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73-27,028

LINTNER, Jr., William, 1931- THE EFFECT OF ULTRASONIC VIBRATIONS ON HETEROGENEOUS CATALYSIS.Newark College of Engineering, D.Eng.Sc., 1973 Engineering, chemical

University Microfilms, A XEROX Company , Ann Arbor, Michigan


THE EFFECT OF ULTRASONIC VIBRATIONS

ON HETEROGENEOUS CATALYSIS

BY

WILLIAM LINTNER, JR.

A DISSERTATION

PRESENTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE

OF

DOCTOR OF ENGINEERING SCIENCE

AT

NEWARK COLLEGE OF ENGINEERING

This dissertation is to he used only with due regard to the rights of the author. Bibliographic references may be noted, but passages must not be copied without permission of the College and without credit being given in subsequent written or published work.

Newark, New Jersey1973


ABSTRACT

The effect of ultrasonic vibrations on the vapor phase decomposition of cumene to benzene and propylene was investigated employing silica-aluminum cracking catalyst.

The catalytic reactor consisted of a 1 cm. diameter stainless steel tube containing a 20 in. long preheater and a ^ in. long catalyst chamber. The catalyst bed was irradiated from above by means of an ultrasonic horn which transmitted acoustical energy directly into the vapor.

The reactor was run at temperatures of 650°F. and 1050°F., frequencies of 26,000 cps and 39,000 cps, feedrates of 20 to 600 gms./hr., power outputs of 0.5 to 1.3

2watts/cm. , and catalyst loadings of approximately 1 to 6 grams.

At temperatures and flow rates where external bulk diffusion controlled the rate of reaction, the application of ultrasound resulted in increases in the mass transfer coefficient up to k0%. In the area where surface reaction and internal pore diffusion controlled, the combined catalyst effectiveness factor - surface reaction rate constant was increased by up to 160%.

Confidence intervals were calculated for the coefficients of the equations expressing log k^ as a function of T and log £ L k 2 as a function of The analysis of

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variance indicated that the increases in mass transfer coefficients and combined catalyst effectiveness factor - surface reaction rate constants were significant at ultrasonic frequencies of 39,000 cps. The increases obtained between frequencies of 26,000 cps and no ultrasound were of lesser significance.

It is postulated that ultrasound causes acoustic streaming within the reactor tube and catalyst pores, resulting in higher transport rates caused by the combined effect of diffusion and forced convection as compared to the effect of diffusion alone in the absence of ultrasound. In addition, acoustic energy may cause localized heating within the catalyst bed, thereby increasing the rate of surface reaction.

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APPROVAL OF DISSERTATION

THE EFFECT OF ULTRASONIC VIBRATIONS

ON HETEROGENEOUS CATALYSIS

BY

WILLIAM KINTNER, JR.

FOR

DEPARTMENT OF CHEMICAL ENGINEERING

NEWARK COLLEGE OF ENGINEERING

BY

FACULTY COMMITTEE

APPROVED: CHAIRMAN

NEWARK, NEW JERSEY

JUNE, 1973

Reproduce with permission of the copyright owner. Further reproduction prohibited without permission.

ACKNOWLEDGMENTS

Many people have given assistance and guidance to the author during almost four years of investigation and it is almost impossible to acknowledge them all. However, the author thanks particularly his advisor, Dr. Deran Hanesian, for his most valuable help from inception to completion of this v/ork.

The author also expresses his sincere appreciation to Mr. Arnold Stev/art, Mr. Gerard Gilkie and Mr. James Nickolson of Macrosonie International, and Dr. Carl Bertsch, formerly of Newark College of Engineering, for their advice in designing the experimental equipment.

He also acknowledges the aid of Mr. Donald Friedeman in constructing the equipment, and the generosity of Dr. Dimitrios Tassios for lending his gas chromatograph for the analytical work. He further acknowledges the generous assistance of Mr. Richard Robertson for helping him employ the computer program for correlation of data.

The author is deeply grateful to his wife, Doris, for typing this dissertation and to his son, William, who inked most of the data curves.

Finally, the author especially thanks his company, L & L Chemical Construction & Engineering Co., for granting him a leave of absence in order to fulfill his residency requirement, and du Pont for their fellowship which helped immensely with the financial burden.

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TABLE OF CONTENTSPage

Chapter I INTRODUCTION 1Purpose and Scope of Investigation 1 Literature Survey 2

Chapter II THEORY 16Continuous Reaction Model 16Reaction Design Equation . 21Ultrasonic Engineering 2k

Chapter III EXPERIMENTAL EQUIPMENT 30Plow Chart 30Peed System 30Regeneration System 32Reactor 32Condenser 36Ultrasonic Horn 36

Piping 38

Analytical Instrumentation 38

Equipment Specifications 39

Chapter IV EXPERIMENTAL PROCEDURE k7

Operating Conditions k7

General Procedure k7

Detailed Procedure 50

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TABLE OF CONTENTS (continued)Page

Chapter V EXPERIMENTAL RESULTS 54Presentation of All Data 54External Diffusion Controlling 66

Surface Reaction and. PoreDiffusion Controlling 83

Activation Energy 95

Summary of Results 102Acoustic Streaming 103Thermal Effects 105

Chapter VI CONCLUSIONS 106

Chapter VII RECOMMENDATIONS 108

Appendix I PHYSICAL PROPERTIES OF CUMENE,BENZENE AND PROPYLENE 110

Appendix II PHYSICAL PROPERTIES OF SILICA-ALUMINA CATALYST 125

Appendix III CONTINUOUS REACTION MODEL 128

Appendix IV GAS FILM DIFFUSION 132

Appendix V SURFACE PHENOMENA 139

Appendix VI PORE DIFFUSION 146

Appendix VII REACTION DESIGN EQUATION 162

Appendix VIII EVALUATION OF REACTION RATE CONSTANTS 173

Appendix IX SAMPLE ANALYSIS 212

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TABLE OF CONTENTS (continued)Page

Appendix X ULTRASONIC ENGINEERING 221

Appendix XI DESIGN EQUATION FOR PSEUDO FIRSTORDER REACTION 246

Appendix XII RATIO OF EFFECTIVENESS FACTOR FORDIFFERENT SIZE CATALYST PARTICLES 254

Appendix XIII THE CARBON-OXYGEN REACTION 263

Appendix XIV DATA 268

Appendix XV THERMOCOUPLE CORRECTION 291

Appendix XVI QUADRATIC REGRESSION EQUATION 294

Appendix XVII EVALUATION OF REACTION ACTIVATIONENERGY 323

Appendix XVIII EVALUATION OF INTRINSIC RATECONSTANT 327

Appendix XIX CALCULATION OF MAXIMUM PROBABLEERROR 331

Appendix XX CALCULATION OF POWER INPUT 334

Appendix XXI SAMPLE CALCULATION OF THE MASSTRANSFER COEFFICIENT 336

Appendix XXII ANALYSIS OF VARIANCE 338

Nomencalture 342

Literature References 349

Vita 356

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LIST OF FIGURESPage

Figure 1 Flow Chart for Experimental Reactor 31Figure 2 Reactor 33Figure 3 Reactor Thermocouple Location

and. Heating Zones 3 +Figure 4 Ultrasonic Horn 37Figure 5 Feed Rotameter Calibration 45Figure 6 Ultrasonic Generator Frequency

Calibration 46Figure 7 Data Sheet 53Figure 8-16 Conversion vs. W/F 56-64Figure 17-22 Mass Transfer Coefficient vs.

Temperature 69-77Figure 23-24 Mass Transfer Coefficient vs.

Temperature 79-81Figure 25-33 Conversion vs. W/F 85-93Figure 34-37 Effectiveness Factor vs.

Temperature 97-100Figure 38 Rate Constants vs. Temperature 104Figure 39 Continuous Reaction Model 131Figure 40 Gas Film Diffusion of A,R and S 134Figure 41 Cross Section of Catalyst Particle

Showing Differential Element 148Figure 42 Cross Section of Plug Flow Reactor

Showing Differential Element 164Figure 43 Plot of vs. W/Fa at Constant

Temperature 176Figure 44 Plot of Reaction Rate vs.

Conversion at Constant Temperature 178

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FigureFigure

Figure

FigureFigureFigureFigure

Figure

FigureFigure

FigureFigure

Figure

Figure

Figure

FigureFigure

LIST OF FIGURES (continued)

^546

47

48-73747576

77

7879

80 81

82

83

84

85 86-111

Plot of Tf/rQ vs.ITPlot of W/Fa - <TXA vs -ln(l-XA ) - XA]

Reaction Constants vs. TemperatureConversion vs. W/FCondenser Flow ChartSchematic Diagram of Sound WaveSine Wave Representation of Sound Wave

Page179

182

184186-211

216223

223Element of Gas in a Tube in Which There is a Longitudinal Sound WaveIntensity Flow ChartSchematic Drawing of a Standing WavePseudo First Order Plot of DataReciprocal Space Velocity vs. ConversionReciprocal Space Velocity vs. Catalyst Particle Diameter at Constant ConversionReciprocal Effectiveness Factor vs. Catalyst Particle Diameter

Conversion vs. WFA0dp

Data Sheet Conversion vs. W/F

225 232

235253

2 57

258

261

262

270297-322

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LIST OP TABLES

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Page1 Application of Acoustical Energy 4-52 Summary of Typical Wave . 28

Characteristics3 Equipment Specifications 39-444 Quadratic Equation Constants 555 Mass Transfer Coeffieicnt 676 Constants for the Equations of Mass

Transfer Coefficients as a Functionof Temperature 68

7 Increase in Mass Transfer Coefficient at Several Peed Rates, Temperatures,and Ultrasonic Frequencies 82

8 Increase of Kinetic Rate Constantat Several Temperatures and Ultrasonic Frequencies 94

8A Constants of the Equations of KineticRate Constants as a Function of Temperature 9^

9 Activation Energy and CharacterizationFactor 101

10 Summary of Values of Reaction RateConstants 185

11 Summary of Typical WaveCharacteristics 242-243

12 Tabulation of Data 271-29013 Quadratic Equation' Constants 29614 Intrinsic Rate Constant and Mass

Transfer Coefficient 330

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1

CHAPTER I

INTRODUCTION

Purpose and Scope of InvestigationConsiderable information is available in the litera

ture concerning the use of ultrasonic vibrations as an analytical tool and as a source of energy. Although most earlier references describe the passive applications of ultrasound, whereby the propagation characteristics of the sound wave are employed, the field has recently expanded into active applications of acoustical energy. These active applications now include the effect of ultrasonic vibrations on chemical reactions. Although considerable information is available concerning sonochemical reactions, much of the data and results are contradictory and almost all the experimentation deals with uncatalyzed liquid phase reactions.

It therefore appeared to this author that because of the paucity of quantitative data a most interesting and challenging research would be the study of the effect of ultrasonic vibrations on heterogeneous catalysis, or more specifically, the effect of ultrasound on the catalytic cracking of cumene.

Selection of system. The cumene system was selected for this study because of the following reasons:


2

1. Thermal cracking of cumene is negligible at the temperatures employed (650°-1050°F.).

2. The reaction is essentially clean with a minimum production of side products.

223. The reaction mechanism was determined by Garver in 1955 published in his Doctoral Thesis, thus providing an experimental base.

97One literature reference published by Zhorov in 1967 indicates that ultrasound effects the rate of this reaction, thereby providing this author with some indication of success.

Investigation plan. The plan of the investigation was to repeat some of Garver's work to obtain a firm basis for the reaction mechanism in the absence of ultrasound, and then to apply acoustical energy to the reaction and attempt to determine the following effects:

1. The effect of ultrasound on the rate of reaction.2. The effect of ultrasound on the kinetic rate con

stant and the external diffusion coefficient.

Literature SurveyEarly references. Literature references to ultra

sonic vibrations, or more accurately acoustical energy, oc-92cur as early as 1927. At that time, Woody developed a

piezoelectric oscillator of quartz which produced frequencies up to 300,000 cps. It is now possible to produce frequencies


3

10of over 9 x 10 cps. Frequency ranges between 20,0009and 10' cps are referred to as ultrasonic and ranges

gabove 10 cps are referred to as hypersonic. This investigation deals with the ultrasonic range between20,000 and 50 ,000 cps.

Classification of acoustical energy. Acoustical energy is generally classified according to its application. Passive applications include those by which the propagation characteristics of the sound wave are employed and active applications are those by which the

psound is used as a source of energy. Greguss has classified several applications of acoustical energy according to the frequency employed. This classification is shown in Table 1. It is interesting to note that when Greguss prepared this summary in 1963, sonochemical effects were limited to liquid phase investigations only.

In addition to frequency, the second important variable in the study of acoustical energy is sound intensity . ^ 1 The intensity of audible sound lies between lO-1^

/ 2and 10 watts/cm. , with the latter value being the threshold of pain. Sound intensities of 120,000 watts/cm. at a frequency of 500,000 cps have been produced in liquids at the Moscow Acoustical Institute. However, the intensities most frequently applied in sonochemical research are those between 1 and 10 watts/cm. Peak intensities of up


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TABLE 1

APPLICATIONS OP ACOUSTICAL ENERGY

Passive ApplicationsPhysical State

of MatterFrequency

cps

1. Theoretical solid state research Solid 109- Q11

2. Computers Solid 107- 09

3. Non-destructive testing Solid 103- o84. Medical diagnostics Solid and Liquid 103- 07

5. Viscoelastic research Solid up to o66 . Seismic research Solid up to 0^7. Measurements, remote control Liquid and Gas 105- o98 . Flow measurements Liquid 103- o39. Viscosity measurements Liquid 103- o3

10. Level determinations Liquid 105- o7

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TABLE 1 (continued)

APPLICATIONS OF ACOUSTICAL ENERGY

Active ApplicationsPhysical State

of MatterFrequency

cps1. Effect on alloys Solid and Liquid up to 10-32. Fatigue research Solid up to 10-33. Colloid chemistry Solidj Liquid and Gas up to 10^

Therapeutical applications Solid and Liquid 105-1075. Boiler scale prevention Liquid A <

10 -io-36. Effect on combustion processes Gas up to 107. Biochemical effects Liquid 105-1078. Sonochemical effects Liquid up to 10^

V_n.

6

2to 1.3 watts/cm. were studied in this investigation because this was the limitation of the equipment employed.

Liquid phase reactions. Many investigations have been reported in the literature describing the effect of ultrasound on liquid phase chemical reactions, but, unfortunately, much of this work has led to erroneous con-

7 3elusions and contradictory results. For example, Shaw'^ reported in 1967 that ultrasound caused scissions of the polymer chain in polysiloxane solutions. He further found that doubling the acoustic intensity at 20,000 cps doubled the degradation rate. Porter^® confirmed this observation that same year when he reported that the average molecular weight of polyisobutylene dissolved in trichlorobenzene was decreased from 4-66,000 to 20,600 by irradiation with ultrasound. Peacocke-' explained this phenomenum in 1968 as a result of his studies of the effect of ultrasound on such linear macromolecules as DNA by stating that the degradation is caused by stresses resulting from the relative movement of the macromolecule and the solvent molecule.

40In contradiction to these observations, Makeevareported in 1967 that polyvinyl chloride prepared bythe bulk polymerization of vinyl chloride and exposedto ultrasound had a higher molecular weight and fewer

28branches. Heymach appeared to add to the confusion


7

when he reported that cavitation resulting from the application of intense acoustical energy selectively degraded polymers by fracturing longer chains at a faster rate than shorter chains. He concluded that ultrasonic irradiation may be a means of sharpening molecular weight distributions.

Effect on reaction rates. In addition to experimentation in the area of polymers and polymerization, many investigators were interested in the effect of ultrasound on reaction rates. Since it was early in the study of this new form of energy, most investigatorsmade no attempt to explain the individual effects of in-

. Ll Lltensity and frequency. For example, in 1965 Mario reported that the reaction kinetics of the hydrolysis of aspirin are pseudo first order with or without ultrasound. He found that the reaction rate was increased with theapplication of ultrasound.

. . h. ?In 1966, Manu reported that ultrasound at21,000,000 cps and k to 12 watts/cm. increased the re

action rate of the oxidation of the aldehyde group in7 7glucose. In 1968, Stolyarov noted that ultrasound at

frequencies of 20,000 to 100,000 cps increased the oxidation rate of aluminum in water at 90°F. During that

filsame year, Prakash showed that the rate of production of iodine from cesium iodide increased with the appli-


8

cation of ultrasound at frequencies of 1,000,000 cps and2 34*intensities of 1.^ to 2.4- watts/cm. In 1969, Kowalska^

noted that ultrasonic irradiation increased the oxidation rate of divalent iron to trivalent iron by 300$.

Acoustic intensity and frequency effect. As more information became available describing the effect of ultrasound on reaction kinetics, investigators became more concerned with the specific effects of intensity and frequency. Most available data indicate that increasing intensity increases the reaction rate, but the data concerning the effect of frequency on reaction rate is highly contradictory. During his study of complex ethers in 1966, Zilberg found that ultrasonic intensity increasedthe reaction rate but frequency variations between300,000 and 1,000,000 cps had no effect. Prakash^0 observed that increasing the intensity increased the sono-chemical decomposition of CgHgBr^. Rice^, Sergeeva^2,

7 8 22Suess' and Geissler J all independently confirmed theobservation that increasing ultrasonic intensity increases

10the reaction rate. In 1967, Chen reported that the reaction rate of the hydrolysis of methyl acetate with HG1 catalyst increased with increasing ultrasonic intensity,but that variations in frequency had no effect, thus con-

68firming Zilberg1s work. However, in 1968, Saracco completed his study of the hydrogenation of olive oil in


9

cyclohexane with Raney nickel catalyst and ultrasound.He discovered that the reaction rate reached a maximum with increasing intensity and then decreased at any frequency. He further observed that maximum reaction rates were obtained at frequencies of 500 ,000 cps.Finally, Paryjczak-^ reported that the zero order rate constant for the sono-oxidation of FeClg decreased with increasing frequency.

Theory developments. In spite of these contradictory conclusions, many investigators attempted to developtheories to explain the sonochemical effect. In 1950,

g 1Weissler' proposed that the chemical reaction rate under the influence of ultrasound is a function of the sound intensity, duration of exposure, pressure, temperature and volume. In 1965, Nosov^ added the proposal that intramolecular rearrangements and cavitation are the effects of the application of ultrasound to chemical reactions. He further stated that electrical discharges occur within the cavitation bubbles which ionize the solvent and solutes, producing highly reactive free radicals.

19Fogler ' agreed with the theory that cavitation increasesreaction rates as a result of his experimentation with the

13liquid phase hydrolysis of methyl acetate. Currell J produced acetylene by the ultrasonic cleavage of cyclohexanol. His results were also consistent with the theory that the


10

sonochemical reaction takes place within the cavitation22bubbles. Kessler^ was able to promote the chemical de

composition of tetralin and methyl naphthalene by ultra-27sonic irradiation at frequencies of 80,000 cps. Griffing '

finally proposed that ultrasound causes cavitation and luminescence simultaneously. Luminescence may be caused by electrical charges within the cavitation bubble or by extremely high temperatures within the bubble. The cavitation bubbles then act as hot spots which may promoteor enhance chemical reactions.

60Prakash found that the sonochemical decomposition of C2H2Br^ increases with increasing ultrasonic intensity.He theorized that ultrasonic energy caused the formation

86of free radicals within the cavitation bubble. Tuchel concurred with the free radical theory as a result of his experimentation with potassium iodide solution oxidations irradiated with ultrasound at frequencies of 870,000 cps.

kq h.i 37In 1968, Margulis Maltsev and Tuxzynski independently arrived at the conclusion that reaction rate enhancement is due to the formation of free radicals within the cavitation holes.

In addition to the hot spot and free radical theories associated with the cavitation phenomenon, some investigators proposed other theories to explain the effect of ultrasound on the rate of chemical reactions. For example,


11

Vladar^ continuously produced CaCOH)^ from pure CaCO^and GOg in a tubular reactor and found that ultrasoundincreased the rate of carbonation. He theorized that theultrasonic energy reduced the particle size of the solids

oilresulting in a higher reaction rate. Gindis studiedthe effect of ultrasound on the electrochemical oxidationof KgMnO^ to KMnO^ at frequencies of 20,000 cps and 25 to30 watts/liter. He found that the degree of oxidation atthe anode was increased by 10% to 65% and concluded thatultrasound increased the current efficiency of the elec-

48trolyte by that amount. Needham applied ultrasound to aspirin in ethanol-water solution and found that although the same reaction order was maintained, the rate of degradation increased. Needham theorized that ultrasound lowered the activation energy, increased the rate of molecular collisions, and increased the rate of movement of the products away from each other.

Diffusion theory. In 1968, Belov^ proposed that ultrasound causes higher reaction rates by acceleration of diffusional processes. In 1969, Kowalska^, as a result of his studies of the application of ultrasonic

++ +++fields to the oxidation of Pe to Pe , also concluded that ultrasound decreases the thickness of the diffusion layer. This work, in addition to other confirming evidence, led this author to believe that ultrasound would effect the


12

rate of diffusion controlled solid-catalyzed gaseous reactions .

Catalyst activity. During the time when many investigators were studying the effect of ultrasound on uncatalyzed liquid phase reactions, some scientists experimented with the effect of ultrasound on catalysts. For

U- oexample, Berger regenerated some catalysts at 900 to1000°C. in the presence of ultrasound at 20 to 100watts/cm. and found that the catalytic activity was

7 5enhanced. Slaczka irradiated nickel and cobalt catalysts with ultrasound during their preparation by the reduction of oxylates and found that their catalytic activity were increased. He concluded that the ultrasonic energy at frequencies of 25,000 cps and 0.3

nwatts/cm. caused an increase in the number of crystal30defects, thus enhancing the activity. In I960, JonesJ

fastened one end of a bundle of catalytically coated wires to an ultrasonic driver while the other end was suspended in a reactor. He noted that the catalytic activity was enhanced for the preparation of ammonia from nitrogen and hydrogen when ultrasonic energy at frequencies of 500 to300,000 cps was applied.

9 7Gas phase reactions. In 1967, Zhorov studied the effect of ultrasound on the catalytic cracking of cumene. Zhorov proposed that the rate of reaction was controlled


13

by the diffusion rate of the reactants and products to and from the catalyst surface. He discovered that the diffusion rate, and hence the rate of reaction, could be increased by the application of ultrasonic vibrations.

Zhorov's equipment consisted of a continuous reactor in which he placed 7.9 gms. of aluminum-silicate catalyst. Gumene was fed into the reactor at a feed rate of 3.0 g"h™°les (W/Fa 0 = 9,468 ) andcracked at 878°P. The reactor was operated without ultrasound for the first half hour and then ultrasonic energy was applied for the second half hour at a frequency of 20,000 cps and an amplitude of 5 to 6 microns.

Analysis of the liquid product (a mixture of cumene and benzene) indicated that the concentration of benzene increased by 20^ as a result of the application of ultrasound. This result serves as the basis for this author's research.

Reaction mechanism. Before any attempt is made to isolate the effect of ultrasound on the catalytic cracking of cumene, it is necessary to first determine the reaction mechanism of this system in the absence of ultrasonic energy.Considerable work was completed in this area from 19^9 through

2*5 82 831967 by such investigators as Greensfelder , Topchieva * -J,12 6^ 22 50 55Corrigan , Rase , Garver , Panchenkov-^ , Perrin^ ,

Zhorov^,-^,9^, Pansing^* and Spozhakina"^. One of the


14

most complete investigations was published by Garver in his Doctoral Dissertation of 1955. Garver determined that the reaction mechanism for the cracking of cumene on silica-alumina catalyst at 850°F., 950°F. and 1050°F. was single site with surface reaction controlling and propylene not adsorbed. His experimentation also lead to the determination of the reaction rate constants.

This author's plan was to extend the work of Zhorov into a more detailed quantitative study of the effect of ultrasound on the solid catalyzed cumene reaction employing Garver's work as the basic starting point. This detailed investigation had never been studied previously as witnessed by the absence of published information concerning the effect of ultrasound on solid-catalyzed gaseous reactions.

DiscussionUltrasound may increase the rate of a heterogeneous

solid catalyzed gas reaction by one or more of the following methods.

1. Increase the number of active sites on the catalyst surface.

2. Increase the rate of diffusional processes:A. External bulk diffusionB. Internal pore diffusion

3. Decrease the reaction activation energy.4. Increase the surface reaction rate.


15

5. Increase the pressure at the mouth of the catalyst pore by the application of acoustic energy.

6. Develop localized thermal effects by the application of ultrasonic energy.

Internal pore diffusion, the surface reaction rate and bhe number of active sites are described in a single constant, ^Lk^, the reaction rate constant. If ultrasonic energy affects any of these three parameters and the data fit the reaction rate model at high flow rates, then can be calculated.

External bulk diffusion is proportional to the mass transfer coefficient, k . At low flow rates, mass transferocontrols the rate of reaction, and therefore the effect of ultrasound on k can be measured at low flow rates.

Acoustic pressure can be calculated and, in fact, the variations in pressure at the mouth of the catalyst pore as a result of the application of ultrasonic energy will be shown to be negligible for the power employed in this investigation.

Localized hot spots on the surface of the catalyst will result in increased surface reaction rate constants and reaction rates. Quantitative measurements of this phenomenon are not possible in this investigation, but these thermal effects will also manifest themselves in CLk^, a measurable quantity.


16

CHAPTER II

THEORY

Continuous Reaction Model

In solid-catalyzed gas-phase reactions, reaction occurs at the gas-solid interfaces. These interfaces lie on the external surface of the catalyst particle and also on the internal surfaces within the catalyst pore. The overall rate of reaction depends upon the availability of these surfaces to the reactants.

For the continuous reaction model, it is assumed that the reaction mechanism consists of seven distinct processes with the rate of reaction controlled by the slowest process.

These processes are described in detail in Appendices III through VII and briefly outlined below.

1. Gas film diffusion of reactants.2. Pore diffusion of reactants.3. Adsorption of reactants.4. Surface reaction5. Desorption of products.


17

6 . Pore diffusion of products.7. Gas film diffusion of products.Gas film diffusion. Gas film diffusion of reactants

and products is handled mathematically as a single simple diffusion process. The equation describing this process is as follows:

1+YA s (1)

r^ = gm moles cumene diffusing toward catalyst sur-£rm molesface per second per gm. catalyst, gm~~sec"

Piji = total pressure, atm.cm.k = mass transfer coefficient, „ , g * sec.

d a b • '■ s i

Da b = diffusivity of cumene in cumene, benzene andcm ^propylene,

<Sf = thickness of stagnant gas film between main gasstream and external surface of catalyst, cm.

cma = superficial surface area of catalyst, — —o ' gm.

H = 82.06 gm mole-°K.T = °K.

^Ab = mole fraction cumene in main gas stream,dimensionless

Ya = mole fraction cumene on catalyst surface,bdimensionless


18

Surface phenomena. The adsorption of cumene onto the catalyst surface, the reaction of cumene on the surface and the desorption of benzene from the catalyst surface are also handled together mathematically. Garver has shown that the following rate equation is consistent with a single site mechanism whereby propylene is not adsorbed and surface reaction is rate controlling.

PA “ Pr pSK

(2)A1 1 + KAPA +

(rA1) = reaction rate, ^ .A1 * gm cat-sec.CT = concentration of total active sites on cata-L 2

lyst surface,0 * gm cat.= forward reaction rate constant for surface

reaction, S.mcm. -sec.= equilibrium adsorption constant for cumene,

_1__atm.

PA = partial pressure of cumene, atm.PR = Partial pressure of benzene, atm.Ps = partial pressure of propylene, atm.Kr = equilibrium adsorption constant for benzene,

1atm.

K = equilibrium constant for overall reaction, atm,

Effectiveness factor. The effect of pore diffusion


19

of reactants and products on the rate of reaction is expressed by applying a correction factor to the rate equation. This correction factor is known as £ , the effectiveness factor. The rate equation now reduces to the following expression:

' Pa " Pr Ps£Lk9K.

