EPA-650/2-73-036
October 1973
Environmental Protection Technology Series
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EPA-650/2-73-036
FEASIBILITY
OF FLUX FORCE/CONDENSATION
SCRUBBING
FOR FINE PARTICULATE COLLECTION
by
Seymour Calvert, Jhuda Coldshmid,
David Lcith, and Nikhil C Jhaveri
A P T , Inc
P 0 Box 71
Riverside, California 92502
Contract No 68-02-0256
Program Element No.lABOI2
ROAP No 2IADL
EPA Project Officer Leslie E Sparks
Control Systems Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20160
October 1973
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This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does
mention of trade names or commercial products constitute endorsement
or recommendation for use.
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FOREWORD
This report, "Feasibility Of Flux Force/Condensation
Scrubbing For Fine Particle Collection", is the final
report submitted to the Control Systems Laboratory for
E.P.A. Contract No, 68-02-0256.
The principal objective of this experimental and
theoretical program was to determine the feasibility of
flux force/condensation (FF/C) scrubbing. The main activi-
ties under the scope of work were:
1. An extension of the existing theoretical treat-
ment of FF/C scrubbing, starting with a review
and analysis of past work and proceeding to
engineering design methods suitable for eval-
uating practical systems.
2. An exploratory experimental study limited to
the evaluation of key features of FF/C
scrubbing.
3. Preliminary engineering and cost analyses of
promising practical cases.
4. Recommendations for future development of
FF/C scrubbing systems.
Dr. Leslie E. Sparks, of the Control Systems Labora-
tory, National Environmental Research Center, Environmental
Protection Agency was the Project Officer for this program.
Dr. Seymour Calvert, of A.P.T., Inc., was the Project
Director.
11
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ABSTRACT
This report presents the results of a feasibility
study of flux force/condensation (FF/C) scrubbing for
fine particle control. FF/C scrubbing includes the
effects of diffusiophoresis, Stephan flow, thermophoresis,
and particle growth due to the condensation of water vapor,
and is not restricted to any specific scrubber configura-
tion. Fine particles are those smaller than 2.0 micrometer
diameter.
The program purpose was to determine whether a devel-
opment program to maximize FF/C effects is warranted and,
if so, to detail the recommended program. The scope of
analytical and experimental work was limited to the
exploration of the most essential features.
Experimental determination of sub-micron particle
collection efficiency in a bench-scale, sieve plate type
FF/C scrubber validated the mathematical model which had
been developed in the analytical phase of this program.
Process designs and cost estimates for the application
of FF/C scrubbing to two fine particle pollution sources
demonstrated its technical and economic potential feasibil-
ity. It is concluded that FF/C scrubbing is an attractive
control method for fine particles when high efficiency
is required and when the gas is hot enough to evaporate
the necessary water vapor. Further development of FF/C
scrubbing is clearly warranted.
This report was submitted in fulfillment of Contract
No. 68-02-0256 by A.P.T., Inc. under the sponsorship of
the Environmental Protection Agency. Work was completed
as of February 17, 1973.
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CONTENTS
Page
Abstract iii
List of Tables v
List of Figures vi
Acknowledgements viii
Sections
Summary and Conclusions 1
Introduction 7
Engineering Design 22
Theoretical Background 27
Mathematical Model, Sprays 44
Mathematical Model, Plates 59
Mathematical Model, Impinging Jet 77
Mathematical Model, Liquid Sheets 83
Experimental 92
Economic Feasibility 118
Future Research Recommendation 133
References 138
Glossary 144
IV
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TABLES
No.
1 Selected References On FF/C Applications 15
2 Collection Efficiency Of Particles By Drops 54
For K =1.1 And Gr = 0.1 At Various
P F
Boundary Layer Thickness
3 Summary Of Plate Computations With Pene- 74
tration Theory Predicted Coefficients
4 Results Of Computer Predictions Of 88
Collection By Sheets
5 Experimental Conditions And Results 111
6 Transfer Coefficients Determined By Il6
Mickley's Method
7 B.O.F. Control System Costs 126
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FIGURES
Np_._ Page
1 Schematic Representation For FF/C Scrubbing 23
On A Sieve Plate.
2 Critical Saturation Ratio For Homogeneous 33
Nucleation Of Water (After Amelin (1967))
3 Critical Saturation Ratio For Water Upon A 34
Plane Substrate Of Given Contact Angle -
Water At 20°C (After Fletcher 1966) .
4 Critical Saturation Ratio For Nucleation Of 35
Water Droplets Upon A Particle Of Given
Radius With cosa At 20°C As Parameter -
(After Fletcher 1966) .
5 Equilibrium Supersaturation As A Function 35
Of Droplet Radius With (im) As A Parameter
(After Howell 1949).
6 Dimensionless Concentration Or Temperature 40
Vs. Dimensionless Distance
7 Saturation Ratio Vs. Dimensionless Distance 43
8 Efficiency Of Single Drop Versus Inertia 51
Parameter At NR , = 9.6 With N™ As Parameter
9 Efficiency Of A Single Drop, n, Versus NFn 52
As A Parameter (NR , = 9.6)
10 Collection Efficiency For 0.5 ym Diameter 57
Particles In A 1 Meter Spray Column
11 Computed Prediction Run #3 For Sieve Plate 71
12 Predictions Of Effect Of Water Vapor Concen- 71
tration On Particle Radius
13 Computed Predictions Run #26 72
14 Computed Predictions Run HIS 72
15 Computed Predictions Run #20 73
vi
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FIGURES
No. Page
16 Computed Prediction For Sheets, Run *1 89
17 Computed Prediction For Sheets, Run #2 89
18 Computed Prediction For Sheets, Run #3 90
19 Computed Prediction For Sheets, Run #4 90
20 Experimental Apparatus 93
21 Operating Characteristics Of The Sieve-Plate 95
22 Particle Generator Assembly 97
23 Sampling System 100
24 Particle Penetration Vs. Water Vapor 113
Condensed
25 Theoretical Vs. Experimental Penetration 115
26 Flow Scheme For B.O.F. Gas Cleaning 123'
27 Flowsheet For FF/C Scrubber On Kraft Liquor 129
Recovery Furnace
VJ.1
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ACKNOWLEDGEMENTS
A.P.T., Inc. wishes to express its appreciation
for excellent technical coordination and for very
helpful assistance in support of our technical effort
to Dr. Leslie Sparks, E.P.A., Project Officer, and
Mr, Robert Lorentz, E.P.A.
Vlll
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SUMMARY AND CONCLUSIONS
Flux force and water vapor condensation effects have
the potential to cause high efficiency collection of fine
particles by scrubbers. These effects can result from the
cooling of a hot, humid gas by contact with cold water.
The temperature gradient causes thermophoresis, which
drives the particles from the hot gas to the cold water
and the water vapor concentration gradient causes diffusio-
phoresis, which also drives the particles toward the water
surface. Condensation of water vapor on the particles will
cause their mass to increase and the particles will then be
easier to collect by inertial impaction.
The object of the research reported here was to
determine the feasibility of using flux force/condensation
(FF/C) effects for fine particle (i.e., particles with
diameter smaller than 2 microns) collection and, if it
appears feasible, to specify the nature of a development
program which would be required to provide a proper basis
for designing practical systems. The results of the study
have established the feasibility of FF/C scrubbing and
have indicated the crucial design questions. At the time
of writing, development is continuing in order to extend
and strengthen the base of engineering design knowledge.
At the beginning of this research it was known from
the literature and previous experience that FF/C scrubbing
"works". The phenomena of thermophoresis, diffusiophoresis
and condensation on particles had been observed and there
were reasonably accurate quantitative theories to describe
each of them when it occured in a simple system. On an
empirical level, there were reports of several scrubber
systems which employed flux forces and/or condensation
either as the result of deliberate planning or happenstance
Missing, however, was an integration of theory of flux
force deposition and particle growth by condensation into
an overall quantitative model which would account simultan-
eously for these phenomena. The model would also have to
include heat and mass transfer, particle collection by
other mechanisms, and the balances for energy, water vapor,
and particles.
The first stage of the research was to put all of the
pieces together for the prediction of particle collection
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in scrubbers of several representative types. Literature
search and a review of theory led to the selection of the
elements which were incorporated into the overall mathe-
matical models. These models have been, and are still
being, refined through a series of evolutionary steps and
have reached the point for some scrubber types where they
are quite comprehensive and appear to be capable of realis-
tic and accurate representation of particle collection so
far as the available experimental data show.
Models for plate scrubbers (as represented by sieve
plates) and packed scrubbers have been developed to the
point where they appear to do a good job of showing the
simultaneous effects of heat and mass transfer for gas/
particles and gas/liquid, diffusiophoresis, thermophoresis,
Brownian diffusion, inertial impaction, and changes in
particle concentration, humidity, and temperature as the
gas flows through the scrubber.
The model for spray scrubbers required appreciable
effort on the computation of particle trajectories for
the combined effects of flux forces and inertial collection
by liquid drops. The influence of flux forces on collection
by drops was found to be defined by a new dimensionless
parameter which is the ratio of flux force deposition
velocity to the gas velocity and which we call the "flux
deposition number". If the flux deposition number is
greater than 0.1, particle collection efficiency will be
good and if it is less than 0.01, efficiency will be poor.
The model for collection from an impinging jet showed that
negligible benefit is given by flux force deposition because
of the very short contact time.
Theoretical analysis showed that, in general, the
particle deposition velocity has to be on the order of
0.1 cm/sec or larger for appreciable collection efficiency
to occur. Diffusiophoresis can produce deposition veloci-
ties this high under the heat and mass transfer conditions
of a realistic scrubber, but thermophoresis generally
cannot. If particle growth due to condensation occurs,
inertial impaction of the resulting two or three micron
diameter particles can give sufficiently high deposition
velocities. Particle growth has the advantage that the
high deposition velocity can persist after the heat and
mass fluxes are dissipated, because once the particles are
enlarged, they can be collected to an increasing degree at
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the cost of relatively little additional pressure drop.
Experiments were designed to explore the regions of
FF/C scrubbing where the mathematical model was most depend-
ent on the several relationships, coefficients, and assump-
tions which had been used. A test aerosol of condensed
dibutyl phthalate smoke particles 0.7 ym diameter was
scrubbed from humid air by a 10 cm diameter sieve plate.
Particle size and concentration, gas and liquid flow rates,
temperatures, and other significant parameters were meas-
ured.
Comparison of the experimental data with the model
required that first the heat and mass transfer coefficients
used in the model be computed from experimental measure-
ments of heat and mass transfer. Predictions of particle
collection efficiency based on the experimental transfer
coefficients were then compared with the experimental
efficiencies. The predictions were sufficiently close to
the experimental data to validate the mathematical model
as a basis for exploration of FF/C scrubbing potentiality.
A number of details remain to be resolved by further effort
despite the fact that the model will give a realistic pre-
diction of flux force effects for the experimental system.
Economic Evaluation
The exploration of the economics of FF/C scrubbing was
started as soon as an apparently realistic mathematical
model was available. Two candidate processes (Basic oxygen
furnace and a Kraft liquor recovery furnace) were selected
for study on the basis of their meeting the criterion that
the gas should ideally be hot enough to evaporate the
necessary water.
This criterion develops from the fact that steam pur-
chased at a cost of $1.32 or more per 1,000 Kg steam ($0.60
or -more per thousand pounds) is expensive and its use must
compete with high-energy scrubber (or electrostatic precipi
tators or fabric filters) on the basis of operating costs.
For illustration, if 0.15 Kg steam were used per Kg of dry
gas (this is a fairly low ratio for FF/C scrubbing), the
steam cost would be about $0.24/1,000 m3 dry gas
($0.20/1,000 Kg dry gas). Cooling water for this case
might cost from about $0.01/1,000 m3 to $0.12/1,000 m3 dry
gas, with $0.03/1,000 m3 being a probable minimum for
cooling tower water.
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The FF/C steam and water costs may be compared with
the power cost for a high-energy scrubber which is capable
of 80% collection efficiency on 0.5 jjm diameter particles
of density 1.0 g/cm3. A venturi scrubber would require a
pressure drop of about 450 cm W.C., which would mean a
power cost of $0.24/1,000 m3 of gas if electricity cost
l.Ot/K.W.H. One can see that at this performance level an
FF/C system could purchase steam and be nearly competitive,
and that it would become more attractive as efficiency re-
quirement becomes more stringent. Generally, it would be
advantageous to FF/C scrubbing if the gas were hot or
moderately hot and humid so that steam need not be purch-
ased.
A preliminary design and cost estimation for the use
of a 99.9% efficient FF/C spray scrubber on a basic oxygen
furnace of 250 ton/heat capacity resulted in a capital
investment of about $1,700,000 and annual operating costs
of about $790,000. Cost given by others for electrostatic
precipitator, fabric filter, and high-energy wet scrubber
systems ranged from about $3,200,000 to $6,000,000 for
capital investment and from $1,200,000 to $2,400,000 for
annual costs. Since the gas is very hot and must be cooled
(usually by water sprays) before it can be cleaned by any
means, this situation js very favorable to FF/C scrubbing.
This design should be revised in the light of the additional
understanding of FF/C scrubbers which has been acquired
since the time when the estimate was made.
For another example of the possibilities for FF/C
scrubbing, a system for up-grading an existing Kraft pulping
liquor recovery furnace air pollution control installation
was compared to two other alternatives. In each of the
three revision alternatives the original 80% efficient
venturi scrubber was replaced with a low efficiency venturi
evaporator and a high efficiency particulate collector was
added as a second stage.
If one added an electrostatic precipitator such that
overall efficiency would be 99% the capital investment would
be $1,930,000 and the annual cost $420,000. A venturi in
series with the first such that overall efficiency would be
97% would require a $710,000 investment and an annual cost
of $32,000. An FF/C system consisting of a condenser
(tubular heat exchanger) and a spray scrubber capable of an
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overall 971 efficiency would require a $610,000 capital
investment and an annual cost of $24,000.
