The Design of Fixed-Bed Catalytic Reactors

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The Design of Fixed-Bed Catalytic Reactors

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PURDUE UNIVERSITY

THIS IS TO CERTIFY THAT T H E THESIS PREPARED U N D E R M Y SUPERVISION

b y _________________ Robert William Olson

ENTITLED

THE DESIGN OF FIXED-BfeP CATALYTIC REACTORS

COMPLIES WITH T H E UNIVERSITY REGULATIONS O N GRADUATION THESES

A N D IS APPROVED BY M E AS FULFILLING THIS PART O F T H E REQUIREMENTS

FOR THE DEGREE OF

Doctor of Philosophy

Professob

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February,

ead of

in

Charge

School

50

TO T H E LIBRARIAN:--

46? THIS THESIS IS N O T TO B E R E G A R D E D AS CONFIDENTIAL

GRAD. SCHOOL FORM 8—3 49—1M

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D epartment

THE DESIGN OF FIXED-BED CATALYTIC REACTORS A Thesis Submitted to the Faculty of Purdue University by Robert William Olson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy February, 1950

ProQuest Number: 27714105

All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is d e p e n d e n t upon the quality of the copy subm itted. In the unlikely e v e n t that the a u thor did not send a c o m p le te m anuscript and there are missing pages, these will be noted. Also, if m aterial had to be rem oved, a n o te will ind ica te the deletion.

uest ProQuest 27714105 Published by ProQuest LLC (2019). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346

ACKNOWLEDGMENT

The author wishes to express his gratitude to Dr* J* M. Smith for his helpful advice, constant interest and encouragement this research.

during the course of

Assistance in the experimental

work from D. G. Bunnell, H, B. Irvin, R. S. Reed, H, W. Schuler and G-.C* Smith

and financial aid

from the Purdue Research Foundation are gratefully acknowledged.

TABLE OF CONTENTS

ABSTRACT....................................................

i

INTRODUCTION..*.............................. ................

1

SCOPE OF THE RESEARCH WORK....................................

7

LITERATURE SURVEY.................. .........................

8 8

Differential Reaction Rates......... ................

* 9

Thermal Conductivities.............. Reactor Design....... ...... ............. .................

11

APPARATUS AND PROCEDURE....................................... 14 PRELIMINARY EXPERIMENTAL WORK.................................

22

DEVELOPMENT OF THE DESIGN METHOD............................... 25 OUTLINE OF THE DESIGN CALCULATIONS.............................

32

Method I....................... ............ .............. 33 Method II................ ............ ................. .

36

Method III

37

Method IV

...... ........... ........... .

38

.................................. ...... .

EFFECTIVE THERMAL CONDUCTIVITIES............................... 39 DIFFERENTIAL REACTION RATE DATA................................ 51 INTEGRAL REACTOR DATA......................................... 65 GROSSMAN DESIGN CALCULATIONS.................................. Calculations at the Mass Velocity of 244 lb./hr.-sq. ft..

.

74 77

Method I*....... ................ ........... ........

77

Method II....... ............................. ...... .

89

Method III

90

................. ...................... ..

Method IV........... ........................... .

93

CALCULATIONS AT OTHER MASS VELOCITIES..........................

94

ANALYSIS OF RATE DATA......................................... 110 Correlation of Surface Rate........ Approximate Equation for Overall Rate............. DISCUSSION OF RESULTS..............

Ill ....122 126

CONCLUSIONS................................................. 132 NOTATION.................................................... 134 LITERATURE CITED............................................. 137 APPENDIX A.................................................. 139 APPENDIX B.................................................. 141 APPENDIX C .................................................. 146 APPENDIX D .............................

151

APPENDIX E .................................................. 158

LIST OF FIGURES PAGE

FIG.

1.

Schematic Diagram of Research Apparatus..................

16

2.

Differential Reactor...................

18

3.

Integral Reactor.

19

4.

Variation of Reaction Rate with Total On-Stream Time...

24

5.

Differential Slice of a Cylindrical Reactor...............

26

6.

Grossman Graphical Plot.............

30

7.

Correlation of Effective Thermal Conductivities

8.

Thermal Conductivity of Air Versus Temperature

9.

Modified Reynolds Number Versus Temperature.

..........

.... ....

..........

41 42 43

10.

Effective Thermal Conductivity Versus Mass Velocity........

45

11.

Ke/R^ Versus Modified Reynolds Number......

46

12.

Comparison of Experimental and Predicted Temperature Gradients without Reaction. .....

49

Comparison of Experimental and Predicted Temperature Gradients without Reaction......

50

13.

14. Original Differential Rate Data at 147 lb./hr.-sq, ft......

56

15. Original Differential Rate Data at 244 lb./hr.-sq. ft

57

16. Original Differential Rate Data at 350 lb./hr.-sq. ft......

58

17. Original Differential Rate Data at 512 lb./hr.-sq. ft......

59

18. 19. 20. 21.

Reaction Rates Versus Mean Percent Conversion at 147 lb./hr.-sq. ft. ................

60

Reaction Rates Versus Mean Percent Conversion at 244 lb./hr.-sq. ft...................................

61

Reaction Rates Versus Mean Percent Conversion at 350 lb./hr.-sq. ft..............

62

Reaction Rates Versus Mean Percent Conversion at 512 lb./hr.-sq. ft......

63

FIG.

22.

PAGE

Radial Temperature Gradients with Reaction at 244 lb./hr.-sq. ft .......

72

23.

Heat of Reaction Versus Temperature.

...............

75

24.

Specific Heat Versus Temperature

............

76

25.

Extrapolated Reaction Rates at 244 lb./hr.-sq. ft

...

78

26.

B Function Versus Temperature at 244 lb./hr.-sq, ft.......

79

27.

A 2 at Center of Reactor Versus Temperature.....

80

28.

ûtZ at Edge of Reactor Versus Temperature

29.

Grossman Graphical Plot for Method I at 244 lb./hr.-sq. ft..

82

30.

Comparisons of Experimental and Predicted Temperature Gradient at n = 0. .............................

83

Comparisons of Experimental and Predicted Temperature Gradient at n = 1...........

84

Comparisons of Experimental and Predicted Temperature Gradient at n = 2.............

85

Comparisons of Experimental and Predicted Temperature Gradient at n = 3............

86

Comparisons of Experimental and Predicted Temperature Gradient at n = 4*.........

87

35*

Grossman Graphical Plot for Method II at 244 lb./hr.-sq. ft.

91

36.

Grossman Graphical Plot for Method III at 244 lb./hr.-sq. ft.....................

92

37*

Grossman Graphical Plot for Method IV at 244 lb./hr.-sq. ft.

94

38.

BFunction Versus Temperature at 147 lb./hr.-sq. ft........

96

39* - BFunction Versus Temperature at 350 lb./hr.-sq. ft........

97

40.

B Function Versus Temperature at 512 lb./hr.-sq. ft.

98

41.

ExtrapolatedReaction

99

42.

Extrapolated

ReactionRates at 350 lb./hr.-sq. ft.......... 100

43.

Extrapolated

ReactionRates at 512 lb./hr.-sq. ft.......... 101

31. 32. 33* 34.

......

Rates at 147 lb./hr.-sq. ft

81

PAGE

FIG.

44.

AZ Versus Temperature...... ..........................

102

45.

Comparison of Experimental andPredicted Temperature Gradients at 147 lb./hr.-sq. ft...... ......... .

103

46.

Comparison of Experimental andPredicted Temperature Gradients at 147 lb./hr.-sq. ft...... .................. 104

47.

Comparison of Experimental andPredicted Temperature Gradients at 350 lb./hr.-sq, ft. .... ......... 105

48.

Comparison of Experimental andPredicted Temperature Gradients at 350 lb./hr.-sq. ft ...... ............. 106

49.

Comparison of Experimental andPredicted Temperature Gradients at 512 lb./hr.-sq. ft ..... .

108

Comparison of Experimental andPredicted Temperature Gradients at 512 lb./hr.-sq. ft ...... .

109

Plot of Reciprocal Reaction Rate Versus Reciprocal Mass Velocity .........................

111A

50. 50A. 51.

Unretarded Rate Versus Percentage Conversion

...... 121

52. Constant D* Versus l/T............. ................ ..

123

53» Constant B1 Versus l/T......

124

......

54» Experimental and Predicted Conversions Versus Mass

Velocity. 128

55* Experimental and Predicted Conversions Versus BedDepth.....

130

LIST OF TABLES PAGE

TABLE 1. 2.

Calculated Slopes for Equation 7 and Effective Thermal Conductivities........ ...................... .

44

Average Values of Kg/K^ Versus BpG and Average Values of ke Versus G....... ................ .

47

3.

Differential Rate Data at 147 lb./hr.-sq. ft

.....

52

4.

Differential Rate Data at 244 lb./hr.-sq. ft............ .

53

5. Differential Rate Data at 350 lb./hr.-sq* ft

.......

54

6 . Differential Rate Data at 512 lb./hr.-sq. ft..............

55

Integral Reactor Data at 147 lb./hr.-sq. ft............. .

66

7.

8 . Integral Reactor Data at 244 lb./hr.-sq. ft..............

6?

Integral Reactor Data at 350 lb./hr.-sq. ft........... .

68

Integral Reactor Data at 512 lb./hr.-sq. ft..,............

69

11. Thermocouple Locations in Integral Reactor............. .

70

9. 10.

12

. Results of Design Calculations at a Mass Velocity of 244 lb./hr.-sq. ft. Using Method 1

..... . 141

13.

Results of Design Calculations at a Mass Velocity of 244 lb./hr.-sq. ft. Using Method II....... ... ..... . 146

14.

Results of Design Calculations at a Mass Velocity of 244 lb./hr.-sq. ft. Using Method III.............. .

15.

151

Results of Design Calculations at a Mass Velocity of 244 lb./hr.-sq. ft. Using Method IV................ . 158

16. Percent Diffusional Retardation at Various Temper­ atures and Mass Velocities..................... ...... 112 17.

Comparison of Don-Retarded Rate Obtained from Experi­ mental Data and Computed from Equation 27.............. 122À

i

THE DESIGN OF FIXED-BED CATALYTIC REACTORS

ABSTRACT

The rapid increase in the use of catalytic reactors for chemical con­ version in recent years has aroused the interest of many investigators concerned with their design.

Fundamental design methods for reactors have

heretofore been lacking and the usual procedure for the sizing of a re­ actor was an empirical one requiring extensive experimental pilot plant studies.

Thus the formulation of a good design method which would re­

sult in the elimination of at least part of the pilot plant work would be a major achievement in saving of time and money. A fundamental design method would include a means for the prediction of the temperature and conversion at every point within the reactor.

In

non-adiabatic reactors this prediction is made difficult by the presence of large radial temperature gradients established because of radial heat transfer.

The magnitude of these temperature gradients depends upon the

thermal conductivity of the gas-solid system, the temperature of the wall of the reactor, the initial temperature of the reactants and the rate of the reaction.