(-r,U = 2 AK

A1 1 + KAPA + KRPR (3)

In the case of irreversible reaction, K approaches infinity and the rate equation then becomes:

_ eLk2KApA _ _ _

1 1 + k a Pa + kr PhThe initial rate of reaction occurs when the partial

pressure of cumene is equal to the total pressure and the partial pressures of benzene and propylene are zero.

eLk2KA7rro “ 1 + K J f (5)

rA1 = reaction rate, g”

r0 = initial reaction rate,

£ = effectiveness factor, dimensionlesscm ^L = total concentration of active sites,-- --'-rr~1 gm cat.

k2 = forward reaction rate constant for surfacereaction, S»=j»2las cm.^-sec.


20

K. = equilibrium adsorption constant for cumene1

atm.Kr = equilibrium adsorption constant for benzene,

_1__atm.

K = equilibrium constant for overall reaction, atm.p^ = partial pressure of cumene, atm.Pg = partial pressure of benzene, atm.Ps = partial pressure of propylene, atm.77" = total pressure, atm.

The effectiveness factor is defined as the ratio of the actual rate of reaction with pore diffusion present to the rate of reaction if the resistance caused by pore diffusion were absent. It is expressed by the following relationship wherein hg is the Thiele Modulus:

tanh h1 _1

h (6)s s

hs (7)

effectiveness factor, dimensionlessh = Thiele Modulus, dimensionless s *rp = radius of catalyst particle, cm.k = forward intrinsic rate constant for surface s

reaction,


21

cmS = total surface of porous catalyst, —v cm.J2D = effective pore diffusivity, cm-‘—

6 S 3 C •

Reaction Design EquationThe reaction design equation is obtained by sub

stituting the rate equation into the plug flow reactor design equation.

W '( - r An) (8)Fa0 / ' A1

W = wt. catalyst, gms.Fa = feed rate of cumene, ^ - rr)0-e— -"o ’ sec.Xa q = initial conversion of cumene, dimensionlessXAf = final conversion of cumene, dimensionless

(-rA1) = reaction rate, Sm moles A Al' * gm cat-sec.

Reaction design equation with external diffusion controlling. For bulk diffusion of cumene from the main gas stream to the surface of the catalyst, the integrated reactor design equation yields the following relationship for the mass transfer coefficient:

XA, RTk = ------ ^ - (9)® (W/FA„)pTaln 1+lAfc

1 + * A s J


22

After substituting the constants and employing the log mean mole fraction for the surface concentration of cumene, the equation reduces to the following:

6.26 XAf Tkg = (w /fAo ) m (1+YAlm) (10)

where,cmk = mass transfer coefficient, g , ’ sec.

XAf = final conversion of cumene, dimensionlessT = temperature, °K.W = wt. catalyst, gms.

= initial cumene feed rate,^o * sec.= log mean mole fraction of cumene in the

bulk stream, dimensionless R = gas constant, 82.06

Pm =- total pressure, atm.2cma = superficial surface area of catalyst, g ~"

^A^ = mole fraction cumene in bulk stream,dimensionless

YAs = mole fraction cumene at catalyst surface, dimensionless

Reaction design equation with surface reaction controlling. For reversible reaction, the reaction design equation is as follows:


23

PA Jro1_2S In (1+XA*) , XA

(1-X*S) I?

+ /?

where,

p =

<§ =

i 1ri (1+XAS) _ 1 nyi (i-<S2xa 2) 2^3 d-XA5) 2 p

1 , 1 ^Lk2kA7T 6 Lk,

Kr£ Lk2KA7T £Lk2KA

1 + 7T‘K

<52(11)

(12)

(13)

(1*0

For irreversible reaction, K approaches infinity,

<S becomes unity and the design equation reduces to the

following expression:

WpAr = ^ XA +/S»[-ln(l-XA ) - XA] (15)

W = wt. catalyst, gms.

'a = feed rate of cumene, Sm..,Mol§.s A1 sec.X^ = conversion of cumene, dimensionless

eL

= effectiveness factor, dimensionlesstotal concentration of active sites, — — *■,* gm catgm


24

kg = forward reaction rate constant for surfacereaction, SS-foles cm.^-sec.

k a

k r

KTT

equilibrium adsorption constant for cumene,_1__atm.equilibrium adsorption constant for benzene,_1__atm.equilibrium constant for overall reaction, atm, total pressure, atm.

Ultrasonic EngineeringFundamental equations. As a sound wave travels

through a gas, small volume elements of the gas containing millions of molecules alternately compress and expand in the direction of the propagation of the sound wave.The sine wave representations of the displacement, transverse velocity, and transverse acceleration are as follows

y = Y cos 2TT(x-Vt) ~7T = Y cos 2TTf(t-f)

v

a

= ZJtf Y sin 27Tf(t-£); vV ' ' 'max47T2f2Y cos 27Tf(t-f)

y = displacement, cm. Y = amplitude, cm.* = wavelength,

max

= 27f fY

= 4TT2f2Y

(16)

(17)

(18)


25

TV

VT = y. , sec.P ^ i o d , cycle

velocity of propagation of wave form,cm. sec.

f = frequency,_ I“ T

cyclessec.

distance traversed Py wave form, cm. time, sec.

x tv = transverse velocity, a = transverse acceleration,

cm.sec.

>m.sec.

Velocity of propagation. The velocity of propagation of a sound wave in a gas is a function on only the physical properties of the gas and not of the characteristics of the sound wave. This is illustrated in the following equations:

12 JL2 2

V 1 1 ^RT/°o*- / 0 M (19)

v =

/ ’o =k =

P =

y =

velocity of propagation of wave form, original gas density, cm.

cm. sec.

cm.2 cm.-sec.^compressibility, ^

pressure, -cm.^ cm-sec.^Gr>trS dimensionless uv

(dyne = gmrcm,) sec.


26

0^ = heat capacity of gas at constant pressure, cal

gm-°C,leatcal

Cv = heat capacity of gas at constant volume,

R =gm-°C.B-31 x 10? ■ 8.31 x 10?

2(erg = dyne-cm. = )S6C •

T = temperature of gas, °K.M = molecular wt. of gas,

Acoustic pressure. The acoustic pressure exerted by the sound wave as it traverses a gas is dependent upon the velocity of propagation and the intensity of the sound. The amplitude of the sound wave is a function of the acoustic pressure.

iPmax ‘ [ V o ™ ] 3 <20>

Y = Pmax27T f/°

= maximum pressure caused by sound wave, max ^ * cm.^/O - original gas density, ^m-sh ■10 cm.J

I = sound intensity, — .cm.^-sec. cm.^-sec.(i q -7 watt-sec.^' erg

cmV = velocity of propagation, — —sec.


27

f = frequency,

Y = amplitude, cm.

Conversion factor: 1 ■ — -dyne-sec.

Typical values of wave characteristics. Values for the velocity of propagation, wavelength, acoustic pressure, amplitude, transverse velocity and acceleration were calculated for cumene at various frequencies and temperatures at the maximum power output and half power output of the equipment. A summary of these calculations is shown in Table 2.

As seen by the table, acoustic pressure as imposed by the sound wave should have little effect on the reaction rate because the pressure fluctuations above and below atmospheric are only a maximum of 1.62 psi at 650°F. and 1.50 at 1050°F. Furthermore, the acoustic pressure is lower at the higher frequency as a result of the mechanical characteristics of the equipment.

This research will, in fact, show that the dependency of reaction rate on power input alone for the range studied is negligible and that frequency alone and frequency together with power input are the important factors. Molecular acceleration, which is a function of both frequency and power, is very high in the ranges studied, as


SUMMARY

OF TYPICAL

WAVE

CHAR

ACTE

RIST

ICS

28

o o Ova o UN*o o OrH •k

ONca

•o

o O OVA O Oo O rHrH •S •

ONCA

o

o O oVA O c ao O VOrH •k •

vOCM

o

o O Onv a O VAo O CMrH •k •

vOCM

rH

o O ov a O v ano O o«k •

ONc a

o

o o oVA o oVO o rH•k •

O nCA

o

O O oVA O c aVO O vo•k •

vOCM

o

o o ONva o 'Avo o CM•k •

VO rHCM

U1• -p CMo -p •

• rH 0 0 6fo CO 5 oo•» #k •kEH Cm H

CA 00 OCM O n CMNO CM O

• •k OO nh •

CM o

<A co COCM ON CMVO CM O• •r OO hF •CM o

VA 00 VACA O n OO n CM rH

• •k oO •

CM O

VA 00 OnCA O nON CM rH• •> oO -3 ‘ •

CM o

o- VA 00CA -d" T—1VA ON o• oO O •CM o

a - VA vOCA Ht- CMVA ON O• •k Oo O •CM o

VO VA coO nt- O noo ON O

• •k Oo O •CM O

VO VA 00O -3- CA00 ON rH• •k oo o •CM o

• • •E E o •o o 0 Ew O•k •k #k> fH

O CM oON CM CA

VA ••k oCMCMrH

vo rH CMoo CAvO VA ••k OrHA -rH

VA VA vo1—1 00 OA- 00 •

•s rHrH VA

COCM

O OCA nh VA-3" IN- ••r •k rHCM VAO-d-

rH o CMIt CACM ••kOrHtH

o

A - ON voCA A -VO CM ••T o

ONVArH

rH rH VAo oo rHVO 00 ••t •* rHrH VOvo

CM

-d" CMVA CA voCM A- •*k tHCM VAA-CA

• • CME o • •o 0 £w 1x0 i—1 •H•k •sX X0 0 0E B ,E


29

indicated in the table. This molecular motion results in higher reaction rates by virtue of increased gas diffusion rates. It will be shown that the increased diffusion rate occurs both in the external diffusion zone and within the catalyst pores.

Detailed derivations of the ultrasonic relationships described in this chapter may be found in Appendix X.


3 0

CHAPTER III

EXPERIMENTAL EQUIPMENT

Flow ChartFigure 1 is a schematic flow chart of the apparatus

employed in this study. Valves and by-pass piping have been omitted from the drawing for the purpose of maintaining simplicity and clarity. Detailed specifications of all the equipment employed are described in Table 3 .

The system consists of two feed tanks to which the cumene is charged, a feed rotameter for metering the feed to the reactor, the reactor and a heat exchanger to condense the cumene and benzene effluent. The small amount of propylene gas formed is vented to the atmosphere.

The apparatus is also equipped with a nitrogen source for pressurizing the feed tanks and blowing down the reactor prior to regeneration. A second rotameter is provided for metering regeneration air to the reactor.

Attached to the top of the reactor is the ultrasonic horn by which the catalyst bed is irradiated with ultrasonic energy.

Feed SystemCumene is charged to the feed tanks whereupon they


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

FIGURE 1FLOW CHART

FOR EXPERIMENTAL REACTORBlow-DownNitrogen Ultrasonic

HornNitrogen

Vapor x Sample

RegenerationAir Product

Feed Tanks FeedRotameter

Reactor CondenserAirRotameter

32

are pressured up to 10 psig with nitrogen. The nitrogen pressure is maintained constant by means of a gas pressure regulator so as to maintain a constant pressure drop across the feed rotameter needle valve. The feed rotameter is employed manually to control the cumene feed rate to the reactor; however, for measurement purposes, the difference in liquid level of the feed tanks for the duration of the run is employed for the average feed rate calculation.

Regeneration SystemAfter each run, regeneration air is fed to the re

actor through the air rotameter at a rate of approximately 0.1 scfm for a period of 2^ hours to regenerate the catalyst by burning off the carbon deposits (see Appendix XIII).

ReactorThe reactor design is illustrated in Figures 2 and

3. It consists of a * in. schedule 80 type 316 stainless steel pipe, 20^ in. long, welded to a 2 in. O.D. stainless steel rod drilled to an I.D. of in. The i in. pipeis encased in a 2 in. O.D. rod drilled to snugly fit the pipe. The casing provides the reactor with mass so as to stabilize the operating temperatures. The reactor is flanged at both ends and is equipped with a \ in. spud


33

27 lA"

FIGURE 2 REACTOR

T2 3A"

20 1/2"

Catalyst Chamber

Preheater 0.302"ID

Reactor Shell2.000"OD


FIGURE 3REACTOR THERMOCOUPLE LOCATION AND HEATING ZONES

Zone 5

Zone ^TITI

Zone 3

1027 l A

TIZone 2

10 "

Zone 1

TI

1/2


35

near the top for catalyst addition and product removal. Inserted within the spud is a ^/8 in. thermocouple well.

The \ in. x 20-| in. long pipe serves as the preheater section, and the upper 2V 6 4 in. I,D. x 6 3 A- in. long cylinder is the catalyst chamber. The end of the thermocouple well inserted within the spud extends down into the catalyst chamber and is immersed in the catalyst bed. The catalyst is supported within the chamber by means of a fine mesh stainless steel screen.

The location of all seven thermocouples and five heating elements are illustrated in Figure 3. Six of the thermocouples, TI-1 through TI-6, are affixed to the outside of the reactor wall and connected to a temperature recorded. The seventh thermocouple, TG-1, is inserted in the thermowell and connected to a temperature controller.

The reactor is heated by five Nichrome V beaded wire heaters located as indicated in Figure 3. The power input to each heater is manually controlled by adjustment of five powerstats. The powerstats controlling the power input to heating zones 3 and k are automatically controlled by the temperature controller which continuously monitors the temperature at TC-1. Constant voltage is maintained to the control circuit by use of a constant


36

voltage transformer.

The entire reactor is insulated with approximately ^ in. of refractory rope and 2 in. of magnesia covered with an aluminum sheath.

CondenserThe reaction products, cumene, benzene and propyl

ene, enter the condenser from the reactor at approximately 650-1050°P. whereupon they are cooled to approximately 75°P. The cumene and benzene are condensed and collected and the propylene, which remains in the vapor phase at this temperature, is vented to the atmosphere.

Ultrasonic HornThe ultrasonic horn is 3 in. in diameter and is

mounted directly atop the reactor by means of a specially fabricated 3 in. by 1 in. adapter flange. The horn is driven by a variable frequency ultrasonic generator with a variable output frequency of 10 ,000 to 50,000 cps.

The maximum operating temperature of the piezoelectric transducer which drives the horn is 300°C.(572°F.) and the minimum allowable operating temperature of the horn to prevent condensation of the highest boiler, cumene, is 153°C. (308°F.). Therefore, it is necessary to maintain the temperature of the ultrasonic horn at approximately 175°G. This is accomplished by recirculating


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

FIGURE 4ULTRASONIC HORN

TI

Waterm

Heated surge pot

Cooler Ultrasonichorn

Recirculationpump

38

heated, oil through the cooling chamber of the ultrasonic horn as illustrated in Figure 4.

The oil is recirculated, through a water cooled, heat exchanger to the ultrasonic horn cooling chamber and thence to an electrically heated surge pot by means of a 1 gpm centrifugal pump. By proper adjustment of the power- stat controlled electric heater and oil flow to the cooler, it is possible to maintain the recirculating oil at approximately 175°C.

PipingAll piping consists of \ in. stainless steel threaded

pipe and fittings and \ in. copper tubing with compression type fittings. Teflon tape is employed on all threaded connections.

Analytical InstrumentationThe quality of the effluent product is analyzed by

use of a gas-liquid chromatograph in conjunction with a single pen strip chart recorder. The chromatograph response was standardized daily by injecting and analyzing a known sample. The analytical system is designed to handle either gas samples taken from the reactor effluent prior to condensation or liquid samples from the condenser effluent. The analysis of the liquid samples proved to be almost identical to that of the gaseous sample. Comparative analyses and conversion calculations are shown in Appendix IX.


TABLE 3

EQUIPMENT SPECIFICATIONS

Feed Tank No. 1ManufacturerMaterial of construction LengthWorking pressureDiameterCalibration

Corning Glass Co. Pyrex conical pipe 36 in.50 psig, max.1 in.10.79 gms. cumene/in

Feed Tank No. 2ManufacturerMaterial of construction LengthWorking pressureDiameterCalibration

Feed RotameterManufacturer Model No.Meter size TypeSerial no.Tube no.ScaleWetted partsPackingO-ringsValve needle taper no. Orifice type Connections Float material Maximum flow rate

Float MaterialGlass Sapphire Stainless steel Carboloy Tantalum

Corning Glass Co. Pyrex conical pipe 36 in.50 psig, max.1§ in.2^.66 gms. cumene/in

Brooks Instrument Co 1357-8506 21357-01F1BAA 7010-^8800 R-2-25-D 250 mm.Stainless steelTeflonKel-F3Small4 in. NPT Sapphire

Gm./Hr. Cumene355 6^0

1,267 2,130 2,300

Calibration (Sapphire float): Figure 5


4 0

TABLE 3 (continued)


Air RotameterManufacturer Tube no.Type no.Serial no.Scale (direct calibration)

Fischer & Porter Co. 02-F-1/8-12-5/70 TII-1077/1-2 TII-1077/10 -6 scfm hydrogen at | psig and 75 P.

ReactorMaterial of construction Overall length Outside diameter Preheater

Material ofConstructionLengthOutside diameter Inside diameter

Catalyst Chamber Material of construction LengthOutside diameter Inside diameter

Type 316 stainless steel 27i in.2 .0 0 0 in.

Type 316 stainless steel 20lr in.2 .000 in.0 .302 in.

Type 316 stainless steel 4 in.2.000 in.0.391 in.

Temperature RecorderManufacturerTypeRangeNo. of points Model no.Serial no.

Temperature Controller

Westronics Inc. Strip chart 0-1200 F.12MIIB/J/DV.5MMIIB336

ManufacturerTypeVolts/cycles Catalog no. Serial no.

Leeds & Northrup Co. Speedomax H 120/60200-901-010-0023-6-024-065-35480-1-1


41

TABLE 3 (continued)


Temperature Controller (continued)Range Chart no.Chart speed Response time Controller series

0-2000 F .6200231 revolution/24 hrs.5.0 seconds, full travel 60

HeatersManufacturerTypeCatalog no. Length, each Power, each Temperature

Cole-Parmer Instrument Co, Beaded Nichrome V wire 3116-1 12 ft.400 watts 2000°F., max.

PowerstatsManufacturerTypePhaseInputOutputAmps, max.Kva, max.

Constant Voltage TransformerManufacturer Catalog no.Type no.PrimarySecondary

Superior Electric Co. 116Single120 volts, 50 /60 cps 0-140 volts 91.3

Sola Electric Co. 20-13-150 D476 CUN-195-130 volts, 60 cps,

single phase 118 volts, 4.24 amps

Refractory RopeManufacturer Style no. Temperature

Johns-Manvilie Thermo-Pac 2300 2300°F., max.


kz

TABLE 3 (continued.)


CondenserMaterial of constructionTypeLengthShell sideTube sideConnectionsCoolant (shell side)Surface area

Ultrasonic Horn

Type 316 stainless steel Tube and shell 36 in.1 in. sched. ^0 pipe1 -5 in. sched. -0 pipe i in. NPT Water 0.^23 ft . 2

Manufacturer Macrosonics InternationalMaterial of construction Type 316 stainless steelModel no.TypeFrequency range Acoustic energy InputSound levelNominal impedenceEfficiencyLengthDiameterWeightOperating temperature Serial no.

Ultrasonic GeneratorManufacturer Model no.Volts /cycles Amps/phase Frequency rangePower output Output impedence Weight Serial no.

FH-15-0 Oil cooled10,000 cps to 100,000 cps25 watts100 wattsAbove 166 db^-00 ohms25%18 in.3 in.11 lb.300°C. max.70-12

Macrosonics International150 LF120/50-60^/single1 0,000-50 .000 cps (Figure 6)20-80 watts 200-^-00 ohms 38 lb.00^05


AC

TABLE 3 (continued)


Heat Transfer OilManufacturerTypeOperating temperature

Thermometer. TI-7ManufacturerTypeRange

Recirculation PumpManufacturerMaterial of constructionModelTypeHorsepowerRpmCapacity

Oil CoolerShell Side

Material of construction Diameter Length

Tube SideMaterial of constructionDiameterLength

Heated Surge PotMaterial of constructionDiameterLength

Gas-Liquid ChromatographManufacturerModel

Monsanto Chemical Co. Therminol FR-1 700°F., max.

Weston Stem and dial 0-300OC.

Eastern Engineering Co. Carbon steel Dll 100 1/8 3,^501 gpm

Type 316 stainless steel 2 in. Sched. ^0 pipe 36 in.Copper £ in.70 turns, 1 in. diameter

Type 316 stainless steel 2 in. sched. ^0 pipe 12 in.

Varian Aerograph Co. A-90-P


TABLE 3 (continued)


Gas-Liquid ChromatographTypePart no.Serial no.Column

Strip Chart Recorder Manufacturer TypeModel no.Range Chart no. Volts/cycles Serial no.

NitrogenManufacturerGrade

AirManufacturerGradeHydrocarbons

HeliumManufacturerGradeHydrocarbons

(continued)Manual temperature

programmer 90P3 3^3-02610$ Carbowax, 20 mesh,

on chrome-W

Minneapoli s-Honeywell Regulator Co.

Single pen strip chart recorder

15307856 - 01 - 05 - 0 - 000 -

030-07136-0 .05 to + 1 .05 mv 9283-NR 120/60 02003303008

Matheson Gas Products Extra dry

Matheson Gas Products Ultra zero 0.1 ppm max.

Matheson Gas Products Zero2 ppm max.


k5

M

o

o

■oo oooo oCM CM tH tH

' UIUU *3utpB0H J0^SUJB^Oa


TDD

TOD

W>

TOD

50D

ouD

7UD

Cumene,

gras/hr.

Freq

uency, 1,000

cps

4-6

FIGURE 6

ULTRASONIC GENERATOR FREQUENCY CALIBRATION

High

Mediuri

20

10

10020Dial Setting


4 7

CHAPTER IV

EXPERIMENTAL PROCEDURE

Operating ConditionsThe operating conditions studied in this investiga

tion were temperatures of 650°F. to 1050°F., feed rates of 20 to 600 gms./hr., catalyst loadings of 0.958 to 5.748 gms., ultrasonic frequencies of 26,000 cps and39,000 cps, and power outputs of 0 .05 to 1.3 ~ ^ ,s.The general procedure followed was to obtain the desired reactor temperature and then feed the cumene at a predetermined rate and catalyst loading. Each run was operated at two different ultrasonic frequencies and in the absence of ultrasound.

General ProcedureThe reactor was purged with air at reaction tempera

ture after each run for a period of approximately 24 hours to burn off any carbon deposit and regenerate the catalyst. Calculations indicate (Appendix XIII) that 10 minutes should be sufficient to burn off the carbon and visual inspection of the reactor after regeneration for 30 minutes indicated it to be free from carbon. Comparison of conversions in the absence of ultrasound between runs employing the same catalyst after many regenerations and nearly the same operating conditions also indicated complete reactivation. For example, comparing Run No. 14.83 with Run No.


48

22.135 shows conversions of 4.5$ and. 4.2$ at feed rates

of 593 gms./hr. and 622 gms./hr., respectively, all other conditions being identical. Similar checks are observed

in many other runs, for example Run No. 33*23 and 36.53*The reactor was also purged with nitrogen after each run and

after each air purge in order to avoid the safety hazard of

hot cumene in the presence of air.

Each time the sonic frequency was changed during a

run, the product collected during the first ten minutes was

discarded and the product produced during the second ten

minutes was blended and sampled as representative of those

operating conditions. Previous work has shown that any de

crease in catalyst activity during a run of this length of

time could be neglected.

Temperature control. The temperature of the reactor

was controlled by manually adjusting two voltage regulators

which monitored the power input to the heating elements

along the preheater section. The catalyst chamber tempera

ture was controlled automatically by an on-off temperature controller connected in series with two additional voltage

regulators which monitored the power input to the heating

elements along the catalyst chamber. The temperature for

this control point was sensed by a thermocouple located in

the catalyst chamber itself (see Appendix XV). A fifth manu

ally operated voltage regulator was employed to control a

heating element located on the product discharge piping.


4 9

The heaters were never turned off so that the reactor was always at temperature equilibrium. When the reactor temperature was changed, approximately 24 hours was allowed for the catalyst bed to again reach temperature equilibrium.

Feed rate control. The cumene feed rate was controlled by pressurizing the feed tank to 10 psig with nitrogen and recording the tank level and time at the start and end of each run. The flow rate was controlled by the feed flow rotameter, but the rate used in any subsequent calculations was the rate obtained by difference of the calibrated feed tank level.

Application of ultrasound. Each run was operated first in the absence of ultrasound and then the ultrasonic generator was activated and frequencies of 26,000 cps and 39,000 cps were irradiated upon the catalyst bed. The order in which the higher and lower frequencies were employed was reversed many times throughout this study.Each run was operated in the absence of ultrasound after each of the frequency activated samples had been taken as a check for decrease in catalyst activity from the start to the end of the run. The analyses of the first and last sample, i.e., the samples taken in the absence of ultrasound were always essentially the same.

Sample analyses. In many instances, the gas stream was fed directly to the gas chromatograph for analysis as


50

a check against the liquid sample analysis. In all cases, both methods of analysis yielded essentially the same conversion calculation. The analysis of liquid samples was preferred, because the same sample was injected a minimum of three times into the gas chromatograph as a check of the analytical technique. The vapor sample, of course, could be injected only once.

The size of the gaseous sample was controlled by filling a small tubing coil with the reaction products and flushing’ the entire coil contents into the chromatograph with helium. Sample size of the liquid was controlled by use of a 10 microliter hyperdermic needle calibrated in 0.2 microliters. The analyses of known liquid samples were duplicated within 1%, indicating sample size control to be adequate.

Detailed ProcedureThe details of the experimental procedure for a typi

cal run are as follows:1. Set the reactor air purge rate at 6.0 scfh

employing the air flow rotameter.2. Adjust the heater controls to obtain the desired

reactor temperature.3. Adjust the automatic temperature controller set

point to the desired reactor temperature.4. Allow approximately 24 hours for the reactor to

equilibrate at the desired temperature.


51

5. Turn on the hot oil recirculation pump and adjust the heater control to maintain the oil at 155-l60°C.

6. Turn off the air purge and purge the reactor with nitrogen for 20 minutes.

7. Shut down the nitrogen purge and pressurize the cumene feed tank to 10 psig with nitrogen.

8. Peed cumene to the reactor at the desired rate employing the feed flow rotameter to monitor that rate.

9. Record the feed tank level and time.10. The first product will appear in 5 to 10 minutes.

Discard the product obtained during the first 10 minutes and collect, blend and sample the product obtained during the second 10 minutes.

11. While maintaining all other operating conditions constant, activate the ultrasonic generator and adjust it to the desired frequency.

12. Discard the product obtained during the first 10 minutes and collect, blend and sample the product obtained during the second 10 minutes.

13. While maintaining all other operating conditions constant, readjust the ultrasonic generator to another frequency.

1^. Discard the product obtained during the first 10 minutes and collect, blend and sample the product collected during the second 10 minutes.

15. While maintaining all other operating conditions constant, shut down the ultrasonic generator.


52

16. Discard the product obtained during the first 10 minutes and collect, blend and sample the productcollected during the second 10 minutes.

17. Record the feed tank level and time.18. Shut off the feed and purge the reactor with

nitrogen for 20 minutes.19. Shut down the power to the hot oil heater and

shut down the recirculation pump.20. Shut down the nitrogen purge and set the air purge

rate at 6.0 scfh employing the air flow rotameter.21. Air purge the reactor for 24 hours at the reaction

temperature prior to starting the next run.22. Thoroughly blend each of the four samples obtained

in steps 10, 12, 14 and 16 to insure uniformity within each sample. Inject a portion of each of the samples three times into the gas chromatograph and calculate the conversion. If the calculated conversion of the samples obtained from steps 10 and16 do not agree within discard the run.(This was never necessary.)

The data sheet employed for this study is shown in Figure 7. Copies of several actual completed data sheets are included in Appendix XIV.