At the level of precision of a preliminary estimate,
there is no appreciable difference between adding a high
efficiency venturi and adding an FF/C system. The FF/C
system has the great advantage that if higher efficiency
than 97% is required, as would be likely, it can be up-
graded for relatively low cost. For example, the overall
efficiency would be increased to 99% for an additional
investment of $150,000 and an annual cost of about $40,000.
This is possible because once the particle size has been
increased by condensation, additional collection efficiency
is much easier to obtain than it would be for the original
particle size.
Conclusions
The results of the preliminary study show that FF/C
scrubbing is capable of high particle collection efficiency
on fine particles and that performance is "accountable"
through the use of mathematical models. Experimental data
served the purpose of verifying the general content and form
of mathematical models and, while the efficiencies measured
for one-plate scrubbers are not very high, the predictions
for multi-plate scrubbers can now be viewed with more
confidence.
Of the several particle collection mechanisms involved
in FF/C scrubbers, diffusiophoresis and inertial impaction
enhancement by particle growth are the two most important.
Preliminary indications are that particle growth is the more
important of the two.
Economic considerations define the most favorable area
of application for FF/C scrubbing as those situations in
which the enthalpy of vaporization is available from the gas
to be cleaned, although for high efficiency collection of
fine particles the purchase of steam can be justified. If
an existing scrubber need be up-graded for the removal of
sub-micron fume it could pay to introduce some steam, even
if it had to be purchased. Another criterion is that the
smaller the particles, the better FF/C scrubbing will look,
because its efficiency is relatively unaffected by particle
size. Cooling water costs can be significant although, de-
pending on the system, charges as high as 4tf/m3 (15(/:/l,000
gallons) can be accomodated.
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The most suitable types of scrubber for FF/C applica-
tion appears to be multi-stage or continuous contact type.
This kind of apparatus can be readily adapted to provide
different conditions and geometry on different plates to
accomodate changing flow rates and particle concentrations.
From the pressure drop standpoint, there should be not much
difference between this and other scrubber types for the
same performance.
Development Required
The research which has been performed up to this point
has established the feasibility of FF/C scrubbing and our
ability to describe the process with engineering design
equations. It has'also shown that the specific details of
heat and mass transfer, the nucleation of condensation, and
other matters have very significant influence on FF/C
mechanisms.
In order to resolve the areas of uncertainty mentioned
above and to further refine the engineering design methods,
a pilot plant development effort is necessary. The pilot
plant scale is important because of the necessity for having
realistic heat and mass transfer conditions. Some addition-
al bench-scale work is also needed to provide a means for
rapid scanning of a variety of conditions. The importance
of particle properties and concentration also dictates that
the effects of their variation be studied.
Next, there must be a pilot plant demonstration test
under the actual conditions of the specific application in
order to ensure the performance and economics of FF/C
scrubbing. Ultimately, we will have to identify the
specific characteristics which are of most significance
and develop test methods for measuring them so that perform-
ance can be predicted and FF/C scrubbers designed without
pilot plant testing.
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INTRODUCTION
Preliminary theoretical predictions which were
carried out as a part of the "Wet Scrubber System
Study" and reported by A.P.T. in the "Scrubber Handbook"
(1972), indicated that flux forces (i.e., forces due to
temperature and composition gradients) and particle
growth due to moisture condensation offered much promise
as a means for separating fine particles from gases. In
order to follow-up and evaluate that lead, Contract No.
68-02-0256 was established to determine the feasibility
of flux force/condensation (FF/C) scrubbers. This report
is the final report for that feasibility study.
The major efforts of the study were to make experi-
mental and theoretical explorations of a key region in
which flux forces would act to separate particles. It
was anticipated that the experimental results would enable
the validation of mathematical models which could be used
with some confidence to predict the technical and economic
potential of FF/C scrubbing. The object was to determine
whether a development program to maximize such forces is
warranted and if so, to detail the recommended program.
FF/C scrubbers were shown in the system study to have
the potential for filling a gap in present day scrubber
technology. Whereas scrubbers as commonly used will collect
fine particles poorly unless high energy is expended in
accelerating the gas, this is not the case for FF/C scrubbers.
By applying forces other than inertia on the particles and/or
by causing the particles to grow so that inertial deposition
is more effective, the FF/C scrubber can give performance
on fine particles which is nearly independent of the size
of the particles entering the scrubber.
FF/C scrubbing involves those forces which result from
temperature, composition, or electric fields in the gas
phase. These include thermophoretic, diffusiophoretic,
photophoretic and electrophoretic forces and the Stefan
flow. The present study is limited only to thermophoresis
and diffusiophoresis (which we define to include both diffu-
siophoretic and Stefan flow forces). Accordingly, we consider
only those FF/C scrubbers where particle removal from the gas
is aided by a temperature gradient, a vapor concentration
gradient, vapor condensation, or combinations of the three.
It is not necessary that all three forces act simultaneously,
but in most actual cases they do.
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For the case of air and water contacting it can
readily be shown that the force resulting from the mass
transfer of water vapor is the dominant force and a FF/C
scrubber is distinguished by vapor condensing inside the
scrubber.
Flux forces may stem from the difference in momentum
imparted to the particle on opposite sides by the molecules
colliding with it or desorbing from it. In the case of a
temperature gradient, hotter (and thus faster) molecules
colliding with the particle will impart a higher momentum
to the particle than the cooler (slower) molecules. In a
concentration gradient, which is accompanied by diffusion
but not necessarily by net motion of the gas phase, the
heavier molecules will again impart a higher momentum than
the lighter molecules.
Another kind of flux force is due to Stefan flow
which occurs when there is a net motion of the gas phase.
The mass transfer can be brought about by evaporation,
condensation or a chemical reaction. It was first suggested
by Stefan in 1881 that near the surface of an evaporating
or condensing body there must exist a hydrodynamic flow of
the medium (directed away from the evaporating and towards
the condensing surface).
It should be noted here that we refer to the combina-
tion of forces due to Stefan flow and to the differential
bombardment caused by a gas composition, or molecular
weight gradient, as diffusiophoretic force.
In case of condensation of vapor molecules which are
heavier than air, then both forces act in the same direc-
tion; toward the condensing surface. If the condensing
molecules are lighter than air (as in the case with water
vapor), the Stefan flow force acts towards the condensing
surface while the molecular weight gradient force acts
away from it. The net force for the condensation of water
from air or flue gas is toward the cold surface because of
the overwhelming effect of Stefan flow.
Flux force effects on particles have been known for
many years and the background is reviewed and discussed in
depth by authors such as Waldman and Schmitt (1966) ,
Goldsmith and May (1966), and Hidy and Brock (1970). The
studies reported by these authors include both theoretical
and experimental work. The experimental systems were de-
signed so as to be readily definable and were much simpler
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than a scrubber in terms of the number of phenomena and
unsteady conditions involved. For example, we find
experimental studies of particle deposition from gas
flowing between flat parallel surfaces under the influence
of a constant heat or mass flux between the surfaces.
Details of pertinent previous studies will be discussed
later in this report.
PRACTICAL APPLICATIONS
Over a period of many years there have been numerous
instances of the use of scrubbers in which FF/C effects
occured. In most of the early pertinent literature, such
as patents issued around the beginning of this century,
there was no deliberate or conscious design to use FF/C
but we can reasonably surmise from the descriptions given
that FF/C effects were active. For example, U.S. patent
no. 1,039,008 (1912) employed sprays to clean blast furn-
ace top gas and we would expect that the hot gas first
became saturated with water vapor and subsequently was
de-humidified by further contact with spray water. Con-
sequently, particle collection could have been enhanced
by FF/C effects. ^
More recent literature reveals a growing awareness
of the potentialities of FF/C scrubbing; often as a means
of explaining anomalously high particle collection
efficiency. Schauer (1951) reported high removal of OOP
smoke when steam was introduced into a venturi scrubber.
Lapple and Kamack (1955) reported that the addition of
steam reduced dust loss at a given air pressure drop.
Semrau et al. (1958) reported that the observed perform-
ance differences between particle collection by a pipeline
scrubber and a venturi-cyclonic spray scrubber were
probably due to differences in the scrubbing liquid temp-
erature .
Description of other cases where particle collection
was enhanced by steam addition can be found in articles
by Demshin et al. (1965), Litvinov (1964) and many others.
However, most of these authors observed the phenomena but
did not study them in detail. Increased collection efficien-
cy due to steam addition was usually attributed to two groups
of phenomena: 1) Flux forces. 2) Particle growth. In
most studies no attempt was made to isolate the various phen-
omena and determine relationships between operating condi-
tions and particle collection efficiency that will permit the
engineering design of a FF/C scrubber.
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More detailed studies of the deliberate use of
FF/C effects can be found in engineering articles after
about 1965 and in the patent literature. These studies
generally fall into one of four categories:
1. Studies of FF/C scrubbers, per se.
2. Studies in other fields such as meteorology
and atomic reactor accidents where particle
growth and phoretic forces were analyzed.
3. Attempts at analyzing the FF/C scrubber.
4. Patent literature.
Studies of Flux Force/Condensation Scrubbers
Rozen and Kostin (1967) studied the collection of
fine oil mist (average particle diameter of 0.3 ym) in a
perforated plate column. They built their column in such
a way that the gas passed first through a plate with warm
water where it became saturated with water vapor and then
through a cold water plate where condensation took place.
Four such plate pairs were in their column and collection
efficiency was studied as a function of temperature of
the plates.
Collection efficiency increased with the temperature
difference between the hot and cold plates. The further
downstream the plates were, the higher was the collection
efficiency. Thus, for example, for a 50°C temperature
difference collection efficiency for the first pair of
hot and cold plates was 45%, for the second pair it rose
to 57.41, for the third pair of plates it reached 74%, and
in the fourth pair collection efficiency came to 90%. They
found that their results could be represented by an empiri-
cal equation relating the particle penetration, "Pt", with
the mass of steam condensed per gram of inlet particles,
"q"
-0-56
Pt = 12.5 q (1)
While these results are encouraging, it is difficult
if not impossible to extrapolate the Rozen and Kostin data
to other installations mainly because of the lack of a
theoretical analysis. Rozen and Kostin presented only their
experimental results and attributed the high efficiencies
to particle growth. Our theoretical analysis of their data
showed that their experimental results could be due to flux
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forces as well as growth. There is also some uncertainty
about their results at high temperatures because of the
possibility of particle loss by evaporation of the oil.
Litvinov (1964 A), (1964 B) , (1965), (1967) and
(1972) did extensive experimental laboratory and industrial
scrubber work on the effect of condensation on particle
collection efficiency in venturi scrubbers followed by a
cyclone or a tray column for mist elimination. In his
1967 paper he reported on the collection of fine carbon
black dust (=1 ym in diameter) and apatite dust in a
venturi scrubber followed by a two stage tray column. In
this paper he presented engineering data which permit the
reproduction of his work. However, his analysis of the
results is very limited and somewhat peculiar. He specu-
lates that neither particle growth nor diffusiophoresis
should have appreciable effect on the collection efficiency
and he suggests that "condensation produces favorable
conditions for coagulation", without even describing a
mechanism for this.
In his 1972 paper Litvinov experimentally studied
three industrial size combinations of dust removal equip-
ment. In all three combinations the first unit is a
precleaner for which he used cyclones or a combination
cyclone and electrostatic precipitator. Next came a
venturi followed by a one or two stage tray column. The
dust used had a mean diameter of =0.8 ym. Here again no
quantitative prediction of collection efficiency is given,
only a description of Litvinov's experiments. This time
the increase in collection efficiency is attributed to a
change in the particle surface properties caused by water
condensation.
Terebenin and Bykov (1972) describe an experiment where
an aerosol of unrefined tin with an arithmetic mean diameter
of 0.128 ym and saturated with steam was passed through a
series of wetted wall rectangular ducts. They analyzed their
scrubber for flux forces and increased sedimentation due to
particle growth. Their conclusion is that the aerosol part-
icles grew through condensation and then settled, largely
due to the action of flux forces. Here again no attempt was
made at generalizing the equation into a design method.
A study of steam injection into a laboratory scale wet
scrubber was carried out by Lancaster and Strauss (1971) .
11
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA 92502
-------
They used redispersed dry agglomerates of ZnO whose size
is defined only as having a mean diameter of 1 ym at low
concentrations and a larger diameter at higher concentra-
tions. The aerosol was injected into a 2" x 4" duct 6'
long to which first steam and then water were injected.
The water drops were then separated by a cyclone. They
measured an increase in particle collection efficiency
which was in direct proportion to the amount of steam
injected rather than the amount condensed and they conclude
that the increase in collection efficiency is due to parti-
cle growth. The use of hot water (same temperature as the
temperature of the saturated air) rather than cold water
in the sprays gave a slightly higher efficiency. This
indicates that diffusio - and thermophoresis were ineffect-
ive in the spray section.
The peculiar dependence of collection efficiency on
the amount of steam introduced rather than that condensed
is attributed by the authors to the mechanism of steam
condensation by self-nucleation on dust particles when
the steam is quenched more by colder gas. The possibility
of additional collection in the cyclone separator due to
FF/C effects is not discussed, nor is sufficient information
given so that it can be checked. One must conclude that the
results of this experiment are valid only for direct steam
injection with the specific geometry and operating condi-
tions studied. No general design methods are presented in
this paper.
Studies In Other Fields
The studies grouped under this category are more basic
and more systematic than those in the first group. Very
thorough analytical studies were carried out by Horst (1968)f
Hales et al. (1970), Hales et al. (1971), Hales and Schwen-
diman (1971). These studies were concerned with a reactor
accident and explored the possibilities for aerosol removal
in an enclosed environment at a condensing steam boundary
layer. Thus, their analyses were confined to liquid sheets
with only natural convection as the air moving mechanism, a
situation which is very unlikely in a scrubber. These stud-
ies are further limited by the lack of experimental confirm-
ation .
