Table Of ContentANALOGUE OP ALTERNATING CURRENT THEORY APPLIED
TO DIFFUSION PROCESSES IN BEDS OF
POROUS CATALYST CARRIERS
/ By
Paul F. D eisler, Jr.
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A DISSERTATION
Presented to the
Faculty of Princeton U niversity
In Candidacy fo r the Degree
of Doctor of Philosophy
Recommended for Acceptance by the
Department of
Chemical Engineering
/
/ June, 1952
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1555 Henry S t.,
Berkeley 9> C alifornia
15 Feb., 1955
Mr.Maic olm Young,
Reference L ibrarian,
The Library, Princeton U niversity,
Princeton; N.J.
Dear Mr. Young:
I am enclosing a correction sheet which should be
copied along w ith my th e sis when a microfilm copy is made.
If you need fu rth e r copies of th is correction sheet,
I believe th at Dr.R.H.Wilhelm of the Chemical Engineering
Department, at the U niversity,has some on hand.
I am happy to have copies made of my th esis whenever you
may receive requests for them. I was not aware th at my
permission was needed for copies to be made, but i f such
is the case, and i f i t is possible for me to give a "blanket
perm ission” rig h t now to cover any future cases of such
requests, then I am happy to give i t .
Very tru ly yours,
Paul F. D eisler, Jr.
S____________• _________________________
A
■I
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r.m-rection Sheet jfc**
V
"Analogue of A lternating Current Theory Applied to Diffusion
Processes in Beds of Porous Catalyst C a rrie rs;f by Paul F. B e is le r,J r.
Ph.D. D issertation, Prjnceton U niversity, 1952.
Pg, 143i f i r s t th ree lin e s should read:
Eq. (30) becomes
£ his
3
j y j i _ u d .1 = o ( D
d g2 (J2 Dr
The boundary conditions fo r Eq, (31 are
Pg. 146, f i r s t th ree lin es should read;
|2| - I n + y2
H L i - ,1-*:,
*1 “ U * + DL ( fe ) \
and
yz ■ i (w + ^ v
Pg. 19. change Equations (18) and (19) to read :
Yl = (<L-) \ ? L f L Dt + m j u
1 I - A I / L L J • (IS)
2Dl_£§_ f I u2 UB + B2 ^ 1/2 ~ -------| (19)
(1 -« L L V ^ T dll lZ 7 ' 2?Dl J
&1 So, c o r v e e i-i'o nS <5. s on Pgr. J 4 6 / A- 4 o v e .
Pg. X/, A f e.ndt 5 A Q-iA-L^ r€d.A :
«. • l e 5 s t/idM 0 . 6 7 °~L» .
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ACKNOWLEDGMENTS
The author wishes to express his g ratitu d e for
the continued and generous guidance, in sp iratio n and
encouragement of Dr. Richard K. Wilhelm throughout the
entire period of th is research. The author is also in
debted to many members of th e . faculty, sta ff, and gradu-- ■
ate student body of the U niversity for advice and counsel,
and is esp ecially anxious to acknowledge the aid of Mr.
Dean Edmonds of the Department of Physics in the design
of the electronic equipment used. Special acknowledge
ment is also' due Mr. Walter T. McKee for his advice and
assistance in the construction of the apparatus.
The author also wishes to thank the Norton
Company for providing experimental porous m aterials for
th is in v estig atio n , and Dr. 0. C. K arkalits and the
American Cyanamid Company for carrying out surface area
measurements.
Special acknowledgement and thanks are due
the Shell Development Company of Emeryville, C alifornia
for providing the fin an cial support for this, investigation.