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

FIGURE 7 DATA SHEET

nun n o . Reactor Diameter, cm.Date Frequency, cosCatalyst, gms. Power, wattsBed Height, cm. Feed Tank Diameter, in.TimeTank Height, in.Rotameter, mm.Rota. Feeri Rata, grns/hr*.Tank Feed Rate,'gms/'hr.Heater No. 1Heater No, ?Heater No. RHeater No. 4Hot Oil HeaterTI-1r op.TI-2. °F.TI-3. °F.Tl-k. op.

h3 H 1 1 o ►

TI-6; op.TI-7. op. (Hot Oil)TC-1t of.UltrasoundW/F. erm cat-sec/em moleCumene T %Benzene. %Proovlene r %Conversion, X

5 4

CHAPTER V

EXPERIMENTAL RESULTS

Presentation of All DataAll the data collected (Appendix XIV) are presented

herein as plots of conversion versus reciprocal space velocity. The best curve fit of the data was calculated for each temperature and frequency employed by the quadratic regression equation:

x = a + b (W/F) + C (W/F)2 (21)

Since the external mass transfer rate is dependent upon feed rate, the equations of these curves are later employed to determine conversion at specific reciprocal space velocities for the calculation of mass transfer coefficients .

The three constants obtained for each condition are shown in Table k. The plot of the curves showing all the data points are in Appendix XVI and the plots for each family of three curves for each frequency are shown for all the temperatures studied in Figures 8 through 16.The data points are omitted for clarity. It is noted that although several of the curves cross at low reciprocal space velocity, the actual data indicate higher conversions at higher frequencies in every case. This is because the shape of the quadratic curves near the origin often does not precisely fit the data points.


55

t a b l e Bi

q u a d r a t i c EQUATION CONSTANTS

Temp.°F.

cps x 10“3 Power a b x 106 C x 101'

650 39 full -0.000959 1.74- -0.91650 26 full -0.00605 1.76 -1 .06650 - off -0 .0066^ 1.75 -1 .10700 39 full 0.0309 1.4-5 0.590700 26 full 0.0253, 0.923 0.790700 - off 0.0205 0.958 0 .650

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Full power = 25 wattsHalf power = 12.5 watts


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65

Conversions obtained at temperatures above 850°P. decreased slightly at higher temperatures at some feed rates indidicating partial coking of the reactor. Although some date were collected at 1050°F., coking of the reactor and catalyst at this temperature caused considerable mechanical difficulty with the apparatus. Therefore, attempts to study the effect of ultrasound at 1050°F. were abandoned.

The quadratic curves presented herein are employed for future calculation purposes only and should not be construed to represent a theoretical model of the reaction mechanism.

It will be shown that on the upper portion of the quadratic curves, at low feed rates, external bulk diffusion is the controlling factor for the reaction rate. On the lower portion of the curves, at high feed rates, the combined effect of surface reaction and internal pore diffusion control the rate of reaction.

Although the quadratic curves show a decrease in conversion at lower acoustical power inputs at low flow rates, it will be shown later that there is, in fact, negligibleeffect on either the mass transfer coefficient, k , or the

’ g*kinetic rate constant, (fLkg.


66

External Diffusion ControllingWhen external bulk diffusion controls the rate of re

action, the mass transfer coefficient, k , is the controlling factor. The mass transfer coefficient is calculated from the following equation derived in Chapter II and Appendix IV:

6.26 XAf TkS = ( W/FAq) ln( 1 + Ya lm) (2?J

The mass transfer coefficient was calculated at three different feed rates corresponding to reciprocal space velocities of 20,000, 50,000 and 80,000 'Ca^"S-— ---. The re-7 , 7 7 gm molesuits of these calculations are shown in Table 5*

Temperature effect. As is shown in the AppendixVI, the mass transfer coefficient is an exponential function of temperature. Therefore, a plot of the logarithm of the mass transfer coefficient versus temperature should yield a straight line. This, in fact, is the case as illustrated in Figures 17 through 22. The equations of the straight lines as obtained by the method of least squares are shown in Table 6. The calculation of the confidence intervals shown in Table 6 is demonstrated in Appendix XXII.

As shown in the graphs, the mass transfer coefficients calculated at 650°F. (6l6°K.) and 700°F. (6*l40K.) fall well below the theoretical curve. The reason for this phenomenon is because external bulk diffusion no longer controls the


Reproduced

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TABLE 5MASS TRANSFER COEFFICIENT

Temp.°F.

fcps

x 10"3 Power

W/20,000

'fa0 =gm cat-sec.

W/50,000

'FA0 = gm cat-sec.

W/80,000

'PA0 = gm cat-sec

pm mole gm mole gm molexAf k , cm* g ’ sec. *Af k cm* g ’ sec. xAf k , ^ ELi- g* sec.

650 39 Full 0.030 0.0085 O.O63 0.0073 0.080 0.0059650 26 Full 0.025 0.0071 0.056 0.0065 0.067 0.004-9650 - Off 0.024- 0.0068 0.053 0.0061 0.063 0.004-6700 39 Full 0.062 0.0180 0.118 0.014-9 0.185 0.0154-700 26 Full 0.0^7 0.014-1 0.091 0.0113 0.150 0.0122700 - Off 0.04-2 0.0126 0.085 0.0105 0.139 0.0112750 39 Full 0.159 0.054-1 0.307 0.04-66 0.388 0.039275 0 26 Full 0.126 0.04-19 0.259 0.0379 0.335 0.0325750 - Off 0.120 0.0397 0.252 0.0367 0.318 0.0304-800 39 Full 0.155 0.054-8 0.286 0.04-4-5 0.374- 0.0389800 26 Full 0.129 0.04-4-8 0.24-9 0.0377 0.333 0.0336800 - Off 0.122 0.04-21 0.24-1 0.0363 0.322 0.0322850 39 Full 0.203 0.0772 0.378 O.O656 0 .4-4-6 0.0511850 26 Full 0.183 0.0686 0.333 0.0588 0.380 0.04-13850 - Off 0.171 0.0635 0.306 0.0502 '0.339 0.0357850 39 Half 0.191 0.0720 0.299 0.04-89 0.372 0.04-02850 26 Half 0.185 0.0694- 0.286 0.04-62 0.351 0.0373850 - Off 0.171 0.0635 0.269 0.0^30 0.339 0.0357900 39 Full 0.187 0.0730 O.3O8 0.0526 0.395 0.04-51900 26 Full 0.158 0.0604- 0.259 0.04-26 0.339 0.0370900 - Off 0.178 0.0690 0.300 0.0509 0.365 0.04-07950 39 Full 0.179 0.0720 O .368 0.0683 0.526 O.O696950 26 Full 0.184- 0.07^3 0.356 0.0654- 0.4-51 0.0559950 - Off 0.170 0.0680 0.321 0.0574- 0.392 0.0^63 ,1000 39 Full 0.270 0.1203 - — -

1000 26 Full 0.265 0.2277 — — — —

1000 - Off 0.24-9 0.1092 - - - -

Note: Full power = 25 watts, half power = 12.5 watts

Reproduced

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TABLE 6CONSTANTS OF THE EQUATION OF MASS TRANSFER COEFFICIENTS

AS A FUNCTION OF TEMPERATUREGeneral Equation: log k = bT + a

w/Fa0

Km cat-sec gm mole

f X10~3CPS a b

99/o Confidence Interval

95$ Confidence Interval

90$ Confidence Interval

ApproximatConfidence

a b a b a b a b80,000 — -2.66 0.00169 0.05 0.00007 0 .03 0.0000*4- 0.02 0.0000380,000 26 -2.75 0.00185 0.28 0.00038 0.15 0.00021 0.11 0.00015 75$ 90$80,000 39 -2.80 0.00203 0.31 0.000*4-2 0.17 0.00023 0.12 0.00017 90$ 97$50,000 - -2.7*4- 0.00193 0.19 0.00026 0 .10 0.0001*4- 0.08 0.00011 - -50,000 2o -2.71 0.00190 0.39 0.0005*4- 0.21 0.00029 0.16 0.00022 30$ 25$50,000 39 -2.32 0.001*4-6 0.28 0.000*4-3 0.15 0.00023 0.11 0.00017 97$ 9 Wo20,000 - -3.39 0.0029*4- 0.05 0.00008 0.03 0.00005 0.02 0.0000*4- - -20,000 26 -3.36 0.00293 0.20 0.0002*4- 0 .12 0.00015 0.09 0.00011 52$ 15$20,000 39 -2.99 0.00253 0.31 0.00013 0.19 0.00008 0.1*4- 0.00006 99$ 99$

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78

rate of reaction at these low temperatures. In fact, even at these low flow rates, surface reaction is so slow at 650°P. and 700°F. that it becomes the controlling factor in the overall reaction rate. At above 850°F. (727°K.) surface reaction rate is very rapid and external bulk diffusion controls the rate of reaction.

Ultrasonic effect. The family of three curves showing each frequency is plotted at the three feed rates in Figures 23, 23A and 2k. In all cases, the mass transfer coefficient and hence the reaction rate is increased with the application of ultrasound. The mass transfer rate also increases at the higher frequencies. For example, at a reciprocal space velocity of 80,000 ^g ^ 'moTe'8'0 ‘ an(i a frequency of 39,000 cps, the mass transfer coefficient is increased by 377 at 1000°F. The increase of mass transfer rates at other conditions are shown in Table 7.

Since in this range of feed rate and temperature reaction rate is directly proportional to the mass transfer coefficient, the results illustrated in Table 7 also apply to reaction rate.

At high feed rates and low temperatures where surface reaction begins to control the rate of reaction, high frequency sound waves appear to have a much greater effect on the reaction rate than at higher temperatures where mass transport controls. This phenomenon is indicated in the


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FIGURE 24

NASS TRANSFER COEFFICIENT vs. TEMPERATURE- 1.0

39,000 cps

- 1.2:f = 26,000 cps

noultrasound

iw/F = 80,000 ' ’ .gm. mole

- 1.6

600 800650 850750700Temperature, °K.

82

TABLE 7

INCREASE IN MASS TRANSFER COEFFICIENT AT SEVERAL FEED RATES, TEMPERATURES AND ULTRASONIC FREQUENCIES

W/FTemp., ft %Increase

%gm mole F . cps Power of :

80,000 650 26,000 Full 2 .080,000 850 26,000 Full 6 .280,000 850 26,000 Half 9.780,000 1000 26,000 Full 9.680,000 650 39,000 Full 2 .280,000 850 39,000 Full 20.580,000 850 39,000 Half 18.280,000 1000 39,000 Full 36.750,000 650 26 ,000 Full 2.750,000 850 26,000 Full 1.950,000 850 26,000 Half 0.750,000 1000 26 ,000 Full 1.350,000 650 39 ,000 Full 35.050,000 850 39,000 Full 19.750,000 850 39,000 Half 13.750,000 1000 39,000 Full 9.520,000 650 26,000 Full 5.720,000 850 26,000 Full 5.420,000 850 26,000 Half 3.720,000 1000 26,000 Full 5.220,000 650 39,000 Full 40.420,000 850 39,000 Full 26.420,000 850 39,000 Half 28.820,000 1000 39,000 Full 16.8

Full power = 25 wattsHalf power = 12. 5 watts


83

data of Table 7 at reciprocal space velocities of 20,000

indicate that ultrasound has a greater influence upon pore diffusion and surface reaction rate than upon external mass transport.

The data points on the graphs represented by triangles are those obtained with the ultrasonic generator operating at half power. Since these points fall on the theoretical curve developed for full power within the 90% confidence interval, it is concluded that power input has no effect on the external mass transfer rate for the range of power input studied in this research.

Surface Reaction and Pore Diffusion Controlling

Reaction rate model. The reaction design equation for surface reaction controlling and propylene not adsorbed as derived in Chapter II is as follows:

gm cat-sec. gm mole and frequencies of 39,000 cps. These data

(1+XA6) XA (l -xA5) 6 2 (23)

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The literature values of K, and are substituted into the surface reaction rate equation and the values of ^Lkg are calculated at each temperature as described in Appendix VIII. All the theoretical curves and the associated data points are also shov/n in Appendix VIII, and the data do, in fact, fit the theoretical model very well.

Ultrasonic effect. When surface reaction controls the rate of reaction, the application of ultrasound increased that rate by increasing the kinetic rate constant, CLk^, which is directly proportional to the overall rate of reaction. The evaluation of the effectiveness factor based upon physical characteristics of the catalyst is shown in Appendix VI.

The graphs of conversion as a function of reciprocal space velocity as calculated by the reaction rate model are as illustrated in Figures 25 through 33. As illustrated by the graphs, the conversion is increased in the presence of ultrasound at every temperature studied. At temperatures above 900°F., the decrease in conversion at some flow rates again indicates possible coking of the reactor.

Table 8 shows the increase in the factor ^ k g at several ultrasonic frequencies and temperatures.


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T A B L E 8

INCREASE OF KINETIC RATE CONSTANT AT SEVERAL TEMPERATURES AND ULTRASONIC FREQUENCIES

9 4

T.. °F.650750850900

% Increase of (f L 2

26,000 cps36%20%

9%4^

39,000 cps 162$

39%

22%

TABLE 8ACONSTANTS OF THE EQUATIONS OF KINETIC RATE CONSTANTS

AS A FUNCTION OF TEMPERATURE

General Equation: log £Lk0 = b T + a

Frequency, cpsNo

Ultrasound 26.000a -1.141 -1.6371.04299% confidence interval 1.06295% confidence .interval 0.677 0.66490$ confidence interval 0.531 0.521b -4812 -411599% confidence interval 1343 131895$ confidence interval 8 57 84090$ confidence interval 671 659Approximate confidence — 65$

39,000-2.53^

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-2801108869454491%


95

For example, at 650°F. an ultrasonic frequency input of 39,000 cps increases the catalyst effectiveness factor by 162#.

Activation Energy

Arrhenius model. The activation energy, E, is calculated from the Arrhenius Law, employing the combined parameter, Llc2 , as rea°kion ^ate constant.

JL£Lk2 = kQe“RT (27)

Figures 3^ through 37 show the logarithm of the parameter £ L k 2 plotted against reciprocal temperature. These plots yield a straight line, the equations for which, calculated by the method of least squares, are as follows and as shown in Table 8A.

No ultrasound: log £Lk0 = -4812 —^— -1.141 (28)2 t or>

26.000 cps: log £ L k 0 = -in 15 — -1.637 (29)d T R .

39.000 cps: log £ Lk? = -2801 -pj— -2 .53^ (3 0)c T R .


96

These calculations, which are described fully in Appendix XVII, yield the values for the observed apparent activation energy as shown in Table 9*

The data in Table 9 indicate that both the observed apparent activation energy and the observed apparent frequency factor decrease as the ultrasonic frequency rises. However, an analysis based on the Thiele modulus would indicate that if ultrasound improves the effectiveness factor, then the apparent activation energy should rise and approach the real activation energy based on kg since € becomes closer to one.

To determine the real effect of ultrasound on and kg, it is suggested that further studies with small particle sizes be made (£~1) to separate these effects.


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T A B L E 9

ACTIVATION ENERGY AND CHARACTERIZATION FACTOR

Frequencyf

Activation Energy, E

kcalCharacter. Factor, kQ gm moles

cps gm mole p;m cat-sec. InvestigatorNo Ultrasound 11 .0 - Eberly 101

No Ultrasound 34.0 - Bezre^No Ultrasound 27 .0 -

0 /:Spozhakina

No Ultrasound 18.0 - TORomanovsknNo Ultrasound 3.0 - Panchenkov"^No Ultrasound 13-2 0.0021 64RaseNo Ultrasound 5.4 0.0700 22GarverNo Ultrasound 12.1 0.0723 Lintner26,000 1 0. 4 0.0231 Lintner39,000 7.1 0.0029 Lintner


102

Table 9 also illustrates the values of activation energy and characterization factor obtained by several other investigators. Considering the wide range of values obtained by other observers, the value calculated by these data appear to be reasonable. It is interesting to note that the total ultrasonic power input to the reactor ranged between ^ .3 and 103.^ which bracketedgm molethe activation energy.

Ultrasonic effect. As shown in Figure 37, the value of the effectiveness factor parameter, (fLkg, increases with increasing frequency. At low values of reciprocal temperature or high values of temperature, the values of

become equal at all frequencies because surface reaction rate no longer controls. At high temperatures, surface reaction rate is very rapid and bulk diffusion from the main gas stream to the surface of the catalyst controls the overall rate of reaction.

The values of 6 Lk^ obtained at half the power output of the equipment are plotted as triangles on the graphs for frequencies of 26,000 cps and 39,000 cps. The plots indicate that this decrease in power input has negligible effect on the value of

Summary of ResultsIn general, all the data lead to identical conclusions.

Ultrasound increases the rate of reaction ahd the reaction


103

rate increases with increasing frequency. Power input has negligible effect on the rate of reaction for the range studied.

Throughout the range of feed rates and temperatures studied, external bulk diffusion controls at low feed rates and high temperatures and conversely, surface reaction controls or pore diffusion at high feed rates and low temperatures. These phenomena are illustrated in Figure 38.

It should be noted that when the dimensions of € Lkg are transposed from t0 > as shown lnAppendix XVIII, it can be plotted as a function of temperature as illustrated in Figure 38. In this figure,CLkg is described as the intrinsic reaction rate constant, k . The scale of the abscissa has been altered to ’ scorrespond to k ,, the mass transfer coefficient scale.This alteration is necessary because the 6 Lk2 term is not a function of k^, the forward rate constant, alone, but also of 6 and L, the catalyst effectiveness factor and the concentration of active sites on the catalyst surface.

Acoustic StreamingThis research shows for the first time that the ap

plication of ultrasonic vibrations to a solid catalyzed gas reaction results in an increased reaction rate with increasing frequency as a result of increased diffusion rates. The diffusion rate is increased both externally from the


104

FIGURE 38

RATE CONSTANTS vs. TEMPERATURE

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Surface Reaction-3.0Controiling

80,000

Extsrnal Diffusion6 Controlliri;

no ultrasound39,OC 0 cps

650 800 850700 750oTemperature K

cn


Lon; k

105

bulk gas stream to the catalyst surface and internally within the catalyst pore.

20Fogler and Lund have independently offered a mathematical explanation for this phenomena which they have identified as acoustic streaming. Their mathematical model states that within a duct, through which there is a concentration gradient, mass transfer occurs by molecular diffusion alone. However, when ultrasound is applied to the duct, small vortex cells are set up in which the gas moves circularly similar to eddy currents. This forced convection within each cell coupled with diffusion between cells results in a faster transport rate within the duct than with diffusion alone.

If one assumes the duct to be a tubular reactor shell or the pore of a catalyst, this model explains the results and conclusions of this research.

Thermal EffectsThe application of acoustic energy to a catalyst bed

may cause "hot spots" within the bed and thereby result in localized accelerated reaction rates. This thermal effect alone or together with increased diffusion rates may explain the increase in reaction rate observed in this research.


106

CHAPTER VI

CONCLUSIONS

The effect of ultrasonic vibrations on heterogeneous catalysis may be summarized as follows:

1. All the data collected at all temperatures and frequencies yield quadratic curves when plotted as conversion versus reciprocal space velocity.

2. In the area where external bulk diffusion controls the rate of reaction, the logarithm of the mass transfer coefficient is a linear function of temperature at all ultrasonic frequencies.The mass transfer coefficient and, therefore, the rate of reaction increases with increasing ultrasonic frequency.

3. In the area where surface reaction and internal pore diffusion control the rate of reaction, the data fit the reaction rate model previously derived by Garver at all frequencies and temperatures, The kinetic rate constant, CLkg, increases with increasing frequency.

5. The activation energy calculated from these data decrease with increasing frequency.

6. Power input appears to affect the rate of reaction in the plots of conversion versus reciprocal space


107

velocity at low feed rates. However, in the logarithmic plots of mass transfer coefficient and kinetic rate constant versus temperature, the effect of power is not statistically significant for the range studied.

7. The increases of mass transfer coefficients and kinetic rate constants obtained at a frequency of 39,000 cps are statistically significant within confidence intervals of 90^. The results obtained at 26,000 cps lie within confidence limits of 50 to 60%, but the raw data lead this author to believe that the lower frequency also increases the rate of reaction.


108

CHAPTER VII

RECOMMENDATIONS

This research demonstrates for the first time the quantitative effect of ultrasonic vibrations on the rate of a solid catalyzed gas reaction. It further demonstrates that this reaction rate is increased in the reactant feed flow range where external bulk diffusion controls and in the range where internal pore diffusion is the controlling factor. Increasing ultrasonic frequency results in faster reaction rates, and power input in the range studied has negligible effect. These phenomena have never previously been quantitatively demonstrated.

It is this author's hope that this research will influence other investigators to continue studies of the effect of ultrasonic vibrations on heterogeneous catalyzed reactions. The areas recommended for further study are as follows:

1. Employ the use of powdered catalyst (Appendix XII) to obtain an absolute value for the forward reaction rate constant, kg. The absolute values of the effectiveness factor, €, could then be calculated at various operating conditions employing standard catalyst. It would then be possible to determine the effect of ultrasound on each parameter alone.


109

112. Study frequencies up to 10 cps and power inputsto 120 •- to expand the range of this study,cm.It is now possible to obtain these conditions with modern ultrasonic equipment, but this equipment is, of course, considerably more expensive.

3. Study the effect of ultrasonic vibrations on systems other than the cumene cracking reaction and silica-alumina catalyst.

k . Investigate the possible thermal effects on the datalyst due to the application of ultrasonic energy.


APPENDIX I

PHYSICAL PROPERTIES OF CUMENE, BENZENE AND PROPYLENE


I l l

PHYSICAL PROPERTIES OF CUMENE. BENZENE AND PROPYLENE

The overall chemical reaction and some of the physical properties of the reactants and products, both published and calculated, are as follows:

Reactionc 6h5-ch-(c h 3)2

ACumene

C6H6 + CH3-CH=CH2

R + S Benzene and Propylene

Physical Properties

M gms__* gm moleSpGMP, °C.BP, °C.° P a t 65 0 ° F . , i i S § § 7

Cp at 1050°F., g S S L Cv at 650°P. ,

ov at io5o°p.,Tc> o k .v — cm2___b* gm molePn , atm.0 3

V _________ ...C* gm moleo

S T , A

Cumene Benzene Propylene120.19 78.11 42.08

0.862 0.879 -

-96.9 5.4 -185152.5 80.1 -48

0 .588 0.541 0.6240.736 0 .682 0.7560.571 0.515 0.5760.719 0 . 65 6 0 .7 0 8

636 .0 5 6 2 .6 365 .0

162.6 9 6 . 0 66 .6

32.2 48.6 4 5.5357 260 181

6.43 5.27 4.678


1 1 2

Cumene Benzene Propylene£a/K, °K. 490 ^40 298 .9

^ C » o Z l e o . 315 X 1 0 -6 312X 10 -6 233 x 1 ( T 6

ÂR’ AS * ~ 5.85 5.55^ a r / k ’ â s / k » ° k * - ^ 383

KT650/ AR» KT650//fAS, K ‘ “ 1.328 1.608KT

-ÂR

1050/ AE * KT1050ÂS» K * " 1 .808 2 .190

6 5 0* \p-as] 650 “ 1.262 1.165

' 3-ArJ 1050^-Âs] 1050 “ 1 .11^ 1.04-3

[d ab] 6 5 0» [d ar] 6 5 0»

[d as] 650» fiSr °*11M °*°956 °-1/u6dab] 1050’ [d ar] 10 50»

1 05 0* °-20^ ° * 1?22 0 .2513d as

Calculation of Critical Temperature of Cumene by the Method of Ed.ul.jee 58

100TTC “ <3U

= normal boiling point = 152.5°C. = 4-25.5°K. Edujlee's contributions:

£At = 9 tc + + 3A tc=q + A THing+ A TP


113

Arp = Eduljee atomic contribution by carbon = -55.32= Eduljee atomic contribution by hydrogen = +28.52

^ TC=C = Eduljee structural contribution by carbon- carbon double bond

= + 56.61

^TRing = Edujlee structural contribution by benzene ring

= +53.52A r p p = Eduljee position contribution by two branches

on the second carbon atom = -1.42

E A t = 9(-55.32) + 12(2 8.5 2) + 3(5 6.6 1) + 53 .52 - 1.42 = 66.29

Tc = = 642°K -

Calculation of Critical Temperature of Gumene by the56Method of Nokay

log Tc = 1.2806 + 0.2985 log S + 0.62164 log Tb (32)

S = specific gravity of liquid = 0.862 cm. jTb = normal boiling point = 152.5°C. = 76 6.9°R.


114

log Tc = 1.2806 + 0.2985 log(0.862) + 0.62164 log(766.9) = 1.2806 + 0.2985(-0.06449) + 0.62164(2.88474)= 1.2806 - 0.01925 + 1.79327 = 3.05462

Tc = H 3 4 °r . = 674°F. = 357°G. = 630°K.

Calculation of the Molar Volume of Cumene at the Normal Boiling Temperature by the Method of Kopps

Vb = ?VbC + 12VbH + VbBing (33)

= Kopps1 additive atomic volume for carbon

= 14.8V.u = Kopps' additive atomic volume for hydrogenOn

= 3.7V.r,. = Kopps1 additive atomic volume for benzenebRmg

= -15.0

Vb = 9(14.8) + 12(3.7) -15.0

= 162.6 °rc-- —gm-mole

Calculation of the Critical Pressure of Cumene by the

Method of Edul.iee

r 104 M

M = molecular weight = 120.19 g ^ m ole


115

Eduljee's contributions:

E A p 9A PC + 1 2 A ph + A Pfiing + A p p

A p Q = Eduljee atomic contribution by carbon

= -9 .3 5

A p£j = Eduljee atomic contribution by hydrogen = + 16.20

^ PRing = Eduljee structural contribution by

benzene ring

= + 84 .5

A pp = Eduljee position contribution by one branch on second carbon atom

= - 1.6E A P = 9 ( -935) + 12 (16 .20) + 84.5 - 1 .6 = 193.15

p = 1.20,.If?—21 IQ— _ op 2 atmC ( 193. 1 5 )2

Calculation of the Critical Volume of Cumene by the Method of Herzog

21.75 TcVc - - p f - S (35)

Pq = 32.2 atm.Tc = 636 . 0°K.

\T - 21.75(636.0) _ cm. C " 32.2 ~ gm-mole


116

Calculation of the Critical Volume of Cumene by the Method of Benson

= Vb(0.^22 log PG + 1.981)

V. = 162.6 • £W*-?-= b gm-molePn = 32 .2 atm.

(36)

VQ = 162.6 0.422 log (3 2.2 ) + 1.981= 162.6 ( 2 . 1 9 5 )

= 3^7 ^gm-mole

Calculation of Lennard-Jones Parameters for Cumene

A

l AK

l.l8Vb = 1.18(162.6)//3 6.43 A_£C_ = 6 3 M = oK 1.30 1.30 y

(1.18)(5.45)(37)

30 1.30

Calculation of the Molar Volume of Benzene at the NormalBoiling Temperature by the Method of Kopps

v b = 6V

vbc

VbH

bC + 6v. „bH + Vbliing= Kopps' additive atomic volume for= 14.8= Kopps1 additive atomic volume for= 3 . 7= Kopps1 additive atomic volume for= -15.0

(38)


117

™ 3Vb = 6( 1^.8) + 6(3.7) - 15.0 = 96.0 gm-mole

Calculation of the Molar Volume of Propylene at the Normal Boiling Temperature by the Method of Kopps

vb = 3Vb 0 +6tfbH (3?)Vb£ = Kopps1 additive atomic volume for carbon

■/bH = Kopps1 additive atomic volume for hydrogen

= 3.7V, = 3(1^.8) + 6(3.7) = 66.6 cm.3b J * ’ * gm-mole

Calculation of the Critical Viscosity of Cumene by the

Method of Uyehara and Watson

^ = (*0)vc

M = 120-1* igSoI?Tc = 636.0°K.VP = 357

°\. cm. 3

C gm-mole

n - .{ .61.•.(?.).(.12Q • 19 . 1 (.6.3 6 . _ 238 micropoise (357)

= 338 x 10"6 " !L■— cm-sec.or, alternatively

), Vi11 _ 7.70 M^Pc*

-----

= 32.2 atm.


