (3-6) and

simplifying yields

If we divide each term by ~W, and take the limit as

~W ---> 0, we obtain;

dW dW dW

Combining with,

gives,

dT Ft Cp t = U(Ta -T)

dW dW

or,

and,

U{Ta-T):~tDdZ + l:(-~HRj )RjfJDAcdZ dT =

since,

dAh = 7tDdZ

dW = PbAcdZ

Substituting into equation {3-7) gives equation (3-8)

1tD2

dT U(T.-T):JtD + 4 Pbl: Rj(-~HRj) =

dZ

{3-7)

(3-8)

26

Equations (3-5) and (3-8) are the two basic equations

which will be used to model a fixed-bed reactor.

Pressure Drop Prediction

For the calculation of the pressure drop for a catalyst

bed, Ergun (31) recommends the following equation:

d~

where

dr

L

es (1-e) p = 150 + 1.75

1-e dr Go

e = void fraction of the bed, dimensionless

dr = effective diameter of particles, m

L = height of the bed, m

dP = pressure drop, Pa

p = viscosity of fluid, Pa-s = kg/(m-s)

Go = superficial mass velocity, kg/(m2-s)

p = density of fluid, kg/m3

For turbulent region, characterized by:

~ = > 100 p(1-e)

Hence, equation (3-9) may be simplified to:

dP =1.75LpVo2(1-e)/(dre3)

(3-9)

As I mentioned before, there are numerous correlations

in the literature for the calculation of pressure drop (15),

the Ergun equation is probably the best.

Model Simulation

In Chapter 2, it was mentioned that there were three

existing types of theoretical models. The mechanism

proposed by Cull and Brenner (12) is one of the simplest

possible mechanisms involving all five hexane isomers and

requires estimation of a minimum number of kinetic

parameters, ie., eight rate constants. This mechanism can

be written as:

27

n-C6<=====> 3-MP <=====> 2-MP <=====> 2,3-DMB <=====>2,2-DMB

The following assumptions were made to simplify the

kinetic model:

1. Reactions from n-C6 to 2,3-DMB occur very fast and

were modeled as being equilibrium controlled.

2. Total moles of hexane in the reactor are conserved

down the reactor. That is, no appreciable side

reactions such as hydrocracking occur.

3. The reactor operates in plug flow.

4. The reaction of 2,3-DMB to nee-hexane is the rate

controlling step.

With these assumptions, we can eliminate rate constants

k1r through k3r and k1t through k3t. Reaction coordinates

can be used to solve for the equilibrium mole fractions

of n-hexane, 3-MP and 2-MP.

28

Numerical Approach

Computer-implemented numerical methods are now commonly

used for solving system of ordinary differential equations.

In order to calculate the equilibrium mole fraction of n-c,,

3-MP, 2-MP, and 2,3-DMB, three linear simultaneous equations

were required to solve for the reaction coordinates. A

numerical method was used to solve these equations, followed

by a fourth order Runge-Kutta method to approximate the two

ordinary differential equations (equations {3-5) and {3-8)).

The detailed approach will be discussed in the following

chapter.

Design Equations for a CSTCR

Another approach uses a Continuously Stirred Tank

Catalytic Reactor (CSTCR) to carry out the isomerization.

Carberry (17) introduced this type of reactor, which

consists of a rotating basket of catalyst particles. This

reactor also accommodates commercial-size pellets and

extruded catalysts. Levenspiel (30) also refers to this

kind of catalytic reactor as a basket-type mixed reactor.

In the theory of continuous stirred tank reactors, an

important basic assumption is that the contents of the tank

are well mixed (32). This means that the compositions in

the tank are everywhere uniform and that the product stream

leaving the tank has the same composition as the mixture

within the tank.

29

Derivation of Mass Balance Equation

Assume the following hypothetical reaction occurs in a

CSTCR

where

kt A<----> B

kr

kt = forward rate constant

kr = reverse rate constant

A CSTCR is used for this reaction system. The volu

metric feed to the reactor is Q, the catalyst weight W, and

the total flow rate is Fto. Since a CSTCR is designed to

operate at steady-state, a steady-state mole balance defines

the performance of the system. The following mole balance

can be constructed:

(component A)

(component B)

OUT = IN +

CaQ = CaoQ +

CsQ = CsoQ +

GENERATION

RrW

RtW

Assuming simple first order reaction,

Rt = kt Ca

Rk = kr C:a

CONSUMPTION

RtW

RrW

Substituting the rate expressions and rearranging

results in the following set of linear equations:

w

Q ( kr Cs - kt Ca ) = 0 (3-10)

30

w F2 = -Ca + Cao + ---- ( ktCA - krCa) = 0 (3-11)

Q

Note that the only unknowns are C& and Ca. These

equations can be solved using Newton's method and the final

concentrations of C& and Ca can be calculated.

The performance equation of a mixed reactor can then be

utilized to calculate the conversion. It appears below:

W Xaou'l' = (3-12)

F&o -R 'a ouT

where

F&o = the molar flow rate of species i, kgmole/hr

Xaou'l' = conversion of reactant

R'&ou'l' = reaction rate, kgmole/(kg of cat -hr)

W = weight of catalyst, kg

Equation (3-12) is derived by Levenspiel (30}.

Derivation of Energy Balance Equation

Consider a mixed flow reactor, in which conversion is

X&, and T1 is the a temperature on which the enthalpies and

heats of reactions are based.

enthalpy of entering feed:

H' 1 = Cp I ( Tl - Tl ) = 0

enthalpy of leaving system:

H" 2 Xa + H' 2 ( 1-XA) = Cp" (T2 -Tl )XA + Cp' (T2 -Tl) { 1-XA)

energy released by reaction:

at T1

31

At steady state the energy balance is:

input = output + accumulation + released by reaction

or,

0 = [ Cp" (T2 -Tl )XA + Cp' (T2 -Tl) (1-XJL) ] + AHRlXA

rearranging,

0 = (Cp"T2-Cp"T1 )XA + Cp' (T2-T1-T2XA+T1XJL) + tJIR1XA

= XJLCp"T2 - XACp"Tl + Cp'T2 - Cp'T1 - Cp'T2XA

+Cp' T1 XA + ltHR 1 XA

= T2 (XaCp" + Cp'- Cp'Xa) - XaCp"T1 - Cp'T1 + Cp'T1Xa

+ ~HR 1 XA

-AH~tlXA + T1 (Cp"XA + Cp' - Cp' XA)

Cp"XA + Cp' - Cp'XA (3-13)

where subscripts 1,2 refer to temperatures of entering

and leaving streams and,

Cp' , Cp" = mean specific heat of unreacted feed stream

and of completely converted product stream

per kgmole of entering reactant A.

H' , H" = enthalpy of unreacted feed stream and of

completely converted product stream per

kgmole of entering reactant A.

~HR = heat of reaction per kgmole of entering

reactant A.

Equations (3-12) and (3-13) are the two basic equations

which will be used for modeling a CSTCR.

Model Simulation

For the CSTCR it was also assumed that the model

proposed by Cull and Brenner (12) was valid and the

assumptions made previously were still valid.

Numerical Approach

32

A program for simulating CSTCR performance called

"HEXCR" was written in the FORTRAN language. Newton's

method was applied to solve two linear equations containing

two unknowns. The detailed procedures will be discussed in

the next chapter.

CHAPTER IV

PROGRAM DESCRIPTIONS AND TESTING

The main purpose of this research is to simulate

chemical reactions in a fixed bed reactor and a CSTCR.

HEXFI and HEXCR are the names of programs developed for

simulating the fixed-bed reactor and the CSTCR, respective

ly. The HEXFI program offers users two kinds of simulation,

one is optimized model, the other is fixed-length model.

The optimized model calculates the equilibrium mole

fractions of hexane isomers at specified condition and

outputs the required reactor length. However, in the fixed

length model, it calculates mole fractions at specified

reactor length. Both programs provide users the option to

simulate isothermal or adiabatic operation. Both models

allow users to see the effects of changing the reactor

operating conditions, such as temperature, pressure,

catalyst weight, etc.. All models were using the FORTRAN

language.

Software Applied

In order to simulate real control panels in the

chemical industry, IBM software (EZVU) was used. This

software can create panels which connect design variables

33

and users together. Users can easily manipulate different

operating conditions from the panels and outputs will be

shown on the panels simultaneously. This software is very

user friendly to the persons who are undertaking

simulations.

Program Organization and Subroutine Descriptions

34

Figures 4,5 show the FORTRAN flow diagrams for the

fixed-bed and the CSTCR, respectively. A short description

of the program subroutines follows.

Fixed-Bed Reactor

DATAN

This subroutine is used in HEXFI and HEXCR. The

function of DATAN is to defined stoichiometric coef

ficients, feed conditions, and it is called at the beginning

of each simulation run.

ARRAY

Subroutine ARRAY also appears in both HEXFI and HEXCR.

It calculates the heat capacities of each isomer, the heats

of reactions, and the Gibbs free energies of reactions at T

K. Heat capacities and Gibbs free energies can be expressed

as polynomials in terms of temperature. Table III and IV

which appear on the next pages are the data sources. A

Cubic Spline polynomial approximation was applied to

' r-- --, RUNGE-KUTTA I

COEFF.S L-- __ _.

I

Figure 4. Program Organization of HEXFI

35

....

CAL. MOL FC LINPAC

r-- --, I NEWTON'S 1 I. -~HOD-- .I

I

Figure Sa. Program Organization of HEXCR

36

N

MAIN PROGRAM

ASSUME

OUTPUT TEMP .

CALCULATE

E.B. EQUATION

NEW OUTPUT TEMP

CONTINUE

Figure Sb. Program Organization of Energy Balance

37

38

N

Figure Sc. Program Organization of Newton's Method

*TABLE I I I

HEAT CAPACITY FOR THE IDEAL GAS STATE

Compound 298.15

Name

n-Hexane 142.59

•2-M.P. 142.21

b3-M.P. 140.12

c 2, 2-DMB 141.46

d 2, 3-DMB I 139.41

•2-methylpantane b3-methylpantane c2,2-dimethylbutane d2,3-dimethylbutane

*TRC TABLE (1985)

Temperature in K

400 500 600 700 800

Heat Capacity Cp 0 (T) in J K-1 mol-l

181.54 217.28 248.11 274.05 296.23

183.51 219.83 251.04 277.40 300.41

181.17 217.48 248.95 275.73 298.74

183.13 220.33 253.13 281.58 306.69

181.71 218.36 250.20 277.40 301.67

1000

331.37

337.23

335.98

348.11

340.58

w \0

"'TABLE IV

GIBBS ENERGY OF FORMATION FOR IDEAL GAS STATE

Compound

I 298.15 Name

n-Hexane I 0.15

a2-M.P. -5.14

b3-M.P. -3.17

c 2 I 2-DMB -8.52

d 2, 3-DMB I -2.90

a2-methylpentane b3-methylpentane c2,2-dimethylbutane d2,3-dimethylbutane

*TRC TABLE {1985)

Temperature in K

400 500 600 700 800

Gibbs Energy of Formation AG(T), in KJ mol-l

58.87 118.96 180.51 243.15 306.28

54.42 115.20 177.52 241.25 304.56

56.15 116.88 179.14 242.25 305.71

53.30 116.41 180.99 246.28 312.59

58.21 120.61 184.56 249.47 314.70

1000

433.73

433.09

434.67

445.06

446.49

""' 0

41

fit the data. Heat capacities and the Gibbs free energies

at any specified temperature can then be easily

approximated. Function CP and function GF are included in

this subroutine predict these values. To reduced program

execution time, ninety points between 298 and 1000 K were to

evaluate heat capacities and Gibbs free energies and the

data was stored in vector form. Therefore, in order to

predict the heat capacities and the Gibbs free energies at

any temperatures, subroutine PROP was used to look up a pre

calculated value.

Subroutine FNC is the heart of HEXFI and it includes

several additional subroutines. Basically, it contains

two differential equations (O.D.E.s). One is the mass

balance equation, the other is the energy balance equation.

In order to evaluate these two equations, it also needs to

call additional subroutines. These subroutines are PROP,

EQCON, SLTRES, RXN. These subroutines have different

functions to calculate the terms appearing in the

differential equations. After finishing calculations, this

subroutine will transfer the values of the two differential

equations to the main program and use the Runge-Kutta method

to evaluate the function values.

Subroutine PROP calculates the heats of reactions, heat

42

capacities and Gibbs free energies at any temperatures

between 298 and 1000 K. As mentioned previously in

subroutine ARRAY, ninety points were calculated by Cubic

Spline approximation in terms of temperature. Other points

between any two known points were evaluated by linear

interpolation.

EQCON

Subroutine EQCON handles the calculation of equilibrium

constants and forward and reverse rate constants. From

subroutine PROP, we can get Gibbs free energies of each

isomers at specified temperatures. Then the following

equations applied:

~Ga o = -R9 T 1 n K

-6GR 0

In K = RvT

-L'lGa o

K = exp( ) RvT

where

R9 = gas constant, 8.314 kj/kgmole-K

T = temperature, K

~GR 0 =standard Gibbs free energy, kj/kgmole

Equilibrium constants for all the reactions in the

mechanism can be evaluated.

By definition, the equilibrium constant is the ratio of

43

forward rate constant to reverse rate constant. That is:

K =

or,

kt = K * kr

where

kr = reverse rate constant, m'/(kg of cat -hr)

kt = forward rate constant, m'/(kg of cat -hr)

The reverse rate constant it is always expressed in

Arrhenius form:

E k = ko exp( --- )

R9 T

where

E = activation energy, kj/kgmole-K

ko = frequency factor

Rg = gas constant, 8.314 kj/kgmole-K

T = temperature, K

If the reverse rate constant has been determined from

experimental data, the forward rate constant is fixed.

SLTRES

Subroutine SLTRES calculates the thermodynamic equi-

librium mole fractions of the following reactions:

44

( 1 ) ( 3)

n-C6 <----> 3-MP <----> 2-MP <----> 2,3-DMB

(2)'

Assume the reaction coordinates for the first, second and

third reactions are EI, EII, EIII, r•spectively. For

example, assume the initial feed compositions is 50% n-

hexane and 50% 3-MP. Nauman (17) proposed an equation to

solve reaction coordinates; i.e.,

N - No = 11 e (4-1)

where N and No are vectors ( N*1 matrices ) giving the final

and initial number of moles of each component, 11 is the

matrix of stoichiometric coefficients, and e is the reaction

coordinate vector ( M*1 matrix ). In more explicit form,

=

llA , I

llB t I

\lA ti I

llB ti I

converting equation (4-1) into our case, it has the

following form:

n-c, 0.5 -1 0 0

3-MP 0.5 1 -1 0 - + + 2-MP 0.0 0 1 -1

2,3-DMB 0.0 0 0 1

EI

EI I

EI I I

or

Nn- c 6 = 0. 5 - EI

N3-HP = 0.5 + EI - En·

N2-KP = 0.0 + EJJ - EJJI

N2,3-DHB = 0.0 + EIII

45

Using equilibrium constants to solve reaction coordinates

for reaction I, it becomes:

( 0. 5 + EI - eu ) * Por (4-2)

( 0 • 5 - e I ) * Por

for reaction II, it becomes:

( EI I - EI I I ) * Por (4-3)

( 0. 5 + EI + EI I ) * Por

for reaction III, it becomes:

( en I + 0. 0 ) * Por K3 = (4-4)

( EI I - EI I I ) * Por

From subroutine EQCON, we have evaluated equilibrium con

stants K1, K2, K3. Hence, equations (4-2), (4-3) and (4-4)

will turn out to be three simultaneous equations with three

unknowns EI I EII and EIII. Subroutine LINPAC then solves

handle these equations for specified condition.