Since physical and chemical processes which depend upon

one another occur simultaneously the design is complicated further. Before any calculation for the prediction of the quantity of catalyst required for a specified conversion can be made, kinetic data for the reaction, effective thermal conductivity of the system, heats of reac­ tion and specific heats must be known and the mechanical design and oper­ ating temperatures must be specified.

ii

This thesis is concerned with the collection of data necessary for design calculations which are not available in the literature, i.e. kinetic data for a specific reaction and the effective thermal conductivity of a gas—solid system.

The air—oxidation of sulfur dioxide was chosen

for study because of its high heat of reaction, the absence of side re­ actions and the good analytical methods available for chemical analysis. The catalyst chosen was 0.2% platinum on an alumina carrier in the form of 1/8 inch cylindrical pellets. The thesis is divided into five sections: 1.

Reaction rate data for the air-oxidation of sulfur dioxide at all

the temperatures and compositions which might occur in a large-scale re­ actor are presented.

These data were obtained at mass velocities of re­

actants of 147, 244, 350 and 512 lb./hr.-sq, ft. over a temperature range of 350 to 475°C. and over a conversion range of 0 to 65% conversion. 2. Effective thermal conductivities of a gas-solid system are pre­ sented at mass velocities of 147, 244, 350 and 512 lb./hr.-sq. ft. and at radial positions of 0.7, 0.8 and 0,9.

Other conductivities calculated by

Bunnell (5) are used in the calculations but not presented herein. 3»

The radial and axial temperature gradients and conversions in a

large scale (integral) reactor were measured. of 6.45% sulfur dioxide and the remainder air.

The reactants consisted Data were observed at

mass velocities of 147, 244, 350 and 512 lb./hr.-sq. ft. 4* Reaction rate and effective thermal conductivity data were used (along with supplementary data) to predict the temperature gradients and conversions in an integral reactor of the same size and operating under the same conditions as that considered in section 3. The calcu­ lated results were compared with the observed results.

iii

5.

An analysis of the reaction rate data was made to determine the

diffusional retardation as a function of mass velocity and to postulate a mechanism for the reaction. Reaction rate data are best obtained in a flow-type reactor contain­ ing a bed of catalyst so thin that relatively small changes in composition occur as the reactant gases pass through the bed.

This type of reactor

is known as a differential reactor and the rates measured therefrom are known as differential reaction rates. Accurate methods of chemical anal­ ysis are required to obtain these data. In making differential rate determinations, air was dried and then metered to a preliminary converter where it was mixed with a portion of a metered sulfur dioxide stream.

Sulfur dioxide was added both before

and after the preliminary converter in order to make reaction rate meas­ urements in the presence of sulfur trioxide.

After conversion of the

portion of sulfur dioxide which passed through the converter, it was mixed with the remaining sulfur dioxide and then sent through a tempera­ ture conditioning bath and a differential reactor.

Samples of reactants

and products were withdrawn before and after the reactor and analyzed by absorption in a caustic glycerine solution and then titrated against a standard potassium iodate solution.

Essentially the same procedure was

followed in the integral reactor runs except that no preliminary con­ verter was used. Effective thermal conductivities are best determined by measurement of both radial and axial temperatures in packed cylindrical beds in which no reaction occurs.

From these temperature data, the effective

thermal conductivity which satisfies the basic partial differential

iv

equation for heat flow in cylindrical tubes through which gases are flowing can be calculated.

The equation is:

The method employed in the solution consists of determining graphically the temperature derivatives with respect to X and Z by measuring the

Z.

A uniform mass velocity across the reactor is assumed and the equa­

tion solved at various radial positions and bed depths for Ke, the only unknown quantity.

When determined in this manner any variations in mass

velocity become absorbed in the effective thermal conductivity values. The conductivity was found to decrease as the tube wall was approached. All of the fundamental reactor design methods developed in recent years have been based upon the solution of the basic differential equa­ tion for heat flow in a cylindrical reactor through reacting gases are flowing,

Wilhelm, Johnson, and Acton (30) obtained an analytical solu­

tion for the solid catalyst temperatures based on the assumptions that the rate of reaction varied linearly with the temperature and that the temperature of the gas within any thin horizontal slice of catalyst bed was uniform because of radial mixing.

Tasker and Wilson (23) suggested

the use of a bulk mean temperature to evaluate the mean reaction rate at every bed depth rather than evaluate the radial temperature gradients. Grossman (9) presented the most simplified method for design which did not involve any serious assumptions. This was a semi-graphical step­ wise integration of the basic differential equations written in incre­ mental form.

Two differential equations were derived:

one for solid

catalyst and one for gases, thus necessitating the use of separate

thermal conductivities for the solid and gas phases. Hougen and Watson (13) modified the method by assuming identical gas and solid temperatures at any point in the reactor.

This eliminated the need for the separate

thermal conductivities and permitted the use of one so-called effective thermal conductivity to take care of all the heat transfer processes. The assumptions made for this solution v,rere that the heat transferred by conduction in the axial direction was considered negligible with respect to that transferred in the radial direction and that the mass velocity across a section perpendicular to direction of fluid flow was uniform. From a heat balance over a differential element of the reactor, the basic differential equation is obtained:

where

A

and B =

-r

A H

Neglecting longitudinal conduction, this equation is converted into in­ cremental form to give: A Az (AX)2

A 2t

+

L

The radius is divided into n equal increments such that X = n A X and the height is divided into k increments.

By denoting the temperature at any

radial position n and any height k as tR k, it can be shown that the in­ cremental equation can be written as:

This equation shows that since it contains no terms with temperature at the k + 1 level, the temperatures at the latter level can be found from a knowledge of the temperatures at the k level.

It can also be shown

that on a plot of temperature versus logarithm of the radial position the temperature at the k + 1 level can be found by a graphical method. tn

is determined by drawing a straight line between the n 4 1 and

n - 1 temperatures at the k level.

The distance between the intersection

of this straight line with the In n abscissa and t^ ^ determines the quan­ tity in parenthesis in the above equation.

When the heat of reaction term,

B AZ is added the quantity in the parenthesis and tfi ^ the temperature at the k + 1 level is established.

BAZ must be evaluated at the conditions

of average temperature and conversion in that increment. The conversion obtained in each increment is determined from the equation: A zp

r

r f B AZS F

After the temperature and conversion at the k 4 1 level is determined for every radial position, the values obtained are used in the next cal­ culation to determine the temperature and conversion at the k 4 2 level. The calculations are continued in this manner until the desired bed depth has been attained.

The procedure for determining the temperature

at the k 4-1 level mentioned above is used at all radial positions except where n = 0 and 1.

At these positions a different approach was necessary

since the point In n where n - O should be plotted at minus infinity, Hougen and Watson (13) suggested that at n = 1, B AZ should be added to the temperature at n - 2.

This establishes the temperatures leaving the

increments at n = 0 and n = 1 respectively.

vii

Four modifications of the design procedure were made and the temper­ ature gradients and conversions at the mass velocity of 244 lb./hr. sc, ft. were calculated by each of these to see which would give the best checks with the experimental results. The above modification is called Method I. Method II takes into consideration the difficulties encountered when a variable effective thermal conductivity is used.

The conductivity near

the tube wall of the reactor is much lower than in the center according to the correlation of Smith and co-workers (22). culated by the equation A 2 = the reactor.

As a result,

Z as cal­

(AX)2GCD , becomes large near the wall of

If the incremental equation is solved without regard for

this variable conductivity, the radial increments near the wall of the reactor will be at a different bed depth than the center radial incre­ ments after the first calculation.

Since the basic equation was derived

and the effective thermal conductivities were calculated on the basis that heat flows radially, at right angles to the direction of gas flow, it is seen that the equation cannot be solved correctly without regard for these differences in A 2.

However, it is an inherent fault in this

method that the increment in the axial direction is related to the radial increment.

They can not be chosen independently of one another.

To

solve the equation and still keep the basic solution method produced by Grossman, a method for starting each set of calculations at a uniform bed depth is proposed.

It consists of interpolating the results obtained

in the increment just completed so that all temperatures correspond to the same bed depth.

In Method II, the same method for calculating the

center temperatures was used as in Method I.

viii

Method III is concerned with a better approach for obtaining the temp­ erature at n = 0 and n = 1.

At n = 0, the temperature leaving the incre­

ment is determined by adding BAZ to t0^ - /(t0 p "

At n = 1 the

temperature change in the increments is determined by direct substitution into the incremental equation letting n = 1, n + l = 2 ,

n - 1 = 0.

This

method was proposed as a result of suggestions made by A. H. Smith of the Mathematics Department at Purdue University. In Method IV the method for determining the temperature leaving the n = 0 is the same as in Methods I and II. in Method III is used.

At n = 1 the procedure followed

The interpolation method for starting each incre­

ment calculation at a uniform bed depth was used in both Method III and Method IV. The following conversions were predicted by the four methods at a mass felocity of 244 lb./hr.-sq. ft.: Method Method Method Method

I II III IV

18.6;i 21.6/ 24.1/ 23.0/

Experimentally the conversion was 29/.

Even though Method III checks the

conversion most closely, the temperatures predicted at n = 0 by this method deviated from the experimental much more than those by the other methods. Closest checks on the temperature gradients were obtained with Method IV;

accordingly this method was used in the design calculations

at the other mass velocities. The following table shows the comparison between the predicted and ex­ perimental conversions at the other three mass velocities.

ix

Mass Velocity

Experimental Conversion 20.6; %

147 350 512

Predicted Conversion 20. 0# 26.9# 21.6%

27.5# 18 %

Irvin (15) predicted 18.6% conversion at the 350 mass velocity and 17.4# at the 512 mass velocity using Method I,

The use of Method IV has

the effect of keeping the temperature near the wall high thus resulting in higher conversions as shown above.

At the 147 and 512 mass velocities,

the predicted temperatures were generally above the experimental values. As seen in the above tabulation, the predicted conversions are also above the experimental conversions. "When the chemical reaction on a catalyst surface occurs much faster than the reactants can be brought to the catalyst surface and the pro­ ducts taken away from the surface, the reaction rate will be affected by the velocity of gases passing the catalyst since the rate of mass transfer is affected by the velocity.

The effect of this diffusional step on the

overall process will decrease as the mass velocity increases.

Hence, a

method of plotting by which the reaction rate data can be extrapolated to infinite mass velocity should permit the determination of the quanti­ tative importance of diffusion and the evaluation of the non-retarded reaction rates.

A plot of the reciprocal of the overall rate, r , versus

the reciprocal of the mass velocity is suggested from the equation: 1 fo

=

1 ^r

+

1 I'd

In this expression, rr is the rate of reaction as there are no diffusional resistances. diffusion.