Goldsmith and May (1966) reported another very important
study. They analyzed the removal of a radioactively tagged
nickel-chromium aerosol 0.02 to 0.2 urn in diameter. The
12
A. P. T. Inc. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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aerosol moved through a vapor gradient box and its
deposition velocity was measured. They proved experi-
mentally the validity of the Waldman equation for diffus-
iophoresis. In another experiment they showed that when
the vapor pressure gradient was not closely controlled
and supersaturation was permitted, collection was due to
particle growth as well as flux forces.
Attempts At Analyzing The Flux Force/Condensation Scrubber
Only a few articles were found in the literature where
the feasibility of a flux force or a FF/C scrubber was
analyzed. These articles were also the ones that came
closest to presenting design methods and design equations.
Sparks and Pilat (1970) presented an analysis of a
spray column with condensation taking place on the drops.
They showed that for example, when K =0.6, where "K " is
the Stokes number, the collection efficiency in a spray
column, where the vapor pressure gradient is 10s mbar/cm,
was 1001 as compared to an efficiency of 0% with no vapor
gradient present. While their equations can serve as a
starting point for the design of a spray column they defin-
itely need refinement and experimental verification.
Davis and Truitt [1972) present a rough economic
analysis of a FF/C scrubber. However, a review of their
work revealed sufficient errors in their theoretical
analysis and experimental techniques that not much can be
obtained from their work to facilitate evaluation and design.
Patent Literature
The patent literature is more obscure than any of the
other groups. It does not describe the experimental work
on which the patent is based and in some cases presents an
idea that was never tried on a large scale. Patents usually
contain much irrelevant information and their descriptive
part usually centers on the equipment rather than on the
design method. Some examples of the patents available which
describe FF/C scrubbers are listed here. Japanese patent
No. Sho 41-41184, Kazuo Matsuzaki - inventor, describes a
FF/C venturi scrubber where the steam is injected tangentially
upstream of the throat. No relationships are given which
permit the design of such a scrubber.
13
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE, CA. 92502
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An article by Takashi Mashita (1971) describes a
system based on the Solivore scrubber. This system is
based on several venturi's in parallel with water sprays
saturating the air upstream of the venturi. Examples of
actual installations are given which permit a rough
estimation by extrapolation of the scrubber performance
from the operating conditions. Other variants of the
Solivore scrubber concept involve a single stage of satura-
tion plus venturi and four stages in series, as described
by Strauss (1966) .
Nucleation and growth by condensation are claimed to
be effective in the crossflow scrubber patented by Teller
where saturated gas enters a packed section and is cooled
with water. This device has been successfully applied to
phosphate fertilizer plant particulate collection.
Background Summation
The studies discussed above are examples of the avail-
able background information on FF/C scrubbing. Table I,
Selected References on FF/C Applications, summarizes the
references and their high points is meant to be illustra-
tive of significant studies rather than a complete listing
of the literature. What can be distilled from a survey of
the background information is a concept of where things
stood at the onset of this feasibility study.
To see this status of knowledge with clarity it is
helpful to consider first the question of what has to be
known in order to design FF/C scrubbers so that their per-
formance and costs can be predicted. In the next section,
therefore, we will turn briefly to discussing what we need
for design.
14
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-------
H
HH
P
AUTHORS YEAR
Semrau K., 1958
Marynowski C. ,
Lande K.,
Lapple C.
Lapple C. , 1955
Kamack H.J.
Schauer P.J. 1951
Rozen A.M., 1967
Kostin V.M.
o
m
03
O
X
m
3
(a
O
m
O
TABLE I - Selected References on FF/C Applications
HIGH POINTS OF STUDY REFERENCE
Attributed increase in collection
efficiency to scrubbing liquid
temperature.
Addition of steam reduced dust
loss at a given air pressure drop.
Addition of steam into a venturi
scrubber increase removal of OOP
smoke.
Studied experimentally the collec-
tion of fine oil mist in a plate
column. They found that:
1. Collection efficiency increased
with the quantity of steam con-
densed and proposed the empiri-
cal correlation
Pt = 12.5 q -°-56 »Pt" is
penetration and "q" = g steam
condensed to g inlet particles.
2. Collection in each pair of plates
is higher than in the preceding
pair. (They attributed the in-
crease in collection efficiency
to particle growth.)
Ind. Eng. Chem.
50, 1615 C1958
Chem. Eng. Prog.
Sl_, 110, (1955)
Ind. Eng. Chem.
43, 1532, (1951)
Intern. Chem. Eng.,
7, 464 (1967)
CO
ro
01
o
10
-------
AUTHORS
YEAR
HIGH POINTS OF STUDY
REFERENCE
Litvinov A.T,
s
CO
o
m
oo
O
X
m
33
CO
1964A His studies concentrated on venturi
1964B scrubbers followed by cyclone or
1965 sieve tray for entrainment separa-
1967 tion. In his 1967 and 1972 papers
1972 he reaches the following conclusions:
1. Phoretic forces are not important
for particles larger than 0.1 uro
in diameter.
2. Condensation of water vapor in a
venturi and a sieve tray column
increases particle removal ef-
ficiency.
3. He gives a design equation for the
venturi based on an experimental
optimum liquid film thickness,
which permits calculation of the
"optimum" quantity of condensed
steam.
4. He gives the equation NNu=0.78 NJ^65
for the heat transfer coefficient from
the gas to the liquid drops.
5. Particle growth does not affect col-
lection efficiency.
6. Tray columns with condensation are
more efficient than venturi with con-
densation in energy consumption.
Khim. prom.
8_, (1964)
Vestn. tekhn ,
i ekonom. inform
5, (1964)
Stal1, 7, (1965)
Zhurn, Priklad,
Khim, 40, 353
(1967) —
«D
10
en
o
to
-------
ff
P
AUTHORS
Terebenin A.N
Bykov, A.P.
YEAR
1972
Lancaster B.W.
Strauss W.
1971
o
m
oo
3
-»i
m
3J
en
O
m
O
CO
ro
S
10
HIGH POINTS OF STUDY
Analyzed the collection of particles
0.128 v>ro in diameter in cluster of
wetted wall rectangular ducts. They
concluded that in the presence of
steam particle removal is attributed
to growth and flux forces. They give
reference to particle growth equation,
the results of which do not agree with
their experimental findings of particle
diameter. No attempt to calculate pene-
tration was made.
REFERENCE
Zh. prikl. khim.
45, 1012, (1972)
Studied the collection of ZnO agglom-
erates with a mean diameter of 1 ym
in a 5 cm x 10 cm rectangular duct
1.85 m long. In different experiments
steam was injected upstream or down-
stream of the aerosol injection port,
and it was assumed that when steam was
injected upstream of the aerosol it
condensed on the aerosol particles. They
concluded:
1. Particle build-up was the major mech-
anism responsible for improved scrubber
performance.
2. Flux forces were not important.
3. For their system the dust penetration
could be correlated with the rate of
steam injection by:
7"n -1 where n and i
Ind. Eng. Chem.
Fund., 10, 362
(1971) —
Q = 0.2
are
-------
BT
n
AUTHORS
Lohs W,
00
s
tn
O
m
CO
O
X
-Nl
3J
m
31
CO
YEAR HIGH POINTS OF STUDY
the scrubber collection effic-
iency with and without steam
addition and "Q" is the steam
injection rate Ib steam/lb air.
4. Steam was used inefficiently in
this particular scrubber.
1969 Fine particle removal efficiency was
studied in a spray column. Na-SO, and
polystyrene aerosol with median part-
icle diameter varying from 0.43 to
0.8 pm and from 0.4 to 1.3 ym respect-
ively. Collection efficiency was im-
proved by steam addition for both
aerosols. The increase in collection
efficiency was higher for the soluble
Na2SO. aerosol. (0.3 - 0.5 vim particles
can be removed at 60% efficiency) The
separation of hydrophobic fine dust is
also increased particularly if the part-
icle surface is rendered hydrophilic by
means of a wetting agent.
Increased efficiency is attributed to
particle growth only though Stefan
flow is mentioned. No equations,
correlations or design method are
attempted.
REFERENCE
Staub 29, 43,
(1969)
to
ro
en
-------
a
o
AUTHORS YEAR
Horst T.W. 1968
Hales J.M., 1970
Horst.T.W.,
Schwendiman
Hales J.M., 1971
Schwendiman L.C.
Horst T.W.
CO
O
m
DO
CO
HIGH POINTS OF STUDY REFERENCE
This series of studies carried out
at Battelle Northwest was concerned
with the transport and deposition of
a radioactive aerosol expected to be
generated by fuel overheating follow-
ing an accident. Their solutions to
the case of aerosol deposition through
laminar naturally-convected boundry
layer are more rigorous than for the
parallel turbulent case. Their con-
clusions were:
1. In a laminar boundry layer the
dominant mechanism is diffusio-
phoresis. In the turbulent case
turbulent deposition may rival
diffusiophoresis.
2. Relationships can be derived be-
tween steam consumption and part-
icle deposition,
3. The rate of deposition of particles
0.5 - 2 ym in diameter in a laminar
boundry layer is independent on part-
icle diameter and depends only on the
operating conditions within the air
steam boundry layer.
4. When particle deposition is assumed
at the mass average velocity of the
fluid, values 20-60% lower than in
the case of flux forces are calculated
for a laminar boundry layer.
Battelle Northwest
reports No. BNWL
848 (1968) , BNWL
1125 (1970) BNWL
SA-3592 (1971)
BNBL-SA-3734 (1971)
CO
M
O1
O
to
-------
D
P
AUTHORS
Goldsmith P. ,
Delafield H.J. ,
Cox L.C.
Goldsmith P. ,
May F.G.
1966
s
en
o
m
CO
O
X
m
U
CO
O
m
O
Sparks, L.E
Pilat M.J.
1970
HIGH POINTS OF STUDY
Experiments with radioactively tagged
nickel-chromium aerosol CParticles
0.02 to 0.2 urn in diameter) gave
deposition velocities close to those
predicted from the Waldman and Baka-
nov et al. equations. Comparison
of thermophoretic velocities with
theoretical predictions shows that
for r > A(r the particle radius,
A - the mean free path under the
given conditions) they vary over a wider
range. Derjaguin equation predicted
a velocity 16% lower and Brock equa-
tion 40% higher than measured. Diffu-
siophoretic and thermophoretic forces
are additive. Experiments of particle
deposition efficiency were run in a
Liebig condenser. The results show that
collection efficiency could be plotted
vs. the rate of steam condensation g/min
Single droplet target efficiencies for
particle collection by the combined
mechanism of inertial impaction and
diffusiophoresis were calculated. These
values were used to calculate overall
collection efficiency in a spray tower.
It was found that condensation can
greatly improve particle collection.
REFERENCE
Quart. J. of
the Reg. Meteor.
Soc. 89, 43,
(1963F"
Chapt. VII in
Aerosol Science,
C.N. Davies ed
(1966)
Atmos . Env. 4_,
1, C1970)
(O
10
in
-------
0 AUTHORS YEAR HIGH POINTS OF STUDY REFERENCE
Davis R.J. 1972 They concluded that diffusio and Instrum. and
Truitt J. thermophoresis would be too expen- Control Systems
sive for use in scrubbers. Particle pp. 68-70,
growth due to condensation followed (Nov 1972)
by turbulent agglomeration is the
best way to increase scrubber
efficiency.
Matsuzaki K. 1970 The invention describes a venturi Japanese patent
scrubber where steam is added No. Sho 41-41184
tangentially upstream of the throat.
Mashita T. 1971 Describes the Solivore scrubber which Indus. Public
t^ is composed of Venturis with water Nuisance 7_, 573,
"-1 sprays upstream and downstream of (1971) ~~
the throat. Several operating condi-
tions are described.
s
CO
O
-n
T]
O
m
CD
8
m
CO
O
m
O
CO
ro
CJI
O
ro
-------
ENGINEERING DESIGN
For an engineering design of an FF/C scrubber one
needs design equations which tie the operating conditions
to scrubber performance. Each scrubber type may require
different equations. (See for example Chapter 5.3 of the
Scrubber Handbook.) Thus, equations which describe a
venturi scrubber would not be adequate for a tray column,
etc.
To predict particle penetration, which is the basic
measure of scrubber performance, one has to know the
particle deposition velocity and the deposition surface
area per unit of gas flow rate. The relevant deposition
velocities are those due to the flux forces, inertial,
gravitational and Brownian diffusional effects. Since
the flux force deposition velocities are functions of
the temperature and vapor pressure gradients, knowledge
of the magnitude of these gradients at various distances
Cor residence times) along the gas path through the
scrubber is needed.
Simultaneously, the inertial and gravitational deposi-
tion velocities are functions of the particle size and
density which in turn change due to any vapor condensation
on the particle. The critical vapor supersaturation re-
quired for nucleation depends upon the particle properties
and the operating conditions. Therefore, to predict
particle growth one must first know the vapor composition
as a function of distance (or time) or travel inside the
scrubber. Vapor composition depends on heat and mass
transfer between gas/particles and gas/liquid. Thus, the
computation of mole fraction water vapor in the gas requires
knowledge of particle size and concentration, gas/liquid
transfer area, heat and mass transfer coefficients, gas
flow rate, and the critical saturation ratio required to
nucleate condensation on the particles. All of these para-
meters change as the gas proceeds through the scrubber.
Figure 1 is a pictorial and verbal representation of
the changes which take place as the gas moves through the
liquid (foam) on a sieve plate, as an example. Comparable
diagrams could be drawn for other types of scrubbers with-
out much change in the major features which are shown.
Also shown are the computations which are needed in order
to compute the changes of magnitude for the variables shown.
22
A. P. T. Inc. POST OFFICE BOX 71. RIVERSIDE. CA 92502
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Plots of Variables
Description
Computations Needed*
.Direction of Gas
Flow
Gas temperature drops
rapidly
Liquid temperature is
fairly uniform.