Subroutine RXN.calculates the globe rate of the final

reaction.

kt 2,3-DMB <====-=> 2,2-DMB

kr

Rate2,2-nMB = kt * C2,3-»MB - kr * C2,2-nMB

46

When the rate is determined it is substituted into equations

(3-5) and (3-8) for calculating the value of the two

differential equations.

LINPAC

This subroutine was written by individuals at Argonne

National Laboratory. It uses partial pivoting and matrix

decomposition with Gaussian elimination to very efficiently

solve large sets of linear equations (33).

CSTCR

NEW TN

Subroutine Newtn is one of the biggest difference

when comparing CSTCR with the fixed-bed design. This

subroutine employs Newton's method in order to solve a set

of two linear equations containing two unknowns. It

includes subroutines DER, FUNC, ADER and FADI. First of

all, let me explain its algorithm and all the functions of

the subroutines.

The algorithm for this case is a two-dimensional

problem and may be represented as simultaneous solution of

the following equations:

47

'b.h (X) 'bf1 (X) dl ( j) + d2 ( j) + f1 ( x< j > ) =

"bX1 x< n bX2 x< j >

"bf2 (X) bf2 (X) dl ( j) + d2 ( j) + f2 ( x< n ) =

OXl x< n 'bX2 x< j >

where

Xl ( j + l ) = Xl ( j ) + d1 ( j )

and

X2 ( j + 1 ) : X2 ( j ) + d2 ( j )

·Note that the superscript (j) or (j+1) indicates the number

of linear approximations that have been used in searching

for the roots. The coefficient matrix for this system of

two linear equations contains all the possible combinations

of partial derivatives of functions, fk(X), with respect to

each independent variable, Xi. This coefficient matrix is

called the Jacobian matrix. For the isothermal case, the

two linear equations are equations (3-10) and (3-11).

Hence, the partial derivatives of these two equations are:

"bil w = -1 - kt

"bC& Q

'bfl w = kr

'bCu Q

"bj 2 w = kt

"bC& Q

48

= -1 - kr 'bCa Q

the above equations are inputed in subroutine DER.

ENGBALS

Subroutine ENGBALS performs the energy balance in a

CSTCR. The energy balance equations are constructed for the

following reactions:

As I mentioned previously, it was assumed to reach

thermodynamic equilibrium very fast. So the energy balance

equations are:

INPUT = OUTPUT + ACCUMULATION + DISAPPEARANCE

The reference temperature was picked to be the same as

the feed temperature.

input term:

Fto * t [YI(i) * Cp(i) * (To-To)]= 0

energy released by reaction:

Ft o * t [ EXC ( i) * fl H ( i) ]

output term:

assuming an output temperature of T1 , the equation

becomes:

Fto * t {YF(i) * Cp(i) * (Tl-To)}

Replacing these quantities in the energy balance gives,

~ {YF(i) * Cp(i) * (Tl-To)}

= - E [EXC(i) * AH(i)]

49

(4-5)

In the above equation, To, EXC(i) and also dH(i), Cp(i) are

function of temperature. In order to satisfy both sides in

equation (4-5), a trial and error method is applied to find

the temperature T1 . Another energy balance for the final

reaction is then required.

2,3-DMB < > 2,2-DMB (I) (II)

OUT = IN + GENERATION CONSUMPTION

(I) H2C1Q = H1 C1 o Q + H2RrW

(I I) H t 2 CI I Q = H t 1 CI I 0 Q + H '2 Rt W

converting (a) and (b) into the following set of linear

equations:

w .h = -H2 CI + Hl c, 0 + (c)

Q

w (d)

Q

Substituting the rate expressions into (c) and (d) and

taking derivatives of each equations with respect to each

variable is done in subroutine FAD!.

w = -H2 - (4-6)

oc, Q

50

"bf 1 w = ( H2 kr ) (4-7)

bCtt Q

'hf2 w = ( H '2 kt ) (4-8)

'hCt Q

'hf2 w = -H '2 - ( H '2 kr ) (4-9)

'hCt I Q

Equations {4-6) to (4-9) are the coefficients of Jocobian

matrix for adiabatic case. After setting up the Jocobian

matrix, we can apply LINPAC to solve for the roots (i.e.,

concentrations at some temperature).

Subroutine THEQ is similar to subroutine FNC in HEXFI.

It also contains several subroutines, such as PROP, EQCON,

SLTRES and ENGBALS. The main difference between THEQ and

FNC is the subroutine ENGBALS. However, the basic function

of this subroutine are similar to what was calculated in

FNC.

Testing and Results

Overview

The programs developed in this study were tested using

the model proposed by Cull and Brenner (12). However, their

experimental data was based on results from data in a batch

reactor and were not suitable verification use. Other

51

literature, listed in references did not supply parameters

and constants related to their experiments. Because of the

above reasons, it was impossible to proceed using this data.

Finally, a copy of operating data from a proprietary source

was obtained and this data was used to validate the model.

The results of the numerical solutions are close to the

proprietary data.

Testing

In industry, there are several isomerization processes

licensed by the Pure Oil Company, British Petroleum and

Phillips Petroleum Company. Generally speaking, their

operating conditions are:

1. isothermal reaction

2. LHSV = 1 - 20

3. reactor charge = 3000 barrels per stream day,

(bpsd)

4. bulk density of catalyst = 40 lb/ft3

5. hydrogen-to-hydrocarbon ratio = 2 : 1

Basically, HEXFI was designed for industrial

simulation. However, adiabatic operation was added in this

study to compare the benefits and shortcomings of each.

Another option supplied allows users to select one of two

objective functions, optimized or fixed-length models. A

few examples are shown below to demonstrate design. Units

used in HEXFI were all converted into the metric system.

52

Control panels of some cases are all listing in Appendix C.

Optimized Model

Figures 18 and 19 in Appendix C show the control panels

for fixed-bed reactor design. Original inputs were set to

be zero. The following operating conditions were then used

as inputs:

Case I

1. isothermal reaction

2. flow rate = 153.5 kgmole/hr

3. feed temperature = 408 K

4. system pressure = 35 ATM

5. tube diameter = 0.05 m

6. number of tubes = 150

7 . bulk density of the catalyst = 640 kg/m3

8. opz = I y I

9. pure n-hexane as feedstock

The final results from the computer monitor are shown

in Figures 20 and 21 in Appendix C. Figure 6 shows that

hexane isomers mole fract~on distributions with respect to

reactor length. From this figure, it is evident that if the

reaction reaches equilibrium conditions, it needs 12.1 m of

reactor length. Comparison of the simulation outputs with

the proprietary source, shows that both sets of data have

similar trends. The equilibrium prediction from HEXFI model

for final mole percent of nee-hexane is 37.69% which is

53

very close to the experimental value of 36.25 \.

Case II

operating conditions:

1. system pressure = 61 ATM

2. other factors are the same as Case I

For this case the pressure was increased to 61 atm and

results are shown in Figure 7. The equilibrium value from

the proprietary data for neo-hexane is 36.25 \ which is

close to the model prediction of 37.69 %. Comparing flow

trends of both sets of data shows that the simulation curves

closely resemble the experimental curves. From Case I and

II, we find that pressure effect does not influence the mole

fraction of neo-hexane. Slightly lower temperature cases

were also tested and shown in Figures 8 and 9. The results

are summaried in Table V. From this table, it can be

summaried that higher temperatures do not favor

isomerization reaction.

Besides the isothermal reaction, HEXFI can also

simulate adiabatic reactors. Case III is a typical case of

adiabatic operations.

Case III

operating conditions:

1. adiabatic reaction

2. other factors are the same as Case I

Results are shown in Figure 10. Comparing Case III

TABLE V

RESULTS OF THE COMPARISON OF EXPERIMENTAL DATA WITH MODEL PREDICTIONS FOR AN ISOTHERMAL FIXED-BED REACTOR

CASE NO. T (K) P (ATM) MODEL PREDICTION! EXPERIMENTAL DATA

1. 408.0 35.0 37.69% 36.25 %

2. 408.0 61.0 37.69% 36.05 %

3. 366.5 35.0 46.84 % 42.75 %

4. 366.5 61.0 46.84 % 41.25 %

---------- - -------------- ----

1. product mole percentage of nee-Hexane

01 ~

with Case I, we notice that the adiabatic reactor has a

lower 2,2-DMB formation than that of the isothermal

reactor. This is because hexane isomerization equilibrium

is favored at lower temperatures.

55

Other adiabatic conditions were also tested and are

plotted in Figures 11 - 13. From these figures, it can be

concluded that although adiabatic reactors give lower mole

fractions of 2,2-DMB, they also require a shorter reactor

length than for isothermal conditions. In general the

initial cost for building an adiabatic reactor is less than

that required to build an isothermal reactor. Furthermore,

Figure 14 through 17 show the difference in temperature

profiles inside a reactor during adiabatic operation. At

the beginning of the reactors, the slopes of the curves are

quite steep. This means that the reactions release a large

amount of heat. After some reactor length, reactions

gradually approach equilibrium and then the temperatures

remain constant.

Fixed-Length Model

In addition to the optimized-model, HEXFI can also

simulate a Fixed-Length reactor. The reason for this model

is sometimes room is available to build a long reactor or

information is required to know the conversion of a reactor

of specified length.

Case IV

1. specified reactor length = 3.0 m

c 0. ~~ 0

\. ·--+-' u ~ 0 -~--1 LL •

Q) -·~ 0. ~~ I

0. 0

Isothermal Reaction 35 ATM, 408 K

/ ------

------

2

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

4 6 8 10 Reactor Length, m

Figure 6. Mole Fraction Distributions of Hexane Isomerization

12 14

01 0\

c 0. ~~ 0

\. ·--+-' 0

~ 0 -~-1 LL •

(J) -

~ 0. ~-l I

0. 0

Isothermal Reaction 61 ATM, 408 K

/ ------

-------

1 2 3 Reactor

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

4 5 6 Length, m

Figure 7. Mole Fraction Distributions of Hexane Isomerization

7 8

01 ..,J

c 0. 0

-+-' ()

0 ~ 0.

(])

0 2 0.

0. 0 2

Isothermal Reaction 35 ATM, 366.5 K

4 6 8 10 Reactor Length, m

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

12

Figure 8. Mole Fraction Distributions of Hexane Isomerization

14 16

01 00

c 0. 0

+-' ()

0 ~ 0.

())

0 2 0.

0. 0 1

Isothermal Reaction 61 ATM, 366.5 K

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

2 3 4 5 6 Reactor Length, m

7

Figure 9. Mole F roction Distributions of Hexane Isomerization

8 9

U'l

"'

§ 0. ·--+-' 0 0 ~

l.L

(])

0 2 0.

0. 0

Adiabatic Reaction Pressure - 35 ATM Initial Temperature - 366.5 K

2

2.2-DMB

2-MP

3-MP

2,3-0MB

n-Hexane

4 6 8 10 Reactor Length, m

Figure 1 0. Mole Fraction Distributions of Hexane Isomerization

12 14

0\ 0

c 0. 0

-+-' u 0 ~ 0.

<l)

0 2 0.

0. 0

Adiabatic Reaction Pressure - 61 ATM Initial Temperature - 366.5 K

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

1 2 3 4 5 Reactor Length, m

Figure 11. Mole Fraction Distributions of Hexane Isomerization

6 7

0'1 ......

0.

c 0. 0

-+-' (.)

0 ~ 0.

Q)

0 2 0. 2

0. 0 1

Adiabatic Reaction Pressure - 35 ATM Initial Temperature - 408 K

2 3 4 5

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

6 Reactor Length, m

Figure 12. Mole Fraction Distributions of Hexane Isomerization

7 8

0\

"'

c 0 _j ~ -

-+-' u 0 ~ 0. 91

(]) -~ 0. ~~ I

0. 0

Adiabatic Reaction Pressure - 61 ATM Initial Temperature -408 K

~

-------

1 2 3 Reactor Length, m

2,2-DMB

2-MP

3-MP

2,3-DMB

n-Hexane

Figure 13. Mole Fraction Distributions of Hexane Isomerization

4 5

0\ w

40

39

39 ~

Q)- 38 L :::::;

-+-'

'2 38 Q) Q_

E 37 Q)

1---37

Pressure - 35 ATM Initial Temperature - 366.5 K

36t~~~~~~~~~~~~~~~~~~~~~~~~~~

0 2 4 6 8 10 Reactor Length, m

Figure 14. Temperature Profile vs Reactor Length of Hexane Isomerization

12 14

0\ ~

40,~------------------------------------------------~

39

39 ~

v"' 38 L

::J -t-J 0 38 L Q) Q_

E 375 Q)

1-37

Pressure - 61 ATM Initial Temperature - 366.5 K

36r~~~~~~~~~~~~~~~~~~~~~~~~~~

0 1 2 3 4 5 Reactor Length, m

Figure 15. Temperature Profile vs Reactor Length of Hexane Isomerization

6 7

0'\ 0'1

43

Y: 42 -

Q) L

::::1

0 415 L Q)

0..

~ 41 ~

40 0 1

Pressure - 35 ATM Initial Temperature - 408 K

2 3 4 5 6 Reactor Length, m

Figure 16. Temperature Profile vs Reactor Length of Hexane Isomerization

7 8

0\ 0\

43

42

~ 42 ...

Q) L ::J

0 41 L Q) a..

~ 41 I-

40 0

Pressure - 61 ATM Initial Temperature - 408 K

1 2 3 4 Reactor Length, m

Figure 17. Temperature Profile vs Reactor Length of Hexane Isomerization .

5

0\ ....:I

68

2. opz = 'N'

3. other factors are the same as Case I

Final results are shown in Figures 22 and 23 in

Appendix c. The mole percentage of 2,2-DMB is 35.64 % at

3.0 m compared with a mole percentage of 37.69% at 12.1 m.

Comparing the outputs for these cases, the following

conclusions can be reached:

HEXCR

1. At the same initial temperature and system

pressure, isothermal reaction can reach higher nee

Hexane mole fractions than the adiabatic case.

2. Higher temperature does not favor the yield of

neo-hexane. For isothermal conditions a reactions,

a reactor temperature decrease of 1 K, increases

the mole percentage of 2,2-DMB by 0.2 %. For

adiabatic operation, an initial temperature

decrease of 1 K, increase the mole percentage of

2,2-DMB by 0.16 %.

3. Pressure has a very little influence on the

conversion of nee-hexane but does affect the

reactor length. Comparing Case I with Case II,

the reactor length in Case II decreases almost 42 %

over that of Case I.

At present, CSTCRs still are used mainly in the

laboratory. This is because it is more complex and

69

expensive to build than a batch or fixed-bed reactor.

Further, the mole fraction of neo-hexane is generally lower

than that of the fixed-bed reactor. The program for

simulating a CSTCR was called HEXCR and supplies two choices

to the user, isothermal or adiabatic operation. At this

time, no published papers and no data is available that

shows that hexane isomerization in a CSTCR. Two basic

simulation runs are illustrated below.

Figures 24 and 25 in Appendix c are the control panels

for the CSTCR.

Initial values of the parameters are set to zero.

Case I.

operating conditions:

1. isothermal reaction

2. reactor charge = 153 kgmole/hr

3. feed temperature = 408 K

4. volumetric flow rate = 125 m3/hr

5. weight of catalyst = 2200 kg

6. pure n-hexane as feedstock

For these parameters~ results are shown in Figures 26

and 27 in Appendix C. The mole fraction of neo-hexane is

significantly lower than that of a fixed-bed reactor using

same amount of catalyst.