The quantity r^ is the retardation of the reaction due to

This retardation would be expected to be a function of gas

X

mass velocity, temperature, composition, and physical characteristics of the catalyst. On the other hand, rr is a function of temperature only. Therefore, if l/rQ is plotted against l/G extrapolation to l/G = 0, at give constant temperature, will^the value of rr at the particular temperature. The importance of the diffusional resistances in affecting the overall rate depends upon the relative rates of rQ and rr. The maximum percent­ age diffusional retardation, (**r - rQ)/rr was 31/o obtained at 400°C. and a mass velocity of 147 lb./hr.-sq, ft. Seven mechanisms for the reaction were proposed for the air-oxidation of sulfur dioxide on a platinum catalyst.

The equations for these mech­

anisms were tested with the non-retarded rates, rr determined by the above extrapolation process; the constants in the equation were evaluated and those equations were rejected which resulted in values of constants anomalous with the catalytic theory. The most probable mechanism was that between the adsorbed sulfur di­ oxide and adsorbed atomic oxygen.

22200 _ ET where K

20.96 E

= e 6740 _ ET

B» -

W 3 R

e

8250 0.682 RT ‘h R D* = e

The rate equation is as follows :

In an effort to obtain a complete rate equation which includes diffu­ sion as well as surface reaction resistances, r^ was evaluated as a function of mass velocity. 1

= +



^

The overall equation is: 1__________

2,9 x 10"4 g-1.45

Using this equation it is possible to estimate with reasonable accur­ acy the overall rate of air-oxidation of sulfur dioxide at any temperature and mass velocity within the range of temperatures and mass velocities investigated.

The equation is limited to a 6,45% sulfur dioxide - in air

mixture however.

1 THE DESIGN OF FIXED-BED CATALYTIC REACTORS

INTRODUCTION

Although catalytic reactors for gaseous reactions have been used in the chemical industry since early in the twentieth century, their use did not become widespread until shortly before World War II*

Since

their advent, commercial size reactors have been developed by tedious and costly experimentation. The general method of investigation involved the evaluation of successively larger and larger units until the jump to commercial size equipment was considered a safe risk.

Though this empir­

ical procedure generally achieved the desired results, it did not lead to a fundamental understanding of the changes that occurred from point to point in a reactor*

Instead, it led only to a knowledge of what

would happen in a given reactor under certain conditions♦ The results could not be used in predicting what would happen in other reactors * From a fundamental standpoint, it would be desirable to be able to predict the physical and chemical processes occurring at every point within the reactor.

For reactions such as the Fischer-Tropsch synthesis

and the oxidation of naphthalene this is especially important. In these cases, the control of temperature is imperative for the prevention of hot spots which may sinter and therefore ruin the catalyst or result in un­ wanted products* As in the selection of any other piece of equipment, the choice of a catalytic reactor for a particular use should be made only after an economic study has been made to determine the effect of the various operating variables on the cost of the equipment and its operation.

The

2 ultimate goal is to obtain that reactor, sized to meet a specified pro­ duction rate, which will result in the most economical operation and construction*

The paramount problem in this study is the prediction of

the results which will be obtained with any particular reactor.

If a

reliable and simple method of predicting the conversions is available, the economic study would be considerably simplified.

Moreover, the time

and expense involved in pilot plant studies could be eliminated. The problem of reactor design is considerably more complicated than the design of equipment involving only the unit operations of chemical engineering.

The rates of chemical reaction and heat and mass transfer

which occur simultaneously depend upon one another and no simple relation­ ship exists between them. In adiabatic reactors, all the heat of reaction is removed by the sen­ sible heat of products and reactants. Hence the conversion in a given catalyst bed can be determined quite simply provided suitable reaction rate data are available. culation is more involved.

Under non-adiabatic conditions however, the cal­ Reactants, products and the catalytic mass

lose heat by radial heat transfer.

This radial heat transfer, occurring

simultaneously with chemical reaction, frequently results in large radial temperature gradients. Therefore, the quantity of reaction occurring at every radial point is difficult to evaluate since it depends upon the rate at which heat is being dissipated to the walls of the reactor.

A funda­

mental design method for a non-adiabatic reactor should thus include a method for predicting these radial temperature gradients and consequently the conversion at every bed depth.

It is the purpose of this thesis to

develop such a method which will check experimental results.

3 The application of any design method to a specific problem requires the following information: 1.

Reaction rate data covering the complete range of temperatures and conversions encountered in a large scale reactor,

2.

Heat transfer characteristics of packed catalytic beds.

3.

Specific heat data for the reactant and product gases.

4.

The heat of reaction.

5.

The density of the catalyst bed,

6.

The type of cooling or heating to be used for temperature control.

7.

The dimensions of the reactor to be investigated.

8.

The temperature of the entering reactants.

9.

The mass velocity of the entering reactants.

With the exception of the first two items, these data are easily ob­ tained from the literature or from the choice of reactor and reaction to be investigated.

Rates of reaction and heat transfer characteristics are

considerably more difficult to obtain. When accurate methods of chemical analysis are available, reaction rates are best determined in a flow-type reactor containing a bed of cat­ alyst so small that relatively small changes in composition occur as the reactant gases pass through the bed.

This type of reactor is known as a

differential reactor and the rates measured therefrom are known as differ­ ential reaction rates.

The dependency of rate on the temperature is gen­

erally very great, so the reactor must be designed such that a fairly uniform temperature can be maintained.

This is usually done by using a

small diameter reactor equipped with adequate heat transfer facilities. Differential reaction rates may also be determined by graphically differentiating the data obtained in isothermal reactors in which

4 appreciable conversion occurs • This type of reactor is known as the in­ tegral reactor.

This method should be used only when the method of chem­

ical analysis is incapable of high accuracy$ it has the added disadvantage of being more difficult to maintain the integral reactor at a uniform temperature. Catalytic reaction rates may be a function of the velocity of gases past the catalyst particles as well as a function of temperatures and com­ position.

The overall reaction process has been logically divided by

Hougen and Watson (13) into five steps :

(l) a mass transfer of reactants

to the catalyst surface, (2) an activated adsorption of the reactants on the catalyst, (3) a surface reaction between the adsorbed reactants, (4) a desorption of products from the catalyst surface, and (5) the mass transfer of the products from the catalyst surface.

The chemical reaction

step can proceed only as fast as the reactants are brought into contact. Therefore the rate of reaction may be limited by the rates of mass transfer or adsorption if these occur slower than the chemical reaction step.

The

relative importance of surface in determining the overall reaction rate can be altered by the operating conditions in the reactor.

For example,

in a flow system where gaseous reactants are passed over a solid catalyst, the rate may be controlled by diffusional resistances if the temperature is high and the catalyst is particularly active.

On the other hand, with

a less active catalyst at a low temperature, the rate of the surface re­ action may be the controlling process. In the present investigation the reaction rates for the air oxidation of sulfur dioxide on one-eighth inch cylindrical alumina pellets coated with 0.2$ platinum were determined at four mass velocities.

These data

were used in design calculations and analyzed to determine the importance

5 of diffusion in the overall process» The determination of the rate of heat transfer from a catalytic bed is of especially great importance in designing non-adiabatic reactors where significant radial temperature gradients are encountered.

In cor­

relating heat transfer data for this purpose, it has been found most satisfactory to express the heat transfer characteristics of a packed bed in terms of an effective thermal conductivity rather than as the usual heat transfer coefficients.

This effective thermal conductivity is the

conductivity which satisfies the basic partial differential equation for heat flow in cylindrical tubes through which gases are flowing.

It is

a function of the catalyst particles, their size, shape and arrangement, the properties of the gas, its mass velocity and temperature.

The

effective thermal conductivities determined by Smith and co-workers (22), which were determined under conditions similar to those studied in this research, were used in the design methods presented in this thesis. In recent years, fundamental approaches to reactor design have been receiving more and more attention.

Most of the methods proposed depend

upon the solution of the partial differential equation derived for flow of heat in cylindrical tubes through which reacting gases are flowing. Differences in solution depend mainly upon the simplifying assumptions made by the various investigators.

Analytical solutions have been pro­

posed but thus far none have been checked with experimental results. The method of Grossman (9) served as the basis for the design modifica­ tions presented in this thesis.

He suggested a graphical solution based

on the partial differential equation written in incremental form.

It con­

sists of dividing the reactor into a number of increments in both the

6

axial and radial directions and then determining the temperature grad­ ients and conversions by a double stepwise integration process.

7 SCOPE OF THE RESEARCH WORK

The work for this thesis was divided into 5 phases : (1)

Differential reaction rate data were collected for the air oxi­

dation of sulfur dioxide at a H the temperatures and compositions which might occur in a large-scale (integral) reactor. tained at mass velocities of 147# a temperature range of

These data were ob­

244, 350 and 512 lb./hr.-sq. ft. over

350 to 475°C. and over a conversion range of 0 to

65% conversion. (2)

An analysis of the reaction data to determine the effect of dif­

fusion on controlling the overall reaction rate was made, (3)

Effective thermal conductivities of gas-solids systems were

measured in conjunction with Bunnell (5).

Only a small portion of this

work is reported in this thesis• (4)

The radial and axial temperature gradients and conversions in an

integral reactor were measured.

A mixture of 6.45% sulfur dioxide and

93*55% air was used as the reactants*

Data at mass velocities of 147,

244, 350 and 512 lb./hr.-sq. ft. were observed. (5)

Differential reaction rates and effective thermal conductivity

data were used to predict the temperature gradients and conversions in an integral reactor. observed results.

The calculated results were then compared with the

8 LITERATURE SURVEY

Differential reaction rates The kinetics of the oxidation of sulfur dioxide with air was first studied by Bodenstein and Fink (4), Knietsch (16), and Taylor and Lenher (24).

Their measurements were made in batch reactors and consequently

are of little value in the development of rate equations for design pur­ poses. Lewis and Ries (1?) investigated the reaction in a flow reactor using a platinized asbestos catalyst.

Differential conditions were approached.

The diffusional retardation of the reaction was assumed to be zero at the mass velocity of the gases used in their investigation.

Uyehara and

Watson (27) developed rate equations for the reaction based upon the prin­ ciples of catalytic theory developed by Hougen and Watson (13) • The Lewis and Ries data were then analyzed using these equations.

It was found that

the data would fit an equation in which the surface reaction rate was the controlling factor in determining the overall rate of reaction. A similar kinetic investigation was made by Tschernitz et. al. (25) who studied the hydrogenation of mixed iso-octenes.

Seventeen rate equations,

based on the assumptions of surface reaction, adsorption of reactants, or desorption of products as the rate controlling steps, were derived and the experimental data fit to these equations by the method of least squares. After the constants in the equations had been determined, those mechan­ isms were rejected which resulted in values of constants anomalous with the catalytic theory.

It was found that the reaction between the adsorbed

iso-octenes and adsorbed hydrogen was the rate controlling step.

9 A similar work was accomplished by Akers and White (l) on the kinet­ ics of methane synthesis from carbon monoxide and hydrogen.

This work

gave rate equations for reaction to give carbon monoxide, which is a by­ product of the reaction, as well as for the reaction to give methane.

Essentially the same treatment is given the data as that given by Tschernitz.