118

( 7. 70) (120.19 ) ( 32.2(636.0

292 micropoise

‘-6 g!L= 292 x 10 cm-sec,

Calculation of the Combined Lennard-Jones Parameters for Cumene, Benzene and Propylene

+VR _ 6.43 + 5.27 _ rAii = 5.85 A

^A ± S . 8.A3 6.7,8 _ aAS

(41)

(42)

-ARK

= [(H-90)(WO)] 4 = 646ok _

eASK

KTi^AR

kt2 = £ a r

KTi _

( \ £k

L\ K

€AS

KT2 -

£sV K 7J6l6°K.464°K.

839°K.464°K.

6l6°K.383°K.

839°K.

(490)(298.9)x2= 383°K.

£As 383°K,

= 1.328;

= 1.808;

= 1.608;

2 . 190;

ft

9

9

AH

AR

AS

AS

650 = 1.262

1050 = 1.114

650 = 1.165

1050 = 1.043

(43)

(44)


119

Calculate the Diffusivity of Cumene in Benzene at 650°F.

DAR 0.0018583t3(jL , JL

\m a + mr/JPT V* ar ft AR

0.0018583 .(6l6)31120.19 78.ll/J(1.0)(5 -85) (1.262)

(45)

DAR 650 = °*°936 ffj;

Calculate the Diffusivity of Cumene In Benzene at 1050 F.

t 3 -1- +n _ 0.001858 AR - 2 QPT V aR ^ A R

Ma Mr I (4 5)

0.0018583 (839) 120.19 + 78.1:

DAR

(1.0) (5.85)2( 1.114)2

1050 = 0 - l 722

Calculate the Diffusivity of Cumene in Propylene at 650°F

DAST 3 — + -1 -)'

120.0018583 ma m s /_

^ A S

(616)30.0018583

1 , 1 120.19 42.08

(l.0 )(5 .554)2(l.165)

Td aJ = 0.1416 ^ 4 - L ASJ 650 sec.

(4 6)


120

Calculate the Diffusivity of Cumene in Propylene at 1050 F,

D 0.0018583AS

pt ^~a s 2^ as

0.0018583 (839) 1 + 1120.19 ^2.08/J(1.0) (5.55^-)2( 1.0^3)

2das] 1050 0.2513

( W

Calculate the Diffusivity of Cumene in Benzene and Propylene

(1 - Ya )DABDYH * YSnrAR °AS

W )

XA 4" XRy r = YS

XA 4" 2YRY = 1 ” Y A. = Y _*R — --- S

1 - IADa b - l - r r ~ i -y a “1 ; r’T ------- r r * r2E>ar 2Das Das

At 650°F.r 1dabJ 650 = 1 , 1 = 1 1 1

dAH 650 dAH 650 ^

= O.Uiti


121

A t 1 0 5 0 ° F .

dab] 1050 +dar 1050 das 1050 0.1722 0.2513

2= 0.2044 -^7— s 0 c *

Calculation of the Heat Capacity of Cumene by the Method of Hougan. Watson and Ragatz2^

U.O.P. characterization factor.

K = (48)G

Tg = boiling point at 1 atm. = 767°R.G = specific gravity at 60°F. = 0.862

K - W " ’ 10'62Empirical equation.Cp = (0.0450K-0.233) + (0.440 + 0.0177K) x 10"3t

-0 .1530 x 10"6t2 (49)

At t = 650°F.

Cp = (0.0450)(10.62)-0.233

+ 0.440+(0.0177)(10.62) (650 x 10"3)

- (0.1530)(650)2 x 10“6

°i> - ° ' 5 8 8 -0T.


At t = 1050°F.

Gp = (0.0450)(10.62)-0.233

+ 0.^+0+(0.0177)(10.62) (1050 x 10"3)

- (01530)(1050)2 x 10"6

CP - °-736

C3.1Gv = Gp - 2<0 gm mole-°G. = 0.719 7 ^ C . (50)

1 20 1 Q £HI§--12U*iy gm-mole

Calculation of the Heat Capacity of Benzene by the Method29of Hougan. Watson and Ragatz

U.O.P. characterization factor.

K = ■(_B).... (i+8)GTg = boiling point at 1 atm. = 636°R.

G = specific gravity at 60°P. = 0.879

tt _ (636) _ q 00K ~ 0.879 ~


123

Empirical equation.

Cp = (0.04-50K-0.233) + (0.440+0.0177K) x 10“3t

- 0.1530 x 10‘6t2 (4-9)

At t = 65Q°F.

Cp = ( 0.04-50) (9 . 78) -0.233

+ 0 .4-4-0+( 0.0177) (9 . 78) (650 x 10“3)

- (0 .1530M 6 5 0 ) 2 x 10"6

°p - o-;*1 i c t t

2 . 0 calr - r — gm-mole-QcT _ n * _c.al_,. /cn\°V _ °P " 70 u — JSM " U*313 gm-°C.gm-mole

At t = 1050°F.

Cp = (0.0^50)(9.78)-0.233

+ 0 .4-4-0+(0 .0177) (9 .78) (1050 x 10"3)

- (0 .1530)(1 0 5 0 ) 2 x 10"6

Cp = 0.682 g^ o Ct

Cv = Gp - 2 *°gm mole-uC. = O .656 -ggoG (50)78 11 _£SL§---' ’ gm-mole


Calculation of the Heat Capacity of Propylene by the

Method of Hougan. Watson and Ragatz2^

Empirical equation.

cp = 1 .97 + (27.69 x io"3)t - (5.25 x 10"6 )T2 (

At T = 650°F. = 1110°R.

Cp = 1.97 + (27.69 x 10_3)(1110)

- (5 . 2 5 x 10"6)(1110)2

*2 0'\r7 c&lr pcm mole-uC. _ n _cal__°p - — ° - 6 2 4gm-mole

CellC - C 2,0 gm mole-°C. = Q _ c a ± ,°V ” °P L±2 08 ___ gm-°C. ^gm-mole

At T = 1050°F. = 1510°R.

Cp = 1.97 + (27.69 x 10”3 )(1510)

- (5 . 2 5 x 10“6 )(1 5 1 0 ) 2

Cp 3 1 , 8 1 1 = 0 .756 ^4 2 .0 8 — - =— ggm-mole

calp Udi°V = CP - ' K"1 = 0.708 - f L - (.

^ • 08 iSrSHIi 6 '


APPENDIX II

PHYSICAL PROPERTIES OF SILICA-ALUMINA CATALYST


126

PHYSICAL PROPERTIES OF SILICA-ALUMINA CATALYST

The catalyst employed in this study was TCC (Thermofor Catalytic Cracking) Silica-Alumina Cracking Catalyst, supplied by the Mobil Chemical Company, Paulsboro Catalyst Plant, Paulsboro, New Jersey. The catalyst is designated as "Durabead 1" by Mobil.

The physical properties and Tyler screen data for the catalyst are as follows:

Loose bulk density 0.7^ cm. JPacked bulk density = 0.82 cm. jParticle density ^ P = 1.28 cm. jTrue solid density = 2 . 3 2 cm. jAverage diameter dP = 0.358 cm.Surface area Sg = 250 x 10^ ■

Average pore diameter d = 72 x 10“ 8

Effective pore diffusivity De = 0 .015 sec.Pore volume Vg = 0.35 £ 2 ^^ gmInternal void fraction e = 0.448External void fraction E = 0 . 3 2

Superficial surface area a s= 1 . cm . 2gm

Equivalent pore radius re = 2 . 8 x 10-7Tortuosity factor 7'" = 5.6

gmcm.

cm.


12?

Radius of catalyst pelletTotal surface of porous

catalystTyier Screen Analysis

On 4 mesh On 5 mesh On 6 mesh On 7 mesh On 8 mesh On 10 mesh Through 10 mesh

rp = 0.179 cm,

Sy = 320 x 10Wt. %2.5

27.0 ^3 A

22.23.9 0.6 .0,3

k cm.2cm. 3

99.9

Calculation of Superficial Area of Catalyst Surface, a

(53)Catalyst Area/Pellet = 47Tr2p pf’loit

Catalyst Wt./Pellet =

acm.1(4JTrP2 pellet''

(3^ pK Pitltd

^rrv 3 —qguj-3 ;i P Pelletgms. Pellet

' P cm.3 Pellet

^jTr 3^ .,gms..371 P/°P Pellet

3 cm.2 catalyst rP/ P catalyst

(5*0

(55)

a =

rp = 0.179 cm./> = 1.28 £ ^ 0 ' * cm.3

(0.179 cm.) (1.28 gjj -j)= 13 .10 cm.2 catalyst

gm. catalyst


APPENDIX III

CONTINUOUS REACTION MODEL


129


In solid-catalyzed gas-phase reactions, it is assumed that the reaction takes place at the gas-solid interface. The interface lies on the external surface of the catalyst and on the internal surfaces within the catalyst pore. The overall rate of reaction depends upon the availability of these surfaces.

For the continuous reaction model, it is assumed that the reaction mechanism consists of seven distinct processes. That process, or combination of processes, which are significantly slower than the others, control the rate of reaction. The seven processes involved in the catalytic cracking of cumene are described below and illustrated in Figure 39.

Gas Film Diffusion of ReactantsReactant cumene (A) diffuses from the main gas stream

to the external surface of the catalyst.

Pore Diffusion of ReactantsReactant cumene (A) diffuses from the external sur

face of the catalyst (mouth of the catalyst pore) into the catalyst pore).

Adsorption of ReactantsReactant cumene (A) is adsorbed onto the surface of


130

the catalyst.

Surface ReactionAdsorbed cumene (A) reacts to form adsorbed benzene

(R) and propylene (S) which is not adsorbed. This single site reaction mechanism was shown in previous work by Garver to be the actual mechanism occurring.

In the dual site reaction mechanism, both products are adsorbed.

Desorption of ProductsAdsorbed product benzene (R) is desorbed from the

catalyst surface.

Pore Diffusion of ProductsProducts benzene (R) and propylene (S) diffuse from

the catalyst pore to the external surface of the catalyst (mouth of the catalyst pore).

Gas Film Diffusion of ProductsProducts benzene (R) and propylene (S) diffuse

from the external surface of the catalyst into the main gas stream.


131

FIGURE 39


MainGas

StreamGas Film Catalyst Pore

For reaction occurring on interior surface of catalystGas FilmMain

GasStream

For reaction occurring on exterior surface of catalystICA Main

GasStream

Gas Film

Catalyst PoreDistance


APPENDIX IV

GAS FILM DIFFUSION


133

GAS FILM DIFFUSION

The gas film diffusion of cumene (A), benzene (R) and propylene (S), which is process one and seven of the reaction mechanism, can be handled mathematically as a simple diffusion process. Reactant A (cumene) diffuses from the main gas stream to the catalyst surface and products R and S (benzene and propylene) diffuse from the catalyst surface into the main gas stream. These phenomena are illustrated in Figure 4-0.

The diffusion rate is calculated as follows:

Material Balance on A

Input - Output + Generation = AccumulationInput =

Output =

Generation =

rate of mass transfer of A into differential element across rectangular surface at z

o.. gm-moles . gm-moles(A cm2) (NA„ ) - LWNa J "I”---lz cm2-sec. sec. (56)

rate of mass transfer of A out of differential element across rectangular surface at z + dz

(Azcm2) N A . d , „ s g m - m o l e s + T r( Na„ ) dz -.z dzv cm^Tsec.

LW dNAzNAz + - d T dz

gm-moles sec. (57)

rate of formation of A within differential element between z and z + dz


134

Main Gas Stream of R , and S

FIGURE 40

GAS FILM DIFFUSION OF A, R, AND S

Stagnant Gas Film Catalyst

dz

R+S

YA

0z


135

= nil (reaction takes place at catalyst surface only, not within differential element) (58)

Accumulation = rate of accumulation of A withindifferential element between z and z+dz

= nil (steady state) (59)Substituting,

dNAzLWNAz - LWNAz - dz = 0dNAz

" LW" d F ^ z = 0- gjfAz = o (60)

dz

Define Fick's Law for System\ a

“AZ = =I>AB— + Ya (NAz + NBz) (61)

From the stoichiometry of the reaction, A — R + S,one mole of A yields one mole of R plus one mole of S;therefore, A diffuses at half the combined rate of R + S, and

Na z = -£n b z Nb z = -2NAz

^ y aNAz - -cDABT i " + YA (NAz - 2NAz}

^y a= -CDA B " ^ i - YANAZ


1 3 6

Naz(1 + w = -cdab~ ^ tcDab ^y a

N a z = " ( 1 + Y A ) T ~ z

cDAB dYA A z _ ” (1+IA ) dz

dNAz d cDab dYA dz “ dz ( 1+YA ) dz

cDAB ^ A _(1+Ya ) dz " C1

Since cDAB is constant at constant pressure and temperature,

cDABln(l+YA ) = ciz + C2

Boundary ConditionsAt z = 0, YA = YAb

At z = & , YA = YAs

Substituting,

d cDAb dYA (62)dz (1+YA ) dz

Integrating


137

c.DABln( l+YAb ) = C2

cDABln(l+YAs) = ci6 + C2

= ci5 + cDABln(l+YAb) _ cDABln(1+Yas) _ cPABln(1+YAb)Cl

cDabh

In (1+YAs )(1+^Ab)

cDabcDABln(l+YA) = In (1+YAs)(l+*Ab)

z + cDAgln(1+YAb)

n (1+YA) _ z n (1+YAs )ln (l+lAb) S ln <l+YAb)

U + X a ) = ( 1 ^ A S)|( l + Y Ab) ( l + Y Ab>«

(1+YAh) v z(1+Ya) ■ (1+ YAP ?

( 1+YA ) = ( 1+YA c) ‘ <l+YAb)1-f (63)

Calculate Molar Flow Through Film

(dMA gm-moles) = ( om2)(N = constant (64)(dt sec.) z z cm -sec.

= oDae_ IX aAz (1+YA ) ds


1 3 8

dNA _ -Az cDa b 8.Yadt

Integrating,

dNA

(1+Ya ) dz

*AC

dt$dz -Az cDa b dYA

(1+x a )xAb

dNA (S) = -AzcDABln (l+YAq)(1+*AJ

1 dNA cDab InAz dt

1+YA«1+YAb

Let A = , external surface area ofZ CjA 'catalyst, cm2 .

Let = kg, mass transfer coefficient,

Let c = PTRT

Let a = superficial area of catalyst surface, cmgm,

a dNAr A = S = 4 F = 0 k Ka l nEX

1+YAbl+YAf

prpkgaRT In 1+YAb

l+YAf (65)

Where rA = gm moles A diffusing toward the catalyst surface per second per gm. catalyst.


APPENDIX V

SURFACE PHENOMENA


140

SURFACE PHENOMENA

The adsorption of cumene (A) onto the catalyst surface, the reaction of cumene on the catalyst surface, and the desorption of benzene (R) from the catalyst surface, which are processes three, four and five of the reaction mechanism, are handled together mathematically. The following reaction mechanisms are possible:

Single Site Mechanism (Propylene Not Adsorbed)

1. Reactant molecule A (cumene) is adsorbed onto the catalyst surface.

A + 1 A • 12. Adsorbed reactant A (cumene) reacts to form

adsorbed product R (benzene) and unadsorbed product S (propylene).

A>1 _« r «1 + s

3. Adsorbed product R (benzene) is desorbed from the catalyst surface.

R • 3. = = R + 1

Single Site Mechanism (Benzene Not Adsorbed)


A + 1 — A* 1


1 ^ 1

2. Adsorbed reactant A (cumene) reacts to form adsorbed product S (propylene) and unadsorbed product R (benzene).

A • 1 R + S-l3. Adsorbed product S (propylene) is desorbed from

the catalyst surface.S-l s + 1

Dual Site Mechanism (Both Benzene and Propylene Are Adsorbed)


A + 1 - A-l2. Adsorbed reactant A (cumene) reacts to form

adsorbed product R (benzene) and adsorbedproduct S (propylene).

A-i + 1 =g ■■,..!= r . ]_ + s • 13. Adsorbed product R (benzene) is desorbed from

the catalyst surface.R • i — ..— " : R + 1

Adsorbed product S (propylene) is desorbed from the catalyst surface.

S • 1 ■ - S + 1

Garver has shown that at the conditions of his study (1.0 atm., 850-1050°F.) the actual reaction mechanism is


142

the single site mechanism with propylene not adsorbed and with the surface reaction controlling. The reaction rate expression for this mechanism is derived as follows:

Reactionskl

1. A + 1 — — — — A*1 (adsorption of A)1

k22. A'l —— r-j— R • 1 + S (surface reaction;2 S not adsorbed)

3. R*1 — r-j— R + 1 (desorption of R)k 3

k4. A — —-— R + S (overall reaction)

Rate equations are now written for each of the reaction steps. Since surface reaction controls and is therefore the slowest step, it is assumed that the adsorption and desorption steps reach equilibrium.

Rate Equations

1. (-**A ) = k1PAC1 - k '1GA1 (66)(adsorption of A; at equilibrium)

2 ‘ ^"rAl^ = k2CAl " k '2PSCR1(surface reaction and S not adsorbed;

controlling)


3. (“rRi) ~ k3CRl " k'3pRGl

(desorption of R; at equilibrium)

1 k3 PR Cl 3 ” Kr " k<3 " CR1

14-3

(68)

k . (-r*A ) = Pfl - k'PpPc, (overall reaction)A-M3 (69)

K = k 1PR PS PA

Calculation of (-r^i) in Terms of Cq

(-rA1) - k2CA1 - k'2PsCRl (70)

CA1

Cri

Ka p a CiKr p r Oi

i - k2 k2KA2 K2 KKr

KAK2 CA1 . PSCR1 . PrG1 PRPST R PAGi Gal cri PA = K

KKK2 = -K

flA

("rAl^ = k2KAPAGl “k2KAPSKRPRG:

KKR

= k2KAC]_ PRPS PA" “K


144-

Definition of Gi

G1 CL " CA1 " CR1 _ GS1

CA1 KAPAG1

CR1 = kRPRCl

GS1 = G not a(isorbed)

Gl = gl " kapAG1 “ KRpRG1G = Gl________1 1 + k a Pa + k r Pr

(71)

Substitute Gl into Rate Equation

PRPSX GLk2KALPA " ’~K~

~rAl " 1 + KApA + Kr Pr (72)

For irreversible reaction, k is very large and k 1 is very small and K approaches infinity. The above then reduces to the following expression:

(-rAl>CLk2KAPA

1 + k a Pa + kr Pr (73)

The initial rate of reaction, r , occurs when the7 o'partial pressure of A is equal to the total pressure,7T, and the partial pressures of R and S are equal to zero.

PRPS.'](_r ) . W a p a - k

A1 1 + KApA + Kr Pr(74)


1 ^ 5

(-rAl) = ro

pa =TT

pfi = ps = 0CLk2KA7T

ro - 1 + K.JT


APPENDIX VI

PORE DIFFUSION


m-7

PORE DIFFUSION

The effect of pore diffusion (processes two and six of the reaction mechanism) on the rate of reaction is expressed by applying a correction factor to the rate equation. The term C^, total concentration of available active sites, is replaced by the product of the terms L, the total concentration of active sites, and £, the ratio of the actual reaction rate to the theoretical reaction rate if the resistance to pore diffusion were absent, f is known as the catalyst effectiveness factor.

The effectiveness factor of spherical catalysts with arbitrarily shaped pores is derived as follows:

Rate EquationPr PspA " - R ~C LkpKA

A ' 1 + Ka pa + Kr ph = kPA ~ i! pfiPS

= ksSgCA - >‘,SSBCBCS (75)

Elow ChartA cross section of the catalyst particle is shown in

Figure ^1. The concentration of cumene on the surface of the particle is CAS and the radius of the particle is rp.


148

FIGURE 4l

CROSS SECTION OF CATALYST PARTICLE SHOWING DIFFERENTIAL ELEMENT

dr


1 4 9

Material Balance on Differential Element, dr.

Input - Output + Generation = Accumulation

Input

(ii-7rr2om2) (Deff^7>

= _47Tr2D ^e dr sec.

moles d- A cm3 dr cm

Output

(47T(r+dr) 2 cm2) (Dq~ ~ )cm"e sec:

dCA _ _d. dr dr

moles dCAIdr cm3

-4 IT (r 2+ 2rdr+dr2) D, dCA d Ga dr 9 dr dr^

dr )

gm moles sec.

cm

Generation

<rA 6Smoa?-Ho;H ^ c g™s oat.) S°l6SA C sec.

gm moles .,, ^ ^ ^ gm cat.s( — £2— ------- (477r^drcm^ (/> p-— 1----)A gm cat-sec. ' P cm!

- (rA ) ( ^ A r2d r ) ® iffl2ies

Accumulation = 0 (steady state)


(76)

(77)

(78)

(79)

1 5 0

Material Balance

-^7Tr2D ^ + ^Ttr2D + 47Tr2D § dr e dr e dr e dr^

+ 8lTrdrD — ^ + 87TrdrD ■ - 4 dre dr e dr2

+(rA )(^7^°pr2dr) = 0

lK r2De " 2 0.r + 87TrdrDe— + (r ) (^J7/°pr2dr) = 0

d2CA ^ 2 dCA ^ /°_P (rA ) = 05e

+ ± + L I 'rA/ = u (80)dr^ r dr D,

Calculation of Rate Equation

(-rA) = ksSg0A - klsSgGRGsAssume irreversible reaction

ks k 's(-rA> = kSSg°A

Substitute Hate Equation Into Material Balance

d-2CA + 2 dCA _ /^ksSgCA _ Q (g2)dr^ r dr De

IntegrateChange of Variable

Let x = CArdx = CAdr + rdCA r(iCA = dx - CAdr


151

cLCa _ 1 dx - Ca _ 1 dx _ x dr r dr r r dr r‘

d2CA =dr

dxdr

_1r2

+ 1 d2x + x(2) 1 dxr dr2 r3 r2 dr

1. d x 2 dx | 2xr dr2 r2 dr r"3

Substitute

1 d2x 2 dx + 2x +2 r2 dr r3 r»2r dr

2 dx r^ dr

2x _ /°pksSFx r3 “ = 0

d2xdr2

ks/^pS£D,

0

General Solution

m =-b* o± Jo +^ks /fpgs'ue

2akS/°PSK

DP

'A r Mlemr + M2e-mr (83)

Boundary Conditions

At r = 0,dCAdr = 0

At r = rp , CA = 0.


152

cLCadr

1 mM1emr - mM2e"mr - 1 _

r2

r2 dCA = r mM1emr - mM2e~mr dr L

Mxemr + M2e-mr

Mierar + M2e-mr

0

Mi = -M2

0

c a ._i_rp

M1emrp + M2e~mrp

H1 - M2

CAsrp = Mie"11*15 - M1e~mrp

CAsrP M1 = emrp - e_IT,rp

Mo = -cAarP2 ~ emrP _ g-mrp

Back Substitute

CA =C r^emr

>mrp _ mrpG rDe-mrs P_______,mrp _ e-mrp

CAsrP „mr ^-mr e - e CAsrP sinh mrr e-mrp _ e-mrp r sinh mrp

Oa° Asr P sinh mr

sinh mri

m =is kS SV

D e De


(84)

153

Calculation of Actual Reaction Rate

Actual reaction rate = Rate of diffusion intocatalyst pellet

cm"-Rp = (^TTVp om2)(De seo )gm moles

d- A cm3 dr cm (85)

r = r.

= -'i-TTr2 DedCAdr r = rp

gm moles sec.

dCA d CAsrp sinh mr °AsrP d sinh mrdr dr r sinh mrp sinh mrp dr r

— _

CAg psinh mrp

CA«rPsinh mrp

rm cosh mr - sinh mr -----------

m cosh mr sinh mrY>*~

R,

~dc 2 CAsrP m cosh mrp sinh mrpdr r=rp sinh mrp r — rp

p p

ca. „s rp

mrptanh mrp - 1

CAfP e

mrprp

= ^ r 2 DeOAsmrp

= U-TTr2 DeCA£.

tanh mrp

1

-1

tanh mrp mrp

kSsV it.'d 1 1De tanh (kSsV )2rp L De

(ks^v iDe ' rPj


1 5 ^

Let hg = mrp = rp ksSyD,

Bp = ^hsrr rpDeCA3 tanh hg_1_hS

(Thiele Modulus)

(86)

Calculation of Maximum Reaction Rate

,L~. t r> Pm v ™ &m molesR = (? 7 T r i W ) ( k c ~ - ) ( S W— o )(Camax 3 R S sec Vcm3 s c m 3 )

bTTripkgSyCAg gm moles 3 sec. (87)

Definition of Effectiveness Factor

€ = effectiveness factor_ actual rate of reaction with pore diffusion present

rate of reaction if resistance of pore diffusion were absent

R,Rmax

^hSTTrpDeCA ci7Tr3k0S;rCAV

3hsDerPkSSV

s1

tanh he

tanh hg hg

i i3rpks2Sv2DeDe§rp2kgSv

he

tanh he_1_hc


155

rpkss'Sys- 1---Dp2tanh hg

_1_

hS

e= tanh hg hg (88)

Calculation of Effective Diffusivity, De

Definition of Effective Diffusivity_ pse

D_ 7- (89)

De = effective diffusivity, cm"sec.

& = fraction voids in catalyst particle 'T' = tortuosity factorDs = combined diffusivity,

1 + 1

cm"sec.

d a b d k

Dab = diffusivity of A in A + R + S, cm"sec.

D^ = Knudsen diffusivity, cmsec.

Molecular Diffusivity of A in A + fi + S

As previously calculated, the molecular diffusivity of A in A + R + S, D^g, are as follows:

cm2[D[DAB 650°P. 0.1141 sec^

ABcm

1050°F. 0.2044 sec>


1 5 6

7 0Satterfield has shown that in the temperature range of 200°K. to 5000°K., DAB is well represented by a power function of temperature, that exponent being 1.82. The relationship between molecular diffusivity and temperature then becomes as follows:

°AB = -°*oo633 + 0.1008 + i o“5t 1.82

Where T is in °K. the values for at several temperatures are as follows:

cm.2T, F . T, K . Dab, sec.

650 616 0.1141700 644 0.124-2750 672 0.134-7800 700 0.14-56850 728 0.1568900 756 0.1684-950 783 0.17991000 811 0.19221050 839 0.2044

Calculation of Knudsen Diffusivity

4r (90)


157

cm3-atm lb.__ gms cmH = (82.06 gm mole °K)(l4.7 in2atm)(454 lb*)(980sec2)g (2.54 f“ ) (2.54 f^)

y gm-cm^______8.32 x 10 mole-0K-sec2

M = 120 10----- ---11 1^u -±y gm mole2Vp- ■p = —Ll

e sg

= pore volume/gm. catalyst, pjj-j-

= 250 x 10/+ g gmr = ( 2) (0.350 g ^ ) = 2.80 x 10-? cm.e (250 x 10^ M ? )gm

r ____ gm-cm^____n - (*0(280 x 10~7cm) 2(8.32 x 10 gm mole-°K-sec?)K „ gms \

12 - , 2 12

(120.19 — &ms, ) gm mole(T°K)

p

Dk = 2.478 x 10"^ Ciri-:sec

The values for D„ at several temperatures are asKfollows:1 •

■ °p9 1 • T, °K. (T°K)^

2cm D^, sec

650 6l6 24.82 0.00615700 644 25.38 0.00629750 672 25.92 0.00647800 700 26.46 O.OO656

850 728 26.98 0.00669


1 5 8

2cm^T, °F. T, °K. (T°K.)2 D^, sec

900 756 27.50 0.00681950 783 27.98 0.00693

1000 811 28.48 0.007061050 839 28.97 0.00718

Calculation of Combined Diffusivity

1 1Ds ~ dab +

1dk

DS

DS

1 1 j650 ” oTvUn + 0.00615 " 1 7 1 A

2650 = °*00^

Similarly, 2cm

T,°F. Ds, sec650 0.00584-700 0.00599750 0.00613800 0.00628850 0.0064-2900 0.00655950 0.00667

1000 0.006811050 0.00694-


(91)

159

Calculation of Effective Diffusivity

Ds a Ds(0.448)De = r 7- = — — = °-080 D<

OT, F. Dq, sec.