Ht. Tr. G/L, G/p
Mass Tr. G/L,
G/p
Enthalpy Bal.
Mass Bal.
Mol fraction water
vapor in gas reaches
equilibrium rapidly.
Same as above.
Particle radius grows
rapidly while satura-
tion ratio is high.
Mass Tr. G/p -
(NeedTG, TL, Mpi
Particle concentration
drops abruptly during
bubble formation, then
fairly uniformly.
Deposition Rate
PC
Diffusiophoretic vel.
rapid when "y" high.
Thermophoretic vel.
drops quickly.
Brownian diffusion is
low for r > 0.05 \im.
Inertial (centrifugal)
dep. increases with
"r ".
P
Temp, gradient
Composition grad.
Slip correction
Tnertial parameter
Centrif. force.
*Mass Tr. G/L = Mass transfer, gas to liquid, G/p = gas to
particles, other symbols are as defined in "Nomenclature",
Figure 1 - Schematic representation for FF/C
scrubbing on a sieve plate.
A. P. T. Inc.
23
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Because of the rapid changes in conditions and the compe-
tition between the particles and the liquid surface for
the condensing water vapor, any realistic design method
must consider the point-to-point conditions.
Availability Of Design Information
In order to carry out the design computations dis-
cussed above, several items of information are required.
On the following page we discuss the various design com-
putations and the state of knowledge regarding them, as
of the time this research was started.
1. The particle growth equation
All the equations which are presented in the litera-
ture are based on a wide and varied set of assumptions
which have to be checked experimentally in order to deter-
mine their applicability to the specific case at hand.
First one must know what saturation ratio is required to
cause nucleation of condensation on a particle of some
specific substance (\vhich probably has not been studied
in this respect). Additional complications occur for
particles 0.5 to 2 ym in diameter, which are in the slip
flow regime under normal pressure and temperature, and
for high vapor concentrations, such as are probable in an
FF/C scrubber. Further, there are probably regions of
higher saturation ratio than exists in the bulk of the
gas phase, and condensation could be initiated there. It
was, therefore, imperative to check the validity and
applicability of the particle growth equation chosen.
2. The overall energy balance for the liquid interface.
This equation used to determine the interface tempera-
ture requires the knowledge of the gas/liquid heat and mass
transfer coefficients, the liquid phase heat transfer co-
efficient, the nature of the interfacial area, and the flow
patterns of the two major phases. The coefficients can be
estimated from the two-film theory, the penetration theory,
or empirical correlations. Experimental coefficients can
be found in the literature but they play a major role in
the prediction of FF/C scrubber performance (particle pene-
trationj and even small errors in the coefficients can cause
a large error in the predicted performance.
24
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In the case of nonconventional designs, experimental
coefficients were unavailable. The geometry of the inter-
face must be idealized if predictive computations are to
be made. We are aware, for instance, from the voluminous
research on mass transfer in plate type equipment for
distillation and gas absorption that simple models depict-
ing the gas phase as spherical bubbles are not quite right
but may yield some useful answers. Local gas velocity and
the overall gas flow pattern will influence both the local
transfer coefficients and the bulk conditions for the
phases in contact in any region. Liquid phase hydrodynamics
has similar effects and is likewise unpredictable.
3. Rate of vapor condensation.
Vapor may condense on the particles and on the collect-
or liquid surface. These two phenomena are governed by the
same equations and coefficients discussed earlier and the
uncertainties which applied there apply also to this case.
Because of the competition and the effect on the driving
force for mass transfer, the two rates must be evaluated
simultaneously.
4. Rate of change of the gas temperature.
The gas temperature changes due to the latent heat of
condensation on the liquid and on the particles, the heat
transferred either to or from the liquid, and heat losses.
All three effects are governed by the equations relating
to particle growth, energy balance for the liquid interface
and heat losses. The uncertainties and limitations of these
equations have been discussed earlier.
5. Rate of particle removal.
Many uncertainties are piled one on top of the other
in the equations used to calculate the particle concentra-
tion. We started by assuming that the particle fluxes due
to the flux and centrifugal forces are additive. In addition
we assumed that when particle collection is due to two con-
secutive mechanisms, the overall penetration is the product
of the individual penetrations. Both these assumptions are
accepted assumptions and are sound theoretically, however,
they had not been proven experimentally.
The accuracy of the deposition velocity equations was
questionable in that there was little experimental evidence
in the range of particle sizes considered in this work. On
25
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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top of this, there was the uncertainty as to the gas
heat and mass transfer coefficients which in turn
determine the gradients necessary for the calculation
of the flux deposition velocities. Interwoven with
this was the effect of unknown interfacial area for
transfer and deposition. With regard to the centrifugal
deposition there were questions concerning the gas flow
radius of curvature and local velocity, especially when
condensing vapor is added.
For plate type scrubbers, an additional removal
mechanism is particle collection during bubble formation,
which becomes especially important after particle growth
takes place. Penetration during bubble formation is a
function of foam density as well as particle properties,
plate geometry, and gas velocity under normal operating
conditions. However, foam characteristics can be different
when condensing vapor is present and there were no experi-
mental data on collection during bubble formation when
vapor is condensing.
One faces the same kind of questions with other
collection geometries, such as drops, packed bed and
jets. No equations were available which would permit
the calculation of drop target efficiency in the presence
of flux forces and the same also applied to jets.
26
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THEORETICAL BACKGROUND
General background on flux force deposition and
particle growth by condensation of water vapor will be
discussed in this section of the report before proceeding
to the use of this knowledge in the development of FF/C
scrubber models. As a starting point it is important to
note that fine particles are in about the same size range
as the mean free path of the gas molecules. Consequently,
the interactions between the particles and the gas are not
the same as they would be for plane surfaces and the gas.
A measure of the departure of the transport processes
in the gas-particle system from the laws of continuum mech-
anics is provided by the Knudsen number, N .
N = — (21
NKn rp W
where "X" is the mean free path of the gas molecules (about
0.07 urn for air at one atmosphere pressure and 40°C) and
"r " is the particle radius. Only in the limit, when
^Kn "* ^ can t'ie £as surrounding a particle be regarded as
a Bontinuum. The other extreme, when N,, •* °°, is usually
referred to as the free molecule regime. The "slip flow"
regime, which applies roughly when 0.25 < N., < 10.0, is
of importance in this program because for particles of
0.1 urn to 2.0 jjm diameter, the Knudsen number runs from
about 1.0 to 15. Maxwell (1890) suggested a procedure for
treating the case of slip flow in which the transport
processes in the bulk of the gas are described by the con-
tinuum equations, but in a very thin boundary layer of gas
next to a surface the non-continuum effects are accounted
for. Thus, the boundary conditions for slip flow allow for
slip of the gas relative to the surface and analagous
"jumps" in gas temperature and concentration between the
surface and the gas.
DEPOSITION VELOCITIES
Several equations have been derived which relate the
flux force deposition velocity of the aerosol particle in
the slip flow regime with the appropriate gradient. For
27
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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the influence of a temperature gradient on particle
motion Epstein (1929) derived:
2k,
u
pT
VT
C3)
r
G
where "ur"j "Pr", and "kr" are respectively the gas viscos
ity, density and thermal conductivity, "T" is the tempera-
ture, "7T" is the temperature gradient and "k " is the
particle thermal conductivity. "
Brock (1962) has corrected Epstein's equation by
accounting not only for the thermal slip but also the
temperature jump and the friction slip. His equation
for the thermophoretic velocity is:
u
PT
3uG C'
kL ^* ^ 1.
/"• +• *T~" ".»»
u Li p
2>G T j1 + 3Cm ^)
2kG + kp * Ct T; kp)
7T (4)
where "C"1 is the Cunningham slip correction factor and
"C " and "C " are the temperature jump coefficient and the
isothermal §lip coefficient respectively. The experimental
values for "C." and "C " are C^ = 2.3 and C =1.25.
t m t m
Bakanov and Derjaguin (1962) claimed that the method of
Epstein and Broek is invalid. They calculated that Maxwell's
expression for thermal creep is too large by a factor of 35
and hence thermal creep is too small to account for thermo-
phoresis. Instead they considered a term in the equation
for the heat flux in the bulk oE the gas which follows from
the third order Chapman-Enskog theory. Applying Onsager's
principle of symmetry of kinetic coefficients, they calcula-
ted an expression for the thermophoretic velocity. Derjaguin
and Yalamov in (1965) improved this by accounting for veloc-
ity slip and temperature jump and got
u
pT
VT
2kr + k + 2C. — k
G p t rp p
(5)
28
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Diffusiophoresis
Diffusiophoresis in the slip flow regime was anal-
yzed by Schmitt and Waldmann (I960) as a hydrodynamic
problem, accounting for a finite gas velocity at the
particle surface due to diffusion slip. For the case
of vapor diffusing through a resting gas they got for
the diffusiophoretic velocity:
u
PD
yr
12 (1
(6)
where "yr" an^ "X " are the mole fractions of the non-
condensible gas and the water vapor, respectively, and
"D" is the diffusivity of water vapor in the gas.
"a " is a numerical constant called the diffusion
i 2
slip factor. Kramer and Kistemaker (1943) calculated it
as :
M - M^
1 2
M +
(7)
Combining equations 6 and 7 yields:
u
PD
y
7
V
D
v
(8)
Derjaguin et al. (1966) derived an equation for diffu-
siophoresis of large particles (r > A) . Their derivation
is similar to the one they used for thermophoresis. They
give for the diffusiophoretic velocity near a condensing
or evaporating drop:
where "p^" is the density of the inert gas and
density of the mixture.
"p " is the
29
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Experimental Results
Experiments by Schmitt (1959) with oil drops and
by Schadt and Cadle (1961) with NaCl particles and
with tricresyl phosphate drops (high conductivity)
0.05 < N.. < 1 agree within =20% with the predictions
of Brock's theory. Derjaguin, et al. (1966) on the
other hand, pointed to convective currents as an un-
controlled source of error in the Millikan condenser
apparatus. They devised new experiments and obtained
data for 0.15 < N., < 0.5 which confirm their theory.
K.n
Measurements of thermophoresis by Goldsmith and
May (1966) with Nichrome aerosol (N., = 1) appear to be
bracketed by the opposing theories. Fulford et al. (1971)
analyzed their experimental results together with those
obtained by Derjaguin et al. (1966), Keng and Orr (1966),
Brock (1967), Schmitt (1959),Schadt and Cadle (1961) and
Calvert and Byers (1967). Their conclusion is that for
particles in the size range of 1. ym "> r ^ 0.1 ym the
Derjaguin equation agrees quite well with the experimental
results. For larger particles they suggest an empirical
correlation based on their experimental data.
Schmitt and Waldmann (1960) pointed out that equations
(6) and (7) are accurate within ^9$ for the prediction of
diffusiophoretic deposition velocity. Goldsmith and May
experimental results with Nichrome aerosol (N., = 1) com-
pares quite well with the theoretical results "predicted
by equations (6) and (7). Derjaguin et al. (1966) however,
showed that Prokhorov and Leonov (1966) data are in better
agreement with equation (9).
Condensation and Particle Growth
The water vapor contained in a saturated or supersatu-
rated aerosol stream may condense on the particles, on the
cold walls of the conduit, or on water surfaces, when
passing through a scrubber. In our case the aerosol parti-
cles are =1 ym diameter, may be soluble, insoluble, wettable
or nonwettable in water, and flow at the same velocity as
the gas surrounding them. Under these conditions the follow-
ing assumptions apply:
1. The vapor pressure increase due to particle
curvature can be neglected for particles of
interest.
30
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2. The increase in heat and mass transfer
caused by the relative velocity between
the gas and the particles can be
neglected.
3. There is no vapor pressure depression due
to the colligative properties for insoluble
particles .
4. Homogeneous nucleation is neglected because
of the aerosol particles present.
Having limited our area of interest, we will look at
the phenomena of nucleation and growth of water drops in
a saturated and supersaturated atmosphere.
Nucleation - The conditions necessary for nucleation to
occur on a surface may be predicted from equilibrium
thermodynamic considerations for a system in stable
equilibrium at a constant temperature when the Helmholz
free energy is minimized. This fact is used to find the
critical saturation ratio, S , for a surface exposed to the
vapor. (See for example Abraham (1968), Fletcher (1966)
and others.)
The saturation ratio is defined as the ratio of the
vapor pressure at the point in question "p " to that of a
plane water surface "p.". °
S = (10)..
It follows from the Kelvin equation that for a given
drop diameter, water droplets grow by condensation if the
saturation ratio is larger than a critical one. For drops
2 vim in diameter the critical saturation ratio is 1.001 and
for drops 0.2 urn in diameter it is 1.01. The rate at which
drops in this size range form spontaneously from the vapor
increases very steeply with supersaturation. For water at
20°C as an example, the rate of nucleation will increase
from 1.2xlO-Vcm3 -sec for S = 3.2 to 1.2xlO'2/cm3 -sec for
S = 3.6 (Amelin, 1967). This is important since around the
critical saturation ratio the rate of nucleation can be
increased substantially by a small increase in the satura-
tion ratio.
31
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The critical saturation ratio is also a function of
temperature. Figure 2 taken from Amelin (1967) shows the
change in the critical saturation ratio for water vapor as
a function of temperature. The critical saturation ratio
for homogeneous water vapor nucleation is always above 2.0,
within our temperature range of interest.
Nucleation by Insoluble Particles - Drops of the critical
radius will form on the surface of insoluble particles at
a higher rate than for self nucleation. Volmer (1939)
developed a modification of the original Volmer-Weber
nucleation theory to include the case of condensation on
a plane surface. He showed that the critical saturation
ratio for insoluble surfaces is a function of the contact
angle between the condensed vapor and the surface.
Figure 3 shows the effect of contact angle on critical
saturation ratio for water at 20°C. The contact angle is
that which is measured between the solid surface and the
liquid surface at the line of contact, and which includes
the liquid phase.