The rate controlling step was found to be the surface re­

action between adsorbed reactant molecules. In all of the above works, the role played by diffusion in transfer­ ring the reactants from the gas stream to the catalyst surface have been considered unimportant.

In extremely fast reactions, however, the dif­

fusional rate may be of major importance.

In a review article, Wilhelm

(28) discussed the relative importance of diffusion and surface reaction in determining the overall reaction rate.

Equations are presented

whereby the resistance due to chemical reaction and due to diffusion can be separated for a first order reaction.

Tu, Davis and Hottel (26) pre­

sent an example of a diffusion-controlled process in their study of the rate of combustion of carbon spheres with air.

At high temperatures

diffusion rates became controlling and a considerable decrease in the effect of temperature was noted.

A similar result was observed by

Barrer (2) who studied the adsorption of hydrogen on charcoal.

Thermal Conductivities Literature concerning thermal conductivities of static porous beds has been surveyed by Wilhelm (28) and Irvin (15).

These thermal con­

ductivities can not be used reliably for packed beds through which fluids are flowing. It has been found by various investigators (3) (18) (28) that because

10 of turbulence in the gas stream, the actual conduction by point to point contact of the particles is a small percentage of the total heat trans­ ferred unless the particles have extremely high thermal conductivity* It was postulated by Leva (18) that the gas flows through a packed bed in small bundles which do not mix appreciably with one another.

Mien the

velocity of the gases increases, however, there is an increased tendency for turbulence in the bundles and intermixing between adjacent bundles. Consequently the rate of heat transfer is increased far beyond that ob­ tained in static beds. Published information on effective thermal conductivities has been lacking until only very recently.

Hall and Smith (ll) estimated effect­

ive thermal conductivities of one-eighth inch cylindrical alumina pellets at a mass velocity of 350 lb./hr.-sq. ft.

Smith and co-workers (22)

continued this work and evaluated effective thermal conductivities at mass velocities of 147, 244, 350 and 512 lb./hr.-sq. ft.

The ratio of

effective thermal conductivity to thermal conductivity of air was found to increase linearly with the modified Reynolds number.

The effective

thermal conductivity was found also to be a function of radial position, i.e. its distance from the wall of the reactor.

It is believed that this

is due to less turbulence in the gas bundles near the wall. Coberly and Marshall (6) calculated effective thermal conductivities by the same method as Bunnell (5) for one-eighth, one-fourth and onehalf by one-fourth inch Celite cylinders at mass velocities from 1215 lb./hr.-sq. ft.

175 to

They found that a plot of effective thermal con­

ductivities versus a modified Reynolds number,

, where Ap was the

external surface area of a particle instead of its effective diameter, gave a straight line correlation.

The points for all three packing

11 sizes fell on the same line, Pigford and co-workers (20) determined the effective thermal conduct­ ivities of settled beds flowing downward through vertical tubes for Ottawa sand and ILnenite ore by a similar method.

An overall effective

thermal conductivity based on the bulk mean inlet and outlet tempera­ tures was determined in their study. Singer and Wilhelm (21) have arrived at an analytical solution for the design of packed cylindrical heat exchangers.

A heat balance for

solids as well as for fluids was considered in this case.

The effective

thermal conductivity in the fluid stream used in their work was the sum of two conductivities, the ordinary fluid molecular conductivity and a contribution due to turbulence. Ke s

kfE / cfË

An equation was presented as follows:

where kf is the molecular conductivity, c the fluid

heat capacity, P the fluid density, bulent eddy diffusivity.

6 the fraction voids and E the tur­

In their analysis, the turbulent eddy dif-

fusivities determined by Bernard and Wilhelm (3) were used. Hougen and Piret (12) have also completed work on the estimation of effective thermal conductivities.

The nature of their work is not yet

known by the author.

Reactor Design Damkohler (?) (8) was the first to discuss the effects of flow, dif­ fusion and heat transfer on the performance and design of reactors.

He

presented a mathematical analysis of the heat transfer in these reactors and suggested that reactor performance be correlated in terms of dimensionless parameters. be effected however.

5

No satisfactory methods of correlation could

12 The new concepts of H.R.Ü. (height of overall reaction unit) and H.G.U. (height of catalytic or surface reaction unit) have been intro­ duced by Hurt (14) as measures of overall reaction rate and surface re­ action rate.

They were used in conjunction with the H.T.U. (a measure

of the mass transfer rate) in correlating reactor performance.

This

approach does not lead to an understanding of the changes occurring at every point within the reactor and therefore is not considered satis­ factory. Wilhelm, Johnson and Acton (30) arrived at an analytical solution for radial solid catalyst temperatures which, when combined with step-by-step heat and material balances in the axial direction resulted in the total temperature distribution. this solution.

They were:

Two major limiting assumptions were used in (l) the rate of reaction varies linearly with

temperature and (2) the temperature of the gas within any thin crosssectional slice of catalyst bed is uniform and constant because of mix­ ing.

Both of these assumptions are now known to have little foundation.

Tasker and Wilson (23) presented a mathematical analysis of the simul­ taneous heat transfer and reaction in which they suggest using the bulk mean temperature to evaluate the mean reaction rate at every bed depth rather than evaluate the radial temperature gradients. Probably the most practical method of design is that presented by Grossman (9)•

His is a semi-graphical step-wise integration of the basic

differential equations for heat flow in the fluid stream and in the solid bed written in incremental form.

Hougen and Watson (13) modified this

procedure by assuming identical gas and solid temperatures at any point in the reactor.

This assumption eliminated the need for evaluating sep­

arate thermal conductivities for the gas and solid.

Grossman made two

13 reasonably good assumptions in his solution.

They are: (l) the heat

transferred by conduction in the axial direction is considered negli­ gible with respect to that transferred in the radial direction and (2) the fluid velocity across a section perpendicular to the direction of fluid flow was uniform..

Assumption (l) was proven satisfactory by

Bunnell (5) in his calculation of effective thermal conductivities, Morales (19) in his recent work on the velocity distribution in packed beds has proven that rod-like flow conditions exist in isothermal beds. Thus assumption (2) is verified, Grossmanfs method was checked with experimental results by Hall and Smith (11) and Irvin (15),

Hall made calculations in the design of a

reactor for air oxidation of sulfur dioxide on one-eighth inch platinum coated pellets using effective thermal conductivities of

0,4 and 0,2

BTU/hr,-ft.-°F, and found that much better agreement was obtained with the latter*

He found that the temperature fell off too rapidly at the

wall of the reactor and that the calculated conversion was far below that obtained experimentally, ities at

Irvin made calculations at mass veloc­

350 and 512 lb./hr.-sq, ft. using an effective thermal conduct­

ivity which was a function of radial position and obtained better agree­ ment. In a published paper. Singer and Wilhelm (21) have derived an ana­ lytical solution for reactor design.

Their limiting assumption is that

the heat of reaction liberated at any point is a linear function of the solid catalyst temperature.

14 APPARATUS AND PROCEDURE

The a p p a r a tu s and p ro c e d u re u s e d i n

th is

t h e same as t h a t u se d b y H a l l and S m ith ( l l )

in v e s t ig a t io n a re e s s e n t ia lly and I r v i n

(15)•

D e t a ile d

d e s c r ip t i o n s o f t h e e q u ip m e n t and p ro c e d u r e a r e g iv e n b y I r v i n

(15)•

ln

o r d e r t o a v o id d u p l i c a t i o n , o n ly a b r i e f s u r v e y w i l l be p r e s e n te d h e r e .

The experimental equipment consisted of the following: 1,

An air filter and drier*

2.

An air flowmeter*

3*

A sulfur dioxide flowmeter*

4*

A preliminary converter*

5,

A temperature conditioning bath.

6* A differential reactor. 7*

An integral reactor.

8. A system for sampling reactants and products• 9.

Apparatus for temperature measurement.

The arrangement of this equipment is shown schematically in Figure 1. Air from the fifteen pound lines in the Chemical and Metallurgical Engi­ neering Building was passed through a fiber-glass filter to remove oil and dirt and then dried in two silica gel driers operated in series* filter was a

The

12 inch by 12 inch cylindrical container which tapered down

to a four inch pipe and drain. and were 30 inches long.

The driers were made from one inch pipe

supporting the silica gel.

They were equipped with retaining screens for The silica gel was regenerated after each

day’s operation by placing it in a forced air circulation tray drier for 3 hours at 300°F. The dried air was metered with a rotameter. meter was supplied by Fischer and Porter Co., Hatboro, Penna.

The rota­ It was

T?

FIG , I

SCHEMATIC

DIAGRAM

OF

APPARATUS

WATER IN W_,A

GAS.E)^jAUST

AIR

TO

s a m p l in g

system

WATER PUMP SO2 C Y L I N D E R CAPILLARY FLOWMETER MANOMETER OI L F I L T E R S I L I C A GEL D R I E R 7. P R E S S U R E R E G U L A T O R 8.FLOWRATOR 9. H E A T E R

AND P R E C O N V E R T E R

10. M O L T E N

L EAD

BATH

11. S T I R R E R 12.E L E C T R I C

G A S _ J ^ f UJ

HEATERS

13.DIFFE R E N T I A L 14.F I L M T

REACTOR

CONDENSE R

16 60 cm, long and equipped with two floats, stainless steel and Dow-metal, to permit a wide range of flow rates.

The pressure and temperature at

the rotameter were measured and these were used in making corrections to get the true flow rate by applying the calibration and correction factors supplied by the manufacturer of the rotameter. In making runs with the differential reactor, the dried air was pre­ heated to reaction temperature with an electric heater and then passed to a preliminary converter (preconverter). Sulfur dioxide was metered with a glass capillary flowmeter and also passed to the preliminary converter. It was withdrawn from a cylinder which was immersed in a constant temper­ ature bath held at 120°F,

It passed through a pressure reducing valve, a

copper heating coil and then to the capillary flowmeter.

The flowmeter

was calibrated for an upstream pressure of 400 mm. Hg. Arrangements were available for admitting the sulfur dioxide either before or after the preconverter so that the reaction rate could be determined at every composition which might occur in an integral reactor. To determine the reaction rate in the presence of sulfur trioxide, a por­ tion of the sulfur dioxide was passed through the preconverter.

This

portion which was converted to the trioxide was mixed with the remaining sulfur dioxide and passed into the differential reactor.

In order to

limit the quantity of experimental work required, all differential and integral runs were made with

6.45% sulfur dioxide and the

r e m a in d e r air.

The preconverter consisted of a stainless steel tube, 4 inches in length and

1.5 inches in diameter, fitted with retaining screens to hold the

catalyst in place.

It was heated with a 500 watt heater and the temper­

ature controlled with a five ampere variac,

A chrome1-alumel thermo­

couple placed in the catalyst bed permitted the maintenance of a constant

17 temperature sufficiently high to ensure complete conversion. After leaving the preconverter, the reactants were passed through a temperature conditioning system to ensure uniformity of temperature be­ fore passing into the differential reactor.