650 0.00046?700 0.000479750 0.000490800 0.000502

850 0.000514900 0.000524950 0.00053^

1000 0.000545

1050 0.000555

Calculation of Thiele Modulus, hg

Definition of Thiele Modulus

kSsVhg rp D(

rp = radius of catalyst particle = 0.179 cm Sv = total surface area of porous catalyst

= 320 x 10^ ^ cm2kg = forward intrinsic rate constant for

cmsurface reaction, sec.


(92)

(93)

1 6 0

Calculation of kg

Initial Rate of Reaction

ro =6Lk?KA 7TT i ^ f r

(94)

Pseudo First Order Reaction (Appendix XI)

r0 = kSSgCAo (95)

Calculate ks

6Lk2K A 7Tks (i + KA7T)sgcAo (96)

kA =

TT =

s =g

equilibrium adsorption constant for cumene,

1 atm.,4 cm^250 x 10 gm

CA, = m i tial cumene concentration, gm m-94.e_§.cm-log CLkg = -4-812 ^0^ -1.14-1 (no ultrasound)

Calculation of hs

h0 = rpsv s De (0 .179) (320 x 104 )' KD~ej

= 320JL2


1 6 1

Calculation of Effectiveness Factor. €

jl [ _ i . j lhg |^tanh hg hg

Summary of Calculations (No Ultrasound)

T °F.

(flkg x 10^gm moles

gm cat-sec.

kg x 1 0 'cm.

sec. hS e

650 0.334 0.499 3.31 0 .63700 0.514 0.789 4.11 0.55750 0 .762 1 .200 5.01 0.48800 1.099 1.778 5.01 0.48850 1.534 2.541 7 .12 O .36900 2 .126 3.605 8.39 0 .3 2950 2.794 4.849 9.64 0.28

1000 3.657 6.486 11.04 0.251050 4.702 8 .526 12.54 0.22

At frequency inputs of 26,000 cps and 39,000 cps the rate constant ^lkg increases as shown previously because the effectiveness factor, £ , or surface reaction rate constant, k2, increases. When the effectiveness factor increases, the Thiele Modulus, hg, must decrease, requiring the effective diffusivity, D0 , to increase. The effect of ultrasound, therefore, may be to increase the diffusion rate of cumene in the catalyst pores.


APPENDIX VII

REACTION DESIGN EQUATION


1 6 3

REACTION DESIGN EQUATION

The reaction design equation is derived by substituting the rate equation for the single site mechanism, S (propylene) not adsorbed, with surface reaction controlling into the plug flow reactor design equation. The derivation is as follows:

Derivation of Design Equation for Plug Flow Reactor Flow Chart (Figure k-2)

Material Balance

Input - Output + Generation = Accumulation

Inputw gm moles A A sec.

Outputgm moles A

sec.Generation

(+r gm moles A A gm cat-sec.

gm moles A sec.

Accumulation = 0 (steady state)

Material Balance

-dPA = (-rA )dW


FIGURE

k2

164

C3X—1MorecoreoEHO Eh-E XW wK s

w■ XO wX X

co Mx Ehxi XX W«x Wo XXX HHo QMEh

owCOCOcoo«o

+ +<C <JX o

X o


1 6 5

F = F - X F A A0 A1 AodF„ = -PA dXA A0 A

^ A = <-rA )dW

dW dXAPA0 " (-rA)

IntegrateW XA,

dWfa o <'rA>

XA,w

FA,* A (-rA ) (97)

Xa o

Calculation of Reaction Design Equation, Surface Reactions Controlling

Rate Equation for Single Site Mechanism, S (Propylene) Not Adsorbed, and Surface Reaction Controlling

(-rA ) € Lk2KAPR PS PA - —

(98)


166

Substitute Rate Equation Into Plug Flow Reactor Design Equation

Xa -p

WPA,

dXA

^ Lk2KA PAPr PSK

1 + k a Pa + kr PrXa o

Solve for Partial Pressures in Terms of Conversion and Total Pressure

Material Balance

Inlet Reactor OutletA na 0=n a0 Na=Na o-Xa Na o NAf=NA0-XAfNA0R NR0=Nr o nr=nr 0+x a na 0 NR=NRo+XAfNAo

S MS0=NS0 Ns=Ns o+Xa NA0 NS=NS0+XAfNAQTotal nA0+nR0+nS0 nA0+nR0+nS0+xanA0 NA0+NRo+Nso+XAfNA0

NaTT (NA0-XANAo)7rPA =

% =

Nip (na0+hRo+Hso+xana0 1

Nr IT (nRo+xanAo)7Tnt (nA0+nH0+ i’,S0+XANA0 )

Ns7T (Ns0+XA“A0)7rN,T (f,Ao+NHo+NSo+XAWAo)


1 6 7

A

PB =

Pc; =

However, % = % 0 = 0

NAod - xa )TT (l - x a )7TnA o (i + XA ) (1 + xA )

x a na 0 1T x a V

«A0 (1 + XA ) (1 + XA )

xAi!A07T x a 7T“Ac '-A • (1 + xA)

Substitute for Partial Pressures in Hate Equation

(“rA> =

r prps6Lk2KA PA " ."K.

1 + k a pa + k r Pr

CLk2KA(i -x a )7T x a 27T2(i+xA ) " (i+x a )2k

k a (i-Xa )7T k a x a TTi + ,. >---- +(i+xA ) (i+xA)

k A (i -x A )jr k a x a tr+ (1+XA ) + (1+XA )

( ~rA > 6 Lk2KA (i-x a )77 x a ^tT 2(i+xA) (i+xa )2k

(i + k a 7T )(-rA) £‘Lk2KA7T[i - ( i + ^ x 2

(2 + KR7T)XA 6'Lk2KA 7T[i - d+?-)xA2](l - k a 7T + kr JT)x 2

6Lk2KA7r[l - (I+^JXa2

+

+


168

(1 + KA J T )

£ ' L k 2K A T r [ l - ( l + | f ) X A 2 ]

H* Pn > =3 __ 1

ie L k 2KArr 1 __1 - ( l + ^ ) X A 2

- y y1 - ^ X a2

y = i , _i6* Lk2KATT ^Lk2

1 + I tK

(2 + k h 7T)x a^Lk2KATT 1 _ ( 1 + 2 L ) X 2K

KrTT6Lk2KATT CLk2KA 7T

*A1 - U + ^ U a 2

i -/9 XA

1 -

^ 2 kR= e L k 2KA r r + 6 L k 2KA

f L . TTl a - i K j


1 6 9

(l - k a 7T + kr7T)x.a 2 CLk2KArr[i - d + ^ ) x A2]

]t-* > h S* X

J

* a 2_€Lk2KA7T 6Lk2KA7T ' CLk2KATT \l~ <l+f )XA*|

1 1 _ Kr XA2 ]6Lk2KA7T 6Lk2 6Lk2KA 1 ” ^1+^ XA2

/ ? - XxA2 (/? )xA2

l - S2x a2 i - 62x a2

6'Lk2KA7T + £Lk2KA " €Lk2KATT ~ €Lk2K r

1 K r4*6 Lk2KA7T £ Lk2 £ Lkt KA

1 + JT'K

(-rA^ 1 - <5 Xzrr-? +A/3 XA ( ? - )XA2

1 - <s V + T - i VSubstitute Rate Equation into Plup; Flow Reactor Design Equation and Integrate

X_Af XAf xAf

WFAo

^dXA<-2 2 1 - d XA

+ /?XAdXAc2 2 1 - h XA

+ (/6 - ¥ ) X A dXA,2 2 1 - £ XA

XAo XA0 XAo


ydXA

- & XA +1 2 5 In '1+Xa SLi-xa5.

y , 1+xa <5Ino 2 5 1 -XA 5

XA0=°

XAf XA

XAdXA-<S2xa+1

X?-252 In 2 2

•5 xA + i = Yjf? ln (-52XA2+i)

XA =o

xAf=xA ¥

XAZ dXA2 -g'XA2+l

(X?-^)XA (x?-^ )- S 2 ’ T ^ "

XA0=0

dXA- S V + l

(X?-^) XA . (X?-*)V-i *T

1 in (1+XA5)25 (1 -XA<5 )

w*7o 25 ln (1+XA§)

(i-Xa 5) A

{jq- y )+ 5T2” 25

( i+ x a5) ln(i-xA5)


171

VJf a

-yo

1 1 j ln (1+XAS) XAi2 S " ^ (1-XA(1-XAS)+ 5^

+/? 1 ln (1+Xa5)/ l n ( l - S 2 X 2 )

2 & (1-XAS) 25*A5 *

(99)

Y =

/S =

6 =

T L k 2KATT + £Lk2

K£ Lk2KA7T ^ kk2kA

R

1 + HK

Calculation of Reaction Design Equation, External

Diffusion Controlling

Rate Equation for External Diffusion Controlling

rA -Pt V ln 1+YAb

RT i+y A((100)

Substitute Rate Equation into Plup; Flow Reactor Equation

«Af

WFA,

dXAPTk p;a ln 1+YAb RT 1+Ya s

XA 0

XAfHT

Pjkga ln 1+YAb1+*A<


172

Calculate Mass Transfer Coefficient, k,r■—.. - , , . , — - — __ I t

XAfRTkg " 1+YA> (101)(W/FA0 )PTaln — ^i+YA as

YAs = 0 (mole fraction cumene at catalyst surface)

R = 82.03 ‘gm mole-°K.T = °K.

™ gm moles cumene feedA o =

W = gms. catalyst p,p = 1.0 atm.

cm^g m.

cm.a = 13.1 -p-

kg sec.XA;p = conversionY., = YA - YAn ^ Ya lm (mole fraction cumene in

YA j_ bulk gas stream)In?fA0

YA = 1.0 (mole fraction cumene at reactor

Y a = ~ ^Af (mole fraction cumene at 1 + X a reactor outlet)

inlet)

1 + XAf

6.261832 XAfT kg = (W/PAo)ln(l+YA M )


EVALUATION

APPENDIX VIII

OF REACTION RATE CONSTANTS


17^

EVALUATION OF REACTION RATE CONSTANTS

As previously derived, the reaction design equation for the catalytic cracking of cumene in a continuous plug flow reactor is as follows:

Wpa

= yo L\2 S 2 5

In (1+XAS) Xa (1-Xa5) +

1 ln ( 1+Xa <§) 1 ln(l-fxAZ )-XA

Where,

2£3 (1-XA«S) 25

1 , 1 CLk2KA7T 6 Lk2

S2 (99)

€ Lk2KA7T + 6 Lk2KAKr

22Garver experimentally determined the reaction rate constants at atmospheric pressure to be as follows:

K, atm.<fLk _sm..m°les

KA j atm.

K — -—R ’ atm.

2 ’ gm cat-sec. 1

V gm cat-sec, ^ * gm mole

cc o o 950°F. 1050°F.2.05 6.22 15.96

1.777 x io“5 2.165 x 10"5 2 .917 x 10

2.2*1 2.13 1.90

2 A 5 1.86 1 A 7

81,300 67,800 52,250


1 7 5

/? gm cat-sec.* gm mole

<5, dimensionless

850°F. 950°F. 1050°F.111,500 83,600 62,500

1.224 1.070 1.031

The above constants were obtained as follows:

Equilibrium Constant, KGarver calculated the thermodynamic equilibrium

constant for the dealkylation of cumene from the logarithms of the equilibrium constants of formation for cumene, benzene and propylene. The values for the equilibrium constants of formation were obtained from Circular C^6l of the National Bureau of Standards.

The equation expressing the equilibrium constant as a function of temperature is as follows:

where K is in atmospheres and T is in Rankine.

Adsorption Constant for Cumene, Ka, and Combined Effectiveness Factor and Forward Reaction Rate Constant for Surface Reaction, (fLk2

Plot W/Fa vs. X. at varying Fa and total pressure,77*, o *»> oand constant temperature, T, as shown in Figure ^3 .

log K = -8,927 - Y + 7.126


176

FIGURE 4-3

W PLOT OF XA VS. FAq AT CONSTANT TEMPERATURE

W gm cat-sec. FAq * Sm mole


177

Rearrange the plug flow reactor design equation.

and extrapolate back to = 0 to find initial rate, rQ , as shown in Figure

Rearrange the initial rate equation.

= gLk2KATT 0 i+ka7T

l~0 = gLk2KATf i+k aTT

TT _ _ j ^ _ J T _r0 fLk2KA + 6Lk2TfPlot — vs. ff as shown in Figure ^5*

Calculate £ Lk2 and from the slope and intercept.

Repeat at 850°F., 950°F. and 1050°F.

a lPA0) = <-rA)w 1 _ dXA

Plot slope, dXA/d^p^— )

o


1 7 8

FIGURE 44

PLOT OF REACTION RATE VS. CONVERSION AT CONSTANT TEMPERATURE

X


1 7 9

FIGURE ^5

PLOT OF VS. Tf

JLrn

£Lk2KA

slope = T L k i

T f


1 8 0

Adsorption Constant for Benzene, Kg

Assume Irreversible Reaction

Reaction Design Equation

WFAo

ln253

(1+XA<5) XA (l-xA<f) ^ 2

4* 1 ln (1+XA5) 1 ln(l-^2X2 )-XA263 (1-Xa6) 2«TJ £2 (99)

For irreversible reaction

K = £ = » 1

7T 12 r „ 1-1 + i r -

= [l + 0

Back substitute

WFAo

lnti+xA ) XA (1-XA ) + 1

+ 1 ln(1+XA) 1 ln(l-XA2)2 TT^T " Z ^A1

<^XA +/?

1 In U + XA)2 (1-XA )(1-XA *) “ Aa

1 ln 12 (1-XA )

Ji!_ = yxA [-ln( 1-XA ) - XA] Aq

( 1 0 2 )


1 8 1

Rearrange the irreversible rate equation:

V/ . =/s[-ln(l-XA ) - XA]

Calculate X at 850°P., 950°F. and 1050°F., and Tf 1,

7T2> and Tf y

y 1 + 16 Lk2KATT Ehkr

Plot WFA, - XA vs. -ln( 1-XA ) - XA1 at 850°F.,

950 F . and 1050 F., and at Tf » Tf2 and TT as shown in Figure k£>.

Calculate from slope of straight line.

Reaction Design Equation Constants Y .ft. and <£

Since K, £*Lk2 , and Kh are now known, If , 3 and cS can be calculated at 850°F. , 950°F. and. 1050°F., and Tf lt Tf 2 and Tf •

Summary of Results

Carver's investigation led to the following values for K, Ka and :

1log K = -8927 T°R + 7.126 (103)


1 8 2

FIGURE 1+6

PLOT OF V/FA, yxA

_W FA,


1 8 3

log Ka = 700| - 0.179A rpOrjT°R ( 1 0 4 )

log K = 2195 -5- - 1.28611 mUpT R (105)

Evaluation of Reaction Rate Constants

For this research, Tf= 1 atm. and CLkR is handledas a single constant. The rate equation then contains four parameters; €Lk2, Ka , Kr and K. The values of the parameters K, Ka and Kr obtained by Garver and extrapolated

computer calculated by curve fitting the data by use of Marquardfs non-linear square fit program.

Table 10 shows the literature values of K, Ka and K r for each of the temperatures studied along with the calculated values of ^LkR at 26,000 cps, 39»000 cps and in the absence of ultrasound.

The graphs of conversion as a function of reciprocal space velocity illustrating all the data points and the calculated theoretical curves are illustrated in Figures 48 through 73- Considerable scattering of the data is apparent at 650°F. because of the low conversions obtained at that temperature and the accompanying analytical errors.

to 650°F. are shown in Figure 47.

These literature values of three of the fourparameters were substituted into the surface reaction rate equation, and the fourth parameter, ^Lk?, was


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APPENDIX IX

SAMPLE ANALYSIS


2 1 3

SAMPLE ANALYSIS

Samples of the reactor effluent were obtained by the following methods:

Gas Sample

The high temperature (650-1050°F.) gaseous effluent is introduced directly into the gas chromatograph via a gas sampling valve. This method proved to be no more accurate than the liquid sample method, even though the sample represents the entire effluent stream.

Liquid Sample

The reactor effluent is partially condensed and subcooled to 70°F. The propylene remains in the gas phase at this temperature and is vented from the system. The remaining liquid phase is injected into the gas chromatograph. Little accuracy is sacrificed by this technique because of the unaccounted for losses of cumene and benzene in the gaseous propylene stream.

The following calculations compare the two sampling techniques, assuming a total cumene feed to the reactor of 100 gm moles and a conversion of 20$.


214

Gas Sample Analysis (No Losses)

Material Balance

% Nf Msms.

gm-moles gm-moles mole % Km-mole Kms.

A 100.0 80.0 66.66 120.19 9,615,20R 20.0 16.67 78.11 1,562.20S 20.0 16.67 42.08 841.60

Total 100.0 120.0 100.0 12,019.00

Conversion

v — . . 120.19(wt.$R)120.19 (wt ,%R) + 78.11 (wt.%A)

120. 19(13.00)120.19(13 .00) + 78.11(80.00)1562.2 1562.2 .20001562.2 + 6248.8 " 7811.0 ~ w

Liquid Sample Analysis (All S Lost, No Other Lot

Material BalanceNo Nf M

Kms.£m-moles gm-moles mole % gm-mole gms.

A 100.0 80.0 80.0 120.19 9,615.20R 20.0 20.0 78.11 1,562.20S - - 42.08 -

Total 100.0 100.0 100.0 11,177.40

Wt J o

80.00 13.00

7.00

(103)

V i t . %

86.0213.98


2 1 5

Conversion

Y _________ 120.19( wt./oR)______ __A 120.19(wt.JgR) + 78.11(wt.^A)

= ______ 120,19(13.98)120.19(13.98) + 78.11(86.02)

= 1 ,680.2562 1 ,680.2562 _1,680.2562 + 6,719.0222 ~ 8,399.2784 " u.-'uuu

Liquid Sample Analysis (Actual Losses)

Vapor Pressure at 70°F. (20°C.)

lop- p = 6 92926 - — 12.06.350 - g 09926 - — 350xug o.ycy^D t+2 0 7 .2 0 2 ~ 20+207.202

= 3.32 mm. Hg

log p , j = 6 89745 - ■ 1 3 P .6 . 35.0. £ 89745 - • 35.P .xog rR 0 .0 9 ^ 9 t+2 2 0 . 2 3 7 20+22 0 .2 37

Pp = 75.15 mm. Hg

P^ = 9.9 atm. = 7,524 mm. Hg

Condenser Flow Chart (Figure 74)

Overall Material Balance

F = L + V (104)120 = L + V


2 1 6

FIGURE 74

CONDENSER FLOW CHART

VT = 70°F.yAyRys

F 120T 1000°F.yfA = 0.6666yfR = 0.1667y*s 0.1667

LT = 70°F.XAXRXS


2 1 7

Component Material Balance

yfAF = yAV + xAL; 80,0 = yAV + x AL (105)

yfRF = yRV + xr L; 20.0 = yRV + xRL (106)

yfsF = ysV + xsL; 20.0 = ygV + xgL (107)

Daltons and Raoult * s LawsX P

Pa = yA7T = XAPA» yA = TT (108)A A* * A A ’ ^A ~ 7f

PR = yRTT = XRPR; yR = U' (109)

xspsps ys^r xrps» ys ~ ff (no)Combine Material Balances and Dalton's and Raoult's Laws

x = 80.0 = 80 0______A L + ^ (120-L) L + 120-L)

80.00.52446 + 0.995632L

= 20.0______________20.0_______R L + ^ ( 120-L) L + 120-L)

20.0_______11.8656 + 0.90112L

20.0 20.0_______S L + 120-L) L + ^||^( 120-L)

20.0______" 1,188 - 8.90L


2 1 8

Trial and Error Solution

Let L = 100.0

80.0XA 0.524-16 + 99.5632 100.08736 ~

XR20..0 20.0

11.8656 + 90 .112 101.9776 "

XS20.0 20.0

1,188 -- 890 298

Let L _ 111 .0

XA80.0 80.0

0.524-16 + 110.51515 111.03931

20.0 20.0XR 11.8656 + 100.024-3 111.88992

20.0 20.0XS 1,188 - 987.9 200.1

Corrected Mole Fractions

XA0.72060.9992 = 0.7211

y _ 0.1787 _ n 1 R 0.9992 “

x = 0.1000 Q ^QQI S 0.9992 • UU1

1.0000

.7993

.1961

.0671

.0625

0.7205

0 .1787

0.10000.9992


2 1 9

Material Balance

N0 % "gm.gm-moles gm-moles mole % gm moles gms.

A 100.0 80.0*4-21 72.11 120.19 9,620.3^R - 19.8*4-68 17.88 78.11 1,550.23S - 11.1111 10.01 *!2.08 *1-67.56

Total 100.0 111.0000 100.00 11,638.13

Conversion

_______ 120.19(wt.#R)A 120.19(wt.%R) + 78.11(wt.^A)

_______ 120.19(13.32)(120.19)(13-32) + 78.11(82.66

1 .600.9308 1,600.9308 +6,456.5726

6 0 0 ..9.308 Q 1QQ n8 ,0 5 7 .5 0 3 * !

Error

c/0 e r r o r _ .(.0,.2,00,0 - 0,.1987) (100 ) /0 error " 0.2000

0 .0 0 1 3 (1 0 0 ) _ n s . ? 0.2000 " 0.65/o

wt.%

0.8266 0.1332 0. 0*4-02 1.0000


2 2 0

Sample Calculation from Actual Data

Run No. 11.53

Analysis (Wt. %)

Liquid Sample_________ GasTest 1 Test 2 Test 3 Average Sample

Cumene 90.62 91.35 91.30 91.09 89.11Benzene 7 .62 7.18 7.18 7.32 7.08Propylene 1.76 1.47 1. 52 1.59 3.81

1 0 0 .0 0 1 0 0 .0 0 1 0 0 .0 0 1 0 0 .0 0 1 0 0 .0 0

Liquid Sample Conversion

X = _______ 120.19(7.32) _ ,, MA 120.191 7.32) + 78.11(91.09) ■“ •'•M'

Gas Sample Conversion

x = _______(120.19.} (7-08) v _ 10 ,A (120.19)(7.08) + 78.11(89.11) "


APPENDIX X

ULTRASONIC ENGINEERING


2 2 2

ULTRASONIC ENGINEERING

Fundamental Equations

Figure 76 illustrates a schematic representation of the instantaneous position of the gas particles through which a sound wave is travelling. The gas particles are each volume elements of gas containing millions of molecules. The drawing shows the alternate compression and expansion of the gas in the direction of the propagation of the sound wave.

Figure 76 illustrates the sine wave representation of the sound wave.

Sound Wave Equation

y = Ycos (x-Vt) = Ycos 27Tf(t-^) (111)

cyuie aei; ayo-Le ^yyuxessec

f 1T

Transverse Velocity

v = ft = ^ Ycos27Tf( t-v ) _ _Ysin2TTf(t-^) [27ff]

v = _2 7TfYsin27Tf( t-^) ( 1 1 2 )


223

FIGURE 75

SCHEMATIC DIAGRAM OF SOUND WAVE

0 0 m

Direction of particle

motionDirection of

wave propagation

FIGURE 76

SINE WAVE REPRESENTATION OF SOUND WAVE

+y

0 rr

Transversedirection

Longitudinal-y direction


224-

Transverse Acceleration

dv _ d_ a dt dt

-2 ?T fYsin27Tf(t--)

= -2 7TfYcos2lTf( t-^) [2TTf]

a = -4TT2f2Ycos2'jTf (t-^) (113)

Velocity of Propagation of Sound Waves in a Gas

Figure 77 illustrates an element of gas in a tube in which there is a longitudinal sound wave. Both the equilibrium and displaced positions are shown.

Newton’s Second Law

F = ma (114 )

PNET = (Po+ P (A cm2) - (p0+ P + A p d,yn| -) (A cm2)u cm^ cm^

= ~ A p a dynes

= (/ o cm2) ( A x cm) =//30a A x gms.m cm-o = dAz cm

dt2 sec2

-ApA =/0 aA x1 ° dt2

d2y = - A p A _dt2 /3oaA x > o A ; d2y = _ JL_ dp dt2 /^o


2 2 5

FIGURE 77

ELEMENT OF GAS IN A TUBE IN WHICH THERE IS A LONGITUDINAL SOUND WAVE

Equilibrium position

x -----------1_ A x —

Displaced position

H y+x ----------- y H


2 2 6

Calculate p

Definition of Compressibility

1 change in volumeoriginal volume change in pressure

_ 1_ dv v dp

Original volume = (Acm2) ( A x cm) = aA x cm Change in volume

= (A x+y+Ay-y cm) (A cm2)-(Ax cm) (A cm = (Ax+Ay)A -AxA = A yA cm3

Change in pressure- (Po+P) + ( pM-th- A p )

2 " po2p0+2p+A P

= § - P°

= Po+F^-^-P q

„ dynes' P cm2

1 A y A cm3 _ A y cm2a A x cm3 dynes P O

L c m ^ Jp A x py^e

Rearrange to Obtain p

rj = “_i— A l = - 1 ^ 1 k A x k dx

pp _ -JL p£y Px k dx2

(115)

)


2 2 7

Substitute into Equation for Newton1s Second Law

d2y _ dt2

1 dp/°o dx

1 ^

/ ’o1_ dfyk dx

dt /°0 k dxChange Variables

Let y = f(x ± Vt) = f(u) = f

^y _ d f _ d f # dud x dx d u dx

du _ d(x - Vt) _ dx dx d x d x = 1

_izc) Xd fdu 1 - 1 = \-d u

d2y d x2 - ,d /. d y _ d / d f \ _ d u" T x l dx' - d x ^ ' - d X

= = j £ r

d u <d / d f \ d ^ * T u (T u )

U cl u ruAx = As = As .d t d t d u

u

cdu d (x - Vt) +„T t - ~ T f — = - v

dy _ df (tv) _ ±v d f d t du d u


2 2 8

Jjrd t2

^ ,-y Jf. = _Jud U c) t

V2 <i2f

J _ ( ±VJ £ ,^ u d u

Substitution

V 2 <j>2f d u2

1 J 2 f /0Qk <J u2

/°o k

V = /00k (116)

Adiabatic Compression

Definition

pv = c (117)CpCV

Differentiate

* dp + p Y v “^dv ir

= 0

dvdp

vV """1 p <3 V X

Substitute into Compressibility Equation

k = . = + l Vv dp (118)


2 2 9

Substitution

V = 1 2 "P ./°°-

pv = nRT nRTP = v

-0 dynes ,R _ergs^ Cm2 — )(i dyne-cm\ (mOK \gm mole-°K' erg ''r> g m s

' 0 cm3 / JVJ gms--- )gm mole

V <y RT M

RTM

(119)

Pressure Variations in a Sound Wave

Pressure Equation

1 dy k dx

Sound Wave Equation

y = Ycos 2T f (x - V t )7 ~

Differentiate and Combine Equations

dydx

(120)

(121)

Ysin 27T(x-Vt) [" 2 7T1 2?TYsin 27T(x-vt)X ~ . X “ ~ A J

2TTy sin p = ~ k T

2TT(x-Vt)7 T


230

_ iV =

. A kV2 = — ~ /°ok

/°oV‘

P =

P =

2lT/OnV2Y sin 27T(x-Vt)d

pmaxsin 27E(x-Vt) A

max

max

277/0 0V2Y 27T/0 o RTY _ ^

= 2 7 7 > 0cPRTYH A Cy

pmax ' 27r«/>oCpRT'cvM

Intensity of a Sound Wave

Work Done on System P

w = - pdv o

k = . 1 ^ 1 vQ dp

dv = kv0dp P

w = +1 kvQpdp = kvQ El2P

kvQp2

(122)

(123)


2 3 1

Energy per Unit Volume

wmaxVn ■§kp*max

Intensity

Definition

I = (energy)

I =

(unit area)(unit time)

<JkpL r ^ r !S)u cm)(Vdt cm)(A cm^)(dt sec)

ikp2 v dyne-cm max cm -sec

V =

k

cpHTv T/O0V'

cyM

/°ocPRT

I =

kv =

^max2/"o

CyM ~CpRT~ 12 CyM

I o o _ cvI\ CpHTI 1

/°o

cvMCpRT


(124)

(125)

(126)

232

FIGURE 78

INTENSITY FLOW CHART

cmsec

cm

cm(V sec.) (dt sec.)