This analysis was extended to condensation on in-
soluble particles by Fletcher (1958), and the results of
his theoretical calculations are plotted in Figure 4 as
the critical saturation ratio vs. drop radius with cos a,
the cosine of the contact angle, as a parameter for water
vapor at 20°C. This plot shows that for fine particles a
saturation ratio of a little over 1.0 will suffice for
highly wettable particles (a =0°, cos a = 1.0). In the
case of non-wettable particles (a approaching 180°) the
critical saturation ratio required for nucleation to occur
is equal to that required for homogeneous condensation.
Thus, most particles will cause nucleation to occur at
lower saturation ratios than for homogeneous nucleation.
Nucleation By Soluble Particles - Nucleation occurs more
readily on soluble particles than insoluble particles.
Raoult's law states that the equilibrium vapor pressure
over a solution is less than that over pure water by a
factor equal to the mole fraction of water in the solution.
Using the Van't Hoff factor, i, to take into account the
dissociation of inorganic salts, Howell (1969) derived an
expression for the equilibrium saturation ratio over a
solution droplet containing "m" moles of a solute. Fig-
ure 5 is a plot of (p-Xp^ - 1) x 102 vs. droplet radius
with "im" as a parameter, "p." is the vapor pressure above
a droplet of solution containing "m" moles of solute, and
"p^" is the vapor pressure above a plane surface of pure
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i
2
O
n
1
I
1-1
u
I—I
H
I-H
U
10 20 30 40 50
TEMPERATURE, °C
60
70
Figure 2 - Critical saturation ratio for homogeneous
nucleation of water (After Amelin (1967) )
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o
I—I
E-
CO
20 40 60 80 100 120 140 160 180
CONTACT ANGLE, DEGREES
Figure 3 - Critical saturation ratio for water upon a
plane substrate of given contact angle -
water at 20°C (After Fletcher 1966).
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10
10"7 I0~6 ID'S lO'*4 10"3
PARTICLE RADIUS, cm
CM
O
Figure 4 - Critical saturation ratio for nucleation
of water droplets upon a particle of
given radius with cos a at 20°C as
parameter. (After Fletcher 1966).
8
ex
H
2
OQ
—i
hJ
-0
-0
0.01
DROPLET RADIUS, (pm)
Figure 5 Equilibrium supersaturation as a function
of droplet radius with (im) as a parameter.
(After Howell 1949) .
35
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water. If, for a given value of "im", the ambient satura-
tion is raised to a value below the peak of the equilibrium
saturation curve on Figure 5, an equilibrium drop size will
be formed. If, however, the ambient saturation reaches the
peak of the curve or higher, spontaneous nucleation, con-
densation and growth will occur.
The curves presented in Figure 5 apply only when the
vapor concentration is higher than the concentration which
is in equilibrium with saturated solution at this tempera-
ture. For example, a saturated solution of NaCI will
reduce the equilibrium vapor pressure of the water by =221;
thus no condensation on the NaCI particles is expected
unless the relative humidity is higher than 78%, which was
found to be the case experimentally (Junge, 1952). In the
case of NaCI, Figure 5 will apply only when the relative
humidity is higher than 78%.
Mixed Nuclei - In any real situation it is unlikely that
the natural condensation nuclei will be described completely
by one of the types we have considered. It is more likely
that a mixture of soluble, insoluble, wettahle and non-
wettable particles will be present. In such a mixture we
should consider two cases:
1. How the mixture would behave as condensation
nuclei.
2. How a particle formed by agglomeration of two
different type particles would behave as a
condensation nucleus.
The first case is fairly simple because those particles
which require lower saturation ratios to nucleate will
nucleate first and grow, thus reducing the degree of super-
saturation in the aerosol. In order to find the exact
proportion of nucleation on the various particles at a
given supersaturation, one should examine the rate of
nucleation and the rate of decrease of supersaturation. In
reality the situation may be complicated by the inhomogen-
eity of the saturation ratio within the aerosol stream, as
is discussed later. However, when the saturation ratio is
below the critical value for each of the different cases,
no nucleation and growth will take place.
The second case, that of a mixed particle, is more
difficult to analyze. Even when all the components of a
36
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coagulated nucleus are similar particles, it may possess
properties differing from those of a simple particle of
the same size. This is due to the fact that its surface
will contain cracks and cavities between the particles,
and these are favoured condensation sites.
If the nucleus consists of a mixture of soluble and
insoluble particles, the nucleation behavior is dominated
by the soluble component. Above the phase transition of
these components the particle is enveloped in a film of
solution, and behaves as a solution droplet in the way we
have already considered. The presence of the insoluble
components enhances the effectiveness of the soluble salts
since less water is required to make a droplet of a given
size and the resulting solution is more concentrated. The
behavior of such mixed nuclei has been examined in some
detail by Junge (1952).
Particle Growth - After a drop of critical size has been
nucleated,it grows at a rate determined by the ambient
environment and conditions at its surface. However, as
vapor condenses on the drop, the drop temperature rises
and hence the conditions at its surface change. Several
equations can be found in the literature describing the
rate of growth, Fletcher (1966), Nuzhnyi et al. (1965)
and Fuchs (1959). In general they all make the same
assumptions and use the same three basis relations:
rate of mass transfer, rate of heat transfer and phase
equilibrium. Fletcher's equation, which accomodates soluble
and insoluble nuclei and is integrated to a comparatively
simple form was used in our early modeling. In our later
and more refined models for particle growth and collection,
however, we use the basic heat and mass transfer equations
in order to avoid some of Fletcher's approximations.
Rate of growth during a condition of constant satura-
tion ratio is given by Fletcher as:
dr
r = G
p at F
a + b
r PI ^"Re'"Sc
£CNDo,NqJ (11)
"r " is the particle radius (cm) at time "t", "S" is the
saturation ratio defined in equation 10, a/r describes the
effect of surface curvature in increasing the vapor pressure
of small drops and "b/r3" describes the effect of solute
37
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content on vapor pressure, "a" and "b" can be approximated
by
3.3xlQ-5 /cm
a T
I
b = 4.3 i m
cm - gmol
drop
(12)
(13)
Where "im" is the number of moles of solute in a drop and
"G_" is defined as:
r
D
GF '
(14)
"Dr" is the vapor diffusivity in air, "p " and "pj" are
respectively the density of the vapor and the liquid, "L^"
is the latent heat of evaporation, "M " the molecular
weight of the vapor, "R" the gas constant = 1.987
(cal/gmole - °K) and "k '' is the gas thermal conductivity.
f(NR »Ngc) and f(NRe»Npr) represent the increase in the
heat and mass transfer coefficients due to the relative
velocity between the gas and the growing nuclei, which is
negligible for fine particles. The correction due to the
surface curvature of the particle, "a/r ", can also be
neglected and "b/r " applies only in the case of soluble
particles. Thus Fletcher's equation reduces to:
dr
p dt
GF I5'1 * 7T
P
where:
DG Pv
PL
Dr LM
IA G M
R T2
p M
Hv v
kG
- 1
(15)
(16)
Particles 1 ym in diameter are in the slip flow regime,
and from Hidy and Brock (1970) we obtain:
DG pv
1 +
LM
M
v
R
-1
(17)
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For high vapor concentrations a second correction is
required due to the Stefan flow. From Fuchs (1959) this
correction is approximated by
Dp jl -
> Pi
+ PG
2P
pv
(1+1.2 N,
1+
1 Pi + Pf
D 1 •••
UG r 2?
LM pv Mv
R T2 k J
-1
(18)
where "p.^" is the vapor pressure at the drop surface, "p "
is the partial pressure in the gas stream and "k " is the
thermal conductivity of the gas corrected for thi Stefan
flow.
Saturation Ratio in Boundary Layer - When considering the
conditions under which particles will nucleate condensation,
it is important to note that the saturation ratio can be
higher in the boundary layer than it is in the bulk of the
gas. This can cause the onset of particle growth sooner
than would be expected based on bulk conditions. Once the
particle surface has been wetted it can serve as a site for
further condensation so long as the saturation ratio ex-
ceeds 1.0. The particles grown by condensation will be
more susceptible to collection by mechanisms dependent on
their mass.
As an example, let us take the case of particle collec-
tion from the interiors of bubbles, and for simplicity we
will treat the boundary layer in terms of penetration
theory. We will discuss the behavior of an element of gas
which is undergoing simultaneous heat and mass transfer as
it moves around the bubble due to gas circulation inside
the bubble. Both composition and temperature distributions
in the gas contacting the water surface are assumed to be
the same as unsteady-state diffusion into (or out of) a
semi-infinite plane sheet. Crank's (Crank, 1956) solution
for this case is shown in Figure 6, a plot of dimensionless
concentration or dimensionless temperature versus dimen-
sionless distance. The dimensionless concentration is the
difference in water partial pressure between any point and
the gas-liquid interface divided by the difference in
partial pressure between the bulk gas and the interface.
Dimensionless temperature is defined in an analogous way
Dimensionless concentration =
P -
PG
(19)
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l.Or
H
i
H
f-
i
(J
f- 0.5
j-
o
a
ex
e?
a
0.4 0.8
X =
(4 Dt)1/2
1.0 1.4 1.8 2.0
x
Figure 6 - Dimensionless concentration or temperature
versus dimensionless distance
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and
T - T.
Dimensionless temperature E = «— (20)
!G i
Dimensionless distance = TT-T- = ^ ^ ^
(4 Dt)1/*
Where:
p = partial pressure of transferring component at a
position "x", atm.
T = temperature of gas at position "x", °K or °C
x = distance from interface, cm
D = diffusivity of mass or heat, cmz/sec
t = penetration time, sec
To get some idea of the magnitudes involved, consider
the common case of a 0.4 cm diameter bubble rising at
20 cm/sec and let us use representative values of the
properties involved. The penetration time for a circula-
ting bubble is estimated from the time it takes for a
1 dia. rise; or 0.02 sec. The diffusivity of water vapor
in air is about 0.25 cm2/sec, so the value of "x" at a
dimensionless distance, X, of 1.0 would be 0.14 cm. The
diffusivity of heat, (k/pC ), is approximately 0.2 cmz/sec
and the value of "x" for "t" = 0.02 sec and a dimensionless
distance of 1.0 would be 0.136 cm.
From the above example, it can be seen that the dimen-
sionless composition and temperature distributions can be
considered identical on the same real distance scale. To
illustrate, we see that at X = 1.0 the real distance to the
interface is about the same (i.e., 0.14 cm) for heat and
mass transfer and that the values of dimensionless tempera-
ture and composition are the same. One can also note that
most of the volume of a circulating bubble 0.2 cm radius
would become involved in the boundary layer, which grows to
about 0.14 cm at the bottom of a rising bubble.
Some examples of gas and liquid conditions were chosen
for illustrative purposes and the saturation ratios which
would occur because of the heat and mass transfer were com-
puted for various positions in the boundary layer as given
41
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by Figure 6. The results are shown in Figure 7, a plot
of saturation ratio vs. dimensionless distance from the
gas/liquid interface. It can be seen that the curves
for a water interface temperature of 20°C and bulk gas
phase conditions of 45°C, S = 1.0 and 60°C, S = 1.0 have
maxima where the saturation ratio goes considerably above
1.0 at a position within the boundary layer.
For the case of a 20°C liquid interface temperature,
gas phase temperature of 30°C, and S = 1.4, there is no
maximum in the curve. It can be seen from these examples
that it is possible for the saturation ratio in the
boundary layer to be higher than that in the bulk of the
gas phase, depending on the temperatures of the gas and
liquid. Consequently, a substance which requires a
critical saturation ratio of 1.5 in order for water to
condense on it could nucleate growth under the 60°C gas
temperature condition, even though the saturation ratio
for the bulk gas phase is only 1.0. Once condensation
starts on a particle it can continue to grow so long as
the saturation ratio is 1.0 or larger.
42
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Curve No .
1
2
3
4
T °C
IG, L
60
45
30
45
T °f
L'
20
20
20
20
S
1.0
1.0
1.4
1.1
0.5
1.0
1.5
2.0
X =
(4 Dt)1/2
Figure 7 - Saturation ratio versus dimensionless distance
43
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MATHEMATICAL MODEL, SPRAYS
Mathematical models were developed for three principal
types of scrubbers; spray, plate, and liquid sheets. The
models were to be used first for the exploration of possible
operating conditions and design variations in order to assess
the capability of each scrubber type when operated in the
FF/C mode and to locate an approximately optimum operating
range. Next, the models would be used for the correlation
of experimental data and then the evaluation and possible
modification of the model in the light of the data.
The models which were developed early in this research
were for plates, as represented by the unit mechanism of
collection from bubbles. They did not allow for particle
growth, simultaneous transfer to particles from liquid,
and other factors. In the course of the program the plate
models were refined; especially since our experimental work
was on plates. As it happened, the mathematical model for
sprays was developed fairly early in the program and was
not revised at the time of writing. Because it is the
oldest model, that for sprays will be presented first, so
that the progressive development of more realistic and com-
plex models during the research will be reported in order
of our increasing understanding of FF/C system modeling.
Spray type scrubbers are represented in fundamental
terms by the unit mechanism of particle collection by drops
or spheres. Collection of particles by spheres due to
inertia alone is discussed in the literature and target
efficiencies have been calculated by many: Langmuir and
Blodget (1946), Ranz and Wong (1952), Herne (1960) and
others. When additional forces are involved, the equations
of motion are different and new solutions are required.
We adopted Sparks and Pilat (1970) approach and solved the
equations of motion of the particle in the "X" and "Y"
direction after including the additional flux force.