This consisted of 13 feet

of one inch stainless steel coiled pipe packed with g inch Raschig rings immersed in a molten lead bath.

The bath was heated electrically

to permit good temperature control with three and a

500 watt finger heaters

1.5 kilowatt heater wound around the bath.

The reactants were next passed to the differential reactor which was also immersed in the lead bath.

The stainless steel reactor was 1.5

inch ID and packed with a catalyst to a depth of only 3/8 inch in order to limit the conversion to a low value and so obtain approximately dif­ ferential rates.

The details of the reactor are shown in Figure 2.

Three chromel-alumel thermocouples contained in 1/8 inch stainless steel tubes were used to measure the center and edge catalyst temperatures and the exit gas temperature.

The catalyst thermocouples were imbedded in

the catalyst pellets. When integral reactor runs were made, no catalyst was placed in the differential reactor or preconverter.

The integral reactor was put into

position directly above the empty differential reactor (see Figure l). A drawing of this reactor is shown in Figure 3» inal two inch diameter stainless steel pipe,

It consisted of a nom­

38 inches long, equipped

with a five inch diameter jacket for cooling and fitted with six inch flanges on either end.

The temperature in the reactor was controlled

by boiling water in the jacket. ing stainless steel screens.

Catalyst was held in place with retain­

The bottom screen was held firmly in place

between two collars screwed into the inside of the reactor.

The top

72

PACKING GLANDS

C R - A L THERMOCOUPLES IN STAINLESS TUBES S T E A M OUTLET

K ^zzzzzzzzzzzZ

PACKED BOILING W a t e r inlet

YZZZZA

INLET vzzzzk

FIG. 2.

IN TEGR A L

7777X

REACTOR

\

F EACTANTS

SCALE

20 screen was wired to the

11 thermocouples which entered the reactor from

the top flange through a packing gland.

The thermocouples, which were

encased in l/8 inch stainless steel tubes and insulated with fiber-glass sleeving, extended to the top of the catalyst level in the reactor. Temperature gradients and conversions were measured at bed depths of zero, two, four, six, and eight indies.

The packed section was 16 inches

deep for all runs in order to duplicate flow conditions. ments at the sisted of

When measure­

2 inch bed depth were made for example, the total bed con­

2 inches of active catalyst and 14 inches of dummy alumina

pellets. The reactor was loaded with catalyst by inverting and pouring dummy pellets in from the bottom until filled up to the tips of the thermo­ couples.

Before the active catalyst was added, the radial positions of

the thermocouples were determined by lowering a circular piece of model­ ing clay until the thermocouples junctions were reached.

The distance

from the wall of the reactor to the impression made by the thermocouple junction was measured and the radial position thus established.

Active

catalyst was poured in until the bottom level of the reactor was reached. The retaining screen was fastened in place and the reactor inverted again. Seven of the thermocouples were embedded in catalyst pellets ; the re­ mainder were in the gas phase.

It was found that the accuracy of the

temperature measurements was not great enough to obtain significant dif­ ferences between the catalyst and gas temperatures. To prevent leakage of reactant gases up the thermocouple tubes and consequent damage to the thermocouples, the upper portions of the tubes were painted with household cement and a mixture of litharge and glycer-

21 ine.

Two copper^-constantan thermocouples were peened into the wall of

the reactor for measurement of the wall temperature. In order to prevent heat losses from the reactant gases before reach­ ing the integral reactor, the lower flange was heated with two heaters. 400°C.

500 watt

In all runs the gases entered with a maximum temperature of At low mass velocity where the heat loss was high, the radial

temperature gradient of the incoming gases was large; for high mass velocities the incoming gas temperature was more uniform* After leaving the differential or integral reactor, the product gases passed through a stainless steel valve, used to control the system pres­ sure at an average value of 790 mm, Hg*

The products next passed through

a falling film type cooler to condense sulfur trioxide and then passed to the vent. Samples of the reactant and product gases were withdrawn through stain­ less steel pipes on either side of the integral or differential reactor. The sulfur dioxide in the gas was absorbed by passing through a solution containing 10% sodium hydroxide and 10% glycerine.

The volume of the gas

sample withdrawn was determined by displacement of water from a gasholder. The quantity of sulfur dioxide was obtained by acidifying the caustic solution and titrating with a standard potassium iodate solution using carbon tetrachloride as the indicator according to the equation: IO3

+

2H

4-

SO3

I

+

HgO

+

SQk

All temperatures read with thermocouples were measured with the aid of a Tÿpe K, Leeds and Northrup potentiometer, Rubicon Spotlight galvano­ meter and Western standard cell. the boiling point of sulfur.

The thermocouples were calibrated against

22 PRELIMINARY EXPERIMENTAL WORK

This research problem was initiated by Hall (10) and Irvin (15)•

They

investigated the use of iron oxide and vanadium oxide as catalysts for this reaction and found that a platinum supported catalyst was most satis­ factory.

A 5% platinum on alumina catalyst was tried but this proved to

be too active and was rejected.

The catalyst finally selected contained

0.2% platinum coated on an alumina carrier in the form of 1/8 by 1/8 inch cylindrical pellets.

It was obtained from Baker and Co., Phillipsburg.

New Jersey. The sulfur dioxide used at first was obtained from Ansul Chemical Co., Marinette, Wis.

Several cylinders of their refrigerant grade material

were used and found to be entirely satisfactory.

However, in the course

of the investigation it was found that some obtained from Ansul had a definite poisoning effect on the catalyst.

A catalyst would undergo a

pronounced reduction in activity when this “poisoning1 1 sulfur dioxide was passed through the bed at the reaction temperature.

The poisoning

effect was reversible, however, and the catalyst would regain its orig­ inal high activity when “non-poisoning" sulfur dioxide was fed to the reactor.

It is believed that the refrigerant grade sulfur dioxide con­

tained an impurity which retarded the reaction, but neither the author nor the Ansul Chemical Co, was able to determine its nature.

Research

grade sulfur dioxide was used in all work after the above trouble was encountered. The activity of a new catalyst was found to drop sharply in the first

24 hours after being placed on-stream and remained essentially constant

23 thereafter.

The reduction in activity is determined by the time meas­

ured from the initial contact with sulfur dioxide rather than the total on-stream time.

Figure 4 shows a plot of the variation of reaction rate

with total on-stream time.

The runs made at

hrs, and

8 hrs. were

made a day apart but plotted with total on-stream time as the abscissa. It is believed that the porosity of the carrier is changed due to the reaction between alumina and sulfur dioxide, thus lowering the cata­ lysts activity.

This is borne out since the catalyst increases in

weight by about 25% indicating the permanent absorption or reaction of some substance with the catalyst. If the air is not carefully dried, the catalyst activity will be greatly reduced.

Water vapor in conjunction with sulfur trioxide reacts

with the carrier to produce aluminum sulfate.

Point A on Figure 4 shows

the effect of introducing moist air into the catalytic chamber. In o rd e r to b a tc h e s i t

o b t a in r e p r o d u c ib le r e s u l t s w i t h d i f f e r e n t c a t a l y s t

was n e c e s s a r y t o p r e t r e a t t h e b a tc h f o r t h r e e h o u rs w i t h d r y

a i r and th e n a ge i t

b y p a s s in g s u l f u r d io x i d e a nd a i r t h r o u g h t h e bed

f o r fo u r h o u rs .

E ven t r e a t i n g t h e v a r io u s b a tc h e s s i m i l a r l y d id n o t

a lw a y s r e s u l t i n

r e p r o d u c ib ility .

t h e a v e ra g e h ad t o be d is c a r d e d .

C a t a ly s t s w h ic h d id n o t c o n fo rm t o

ZH

F IG.VR E A C T I O N OF

"ON

R A T E

AS

STREAM"

A

F U N C T I O N

TIME

T E M P E R A T U R E - 411° C,

REAC

T 10 N

RATE

MASS

VELOCITY

~ 245

LB. / H R . - SO . F T .

.050 .04 8 .046 .044 . 042 .040 .038 0

2

4

"ON

6

8

10

12

S T R E A M "

14

16

TIME,

18

HRS.

20

25 DEVELOPMENT OF THE DESIGN METHOD

A method for reactor design developed by Grossman (9) and modified by Hougen and Watson (13) served as the foundation for the design calcula­ tions in this thesis.

It was based upon the solution of the differential

equation which represents the temperature distribution in a cylindrical reactor.

An equation can be derived for both gas and solid catalyst.

In

the following analysis, however, it was assumed that the temperature in the gas and solid at any point were identical.

This assumption results

in considerable simplification since one differential equation will then represent the conditions of both the solid and gas. Figure 5 shows the differential circular slice around which the heat balance is derived. height dZ.

The slice has an inside radius of X, width dX and

dq^ and dq^ represent the heat entering and leaving in the

reacting gases,

dq^ and dq^ represent the heat entering and leaving the

incremental volume by radial conduction,

dq^ and dq^ represent the heat

entering and leaving the section by longitudinal conduction. liberated by chemical reaction is denoted by dq^. G C -t

2TTXdX dZ

2TTXdX

2 T T (X + dX )dZ

The heat

Z6 F IG U R E D IF F E R E N T IA L

S L IC E

S'

OF A C Y L IN D R IC A L REACTOR

l

dX

dq+

dZ

27 dq^

=

-Ke à jt ^

dxj

2TT(X4-dX)

Y * 1 dq?

s

-r P b A H

2TTXdXdZ

If these quantities are combined by heat balance and simplified the following expression results : =

A

A

1 à t

+

^ X2

^ Z. X Where

à 2t

V Ke

=

and

B

+

à 2t I

+

B

(1)

à Z2j

X

à X

=

~r P r AH

% represents the heat transfer by conduction in the

term.

direction of gas flow. The magnitude of this term is small withrespect to the conduction in the radial direction.

It will be neglected in this

design method but it was not neglected in calculating K . The solution requires several other simplifying assumptions: 1.

Uniform mass velocity was assumed over the cross-section of the reactor.

2.

The radial and longitudinal mixing of the fluid is considered negligible.

3.

An effective thermal conductivity, Ke, could be assigned to account for the complex lateral heat transfer mechanisms.

Neglecting longitudinal conduction, this equation is converted into in­ cremental form to give:

A

zt

=

A&Z (AX)2

[a A L

Following the method

+

A X A xtl

X of Schmidt

radial and axial increments is chosen:

t

BAZ

(2)

J (32) a definite

relationbetweenthe

Az

=

L M L 2 2A

(3 )

The radius of the reactor was divided into n equal increments such that X s n ù X and the height is divided into k increments, Z = kAZ. Equation 2 can then be written as:

(4) Equation 4 is to be integrated in the axial direction to obtain the temperature rise and conversion in the first increment whose height is AZ.

Since the radius was divided into n increments, equation 4 must be

integrated for each of these increments• By equation 3, A Z will depend on the heat capacity of the fluid and the effective thermal conductivity of the gas-solid system in the axial increment from k to k+1. The first and second differences of temperature in equation 4 at a given bed depth can be expressed in terms of the temperatures at the boundaries of the increments as follows :

Substituting these into equation 4» the working equation is obtained:

The important feature of this equation is that it contains no terms with temperature at the k+1 level.