2 3 3

Definition of a Decibel

/ 9 = 10 log ^o

(127)

/3 - sound intensity level, decibels

Io16 watts

P,max 0.002 at Io„n-16 watts .10 T— 1in aircm

Standing Waves

Definition

Standing waves are caused as a result of the reflection of sound waves back from the end of a tube. The total displacement is the sum of the displacements of the original wave and the reflected wave. Whereas, in a travelling wave the amplitude remains constant as the wave form progresses, in a standing wave, the amplitude fluctuates and the wave form remains fixed.

Derivation of Standing Wave Equation

Displacement of Original Wave

yx = Ycos . § p x“vt) (128)

Displacement of Reflected Wave

( 1 2 9 )


2 3 ^

Total Displacement

y = y1 + y2 = Ycos

Ycos

= Ycos

2jT_( x-'/ t)

27T(x-vt) L A-

27T(x-vt)A.

Ycos

- Ycos

- cos

2?T ( - x - V t ) A-

2TT(x+vt)A

27T(x+Vt) A.

y = Y<2sin

cos (c< - ) - cos ( +/<3 ) = 2sine^sin/<?

27TxA s m 2TTvt_ _ _

1 = 7TV = fA.

y = 2Ysin 27Tx s m 27Tf A tA = 2Ysin 2TT:

A sin [2TT ft]

y = 2Ysin(27Tft)-1 2IT xsin A

Figure 79 defines the various terms associated with a standing wave.

Fundamental Frequency

f = ° aU

A o =

V cpRT'. ~ V f.


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

FIGURE 79

SCHEMATIC DRAWING OF A STANDING WAVE

A

y " ^maxp = 0

Displacement antinode Pressure node

y = 0P = Pmax

Displacement node Pressure antinode

235

236

v_ CpRT , CVM-

12

"Tuned11 Wavelengths and Frequencies

4L 3i

5i|Ln

CpRT' 2 _1_ CpRT' 2 3 CpRT 2 _5_ CpRT. CyM- 4L . CVM. - cvM. 4l - cvMj

n

n = 1,3,5,7,9,etc.

Summary of Ultrasonic Engineering Equations

Sound Wave Equation

y = Ycos

y = Y J max

2ir u-vt) 7 T “ = Ycos 27Tf(t-*)

Vf

Transverse Velocity

v = -2 7TfYsin27Tf(t-^)

vmQV = 27TfYITISIX


=-47r2f2Ycos2TTf(t-^)

(130)

(111)

(112)

(13D

( 1 1 3 )


2 3 7

amax = 47r2f2Y (132)

Velocity of Propagation

V =1 1

1 1 s " V r t] 2. /OoK M J (119)

Acoustic Pressure

P =

max

s m 27T(x-Vt) A

27T/0 0V 2Y 27T>o o RTY 2 Tf/P0cpRTY7 " M X “ M A c,"V

(133)

cpRT- [ W ]

CpRTcVM_ (122)

Intensity2

j _ pmax c £2/00LoPBT (126)

/? = 10 log = 10 log —cm2

(127)

Amplitude

Y = pmax2 7 T f ^ 0

' v.CpRT.

1s

(13*0


2 3 8

Standing Wave Equation

2 7T xy = [2Ysin(2 7fft)] sin- A (135)

"Tuned11 Wavelength and Frequencies

A = 5

f =

Min12cpRT" 2 1 "cpRT 2 3 cpRT 2 5 cpRT

L °vMJ 4L* I CVMJ L 4L» .CVM Jn4L

n = 1,3,5,7,9,etc.

Typical Values of Wave Characteristics

The following values are calculated at the extreme temperatures employed in this research, 650°F. and 1050°F., and at the two frequencies studied, 2 6 ,000 cps and 39,000 cps. Additionally, the calculations are made at the maximum power output of the equipment at each frequency and at one-half that power output.

Power Output

/3 = io log ±- io(127)

/G = power output, decibels = 161 db at 26,000 cps = 150 db at 39,000 cps

.-16 wattsI0 = constant, 10 cm4

I = intensity, wattscm^


2 3 9

At 26,000 cps,

l0s t; = = T r = 16-1

= 1 .259 x 10160

1 = (1 .259 X 10l6)(10"16) = 1 .259 -— -Iscm^At 39j000 cps,

lop- — = = 1 5 0I0 10 10 i:?,u

15JL = 10 IoI = (1015) (10“l6) = 0.100 W & t scm^

The following calculations are for a temperature of650°P., a frequency of 26,000 cps and an acousticalintensity of 1 .259 ^at|s.cm^

Acoustic Pressure

'cpRT CVM^max = [2/V] (122)

. PM (1.0 atm)(120.19 P ^ m o T e ) n/O - -- = rf— i----= 0.00238 ---- --

RT (82.06 — uy) ( 6i 6°k7 cm3gm mole UK

I = (1 .25 9 i s a ^ x i o 7 ^ .sa=sm ) = 1 .25 9 x 107cm^ watt-sec cm-sec


2k 0

CpCV

°-S88 ^0.571 gm-uC

1.030

R = 8 .31 x 107 — ga=9s-----sec^-gm mole- K

T = 6l6°K.

M = 120.19 — g — ,' ■■ gm-mole

max(2 )(0.00238 gnis / 8 ^ 3 ) (1 .259x10° dynes

cm-sec .gm-cm

X'2

1 dyne-sec^n wt>t(1.030)(8.31x10' R f i n 2 - g m mnle.oK )(6l6°K)

gm-cm

120 IQ — snui--U* y gm moleQ M.<t 4(5 9.928x10^ -s-ec) 2{k.3868xl08 ^-p)r*m2 - *sec

= ( 7.7^1xl02) (1 .^7xl02) dyn|scm

i .i z o x i o5 cm2

_ (1.120xl05 d4 !!y)(2.2^81xl0‘~6 ~max cm ■) _

(0.155 cm^

dyne = 1. 6i

Velocity of Propagation

V = 'cpRT

7 gm-cm'_______(1. 030) ( 8. 3lxlO sec2_gm inole_oK ) (6l6 K)

(120.19 — SHls ) gm mole


14

lbin^

( 1 1 9 )

2 4 1

V = 2 0 , 9 4 5 H j -

AmplitudepY = max CyM

STTf^p LCpRTj 27ff/0pmax

oV ( W

(1.120x105 iei£)(1 Kg--°m )cm2 avne-sec2 /(2TT)(26,000 5^X0.00238 f®§)(20,945 ffj)

Y = 0 ,0138 cm.

Transverse Velocity

v = 2 77fY (13 1)max= 2Tf( 26 ,000 ^ 5 X 0 .0138 cm)

=2,254 cm.max 7 sec.


a•max = W 2f 2l = 2^ fvmax (132)_ 2-71(26,000 ^r>(2.254 ^

(980 cn/sec2)g

amax = 375,734 g

The results of similar calculations for temperatures of 650°P. and 1050°P., frequencies of 26,000 cps and 39*000 cps, and power outputs of full power and one-half power are shown on the following Table 11.


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TABLE 11

SUMMARY OF TYPICAL WAVE CHARACTERISTICS

T, temperature, F. 650 650 650 650

f, frequency, 26,000 26,000 39,000 39,000

Power output full half full halft . . .. watts I, intensity, -cm. 1.259 O .630 0 .100 0 .050

crm qp , gas density,' ° cm-' 0.00238 0.00238 0.00238 0.00238

cp//°v 1.030 I .030 1.030 I .030

cmV, velocity of propagation, ——b v O 20,9*15 20,9*15 20,9*15 20,9*15

A , wavelength, cm. 0.806 0.806 0.537 0.537p , acoustic pressure, max 2.Y1Z 1 .62 ' 1.15 0 .Ifo 0 .32

Y, amplitude, cm. 0.0138 0.0098 0.0026 0.0018cmvmax> transverse velocity se0 2,25*1 1,601 637 Zi4l

amax, transverse acceleration, g. 375,73*1 266,881 159,279 110,270

Z\\Z

Reproduced

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TABLE 11 (continued)

SUMMARY OP TYPICAL WAVE CHARACTERISTICS

T, temperature, P. 1050 1050 1050 1050

f, frequency, s*c 2 6 ,0 0 0 2 6 ,00 0 39,000 39,000Power output full half full halfI, intensity, cm^ 1 .2 5 9 0 .6 3 0 0.100 0 .0 5 0

*3 , gas density,' O cm_5 0 .0 0 1 75 0.00175 0.00175 0.00175

cp//cv 1.024 1.024 1.024 1.024p mV, velocity of propagation, ---sec 24,298 24,298 24,298 24,298

^ , wavelength, cm. 0.935 0.935 0.623 0.620p , acoustic pressure, — -msx j_n 2 1.50 1.06 0.42 0 .3 0

Y, amplitude, cm. 0.0149 0.0105 0.0028 0.0020cmvmax» transverse velocity, sec 2,434 1.715 686 490

a , transverse acceleration, g.lilctX 405,740 285,885 171,531 1 2 2 ,5 2 2 -P-

2 4 4

Summary of Ultrasonic Engineering Nomenclature

cmV = velocity of propagation of wave form, -— 7sscY = amplitude, cm.

A = wave length, " -gf-

t = time, sec.x = distance traversed by wave form, cm. y = displacement, cm.

f = frequency, s^ ~ g~

T = Perlod.cmv = transverse velocity,

a = transverse acceleration,sec

cmsec2

g = conversion factor, 980 ^^ne-s tac * gm.p - original gas density, ~' 0 emu

2 2 1 cm-secdyne’ gm *-«— sec

cP

k = compressibility, SHi=§M.c. (dyne = M )

CVCeilCp = heat capacity of gas at constant pressure,

Cellc^ = heat capacity of gas at constant volume, — - -g-g

R - 8 Si x 107 = 8 01 x 107 dyne-cm ,“ x 1U mole-°K a *J>1 x 10 gm mole-°K

(erg = dyne - cm = SHl=cjp£)sec^


2^5

T = temperature of gas, °K.

M = molecular weight of gas, — Sm s —^ * gm-mole

p = pressure, f--cm^

Pmriv = maximum pressure caused by sound wave, max cm2

I = intensity, — F ^ _ , ^ e ^ c m (10-7 watt-se0)cm -sec cm -sec er£

/S - sound intensity level, decibels -16 wattsI0 = 10 cm^

L = reactor length, cm. n = 1,3,5,7,9,etc.


APPENDIX XI

DESIGN EQUATION FOR

PSEUDO FIRST ORDER REACTION


2^7

DESIGN EQUATION FOR PSEUDO FIRST ORDER REACTION

Plup; Flow Heactor Design Equation

XAfW dX■A

^ F T T (136)PAo j ' A XA0

VJ = wt. catalyst, gms.

PA = feed rate of A, moles AAo * sec.XA q = initial conversion of A

XAj, = final conversion of A

( —rA) = reaction rate,A * gm cat-sec

Reaction

c 6h 5- ch-(c h 3)2 c 6h 6 + c h 3- ch= c h 2

Gumene Benzene Propylene

kA - R + Sk*

Rate Equation

(-rA ) = kpA - k'pRps (137)

nART PA = = GART

nHRTP r - \j ~ G r R T

ruRTPS = — = CSRT


2^8

(~rA ) = kHTCA - k'(BT)2CRCs

(-r.) = reaction rate, gi71 moles A A gm cat-sec

PA , Pr» P5 = partial pressure, atm.

k = forward reaction rate constant for overallreaction, ----’ gm cat-atm-sec

k' = reverse reaction rate constant for overallreaction, £BU!l°ie| -

gm cat-atm^-sec

R = 82.06 ~ 3=f,tm0vgm mole-°K

T = °K.CA , CR , Cs = concentration, finL_mol.es

Substitute Rate Equation into Plug Flow Reactor Design Equation

XAfW _ f ^LXa 0

' j kHTCA - k'tRD^CjjOg (138)

XAo

Assume Pseudo First Order Reversible Reaction

Reactionkp

A ----- - Rk 1 p


2 ^ 9

Rate Equation

(-rA ) kpCA - k'pCR (139)

kp cRek'p " CA " CAe

Material Balance

A

R

Total

InletNAo=NA .

% o = % 0

Reactor OutletNa =--Na 0-Xa Na 0

% = N r o-x a nAo

nA0+NRo NAq+nR0

NAf=NA0“XAfNA0

NRf=NR 0+xAfNA0

nA0+nR0

% _ MA0-XANAn = NAoii^A), = cAo(l-XA) = GA0"GAoXA CA = V v V

Nr NRo+Xa NAo _ + 5AoXA = Cr^ + CAriXACR = T = ~ v v

Substitution

(-rA ) = kp(CAo-0AoXA ) - k'p (CHo + 0AoXA )

= kp0Ao(l-XA ) - k'pcAo < +XAAt Equilibrium

CRok =

CR0 + Ga 0Xa GA0 XAek». CArt - Ca A 1 - XA,


250

^ 2 + x a = (l-XAe) Ca „ A® k'0h o kp <l-XAe ) - XAe°A0 k 'p

Substitution

(-rA ) = kpCAn(l-XA ) - k'pCAP Ao F Ao[E_ (i-xAfi) - xAe + xAk'

= kp0Ao-kpcAoxA-kpcAo+kpcAoxAe+k'pCA0XAe"k'pcAQXA

= kp(oAoxAe-cAoxA ) + k'p(cAoxAe-cAoxA )(-rA ) = (kpPk'p)CAri(XA<s-XA )P p' Ao Ae (14-0)

Substitute Rate Equation into Plug Flow Reactor Design Equation

w dXAFao j <kp+k,p)CAo(XAe-XA>

Initial rate (XA = 0)

ro = (kp+ k 'p)GA0(XAe-XA) = (kp+k'p )CA0XAer

(kp+k'p)CA0 - Xa°


251

XAf

W _ XAe I dXAPAo ro (X e~XA>

XAoIntegrate

WFA, -ln(XAe-XA )

XAf X XA(

XAq=0o

, ,XAe-XA%

XA, -ln(1 - XA XA,

W XAe InFa _ r Ao ro

-Xa (3Al)XAe J

Calculate XAf

'RaK = CA„ + Xa

1 - xAo

K =

Gr o = 0

XAe1 - XAc

:A r = k - kxa

XAf KK + 1


252

Tabulate Results

T. °F • K , atm. XA"e850 2.01 0 .6 2 6950 6.21 0.861

1050 15.96 0.9^2

r 1w xA

Plot ^A0 vs> in 1 “ *AeJ as Shown in Figure 80 toDetermine ro

This plot can now be employed to calculate the initial reaction rate, r , as a check against the values determined by extrapolation of the reaction rate vs. conversion curves.


2 5 3

W gm cat-sec FAq» gm mole

FIGURE 80

PSEUDO FIRST ORDER PLOT OF DATA

950 F. 0.861

Slope =

1In


APPENDIX XII

RATIO OP EFFECTIVENESS FACTOR FOR

DIFFERENT SIZE CATALYST PARTICLES


2 5 5

RATIO OP EFFECTIVENESS FACTOR FOR

DIFFERENT SIZE CATALYST PARTICLES


WpA, = X

in(1+XA5 ) Xa( 1-XA 5 ) 5 2

■ f i

i in( i+xa <5 )2 s, 3 (1-XA 5 ) 2 S 2

1 ln(l-^2XA2) Xa£ 2

(99)

eLk2KA7T Lk22 Kr

& " eLk2KA7T + 6" Lk2KA

1 + 21K

At constant conversion, pressure and temperature, &

and X^ are constant and the reaction design equation reduces to the following:

WpA, «fLk2KA7t <SLk2

_1_6_i_€

Lk2K a7T Lk2

Ci +

'1 +

+ KrCLk2KaTT ^Lk KA

Lk2KA7T + Lk2KAkb.

c3 G1 + C2

ce 5 (1^2)


2 5 6

Ratio of Reciprocal Space Velocity

WPAoJW

PAo

1 =

2

£ 2

^2e.

(1^3)

Plot W/PAq v s . XA for Various Size Catalyst Particles as

Shown in Figure 81

Plot W/Pa0 v s . dp at Constant and Extrapolate to dp = 0

as Shown in Figure 82

Calculate Effectiveness Factor Employing; Example Data

CatalystNo.

^Pcm,

r W 1_FaoJ0W p;m cat-sec w

PA » Sm mole PAo

0 0 l.i o ii t-. w*

• • [—1

1 o.o^5 1.3 f 1.1l ~ 1.3

2 0.33 5.7 ^ l.l 2 " 5.7

3 0 A 3 7.6 l.l

0.53 10.0 fT 1.1 ^ 10.1

= 1.00

= 0.85

= 0.19

= 0.15

r = 0.11


2 5 7

FIGURE 81

RECIPROCAL SPACE VELOCITY VS. CONVERSION

0.28

7.61.3 5.7 10.0wPA0


2 5 8

FIGURE 82

RECIPROCAL SPACE VELOCITY VS. CATALYST PARTICLE DIAMETER AT CONSTANT CONVERSION

(XA = 0.28)

1

dP


2 5 9

Relationship Between Effectiveness Factor and Catalyst Particle Diameter


WPAoj

= -p- f(X^) at constant temperature (14^)and pressure

If only the outside surface of the catalyst is effective, then £ = C^a, where

= a constant

a = outside surface area of catalyst cm^unit mass » gm

= (4 TTrp2 7^ )

(3 ^ rP3/°P pellet

2di j f (~Z~)

6dp^d p ^ p

dp/^p

6C6dp/^p

dp = Gy _1_

£


260

XA plot of dp vs. £ should yield a straight line if this assumption is true as shown in Figure 8 3.

J X = _X_ f(xA ) = f(xA )PAo ^1 c7

W = x f(xA ) = G8f(xA ) (145)PA0dP C7

Data for all size catalysts should fall on thecurve of V/ vs. XA .

pA0dp


2 6 1

FIGURE 83

RECIPROCAL EFFECTIVENESS FACTOR VS. CATALYST PARTICLE DIAMETER

d p , cm.


2 6 2

FIGURE RE

CONVERSION VS. WL % dPD

XA


APPENDIX XIII

THE CARBON-OXYGEN REACTION


26^

THE CARBON-OXYGEN REACTION

During several of the initial runs in this study, a problem was encountered with carbonization of the cumene at reaction temperatures of 1000°F. and subsequent plugging of the reactor and fouling of the catalyst. Carbonization was sometimes so severe that it was often very difficult to remove the preheater from the reactor to clean it.

This problem was solved by purging the reactor with air at reaction temperature for hours after each run to burn off the carbon.

The Carbon-Oxygen Reaction Rate Equation

For the reaction

0 + 02 ► 002

B(S) + A(g) -------- — gaseous product,37Parker and Hottell^' have shown that the rate equation for

surface reaction controlling is as follows:

4.32 x lO1^ -*<4.000 _r = g.----- k e rt (1*1-6)B rn g

- gm.moles carbon reacted sec-cnk

T = °K.CA™ = concentration of oxygen, -moles S cm-3

« ■ 1 -98 r f k s g


2 6 5

Calculation of Rate Constant, ks

4.32 x lO1^ e~— - k = —^ — 1----- e rtS rjnvj

cmk = rate constant, ---s * sec

= (850°P.)^ = (7270K)‘ = 27°K^

44,000 — p-a^r- * p;m mole,14 -, . 4.32 x 10 e m oft---- Pff.l ---- ) ( 797°K)s " 27 U , V gm mole-°K

0 .15 9 8 x lO1^ e" 3 0 * 6

(0 .1 5 9 8 x lO1^)(5.137 x lO"1^) = 0.821 cmsec

Calculation of Oxygen Concentration, CAg

c = ___________ (1 .0 atm. ) (0 .2 1)_________Ag (0.0821 |jrf ^ t ^ ><727°K ><1000 Xlter1

= 3.52 X 1 0 - 6 g m -m °^-escitP

Calculation of Reaction Rate

■r B = k s CA g = < 0 - 8 2 1 ^ 5 ) ( 3 - 5 2 x I Q ' 6

= 2 .8 9 x 1 0 - 6 P r o l e s cm^-sec


2 6 6

Calculation of Maximum Weight of Carbon

Assume 5% carbonization at a feed rate of 600 gms./hr. cumene for 30 min.

(600 SffiS) (o,o5 ) (o .5 hrs) (12.011gms. carbon =

(120 12 — — ) tizu.iz gm mole;

= 1 .5 gms. carbon

Calculation of Available Surface Area

Reactor

S _ — (0.767 in)(20.5 in) _ 3i26 om2H (2 .5^ f®)2

Preheater

(0 .7 6 7 in.) ,(2 0 5 m ) = 7 i6 6 on]2

12.5* f®>2

Catalyst2

S = (13.1 ~ 5.7^8 gms) = 7 5 .3 0 cm2o gm

Total area = 86.22 cm2

Required Reaction Time(1.5 gms)t —<12-011 iifsk 2-8 10'6 ^ ' 60 ^ 86-22 om2>

= 8.^ min.


2 6 7

On several occasions, after two 20 minute runs, the reactor was purged at 850°P. for 30 minutes with air. The reactor was subsequently disassembled and found to be essentially free from carbon.


APPENDIX XIV

DATA


2 6 9

DATA

The following Table 12 lists all the data collected in this research. The digits before the decimal point in the Run No. signify a series of runs made at the same temperature. The first or first and second digits after the decimal point signify runs made at the same temperature and feed rate. The last digit after the decimal point signifies the following:

1 - 39,000 cps2 - 26,000 cps3 - no ultrasound

A coding system was necessary to avoid confusion since a total of ^79 runs were made, involving some 64-0 samples and 1,920 gas chromatograph analyses.

In every case, a run in the absence of ultrasound was made before and after the application of ultrasound. The analyses reported are the average of six samples, three samples being taken before and three samples after.

The order in which the 39,000 cps and 26,000 cps ultrasonic frequencies were applied were randomly reversed throughout the entire investigation.

Conversions were calculated from liquid samples, but were checked often against gas samples taken directly from the reactor.

Figure 85 illustrates an actual data sheet.


Reproduced

with perm

ission of the

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without

permission.

FIGURE 85 DATA SHEET

Run No.DateCatalyst, gms.Bed Height, cm.TimeTank Height, in. Rotameter, mm.Rota. Feed Rate, gms/hr, Tank Feed Rate, gms/hr. Heater No. 1 Heater No. 2 Heater No. 3 Heater No. 4 and No. 5 Hot Oil Heater TI-1,°F.TI-2,°F. t i -3,o f .TI-4,°F.TI-5,°F.TI-6,°F.TI-7,°F. (Hot Oil)TC-1,°F.UltrasoundW/F,gm cat-sec/gm mole Cumene, %Benzene, %Propylene, %Conversion, X Nitrogen Purge Air Purge

16.15-1-725.7^8

Reactor Diameter, cm. Frequency, cps Power, watts

0.992 39,26 2510. 158 Feed Tank Diameter, in. 1

1225 124-5 1330 1350 14-10 14-30 1450 151032.85 32.85 31.05 30.4-0 29.70 29.00 28.20 —

- 26 26 26 26 26 26 _

— 25 25 25 25 25 2524-40

-

40 4-0 40 4-0 4-0 40 4-04-0 4-0 40 4-0 4-0 4-0 4-0 4-040 40 40 4-0 40 4-0 4-0 4040 40 4-0 4-0 4-0 4-0 4-0 40110 110 110 110 110 110 110 11070 70 70 70 70 70 70 70

710 710 710 710 710 710 710 710750 750 750 750 750 750 750 75 0750 750 750 750 750 750 750 750750 750 750 750 750 750 750 750750 750 750 750 750 750 750 750350 34-8 34-6 34-8 350 352 354- 352750 750 750 750 75 0 750 750 750off off off off 26 39 off —

- - — — — - 102,900 —

- - - 82.66 77.98 76.15 8 3.16 —

- - - 15.69 20.4-0 22.23 15.24-- - — 1.65 1.62 1 .62 1.60 —

- - - 22.6 28.7 31.0 22.0on off off off off off on off

off off off off off off off onro-<io

Reproduced

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without

permission.

Run Catalyst No. gms.

3.11 5.73 .1 2 5.73.21 5.73.22 5.73.31 5.73.32 5.73.41 5.73.42 5.73.51 5.73.52 5.73.61 5.73.62 5.73.71 5.73.72 5.73.81 5.73.82 5.73.91 5.73.92 5.75.11 0.9585.12 0.9585.13 0.9585.21 0.9585.22 0.9585.23 0.958

Bed Ht. Bed Dia. cm. cm.

10.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.99210.2 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.992

TABLE 12

TABULATION OP DATA

Ultrasound Feed Rate gms/hr

W/F gm cat-sec Temp.

°F.

XConvers

Pcps watts gm molemm 194 12,730 850 29.1- - 102 24,200 850 30.9- - 293 8,430 850 15.8- - 387 6,380 850 9.1- - 500 4,930 850 9.8- - 589 4,200 850 3.2- - 99 25,000 950 39.7- - 198 12,480 950 2 6.5- - 304 8,125 950 19.0- - 387 6,380 950 6.6- - 496 4,980 950 13.5- - 589 4,190 950 4.2- - 97 25,500 1050 51.3- - 194 12,750 1050 32.3- - 302 8,170 1050 23.4- - 407 6,075 1050 17.9- - 5 H 4,830 1050 14.8- - 600 4,120 1050 9.139,000 25 99 4,180 850 7.86

26,000 25 99 4,180 850 6 .67- - 99 4,180 850 6.2039,000 25 193 2,150 850 3.73

26,000 25 193 2,150 850 3.01- - 193 2,150 850 2.87

271

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without

permission.

Run Catalyst Bed Ht. Bed Di;No. sms. cm. cm.

5*31 0.958 1.693 0.9925.32 0.958 1.693 0.9925.33 0.958 1.693 0.9925.41 0.958 1.693 0.9925 A 2 0.958 1.693 0.9925.43 0.958 1.693 0.9925.51 0 .958 1.693 0.9925.52 0.958 1.693 0.9925.53 0.958 1.693 0.9925 .61 0.958 1.693 0.9925 .6 2 0.958 1.693 0.9925.63 0.958 1.693 0.9926.11 0.958 1.693 0.9926 .12 0.958 1.693 0.9926 .13 0.958 1.693 0.9926.21 0.958 1.693 0.9926 .2 2 0.958 1.693 0.9926.23 0.958 1.693 0.9926 .31 0.958 1.693 0.9926 .3 2 0.958 1.693 0.9926.33 0.958 1.693 0.9926.41 0.958 1.693 O .9926.42 0.958 1.693 0.9926.43 0.958 1.693 0.992


TABULATION OF DATA

Ultrasound Feed Rate gms/hr

W/F gm cat-sec Temp.

op.X

Convers%CPS watts gm mole

39,000 25 296 1,400 850 2.3526,000 25 296 1,400 850 2.15

- - 296 1,400 850 1.6539,000 25 392 1,158 850 1.3226,000 25 392 1,158 850 1.15

- - 392 1 ,158 850 0.76339,000 25 501 327 850 0.42926,000 25 501 827 850 0.275

- - 501 827 850 0 .23839,000 25 586 707 850 0 .81626,000 25 586 707 850 0.669

- - 586 707 850 0.50539,000 25 99 4,180 950 7 .0226,000 25 99 4,180 950 5.69

- - 99 4,180 950 5.3039,000 25 192 2,150 950 3.0626,000 25 192 2,150 950 3.01

- - 192 2,150 950 3 .2639,000 25 285 1,453 950 2.0326,000 25 285 1,453 950 1.80

- - 285 M 5 3 950 1 .6239,000 25 382 1,083 950 0.73426,000 25 382 1,083 950 0 .6l6

- - 382 1,083 950 0.671 ZiZ

Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Run Catalyst Bed Ht. Bed Dia No. gms. cm. cm.