A force balance on the particle in the "x" direction
gives for the case where Stokes law applies:
du 1 F
— = - (vx * V + HT (22)
dt T x x p
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and
Fx = 6" "G rp UF (23)
2r° pD
T = particle relaxation time = Q p—*- (sec)
VG
v = gas velocity in "x" direction, cm/sec
X
u = particle velocity in "x" direction, cm/sec
J\
m = particle mass, g
F = flux force acting on particle in "x" direction, dynes
j\
UF = particle velocity due to flux force, cm/sec
The equations of motion can be put in dimensionless
form by the use of the following new dimensionless para-
meters and variables:
x Y - vy vv - * vn
X = —• Y = —• v = — • v = —• t = -
A - r ' r ' VX - v ' VY - v ' C - ^FT
d a o o d
2 p r" VQ
K = g ^—p = inertial impaction parameter (24)
G d
and
GF E K v~ (25)
P o
Where:
X = distance from center of drop in "x" direction, cm
Y = distance from center of drop in "y" direction, cm
VQ= velocity of undisturbed gas stream relative to sphere,
cm/sec
Substituting values of "v " for potential flow, from Fuchs
(1964), we obtain the differential equations in their final
form:
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dX 2 X2 - Y2 GF * = 1_ (2g)
_
dt2 K dt 2 K (X2 + Y2)25 (X2 + Y2) * K
c cr *
_ - , . .
dt2 K dt 2 K (X2 + Y2)25 (X2 + Y2)1/2
P P
= 0 (27)
Equations (26) and (27) can be solved if boundary conditions
are specified and if an expression for "G " is available.
FLUX DEPOSITION
Equations (26) and (27) show that the two parameters, K
and G_, are required to define particle motion under the in-p
fluence of inertial and flux forces. It will be shown later
that the product of these parameters is a new parameter which
defines the effect of adding flux forces to a system involving
only inertial force. Equation (25) can be rearranged to yield
the product:
v r UF _ Particle transport by flux forces „
D P ~ v --- - - = PD
v o Particle transport by fluid flow
(25)
The dimensionless parameter "v /UF" is related to the
Peclet number since it is an indication of the relationship
between convective and flux force transfer of particles
diffusing to a boundary surface. The Peclet number, usually
given N = v d/D, is the characteristic ratio for convec-
tive diffusion. It represents the ratio of the rate of
transport by fluid motion to the rate of transport by molec-
ular processes. We will refer to the ratio "UF/V " as the
Flux Deposition number, N™.
Significance of Flux Deposition Number
To show the relationship of N to Np , we can start
with consideration of a diffusional procesl where the flux
is given by:
NA = ~D = UDM CA (9mol/cm2-sec) (28)
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where:
U-™, = deposition velocity for mass transfer, cm/sec
DM
c. = concentration of transferring component ("A"),
gmol/cm3
If the concentration gradient is linear, there is no
equilibrium pressure above the interface (i.e., no "back-
pressure") and the boundary layer thickness, "6", is pro-
portional to drop diameter, "d":
dc co c (29)
dx 6 d
Therefore:
v
3 « UDM, and, Npe a ^°-
or:
Npe = -°-, if 6 = d (30)
The form of the modificed Peclet number in equation (30)
will apply to any deposition process for which the flux can
be described by equation (28). Thus we should expect to
find comparable mathematical models and empirical correlations
for deposition with diffusion and that with flux forces.
It is instructive to look for an estimate of the quan-
titative significance of Np^. Deposition rate on a sphere by
any flux or diffusional mechanism will follow the same form
as the following equation
(4irrd2)NF = uFn (4Tird2), no./sec (31)
The rate at which particles approach the sphere is given by:
vQn (nrd2) = convection rate to sphere (32)
The fraction of the particles convected to the sphere which
deposit on the sphere (i.e., the collection efficiency) is:
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4TT r,2 up n 4 u
0 = __a_Z_P. —* = 4 NpD (33,
irr* v c v
o o
Thus, for a single drop if NFD is greater than 0.1,
collection efficiency is good. If Np[) number is less than
0.01, collection efficiency will be only a few percent or
less. In situations where there is collection on a series
of drops, the efficiency of each drop need not be so high
in order to obtain a suitable overall efficiency for the
sequence of drop contacts. For example, the particle
penetration of a counter-current spray tower with a water/
gas ratio of 1.0J,/m3, drops 0.04 cm diameter, a height of
3 meters, and a gas velocity of 120 cm/sec and spray losses
on the walls equal to 80% of the inlet water is approximately:
Pt = exp(-lO.On) (34)
If a penetration of 0.1 (i.e. 90% collection efficiency)
is desired, the collection efficiency for a single drop
would have to be 0.23 (23%). If the single sphere efficiency
were 0.023, the overall penetration would be about 0.8.
Thus the approximate NFD range of 0.1 to 0.01 to distinguish
good from poor performance for a single sphere is also about
the right magnitude for a spray scrubber.
SOLUTION OF THE EQUATIONS OF MOTION
Let us now take up the solution of equations (26) and
(27) for particle collection under the influence of flux
forces. The velocity and trajectory of the particle is
determined by the resultant force and the air flow field
around the particle. In order to formulate this situation
mathematically, the following assumptions are made:
1. All the assumptions made by Langmuir and Blodgett
(1946) for collection due to inertia alone apply also in
this case.
2. The time scale for the interaction between a single
particle and a single drop is small compared to the time
scale of changes in the drop and gas temperature and humidity.
Thus the temperature difference between the gas and the drop
is assumed constant. This assumption was checked numeri-
cally and found correct within 1%.
3. All the resistance to heat transfer is assumed to
be in the thermal boundary layer. The boundary layer thick-
ness is estimated from the heat transfer coefficient ob-
tained from the Whitaker (1972) equation:
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NNU = 2 + °'4 V "Pr°"
A heat balance around the drop gives:
kr
Q = h AT = - AT (96)
h' dd dd
Substituting for "h" in N = - -
Other equations for the boundary layer thickness yield
other values for "6". These values range from -0.5 r^
to -2 r^.
4. The thermal boundary layer was assumed to be of
a constant thickness in the front half of the sphere. The
thickness varies with the Reynolds number of the sphere
as can be seen from the previous assumption. This is an
approximation, since the velocity boundary layer thickness
approximately doubles from the stagnation point to an angle
of 90°, Schlichting (1960).
5. The temperature gradient in the thermal boundary
layer is assumed constant. This was calculated to be ap-
proximately the case for a flat plate and N * 0.6,
Schlichting (1960).
6. The thermophoretic force acts on the particle only
inside the thermal boundary layer.
7. Collection in the back of the drop was neglected.
This assumption is correct for low drop Reynolds numbers.
8. G_ is constant inside the boundary layer.
r
Integration
Equations (26) and (27) were integrated for boundary
conditions which are consistent with the assumptions given
above. The boundary conditions are:
X = -»
•V «„
Y = Y
o
dX _ ,
= 0
dt
at t = 0 (37)
49
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA 92502
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G = 0 for (X2 + Y2)>(1 + 6)
r
G-, = G-, for (X2 + Y2)*(l 4- 6)2
t r
These equations were solved numerically on a digital
computer using a Runge-Kutta method. The solution was
started at x = -5.0. Figure 8 is a plot of target ef-
ficiency vs. "K " with Np^ as a parameter for NRgd =9.6.
To illustrate the significance of Figure 8, weQmight
consider a case with initial gas temperature of 100 C
and initial liquid temperature of 20 C, for which we com-
pute upT =0.03 cm/sec. It follows from Figure 8 that
under these conditions the effect of thermophoresis is
very small. If the drop diameter were, say 200 urn, its
settling velocity would be about 74 cm/sec, and NFD would
be about 2.5x10 , which is indicative of very poor
collection efficiency due to flux force.
DIFFUSIOPHORESIS AND INERTIA
The solutions of equations (26) and (27) and the re-
sulting Figure 8 are valid for the case of diffusiophoresis
and inertia and the sum of thermophoresis and inertia.
Figure 8 is also a representation of collection efficiency
when any number of forces are acting simultaneously;
given that deposition velocity, upl is defined as:
Up=u_+u+ any other deposition velocity (38)
and:
u^
(39)
Three dimensionless numbers, K , N , and NRe deter-
mine the collection efficiency of particles by drops when
the particles are subjected to the simultaneous action of
inertia and flux forces. We have reduced the role of the
Reynolds number by assuming potential flow around the drop.
From Figures 8 and 9, which is a cross plot of Figure
8, several conclusions can be drawn:
1. Collection efficiency increases with the increase
in "K " and "N " .
p FD
50
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I?
03
g
5
S
o
m
to
ro
en
s
>~
2
i—i
U
i—i
U-
O
M
H
U
O
U
U4
J
O,
O
CA
Q
5x10
- 2
10'1 1
INERT IAL PARAMETER, K
P
Figure 8 - Efficiency of single drop versus inertia
parameter at NRgd =9.6 with M as parameter
10
-------
1.2
Figure 9 - Efficiency of a single drop, n, versus N™ with
K as a parameter (NR , = 9.6).
52
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2. The higher "K " is (and the larger the particles),
the smaller is the effect of the flux force on collection
efficiency.
3. At low "Kp" values collection efficiency increases
with decrease in "Kp". This may be attributed to the lower
stream velocities and the longer time in which the particle
is subjected to the flux forces.
4. Collection efficiency can increase above 100%
for high values of "UD/U". This stems from the fact that
particles can be moved to the drop from positions outside
the projected frontal area in the gas stream.
We can make some general observations about the probable
importance of flux force deposition mechanisms by estimating
ranges of N D and then interpreting these values in the light
of Figures 8 and 9. For example:
1. For poorly conducting particles in the fine size
range and a temperature range of 0°C < AT < 80°C, flux
deposition number is 0.04 > N D > 0.0007. This means that
in this range thermophoresis is not important.
2. Diffusiophoresis can be very important for fine
particles because with a water vapor partial pressure range
of 0.13 < pv < 0.65 atmospheres, the flux deposition number
range is 2.5 > !!„„, > 0.01.
r D
Collection efficiency as shown in Figures 8 and 9 is
for NRe =9.6 which is the NRe of a free-falling 200 ym dia-
meter water drop. The boundary thickness, as already men-
tioned, is a function of the Reynolds number and for the
case presented in Figure 8 and 9 it was taken as 0.56(r^).
Since these calculations are for potential flow, a change
in the Reynolds number will change only the thickness of
the boundary layer. To see the effect of changing the
boundary layer thickness on the collection efficiency, Table
II shows the change in
n vs. 6 = —, at K = 1.1 and G,, = 0.1.
rxi P F
53
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TABLE II
Collection Efficiency of Particles by
Drops for K = 1.1 and Gp = 0.1 at
Various Boundary Layer Thickness
6
n
0
0.5
0.56
0.58
1
0.62
2.2
0.69
We see that the thickness of the boundary layer has a
small but noticeable effect on collection efficiency.
PARTICLE GROWTH
When humid hot air is passed through a spray column,
cooling and dehumidification take place. Transfer of heat
and vapor from the gas to the drops occurs and particles
are collected by the drops due to the combined effect of
inertia, diffusiophoresis, and thermophoresis. At the
same time, if the saturation ratio is high enough, particle
growth starts. As shown in the previous section, diffusio-
phoresis is significant for the temperature range of
interest, but thermophoresis can be neglected.
A mathematical model for particle collection by dif-
fusiophoresis and inertial impaction in a spray column
was developed and solved as follows:
1. Computations were made for small increments of the
spray column; ranging from 0.1 to 2.0 cm high. After the
increment height was chosen the conditions calculated and
compared to the conditions calculated from one half of
this height. If the difference was not significant the
original increment height was used for further calculations.
2. Gas humidity and temperature, liquid temperature,
and interfacial humidity and temperature were calculated
for each section in the method presented in Brown (1950).
These conditions were assumed constant throughout the
section, "hj." an<* "^G"' tne neat transfer coefficients
inside the drop and on the gas side, were estimated from
penetration theory and equation (35).
3. Particle growth was computed by means of Fletcher's
equation, modified by the use of a factor "a", so that:
A. P. T. Inc.
54
POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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Dr P<~ \
-^
-------
= gas flow rate, m3/sec
terminal settling velocity of drop, cm/sec
linear velocity of gas, cm/sec
height of increment, cm
n- = collection efficiency of drop under increment
1 conditions, fractional
The overall penetration of the increments where cooling and
dehumidification take place was calculated from
Ut =
UG =
AZ =
n
Pt = n Pt. = exp -
C -L
4 QG rd (ut
n
(42)
Penetration for the rest of the column, where heat and mass
transfer are small and affect collection efficiency only
slightly, was calculated from
Pt = exp -
3 QT u. (Z-n AZ)
LJ t
4 QG rd (ut - UQ)
(43)
where n = nn-
The overall collection efficiency is :
E = 1 - Pt = 1 - (Ptc Ptn)
(44)
Figure 10 shows Ee = (1 - Ptg) and ET = (1 - PtT) for
a 1 meter countercurrent spray column as a function of "a"
for 0.5 urn diameter particles of density 1 g/cm3 and inlet
concentration of 106/cm3. The gas entered at 35°C and left
at 33.2°C, while the liquid entered at 20°C and left at
25.3°C. Gas inlet humidity, "Y " was 0.155 g/g, corresponding
to a saturation ratio of about 3.5 at 35°C; and the outlet
was 0.077 g/g, corresponding to a saturation ratio of about
2.1. Liquid to gas flow ratio was 58,/m3, drop size 0.05 cm
diameter, and linear gas velocity 60 cm/sec.
56
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overall collection —
efficiency
collection efficiency
in section where flux"
forces are active
0.2 0.4 0.6 0.8
FRACTION OF PARTICLE GROWTH, a
1.0
Figure 10 - Collection efficiency for 0.5 ym diameter
particles in a 1 meter spray column
57
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It can be seen that with no particle growth, a col-
lection efficiency of 33% was calculated, while for full
particle growth collection efficiency rose to 92%. It
should be borne in mind that there are several points of
uncertainty in the computation so that one should view
these results as being only approximate. For one thing,
the liquid to gas ratio is rather high so the wall losses
and agglomeration of drops would cause the active spray
holdup and its efficiency to be less than assumed. If,
as might realistically be assumed, half of the spray were
lost to the walls, the efficiency would drop from 92%
to 74%.