As a result the temperature at the k+1

level can be found from a knowledge of the temperature at the k level. Grossman (9) solved this equation graphically by making a plot of log n (logarithm of the number of the increment counting zero as the center of reactor) versus temperature.

From the geometry of a plot such as this

29 shown in Figure 6, it can be shown that PN is equal to the quantity in the parenthesis in equation 5*

The basis for this fact lies in the

following: RP SO

a

MR = MS

n = In n-1 In n+1 n-1

ln(n) - In(n-l) ln(n+l) - In(n-1)

It can be shown that the ratio of the logarithms above can be approx­ imated by the firsttwo terms of a series* PN

- RP -

BN

= 30(1

2 but Since

then

Then:

- _1_) -RN 4n

SO

= tn+ljk

- tn_ljk



= ^n,k

- Vl.k

PN

=

i )}n+l,k 4 tn-l)k



2tn,k +

(tntl,k “ Vl.k'*]

Using equation 5, the temperature at the k + 1 level can be found by making a plot similar to Figure

6; tn>k+l

determined by drawing a

straight line between the n+1 and n-1 temperatures, The distance be­ tween the intersection of this straight line with the In n abscissa and tn^ determines PN on Figure

6. When the heat of reaction term, B&Z,

is added to PN and tn^ the temperature at the k + 1 level is estab­ lished.

B A Z must be evaluated at the conditions of average temperature

and conversion for that increment. The foregoing procedure was followed at all radial positions except where n ■ 0 and 1. At these positions a different approach must be used since the point. Inn where n =

0, should be plotted at minus infinity.

The method used will be discussed in the following section. temperature and conversion at the k +

After the

1 level are determined for every

'SO

FIGURE i— I F-i O H' l.l C C) -1 < s ce rw

H

ro

X! F h

o

y > M rH O w

U3

ju ü. w

M Q O

Cti

o

s:

o

n Fh < — 1 III =c O

o

CO

xO

C Vl

v m/ s h

TEMPERATURE

4-2

H to

rm

\\ \\ v 340

V

---- Experimental ----

Method III

----

Method IV

s X

0.6

x\

x/x = 0 .2

\

300 Ws

%

XX XX \

*x.

/

//

260

X \

220

/

x X x

X

'XX x >

-

180

< ^ ^ 5

140

100 Bed Depth, Feet

51 DIFFERENTIAL REACTION RATE DATA

Differential reaction rate data at mass velocities of 147, 244, 350 and 512 lb./hr.-sq. ft. (based upon the cross-sectional area of the empty reactor) are shown in Tables 3 , 4 , 5 and 6.

These data were ob­

tained using only one initial concentration of reactants (6.45$ sulfur dioxide and the remainder air) fed to a differential reactor containing 10.5 grams of active catalyst.

The effect of restricted composition

changes on the rate were determined by passing part of the sulfur diox­ ide through a preconverter upstream from the reactor.

Runs were made

passing up to 70% of the sulfur dioxide through this preconverter.

The

reaction rate was then expressed as the function of one composition change variable, the extent of conversion. Plots of the reaction rate versus temperature were made from the original data with parameter of constant percentage conversion entering the reactor.

These plots for the four mass velocities are shown in

Figures 14, 15, 16 and 17.

Values from these curves were read and cross­

plots of reaction rate versus mean percentage conversion with tempera­ ture as the parameter were made. 19, 20 and 21.

These plots are shown in Figures Id,

Mean percentage conversion is defined as the average

of the conversion entering and leaving the reactor, thus this latter method of representing the data gives a better representation of aver­ age conditions. Because of the highly exothermic nature of the reaction investigated, it was impossible to maintain the catalyst at a uniform temperature for all runs.

The thermocouples at the edge and center of the reactor

TABLE S DIFFERENTIAL REACTION RATE DATA MASS VELOCITY =

U7 lb8./(hr.)(aq.ft.)

PreGram Moles Gram Moles Edge Center Mass $ Conversion Center % S02 Lead Converter of in % Total of * in Catalyst Gas Velocity Catalyst Run Batb Air/Win. Lbs./(Hr.)(Sq.ft.) Reactants Preconverter Conversion So. Temperature Temperature Temperature Temperature Temperature S02Aiin. °C °C °C °C

Mean Conversion Weight Reaction Rate Bed of in Diff.Reactor Catalyst Temperature g.moles/(hr.)(g.catalyst) °C (grams)

%

B-6

344ol

354.8

351.2

350.2

473.

0.0281

0.410

147.

6.12

0.0

8.32

8.32

10.5

353.

0.0133

B-7

367.8

388.4

381.2

379.9

477.

0.0282

O.4O9

147.

6.147

0,0

12.72

12.72

10.5

385.

0.0205

.384-0

411.9

402.0

400.3

482.

0.0285

0 .4 U

148.

6.22

0.0

18.84

18.84

10.5

400.

0.0307

B-9

404-5

445.0

431.1

427.6

474.

0.0284

0,411

148.

6.21

0.0

28.49

28.49

10.5

433.

0.0463

B-10

435-1

490.0

475.0

465.8

473.

0.0285

0.4U

148.

6.16

476.

0.0650

348-0

363.0

359.2

358.0

515.

0.0283

0.409

147.

6 .4 6 -

B-13

376.0

397.0

389.7

388.1

517.

0.028

0.408

146 .

6.45

B-U

391-0

420.8

410.8

408.2

516.

0.0282

0.408

147.

6.45

B-15 B-16

366.0 386.2

371.5

369.6

368.8

508.

0.0283

0.410

147.

6.45

24.2

397.5

393.9

392.3

507.

0.0283

0.409

147.

6.45

24.21

31.7

3-17

416.0

438.9

431.5

428.5

507.

0.0285

0.409

147.

6.50

24.2

447.1

479.1 410.9

470.2

464.3

507.

0.0286

0.410

147.

6.49

24.21

402.9

401.0

500.

0.0283

0.410

147.

6*44

440.9

430.0

426.2

500.

0.028

0.410

147.

480.9

468.9

461.9

500.

0.0282

147.

B-S

B-12

3-18

0.0

39.84

39.84

10.5

/4 .6 3

10,30

'6.17

4.55

18.05

13.50

10.5 10.5

4.48

24.32

19.84

28.15

3.95 7.48

10.5

40.15

15.90

48.45

24.23

26.39

6.43

11.3 10.91

6,45

10.5

354.

0.010

387.

0.0218

10.5

409.

0.0321

10.5

364. 389.

0.0064 0.0121

10.5

429.

0.0259

10.5

468 .

0.0396

15.07

10.5

400.

0.0244

33.75

22.83

10.5

42.17

. 31.65

10.5

429. 468.

0.0369 0.0511 0.011

:

3-19 B-20 B-21 B-22

387.0 407.9 . 438.0 389.0

395.1

394.0

500.

0.0284

148.

6.47

35.8

42.52

6.74

10.5

390.

B-23

417.7

398.4 436.0

0.410 0.411

430.0

427.6

500.

0.0285

0.411

148.

6.48

35.41

48.2

12.31

426.

3-24

448^.6

473.0

466.0

461.0

0.0235

0.412

148.

6.47

35.0

53.1

18.1

B-25 3-26 3-27 B-28S

407.4 437.4 475.5 373.8

410.3 • 443.1

409.3

409.5

0.0283

6.45

484.4

482.0

480.6

517.

0.0284

147. 147.

6.45 6.48

389.2

382.1

--

434.

0.0284

0.409

147.

6.43

66,4 66.3^ 66,2 0.0

410.

441.1

0.411 0.411 0.410

147.

441.5

500 ' 518. 517.

10.5 10.5

3-298 3-308

389.3 413.9

410.8

4.OÔ.8

4% .

0.0281

146 .

6.42

444.3

430.5





4M .

0.0279

0.408 0.408

146.

3-318

443*2

482.6

465.8

--—

453.

0.0279

0.408

146.

.0 .0 2 8 3

Average Mass Velocity = 147. 1 Average preeonvereion from 2 ruas.

68.3

1.9

70.43

4.13

73.1 8.98

8.98

10.5 10.5 10.5 5.1

13.06

13.06

5.1

6.38

0.0 0.0

18.0

17.97

6.38

0 .0

24.6

24.6

6.9

463.

0.0209 0.0295

483.

0.0031 0.0067 0.0112

■ 386.

0.0298

5.1

- 406. 438.

0.0433 0.0591

5.1

475.

0.0809

442.

TABLE

4r

DIEFEBESTIÂL REACTION BATE DATA MASS VELOCITY =

Bun No.

2 U lba./(hr.)(aq.ft.)

Gram Moles Gram Moles Mass % Conversion Center PreEdge Center * 90g Lead Velocity in in of % Total Converter of Gas Catalyst Catalyst Bath SOg/Min. Air/Min. Lbs./(Hr.)(Sq.ft.) Reactants Preconverter Conversion Temperature Temperature Temperature Temperature Temperature °C ° e ° e °C °C

»

C-71

339.8

417.2

407.9

409.4

C-72

345.5

353.7

350.1

350.6

378.0

246.

6 ,36

0.0

' 0.682

245.

6.45

0.0

4.86

4.86

0.683

245.

6.45

0.0

8.68

8.68

245.

6.47

0.0

25.3

6 .46

30.4

30.8

0.0473

0.682

481.

0.0471

471.

0.0470

504.

Conversion Height Mean Reaction in of Bed Rate ; Diff.Reactor Catalyst Temperature g.molee/(hr.)(g (Grams) 56

15.7

C-73

368.5

381.9

377.3

C-74

413.5

452.5

4 39 .4

441.3

485.

0,0472

0.682

C-75

348.0

348.4

348.2

347.9

516.

0.0471

0.682

245.

C-76

379.3

381.7

380.6

380.4

514.

0.0470

0.682

245.

6.45

30.1

32.1

482.

0.0471

0.680

245.

6 .4 6

0.0

10.2



15.7

25.3 0.43

2.05 10.2

10-;5

413.

0.0424

10.5

352.

0.0130

10.5

380.

0.0232

10.5

447.

0.0681

10.5

348.

0.0011 0.0055

10.5

381.

10.5

390.

0.0275 .0.0125

375-9

392.3

387.4

388.0

0-79

398.9

406.7

404.3

404.5

509.

0.0470

0.683

245.

6.44

29.2

33.9

4.65

10.5

406.

0-80

427.1

442.8

437.6

438.0

505.

0.0470

0.683

245.

6.45

29.2

39.1

9.85

10.5

441.

0.0264

0-81

355.1

358.3

357.0

356.7

512.

0.0469

0.682

245.

6.44

13.9

16.7

2 .7 9 -

10.5

358.

“ 0.0075

0-82

379.5

387.7

384.5

384.5

512.

0.0471

0.682

245.