6.51 0.9586 .5 2 0.9586.53 0.9586 .61 0.9586 .6 2 0.9586 .6 3 0.9587 . U 0.9587.12 0.9587.13 0.9587.21 0.9587.22 0.9587.23 0.9588.11 0.9588.12 0.9588.13 0.9588.21 0.9588.22 0.9588.23 0.9588.31 0.9588 .32 0.9588.33 0.9589.11 1.9169.12 1.9169.13 1.916

1.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9921.693 0.9923.386 0.9923.386 0.9923.386 0.992


TABULATION OF DATA

W/F XUltrasound Feed Rate gm cat-sec Temp. Conversion cps watts gms/hr gm mole QF. %_____

39,000 25 4-91 84-3 950 0.69126,000 25 491 84-3 950 0 >92- - 4-91 84-3 950 0.326

39,000 25 593 698 950 0.27726 ,000 25 593 698 950 0.24-9

- - 593 698 950 0.25839,000 25 98 4-, 225 1050 5.3926 ,000 25 98 4-, 225 1050 4-. 01

- - 98 4-, 225 1050 3.9839,000 25 211 1,963 1050 2.5026,000 25 211 1,963 1050 2.70

- - 211 1,963 1050 3.9539,000 25 98 4-,230 1050 5.9726,000 25 98 4-,230 1050 5.35- - 98 4-,230 1050 5.1739,000 25 205 2,020 1050 2.76

26,000 25 205 2,020 1050 2.21- - 205 2,020 1050 2 .32

39,000 25 304- 1,363 1050 1.5926y000 25 304- 1,363 1050 1.53- - 304- 1,363 1050 2.06

39,000 25 92 8,980 950 16 .6226,000 25 92 8,980 950 13.56

- - 92 8,980 950 12.26

Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.


TABULATION OF DATA

RunNo.

Catalyst ffms.

Bed Ht. cm.

Bed Dia. cm.

Ultrasound cps watts

Feed Rate gms/hr

W/F gm cat-sec gm mole

Temp. F .

XConver

%

9.21 1.916 3.386 0.992 39,000 25 202 4,090 950 6.339 .2 2 1.916 3.386 0.992 26,000 25 202 4,090 950 6.539.23 1.916 3.386 0.992 — — 202 4,090 950 7.009.31 1.916 3.386 0.992 39,000 25 306 2,980 950 5.179.32 1.916 3.386 0.992 26,000 25 306 2,980 950 4.979.33 1.916 3.386 0.992 — — 306 2,980 950 4.979.41 1.916 3.386 0.992 39,000 25 l}-22 1,965 950 3.089.42 1.916 3.386 0.992 26,000 25 422 1.965 950 2.599.43 1.916 3.386 0.992 — 422 1,965 950 2 .389.51 1.916 3.386 0.992 39,000 25 495 1,673 950 1.549.52 1.916 3.386 0.992 26,000 25 497 1,673 950 1.529.53 1.916 3.386 0.992 — — 495 1,673 950 1.419 .61 1.916 3-386 0.992 39,000 25 606 1,368 950 1.889 .6 2 1.916 3.386 0.992 26,000 25 606 1,368 950 1.699.63 1.916 3.386 0.992 — — 606 1,368 950 1.4610.11 1.916 3.386 0.992 39,000 25 112 7,390 850 6 .0910.12 1.916 3.386 0.992 26,000 25 112 7,390 850 4.79

1 0 .13 1.916 3-386 0.992 — — 112 7,390 850 5.1210.21 1.916 3-386 0.992 39,000 25 203 4,080 850 4.3010.22 1.916 3.386 0.992 26,000 25 203 4,080 850 3.8510.23 1.916 3.386 0.992 — — 203 4,080 850 3-5710.31 1.916 3.386 0.992 39,000 25 310 2,670 850 2.1410 .32 1.916 3.386 0.992 26,000 25 310 2,670 850 2.3410.33 1.916 3.386 0.992 - - 310 2,670 850 2.00

Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Run Catalyst Bed Ht. Bed Dia.No. gms.

10.41 1.91610.4-2 1.91610.4-3 1.91610.51 1.91610 .52 1.91610.53 1.91610.61 1.91610.62 1.91610.63 1.91611.11 5.74-811.12 5.74-811.13 5.74-811.21 5.74-811.22 5.74-811.23 5.74-811.31 5.74-811.32 5.74-811.33 5.74-811.4-1 5.74-811.4-2 5.74-811.4-3 5.74-811.51 5*74-811.52 5.74-811.53 5.74-8

cm._____ cm.

3. 386 0 .9923. 386 0 .9923. 386 0 .9923. 386 0 .9923.386 0 .9923.386 0 .9923. 386 0 .9923. 386 0.9923. 386 0 .992

10. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0 .99210. 158 0.99210. 158 0 .992


TABULATION OF DATA

W/F XUltrasound Feed Rate gm cat-sec Temp. Convers:cos watts gms/hr gm mole °F . %

39,000 25 393 2,110 850 1.9726,000 25 393 2,110 850 1.67

- — 393 2,110 850 1.5339,000 25 4-84- 1,73A 850 1.2926,000 25 4-84- 1,714- 850 1.09- - 4-84- 1,71^ 850 0.84-0

39,000 25 609 1,370 850 0.63726,000 25 609 1,370 850 0.4-15- - 609 1,370 850 0.4-98

39,000 25 108 23,100 1000 29.326,000 25 108 23,100 1000 26 .3- - 108 23,100 1000 24-.2

39,000 25 208 11,950 1000 21.226,000 25 208 11,950 1000 24-.1

- - 208 11,950 1000 23 .639,000 25 302 8,250 1000 17.726,000 25 302 8,250 1000 16 .8

- - 302 8,250 1000 16 .839,000 25 4-26 5,84-0 1000 13.026,000 25 4-26 5,84-0 1000 12.5

- — 4-26 5,84-05,150

1000 13.639,000 25 4-84- 1000 12.126,000 25 84- 5,150 1000 10.6

- - 4-84- 5,150 1000 11.0

275

Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Run Catalyst Bed Ht. Bed Dia.No. gms.

11.61 5.74811 .62 5.7481 1 .63 5.74812.11 5.47812.12 5.74812.13 5.74812.21 5.74812.22 5.74812 .23 5.74812.31 5.74812.32 5.74812.33 5.74812.41 5.74812.42 5.74812.43 5.74812.51 5.74812.52 5.74812.53 5.74812.61 5.74812.62 5.74812 .63 5.74813.11 5.74813.12 5.74813.13 5.74813.21 5.748

cm._______cm.

10,.158 0 .9921 0,.158 0 .99210..158 0 .99210,.158 0 .99210,.158 0.99210,.158 0 .99210,.158 0 .9921 0,.158 0 .99210,. 158 0 .99210,.158 0 .99210,.158 0 .99210,.158 0 .99210., 158 0 .99210,.158 0 .99210,.158 0 .99210,.158 0 .99210,.158 0 .9921 0,.158 0.9921 0..158 0 .9921 0..158 0 .9921 0,.158 0 .9921 0,.158 0 .9921 0 ,,158 0 .9921 0,.158 0.99210..158 0 .992


TABULATION OF DATAW/F X

Ultrasound Feed Rate gm cat-sec Temp. Conversion cps watts gms/hr gm mole °F. %______

39,000 25 593 4,200 1000 8.4926,000 25 593 4,200 1000 8.39

- - 593 4,200 1000 7.9439,000 25 101 24,600 950 27.226,000 25 101 24,600 950 22 .9

— — 101 24,600 950 22.039,000 25 201 13,400 950 16.126,000 25 201 13,400 950 16.0

— — 201 12,400 950 16.039,000 25 321 7,750 950 14.426,000 25 321 7,750 950 12.4

- - 321 7,750 950 11.939,-000 25 41? 5,975 950 10.626,000 25 417 5,975 950 10.1

- - 417 5,975 950 9.9339,000 25 483 5,150 950 9.3226 ,000 25 483 5,150 950 9.67

- - 483 5,150 950 8.9739,000 25 589 4,230 950 8.0826,000 25 589 4,230 950 8.13

- - 589 4,230 950 7.6239,000 25 102 24,400 900 13.126,000 25 102 24,400 900 11.8

- - 102 24,400 900 12.039,000 25 212 11,730 900 11.6

Reproduced

with perm

ission of the

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ner. Further


without

permission.


TABULATION OF DATA

W/F XRun Catalyst Bed Ht. Bed Dia. Ultrasound Feed Rate gm cat-sec Temp. Conversion Ho. gms. cm. cm. cps watts gms/hr gm mole °F. % ______

13 .22 5.748 10.158 0.992 26,00013.23 5.748 10.158 0.992 —

13.31 5.748 10.158 0.992 39,00013 .32 5.748 10.158 0.992 26,00013 .33 5.748 10.158 0.992 —13.41 5.748 10.158 0.992 39,00013 .42 5.748 10.158 0.992 26,00013 .43 5.748 10.158 0.992 —

13.51 5.748 10.158 0.992 39,00013 .52 5.748 10.158 0.992 26,00013 .53 5.748 10.158 0.992 —13.61 5.748 10.158 0.992 39,00013 .62 5.748 10.158 0.992 26,00013 .63 5.748 10.158 0.992 —14.11 5.748 10.158 0.992 39,00014.12 5-748 10.158 0.992 26,00014.13 5,748 10.158 0.992 —14.21 5.748 10.158 0.992 39,00014.22 5.748 10.158 0.992 26,00014.23 5.748 10.158 0.992 —14.31 5.748 10.158 0.992 39,00014.32 5.748 10.158 0.992 26,00014.33 5.748 10.158 0.99214.41 5.748 10.158 0.992 39,00014.42 5.748 10.158 0.992 26,000

25 212 11,730 900 10.6- 212 11,730 900 9.8825 331 7,520 900 10.525 331 7,520 900 9.71- 331 7,520 900 9.7825 425 5,870 900 7.9825 425 5,870 900 8.37- 425 5,870 900 8.1825 510 4,880 900 6.7325 510 4,880 900 6. o4- 510 4,880 900 6.6425 639 3,900 900 7.0425 639 3,900 900 5.92- 639 3,900 900 5.6325 38 65,500 850 30.425 38 65,500 850 21.3- 38 65,500 850 20.525 87 28,600 850 26.725 87 28,600 850 26.1- 87 28,600 850 26.525 103 24,200 850 24.025 103 24,200 850 21.4- 103 24,200 850 20.325 220 11,320 850 15.025 220 11,320 850 13.9

2 77

Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.


TABULATION OF DATA

RunNo.

Catalyst . £ms .

Bed Ht. cm.

Bed Dia. cm.

Ultrasound cos watts

Feed Rate gms/hr

W/Fgm cat-sec Temp, gm mole °F.

XConver

%

14.43 5.748 10.158 0.992 220 11 320 850 12.414.51 5.748 10 .158 0.992 39,000 25 293 8 480 850 10.314.52 5.748 10.158 0.992 26,000 25 293 8 480 850 9.0814.53 5.748 10.158 0.992 — — 293 8 480 850 9.2014.6l 5.748 10.158 0.992 39,000 25 388 6 409 850 8 .5214.62 5.748 10.158 0.992 26,000 25 388 6 409 850 6.9314.63 5.748 10.158 0.992 — — 388 6 409 850 6.2214.71 5.748 10.158 0.992 39,000 25 526 u 730 850 5.7 814.72 5.748 10.158 0.992 26,000 25 526 4 730 850 5.5814.73 5.748 10.158 0.992 — — 526 4 730 850 5 • 6114.81 5.748 10.158 0.992 39,000 25 593 4 200 850 7.4714.82 5.748 10.158 0.992 26,000 25 593 4 200 850 5.9214.83 5.748 10.158 0.992 — _ 593 4 200 850 4 .5113.71 5-748 10.158 0.992 39,000 25 25 99 500 900 26.113.72 5.748 10.158 0.992 26,000 25 25 99 500 900 22.313.73 5.748 10.158 0.992 - - 25 99 500 900 23.913.81 5.748 10.158 0.992 39,000 25 45 54 800 900 28.113.82 5.748 10.158 0.992 26,000 25 45 54 800 900 23.613.83 5.748 10.158 0.992 — 45 54 800 900 21,512.71 5.748 10.158 0.992 39,000 25 28 90 500 950 63.312.72 5.748 10.158 0.992 26,000 25 28 90 500 950 51.212.73 5.748 10.158 0.992 — — 28 90 500 950 43.212.81 5.748 10.158 0.992 39,000 25 32 77 100 950 52 .612.82 5.748 10.158 0.992 26,000 25 32 77 100 950 44.112.83 5.748 10.158 0.992 - - 32 77 100 950 36.1

ho-S3CO

Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Run Catalyst Bed Ht. Bed Dia, No. gms. cm. cm.

15 .11 5..74815 .12 5..74815 .13 5..74815 .21 5..74815 .22 5.,74815 .23 5-.74815 .31 5-.74815 .32 5.,74815 .33 5.,74815 .41 5.,74815 .42 5..74815 A 3 5.,74815 .51 5..74815 .52 5-.74815 .53 5.,74815 . 6l 5.,74815 .62 5.,74815 .63 5.,74815 .71 5.,74815 .72 5.,74815 .73 5.,74815 .81 5..74815 .82 5.,74815 .83 5.,748

10,.158 0 .99210,.158 0 .99210,.158 0 .99210,.158 0 .99210..158 0 .99210,.158 0 .9921 0,.158 0 .99210,.158 0 .9921 0..158 0 .99210,.158 0 .99210..158 0 .99210..158 0 .99210,.158 0 .99210,.158 0 .99210..158 0 .99210..158 0 .9921 0..158 0 .99210.,158 0 .9921 0.,158 0 .9921 0..158 0 .99210..158 0 .9921 0 ,.158 0 .99210.,158 0 .99210..158 0.992


TABULATION OF DATAW/F X

. Ultrasound Feed Rate gm cat-sec Temp. Conversion cps watts gms/hr gm mole °F. % ______

39,000 25 23 111,000 800 57.226,000 25 23 111,000 800 49.3

— - 23 111 ,000 800 48.939,000 25 34 73,300 800 33-926,000 25 34 73,300 800 30 .2

- - 34 73,300 800 28.939,000 25 103 24,100 800 34.526,000 25 103 24,100 800 27.9

- - 103 24,100 800 26 .339,000 25 187 13,350 800 20.926,000 25 187 13,350 800 18.2- - 187 13.350 800 15.739,000 25 291 8,570 800 12.0

26,000 25 291 8,570 800 9.80- - 291 8,570 800 9.3439,000 25 391 6,375 800 8.68

26,000 25 391 6,375 800 7.18- - 391 6,375 800 5.6839,000 25 499 5 ,000 800 7.3926,000 25 499 5 ,000 800 5.66- - 499 5 ,000 800 4.3239,000 25 618 4 ,030 800 5.56

26,000 25 618 4 ,030 800 4.93- - 618 4 ,0 30 800 4.07

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00 CO 00 CO CO 00 X) 00 CO CO JO OO CO CO CO CO 00 X) GO 00 CO 00 CO 00 crJd d d d -3- j ! d d d d d d .j- d -j- d d d d d d d d d dC-CN-C-CN-C 'CrCN-CN-CN-CN-CrCN-CV-CrCN-C-CN-CN-O-C-C'-CN-C-C-C-

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12 (c

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2 8 2

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• * • • • • • • ■ • • • • • • • • • • • • • • •W H H ^ O l r t C M r t H O O O H O O C O ' A i A N H O O O O

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O O O O O O O O O v p u N U O O O O O O O O O O O O O U M A i n O O O iriCT|ir$M N CM Q\ O N O N O O O O O O H H HCM O.) CM pt~ p}' .cj* CM CM CM r—I i—! r—I t H t — I t — I O O CO On On On r—I *—I *—I

n o CP C O p f -)■ J j- CM CM C\! CO 0 0 CO N O ' . O O H H H O C ! O H H H UN, VP, u p CM CM CM rH T-l tH 0 0 00 GO CO OP CP r-1 rH rH

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Xj CO h h h w c j M n r , o p p I- _-± p}- OO CM CMO Eo r r

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•P CO o o O O O O o o o o o o o o o oi—I p | «n | n w | * , r » | • * • - 1 r - n I N * N 1 M 1Co cn ON VO ONVO ONVO On nO O' ■ '-Ci ON VO O '- O G -.'X i

CO CM o p cm n w cnn, cm f^NCM o p cm OP CM raoo

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• • • • • • • • • • • • • • • « • • • • • • • «O O O O O O O O O O O O O O O O O O O O O O O O

co co oo co oo oo oo co co co co co - / j co co -X) on co oo co cn oo on u o u p u p u p u p \ p , u p u p u p u p u p u p u p u p u p u p u p u p v o , u p u p u p u p u p^— t r — t x— I r H r H r H i — 1 x— I r — I r — I x—) x— ! x— I x— I r H r— I r H t H r H r H r — I r —t t H t H

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co co oo co co 00 on co o n on x> co on co oo oo co co on co -o co co oo -p t p f p f p}- p]- Ph p !' - f p}- - Y H .^h p f p f p f ph p>- p}- p f p}- p)- -)■ p f p f O-C'-C'-Cn-C'-[>-£VCn-Cn-[C'--{>-£>-Jn-!>-[N'-I>-!>-[>-C'-Cn-0-Cn-IN-

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CM CM CN] cm CM CM CO CO CO■M- UN UN UN

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• • • • •

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UJ CO -Xi 00 TJ X) OO OO CO CO t o OO OO CO 0 0 CO !X) -Xj 30 X ) 00 CO CO 'JO -3* »“t .tr “)• nr nr -c)- nf n± -nh nfr -ch nf -nh -3* -3* -3* -nh -d* ih O - (N_ O'— CN— N - C''- iN* CN- 'IN- O - N - CN- CN- iS - O - N - N - CN CN CN N - N - CN CN

• « • • • • • • • « • • * • • • • • • • • • • •UN '-CN UN iPrUN, UNUNUNUNUnUN'CNUNUNUNUN’UNUNUNUNU'.UNUNUN

H CM C N h tM X H CM T i H CM C N h CM C N —I CM C N h CM C O h W CN C t -or -or ! > - !> - [> - c o CO GO rH ,H *H CM CM CM X X OX X N x}- x )- x }- UN UN UN,

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TABLE

12 (continued)

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TABLE

12 (continued)

2 8 5

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M CM h 4- H IS C M C C H N ' - O H CO-pFO U S C Q O O D O / T i S > A O ' S i r \ ' P i O S O O O > A i n c M O ' A « • • • • • • « • • * « • • • • • • • « • • • •G nnO u s C - us.:}- US O OO 4 ' O C n O S S On C S -\0 nO COCO US OS

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o o o o o o ovo US us U S O O Oo- o- c- p- cn- o- r-

p, • O o o O o o o o o o o o o o o o oEGs Oo o o o o o v p usUS US ususususUS USa)O CO CO CO '-000 CO CO P ~ IS P - cr P - P - P - CO P - P -

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Reproduced

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i'iunNo.

25.2125.2225.2325.3125.3225.3325.5125.5225.5325.5125.5225.53 22.11 22.12 22.1322.1522.15 22.21 22.2222.2322.2522.2522.3122.3222.33

dalyst Bed Ht. Bed Di;rrms. cm. cn.

5.758 10.158 0.9925.758 10.158 0.9925-758 10.158 0.9925. 758 10.158 0.9925.758 10.15S 0.9925.758 10.158 0.9925.758 10.158 0.9925.758 10.158 0.9925.758 10.158 0.9925-758 10.158 0.9925.7 53 10.158 0.9925.758 10.158 0.9925.758 10.156 0.9928.758 10.158 0.9925. 758 10.158 0.9925.753 10.158 0.9925.758 10.158 0 Q9?W % y y

5.758 10.156 0.9925.758 10.158 0.9925.758 10.153 0.9925.758 10.158 0.9925.75c! 10.156 0.9925.78-8 10.158 0.9925.7d8 10.158 0.9925.78 8 10.153 0 99e * ✓ / —

tABLE 12 (continued)

rABULATio:: of data

V.'/F XUltrasound Feed Bate urn cat-sec Temn. Conversioncos____ v:at ts uns/hr ,.-m mole °P. /&

39,000 25 76 32,725 700 3.7526,000 25 76 32,725 700 6.35- - 76 32,725 700 5.60

39,000 25 229 10,361 700 ’■ 6226,000 25 229 10,861 700 } o0

- - 229 10,861 700 3.0039,000 26 261 9,529 700 5.5026,000 25 261 9,529 700 3.59

- 261 9,529 700 2.8539,000 25 352 7,066 700 5.0126,000 25 352 7,066 700 3.05

- 352 7,066 700 2.6539,000 25 25 99,500 850 57.739,000 12.5 25 99,500 850 51 .526,000 25 25 99,500 850 50.226,000 12.5 25 99,500 850 39.5

- 25 99,500 850 36 .639,000 25 33 75,500 850 39.739,000 12.5 33 75,500 850 35.626,000 25 33 75,500 850 32.226,000 12.5 33 75,500 850 30.0

- 33 75,500 850 28.039,000 25 9-7 52,800 850 35.539,000 12.5 6? 52,800 850 23.026,000 25 6? 52,800 850 29.2

286

TABLE

12 (continued)

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28 7

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TABLE

12 (continued)

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• • • • • • • • • • • • • • • • ■ • • ■ • • • r e

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TABLE

12 (continued)

<ft<Q

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2 8 9

O rH >A rH CMC h f M u > o o o c M n n ca.;}- v a c A ft. u a ^ }- co c o f t - va, ft- ca t-i u^ir.io • • • • • » • • • • • « • • • • « * > • • • * ■ • •

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VA

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• • • • • • • • • • • • • • • • • • • • • • • f t •O O O O O O O O O O O O O O O O O O O O O O O O O

CO CO 00 03 CO CO 03 CO CO CO CO CO 03 CO X) CO CO CO CO CO 03 CO CO CO 03 U3 Up IA ^ UP Lp V p irP -O VO VP\ UO ^ i p LP\ i p LPO-P Vp UP UP

x— ! t—I rH i— I i—( x— I i— ! x—I x—I x— t x— I x— I rH x—I X—I X— I tH rH '—I x—I *—I tH X— I r—I i— 1 • « • • • • • • • • • • » • • • • • • • • « • • •

o o o o o o o o o o o o o o o o o o o o o o o o orH rH x—1 rH rH rH rH x—I rH rH x—I rH rH rH r—1 x—I rH rH rH x—i rH rH v-H rH rH

CO CC CO CO CO 0 0 CO CO CO 0 3 0 3 CO -JO CO :X) CO CO CO c/3 CO 0 0 0 3 0 3 CO' CO 3 - ft ft it ft ft ftft ft 3 .ft- f t - ft f t f t f t -ft f t f t f t f t f t f t - ft! > - C N - C N - C N - t > - C N - C N - 0 - C N - C N - C N - C N - t > - C > - C N - C N - C N - t N - C N - ! N - O - C N - C N - C N - [ > -

u n , v a v a vtn, vta v a v a v a v r \ vo! vr~\ v a v a v a v a v a v a v a v a u n , > A v a u n , v a v a

f t va

CA CA rH CM CA t-I CM CA rH CM CA rH CM CA ,H CM CA tH CM CA rH CM CA rH CM H H H H H H H H H H H H H H H H H H H H C M N N H H

• • • • • • • • • • • • • • • • • • • • • • • A •

C M C M v O V O ' O C N - C N - C N - C O C O C O O N O N O N O O O r H r H r H T H r M T - l C M C MCMCMCMCMCMCMCMCMCMCMCMCMCMCMCACACACACACACACACACACA


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Hun Catalyst Bed Ht. Bed Dia No. gms. cm. cm.

3 2.13 5,.79-83 3.11 5,.7E833. 12 5..7E833. 13 t,.7E833. 21 5 '.• 7E833. 22 5..7-833. 23 5..79-83^. 11 5,.7E834. 12 5..7^634. 13 5..7E63^. 21 5 .. 7^83^. 22 5 ■,7^83^. 23 5..7E835. 11 5.,7E835. 12 5.,7E835. 13 5..7E835. 21 5..7^335. 22 5.,7E835. 23 5..?E836. 13 5 .,7E836. 23 5.,7^836. 33 5., 7E836.^3 5..79836. 53 5.,7E8

10,.158 0,.9921 0,.188 0,.99210,.158 0,.99210,.158 0,.99210,.158 0,.9921 0,.153 0,.99210,.159 0,.99210,.158 0,.99210,.158 0,.99210,.158 0, QQ9 » / ; c.10,.158 0,.99210,,158 0,.99210,.158 0,.99210..158 0,.99210,.158 0 ,.9921 0..158 0,.99210,.153 0 ,.99210.,158 0 ,.99210,.150 0 ,.99210.,15S 0..99210..158 0,.99210,.158 0 ,.9921 0.. 158 0 ..99210.. 158 0,.992


TABULATION OF DATAw/F

Ultrasound Feed Hate r;m cat-sec cps watts nms/hr nm mole

- - 31 81 ,00039 ,00 0 25 33 76 ,2002 6 ,00 0 25 33 76 ,200

- - 33 76 ,20039 ,00 0 25 25 9 8 ,1002 6 ,00 0 25 25 9 3 ,10 0

- - 25 93 ,10 03 9 ,00 0 25 60 E l ,20026 ,000 2F 60 E l .200

— — 60 E l .20039 ,000 25 E2 5 8 ,80 026 ,000 25 9-2 58 ,800

- — 9-2 58 ,80 039 ,000 25 25 101 ,00026 ,00 0 25 25 101 ,000

— — 25 1 01 ,00039 ,000 25 20 12E , 30026 ,000 25 20 12E ,300

- - 20 12E ,300- - 125 19 ,900- - 82 30 ,10 0- - 62 3 9 ,80 0— - E l 6 0 ,20 0- - 31 79 ,900

XTemp. ConversionOo j

850 33-5900 EE. 9900 37.2900 33.9-900 E9 .9900 EE . 5900 E2.1650 5.70650 5.11650 E . 82650 5.88650 5.91650 5.E2800 39.9800 37.1800 39-.9800 93.9800 39.6800 38.1900 19.1900 27.6900 39-. 3900 El .6900 El .2 290

APPENDIX XV

T H Eli M 0 CO UPLE C OH RE CTI ON


2 9 2

THERMOCOUPLE CORRECTION

The reaction temperature of all runs was controlled by a Leeds & Northrup Speedomax Temperature Controller. The controller maintained the desired temperature by enerpjizlnp; and de-enerpizinpr the reactor heaters. The control temperature was sensed by a thermocouple which was inserted in a thermocouple well. The tip of the thermocouple well was located inside the reactor and into the catalyst bed.

Because of the heat conduction from the tip of the thermocouple well to the cooler external end of the well, the temperature at the thermocouple junction will be less than the actual r,as temperature passing by the tip.Bird^ has shown this error to conform to the following equation:

'IT = temperature indicated by thermocouple, 950°F.

T = temperature of cool end of thermocouple well, 570°F.

T = actual p:as temperature, °ii’.3. 'h = heat transfer coefficient, 120 Op

L = length of well, 0.708 ft.

T1 a (1^7)w a


293

B tuk = thermal conductivity of metal, 60 t y, u g~"* hr-ft^- F,B = thickness of well, 0.00692 ft.

= - 1 - . = - - 1 - = 0.00000612570 - Ta cosh 12.04 163,376

Ta = 950°F.

Therefore, the error is i.nsiynif icant and the thermocouple does sense the actual a3 temperature.


APPENDIX. XVI

QUADRATIC REDRESSION EQUATION


295

QUADRATIC REGRESSION EQUATION

All the data collected at each temperature and frequency are presented herein as plots of conversion versus reciprocal space velocity. The curves best fitting the data were calculated by the quadratic regression method to fit the following equation:

n - number of data points.