Case II.

operating conditions:

70

1. adiabatic reaction

2. other conditions are the same as Case I

Results for the two cases are shown in Table VI. From

this table, we find that isothermal reaction gives higher

mole fractions of nee-hexane than that of adiabatic

operation. This is because higher temperature does not

favor the formation of nee-hexane.

made:

From the above cases, the following conclusions can be

1. For isothermal operation, a temperature decrease of

1 K, increases the mole fraction of nee-hexane

by 0.04 %. For adiabatic operation, a temperature

decrease of 1 K, increases the mole fraction of

nee-hexane by 0.03 %.

2. A CSTCR requires more catalyst than fixed-bed

reactor.

3. If we have equal catalyst weight a large number of

CSTCRs connected in series will behave as a plug

flow reactor.

4. If the volumetric flow rate increases, the final

mole fraction of nee-hexane decreases. This is

a function of reactor residence time.

TABLE VI

RESULTS OF THE COMPARISON OF ISOTHERMAL AND ADIABATIC OPERATION OF A CSTCR

CASE Ti (K) Tt (K) MODEL PREDICTION!

Isothermal 366.5 366.5 13.14 \

Isothermal 408.0 408.0 11.37 \

Adiabatic 366.5 435.1 11.39 \

Adiabatic 408.0 469.1 10.07 \

1. product mole percentage of nee-hexane

-...1 .....

CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

Conclusions

The purpose of this study is to simulate an ideal plug

flow reactor and a CSTCR for hexane isomerization. An

isomerization catalyst, Pt-Al203 and proprietary data were

used to validate the model.· In actual operation, hydrogen

and chloride are added to the reactors in order to prevent

hydrocracking and keep the activity of the catalyst.

In summary, the models developed in this study can

perform the following:

1. The optimized-length model of a fixed-bed reactor

predicts that the distribution of hexane isomers

optimal and the optimal length under specified

operating conditions.

2. The fixed-length model of a fixed-bed reactor

predicts the distributions of hexane isomers at

specified reactor length.

3. The CSTCR model evaluates the distribution of hexane

isomers at different input conditions.

In this study several conclusions can be made from

model output data.

72

73

1. High temperature does not favor the isomerization

process and isothermal operation gives higher yields

of neo-hexane than that for adiabatic reaction for

both optimized and fixed-length models.

2. Pressure does not affect the yield of neo-Hexane,

but does influence the optimal reactor length.

3. Pressure drop in most fixed-bed reactors will be

small compared to total system pressure and

therefore can be neglected.

Recommendations

1. The ideal gas law was used in both reactor models to

evaluate concentrations, however, since this system

operates at high pressure, the gases do not behave

as ideal gases. Therefore, it is suggested that a

more accurate equation of state such as Redlich

Kwong or Peng-Robinson be used instead of the ideal

gas law. Generally speaking, equilibrium constants

are defined in terms of fugacities or activities and

are not dependent upon the pressure. The behavior

is explained in Appendix D.

2. This study did not consider any side reactions. It

is recommended that these reactions be included in

future work to more realistically model the hexane

isomerization process.

3. It is recommended that additional experimental data

be obtained to test the model for other catalysts.

This model can not be generalized until additional

kinetic data is generated for a specific catalyst.

4. The equilibrium assumptions of the first three

reactions are probably reasonable, but should be

verified with experimental data.

74

LITERATURE CITED

1. Belden, D. H., Haensel V., Starnes, W. G. and Zabor, R. C. J. Oil & Gas, 55{20), 142 {1957).

2. Bland, W. F. and Davidson, R. L., "Petroleum Processing Handbook", McGraw-Hi 11 Book Company, Inc. , New York {1967).

3. Hydrocarbon Processing, "Isomerization", 62{9), 120, (1984).

4. Gary, J. H. and Handwerk, G. E., "Petroleum Refining", Marcel Dekker, Inc., New York (1975).

5. Little, D. M., "Catalytic Reforming", PennWell Publishing Company, Oklahoma {1985).

6. Guthier, Virgil, "Petroleum Products Handbook", McGraw-Hill Book Co., New York {1960).

7. Brooks, B. T., Boord, C. E., Kurtz, S. S.and Schmerling, L., "The Chemistry of Petroleum Hydrocarbons", Reinhold, New York (1955).

a.- Evering, B. L., d'Ouville, E. L., Lien, A. P. and Waugh,R. C., Ind. Eng. Chern., 45{3), 582 {1953).

9. Evering, B. L. and Waugh, R. C., Ibid., 43{8), 1820 (1951).

10. McCaulay, D. A., J. Am. Chern. Soc. 81, 6437 {1959).

11. Scheider, V. and Frolich, PerK., Ind. Eng. Chern., n_(12), 1405 {1931).

12. Cull, N. L. and Brenner, H. H., Ind. Eng. Chern., ~{10), 833 (1961).

13. Smith, J.M., "Chemical Engineering Kinetics", McGrawHill, New York {1956).

14. Shah, Y. T., "Gas-Liquid-Solid Reactor Design", McGrawHill International Book Company, New York (1979).

15. Leva, M., Chemical Engineering, ~{5), 115 {1949).

75

76

16. Nauman, E. B., "Chemical Reactor Design", John Wiley & Sons, Inc., New York (1987).

17. Carberry, J. J., Ind. Eng. Chern., 56(11), 39 (1964).

18. Tarhan, M. Orhan, "Catalytic Reactor Design", McGraw-Hill, New York (1983).

19. Hydrocarbon Processing., "Isomerization", 49(9), 195, (1970).

20. Prasher, B. D., et. al., Ind. Eng. Chemical, Process Div. Develop., 17, 266 (1978).

21. Oil & Gas J., "Penex", 63(14), 135 (1965).

22. Pet. Engr., "Penex Catalytic Isomerization", 32(2), 19 (1960).

23. Grote, H. W., Pet. Ref., 35(7), 148 (1956).

24. Oil & Gas J., "Isomerate Process", 63(14), 136 (1965).

25. Oil & Gas J., "New Process Expands High Octane PoolPure Oil Company's Isomerate Process", 54(52), 86 (1956).

26. O'May, T. C. and Knights, D. L., Hydrocarbon Processing & Petroleum Refiner, 41(11), 229 (1962).

27. Butt, J. B., Catalyst Deactivation, Adv. Chern. Ser., 148 (1975).

28. Beecher, R. and Voorhies, A., I & EC Product Research and Development, ~(4), 366 (1969).

29. Smith, J.M., "Chemical Engineering Kinetics", McGrawHill, New York (1970).

30. Levenspiel, 0., "Chemical Reaction Engineering", 2nd ed., John Wiley & Sons, Inc., New York (1972).

31. Ergun, S., Chemical Engineering Process, 48(2), 89 (1952).

32. Coulson, J. M. and Richardson, J. F., "Chemical Engineering", Vol 3, Page Bros Ltd., Great Britain (1979).

33. Riggs, J. B., "An Introduction to Numerical Methods for Chemical Engineers", Texas Tech University Press, Texas (1988).

APPENDIXES

77

APPENDIX A

COMPUTER PROGRAM FOR HEXFI

78

$debug

c~--------------ABSDAC! _________ _

c c c c c c c c c c

!HIS PROGRAM CAl BE USED !0 DESIGJf A FIXED BED REActOR II NHICH fBIRE AR! MOL!IPLE R!AC!IOifS OCCORIIG UIDBR ISO!JIERMAL COIDifiOif OR ADIABAtiC COifDITION. !HIS MODEL ASSIJM!S PLUG PLOW AID I!GL!C'lS AXIAL DISPIRSIOI AID RADIAL !EMPERATORE GRADIA!f!S WI'lHIIf !HE BED. THE DESIGN IQOATIOIIS ARE IlfTIGRAT!D OSIIIG A POOR!Il ORDER ROIIGE·KUHA METHOD WI!R A VARYIIG STEP SIZE. THE STEP SIZE IS S!'l' SUCH !RAT 'lHBR! IS A C!R!AII CRAIG! II fBE T!MPERA'l'I1RE OR MOLE PRACTIOIIS OF !HE RBACI'Ain'S.

C, _______ _ IOM!ICLATURE -------

c~------------------------------------c c c c c c c c c c c c c c c c c c c c

D - !HE DIAMETER OP !BE REACTOR TOB!, M P - 'I'll! SYS!!M PRESSOR!, A!M Q - !HI VOLUME!RIC PLOW RAT!, M• /HR T - !!MP!RATORE, K If - CATALYS! WEIGHT I KG Zl - 'I'll! LDGTH OP !HE REActOR !UBE, M ZSP - REAC!OR LDG'l'll SPECIFIED BY USER, M ID - FLAG NHICH DETERMIIIES REACTIOII TYPE NC - THE NUMBER OF CHEMICAL COMPOmrJ'S IR - !HE lUMBER or CHEMICAL RBAC!IOifS DZ - THE AXIAL STEP SIZE, M DZT - !HE AXIAL STEP SIZE BASED UPOII A 10 K T!MPERATORE PTO - THE !O'l'AL MOLAR PLOW RATE A'!' 'l'HE IlfLET PLOW RATE,

PTRTifT -F(I)

KGMOLES/HR PLOW RATE Ill A SIIIGL! TOB!, KGMOLE/HR lfO OP !UB!S Ilf REACTOR

- FOR I=S, THE MOLAR FLOW RAT! OF THE I-TH COMPOif!IT, KGMOLES/HR) ; FOR I= 6, fBE REACTOR TEMPERATURE, K

C R(I) c

- fBE RATE OF THE I-TH REACTIOif, KGMOLES/(KG OF CA'l'-HR)

c c

B(I) - THE COifSTANT TERM Ilf THE ITH EQUATION FMPl - PEED MOL! PERCENTAGE OF n-HEXAIIE

C FHP2 - PEED MOLE PERCDTAGE OF 3-METHYLPANTAIE C FMP3 - FEED MOLE PERCEif'l'AGE OF 2-METHYLPANTANE C PMP4 - PEED MOLE P!RCDTAGE OF 2,3 DIMETHYLBUTANE C PMPS - PEED MOLE PERCENTAGE OF 2,2 DIMETHYLBUTANE C FMP6 - PEED MOLE PERC!lfTAGE OF IlfERT GAS C PMPl - PRODUCT MOLE PERCENTAGE OF n-HEXAifE C PMP2 - PRODUCT MOLE PERC!IfTAGE OF 3-ME'l'HYLPANTANE C PMP3 - PRODUCT MOLE PERCEif'l'AGE OF 2·M!'l'HYLPAN'l'Aif! C PMP4 - PRODUCT MOLE PERCENTAGE OF 2,3-DIMETHYLBUTANE C PMP5 - PRODUCT MOLE PERCENTAGE OF 2,2-DIMETHYLBUTAME C PMP6 - PRODUC! MOL! or INERT GAS C THCAP - THE TOTAL HEAT CAPACITY OF THE REACTION MIXTURE C ,KJ/K C YO(I) - THE MOLE FRACTION OF THE I-TR COMPONENT IN THE C PEED

79

C CP( J) - !HI HEAT CAPACITY OP THE J-TH COMPOif!lfT AT C TEMPERA!URI T, KJ/(KGMOLE-K) C PP(I) - THE DERIVATIVE OP P(I) HI!H RESPECT TO Zl C CA( I) - THE BEAT CAPACITY OF THE I -TH COMPOm'l', C KJ/(KGMOL!-K) C BULD!If - !BE BULK DDSITY OP '!'BE BED, KG/M' C TDHRXIf - 'I'll! I!T HEAT OP R!ACTIOJ, KJ/MS-HR) C EXC(I) - REACTION COORDINATE, I=1,3 C A(I,J) - 'I'll! COEPICIDT OP THE J'l'H VARIABLE II 'l'HE ITH C EQUATION C CAYl(I)]-C CAY2(I) > 'l'HE K'S USED IN THE RUIGE-KUTTA M!THOD C CAY3(I) C CAY4(I) C PSAVE(I) - A VECTOR WHICH SAVE '!'BE VALUES OF P(I) C GAM(I,J) - THE STOICHIOMETRIC COEPFICI!IfT OF THE I-TH C COMPOIEKT IN '!'HI J-THE REACTION C GP!RV(I) - THE GIBBS PRE! BJERG! OF THE I-TH R!ACTIOif, C KJ/KGMOLE C CPV(I,J) - A VECTOR COJTAIIIIG HEAT CAPACITIES OF C COMPOK!IfT I AT DiSCRETE VALUE OF C TEMP!RA'lURE, KJ/(KGMOLE-K) C DHRXIf( I) - THE HEAT OF REACTION OF THE I -TH REACTION C KJ/KGMOLE C DBRXV(I,J) - A VICTOR CONTAINING THE HEAT OF REACTION C OF THE I-TH REACTIOif AT DISCRETE VALUES C OF TEMPERATURE, KJ/KGMOLE c----------------------------------------------------------c INPUT FORMAT DESCRIPTION------, c C INPUT DATA FOR HEXANE ISOMERIZATION AND SET UP CPV C AND BlAT OF REACTION. c ~----------------~ c C THIS PILE CONTAINS ALL THE SCREEN C INPUT VAULES AKD DEPINITIOIS c

$S'l'ORAGE:2 INTEGER RC DOUBLE PRECISION PP(lO),PSAV(lO),TS DOUBLE PRECISION CAY1(10),CAY2(10),CAY3(10),CAY4(10) COMMON /DHRX/ DHRXN(4),T,YO(l0) COMMOif /DATA6/ P,GAM(5,4),D COMMON /DATAS/ JC,PTO,P(lO),IR COMMON /CATAP/ BULDEN DIM!IfSION YP(lO)

c ~-------------------------------~ C !HIS PROGRAM APPLIES SOPTHARE EZVU DEVELOPED BY IBM C DEFIKE IKPUT AND OUTPUT VARIABLES FOR SCREEN C HEX1,HEX2,HEX3 c ~----------------------------~

80

RC=O CALL ISPPPV(4,'T P7',RC,T,4) CALL ISPPPV(4,'P PS',RC,P,4) CALL ISPPPV(4,'D P5',RC,D,4) CALL ISPPPV(S,'OPZ C' ,RC,OPZ,4) CALL ISPPPV(S,'Zl P7' ,RC,Zl,4) CALL ISPPPV(S,'AI Pl',RC,AI,4) CALL ISPPPV(6,'0PZ1 C',RC,OPZ1,4) CALL ISPPPV(6,'ZSP P7',RC,ZSP,4) CALL ISPPPV(6,'FTO P7' ,RC,Pf0,4) CALL ISPPPV(7,'T!MP P7',RC,TIMP,4) CALL ISPPPV(7,'PMP1 P6',RC,PMP1,4) CALL ISPPPV(7,'PMP2 P6',RC,PMP2,4) CALL ISPPPV(7,'PMP3 P6',RC,PMP3,4) CALL ISPPPV(7,'PMP4 P6',RC,PMP4,4) CALL ISPPFV(7,'PMP5 P6',RC,PMP5,4) CALL ISPPPV(7,'PMP6 P6',RC,PMP6,4) CALL ISPPPV(7,'PMP1 P6',RC,PMP1,4) CALL ISPPPV(7,'PMP2 P6',RC,PMP2,4) CALL ISPPFV(7,'PMP3 P6',RC,PMP3,4) CALL ISPPPV(7,'PMP4 P6',RC,PMP4,4) CALL ISPPPV(7,'PMP5 P6',RC,PMP5,4) CALL ISPPFV(7,'PMP6 P6',RC,PMP6,4) CALL ISPFFV(9,'BULDEN F6' ,RC,BULDEN,4)