Reducing the degree of supersaturation in the incoming
gas by raising its temperature, reduces collection effi-
ciency markedly even if the humidity is not changed. At
the time these calculations were made it seemed reasonable
to assume that as high a saturation ratio as 3.5 could be
attained in the inlet gas. Experimental experience ob-
tained later in this program leads us to have serious
doubt that saturation ratios much higher than 1.0 can be
attained in realistically dirty effluent gas streams. For
these and other reasons relating to computational techniques,
the present spray model should be considered as a first
exploratory step.
58
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MATHEMATICAL MODEL, PLATES
Plate type scrubbers are represented to a first approxi-
mation by the unit mechamism of transfer from bubbles. Thus,
while the model which is described in the following section
is defined in the specific terms of a sieve plate, it is
suitable for expressing the particle collection behavior
of scrubbers in which bubble formation and rise through liquid
are the principle mode of gas/liquid contacting. In order to
compute the simultaneous effects of transport and particle
deposition phenomena in plate type scrubbers, a set of equa-
tions was developed as described below. The final set of
equations describes the following phenomena:
1. Heat and mass transfer between bubbles and liquid.
2. Heat and mass transfer between bubbles and
particles suspended in bubbles.
3. Particle growth due to condensation.
4. Particle deposition by:
a. Diffusiophoresis
b. Thermophoresis
c. Centrifugation during bubble rise
The following general assumptions were made:
1. Gas bubbles are spherical, constant diameter
(d, =0.4 cm, usually), and perfectly mixed internally
(except for the interfaces).
2. Gas properties are as for air and water vapor.
3. Foam density is constant throughout the foam layer
on the plate.
4. Liquid bulk temperature is constant throughout the
foam, although the liquid-bubble interface temperature can
vary.
5. Particles are mono-disperse, wettable, insoluble
spheres.
6. Condensation on particles can occur whenever the
saturation ratio is 1.0 or larger.
59
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7. All the particles are subjected to condensation
and growth.
PARTICLE GROWTH
The rate of change of particle radius is given by a
mass balance,
% _ "'PC 'PG - PPJ' /,»_,
at PM Uec'
Where :
2 DQ P / gmol \
k" G = - ( - 1 = mass transfer coefficient
p RT,, d p_M \cm2-sec-atm/ particle to gas ..,.
tj P DM [ *t O )
PG = water vapor partial pressure in bulk of gas bubble, atra
P = total pressure, atm
p_M= mean partial pressure of non- transferring gas, atm
d = particle dia, cm
TG = gas bulk temperature, °K
p = molar density of water, gmol/cm3
For air and water:
1 75
T
DG - °-256
so
2.85xlO"7(TG)°-75
' =
It can be shown that "PDi" is close to "pG" so that
PBM = d'Pg) for tne ca^e of particle growth.
60
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Particle growth over a finite period is given by the
integration of equation (45) after substitution of equation
(46).
=
RTG PM PBM
where At = time of growth, sec.
In our present computational programs, equation (48)
is not applied when p . > pQ, because this would imply
particle evaporation. P It would be possible to write a
computer program which would allow the evaporation of only
the water film on a particle, but this has not been necessary
thus far.
The vapor-liquid equilibrium relationship for water can
be approximated within a few percent by:
p „ = exp (13.64 - 5-lxl°3 ) (atm) (49)
p = water vapor partial pressure in equlibrium at T °K
Particle temperature can be computed from an energy
balance:
/p C r \ d T . ,
h G(T i - TG) + (-E—2E—£) E- = k LM (pG - p .) (50)
\ 3 / dt
Where:
h 2k a 7.5X10"5 / cal \ = particle to gas heat
P p rp \cm2-sec-°K/ transfer coefficient
C = heat capacity of particle, cal/g-°K
k = thermal conductivity of gas, cal/cm2-sec-°K/cm
and
LM - 10 "* [ - 5-J = latent heat of vaporization for water
61
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The second term on the left side of equation (50) re-
presents the effect of particle heat capacity and it is
neglected in the computation. It can be shown that the
product of particle mass and heat capacity is a very small
percentage (generally less than 1%) of the product of gas
mass and heat capacity. Thus, for a given change in tem-
perature, most of the energy goes into increasing gas
enthalpy.
An explicit solution for particle surface temperature
was provided by an alternate solution to equation (50).
This solution involves the approximation that the vapor-
liquid equilibrium relationship is linear over a small range
of temperature or vapor pressure (see equation 54). If we
define a temperature, T*, which is the saturation (equili-
brium) temperature corresponding to the partial pressure of
water in the bulk gas, pr, we can show that:
Pr. * Pr
.
pi
= C,
(52)
k pG LM
and
T— T —
• *• i-> ~
pi G
r i 1
C2
1 + —
L m J
(T* - TQ)
(53)
Where:
I"
m = slope of eq. line = (0.042) p_ + 5x10
and
/atm
\°K
(54)
T* =
5,100
13.64-ln p
(55)
'G
.-"*
Because C-^ 4x10" (atm/°K), the particle temperature, T .,
will be within a few degrees of T*, rather than being at ^>1
approximately the gas temperature, TG. For example, at
PG = 0.1, m = 4.7xlO~3and C2/m = O.OH5. Thus,
T . - Tr * 0.925 (T* - T_)
pi t> G
62
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HEAT AND MASS TRANSFER IN BUBBLES
The overall energy balance for a bubble interface is
given by
k'bG ab LM(PG - PLi)AP dz =
hbL Sb(TLi - TL)Ap dZ+hbG ab(TLi - TG)Ap dZ (56)
where :
0 P ^2
. ' G 1.13P /DG\ gmol . ,
k bG = - - - j — ] — 2 - = mass transfer
p_M RT_ pOM \ 0D / cm2-sec-atm coefficient, bubble
DM. vj BM x o ' . . . ,
to liquid
(57)
a, = surface area of bubbles/unit volume of foam, cm2 /cm3
A = area of plate, cm2
0R = surface renewal time, sec
B
TL = temperature of liquid bulk, °K
For a bubble diameter = 0.4 cm and bubble rise velocity
20 cm/sec, the time to rise 1 diameter = 0.02 sec. If "0B"
is evaluated as 0.02 sec for the penetration theory models
represented by equations (57) and (58), the coefficients for
air and water properties are as follows:
kG = l.exlO"* gmol/Cm2-sec-atm (59)
hbG ~ °-022 (TG* cal/cm2-sec-°K (60)
It should be noted that boundary layer theory would pre-
dict coefficients about half these and that the computation
of dif fusiophoresis deposition from equation (59) yields a
very high velocity. Thus, we are cautioned to view equations
63
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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(59) and (60) as rough approximations which may be used until
experimental data are available.
The heat transfer coefficient from the interface to the
bulk liquid is approximated through penetration theory as:
'bL = 2 U ^ kX) = °-31 f ~ ^ (61)
Combining equations (55), (50), (60), and (61) yields:
1.6(pr - pT.
- 0.31 (T_. - TT) - (T_. - T) = 0
Ll L ^ Ll
(1 - PG/2) TG (62)
In equation (62), p is approximated as (1 - PG/2) because
p. . is usually very low.
Condensation of water from the gas bubble will cause
both a decrease in gas flow rate and composition, as given
by:
G dp_ dM gmol H90 vapor
-d(G y) = -- Z- = — H - = - (63)
(1~PG) dt cm2 of plate area-sec
where G = molal gas flow rate per unit area of plate,
gmol/cm2-sec
y = mol fraction water vapor
The mass of water vapor transferred is given by:
gmol H?0 vapor
dNT = dM + dMb = — - * - (64)
F cm of plate area
The transfer rate to particles is,
dM 4Ti (r* - r,3)
V dZ> (^ (65)
P dt 3(18) At p
64
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where:
n = number concentration of particles in gas, no./cm
t = time interval, sec
V. = volume fraction bubbles in froth, cm3/cm3
b
and the mass transfer rate to the bubble interface is,
dMb
» /nr- = k Kr «H (Pr - Pf) A dZ (^±) (66)
p dt bG b vrG rLi p \ sec/
where: dZ = height of bubble rise in time "dt"
In the difference calculation procedure used for the
machine computations, equations (64), (65), and (66) are
combined to give:
(65)
The change of gas temperature due to sensible heat transfer
is defined by an energy balance as follows:
G CPM ATG = hbG ab ^Li'V AZ + 6Mpx10' ( a** ) <66>
or
AQ. + AQ,
(67)
A0
Where C M = molar heat capacity of gas, cal/mol-°K
and AQ = heat transferred in time A0, per cm2 of plate area
The particle area per cm3 foam is:
ap = np (41T rp2) (1'F) = np Vb (4 «P2) c (68}
65
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The bubble surface area per cm3 foam is assumed constant
and given by:
The change in gas flow rate is approximated by:
G = ^ /gaolJV Q)
At \cm2
PARTICLE DEPOSITION
Particle deposition by Brownian diffusion is not very
effective on particles in the >0.1 pro dia. size range, and
was not included, although it could have been included with
little difficulty. The collection which occurs during the
period of bubble formation can be predicted separately by
means of equation (71) and it was not included in this
model.
PtF = exp - (40 F£2 Kp) (71)
where
F = foam density, volume fraction liquid
Ptp = particle penetration for collection during bubble
formation, fraction
K = inertial impaction parameter
P " 9 »G dh
d = aerodynamic diameter of particle
It should be noted that collection by impaction during
bubble formation is not very important for one tray and
66
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particle diameter smaller than 1 ym. But if the particles
grow during their stay in the first tray, this mechanism
will become very important in collecting the particles
on the second tray and following trays.
For the present, we are looking at what happens after
the initial collection by impaction. The total particle
flux from the gas to the liquid is defined as the sum of
fluxes due to diffusiophoresis, thermophoresis, and centri-
fugation.
M - M 4. M -u w /no. particles\
Ns ~ ND + NT + NC f 1
1 cm -sec
J
and the flux is related to the deposition velocity and
particle concentration by:
Ns = ups np (73)
For a spherical bubble of radius "r. ", the rate of change of
particle concentration is:
dn~
_J£ = /£_\N =l-^}u_ (74)
dt \rb/
Where,
u = u + u _ + UG = sum of deposition velocities (75)
and the penetration for a period = At:
3
Pt = exp -
=r- (u ) At (76)
rb
Diffusiophoretic deposition velocity is:
•/M, D
_ __ ± G _ / v
(sec/
dy /cm
dr (sec
67
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UpD = Cl °G (l^y)
where M, = molecular weight of water, g/mol
Mp = molecular weight of non-transferring gas, g/mol
and for air and water it can be shown that:
C, - 0.85 (dimensionless) over the range from y = 0.1 to 0.5
The composition gradient can be related to the mass
transfer coefficient as:
dy _dp _ RTG k bG(PG-PLi)
dr dr D,
Therefore, substitution from equations (57), (59) and (78)
into (77) yields:
_
u _ * 0.85 RT,, (1.6x10 ) fa ljl - (79)
P° G (1 - PG/2)
(p - p . ) T
u _ = 0.0112 — ^ - — — - (cm/sec) (80)
P° (1 - PG/2)
Thermophoretic deposition velocity is :
u - -z' G dT
UPT ~ z p-f 55F
and the gradient is estimated from:
(TG - TLi> (EH)
dTG hbG
dx ]
Using Brock's value for Z1 = 0.25 C', we have for air and
water vapor:
68
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u T * 1.35x10'* (C'T,^2 AT) (cm/sec) (83)
Where:
AT- = (Tr - T_.) (°K) (84)
G la LI
C1 = (l + -* — ) = Cunningham slip correction (85)
\ P
Centrifugal deposition velocity is:
2 r 2 p C1 v. 2
u _ -- * - P - E. = K (86)
P 9y rb
and for rfa = 0.2 cm, p =1.0 g/cm3, and vt = vb = 20 cm/sec ,
rn C<
u _ = -E= - (7.4xl08) (cm/sec) (87)
Note that "u " is dependent upon "v. 2" and is quite sensi-
tive to the issumed values of "v, " and "r. ".
PREDICTIONS
A computer program was written to solve the mathematical
model comprising the equations given above, and some pre-
dictions of performance were computed. As a representative
case, we took bubble diameter to be 0.4 cm, foam density 0.5
(volume fraction gas) , and bubble rise velocity to be 20
cm/sec. The first computations were for the following
conditions:
particle radius = 0.5 ym
particle concentration = IxlO6 particles/cm3
gas molar flow rate = 0.003 gmol/cmz-sec
foam height = 8.0 cm
69
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The predicted penetration for these conditions was much
lower than experimental data such as Rosen and Kostin (see
Figure 4.6.4-7 in Scrubber Handbook). Because of this and
the uncertainties about the transfer coefficients, the heat
and mass transfer coefficients for the gas phase, bubble to
liquid transfer were decreased to 1/2 the values given by
equations (59) and (60). The lower values are in line with
the predictions given by boundary layer theory and the
penetration resulting from their use are of a more realistic
magnitude. The predictions which are discussed in the re-
mainder of this section were made on the basis of 1/2 the
values given by equations (59) and (60) until experimental
data was available.
As will be seen later, under experimental work, the
liquid phase heat transfer coefficient and the interfacial
area for transfer seem to be quite different than those
assumed. The approach we have taken is to devise the best
model possible based on existing information, devise and
perform experiments to test the predictions of the model,
and then revise the model to fit experimental findings.
Because of that, we will describe only the general features
of the predictions based on 1/2 the simple penetration
theory transfer coefficients in this section.
It is enlightening to explore the predicted effects
of process variables as shown in Figures 11 through 15
and Table III. Table III summarizes the conditions and
results for 20 computer runs. Bear in mind that while the
general trends are in line with experimental results, the
predictions give lower penetrations than experimentally
observed, apparently because of the liquid phase heat
transfer coefficient used. In all of these runs the total
foam height was 6 cm; so the bubble residence time was
0. 3 sec.
