Table Of ContentThe Pennsylvania State College
The Graduate School
Department of Chemical Engineering
PREDICTION OF COMPOSITION CHANGES AND GRADIENTS
IN SELECTIVE ADSORPTION COLUMNS
A Thesis
by
Rosario Joseph Lombardo
Submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
June 1951
Approved:
-77, ^ 3,. /*r/
<3 / /?£-/
ACKNOWLEDGMENT
The author wishes to express his deep appreciation
and sincere thanks to Dr0 Arthur Rose for his guidance,
encouragement and interest in this investigation; to
Dr. D.S. Cryder, Head of the Department of Chemical En
gineering, who made this investigation possible; to the
Research Corporation for financial assistance with the
computations; to Mr„ TCJ. Williams for his care and pa
tience in programming and carrying out the IBM calcula
tions; to Miss Patricia Peters and Mr., Jerome Sekerke
for their careful and painstaking work during the early
tedious phase of the calculations; to Dr. M 0R. Fenske
and Dr. D. Quiggle who provided some of the material
used in the investigation; to the faculty and graduate
students of the Department of Chemical Engineering for
their cooperation and interest; and to my wife, not
only for her assistance with this thesis, but for the
many willing sacrifices she has made.
ii
CONTENTS
INTRODUCTION......................... . . . . . . . . . . 1
HISTORICAL ................................................. 2
SECTION I
DETERMINATION OF LIQUID-ADSORBATE EQUILIBRIA . . . 7
A. BASIS FOR EXPERIMENTAL METHOD.............. 7
B0 DERIVATION OF EQUATIONS ........................ 9
C. MATERIALS, APPARATUS, PROCEDURE, AND
EQUILIBRATION TIME . . . ................... .. H
D. RESULTS OF PHASE EQUILIBRIUM S T UDIES ...... 17
E. DISCUSSION OF RESULTS . . . . . . . . . . . . . 38
Fo THEORETICAL RELATIONSHIP BETWEEN VAPOR-LIQUID,
VAPOR-ADSORBATE, AND LIQUID ADSORBATE
SEPARATION FACTORS ............................ 38
SECTION II
APPARATUS, PROCEDURE, AND EXPERIMENTAL DATA FOR
SELECTIVE ADSORPTION EXPERIMENTS IN COLUMNS . . . . 41
SECTION III
BATCH ADSORPTION CALCULATIONS . . . . . . ........... 54
A. CONCEPT OF STATIC, DYNAMIC, AND TOTAL
HOT iDUP c . a . . . 0 3 . . a o . o o . 33
B. ASSUMED MECHANISM FOR THE ADSORPTION PROCESS. . 59
C. FRACTIONATION EQUATIONS , . 60
D. SAMPLE CALCULATIONS FOR A FRACTIONATION
PROCESS . . . . . . . . . . . . . . . . . . . . 70
E. RESULTS OF SAMPLE CALCULATIONS . . . . . . . . 71
ill
CONTENTS (cont * d„)
SECTION III (cont’d.)
F. SAMPLE CALCULATIONS FOR SMALLER UNIT QUANTITIES
OF G E L ................... « . . . ............... 74
G. COMPARISON OF CALCULATED AND EXPERIMENTAL
RESULTS . . . . . . . . . 76
H. COMPARISON OF CALCULATED DATA WITH EXPERIMENTAL
DATA OF MAIR et al„ . . . „ . . « . . . . . . . 78
I. CALCULATED EFFECT OF HT ON COLUMN OPERATION . . 83
J. DISCUSSION OF CALCULATIONS . . . . . . . . . . . 88
SECTION IV
DEVELOPMENT CALCULATIONS ........ 94
A. MECHANISM AND EQUATIONS . . . . . . . . . . . . 95
B. SAMPLE CALCULATIONS AND RESULTS . . . . . . . . 98
C. COMPARISON OF CALCULATED AND EXPERIMENTAL
DEVELOPMENT RESULTS . .......... 99
SECTION V
METHOD OF COMPUTATION FOR TERNARY SYSTEMS . . . . . 106
SECTION VI
IBM DIGITAL COMPUTER PROGRAMMING FOR ADSORPTION
CALCULATIONS . . . .................................. 108
CONCLUSIONS 112
iv
CONTENTS (cont'd.)