~ I SliT PUIICTIOII KEYS

ZFlO='QUI'l'' ZCMD=' I

ZATR='HRI' c .----------, C SE'l' INITIAL VALUES OF C PUICTION KEYS c '----------'

CALL ISPFPV(6,'ZATR C',RC,ZATR,4) CALL ISPFPV(6,'ZF01 C' ,RC,ZF01,4) CALL ISPFPV(6,'ZF02 C',RC,ZF02,4) CALL ISPFPV(6,'ZF03 C' ,RC,ZF03,4) CALL ISPFPV(6, 'ZFlO C' ,RC,ZF10,"4) CALL ISPFFV(6,'ZCMD C' ,RC,ZCMD,4)

c r-------------------, C INPU'l' VARIABLES FOR SCREEN HEX1,HEX2,HEX3 C GET DEFAULT VALUES PROM PROFILE c '-----------------~

CALL ISPFP(S,'VGET D P',RC) CALL ISPFF(S,'VGE'l' P P',RC) CALL ISPPF(S,'VGET T P',RC) CALL ISPFF(9,'VGE'l' Zl P' ,RC)

81

CALL ISPFF(lO, 'VGET OPZ P' ,RC) CALL ISPFF(lO, 'VG!! P"1'' P' ,RC) CALL ISPFF(lO,'VG!T ZSP P',RC) CALL ISPFF(ll,'VGET TEMP P' ,RC) CALL ISPFF(ll,'VGET PMPl P',RC) CALL ISPFF(ll,'VG!T PMP2 P',RC) CALL ISPFF(ll,'VGET PMP3 P',RC) CALL ISPFF(ll,'VGET FMP4 P' ,RC) CALL ISPFF(ll,'VGET FMP5 P',RC) CALL ISPFF(ll,'VGET PMP6 P',RC) CALL ISPPF(ll,'VG!T PMPl P',RC) CALL ISPFP(ll,'VGET PMP2 P',RC) CALL ISPFF(ll,'VGET PMP3 P',RC) CALL ISPFF(ll,'VG!f PMP4 P',RC) CALL ISPFP(ll,'VGET PMPS P',RC) CALL ISPPP(ll,'VGET PMP6 P',RC) CALL ISPPP(ll, 'VGET OPZl P' ,RC) CALL ISPPF(13,'VGET BOLDEN P' ,RC)

~ I sr.IR! SCHill IIPU!S I CALL ISPFF(14,'DISPLAY OPTION' ,RC) IP((OPZl.!Q. 'a').OR.(OPZl.!Q. 'A')) GOTO 777 IF((OPZl.!Q. 'b').OR.(OPZl.!Q. 'B')) GOTO 101

101 ZCMD=' CALL ISPFF(lO,'VG!T ZSP P' ,RC) ZFOl='H!Xl' ZF02='HEX2' ZP03='HEX3' CALL ISPFP(13,'DISPLAY KEYS!' ,RC) CALL ISPFP(12,'DISPLAY H!Xl',RC)

IP{ZCMD.!Q.'QUI!') CALL EXIT IP(ZCMD.EQ. 'HEX2') GOTO 200 IF{ZCMD.EQ.'HEX3') GO'l'O 300 IF(OPZ.EQ. 'N') GOTO 777 IF(OPZ.EQ.'n') GOTO 777 GOTO 102

200 ZCMD=' CALL ISPPP{13,'DISPLAY KEYS2',RC) CALL ISPPP{l2,'DISPLAY HEX2',RC)

IP{ZCMO.EQ.'QUIT') CALL EXIT IP{ZCMD.EQ.'HEXl') GOTO 101 IP(ZCMO.EQ. 'HEX3') GOTO 300 GOTO 102

300 ZCHO=' CALL ISPPP{13,'DISPLAY KEYS3' ,RC) CALL ISPPP{l2,'0ISPLAY HEX3',RC)

IF(ZCMO.EQ.'QUIT') CALL EXIT

82

IP{ZCMD.EQ. 'HEX2') GO TO 200 IP{ZCMD.EQ.'HEX1') GO TO 101 GOTO 102

777 COift'llftJE CALL ISPPP{9,'VGET Z1 P',RC)

ZF01='HEP1' ZP02= 'HEX2 I ZP03='HEP3' ZCMD=' I

CALL ISPPF{13,'DISPLAY KEYS1',RC) CALL ISPFF{12,'DISPLAY HEF1',RC)

IP{ZCMD.EQ. 'QUIT') CALL EXIT IF{ZCMD.EQ.'HEX2') GOTO 201 IF{ZCMD.EQ.'HEP3') G0'1'0 301 IP{OPZ.BQ.'Y') GOTO 101 if{OPZ.EQ.'y') GOTO 101 GOTO 102

201 ZCMD=' CALL ISPPF{13,'DISPLAY KEYS2' ,RC) CALL ISPFF{12,'DISPLAY HEX2' ,RC)

IF{ZCMD.EQ.'QUIT') CALL EXIT IF{ZCMD.EQ.'HEF1') GOTO 777 IP{ZCMD.EQ.'HEF3') GOTO 301 GOTO 102

301 ZCMD=' CALL ISPFF{13,'DISPLAY KEYS3' ,RC) CALL ISPFF{12,'DISPLAY HEF3',RC)

IP{ZCMD.!Q.'QUIT') CALL EXIT IF{ZCMD.!Q.'HEF1') GOTO 777 IF{ZCMD.EQ.'HEX2') GOTO 201 GOTO 102

102 ZCMD=' c ++++++++++++++++++++++++++++++++++++++++ C + STARTING MAIN PROGRAM + c ++++++++++++++++++++++++++++++++++++++++ c ~-------------------------, c c c

SET UP INITIAL DATA INFORMATION 1. ADIABATIC {ID=1) 2. ISOTH!RMAL{ID=2)

c ~------------------------~

ID=l IF {AI.GT.l.S) ID=2

T=T!MP

83

~ I PLOI Rl!l II A SIBGLE IVBBI

F'l'R = rro /m Cr-------------., C IKPOT IKITIAL MOLE FRACTION C OP 1-HIXAKE ••. !0(1) C 3-MP ....... Y0(2) C 2-MP •••.••• Y0(3) C 2,3-DMB •••• Y0(4) C 2,2-DMB ..•• YO(S) C IM!RT ••..•. Y0(6) C.__ _________ __,

Y0(1)=PMP1/100. Y0(2)=1!'MP2/100. Y0(3)=1!'MP3/100. Y0(4)=1!'MP4/100. YO(S)=I!'MPS/100. Y0(6)=1!'MP6/100.

SET UP DATA POR REACTOR MODEL c~ I ~---------~

CALL DATAlf c r----------------------------~ C CALCULATE HEAT CAPACITIES AID REACTION HEATS c ~--------------------------~

CALL ARRAY

g I IJI!IALIZE REACTOR DIS!!ICE, II (M!!ER)

Z1=0.0 c r--------------------------~ C INITIALLY ASSUME MOLE FRACTION OF C N!O-HEXAlfE c ~------------------------~

COC1=0.0 c ************************************ C * BEGIN INTEGRATION LOOP * c ************************************

1 CALL FMC (F,FP,YO,ID) TS=O.ODO

c~ I CALCULATE NEW STEP SIZE ~--------~

84

Cr--------------. C ISOTHERMAL CASE C --> USING CONCEKTRATION CHANGES C'---------------J

RT=ABS(FP(5)/FTR) IF (RT.GT.TS) TS=RT DZ=2.5E-4/TS IF (ID.EQ.2) GOTO 35

Cr-----------, C ADIABATIC CASE C -> USING !BMP!RA'rUR! CHANGE C'-------------1

DZT=l0.0/ABS(FP(6)) IF(DZT.LT.DZ) DZ=DZT IF(DZ.Gf.l) DZ=O.OlO

c >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> C > STARTIKG RUKG!-KUT!A > c >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

35 DO 3 1=5,6 3 FSAV(I)=F(I)

CCC I _ SET UP CAYl(I)

DO 4 1=5,6 4 CAYl(I)=PP(l)

DO 5 1=5,6 5 P(I)=FSAV(I)+O.SO*DZ*CAYl(I)

CALL FNC(F,FP,YO,ID)

CCC I _ SET UP CAY2(I)

DO 6 I=5,6 6 CAY2(I)=FP(I)

DO 7 I=5,6 7 F(I)=FSAV(I)+0.50*DZ*CAY2(I)

CALL FNC(F,FP,YO,ID)

CCC I _ S!'l' UP CAY3(I)

DO 8 1=5,6 8 CAY3(I)=PP(l)

DO 9 1=5,6 9 P(I)=PSAV(I)+DZ*CAY3(I)

CALL FNC(F,FP,YO,ID)

CCC I _ SEf UP CAY4(I)

85

DO 10 1=5,6 10 CAY4(I)=FP(I)

c r----------. C CALCULATE THE HEN VALUES C OF F{I) AT Z1+DZ c L...----------1

DO 11 1=5,6 11 F(I)=FSAV(I)+DZ/6.0*(CAY1(I)+2.0*CAY2{I)

&+2.0*CAY3(I)+CAY4(I)) C<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< C END OF RUNGE-KUTTA METHOD!!! C<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

C\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ C IF USER CHOOSE OPTIMIZED MODEL C CHECK WHETHER REACTION REACHES EQUILIBRIUM OR NOT C\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

IF((OPZ.!Q.'y').OR.(OPZ.EQ. 'Y')) THEM COC2=F(S)/PTR !RLIM=(COC2-COC1)*FTR COC1=COC2 IF(ERLIM.LT.O.OOOl) GOTO 100

EHDIF c r--------------~ C CALCULATE MEN MOLE PRACTIOI OF lEO-HEXANE AID C HEN HOLE FRACTION OF 2,3-DIHETHYLBUTAHE c L...--------------~ ~ l1111 MOLE PIW:'IIOR or REO-HWIII j

YP(S)=F{5)/FfR

g lm MOLE PIW:'IIOII or 2, 3-DIIB I

Y0(4)=Y0(4)-(YP(5)-Y0(5))

~ I ASSIGR Yr 10 YO I YO(S)=YF(S)

~ I MOLE PIW:'IIOII or IIIIR'I CAS I YF{6)=Y0(6)

~ I CALCULATE !'liE BI!ACI'OR LI!IIGtll, -I

86

Zl=Zl+DZ c ~---------------------, C DE'l'ERMIKE WHETHER THE REACTOR C LEKGTH OVER THE SPECIFIED C LEKGTH OR NOT c ~--------------------~

I P ( ( OPZ . EQ. 1 n 1 ) • OR • ( OPZ . EQ. 1 lf 1 ) ) THEif ERLilf=ZSP-Zl IF{ERLIN.LT.O.O) GOTO 100

ElfDIP

CCC I . ITERATE RUlfGE-KUTTA

GOTO 1

CCC I *** PINAL OUTPUTS ~--------------~

***

100 CONTINUE c ~--------~--------~ c c c c c c c

MOLE PERCENTAGE OF I-HEXANE ..••• PMP1

3-MP ......•.. PMP2 2-MP ..•.•.••. PMP3 2,3-DMB ...•.. PMP4 2,2-DMB •..•.. PMPS INERT •••..••• PMP6

c ~----------------------~ PHPl=Y0(1)*100. PMP2=Y0{2)*100. PMP3=Y0{3)*100. PMP4=Y0{4)*100. PHP5=Y0{5)*100. PMP6=Y0{6)*100.

~ I PIIAL RIIIC'IOR I'EIIPIRA!URE, I

'f=P{6)

IP({OPZ.EQ. 'y 1 ).0R.{OPZ.EQ.'Y')) GO!O 101 IP{{OPZ.EQ. 1n').OR.(OPZ.EQ.'I')) GOTO 777

STOP ElfD

c ++++++++++++++++++++++++++++++++++++++ C + END ! of MAIN Program + c ++++++++++++++++++++++++++++++++++++++

87

c r---------------------------------~ C THIS SUBROUTIME SUPPLIES THE MAJORITY OF THE DATA C FOR THE FIXED-BED REACTOR MODEL. THIS SUBROUTINE IS C USER SUPPLIED AND PROVIDES DATA, FEED CONDITIOBS, C STOICHIOMETRIC COEFFICIENTS, HEATS OF REACTIONS, c~-------------------------------'

SUBROUTINE DATAN COMMON /DHRX/ DHRXH(4),T,Y0(10) COMMON /DATAS/ NC,FTR,F(10),NR COMMON /DATA6/ P,GAM(5,4),D COMMON /CATAP/ BULDEH

CCC I _ THE lfUMB!R OF REACTIONS

NR=4 Cr-------------------~ c HUMBER OF COMPOif!N'l'S I C (EXCEPT THE INERT GAS BECAUSE IT C DOESN'T REACT WITH OTHER REAC'l'ANTS) c~-----------------------'

NC=S Cr----------------------~ C THE StOICHIOMETRIC COEFICIEI'l'S C ** IBITIALIZE GAM(I,J) ** C'-------------------------'

DO 1 I=1,NC DO 1 J=1,1fR

1 GAM(I,J)=O.O Cr----------------------, c c c

(1)n-H!XAif! <--> (1) 3-methylpantane

l____>GAM(1,1) l_____>GAM(2,1) C'-------------------'

GAM(l,1)=-l.O GAM(2,1)=1.0

c r---------------------, c (1) 3-methylpantane <---> (1) 2-methylpantane

~ l_____>GAM(2,2) I >GAM(3,2) c .__ ____________________________________ ~

GAM(2,2)=-l.O GAM(3,2)=1.0

c r------------------------------------~ C (1) 2-methylpantane <--> (1) 2,3-dimethylbutane

~ l_____>GAM(3,3) l__>GAM(4,3) c~------------------------------------~

88

GAM(3,3)=-l.O GAM(4,3)=1.0

c .----------------------------------, c (1) 2,3-dimethylbutane <------> (1) 2,2-dimethylbutane

~ l______>GAM(4,4) l_____>GAM(5,4) c ~--------------------------------~

GAM(4,4)=-l.O GAM( 5 ,4)=1.0

c ~----------------~ C CALCULATE THE INLET C MOLAR FLOW RATES, (KGMOLE/HR) c ~------------------~

DO 2 I=1,lfC 2 F(I)=YO(I)*FTR

c ~------------...., C SET F(6) STANDS FOR C 'l'HE T!MP Ilf THE SYST!M c ..._ ______________ __.

F(NC+l )=T

RETURN !KD

c ******************************************************* C * THIS SUBROUTINE CALCULATES THE HEAT CAPACITIES OF * C * EACH SPECIES AND THE HEATS OF REACTIOlfS AT T (K). * c *******************************************************

SUBROUTINE ARRAY COMMOlf /DATAS/ lfC,FTR,F(10),lfR COMMOlf /DATA6/ P,GAM(5,4),D COMMON /DHRX/ DHRXlf(4),T,Y0(10) COMMON /VECTR/ DHRXV(4,1SO),CPV(5,1SO),GFERV(4,150) DOUBLE PRECISION SUM

c ~----------------------~ C DECIDE THE IlfTEGRATIOlf INTERVAL, C ( 'l'!MP RANGE FROM 298.15 to 1000 II:) c ..._ ______________________ ~

TI=298.15 DT=(1000.-TI)/90.

c ~------------------------~ C REACTIOK HEAT (KJ/KGMOL!) AT 298.15 K c C n-H!XAK! <------> 3-M!THYLP!KTAJIE (3-MP) c L-------------------------~

DHRXV{1,1)=-5.050*1000.