The resulting three constants for each operating condition are shown in Table 13 end the data and calculated curves are shown in Figures 86 through 111.

The quadratic regression curves were employed only to evaluate conversion at the specific reciprocal space velocities

significance of the mass transfer coefficient as a function of temperature as calculated from the conversion versus reciprocal space velocity information obtained from the regression lines was then determined.

(21)

and ,

( 1 4 8 )

(1 5 0 )

(1 49 )

where,

of 20,000, 50,000 and 80,000 . The statisticalgm mole


2 9 6

TABLE 13

QUADRATIC EQUATION CONSTANTSf

Temp.°F.

cps q x 10"J Power a b x 106 c x 10^

650 39 full -0.000959 1 .74 -0.91650 26 full -0.00605 1 .76 -1.06650 — off -0.00664 1.75 -1 .10700 39 full 0.0309 1.45 0.590700 26 full 0.0253 0.923 0.790700 — off 0.0205 0.958 0.65075 0 39 full 0.0231 7.55 -3.74750 26 full 0.0051 6 .66 -3.17750 — off -0.0054 7.00 -3.70800 39 full 0.0453 5.97 -2 .32800 26 full 0.0308 5.32 -1.93800 — off 0.0226 5.41 -2.09850 39 full 0.0282 9.92 -5.87850 26 full 0 .0252 9.04 -5.76850 — off 0.0258 8.40 -5.60850 39 half 0.0989 5.01 -2.00850 26 half 0.0974 4.79 -2.03850 — off 0.0258 8.40 -5 .60900 39 full 0.0877 5.33 -1.86900 26 full 0.0789 4.16 -1.13900 off 0.0655 6.26 -3.15950 39 full 0.0359 7.52 -1.75950 26 full 0.0256 8.76 -4 .3 0950 — off 0.0255 8.12 -4.42

1000 39 full 0.0215 20.3 -39.51000 26 full -0.0224 29.4 -75.21000 — off -0.0213 29.8 -81.5


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10-3

gm.cat.-sec.

’ gm. mole

309

COOnootH

&4

CO>soI—IcnKWOo

UN,CM

u00

oo

un,!>-

UCM

OOO O OO O

•o<D (1)CO rH1o• E

4-5n5 •o E

• b£Ebf.

ON,

*Ph

oUN,

o-3- oc oCM

oo

X ‘N0ISH3M0D


3 i o

On

On

o

Un

U1 >sOMCOCC,W!goo

C\!OOOvOCO CM

OO

u>iCM

OO O O O O O

•o0 0CO i—I1o• E

■pcd •o E• h CEhi

•*r~-\

OT—I

X&H

o'A O-ch oa~\

oCM Oo

X ‘NOISH3ANOO


3 U

ooaC£CO'J)HCl,

\

w>oMCOww>oo

tH

CVOOOo

CO

ooT-I

oU~N

oooCO,oo oo

CMoo ooo

CiIoX&H

X *NOISH3ANOO


prm. ca

t. -sec

ffm. mole

312

o

rC:=>C3

w>53oMCOPCw%ou

CMr-H

oo

ouocorH

OOo

Ooo

oo o

ooo

1—I

•oQ) 0)ra i—1i o• E-PnJ *o E• blEix

CO

&H\

X * N0ISH3AN00


3 1 3

CMO

r-n\

to>OMcn

woo

ovr*

— ■a

oo

U>! CV_

ooo ooo o

X

o o oo~\ oCM oo

X * N0ISH3AN00


i n“3

gm.c

at.-sec.

’ gm.

mole

CONVERSION vs.

W/F

CM

-P

Oo

ooooo oo

olA O oCA

OCM

OO

X ‘N0ISH3M00


CONVERSION vs.

W/F

315

u n

oBh o0 OOO \0 O N cm

oo

o-

oUN,

UN,CM

OOoUN,

oo oo ooCM

Oo ooo

0 0) w1a4Jo•

Eh i

C*N,IoX&H

CDI—IoE

X * N0ISH3AM00


316

o

wi-V"

Oh

m>OMCOKWOo

w\CV0 “oooON

O

CM

ooo o o o o

Io

XOh

oVTN O o O(M oo

o

X * NOISH3AN00


Til . C

3.1

. —SBC

.

gm.

mole

3 1 7

:oXxx

in>X O i—I CO05w§oo

JO

CM

i—I

oo

oooo ooo

Cm

O o-ch o oCM oo

X ‘N0ISH3AN0D


1 o“3

gm.cat.-sec.

’ gm.

mole

318

oaa:=>ahHa

a3co>oMCO«aoo

oo

vr>,CM

=8°ooO oOOOoo oo

0 0 CO1-pctio

•6hi

CDr~ iOBBhD

r>iIoX

vr\ -3- <r> CM

x ‘NOisaaANOO


319

COo

£3S3M

Pi rH

oo

w>13oH

oinoo

m'CM

OOOO OOOO oo

X

ino

-cho

cno

CMo

oo

X *NOISH3ANOO


i 0-3

gm.cat.-sec.

’ gm. mole

320

ONo

ax

coMa

a

to

aoMCO

a£oo

ooo -PrH

OC\J

O 1—1

oooo

oo

oo

oo

•oa) CDCO i—1I O« E

-p•

o E• b £

Ehi

<r>io

Xfo

X ‘N0ISH3AN00


CONVERSION vs.

W/F

321

o

cm

oooooox—I

oC M

O

ooo ooo o

•0Q) <uW 1—1t 0• E-Pcd •0 E• hr:Efcr

c^

X

o o•4- o oCM

oo

X ‘NOISH3ANOO


322

13a

oooo

oo o0

o •CM o

-p

o

o%—I

o

oo oo ooo

o o oC'* oCM

oo

X ‘N0ISH3AN00


APPENDIX XVII

EVALUATION OF REACTION ACTIVATION ENERGY


3 2 4

EVALUATION OF REACTION ACTIVATION ENERGY

Arrhenius' Law

Arrhenius' Lav;, which describes the reaction rate constant as a function of the reaction activation energy and temperature is a follows:

k = k e RT (151)

where,

k = reaction rate constant, ^ " cat'-fec

kn - frequency factor, — o * -r j cat-sec, . . . cal

a = activation energy ----- =—’ ym moleT = temperature,°K

calH = conversion factor, 1.98 mole oK _

For solid catalyzed, reactions, the surface reaction rate corrected for pore diffusion, £ Lk^, is substituted for k, the reaction rate constant. After this substitution is made, the natural logarithm of the equation is taken in order to obtain a linear function of reciprocal temperature.

JL£ b k 2 = kQe“ RT (152)

/- EIncLkp = In k0- In e

■ ln ko- iff


3 2 5

In € L k ^ = | Ur + In kQ (153)

Calculation of Activation EnergyKIn the above equation, - — is the slope of the straight

line obtained when In is plotted against reciprocaltemperature.

As shown in Chapter V, the equations for the curvesat the frequencies studied are as follows:

1no ultrasound: log^Lk^ = -4812 -1.l4l (154)

In CLk£ = -6 1 5 7 -2.628

26.000 cps: log € Lk2 = -4115 -1.637 ( 155)

In €Lk2 = -5265 -3.770

39.000 cps: log£Lk2 = -2801 — -2.53^ (156)1In 6Lk2 = -3584 ^ -5.836

The calculation of activation energy, E, from the constants associated with reciprocal temperature obtained from the above equations yield the following results:

no ultrasound: - ^ = -6.57; E = (6157)(1.98)= 1 2 . 1 koalgm mole

26,000 cps,: - § = -5265; e = (5265)(1 .9 8):= 10 4 ■ k c a lgm mole


326

39,000 cps: - § = 3584; E = (3584)(1.98)n i kcal

gm mole

Calculation of the Characterization Factor

No ultrasound: In kn = -2.628

o (

ii 0.0723 gm moles gm cat-sec.

26,000 cps: In ko ■ -3.770

IIoX

0 . 0 2 3 1 gm moles gm cat-sec.

39,000 cps: In k = o 5.836

FT O II 0.00293 gm moles gm cat-sec


APPEND IX XVIII

EVALUATION OF INTRINSIC HATE CONSTANT


328

EVALUATION OF INTRINSIC HATE CONSTANT

In order to plot CLk^ as a function of Kelvin temperature on the same paraph as the mass transfer coefficient, kfr, the equations for € Lk^ as a function of

of 6"Lk0 in these equations are -■ rn which must be2 1 km cat-sec

Hankine temperature must be transformed. The dimensions-ILL km c mtransposed to to correspond to the dimensions of k .sec k

This is accomplished by the following calculations:

No Ultrasound

lor 6 Lk0 = -4812 -1.141 (154)2 Toi{

I p i ), km moles wap rw cm —a,tm \ / rnOi/ \( 2 km cat-secJ(c32- ^ mole-0K )(1 K)

(1 atm) (13.1 — — r) krn cat

T°H = 1.8°K

lor k„ = lo,k CLk„ + lop; T°K + lor -8?!0?S ± j • -L

lok k = -4812 — — -1.141 + lor T°K + lop 6.26183203 1. 8'i K

lok ks = 26- 3 . 8a + lor T°K - 0.3443293 (157)

Frequency = 26.000 cps

lor 6 L k = -4115 -5-; -1.637 (155) 1. h .

lor kg = -22M ,,3&6.6. + lor t°k - 0.8399895 (158)


3 2 9

Frequency = 39.000 cps

loft CLk2 = -2801 ;4- -2.53^ (156)X -Li

lop = -!XliJ1288 + 1q rjloK _ 1#73681?1 U 5 9 )

s T K

The values of lop kc, calculated at each temperature

and frequency are shown in Table id. Some of the values

of the mass transfer coefficient, k , are also indicated

in the table.


3 3 0

-3*T—1

mc

E7Jw 1-1 O I—IMOoElrXHco'X<*-r<EhCOr/)

Cl

bC

0CD OW <D II OI 1—I Q r/3

-P 0 Ci pcd E ON O0 CP

EE fcthr 0

Ooo«*

oPJ

wII OoCi—1 •» p.

vO o CM

CP ONCM

•

tH1

at CO 1-H0 t , d VPx i -p d •

rH 0 t—i 1—1-.3 w 1 1

00orH1

£>-rH

QN

OI

vO 0 vr>> coup CP tH On

• * • •r—1 tH tH O

rHI

0 0hr; a) II 0 CP —V C-- up0 CO CD O to up ^ r CM tH

1—1 1 1—1Cl •» p • • • •

p O On O tH tH tH tHcd E CP 1 1 1 10

EE hr Ohr II O rH tH UP up

O CO vO CP CM0 Ci - 0 • • • •

0 •..0 0 T-t tH tH tH0 CM 1 1 1 10CO 1

ct3 rd CM OJ X) CPII 0 f-i s' NO CP CM

p p • • • •Pi rH O tH rH tH rH

p i CO 1 1 1 13:Eh OCO II O<-* O COO Ci •* PO On O

CPElEh<0 Mto

1-1PH1 —ir-i

V J

Wio

IIo o o wCl •* p VO O

CNJ

Icd rdo ?h £

P -p c rH OCO w

Eh O

Eh fo O

P- -3- CM r-l CM CM CP up-X. CP CM p 0 On CO p-• • • • • • • •CP1 CP1 CP1 CP1 XV1 CM1

CM1 PI1

NO CO t—1 VO 00 On P- upp- up -d- CM tH On co p-• • • • • • • •CP1 CP1 CP1 CP1 CP1 CM1

CM1 CM1

ON p- On CM VO t—| VO CPCO VO CP p O CO p-• • • • • • • •CP1 CP1 (p1 CP1 CP1 CP1CMI CM1

VO CM 0 p- up CP PtH .3- P- 0 CM VP CO HvO NO vO p- p- p- p- 00

0 0 O 0 0 0 0 Oup 0 up 0 up 0 up OvO p- P~ CO CO On ON O1—i


APPENDIX XIX

CALCULATION OF MAXIMUM PROBABLE EUHOH


332

CALCULATION OF MAXIMUM PROBABLE FLUOR

Reciprocal Space Velocity, ^ ’’Aq

d(W/t,'An) Faoc1W - WdI'An chJ WdFA= i v = pAo ■ P a n

ri(tJ/l?Ao) L F l oW/1’A0 ' W - PA0

The maximum probable error is the sum of the individual errors. Therefore,

d t ^ A p ) dVi < 'AqH / V A o ' l'J + l''A0

For example,Vi = 5. yi-t-B rms. - 0.001 Am.

FAn = 200 t 0 . 8 ^Lo J hr. " h r .

Vi/F PA0

A error = 0 Jv? j/0

d t ; £ o) = § f $ r | + f u j " 0 .0 00 1 73 9 + O.oodo = O.OOH-17

••/l'A0 = ,9-39 - 53

Conversion, Xa

120.19U_______AA 120.19H + 78.HA

= (120.19R+78.11A)(120.19)dR-120.19H(120.19dU+78.lldA)A (120.192 + 78.11A)2

_ 120 .19dii (120.19)2Kdr _ (120.19) ( 78.11)HdA120.19H+78.11A ~ (120.192+78.1 1 A ) 2 " (120.19H+78.lldA)2


3 3 3

&Xa d!i 120.19 dR *A ^ (120.19IM-78.11A)

For example,

R = 7.32% - 0.12%

A = 91.09% t 0.53%

dXA = 0.12 + 120.19(0.12) XA 7.32 120.19(7.32)

% error = 2.3^%

XA = 11.0% ± 0.2%

■ 7 8 .1 1 d.A ( 1 2 0 . 1 9 2 + 7 8 . 11A)

+ 78.11(0.57) 78.11(91.09)


APPENDIX XX

CALCULATION OP POWER INPUT


335

CALCULATION OF POWER INPUT

The maximum total power output of the ultrasonic horn employed in this research was 25 watts according to the manufacturers specifications. The power input per mole of reactor feed at the lowest and highest feed rates studied is as follows:

Power Input at Feed Rate of 25 gms./hr.

PJoule(25 watts)(1 watt-sec

J oules

kcalgm-mole

><25 g ^ K i o o o j#r)) ( 3600 gj5 ) (120.19 1hr gm mole

calkcal

Power Input at Feed Rate of 600 gms/hr.

p (25 wat Joulewatt-secJoules

kcalgm-mole


APPENDIX XXI

SAMPLE CALCHLATION OE THE MASS TRANSFER COEFFICIENT


337

SAMPLE CALCULATION OF THE MASS TRANSFER COEFFICIENT

The mass transfer coefficient is calculated from the following equation derived in Chapter II and Appendix IV:

6.26 XAf TS (W/FA n ) m ( l + YALM)

(22)

Some actual values for the parameters are as follows:

W/Fa = 20,000 gn?-gat.rsec. ao ’ gm moleT = 850°P. = 72?°K.

x A f = 0 .1 7 1

_ A f _ 1-0.171 . 0.829 .° 1+xAf 1+0.171 1.171

1 - X a o 1 - 0 . 7 0 8 0 .2 9 2

L« = H g T x r / - ° - W 5

Substitution of the above values into Equation (22) yields the following:

(6.26)(0.171)(727) . cmg (20,000) In (0.84-5) sec


APPENDIX XXII

ANALYSIS OP VARIANCE


339

ANALYSIS OF VARIANCE

The confidence intervals for the coefficients of the linear equations expressing log k as a function of T ando

■ilog 6 Lk2 as a function of ^ are calculated as illustrated in the following example.

Linear Equation at ^ F = 80,000 cat-sec ultrasound________ ________________o_____ ’_____ gm mole_____

log k = 0.00169T - 2.66t J

Let y = log k£xab

- 2.66 0.00169

Calculate Sy and Sy

xn x x2 - ( z x)2

n( n - 1)n = 5 (number of data points)

x2 = 2,653,227 ( 2 l x ) 2 = ( 3637) 2 = 13,227,769

S = x(5)(2,653,227)-13,227,769 = ^3.798

s = y

n r y 2 - (r y)2 n( n - 1)

n = 5y = 10.3368^5

( 2: y )2 = (-7.181^3)2 = 51.572936


340

s = y

5(1 0.336845)-51.572936jCifj = 0.074595

Calculate r

bSr = = .(0.,Q,0l69) (lJ-3 .798) _ 0002729Sy 0.074-595 ” 992^^9

Calculate Sy.x

S = S y x y

(n-l)(1-r )(n-2)

= 0.0010689

Calculation of Sa and S ,

= 0.074595 4(0.01539115)3

S = S . a y *x

;2 -

-21 + xn ( n - D S * 2

1

r x 2n 5

= 529,100.76

So = (0.0010689)clI + 529.ioo.765 4(43.798)2 = 0.0088889

Ssn = y-x

b ( n - l ) t f c ( 4 ) 4 ( ^ 3 . 7 9 8 )(0.0010689) „3— ----<-!— = 0.0000122

Calculate 99% Confidence Interval

fcn-2, t3,99 5.841

a = -2.66 - t- QQSo = -2.66-(5.841)(0.0088889) = -2.66^0.05j , 7 7 u

b = 0.00l69-t^ 99Sfe = 0.00l69-(5.84l)(0.0000122)

= 0.00169^0.00007


3 ^ 1

Calculate 95% Confidence Interval

tn-2, " t3,95 " 3.182

a = —2.66—(3*182)(0.0088889) = -2 .66^0 .03

b = 0,00169-13.182)(0.0000122) = 0.00169-0.0000*4-

Calculate 90$ Confidence Interval

tn-2, = fc3 ,90 = 2 *338a = —2.66—(2.358)(0.0088889) = -2.66±0.02 b = 0.00l69-(2.358)(0.0000122) = 0.00169-0.00003

The confidence intervals are similarly calculated for the remaining relationships.


3^2

NOMENCLATURE

A = reference to curnene9A = area, cm”

?piD *a = superficial surface area of catalyst, gm cma = transverse acceleration, ---5-sec^

C = total concentration of A + H + S, cm 3C. = concentration of cumene, ltm—m.Qj-.e A cm 3

C* = eciuilibrium concentration of benzene,e cm 32

CAt = concentration of active sites occuoied by A, — -— 7- 1 J ’ gm-cat

CAo = concentration of cumene on catalyst surface,s cm3CT = total concentration of available active sites, cn?-”■■■■■■ E ’ gm catC-i = concentration of unoccupied active sites, — — — r 1 gm cat

calgm-°C.

2

q 1Gp = heat capacity of gas at constant pressure, ■ ■ Op

G,. = concentration of benzene, -9.3es u cm3Cw = equilibrium concentration of benzene, ---9---cm-5

2Cgp = concentration of active sites occupied by H, 01,1

Cn = concentration of propylene,0 cm-5

gm cac

pcm^Ggn = concentration of active sites occupied by S. —^ — r’ gm catC,, = heat capacity of gas at constant volume, ■

v * gm -°G .


2cmD. . - diffusivity of cumono in benzene, — —ri 11 ot»G

2cmD.r, = diffusivity of cumene in propylene, — —A o o O u2r*mD = effective pore diffusivity, ——— e sec

2Dv = Knudsen diffusivity,I\ o o O

2pmD - combined diffusivity, — — s ’ secd = average diameter of catalyst pore, cm.

dp = diameter of catalyst particle, cm.ym calv. = activation enerpy, 'rm_mole

F = feed rate,

F = force, dynesi._ ym-moles . ym-molesFa = initial cumene teed rate, ---- or 1 Gec-

(see text) f = frequency, c^ ^ 5-

G = superficial mass velocity of yas normal to catalyst bed, ---cnr -sec

dyne:= conversion factor, 980’ k„sv -khg = Thiele modulus = mrp = rp — , dimensionles

........... erg; dyne-cm. „ „-7 watt-seci1 = intensity, om2_seo, c^-sec U 0 — — )16 watts1 — 1U qo cm^

K - equilibrium constant for overall reaction, atm K2 = equilibrium constant for surface reaction, atm


344

= equilibrium desorption constant for H, atm.iKa = equilibrium adsorption constant for A, —r —h q, yj m •1K,j = equilibrium adsorption constant for R, -t—* * ct urn •

k = forward. reaction rate constant for overall reaction,pm moles

pm cat-atm-sec

k = comoressibility, -— 411 crn~rec..' (dyne = ^7 ’ dyne* pm sec2

k 1 = reverse reaction rate constant for overall reaction,pm rnoles____

pm cat-atm^-seck ~ constant,0 * sec

. _ , . _ pm molesk. = rate constant for adsorption of A, p 71 - ’ cm^-atm-sec

k' = rate constant for desorption of A, mole^1 cm -sec

kp = forward reaction rate constant for surface reaction,pm moles cm2-sec

k'p = reverse reaction rate constant for surface reaction,pm moles cnr--atm-sec

k^ = equilibrium desorption constant for R, atm.rrm molesk' = rate constant for adsorption of H. — H— f-----3 cm^-atm-sec

k = mass transfer coefficient,£ sec

kp = oseudo first order forward reaction rate constant,3 citk

pm cat-seck'p = pseudo first order reverse reaction rate constant,

cm3pm cat-sec


3 45

ko = forward intrinsic rate constant for surface reaction,o

cmsec

1„ = reverse intrinsic rate constant for surface reaction, /+cm______p;m mole-sec

L = reactor length, cm.2

L = total concentration of active sites, — — — r-’ gm cat

1 = unoccupied active catalyst site, dimensionless

M molecular weight, — tULe—’ gm molm = mass, gms' = number of moles of A, Km moles“A

KrA0 = initial number of moles of A, Km moleswA f = final number of moles of A, g m moles-Ia „ = nate of mass transfer of A in z direction, lesrtz ’ cm^-sec

= nate of mass transfer of H + 3 in z direction, m°l.g.v ^z ’ cmz.-secM,p = total number of moles, gm-molesn = 1,3,5,7,9, etc.P = vapor pressure, mm. Hkp = partial pressure, atm.

dyne sp = pressure, — T ~cm^Pq = critical pressure, atm.

dvne sp = maximum pressure caused by sound wave, —1*-r— max cm2p,p = total pressure, atm.

3P = ideal Kas constant, 82.06 ■- - ■* gm mole- K.


346

ft - reference to benzeneft = ideal p;as constant, 1.987 —’ rm mole- Kr _ p, q-i y 1 n 7 erf<;s dyne-cm.

p;m mole-OR’ ym mole-°K( e r r , = dyne-cm = )sec^

ft = fteynold's number, dimensionless2ft = ideal yas constant, 8.3 x 10^ 4m.~cln -----'■ v,m mole-K-sec^

4 = maximum reaction rate, 4rn molesmax ’ sec.ftp = rate of diffusion into catalyst pellet,

r = initial rate of reaction,sec.

ym moleso ' * r . m cat-sec

r^ = ym moles A diffusing7; toward catalyst surface porsecond per pm catalyst, 4Hl~-mo.4ef.

’ ;>;m.sec.(-rA ) = reaction rate, A-A]_ ’ pm cat-sec

re = equivalent radius of pore, cm.rp = radius of catalyst particle, cm.S = reference to propylene

SEX ~ external surface area of catalyst, cm2 Sp. = total surface area of porous catalyst, cm2

cm23,, - total surface of porous catalyst = P pS , -k~- 7 ' ^ K cmoT = temperature, °K. m • j sec1 = Period-t = time, sec.

t = temperature, °G.

= critical temperature, °C,


3 ^ 7

\r cmvelocity of propagation of wave form, ecV, = molar volume at the normal boil.iny point, — c —b 1 1 ’ ym mole

cm3= critical molar volumeG ' - - s ym-mole3cmcore volume, —1 fi-nym

cmtransverse velocity, --ec3v = volume, cm-

■:! = v;oiy;ht catalyst, r:ms.VJ = work done on A .system dyne-cm, erys.

':l - wciyht of catalyst, yms.cX = distance traversed by wave form, cm.

= conversion of A, dimensionless

xAf

oY = mole fraction in yas phaseY = amplitude, cm.

mole fraction of A, dimensionless

;<Ap = equilibrium conversion of cumene, dimensionles: final conversion of A

X = initial conversion of A

V"AYA, = mole fraction of A in bulk stream, dimensionless•b

mean m°le fraction of cumene in the bulk stream dimensionless

Y^r, = mole fraction of A at catalyst surface, dimensionless

y = displacement, cm. z = distance in z direction, cm.


3^8

/ 3 - sound, intensity level, decibels

p(jv= thickness of stagnant yas film between main yas

stream and external surface of catalyst, cm.£ = void fraction in packed catalyst bed, dimensionles:6 - catalyst effectiveness factor, dimensionless

"/K = Lennard-Jones parameter, °K.O = catalyst internal void fraction, dimensionlessA = wave length, ■ ■cm,-1*.’ cycle7T = total pressure, atm./b = fluid density,' cmb

/°jj = bulk density of catalyst bed, emurrjn ^/°n = initial .yas density, £j—r-

' emuynu cm.

true density of solid material in porous catalyst,

/b = catalyst oar tide density, of particle volume/ 1 “ cm3

do

= Lennard-Jones parameter, A T" = tortuosity factor, dimensionless

= critical viscosity,

^7^ = collision integralcm-sec

ymscm3


349

LITERATURE REKEREHCE3

1. Aerctin, E.G., Timmerhaus, K.D., and Fonler, M.S.,A . I. Gh. E . Journal, Vol. 13, 196?, p. 453.

2. Arkharurel1 skii, M.S., Zh. Fiz. Khim., Volume 43,1969, pp. 942-945!

3. Belov, 13.2'., U.S.S.F. Patent Mo. 226,328,September 5~! 1968.

4. Border, Heinz, German Patent I!o. 1,279.660,October 10, 1968

5. Bezrc, Valid. E., Romanovskii, B.V., and Topchicva,K Kinot. Katal., Vol. 9, 1963, pp. 931-934.

'6. Bird, 11. Byron, Transport Phenornena. liew York:John l.'iley and Sons, Inc. , 1963, pp. 539-531 .

7. Boucher, B.M.G., Tov;ey, J.P., and Tobin, C.D.,Besearch and Development, Fobruary, 1966.

3. Boucher, R.H.G., British Chemical Enrineerinp;.Vol. 15, 1970, pp. 363-367.

9. Brown, Ghar1cs Edwin, Effect of Catalyst Particle Size on the Bate of Synthesis of Methyl Alcohol in an Internally-Recycled Difference ueactor, Doctoral Dissertation, University of Connecticut,1969, 205 pa,ye s.

10. Chen, J.W., and Kalback, W.M., Industrial andEnyineeriny Fundamentals, Vo l~ . TT, Uo. 2~, Fay1967, pp. 175-178".

11. Christie, Dan Edwin, Intermediate College Mechanics.Hew York: McGraw-Hill Book Company, Inc., 1952,pp. 424-425.

12. Corriyan, T.E., Garver, J.C., Rase, H.R., andKirk, R . S . , Chemical Enyineerinp- Progress,Vol. 49, 1953, PP. 603-610.

13. Currell, Douglas L., Na^y, Stanley S., Journal ofthe Acoustical Society of America. Vol. 44, Uo. 5,1968, pp. 1201-120 3.


3 5 0

1 6. Fcdo t ov, A . M . , U.S.S.P. Patent Mo. 212,900 ,September 5, 1908.

15. Pooler, S., "Studies in Ultrasonic Meaction Kinetics,"Symposium on Selected tapers - Part I , American Institute of Chemical Engineers, November 26,-30,1967.

16 . Foyler, S., Sound and Vibrations. Vol 1, Mo. 8,August, 1967, pp. 17-21.

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356

VITA

William Lintner, Jr. was born in

in He received his B.S.Ch.E. from the

Massachusetts Institute of Technology in 1953 and his

M.S.Ch.E. from Newark College of Engineering in 1965.

The research for his doctoral dissertation was

accomplished in the Chemical Engineering Laboratories

of the Newark College of Engineering during the period

between September, 1969 and November, 1972. Financial

assistance for the research was provided by Newark College

of Engineering and the du Pont Fellowship which was

awarded during 1972.

Mr. Lintner is a member of the American Institute of

Plant Engineers and is a licensed Professional Engineer.

He is married and has two children.

He is presently a partner in Chemical Systems, Inc.,

a chemical engineering design and construction firm.

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