APPENDIX
ADSORPTION EQUATIONS FOR CONSTANT INCREMENTS . . . . 113
CALIBRATION DATA
VOLUME FRACTION v8. REFRACTIVE INDEX . .................117
NOMENCLATURE . .......... 121
GLOSSARY.......... 125
BIBLIOGRAPHY . ............... 127
LIST OF TABLES
TABLE I EXPERIMENTAL VALUES FOR VOLUME ADSORBED PER
GRAM OF ADSORBENT AT 20°C................. .. 10
TABLE II EQUILIBRATION TIME EXPERIMENT................ 17
TABLE III SUMMARY OF LIQUID-ADSORBATE EQUILIBRIA
INVESTIGATED.................................. 18
TABLE XV - XIII
LIQUID-ADSORBATE EQUILIBRIUM DATA............ 19-27
TABLE XIV SUMMARY OF EXPERIMENTAL COLUMN RUNS......... 43
TABLE XV - XXIV
DATA FOR EXPERIMENTAL COLUMN R U N S............ 44-53
TABLE XXV FRACTIONATION CALCULATIONS (Rp = 1.10). . . . 72-7
TABIE XXVI FRACTIONATION CALCULATIONS (Rp = 0.939) . . . 31-82
TABLE XXVII
FRACTIONATION CALCULATIONS (H<p = 1.00) . . . 85
TABLE XXVIII
FRACTIONATION CALCULATIONS (Bp = 1.05) . . . 86
CONTENTS (cont’d.)
TABLE XXIX DEVELOPMENT CALCULATIONS (HT = 1.05) . 100-102
TABLE XXX - XXXIII
CALIBRATION DATA
VOLUME FRACTION vs. REFRACTIVE INDEX .116-119
LIST OF FIGURES
FIGS. 1-10 PLOTS OF LIQUID-ADSORBATE EQUILIBRIA . .26-39
FIG. 11 SCHEMATIC COLUMN DIAGRAM . ............. .65
FIGS. 12-13
COMPARISON CF CALCULATED AND EXPERIMENTAL
RESULTS FOR THE FRACTIONATION PROCESS . 77,79
FIG. 14 CALCULATED EFFECT OF Hm ON COLUMN
RESULTS . .........7 ................... 87
FIG. 15 FRACTIONATION EXPERIMENT
TOLUENE - n-HEFTANE
COMPOSITION OF EFFLUENT vs. TOTAL VOLUME
OF EFFLUENT . . . . . . . . ............. 91
FIG. 16 FRACTIONATION EXPERIMENT
TOLUENE - n-HEPTANE
COMPOSITION OF EFFLUENT vs. % TOTAL
VOLUME OF EFFLUENT . . . . . . . . . . . 92
FIG. 17 COMPARISON OF CALCULATED AND EXPERIMENTAL
RESULTS OF DEVELOPMENT OPERATION . . . . 103
FIG. 18 EXPERIMENTAL RESULTS OF DEVELOPMENT
OPERATION ON 8 mm. COLUMNS . . . . . . . 104
INTRODUCTION
This thesis deals with a method for predicting the
composition at various times and at various points in a
column in which a binary hydrocarbon liquid mixture is
flowing past a granular adsorbent. The method consists of
a stagewise, stepwise analysis of column operation based on
material balance equations and detailed knowledge of the
liquid-adsorbate equilibria for the system. The calcula
tions are made for a moderately complex case of the frac
tionation of a binary hydrocarbon mixture as well as for a
simplified development operation. Specific illustrations
are given for these two cases for the system benzene-
n-hexane on silica gel. Reasonable agreement between cal
culated and experimental results is demonstrated. The
assumptions made regarding the column operation are listed
and discussed. A simple method for the extrapolation of
the calculated results to apply to columns of varying
diameter is presented. A description of IBM punched card
computer operation involved in the numerical solution of
the material balance equations is presented. The possible
application of the method for the prediction of column
phenomena involving ternary mixtures is discussed. The work
includes derivation of equations which facilitate the deter
mination of liquid-adsorbate equilibria. Basic equilibrium
data is presented for several binary mixtures on three
adsorbents. A theoretical relationship between the vapor-
adsorbate and liquid-adsorbate separation factors is derived
Information is presented on column preparation and operation
HISTORICAL
Adsorption phenomena have been the subject of intensive
research for many years. Dietz (A) has compiled an excellent
bibliography of adsorption literature for the years 1908-1942.