89

c r-------------------------~ C REACTION HEAT (KJ/KGMOLB) AT 298.15 K C 3-MBTHYLPEMTAME <------> 2-METHYLPEHTANB c ~------------------------------------~

DHRXV(2,1)=-2.580*1000. c r-----------------------------------------~ C REACTION HEAT (KJ/KGMOLE) AT 298.15 K C 2-ME'l'HYLPEM'l'AME <-> 2,3-DIMETHYLBUTAME c ~----------------------------------------------~

DHRXV(3,1)=-2.250*1000. c r-----------------------------------------------------~ C REACTION HEAT (KJ/KGMOLE) AT 298.15 K C 2,3-DIME'l'HYLBUTAJE < > 2,2-DIMETHYLBUTANE c ~----------------------------------------------------~

DHRXV(4,1)=-7.880*1000. c----------------------------------------------------------c C CALCULATE REACTION HEAT AT EVERY DT, (KJ/KGMOLE) C---------- From T=298.15 K TO 1000 K c C For e1ample: 1st reaction c c c c c c c c c c c c c c c c c c c c c c c c c c

n-Heiane <--> 3-Methylpantane

IT2 (Cp'-Cp)dT = heat of reaction

Tt

where Cp'= heat capacity of 3-MP Cp = heat capacity of n-Hexane

p.s. 1st reaction: I=l TI=298.15 K (referance temp) sum=O.O K=2

we want to evaulate reaction heat at 305.98 K (TI+DT) SUIFO.O+DT*GAM(l,1)*Cp(1,305.98)=-DT*Cp(1,305.98) sum=sum+DT*GAM(2,l)*Cp(2,305.98)=-DT*Cp(l,305.98)

+DT*l*Cp(2,305.98) sum=sum+DT*GAM(3,1)*Cp(3,305.98}=-DT*Cp(1,305.98)

+DT*Cp(2,305.98)+DT*O.O*Cp(3,305.98) =-DT*Cp(1,305.98)+DT*Cp(2,305.98)

SUIFSum+DT*GAM(4,l)*Cp(4,305.98) =-DT*Cp(1,305.98)+DT*Cp(2,305.98)

sum=sum+DT*GAM(S,l)*Cp(5,305.98) =-DT*Cp(1,305.98)+DT*Cp(2,305.98)

C Therefore, heat of reaction with respect to referance C temp is delta H= DT*( Cp(2,305.98)-Cp(1,305.98)) c-----------------------------------------------------------

90

DO 4 I=l,KR TI=298.15 SOM=O.ODO DO 5 K=2,91 TI=TI+DT DO 6 J=l,NC SOM=SUM+DT*GAM(J,I)*CP(J,TI)

6 CONTINUE

IF (TI.GT.lOOO.) GOTO 4 c ~-----------------------, C NEW VALUE OF REACTION HEAT c AT (T+dT) with respect to 298.15 K c ~----------------------~

DHRXV(I,K)=DHRXV(I,K-l)+SUM

5 SUM=O.ODO 4 CONTINUE

c --------------------------------------------------------c +CALCULATE THE GIBBS ENERGY OF FORMATION OP EACH REACTION+ C ------------- GF!RV(I,J), (KJ/KGMOLE) -------------C For example: 1st reaction C referance temp=298.15 K C 0'1'=7.8 K C new temp to evaulate : 305.9 K c suml=O.O c c c c c c c c c c c c c c c c c

n-Hexane <--> 3-methylpantane

show steps: suml=GAM(l,l)*GF(l,305.9)+suml =-l*GF(l,305.9)+0.0

suml=GAM(2,l)*GF(2,305.9)+suml= =l*GF(2,305.9)-GF(1,305.9)

suml=GAM(3,1)*GP(3,305.9)+suml=GP(2,305.9)GF(l,305.9)

suml=GAM(4,l)*GP(4,305.9)+suml=GP(2,305.9)GP(l,305.9)

suml=GAM(5,l)*GP(5,305.9)+suml=GP(2,305.9)GF(l,305.9)

Therefore, Gibbs energy of formation of 1st reaction at t+dt GP!RV(l,305.9)=suml

c-----------------------------------------------------------

DO 34 I=l,KR '1'1=298.15 SUMl=O.O DO 35 K=2,91 TI=TI+DT DO 36 J=l,KC

91

SUM1=GAM(J,I)*GF(J,TI)+SUM1 36 CONTIKUE

IF (TI.GT.1000.) GO TO 34 GFERV(I,K)=SUMl

35 SUM1=0.0 34 CONTIKUE

c ~-----------------------, C SET UP CPV(I,J} -->> CONVERT EVERY C VALUE OF Cp(i,ti) INTO VECTOR IN C ORDER TO USE LINEAR INTERPOLA'l'ION c ~----------------------~

DO 10 I=1,NC '1'1=298.15 DO 11 J=1,90 CPV(I,J}=CP(I,TI)

11 TI=TI+D'l' 10 CONTINUE

RETURN ElfD

c ***************************************** C * THIS FUNCTION CALCULATES THE HEAT * C * CAPCAITY OF EACH SPECIES * C * FROM 200-1000 (K} (KJ/KGMOLE-K} * c *****************************************

f*ckCTIOB CP(I,T} IF (I.EQ.1) GOTO 1 IF (I.EQ.2) GO'l'O 2 IF (I.EQ.3) GOTO 3 IF (I.EQ.4) GO!O 4 IF {I.EQ.5) GOTO 5

1 CP=(-1.0540+1.39E-1*T-7.449E-5*T2+1.551!-8*TS)*4.184 RETURN

2 CP=(-0.570+1.359E-1*T-6.854E-5*T2+1.202E-8*T')*4.184 RETURlf

3 CP=(-2.5240+1.477E-1*T-8.533E-5*T2+1.931E-8*'1'')*4.184 RmJRI

4 CP=(-3.489+1.469E-1*'1'-8.063E-5*T2+1.629E-8*TS)*4.184 RETORI

5 CP={-3.973+1.503E-1*T-8.314E-5*T2+1.636E-8*T')*4.184 RETURlf EHD

c ******************************************* C * THIS FUICTIOI CALCULATE THE GIBBS FREE * C * ElfERGY OP PORMATIOif OP HUAMI ISOMERS * C * FROM 200-1000 K, KJ/KGMOL! * c *******************************************

PUICTIOK GP{I,T) IF (I.EQ.l) GOTO 1 IF (I.EQ.2) GO!O 2

92

IF (I.EQ.3) GOTO 3 IP (I.EQ.4) GOTO 4 IF (I.EQ.S) GOTO 5

1 GP=-0.000087*TS+0.219336*T2+453.119366*T-151738.80896 RETURN

3 GF=-0.000092*TS+Q.225563*T2+458.412884*T-158998.25354 RETURN

2 GP=-0.000085*TS+0.216435*T2+460.331617*T-156934.60254 RETURN

5 GF=-0.000092*TS+0.224945*T2+481.313618*T-169166.74548 RETURN

4 GF=-0.000091*TS+0.22493*T2+473.536175*T-161194.52295

RETURN END

c ******************************************************** C * THIS SUBROUTINE CALCULATE THE DERIVATIVE OF P(I) * C * WITH RESPECT TO Z. THE DERIVATIVES ARE CALCULATED * C * PROM MATERIAL BALANCE WHEN P(I) IS THE MOLAR PLOW * C * RATE OF A COMPOlfm AND PROM ElfERGY BALANCE WHEJ * C * P(I) IS THE TEMPERATURE. * c ********************************************************

SUBROUTINE PNC(P,PP,YO,ID) COMMON /CATAP/ BULDEN COMMOI /DATAS/ NC,FTR,Y(lO),NR COMMON /DATA6/ P,GAM(5,4),D DIMENSIOM P(lO),EK(4),FK(4),RK(4),YO(lO) DOUBLE PRECISIOlf PP(lO),CA(S),DHRXN(4),R(4),GPERN(4) DOUBLE PRECISION TDHRXN,THCAP,CONC(S),EXC(3)

c~ I _ REACTOR PRESSURE, (ATM)

PO=P

REACTOR TEMPERATURE, K c~ J ~----------------------------~

T=P(6) c r---------------------------------------------------------~ c_ CALCULATE THE VOLUMETRIC PLOW RATE, (MS/HR) C Using Ideal Gas Law, PV=nRT c ~--------------------------------------------------------~

QO=PT0*22.4*T/273.15/PO c r-----------------------------------------------------~ C CALCULATE 'l'HB HEATS OP RBAC'I'IOifS, HEAT C CAPACITIES AID GIBBS EIERGIBS AT AIY TEMP C B!TWE!If, 298 -1000 K C Using linear interpolation c ~----------------------------------------------------~

93

CALL PROP(T,DHRXN,CA,GFERN) c r-----------------------~ C CALCULATE THE EQUILIBRIUM CONSTANTS C ,FORWARD AND REVERSE RATE CONSTAM'l'S c ~----------------------~

CALL EQCON(EK,FK,RK,F,GFERN) c r-----------------------------~ C CALCULATE THE EQUILIBRIUM MOLE C ,FRACTIONS OF HEXANE ISOMERS. C Using 'LINPAC' To Solve Reaction Coordinates c ~----------------------------~

CALL SLTRES(EK,YO,EXC) c r----------------------, C CALCULATE THE CONCENTRATION OF C 2,3-DMB AKD NEOHEXAKE, KGMOLE/M' c ~--------------------~

DO 80 I=4,5 80 CONC(I)=FTO*YO(I)/QO

~ I CALCULATE Till! GLOBE RAI'I or FORTI! REACTION I CALL RXH(R,CONC,FK,RK) R(4)=R(4)*BULD!N

~ I ID,2, ie. ISDTB!RMAL COIDI!IOI I IF (ID.EQ.2) GOTO 75

c ~--------------------------------~ C CALCULATE THE NET HEAT DUE TO R!ACTIOif, KJ/KGMOLE c ~--------------------------------~ C by energy balance equation: c c dT/dZ = (xOZ/4)* t(bulk(-dH)) I t(Fi*Cpi) c I< >1 1<->1 c part A part B c f< >I C part C c ~--------------------------------~ c C part A c

SRXN=O.O DO 77 1=1,3

77 SRXK=!XC(I)*FTR*DHRXIf(I)+SRXN SRXI=SRXI*BULD!I TDHRXN=SRXK+R(4)*DHRXIf(4)

94

c c c

part B

THCAP=O.ODO DO 3 I=l,lfC

3 THCAP=THCAP+FTR*YO(I)*CA(I) Cr---------------. C PERFORM THE ENERGY BALANCE (K/M) C part C c ~-------------~

FP(6)=(-TDHRXN*3.14159DO*D*D/4.DO)/THCAP c ~------------------------~ C PERFORM THE MATERIAL BALANCE, (KGMOLE/HR/M) c C dFi/dZ= BULK*(,DI/4)* tRi c ~----------------------------~

75 FP(S)=R(4)*3.14159*D*D/4.0DO

RETURJf END

c ********************************************************** C * THIS SUBROUTIIE CALCULATES THE HEAT CAPACITY AID * C * THE HEATS OF REACTIONS FOR A GIVEN TEMPERATURE BY * C * LINERALY INTERPOLATING BETWEEN VALUES OF CPV( I, J) AlfD* C * DHRXV(I,J), RESPECTIVELY. * c **********************************************************

SUBROUTINE PROP(T,DHRXK,CA,GPERI) DOUBLE PRECISIOK DHRXK(4),CA(5),GFERB(4) COMMON /VECTR/ DHRXV(4,1SO),CPV(5,150),GFERV(4,150) COMMON /DATA5/ KC,FTR,F(10),BR

DT=(1000.-298.15)/90. • I=IFIX((T-298.15)/DT)+1

PRO=(T-298.15-DT*FLOAT(I-1))/DT Cr----------------. C CALCULATE THE HEATS OP REAC'l'IOKS C AT SPECIFIED T!MP, KJ/KGMOLE C'---------------A

DO 1 J:l,lfR 1 DHRXI(J)=DHRXV(J,I)+PRO*(DHRXV(J,I+1)-DHRXV(J,I))

c r---------------------------~ C CALCULATE THE HEAT CAPACITIES OP C ISOMERS AT SPECIFIED T!MP, KJ/KGMOLE-K c .__ _______________________ ~

DO 2 J:l,KC 2 CA(J)=CPV(J,I)+PRO*(CPV(J,I+l)-CPV(J,I))

95

c r----------------------, C CALCULATE THE GIBBS EHERGI!S C AT SPECIFIED TEMP, (KJ/KGMOLE) c ~--------------------~

DO 3 J=l,IfR 3 GFERK(J)=GFERV(J,I)+PRO*(GFERV(J,I+l)-GFERV(J,I))

RETURN END

c ********************************************************** C * THIS SUBROUTINE CALCULATES THE EQULIIBRIUM * C * CONSTANTS OF EACH REACTIOif AND THE FORWARD AND REVERSE* C * REACTION RATE CONSTANTS. * c **********************************************************

SUBROUTINE EQCON(EK,FK,RK,F,GFERN) DIMENSION EK(4),FK(4),RK(4),F(l0) DOUBLE PRECISION GFgRN(4)

C-- REACTOR TEMPERATURE

T=F(6) c r---------------------------, C CALCULATE EQUILIBRIUM COISTAlfT OF NORMAL C HEXANE TO IT'S ISOMERS C delta G=-RT*lnK c ~------------------------~

DO 5 1=1,4 5 EK(I)=EXP(-GF!Rif(I)/(8.314*T))

c r---------------------------, C CALCULATE REVERSE REACTIOI RATE CONSTANTS, C (FTS/LB of CAT-HR) C kr=k·elp(-E/RT) c ~------------------------~

TR=9./5.*(T-273.15)+32.+459.67 RK(4)=5.24*1000.* EXP(-9.55*1000./10.7302/TR)

c r-------------------------------------, C CALCULATE FORWARD REACTION C RATE CONSTANTS, (FTS/LB-HR) c K=kf/kr -----> kf=K*kr c ~-------------------------------------'

FK(4)=RK(4)*EK(4) c r-----------------------, C COIIV!RT FORWARD AID REVERSE C RATE CONSTANTS TO, MI/KG-HR) c ~------------------~

FK(4)=FK(4)*0.06243 RK(4)=RK(4)*0.06243

96

RETURN DD

c ********************************************************** C * THIS SUBROUTINE CALCULATES THE RATES OF EACH REACTION * C * GIVEN THE COMPOSITION AND TEMPERATURE. THE DEFINITION * C * AND UNITS OF THE VARIABLES CAN BE FOUND IN THE * C * NOMENCLATURE SECTION OF THE MAIN PROGRAM. * c **********************************************************

SUBROUTINE RXN(R,CONC,FK,RK) COMMON /DATAS/ NC,FTR,Y(10),NR DOUBLE PRECISION R(4),CONC(S) DIMENSION FK(4),RK(4)

c r-----------------------------~ C CALCULATE THE GLOBE REACTION RATE C OF FORTH REACTION, KGMOLE/(KG OF CAT-HR) c ~----------------------------~

R(4)=FK(4)*CONC(4)-RK(4)*CONC(5)

RETURN END

c ********************************************************** C * THIS SUBROUTINE SOLVE 3 EQUATIONS SIMULTANEOUSLY IN * C * ORDER TO FIND THE THERMODYNAMIC EQUILIBRIUM MOLE * C * FRACTION OF N-HEXANE, 3-MP, 2-MP, 2,3-DMB. * c **********************************************************

SUBROUTINE SLTRES(EK,YO,EXC) DOUBLE PRECISION A(3,3),B(3),EXC(3) DIMENSION EK(4),Y0(10)

INTEGER IPVT(3)

C*** NOTE THAT A,B,X,IPVT MUST BE DOUBLE PRECISIONED AND DIMENSIONED BY c C---- NUMBER OF UKKHOWKS (REACTION COORDINATES) C

N=3 c---------------------------C ZERO B(I) AND A(I,J)

DO 1 I=1,N B(I)=O.O DO 1 J=l,N

1 A(I,J)=O.O

C SET THE NONZERO VALUES OF A(I,J) AND B(I)

A(l,l)=EK(l)+l. A(1,2)=-l. A(2,1)=EK(2) A(2,2)=-EK(2)-l.