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CONTENTS
Page
ABSTRACT ‘ i
PART I: A pplication of Method to
D iffusional S tu d ies..................................... 1
In tro d u ction ...................................................... 1
Theory..................................................... 7
Experim ental...................................................... 27
Apparatus........................ 27
ExperimentalT echnique.................... 47
C alcu latio n s.......................................... 55
M aterials................................................. 60
R esu lts.................................... 62
Range of V ariables........................... 62
Experiments with Porous
P e lle ts ....................................... 63
Experiments with Non-Porous
P e l l e t s . . . . . . ....................................... 69
Precision and R eproducibility. 69
D iscussion......................(........................... 72
Experiments with Porous
P e lle ts ...................................................... 72
Experiments with Non-Porous
P e lle ts ...................................................... 83
Ju stific a tio n of Assumptions
Used in O riginal D erivations.. 85
General Conclusions .......... 85
PART II: Rapid Gas Analyzer Using Ionization
by Alpha P a rtic le s ....................................... 87
Introduction...................................................... 87
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gage
Theory and Design C on sid eratio n s... 89
Apparatus........................................... 105
Flow System............................................ 105
Alpha P article Source.................... 105
Analyzer Chamber................................ 108
Measuring and R e c o rd in g ....... 112
A nalytical Cell Voltage Supply 115
Experimental Procedure and R esu lts.. 115
D iscussion ............................................ 132
APPENDICES.................................................................................................. 137
APPENDIX A: D erivation of Equations............................... 137
APPENDIX B: Sample C alculations....................... 151
APPENDIX C: Tabulated D ata ........................................... 169
NOMENCLATURE ............................. 179
L iteratu re C ited ................................................................................... 182
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i
ABSTRACT
In Part I of th is d isse rta tio n the experimental
application of a technique new to the study of mechanisms
operating in ca taly tic reactors is described. The meth
od is based on the th eo retical work of Rosen and Winsche1'’1'
who have.adapted mathematical methods used in altern atin g
current theory to systems in which chemical or physical
rate processes operate. In the present case the diffusion
mechanisms occurring in a fixed bed of porous ca taly st
supports are studied.
Experimentally, binary gas m ixtures, flowing
at constant flow rate but varying p erio d ically and
sinusoidally in composition with time, are passed into
the packed bed. The d iffusion mechanisms acting in the
bed cause a decrease in amplitude and a s h ift in phase
of the composition wave as i t passes through the bed.
Equations re la tin g the in flu en t and efflu en t composition
waves are derived, so th at from experimental measure
ments of wave amplitudes and phase angle the diffusion
co efficien ts for the diffusion ra te mechanisms acting
are obtained. The chief advantage of th is method of
measurement is th at several d iffe re n t co efficien ts may
be obtained from a single set of experiments on the system
of in te re st, while older methods of measurement generally
require separate experimental methods and apparatus for
each co efficien t measured.
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Three binary gas systems were employed:
Hg-Ng, CgH^-Ng, and C2H6”N2 * 0ne bed Porous solids
was studied, 1/8" Norton alundum, spherical, c a taly st
supports. Plow rates were a l l in the viscous flow
region, a ll Reynold's Numbers being below 100, and the
highest frequency used was 0.487 rad ian s/sec.
The important mechanisms were found to be
diffusion in the porous spheres, and diffusion in the
gas phase in the d irection of flow (or longitudinal
d iffu sio n ). Solid diffusion, longitudinal d iffusion,
and adsorption equilibrium co efficien ts were obtained,
and a ll were found to be inv arian t with composition.
Solid diffusion and adsorption equilibrium co efficien ts
agree with values estim ated a p rio ri. The longitudinal
d iffu s iv itie s obtained represent, to th is au th o r's best
knowledge, the f i r s t measurements of th e ir kind ever
made.
Some experiments were made using non-sinusoidal
waves to demonstrate th at harmonic analysis of such waves
makes possible the exploration of frequencies above the
cap ab ility of the wave generator to produce.. By th is
means the frequency range was extended to 0.955
rad ian s/sec.
Experiments were also carried out with a bed
of non-porous 3 nim glass beads to check certain assumptions
made in the derivation of the equations.
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Part II of th is th esis describe^ the a n a ly ti
cal device developed for the instantaneous measurement
of the compositions of the gas streams entering and
leaving the packed bed- The operation of the gas
analyzer is based on the fact th at the e le c tric a l co n
d u ctiv ity of a gas exposed to a fixed source of ion
izing radiations is a function of the composition of the
gas. Alpha rays are used in th is case as they exhibit
advantageous properties compared with other ra d ia tio n s .
In its present form the analyzer is applicable
to almost any binary gas mixture, although i t is adapt
able to use with multicomponent systems. Its chief ad
vantage is its low response time, of the order of 0.003
seconds. Other advantages of th is instrument include
low cost, an easily recorded output, sim plicity of con
stru ctio n , and ad ap tab ility of form.
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