6.47

13.9

19.8

5.15

10.5

386.

0.0138

0-83

412.0

432.7

425.0

425.5

512.

0.0470

0.682

245.

6.45

13.91

26.3

10.5

4% .

0.0331

0-84

436.6

467.1

456.5

456.8

512.

0.0472

0.682

245.

6.47

13.91

33.5

19.6

10.5

462 .

0.0525

0.681

245.

6.45

28. 9I

43.3

14.4

10.5

469.

0.0388

0.682

245.

6.45

42.4

4 6 .6

4.2

10.5

405.

0.0112

7.78

10.5

439.

0.0209

10.5

459.

0.0269

0-78

0-85

448.7

472.2

466.2

463.9

496.

0.0470

0-86

398.9

406.2

403.8

403.7

525.

0.0470

12.4

0-87

428.1

440.5

436.3

436.2

525.

0.0470

0.680

244.

6.45

42.4

50.2

0-88

446.4

461.3

455.9

455.9

526.

0.0471

0.679

244.

6.48

42.1

52.1

10.6

0-89

400.3

403.1

401.4

401.4

529.

0.0471

0.684

246.

6-45

61.9

63.9

2.0

10.5

402.

0.0054

0-90

437.6

443.5

440.8

440.7

530.

0.0471

0.684

246.

6.45

61.91

66.2

4.3

10.5

442.

0.0116

0-91

458.6

466.0

463.0

462.6

529.

0.0471

0.683

246.

6.45

62.9

67.9

5.0

10.5

465 .

0.0134

C-125S

371.1

380.5

376.7

400.9 433.7

418,8 462.9

411.3 451.9

4.24 10.2 16.8

4.24

0-1268 0-1278

-- —— --

379. 416. 458.

0.0237 0.0572

1

Preconversion of previous run.

_

493.

0.0475

0.682

245.

6.38

0.0

503. 499.

0,0475 0.0475

0.682 0.681

245. 245.

6.38

0.0

6.39

0.0

Average Mass Velocity = 245

5.10

10.2

5.10

16.8

5.10

0.0940

TABLE S

'

DIFFEEEHTIAL REACTION RATE DATA MASS VELOCITY =

35U lbs./(hr.)(eq.ft.)

# Conversion PreCenter MaSS Gram Moles Gram Moles % so2 Edge Center Lead in % Total of Velocity in Converter tGas of Catalyst Catalyst Bath Run Air/kin. Preconverter Conversion Temperature Temperature SOg/Min. Lbs./(Hr.)(Sq.ft.) Temperature Reactants No. Temperature Temperature °C °C °C °C °C 344-4

A-7

349.8

349.0

348.2-

Mean ; % Conversion Weight Reaction Rate of Bed ! in : Diff.Reactor Catalyst Temperature g.moles/(hr.)(g (grams) °C

439.

0.0677

0.972

350.

6.39

0.0

2.81

2.31

10.5

349.

0.0109

0.973

350.

6.40

0.0

8.25

8.25

10.5

388.

0.0319

A-3

375-3

388.8

386.9

384.9

515.

0.0676

A-9

401.8

427.2

423.0

419.5

497.

0.0677

0.972

350.

6.39

0.0

15.8

15.85

10.5

425.

0.0615

A-10

425.1

463.2

457.2

451.5

499.

0.0677

0.973

350.

6.395

. 0.0

24.2

24.22

10.5

461.

0.0938

A-ll

351.9

353.3

353.6

353.0

508.

0.0678

0.975

'351.

6.37

17.6

19.0

1.36

10.5

353.

0.0053

A-12

389.5

397.0

396.1

394-9

509.

0.0676

0.972

350.

6.36

16.71

23.0

5.37

10.5

' 396.

0.0241

A-13

421.7

•438.9

436.7

434.0

507.

0.0676

0.974

350.

6.36

16.7

29.8

13.02

„10.5

438.

0.0504

383.7

392.1

392.5

392.7

486 .

0.0680

0.972

350.

6.41 .

31.0

34.0

2.97

10.5

392.

0.0115

36.8

5.6

10.5

429.

0.0228

43.4

12.0

A—14

0.973

350.

6.40

31.22

0.0679

0.972

350.

6.40

31.4

0.0680

0.978

352.

6.36

A-15

421.2

429.4

428.7

430.8

490.

0.0680

A-16

465.5

483.3

479.5

483.5

498.

391.8

392.1

491.

392.0

10.5

482.

0.0465

51,7

1.35

10.5

392.

0.0052

A-17

390.5

A-13

439.9

445.2

444.2

445.3

490.

0.0679

0.978

352.

6=36 '

50.53

54.6

4.1

10.5

445.

0.0159

479.0

488.8

486.5

488.2

491.

0.0679

0.976

351.

6.37

50.6

57.3

6.7

10.5

488.

0.026

A-21

390.1

408.7

401.9

404.8

405.

0.0679

0.974

351.

6.37

0.0

10.1

10.1

A-22S

382.3

393.8

389.5

----

491.

0.0679

0.970

349.

6.36

0.0

484.

0.0682

0.969

349.

6.385

0.0

486.

0.0679

0.969

349

6.34

0.0

11.5

11.5

486.

0.0679

0.969

349.

6.35

0.0

14."

14.7

A-19

A-23S

408.4

428.4

420.0

A-24S

423.7

447.3

438.4

A-25S

444.6

473.5

462.4

Aversga î-iass Velocity — 350 1 2 3

% Preconversion from run â-13. $ Preconversion is average of runs %Preconversion is average of runs

14 and 16. 17 and 19.

5.50 9.48

IQ.5 .

406.

0.0393

5.5

•5.1

392.

0.044

9.48

5.1

425,

0.0761

5.1

443.

0.092

5.1

467.

0.117

TÂBLB é DIFFERENTIAL REACTION RATE DATA MASS VELOCITY —

5U Ibe./Qir.)(sq.ft.)

PreGram Moles Gram Moles Mass % Conversion Center Edge Center Lead *% of of Converter Velocity in % Total Gas Catalyst In Catalyst Bath Run Air/Min. Temperature SOp/Min. Temperature Lbs./(Hr.)(Sq.ft.) Temperature Reactants Temperature Preconverter Conversion So. Temperature °C °C *°C °C °C D-55

348.9

Reaction Mean J % Conversion Weight Rate Bed of in ' . r Diff.Reactor Catalyst Temperature g.moles/(hr.)(g °C (grams)

354.8

352.3

353.2

364.

0.0980

1.45

518.

6.39

, 0.0 ,

2.34

2.34 ,

10.5

354.

0.0131

390.0

382.

0.0982

1.45

520.

6.38

0.0

6.75

6.75

10.5

390.

0.0378

D-56

378.0

392.4

387.9

D-57

404.0

430.0

422.3

424.2

422.

0.0980

1.45

521.

6.32

0.0

,12.1

12.1

10.5

427.

0.0677

D-58

433.1

480.1

468.0

471.5

475.

0.0982

1.46

522.

6.32

0.0

21.2

21.2

10.5

475.

0.119

D-59

369.8

371,3

370.8

370.8

466 .

0.0984

1.45

521.

6.35

20.9

22.6

0.64

10.5

371.

0.0095

D-60

402.8

410.0

406.7

408.2

466 .

0.0984

1.45

522.

6.34

20.91

26.3

4.28

10.5

409.

0,0241

d-61

402.8

410.4

407.0

408.3

476.

0.0982

1.42

511.

6.45

20.91

25.5

4.63

10.5

409.

0.0260

442.5

444.6

477.

0.0982

1.42

512

6.44

20.91

29.3

8.38

10.5

446.

0.047

10.5

477.

0.0661

D-62

432.1

448.0

D-63

458.0

480.9

472.5

475.5

477.

0.0982

1.42

511.

6.46

21.5

33.3

11.80

D-64

388.1

391.0

389.8

390.0

491.

0.0978

1.43

513.

6.41

37.6

39.4

1.80

10.5

390.

0.010

426.

0.0226

D-65

419.1

427.0

423.7

424.8

490.

0.0977

1.43

513,

6.40

37.3

41.3

4.05

10.5

D-66

402.0

405.1

404.1

405.0

496.

0.0976

1.40

511.

6.49

54.5

55.4

0.90

10.5

405.

0.005

497.

3.58

10.5

468 .

0.020

D-67

461.4

469-5

466.7

468.2

D-68

387.6

392.6

390,8

392.2

432.3

0.0976

1.40

511.

6.49

54.51

58.1

500.

0.0984

1.43

514.

6.43

33.8

36.2

2.41

10.5

392.

0.0136

499.

0.0981

1.43

514

6.42

34.81

38.8

4.06

10.5

434.

0.0281

510.

6.47

0.0

5.46

5.46

5.1

402.

0.063

9.11

9 .U

5.1

441.

0.105

12.91

5.1

476.

0.149

D-69 ■ 424.8

436.0

D-70S

403.9 ,

400.0

--- r

4#.

0.0981

1.42

-- —-

476.

0,0982

1.42

511.

6.47

/ 0.0

472.

0.0981

1.42

510.

6.47

0.0

391.8

D-71S

424.1

443.9

436.8

D-72S

453.7

480.0

472.1

434.4

Average Mass Velocity = 514. 1 Preconversion from previous run.

12.9

,

I+.00

Mean

Bed

Temperature

1).20

360 FIGURE IH ORIGINAL REACTION RATE DATA MASS VELOCITY = llj.? Ib./hr.-sq.ft

320

O.O3

O.0I4.

0 .0 5

0 .0 6

0 .0 7

Reaction Rate, G* Moles/Hr.-G. Catalyst

0.08

0 .0 9

0 .1 0

Mean

Bed

Tempe ira ture

5 7

FIGURE AB­ ORIGINAL REACTION RATE DATA

MASS VELOCITY = 2!^ Ib./hr,-sq,ft

O0.0I).

0 .0 5

o»uo

0 .0 7

0 .0 6

Reaction Rate, G* Holes/Hr.-G. Catalyst

0 .0 9

0.10

0.11

S e

$00

Mean

Bed

Temperature

Lj.8o

il-20

1^00

380

360 Figure /6 ORIGINAL REACTION RATE DATA MASS VELOCITY & 3$0 Ib^/hr.-aq.ft

320

0.02

0.10 Reaction Rate, G. Moles/Hr.- G. Catalyst

0.12

S9

460 21

0 Perce nt Convorsio, (Large Bed)

0 Pe rcent Ccinversioic (Sme 11 Bed)_________

4

Ij.20

14-00

Mean

Bed

Temperature

o O

360

FIGURE /Z ORIGINAL REACTION RATE DATA MASS VELOCITY = $12 Ib./hr.-sq.ft

320

02

0.06

.

0.08

0.10

React'ion\ Rate, G. Moles/Hr.-G. Catalyst

O.I2

60

O

CD

ÜJ

O

o

FIGURE 3Z SÏÏK^KSS1* 0F ^XPBRIMLKTAL AND PrOLDICTLD TSMPERATURL GRADIENTS

Radial PositIon = 0.2 MASS VELOCITY

244 lb./hr.-fl-.ft

\\

Experimental Method T

Method TT

Method TV 0

0.3 ‘

0*4 '

Bed Depth, Feet'

°«5

0.6

Q.