97

A(2,3)=1. A(3,2)=EK(3) A(3,3)=-EK(3)-l. B(l)=YO(l)*EK(l)-Y0(2) B(2)=Y0(3)-Y0(2)*!K(2) B(3)=Y0(4)-!K(3)*Y0(3)

C SOLVE REACTION COORDINATES EXC(l),EXC(2),EXC(3)

C CALL LINPAC c

CALL LIMPAC(N,A,B,EXC,IPVT)

YO(l)=YO(l)-EXC(l) Y0(2)=Y0(2)+EXC(l)-EXC(2) Y0(3)=Y0(3)+EXC(2)-EXC(3) Y0(4)=Y0(4)+EXC(3) YO(S)=YO(S)

RETURN END

98

APPENDIX B

COMPUTER PROGRAM FOR HEXCR

99

$debug

C ************************ ABSTRACT *********************** c * * C * This program calculates the performance of an * C * CSTCR . Using a steady state mole balance for each * C * species, a system of two linear equations containing * C * two unknown is generated. This system of equations * C * is solved using the 11 Newton's Method 11 • * c * * C * ****************** NOMENCLATURE ********************* c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c * c *

W - weight of catalyst, kg Q- volumetric flow rate, ~/hr N - no. of linear equations TM - average temperature, K NC - no. of components NR - no. of reactions ID - flag which determine reaction type CDO - initial concentration of 2,3-DMB, kgmole/~ CEO - initial concentration of 2,2-DMB, kgmole/ms FTO - total flow rate, kgmole/hr HHl- enthalpy of 2,3-DMB at temp tz, kj/kgmole HH2- enthalpy of 2,2-DMB at temp t2, kj/kgmole HGl - enthalpy of 2,3-DMB at temp t1, kj/kgmole HG2- enthalpy of 2,2-DMB at temp t1, kj/kgmole TIN - feed input temperature, K TOUT - product output temperature, K CONS - conversion PMPl - feed mole percentage of n-hexane FMP2 - feed mole percentage of 3-MP FHP3 - feed mole percentage of 2-MP FMP4 - feed mole percentage of 2,3-DMB FHP5 - feed mole percentage of 2,2-DMB FMP6 - feed mole percentage of inert gas PMPl - product mole percentage of n-hexane PMP2 - product mole percentage of 3~MP PMP3 - product mole percentage of 2-MP PMP4 - product mole percentage of 2,3-DMB PMP5 - product mole percentage of 2,2-DMB PMP6 - product mole percentage of inert gas YO(I) - mole fractions of hezane isomers, I=l,S Y0(6) - mole fraction of inert gas PX(I) - value of linear equation RK(4) - reverse rate constant, ~/(kg of cat-hr) FK(4) - forward rate constant, ~/(kg of cat-hr) EK(I) - equilibrium constants, dimensionless CP(I) - heat capacity of the i-th component at

temperature t, kj/(kgmole-K) EXC(I) - reaction coordinates, I=l,3 GPERK(I) - gibbs free energy, kj/kgmole CPV(I,J) - a vector containing heat capacities of

component i at discrete value of

100

C * temperature, kj/{kgmole-K) C * DHRXN(I) - the heat of reaction of the i-th reaction c * ,kj/kgmole c ********************************************************* c c c c c c c c c c

I INPUT DESCRIPTION I The initial guesses are specified in the main program

as well as the error criteria and the number of linear equations. The functions are specified in subroutine ~UNC AND ~ADI, the partial derivatives of the functions with respect to the independent variables are specified in subroutine DER and ADER.

C***********************************************************

$storage:2

INTEGER RC DIMENSION X{2),FX{2) COMMON /DHRX/TIN,Y0{6),yd{6) COMMON /ONE/ Q,CDO,CEO,HHl,HH2,HGl,HG2 COMMON /DATA5/ NC,PTO,NR DIMENSION RK(4),PK{4) DOUBLE PRECISION CA{5),GFERN{4),DHRXN{4)

~ I set up data for EZVU I RC=O CALL ISPPFV{S,'AI Pl',RC,AI,4) CALL ISPFFV(6, 'TIN F5' ,RC,TIN,4) CALL ISPFFV{7,'TOUT F5',RC,TOUT,4) CALL ISPPPV( 4, I Q PSI ,RC,Q,4) CALL ISPPFV{6,'FTO F5',RC,PT0,4) CALL ISPFPV{4,'W F5',RC,W,4) CALL ISPFFV{7,'FMP1 F6',RC,FMP1,4) CALL ISPPPV(7,'PMP2 F6' ,RC,PMP2,4) CALL ISPPFV{7,'FMP3 P6',RC,FMP3,4) CALL ISPPPV(7,'PMP4 F6',RC,FMP4,4) CALL ISPPPV(7,'FMP5 F6',RC,FMP5,4) CALL ISPFPV{7,'FMP6 F6',RC,FMP6,4) CALL ISPFFV(7,'PMP1 F6',RC,PMP1,4) CALL ISPPPV{7,'PMP2 F6',RC,PMP2,4) CALL ISPFFV{7,'PMP3 F6',RC,PMP3,4) CALL ISPFFV{7,'PMP4 P6',RC,PMP4,4) CALL ISPFFV{7,'PMP5 F6',RC,PMP5,4) CALL ISPFPV(7,'PMP6 F6',RC,PMP6,4)

~ set function keys I

101

c

ZF10='QUIT' ZCMD=' I

ZATR='WRI I

ZF01='CSR1' ZF02='CSR2'

C set initial values of function keys c

c

CALL ISPFFV(6,'ZATR C',RC,ZATR,4) CALL ISPFFV(6,'ZF01 C' ,RC,ZF01,4) CALL ISPFFV(6,'ZF02 C' ,RC,ZF02,4) CALL ISPFFV(6,'ZF10 C' ,RC,ZF10,4) CALL ISPFFV(6,'ZCMD C',RC,ZCMD,4)

c data for screens csl,cs2 C get default values from profile c

c

CALL ISPFF(lO,'VGET TIN P' ,RC) CALL ISPFF(S, 'VGET Q P',RC) CALL ISPFF(lO,'VGET FTO P' ,RC) CALL ISPFF(S, 'VGET W P' ,RC) CALL ISPFF(ll,'VGET FMPl P',RC) CALL ISPFF(ll,'VGET FMP2 P',RC) CALL ISPFF(ll,'VGET FMP3 P',RC) CALL ISPFF(l1,'VGET FMP4 P',RC) CALL ISPFF(l1,'VGET FMPS P',RC) CALL ISPFF(11,'VGET FMP6 P' ,RC)

C start screen inputs c

101 ZCMD=' CALL ISPFF(l3,'DISPLAY KEYC1' ,RC) CALL ISPFF(12,'DISPLAY CSR1',RC)

IF(ZCMD.EQ.'QUIT') CALL EXIT IF(ZCMD.EQ. 'CSR2') GOTO 202 GOTO 303

202 ZCMD=' CALL ISPPP(13,'DISPLAY KEYC2' ,RC) CALL ISPPP(12,'DISPLAY CSR2',RC)

IF(ZCMD.EQ. 'QUIT') CALL EXIT IF(ZCMD.EQ.'CSR1') GOTO 101 GOTO 303

303 ZCMD=' c c id=1 for adiabatic condition C id=2 for isothermal condition c

102

ID=1 IF(AI.GT.1.5) ID=2

~ I assume isothermal case

TOUT= TIN c C input initial mole fraction c of n-hexane ----> Y0(1) C 3-HP > Y0(2) C 2-HP > Y0{3) C 2,3-DHB --> Y0(4) C 2,2-DHB --> YO(S) c

c

Y0(1)=FHP1/100. Y0(2)=FHP2/100. Y0{3)=FHP3/100. Y0(4)=FHP4/100. YO(S)=FHPS/100. Y0{6)=FHP6/100.

C let yd(i) be yo(i) c

yd=yo c c check initial condition c

IF((W.EQ.O.).AND.(ID.EQ.l)) GOTO 555 IF((W.EQ.O.).AND.(ID.EQ.2)) GOTO 320

c c set up data for reaction model c

CALL DATAlf c C calculate heat capacities C and reaction heats c

CALL ARRAY c C make initial guesses of Newton's method C x(1) = concentration of 2,3-DMB C x(2) = concentration of nee-hexane c C unit : (kgmole/~) c

X(l)=lO.O

103

X(2)=10.0 c C calculate the thermo equilibrium c mole fraction of hexane isomers c

c c

TINN=TIN CALL THEQ{YD,FK,RK,TINN,ID)

C convert mole fractions into concentrations, C (kgmole/ml) c C cdo = new cone. of 2,3-DMB C ceo = new cone. of nee-hexane c

c

CDO=YD(4)*FTO/Q CEO=YD(S)*FTO/Q

IF(ID.EQ.l) GOTO 139

C perform isothermal condition c c call Newton's method C calculate the output cone. of 2,3-DMB & neo-hexane c

CALL NEWTN(X,FX,K,FK,RK,ID,TINN,TOUT) c C From Newton's method, we can find the final C conc.s of 2,3-DMB [x(1)] and nee-hexane [x(2)]. c Then convert them into mole fraction, YD(4) and C YD(S). c

c

YD(S)=X(2)*Q/PTO YD(4)=X(l)*Q/FTO GOTO 224

C adiabatic case (id=1) c

139 COift'INU!

~ I assumed the final output teoperature

TOUT=TINN+lOO. 145 CALL KEWTJ(X,FX,W,PK,RK,ID,TINN,TOUT)

104

c c c c c c c

calculate the conversion the following reaction for adiabatic case:

2,3-DHB <--==> neo-hexane

CONS=W*{FK{4)*X{l)-RK{4)*X{2))/{YD{4)*FTO) c c using average temperature to estimate the C heat capacities of 2,3-DMB and neo-hexane c

TM={TINN+TOUT)/2. CALL PROP(TM,DHRXN,CA,GFERN)

~ I check convergence I USUM=CA{S}*TINN*CONS+CA(4)*TINN-CA{4)*TINK*CONS-

Hl*CONS DSUM=CA{S)*CONS+CA(4}-CA(4)*CONS TF2=USUM/DSUM TERML=ABS{TF2-TOUT) TOUT=TF2 IF{TERML.LT.l.O) GOTO 542 GOTO 145

~ end of adiabatic case I c C print out results of c isothermal condition c

224 CONTINUE c C calculate the conversion of the following reaction C for isothermal case c C 2,3-DMB <~> neo-Helane c

CONS=W*{PK{4)*X(l)-RK(4)*X(2))/{YD(4)*PTO)

~ I **** final outputs to BZVU ****

320 CONTINUE

105

C > Isothermal condition <-----. c C moles of hexane isomers at the end of the C reaction (convert into percentage form) c C PMPl ----> n-hexane C PHP2 -> 3-HP C PMP3 ----> 2-MP C PMP4 ----> 2,3-DHB C PMPS ----> 2,2-DMB c PHP6 -> inert gas c

c

PMP1=YD(1)*100. PMP2=YD(2)*100. PHP3=YD{3)*100. PMP4=YD(4)*100. PHP5=YD(5)*100. PHP6=YD(6)*100.

GO'i'O 101

C adiabatic condition c C final outputs to EZVU c

542 COifTINUE

YD(S)=YD(S)+YD(4)*CONS YD{4)=YD(4)*(1.-CONS) CONS=CONS*lOO.

555 COif'l'IlfUE C > Adiabatic condition <------. c C moles of hexane isomers at the end of the C reaction (convert into percentage fora) c c PHP1 -> n-hexane C PMP2 ----> 3-MP C PHP3 ----> 2-MP C PMP4 -> 2,3-DMB C PHP5 -> 2,2-DHB c PMP6 -> inert gas c

PHP1=YD(1)*100. PHP2=YD(2)*100. PHP3=YD(3)*100. PHP4=YD(4)*100. PHP5=YD(5)*100. PHP6=YD(6)*100.

106

107

GOTO 101 666 STOP

END c c end of the main program!!! c

c ******************* ABSTRACT ************************ c * * c * THIS SUBROUTINE CALCULATES THE PARTIAL DERIVATIVES* c * OF THE FUNC'l'IONS WITH RESPECT TO THE INDEPENDENT * c * VARIABLES. A(I,J) REPRESENTS THE PARTIAL OF THE ith* c * FUNCTION WITH RESPECT TO THE JTH VARIABLE. * c * (ISOTHERMAL CASE) ·t

c ******************************************************* c

SUBROUTINE DER(N,A,FK,RK,W) DIMENSION A{2,2) COMMON /ONE/Q,CDO,CEO,HH1,HH2,HG1,HG2 DIMENSION RK(4),FK(4)

DO 1 I=1,N DO 1 J=1,N

1 A(I,J)=O.O A(1,1)=-1.-W/Q*FK(4) A(1,2)=RK(4)*W/Q A{2,1)=W/Q*FK(4) A(2,2)=-1.-W/Q*RK(4)

RETURN END

c ******************* ABSTRACT ************************ c * * c * THIS SUBROUTINE CALCULATES THE PARTIAL DERIVATIVES* c * OF THE FUNCTIONS WITH RESPECT TO THE INDEPENDENT * c * VARIABLES. A{I,J) REPRESENTS THE PARTIAL OF THE ith* c * FUNCTION WITH RESPECT TO THE JTH VARIABLE. * c * (ADIABATIC CASE) * c ******************************************************* c

SUBROUTINE AD!R(N,A,FK,RK,W) DIMENSIOI A(2,2),RK(4),FK(4) COMMOI /ONE/ Q,CDO,CEO,HRl,HH2,HGl,HG2

DO 1 I=1,N DO 1 J=1,lf

1 A(I,J)=O.O

A{l,1)=-HR1-(HH1*W/Q)*FK(4) A(1,2)=(HHl*N/Q)*Rk(4) A(2,l)={HH2*W/Q)*FK(4) A{2,2)=-RH2-(HH2*N/Q)*RK(4)

RETURN END

c * ***************************************************** C * THIS SUBROUTINE CALCULATES THE VALUES OF EACH * C * LINEAR EQUATION GIVEN THE VALUE OF X(I) AND N. * C * THESE VALUES ARE SUPPLIED TO THIS SUBROUTINE WHEN * C * IT IS CALLED BY N!HTN. (ISOTHERMAL CASE) * c *******************************************************

SUBROUTINE FUNC(X,FX,FK,RK,W) COMMON /ONE/Q,CDO,CEO,HHl,HH2,HGl,HG2 DIMENSION RK(4),FK(4),X(2),FX(2)