The increasing number of publications in more recent years is
evidence of the growth of interest in this field. There has
been no attempt made in this thesis to list in detail the
numerous articles published in this general field of inves
tigation. Rather the references described are those which
are directly related and pertinent to the specific problems
dealt with in the investigation.
The mathematical treatment of batch adsorption prooesses
has been attempted by several investigators. Wilson (13)
in ”A Theory of Chromatography” assumed the volume between
particles of adsorbent to be negligible; that equilibrium
was attained instantaneously, and that diffusion effects
could be neglected. The adsorption isotherm was used to
express the liquid-adsorbate equilibria and differential
equations derived which related the rate of migration of a
band of adsorbed solute to the volume of solvent passed
through the column for the case of a single solute. The
equations predicted qualitatively the separation obtained
and the uniformity and sharpness of the adsorbed band.
The assumption of negligible volume between particles
of adsorbent was eliminated by De Vault (5), who further
extended Wilson’s treatment of the problem while retaining
the concepts of instantaneous equilibrium and negligible
diffusion effects and the adsorption isotherm for a single
solute. The differential equations developed were complex,
but did present reasonable agreement with previously published
data on adsorption of high molecular weight organic acids.
The derivation was extended to include equations for multiple
solutes with a corresponding increase in their complexity.
No general solution to these latter equations was found.
Thomas (11) has presented a kinetic treatment of adsorp
tion theory leading to a Langmuir-type isotherm at equilibrium
The rate of adsorption was assumed proportional to the pro
duct of the "concentration of empty holes" on the adsorbent
and concentration in solution of the material being adsorbed.
The overall rate was assumed determined by chemical effects
alone and equal to the difference between rates of adsorption
and desorption. Equations for the rate constants were given.
Qualitative agreement between calculated and experimental
work was demonstrated for the case of a single solute. The
author developed equations for multiple solutes, but found
them of such a complex nature as to render a solution impos
sible.
Amundsen (1) has presented differential equations for
adsorption by a bed from a stream of fluid assuming adsorp
tion occurs irreversibly at a removal rate proportional to
adsorbate concentration in the fluid stream and to the dif
ference between the saturation capacity and the actual
amount of adsorbent held in a unit volume of bed. In a
later publication (12), Amundsen developed equations
for adsorption and desorption in a bed of adsorbent under a
number of different circumstances such as variation of inlet
composition to the bed, and desorption pressure exerted by
the adsorbate. The work in both instances was of a theor
etical nature, there being no experimental data presented.
Martin and Synge (10) have presented a very interest
ing proximate mathematical analysis of a liquid chromatogram.
The liquid chromatogram consisted of a column filled with a
granular material such as silica, which was subsequently
saturated with water. The substance to be separated, which
was in solution in a second liquid immiscible with water,
was then Introduced to the top of the column, the separation
occurring in the column depending upon differences in the
partition of the substance to be separated between the two
liquid phases. The separation did not depend on differences
in adsorption between the solid and liquid phases, the silica
acting merely as a mechanical support for the liquid phases.
A constant partition coefficient was assumed, it being in
dependent of the absolute value of the solute concentration
and of the presence of other solutes. It was pointed out
that in practical instances the partition coefficient is
not a constant. The proximate method gave results which
checked experimental data with a good accuracy.
In the related field of liquid-adsorbate adsorption
equilibria Mair et al., (9) have concerned themselves
with the determination of such equilibria by column and
desiccator experiments. A separation factor analagous to