FIOURK 3Z CüiSPviHISOii OF BXPkRIMLKTAL AND PR^DICTKD TEMPERATURE GRADIENTS Radial Position— 0.4 MASS VE10GITY 244 lb.Ar.*sp.ft. 480

• 440 .

/

\\

400

o

Temperature

o

1

\ \N

360

VV .w

\

\ \

320

vv \\ \

280



V

j

\

x \ \ \ \ \ \ " V ■*.\X\ \ \

\

\ X

\

240

\ x X

X

X X x x v

\ X

\

IEGEND

X * x

160

S:

^ X .

" x .

120 led Depth, Feet

FIGURi;

34 -

COMPARISON OF EXPERIMENTAL AND PREDICTED TEMPERATURE GRADIENTS Radial Position = 0.8 MASS VELOCITY 244 lb./hr.-sq.ft

440

Experimental

400

Method I Method II

360

Method III

o

o

Temperature

Method IV

240

200

160

120

0.1

0.2

0.3

0 .4

Bed Depth, Feet

0.6

0 .7

88 at radial positions of 0.6 and 0.8 where little reaction occurred.

At

all radial positions the agreement between the experimental and calcu­ lated temperatures were very poor; the difference amounted to as much as 70°C. for each radial position.

The poor agreement is the result of im­

properly using a variable thermal conductivity.

When a variable conduc­

tivity is used, the axial increments near the tube wall are approximately double those at the center of the bed.

This results because of the low

conductivities near the tube since the axial increment is calculated from the equation, & Z

=

(AX.)^ G-Cp ♦ In the increment calculation 2Ke number 15, Table 12, it can be seen that at n = 4 was at a bed depth of

1.08 ft. whereas the radial increment at n = 0 was at 0.62 ft*

Both of

these increment calculations were made as solutions for equation

5 which

was derived for radial heat transfer perpendicular to the gas flow.

The

solution is obviously inconsistent with the equation, yet it was made to get a comparison with the calculations of Hall (10), Irvin (15) and Smith (33) which were made by this method,

Irvin and Smith's solutions

were made according to this Method I and obtained wall temperatures (at the radial position of

0.8) and center temperatures at radically differ­

ent bed depths in the same increment calculation.

Hall's solution was

more nearly theoretically correct since he used a constant thermal con­ ductivity at all radial positions. The axial increments at the tube wall and center were then only slightly different, the difference being the result of the very small variation in the specific heats of the gases. Figure 29, the plot used in the graphical solution, shows that the steps in temperature between consecutive increment calculations were not uniform.

This is also due to the inherent inaccuracies of Method I.

89 The most important goal in designing catalytic reactors is obtaining the correct temperature gradients.

If these are obtained and reliable

reaction rate data are available, accurate estimations of the conver­ sions in the reactor should be possible.

Experimentally it was found

that essentially all the conversion, 29%) had been obtained at a bed depth of four inches. The calculated conversion had reached a maximum of 18.2% at 2.4 inches.

The conversion at n = 0 was 73% while it was

only 2.2% at n = 4 and 0% at n = 5* tween the radial position of

Since

36% of the total area was be­

0.8 and the tube wall, the overall conver­

sion was limited by the low conversion in this region.

Method II As was seen in Method I when calculations are made using a variable thermal conductivity, the axial increments at the center and near the wall were not equal. Unless corrections for these unequal increments is made, the equation 5 will be solved incorrectly.

If the axial in­

crements could be chosen independently of the radial gradients, the error could be eliminated.

However, the fixed relation between the

radial and axial increments is the foundation for the simplification of solution proposed by Grossman.

Without this an entirely new approach

to the problem would have to be made. Method II is proposed as a modification of the Grossman method.

In

this plan each new increment calculation is started at a uniform bed depth.

The results that are obtained in the calculation are interpol­

ated so that the temperatures and conversions leaving each radial posi­ tion will correspond to the same bed depth.

The tabulated calculations

for Method II are shown in Appendix C, Table 13 * The plot of logarithm

90 of radial position versus temperature used in the graphical solution is shown in Figure 35»

The steps between successive increments is uniform

in contrast to those shown in Figure 29 as calculated by Method I.

A

comparison between the calculated and experimental temperature gradients is shown in Figures 30, 31* 32, 33 and 34»

The agreement between these

temperatures was considerably better than in Method I; the maximum devi­ ation at radial positions of

0, 0,2 and 0,6 amounted to approximately

40°C. At radial positions of 0,4 and 0.8 the maximum deviations were approximately 30°C,

At radial positions of 0.4, 0.6 and 0.8 the calcu­

lated temperatures were well below the experimental values at all bed depths. The calculated conversion at n = 0 was 76.8%, 219% at n - 4 and zero at n = 5#

The overall conversion was 21.6% as compared to 29% experi­

mentally.

Method III The tabulated calculations for Method III are presented in Appendix D, Table 14.

The logarithm

shown in Figure 36.

of radial position vs. temperature plot is

Comparisons between the experimental and calculated

temperature gradients are shown in Figures 30, 31* 32, 33 and 34.

The

same method for starting each increment calculation at a uniform bed depth was used as in Method II. adding

At n = 0, tQ k +

to tQ^k — l/4(tQ^k —

mined by substituting in equation ?•

was determined by

At n = 1, t^^k ^ ^ wa,s deter­ The calculated conversion was 24.1%,

a better check than obtained by Methods I and II.

However the calculated

temperature gradients at n = 0 were approximately 90°C. higher than the experimental values.

At all other radial positions, notably at 0.4, the

S>f

muais, asTLMPhftATUrt». VERSUS RADIAI POSITION Method II

0 244 Ib./kr.-ao.ft

420

400

380

360

340

320

-300 280

260 240

220 200 180

160 140

12." 100 Radial Position, n

9Z FIGURE 3t> TEMPERATURE VERSUS RADIAL POSITION Method III 0

244 l b . / ^ i r . - s q . f t .

”2

3

Radial position, n

93 agreement was very good. n =

The method for determining the temperature at

0 was responsible for keeping the center temperature high.

Method IV In Method IV the temperature at n = 1 was determined by the same means as in Method III.

The same procedure was followed for starting each in­

crement calculation at a uniform bed depth as was used in Methods II and III.

Because the temperatures at n = 0 were maintained very high in

Method III, a new procedure was used at this position. od t(^k

By the new meth­

i was determined by adding B & Z to t-^^.. This is the same as

the plan used in Method I at this position. The tabulated calculations are shown in Appendix E, Table 15.

The

logarithm of radial position vs. temperature plot is shown in Figure 37. Comparisons between the calculated and experimental temperature grad­ ients are presented in Figures 30, 31, 32, 33 and 34* Although the conversion calculated by this method was slightly less than determined in Method III, the temperature gradients were consider­ ably better at n =

0, the maximum deviation being 40°C. At n = 1, 2 and

4 the maximum deviation was approximately

20°C; at n = 3 the maximum

deviation was approximately 30°C. The conversion at n - 0 was 61% and at n = kj 2.9% resulting in an overall conversion of £3%. of

3*6 inches.

The conversion was obtained at a bed depth

94

FIGURE 37 TEMPERATURE VERSUS R A D I A L POSITION MET H O D IV

G

244 l b . / h r . - a q . f t .

340

320 300 280 260 240

220 200 180

160

140

120

100 Radial Position, n

95 Calculations at Other Mass Velocities Since the best check was obtained with experimental results with Method IV at the 244 mass velocity, this method was used in making cal­ culations at mass velocities of 147, 350 and 512 lb,/hr,-sq. ft.

Plots

of the B function versus temperature for these mass velocities are shown in Figures 20 and 21.

39 and 40.

Reaction rate data are shown in Figures IB,

Extrapolated reaction rates are shown in Figures 41, 42 and

43» A Z is plotted versus temperature in Figure 44. The temperature gradients calculated by Method IV at the 147 mass velocity agree remarkably well with the experimental values. A compar­ ison is shown in Figures 45 and 46.

At radial positions of 0.2, 0.4,

0.6 and 0.8 the maximum deviation is approximately 15°C.

At a radial

position of zero, the agreement is poorer, the deviation being approxi­ mately 70°C.

As a result of the good agreement in temperature gradients,

it should be expected that the predicted conversions would check the experimental values. This was found to be true; the maximum conversion obtained experimentally was

20.7$ versus 20$ by prediction at a bed

depth of 2*2 inches. As a result of the non-uniform'entering tempera­ ture gradient,

78.8$ was converted at n = 0 and 0.74$ at n = 4.

At the 350 mass velocity, the predicted temperatures were within 20°C. of the experimental values at radial positions of

0.2, 0.4, 0.6 and 0.8.

Poorer agreement was obtained at the center of the reactor.

Plots of

the experimental and predicted temperature gradients are shown in Fig­ ures 47 and 48. 26.9$,

The experimental conversion was 27.5$ and the predicted

Experimentally this conversion was attained at a bed depth of

2 inches; by calculation it was reached at 4.6 inches.

10

46c

-Q—-peT-c m t Conversion

FIGURE

38

B FUNCTION VERSUS TEMPERATURE MASS VELOCITY = l4? Ib,/hr.-sq.ft

.00

9 7

520k

48C

46C

44C

B FUNCTION VERSUS TEMPERATURE MASS VELOCITY

350 Ib./hr.-aq. ft

32C

30C

28i 400

800

1208

B Function, °C./ft.

1600

2000

2400

2800

3200

98 520

Tempera ifure

.♦ D »

PIQURE 4 0

B FUNCTION VERSUS TEMPERATURE

360 MASS VELOCITY - $12 lb./hr. sq.ft

320

280

200

>00

100

1000 ■

1200

âÇ o Q

56ô

ô

1800

B FUNCTION, ° C . / n .

2000

3200

99 o.io

0.08 0.06 FIGURE 4-i 0.04

REACTION RATE / EXTRAPOLATION PJjOT MASS VELOCITY 147 lb.Ar.-sq.ft.

0.02

0.006

0.002

0.001

0.0006-

1.3

1.4

1.5

1.6

1.7

1.8

Reciprocal Absolute Temperaturej l/T 0K. x 10^

I

1.9

0.10

0 .0 8

0.06 0 .0 4

REACTION RATE EXTRAPOLATION PLOT

MASS VELOCITY 351 lb./hr.-ft* 0.02



0.006

à 0 .0 0 4

0.002

©

0.0008 0.0006

0.0004

1 .4

1 .7

Reciprocal Absolute Temperature, l/T°K» x 10

/ût 0.10

0.08 0.06 FIGURE 4 - 3

0.04

REACTION RATE EXTRAPOLATION PLÛT MASS VELOCITY 512 lb./hr.-ft .2

0.02 \

\

\

■p

t n b .01