FX(l)=CDO-X(l)+W/Q*(RK(4)*X(2)-FK(4)*X(l)) FX(2)=-X(2)+CEO+W/Q*(FK(4)*X(l)-RK(4)*X(2))

RETURN END

c * ***************************************************** C * THIS SUBROUTINE CALCULATES THE VALUES OF EACH * C * LINEAR EQUATION GIVEN THE VALUE OF X(I) AND H. * C * THESE VALUES ARE SUPPLIED TO THIS SUBROUTINE WHEN * C * IT IS CALLED BY NEWTN. (ADIABATIC CASE) * c *******************************************************

SUBROUTINE FADI(X,FX,FK,RK,W,Tl,T2) COMMON /OK!/ Q,CDO,CEO,HHl,HH2,HGl,HG2 DIMENSIOK RK(4),FK(4),X(2),FX(2) DOUBLE PRECISION CA(5),DHRXN(4),GFERK(4)

CALL PROP(Tl,DHRXN,CA,GFERN) CA3=CA(4) CA4=CA(5) Hl=DHRXN(4) TM=(Tl+T2)/2. CALL PROP(TM,DHRXN,CA,GF!RK) CAl=CA(4) CA2=CA(5) HHl=-CAl*(T2-298.15)-176.80*1000. HH2=-CA2*(T2-298.15)-184.68*1000. HG1=-(Tl-298.15)*CA3-176.8*1000. HG2=-(Tl-298.15)*CA4-184.68*1000. FX(l)=-HHl*X(l)+CDO*HGl+(W/Q)*(RK(4)*X(2)*HHl-

FK(4)*X(l)*HHl) FX(2)=-HH2*X(2)+CEO*HG2+(W/Q)*(FK(4)*X(l)*HH2-

RK(4)*X(2)*HH2)

RETURN END

C ttttttttttttttttttt ABSTRACT tttttttttttttttttttttttt

c * * C * THIS SUBROUTIKE EMPLOYES NEWTOK'S METHOD IN * C * ORDER TO SOLVE A SET OF H LINEAR EQUATIONS * C * CONTAINING N UHKNOHHS. THIS SUBROUTINE IS *

108

c * CALLED BY THE MAIN PROGRAM AMD IS CCSUPPLIED * c * THE VALUES OF THE INITIAL GUESS FOR X(I)'S AS * c * WELL AS THE VALUE OF K. THIS SUBROUTINE USES * c * THE VALUES OF THE FUNCTION FROM FUNC AND THE * c * VALUES OF THE PARTIAL DERIVATIVES OF THE * c * FUNCTION IN ORDER TO DETERMINE THE SOLUTION. * c * THIS C METHOD USES THE LIBRARY ROUTINE LINPAC * c * TO SOLVE THE C SYSTEM OF LINEAR EQUATION USED * c * BY NEWTON'S METHOD. * c ****************************************************** c

c

SUBROUTINE NEWTN(X,FX,W,FK,RK,ID,T,T2) DIMENSION A{2,2) ,X(2) ,FX{2) ,B{2) ,RAT{-2) ,FK{4) ,RK( 4)

DOUBLE PRECISION AA(2,2),BB{2),XX{2) INTEGER IPVT{2)

N=2 ERLIH=l.OE-3

1 CONTINUE ITEST=O

C HAKE FUNCTION EVALUATIONS c

IF {ID.EQ.1) GOTO 10 CALL FUNC{X,FX,FK,RK,W) GOTO 4

10 CALL FADI{X,FX,FK,RK,W,T,T2) c c set up constant terms c in jacobian matrix c

4 DO 3 I=1,N 3 B(I)=-FX(I)

~ I evaluate JACOBIIX matri1 I IF(ID.EQ.1) GOTO 15 CALL DER(N,A,PK,RK,H) GOTO 20

15 CALL ADER(N,A,FK,RK,W) c C establish coefficients C in jacobian matrix c

20 DO 32 I=1,N

c

DO 32 J=l,N 32 AA(I,J)=A(I,J)

DO 35 I=l,N 35 BB(I)=B(I)

C Using linpac to solve jacobian matrix c C CALL LINEAR EQUATION SOLVER c

CALL LINPAC(N,AA,BB,XX,IPVT)

~ I make an improved value for x(i)

c

DO 5 I=l,N RAT(I)=XX(I)/X(I)

5 X(I)=X(I)+XX(I)

C CHECK FOR CONVERGENCE c

c

DO 125 I=l,N 125 IF(ABS(RAT(I)).GT.ERLIM)ITEST=ITEST+l

IF(ITEST.NE.O)GO TO 1 RETURN END

C This subroutine supplied the majority of the C data for the CSCTR reactor model. Feed conditions, C stoichiometric coefficients of reaction model. c

SUBROUTINE DATAN COMMON /DHRX/ TIN,Y0(6),YD(6) COMMON /DATA5/ NC,FTO,NR COMMON /DATA6/ GAM(5,4)

~ I The nuober of reactions

MR=4 c C THE NUMBER OF COMPONENTS, c (except the inert qas because it C dosen't react with other reactants) c

NC=5

110

c c c c

1 c c c c c

c c c c c

c c c c c

c c c c c

The stoichiometric coefficients ** INITIALIZE GAM(I,J) **

DO 1 I=1,NC DO 1 J=1,NR GAM(I,J)=O.O

(1) n-HEXANE <-------> (1) 3-methylpantane

l____>GAM(1,1) l_____>GAM(2,1)

GAM(1,1)=-l.O GAM(2,1)=1.0

(1) 3-methylpantane <--> (1) 2-methylpantane

L_____>GAM(2,2) I >GAM(3,2)

GAH(2,2)=-l.O GAM(3,2)=1.0

(1) 2-methylpantane <--> (1) 2,3-dimethylbutane

l_____>GAM(3,3) l______>GAM(4,3)

GAM( 3 I 3) =-1. 0 GAM( 4,3)=1.0

(1) 2,3-dimethylbutane <----> (1) 2,2-dimethylbutane

l______>GAM(4,4) l_____>GAM(5,4)

GAM(4,4)=-l.O GAM(S,4)=1.0

RETURN END

c ******************************************************* C * THIS SUBROUTINE CALCULATES THE HEAT CAPACITIES * C * OF EACH SPECIES AND THE HEATS OF REACTION AT T * C * (K). * c *******************************************************

SUBROUTINE ARRAY COMMON /DATAS/ NC,FTO,NR COMMON /DATA6/ GAM(5,4) COMMON /DHRX/ TIN,Y0(6),YD(6)

111

c

COMMON /VECTR/ DHRXV(4,150),CPV(5,150),GFERV(4,150) DOUBLE PRECISION SUM,SUM1

c decide the integration interval C (temp range from 298.15 to 1000 K) c

c

TI=298.15 DT=(1000.-TI)/90.

C REACTION HEAT (KJ/KGMOLE) AT 298.15 K c C n-HEXANE <-.-> 3-METHYLPANTANE (3-MP) c

DHRXV(1,1)=-5.050*1000. c C REACTION HEAT (KJ/KGMOLE) AT 298.15 K c C 3-M!THYLPAlf'l'Alf! <--> 2-M!THYLPANTANE c

DHRXV(2,1)=-2.580*1000. c C REACTION HEAT (KJ/KGMOLE) AT 298.15 K c C 2-M!THYLPAlfTAlf! <--> 2,3-DIMETHYLBUTAifE c

c c c c c

DHRXV(3,1)=-2.250*1000.

REACTION HEAT (KJ/KGMOL!) AT 298.15 K

2,3-DIMETHYLBUTAN! <--------> 2,2-DIMETHYLBUTAlf!

DHRXV(4,1)=-7.880*1000. C++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C CALCULATE REACTION HEAT AT EVERY T+DT, (KJ/KGMOLE) C--------- From '1'=298.15 K TO 1000 K c For e1ample: lst reaction C n-Hez:ane --> 3-Methylpantane c c c c c c c c c c

IT2 (Cp'-Cp)dT = heat of reaction

T1

where Cp'= heat capacity of 3-MP Cp = heat capacity of n-Hexane

112

C p.s. 1st reaction: 1=1 C TI=298.15 K {referance temp) C sum=O.O C K=2 C we want to evaluate reaction heat at 305.98 K {TI+DT) C sum=O.O+DT*GAM(1,1)*Cp{1,305.98)=-DT*Cp(1,305.98) C sum=sum+DT*GAM(2,1)*Cp(2,305.98)=-DT*Cp(1,305.98) C +DT*1*Cp(2,305.98) C sum=sum+DT*GAM(3,1)*Cp(3,305.98)=-DT*Cp{1,305.98) C +DT*Cp(2,305.98)+DT*O.O*Cp(3,305.98) C =-DT*Cp(l,305.98)+DT*Cp(2,305.98) C sum=sum+DT*GAM(4,1)*Cp(4,305.98) C =-DT*Cp{l,305.98)+DT*Cp(2,305.98) C sum=sum+DT*GAM(5,1)*Cp(5,305.98) C =-DT*Cp(1,305.98)+DT*Cp{2,305.98) c C Therefore, heat of reaction with respect to reference C temp is delta H= DT*{ Cp(2,305.98)-Cp{l,305.98)) c C+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

c

DO 4 I=1,NR TI=298.15 SUM=O.ODO DO 5 K=2,91 TI=TI+DT DO 6 J=1,HC SUM=SUM+DT*GAM{J,I)*CP{J,TI)

6 CONTINUE

IF (TI.GT.1000.) GOTO 4

c new value of reaction heat C at (t+dt) with respect to 298.15 K c

DHRXV(I,K)=DHRXV(I,K-l)+sum

5 SUM=O.ODO

4 CONTINUE c C CALCULATE THE GIBBS ENERGY OF FORMATION C OF EACH REAC'l'IOH C "PERV(I ,J), (KJ/KGMOLE)---t c C For example: 1st reaction C reference temp=298.15 K C DT=7.8 K C new temp to evaluate : 305.9 K c suml=O.O c C n-Hexane <--> 3-methylpantane

113

C Show steps: C suml=GAM(l,l)*GF(1,305.9)+suml C =-1*GF(1,305.9)+0.0 c c sum1=GAM(2,1)*GF(2,305.9)+sum1 C = l*GF(2,305.9)-GF(l,305.9) C sum1=GAM(3,1)*GF(3,305.9)+sum1 C =GF(2,305.9)-GF(l,305.9) C suml=GAM(4,1)*GF(4,305.9)+suml C =GF(2,305.9)-GF(l,305.9) C suml=GAM(5,1)*GF(5,305.9)+suml C =GF(2,305.9)-GF(l,305.9) c C Therefore, Gibbs energy of formation C of 1st reaction at t+dt C GFERV(1,305.9)=suml c c

DO 34 I=1,lfR TI=298.15 SUMl=O.O DO 35 K=2,91 TI=TI+DT DO 36 J=l,NC SUM1=GAM(J,I)*GF(J,TI)+SUM1

36 CONTINUE IF (TI.GT.1000.) GO TO 34 GFERV(I,K)=SUMl

35 SUM1=0.0

34 CONTINUE c C SET UP CPV(I,J) ---->> convert every value of C Cp(I,TI) into vector in order to use linear C interpolation c

c

DO 10 I=l,lfC TI=298.15

DO 11 J=l,90 CPV(I,J)=CP(I,TI)

11 TI=TI+DT 10 CONTINUE

RE'l'URlf EHD

C This function subroutine calculates the heat C capacity of each species from 200 - 1000 (K) C (KJ/KGMOLI!!-K) .C

FUNCTION CP(I,T)

114

c

IF (I.EQ.1) GOTO 1 IF (I.EQ.2) GOTO 2 IF (I.EQ.3) GOTO 3 IF (I.EQ.4) GOTO 4 IF (I.EQ.5) GOTO 5

1 CP=(-1.0540+1.39E-1*T-7.449E-5*T2+1.551E-8*TS)*4.184 RETURN

2 CP=(-0.570+1.359E-1*T-6.854E-5*T2+1.202E-8*TS)*4.184 RETURN

3 CP=(-2.5240+1.477E-1*T-8.533E-5*T2+1.931E-8*TS)*4.184 RETURN

4 CP=(-3.489+1.469E-1*T-8.063E-5*T2+1.629E-8*TS)*4.184 RETURN

5 CP=(-3.973+1.503E-1*T-8.314E-5*T2+1.636E-8*TS)*4.184 RETURN END

C This function calculates the gibbs free C energy of formation of hexane isomers C from 200-1000'K, KJ/KGMOLE c

c

FUNCTION GF(I,T) IF (I.EQ.1) GOTO 1 IF (I.EQ.2) GOTO 2 IF (I.EQ.3) GOTO 3 IF (I.EQ.4) GOTO 4 IF (I.EQ.S) GOTO 5

1 GF=-0.000087*T'+0.219336*T2+453.119366*T-151738.80896 RETURN

3 GF=-0.000092*T'+0.225563*T2+458.412884*T-158998.25354 RETURN

2 GF=-0.000085*TS+0.216435*T2+460.331617*T-156934.60254 RETURN

5 GF=-0.000092*TS+0.224945*T2+481.3136l8*T-169166.74548 RETURN

4 GF=-0.00009l*TS+0.22493*T2+473.536175*T-161194.52295 RETURN END

c This subroutine calculates the rate constants, c heat capacitites and also the output temperature of C reaction n-hexane -----> 2,3-DMB c

SUBROUTINE THEQ(YO,FK,RK,T,ID) COMMON /DATA5/ NC,FTO,NR COMMON /DATA6/ GAM(5,4) DIMENSION EK(4),FK(4),RK(4),Y0(6) DOUBLE PRECISION CA(5),DHRXN(4),GFERN(4)

115

DOUBLE PRECISION EXC(3) c C Calculate the heats of reactions, heat c capacities and gibbs energies at any temp C between (298 -1000 K) C Using linear interpolation c

CALL PROP(T,DHRXH,CA,GFERN) c C Calculate the equilibrium constants, C forward and reverse rate constants c

CALL EQCON(EK,FK,RK,GFERN,T) c C calculate the equilibrium mole fractions C of hexane isomers C Using 'LINPAC' To Solve Reaction Coordinates c

c

CALL SLTRES(EK,YO,EXC) IF(ID.EQ.2) GOTO 100

C do energy balance c

c

c c c

c

CALL EKGBALS(YO,EXC,DHRXN,T)

100 RETURN END

SUBROUTINE ENGBALS(YO,EXC,DHRXH,T) COMMON /DATAS/ NC,FTO,KR DOUBLE PRECISION EXC(3),DHRXN(4),CA(S),GFERN(4) DIMENSION Y0(6),EK(4),FK(4),RK(4)

input term =0

C disappearance term c

SDIS=O.O DO 20 I=1,3

20 SDIS=EXC(I)*FTO*DHRXH(I)+SDIS

c C input=output+acc+disapp c

116

DIF=-SDIS

~ I output term

'l'M=T TE=T INX=1

50 CALL PROP(TH,DHRXN,CA,GFERN) SOUT=O.O DO 25 !=1,4

25 SOUT=SOUT+(TE-T)*CA(I)*YO(I)*FTO ERH1=ABS(DIF-SOUT) IF(INX.EQ.1) GOTO 77 ERH=ERH2-ERH1 IP(ERM.LT.O.) GOTO 100

77 ERH2=ERH1 TE=TE+0.2 INX=INX+1 CALL PROP(TE,DHRXN,CA,GFERN)

. CALL EQCON(EK,FK,RK,GFERN,TE) CALL SLTRES(EK,YO,EXC) TH=(TE+T)/2. GOTO 50

100 T=TE

110 RETURN END

c ********************************************************** C * THIS SUBROUTINE CALCULATES THE HEAT CAPACITY AND * C * THE HEATS OF REACTIONS FOR A GIVEN TEMPERATURE BY * C * LINEARLY INTERPOLATING BETWEEN VALUES OF CPV(I,J) AND* C * DHRXV(I,J), RESPECTIVELY. * c **********************************************************

SUBROUTINE PROP(T,DHRXN,CA,GFERN) DOUBLE PRECISION DHRXN(4),CA(5),GFERK(4) COMMON /VECTR/ DHRXV(4,150),CPV(5,150),GFERV(4,150) COMMON /DATA5/ NC,FTO,MR

DT=(1000.-298.15)/90. I=IFIX((T-298.15)/DT)+1 PRO=(T-298.15-DT*FLOAT(I-1))/DT

c..---------------, C CALCULATE THE HEA'l'S OF REACTIONS C AT SPECIFIED TEMP, KJ/KGMOLE C'--------------'

DO 1 J=1,MR 1 DHRXN(J)=DHRXV(J,I)+PRO*(DHRXV(J,I+1)-DHRXV(J,I))

117

c .--------------------------, C CALCULATE THE HEAT CAPACITIES OF C ISOMERS AT SPECIFIED TEMP, KJ/KGMOLE-K c ~------------------------~

DO 2 J=l,NC 2 CA(J)=CPV(J,I)+PRO*(CPV(J,I+l)-CPV(J,I))

c .----------------------, C CALCULATE THE GIBBS ENERGIES C AT SPECIFIED TEMP, (KJ/KGMOLE) c ~--------------------~

DO 3 J=l,lfR 3 GFERN(J)=GFERV(J,I)+PRO*(GFERV(J,I+l)-GFERV(J,I))

RETURN END

c ********************************************************** C * THIS SUBROUTINE CALCULATES THE EQUILIBRIUM * C * CONSTANTS OF EACH REACTION AND THE FORWARD AND REVERSE* C * REACTION RATE CONSTANTS. * c **********************************************************

SUBROUTINE EQCON(EK,FK,RK,GFERN,T) DIMENSION EK(4),FK(4),RK(4) DOUBLE PRECISION GFERN(4)

c .---------------------------, C CALCULATE EQUILIBRIUM CONSTANT OF NORMAL C HEXANE TO IT'S ISOMERS C delta G=-RT*lnK c ~------------------------~

DO 5 I=l,4 5 EK(I)=EXP(-GFERN(I)/(8.314*T))

c .-------------------------~ C CALCULATE REVERSE REACTION RATE CONSTANTS, C (FT'/LB of CAT-HR) C kr=k·elp(-E/RT) c ~------------------------~

TR=9./5.*(T-273.15)+32.+459.67 RK( 4) =5. 24*1000. * !XP( -'1. 55*1000. /1.987 /TR)

c .--------------------, C CALCULATE FORWARD REACTION C RATE CONSTANTS, (FTS/LB-HR) C K=kf/kr -----> kf=K*kr c ~------------'

FK(4)=RK(4)*EK(4) c .-----------, C CONVERT FORWARD AJID REVERSE C RATE CONSTANTS TO, MS /KG-HR) c .__ _________ _,

FK(4)=FK(4)*0.06243 RK(4)=RK(4)*0.06243

118

RETURN END

c ********************************************************** C * THIS SUBROUTINE SOLVE 3 EQUATIONS SIMULTANEOUSLY IN * C * ORDER TO FIND THE THERMODYNAMIC EQUILIBRIUM MOLE * C * FRACTION OF N-HEXANE, 3-MP, 2-MP, 2,3-DMB. * c **********************************************************

SUBROUTINE SLTRES(EK,YO,EXC) DOUBLE PRECISION A(3,3),B(3),EXC(3)

DIMENSION EK(4),Y0(10) INTEGER IPVT(3)

C*** NOTE THAT A,B,X,IPVT MUST BE DOUBLE PRECISIONED AND DIMENSIONED BY c C---- NUMBER OF UNKNOWNS (REACTION COORDINATES) C

N=3 c---------------------------C ZERO B(I) AND A(I,J)

DO 1 I=l,N B(I)=O.O DO 1 J=l,N

1 A(I,J)=O.O

C SET THE NONZERO VALUES OF A(I,J) AND B(I)

A(1,l)=EK(1)+1. A(l,2)=-l. A(2,l)=EK(2) A(2,2)=-EK(2)-l. A(2,3)=1. A(3,2)=EK(3) A(3,3)=-EK(3)-l. B(l)=YO(l)*EK(l)-Y0(2) B(2)=Y0(3)-Y0(2)*EK(2) B(3)=Y0(4)-EK(3)*Y0(3)

C SOLVE REACTION COORDIMATES EXC(l),EXC(2),EXC(3)

CALL LINPAC(H,A,B,EXC,IPVT) YO(l)=YO(l)-EXC(l) Y0(2)=Y0(2)+EXC(l)-EXC(2) Y0(3)=Y0(3)+EXC(2)-EXC(3) Y0(4)=Y0(4)+EXC(3) YO(S)=YO(S)

RETURN END

119

APPENDIX C

LISTING OF CONTROL PANELS

120.

************************ Hexane Isomerization

Fixed-Bed Reactor 300 -- 1000 K

REACTOR CONDITION

1= ADIABATIC RX PLEASE PICK EITHER 1 OR 2 2= ISOTHERMAL RX [ 0] .

FEED ->~ ~

0 0 0 0 o.l

opz:N

0 0 0 0

0 0 0 0 0

o o o o o.oo m 0000011

0 0 0 0 u L»- PRODUCT

F2 HEX SCREEN 2

I Final Mol% NEO

I 0.000

F3 HEX SCREEN 3

NO OF TUBES o.o TUBE D (M) 0.000

FEED CONDITIONS

FLOW RATE (KGMOLE/HR) 0.0000

TEMP ( K) 0.0000

PRESSURE 0.0000

BULK DEN OF CAT. (KG/M~3) 0.0000

FlO QUIT

Figure 18. Control Panel 1 for Fixed-Bed Reactor Initial Parameter Settings

ATM

I-' IV ......

INPUT. REACTANTS MOLE %

HEXANE ISOMERIZATION 300-1000 K

OUTPUT PRODUCTS MOLE %

N-HEXANE [100.0] % N-HEXANE 0.000

3 - MP o.ooo % 3 - MP 0.000

2 - MP 0.000 % 2 - MP 0.000

2,3-DMB 0.000 % 2,3-DMB 0.000

NEO-NEXANE 0.000 % NEO-HEXANE 0.000 (2,2-DMB) (2,2-DMB)

INERTS. 0.000 % INERTS 0.000

Fl HEX SCREEN 1 F3 HEX SCREEN 3 FlO QUIT

Figure 19. Control Panel 2 for Fixed-Bed Reactor Initial Parameter Settings

%

%

%

%

%

%

..... 1\.) 1\.)

************************ Hexane Isomerization

Fixed-Bed Reactor 300 -- 1000 K

FEED ->>~ I I Final Mol% NEO

I .... ··l

opz:Y

0 0 0 0

0 0 0 0 0

o o o o 12.1 m 0000011 .... u

L»- PRODUCT

F2 HEX SCREEN- 2

37.69

F3 HEX SCREEN 3

REACTOR CONDITION

1= ADIABATIC RX 2= ISOTHERMAL RX [2]

NO OF TUBES 150. TUBE D (M) 0.050

FEED CONDITIONS

FLOW RATE (KGMOLE/HR) 153.50

TEMP ( K) 408.00

PRESSURE 35.000

BULK DEN OF CAT. (KG/M-3) 640.00

FlO QUIT

Figure 20. Control Panel 1 for Fixed-Bed Reactor Optimized Model, Isothermal Reaction

ATM

---

I-' IV w

HEXANE ISOMERIZATION 300-1000 K

~ I INPUT REACTANTS MOLE % f;~::;.

:-:\'::{

.;:-:-::: :-:-:-:·:~-

~?{

f N-HEXANE (100.0) % 0

=~ :-:-:-:~-:-1 ~~~;~::~E 0.000 % I I INERTS 0.000 %

n I OUTPUT PRODUCTS MOLE % q ~

~ ~

~ N-HEXANE 7.825 % 0 I ~

I :.:_::8 :~::: :I ~!}!-------- ------.....::: I NEO-HEXANE 37.69 % ~ ftl (2,2-DMB)

-------<.:H if"( INERTS 0.000 % /:j

Ft HEX SCREEN 1 F3 HEX SCREEN 3 FlO QUIT

Figure 21. Control Panel 2 for Fixed-Bed Reactor Optimized Model, Isothermal Reaction

...... N ,j:>.

****~******************* Hexane Isomerization

Fixed-Bed Reactor 300 -- 1000 K

FEED ->~ I 1 Final Mol% NEO

I 35.64 .... ·•l 0 0 0 0

0 0 0 0 0

o o o o 3.00 m

OOOOOJ 0 0 0 0

L»- PRODUCT '· ~

opz:N

F2 HEX SCREEN 2 F3 HEX SCREEN 3

REACTOR CONDITION

1= ADIABATIC RX 2= ISOTHERMAL RX. [2]

NO OF TUBES 150. TUBE D (M) 0.050

.FEED CONDITIONS

FLOW RATE (KGMOLE/HR) 153.50

TEMP ( K) 408.00

PRESSURE 35.000

BULK DEN OF CAT. (KG/M- 3) 640.00

FlO QUIT

Figure 22. Control Panel 1 for Fixed-Bed Reactor Fixed-Length Model, Isothermal Reaction

I

ATM

1-' 1\J ()1

INPUT REACTANTS MOLE %

HEXANE ISOMERIZATION 300-1000 K

OUTPUT PRODUCTS MOLE %

N-HEXANE [100.0] % N-HEXANE 8.086

3 - MP 0.000 % 3 - MP 17.40

2 - MP 0.000 % 2 - MP 29.60

2,3-DMB 0.000 % 2,3-DMB 9.252

NEO-NEXANE 0.000 % NEO-HEXANE 35.64 (2,2-DMB) (2,2-DMB)

INERTS 0.000 % INERTS 0.000

Fl HEX SCREEN 1 F3 HEX SCREEN 3 FlO QUIT

Figure 23. Control Panel 2 for Fixed-Bed Reactor Fixed-Length Model, Isothermal Reaction

%

%

%

%

%

%

...... IV 0'1

*********************** HEXANE ISOMERIZATION

CSTCR 300 1000 K

"1 11 or "2" only

•• •• •• ••

Reactor condition

1. Adiabatic Rx 2. Isothermal Rx (OJ

>> Feed condition <<

Flow rate (kgmolefhr) 0.0000

Volumetric flow rate 0.0000 (m-3/hr)

=>~ spinning shaft

Tout= o.oooo >>=

Product out

K

Temperature ( K) 0.0000

weight of cat. (kg) 0.0000

Feed in Neo mol% = o.ooo %

F2 HEX SCREEN 2 FlO QUIT

Figure 24. Control Panel 1 for CSTCR · Initial Parameter Settings

I

1-' IV -....]

HEXANE ISOMERIZATION 300-1000 K

INPUT"REACTANTS MOLE% OUTPUT PRODUCTS MOLE %

N-HEXANE [100.0) % N-HEXANE

3 - MP 0.000 % 3 - MP

2 - MP 0.000 % 2 - MP

2,3-DMB 0.000 % 2,3-DMB

NEO-HEXANE 0.000 % NEO-HEXANE (2,2-DMB) (2,2-DMB)

INERTS 0.000 % INERTS

Fl HEX SCREEN 1 FlO QUIT

Figure 25. Control Panel 2 for CSTCR Initial Parameter Settings

0.000

o.ooo

o.ooo

o.ooo

o.ooo

0.000

%

%

%

%

%

%

...... 1\J 00

*********************** HEXANE ISOMERIZATION

CSTCR 300

•• •• •• ••

=>~ Feed in

spinning shaft

1000 K

~ II out= 408.00 ~>>= Product out

Neo mol% = 11.37 %

F2 HEX SCREEN 2

K

Reactor condition

1. Adiabatic Rx 2. Isothermal Rx [2]

>> Feed condition <<

Flow rate (kgmole/hr) 153.00

Volumetric flow rate 125.00 (mA3/hr)

Temperature · ( K) 408.00

weight of cat. (kg) 2200.0

-------- --- ----

FlO QUIT

Figure 26. Control Panel 1 for CSTCR Isothermal Reaction

I

...... "-> 1.0

HEXANE ISOMERIZATION 300-1000 K

INPUT REACTANTS MOLE % OUTPUT PRODUCTS MOLE %

N-HEXANE [100.0] % N-HEXANE

3 - MP 0.000 % 3 - MP

2 - MP 0.000 % 2 - MP

2,3-DMB 0.000 % 2,3-DMB

NEO-HEXANE o.ooo % NEO-HEXANE ( 2, 2-DMB) (2, 2-DMB)

INERTS o.ooo % INERTS

Fl HEX SCREEN 1 FlO QUIT

Figure 27. Control Panel 2 for CSTCR Isothermal Reaction

12.56

27.03

45.99

3.038

11.37

0.000

%

%

%

%

%

%

...... w 0

APPENDIX D

EFFECT OF PRESSURE UPON THE EQUILIBRIUM CONSTANT

This appendix explains that the effect of pressure on

the equilibrium constant.

As mentioned earlier, ~Go is based upon a fixed initial

and final state and is not influenced by the conditions at

any intermediate point. In fact, pressure does affect

equilibrium yield for a gas phase reaction. This effect of

pressure can be accounted for in the relationship between

Ky, K. The detailed steps are shown below.

For reaction aA + bB ---> cC + dD

fi v = flli v Yi P

where

fiv = the fugacity of components

fl!iv = mixture fugacity coefficients

Yi = mole fraction in the gaseous mixture

P = Total pressure

Using this expression for the fugacity, K becomes

c d

[fl!P]c [fl!P]D K =

• b

[fl!P]A [fl!P]B

c d

Yc YD

• b

YA YB

131

(D-1)

where Ky = equilibrium constant in terms of

mole fractions.

132

Assuming the mixture fugacity coefficients are equal to

unity is equivalent to assuming that the gas phase behaves

as an ideal solution. With this simplification, equation

(D-1) becomes

K = [p(c+d)-(a+b)] Ky; ( •:· c+d-a-b = 0 )

= Ky

Therefore, pressure does not affect the equilibrium yield if

ideal gas behavior is assumed.

Tai-Chang Kao

Candidate for the Degree of

Master of Science

Thesis: CHEMICAL PROCESS SIMULATION OF HEXANE ISOMERIZATION IN A FIXED-BED AND A CSTCR REACTOR

Major Field: Chemical Engineering

Biographical:

Personal Data: Born in Taipei, Taiwan, Republic of China, August 3, 1963, the son of Ming-Pan & SuChu Kao.

Education: Graduated from Cheng-Kwo High School, Taiwan, R.O.C., in June 1981; received the Bachelor of Science degree in Chemical Engineering from Tunghai University, Taiwan, in June 1986; completed requirements for the Master of Science degree at Oklahoma State University in May, 1991.

Professional Experience: R & D assistant engineer of Shin-Kwong Synthetic Fibers Company in Taiwan, 1988. Employed as a teaching assistant at Oklahoma State University during the Fall semester of 1990 and Spring semester of 1991.