In all figures, the "Y" axis ranges from 0. to 1.0 and
the "X" axis denotes time, with each increment of the
digital computation, At = 0.02 sec. In order to fit all
four curves into the range from 0. to 1.0, we plotted the
following:
S'= = - - (88)
2[exp (13.64) - 5,100/T-)]
70
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w
nj
<
u
p
w
o
2
S/2
n = 3.5xl03
1.0
0.5 ._
n = 3. 5x103
0.1 0.2
TIME, sec
0.3
0.1 0.2
TIME, sec
0.3
Figure 11
Computed prediction
Run #3 for sieve plate
A. P. T. Inc.
71
Figure 12
Prediction of effect of water
vapor concentration on particle
radius.
POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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0.1 0.2
TIME, sec
0.3 0 0.1 0.2 0.3
TIME, sec
Figure 13
Computed predictions
Run # 16
Figure 14
Computed predictions
Run I 18
72
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0.1 -
0.1 0.2 0.3
TIME, sec
Figure 15
Computed predictions
Run ti20
A. P. T. Inc.
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Table III
SUMMARY OF PLATE COMPUTATIONS WITH PENETRATION
THEORY PREDICTED COEFFICIENTS
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TG
°C
30
45
45
30
45
45
45
45
45
45
45
45
30
30
45
60
60
60
60
60
PG
Atm
0.093
0.093
0.093
0.093
0.093
0.09
0.08
0.07
0.03
0.025
0.093
0.093
0.093
0.093
0.08
0.19
0.19
0.19
0.19
0.19
TL
°C
19
19
19
19
21
21
21
21
21
21
21
19
19
19
21
20
20
20
20
20
Initial
r . ym
P
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.25
0.25
0.25
0.25
0.25
#/cm3
3,500
3,500
3,500
3,500
3,500
3,500
3,500
3,500
3,500
3,500
3,500
10s
10s
106
10s
10 3
107
]06
10s
108
G
gmol/
cm2 -sec
0.003
0.003
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.006
0.009
0.006
0.006
0.006
0.006
0.003
0.003
0.003
0.003
0.003
Final
r , ym
P
4.7
3.0
2.8
6.6
2.55
2.35
1.3
0.36
0.33
0.33
2.55
2.55
4.7
3.3
1.32
4.2
1.4
3.1
4.0
0.68
Final
Pt
0.1
0.38
0.37
0.09
0.39
0.43
0.55
0.62
0.83
0.85
0.39
0.38
0.09
0.23
0.55
0.13
0.28
0.19
0.15
0.31
74
A. P. T. Inc.
POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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T, = TG " TL present AT (89)
T_ - TT original AT
(jO Li
Pt = n /n = Present particle cone.
p po original particle cone.
1 _ _pg _ original particle radius
rp r present particle radius
Figure 11 shows the predicted results for computer run
#3, in which the air starts out saturated at 45°C and contacts
water at a constant temperature of 19°C. The saturation ratio
rises above 1.0 so there is particle growth, as shown by the
curve for "r1" (which decreases as particle size increases).
Particle penetration decreases almost linearly with time (or
bubble rise distance), as does air temperature.
Figure 12 shows only the predicted particle time para-
meter for runs #3, 6, 7, and 8. It can be seen that as the
initial air saturation decreases (all other factors being
the same for runs #6, 7, and 8) the amount of condensation
decreases. In run #8 there is a small amount of particle
growth (about 5%) at the end of the 0.3 sec (corresponding
to 6 cm of rise at 20 cm/sec for a 0.4 cm dia. bubble).
Figures 13, 14, and 15 show the predictions for runs
16, 18, and 20, respectively. The only output parameter
changing in these runs is particle concentration, which is
103 particles/cm3 for Figure 13, 106 for Figure 14, and 108
for Figure 15. One can see the effect of increasing particle
concentration as it decreases the saturation ratio and
particle growth, while increasing the outlet air temperature
and particle penetration.
To get some perspective in accustomed engineering units,
one might note that 106 particles/cm3 corresponds to about
0.137 g/m3 (0.06 grains/ft3) if particle density is
2.0 g/cm3 and particle diameter is 0.5 ym. This would
represent a few percent of the particulate mass if the
concentration from a source were 2.3 to 4.6 g/m3 (1 or 2
grains/ft3), so it would be on the order of a realistic
fine particulate concentration. Obviously, it would be
advantageous to remove as much of the larger particles as
75
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE, CA. 92502
-------
possible before raising the saturation ratio above 1.0.
This last statement will be even more important for higher
fine particle concentrations, such as have been reported
for ferroalloy furnace emissions.
The plate scrubber model and the computation procedure
described in this section proved to be of proper form to
describe FF/C scrubbing to the extent that theoretical and
empirical information is available. The various coefficients
and quantities used may be adjusted to fit new experimental
data as it becomes available. As discussed previously, the
development of a useful and reliable design method is an
iterative procedure which can continue to upgrade the method
as well as to increase our perception of experimental
reality.
76
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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MATHEMATICAL MODEL, IMPINGING JET
The approach to calculating the collection efficiency
of particles from a jet impinging on a plate was similar
to that taken for predicting collection efficiency by a
drop. The particle trajectory was calculated from its
initial conditions and the forces acting on it. In de-
riving the equations of motion we followed the method out-
lined by Mercer and Chow (1968) adding an additional term
to the equation which described the flux force. To
simplify the solution we assumed a constant flux force
gradient in the space between the jet and the impact ion
plate.
A force balance leads to the following set of differen-
tial equations in dimensionless form, comparable to equations
(26) and (27), where vapor gradient exists in the jet space:
- - (vx - ux) + KD (92)
dt2 K * X U dX
P
— = — (VY - uy) - Kn 21 (93)
dt2 K x dY
Where
9 yr (0.85) D
KD = « (94)
2 pp V uo2 u - y>
The same equations will result when a thermal gradient is
present, with "KD" replaced by "KT" and "dy" by "dTG".
The flow field assumed by Mercer and Chow is
X "* ' -(1 + AY) < Y < (1 + AY)
3
for
-3 < X < 0 (95)
77
A. r. T. Inc. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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-(1 + AY) > Y > (1 + AY)
vx = 0 for
-3 < X < 0
The boundary conditions are:
vv = uv = 1 for X = -0
A A
uy = 0 for t = 0
The flux force is defined by:
= const, and = 0 for -d + AY) < Y < (1 + AY) (97)
dX dY
£2 = dY. = o for -(1 + AY) > Y > (1 + AY) (98)
dX dY
Where
Y =
v = —
X V
"• 2X
X = — = diraensionless distance
W
2Y
= — = dimensionless distance
W
v
= — = dimensionless velocity
o
vv
v = — = dimensionless velocity
~ 2t vu ,. •
t = —rj—0- = dimensionless time
W = jet width, cm
s = distance from jet nozzle to plate,
2s
g = — = dimensionless }et spacing
cm
W
78
A. P. T. IDC POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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Y = [Y I, the ordinate of a given streamline
at X = -8
y = mol fraction water vapor
Note that the factor 0.85, which accounts for molecular
weight gradient effect, is as discussed previously, and
2 P.
(99)
PG TG
The solution to equations (92) and (93) with the
boundary conditions given by equation (95) in the region
-(1 + AY) < Y < (1 + AY) is:
X = exp{-t/2K)
(K -1) cos 1±- +
U 2K
sin
2K
(100)
where y =
fl) cxp h6-1**]
£' 2K
P J
0.5
4 K -$1
'
B J
e-1 [(£+!)
[2Kp
0.5
[3+4 K 1
P
1 s
i K dy
K P ^
D KD dX
(101)
Outside of this region:
X - (X)1+y = K
o c
dX
dt
1 - exp
K
(102)
From these solutions target efficiency was calculated as
a function of "K " and "3" using a digital computer. The
79
A. P. T. Inc.
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maximum values of "K " and "K " in our range of interest were
found to be between 10-6 and 4x10"3. These calculations showed
that flux forces have practically no effect on the impaction
from a jet. The same results were obtained for particle
growth. The reason for these results lies in the very short
residence time of the particle in the collection region which
is measured in KT11 to 10~3 seconds as compared to =0.1
seconds in the bubble and =0.25 seconds in the spray column.
For impinging jets, flux force/condensation scrubbing
would have its major effect where particle growth occurs
prior to impingement. Thus, while negligible collection
would be caused by phoretic forces, scrubbers incorporating
impinging jets as a unit mechanism for particle collection
are still to be considered as a possible alternative. A com-
posite scrubber involving condensation and growth in a pri-
mary stage and impingement in a secondary stage might be
desirable for some applications.
80
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE, CA. 92502
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MATHEMATICAL MODEL, LIQUID SHEETS
This section describes the development of a mathematical
model for particle collection by liquid sheets. Following
the conceptual framework of the Scrubber Handbook, liquid
sheets are the basic geometric element involved in the unit
mechanism which describes collection in packed columns,
wetted wall columns, wetted plates, and similar devices.
Included in the treatment are the following effects:
1. Diffusiophoresis
2. Thermophoresis
3. Particle growth by condensation
4. Centrifugal deposition
5. Gravitational settling
Collection by Brownian diffusion is not included be-
cause of its small effect on particles in the size range
of immediate interest. Turbulent diffusion is also not
included because the gas flow in long, straight geometries
(such as wetted wall columns and the like) will generally
be at Reynolds numbers of only a few thousand. For systems
involving short curved geometric elements (such as packed
columns) the deposition is dominated by centrifugal
(inertial) impaction and turbulence serves mainly to mix
the particles in the gas stream.
The first model worked out is for counter-current flow
in fairly straight systems such as wetted wall (cylindrical
or flat plates) columns. As will be seen, the modification
of a few terms can adapt the model to packed beds and
similar devices where the contact or surface renewal times
for gas and liquid are relatively short. A digital computer
was used to solve the simultaneous differential equations
for heat and mass transfer and particle growth and collect-
ion.
81
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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P2
The accompanying sketch
illustrates the geometric
relationships and the flow
directions. Gas enters the
bottom of the column at a
superficial molal flow rate
(wet gas) of "G",
gmol/cm2-sec, a temperature
of "TG" °K, water vapor
partial pressure of "p" atm,
particle concentration of
"n " particles/cm3, and
particle radius of "r " cm.
Liquid leaves the bottom of
the column at a superficial
molal flow rate of "L",
gmol/cm2-sec and a temper-
ature of "T, ".
Li
'G2
L2
r
G + dG xL+dL
. J Ji.
j
"ill"
G S L
i
J.
dZ Z
T
(
I -,
Gl
Pi
'Ll
The heat balance about a differential element of the
gas-liquid sheet interface is found, as for the case of
bubbles, by equating the rate of latent heat evolution for
condensation to 'the rates of heat transfer to the gas plus
the rate of heat transfer to the liquid bulk. We obtain:
nr
KT
- Ti
TL - 0
(103)
The heat balance about the gas phase in an element of
the column involves heat transfer from the liquid sheet and
the particles (if there is condensation on the particles) ,
temperature change of the particles, and temperature change
of the gas. It can be shown that the product of mass times
heat capacity for the particles is a very small percentage
(generally less than li) of "m C " for the gas; so particle
82
A. P. T. Inc.
POST OFFICE BOX 71, RIVERSIDE, CA. 92502
-------
heat capacity is neglected, (i.e., the last term on the
right of equation (104) is neglected).
h, a (T. - TG) dZ * hp ap (Tp - TG) np e ^ -
Cp d[G TG) * mp Cpp RT d (np G Tp) (104)
where:
a = gas/liquid interfacial area per unit volume of scrubber,
cm2/cm3
e = volume fraction open space in scrubber
a = surface area of particle, cm2
h = heat transfer coefficient, particle to gas
P cal/cm2-sec-°K
A heat balance for liquid flowing through the differen-
tial element is formed by equating the rate of heat transfer
to the temperature change of the liquid.
-C . d(L T.) = hT a (T. - TT)dZ (cal/cm2 col.-sec) (105)
pL L L i L
The change (decrease) in liquid flow rate as one
computes up the column is obtained from a mass balance in
which the condensation rate equals the rate of gain (or loss)
of liquid flow rate.
s\
-dL = kG a (pG - pi) dZ (g mol/cm2 col.-sec) (106)
Note that for co-current flow the signs of equations (105)
and (106) would be changed.
The change in gas flow rate is obtained from a mass
balance which equates the rates of condensation on particle
plus sheets to the rate of loss of water vapor from the
83
A. P. T. IDC POST OFFICE BOX 71. RIVERSIDE. CA. 92502
-------
gas phase.
-d(G PG) = kG a (pG - p.) dZ + kp ap np e (pG - Pp) dZ
(gmol/cm2 col.-sec) (107)
The.rate of growth of particles is computed, as for
the case of bubbles, by means of the following equation:
2 Dr p(pr - p .) At
r* - r2 = ^ (cm2) (also 4.3.4-19 in (108)
r !„ p.. p™. Scrubber Handbook)
b M DM
Note that equation (108) is solved for the "bulk" value of
partial pressure, "PG". It has been shown earlier in this
report that growth can occur in the boundary layer even
though "Pp" is below saturation. For the present, we
neglect this effect.
Gas phase mass transfer coefficient is taken to be
the conventional one for pipe or channel flow:
s\
kr d
-jr— RTr = 0.023 ND °-83 Nc OJ"' (109)
Dn G Re Sc
u
If air and water properties are used as for the bubble
case, we can reduce equation (109) to (110):
yQ « 6xlO'7 T (g/cm-sec - °K) x °K
PG * 0.34/T g/cm3
DG * 1.2x10-* (T)1'75 cm2/sec
0.023 (u)°-83 (D )0'56 75xlo-3 r°'83
k * G = 3.75x10 = G
G (vG)°-1( d0'17 RTG d°'17 e
If we assume that the gas phase heat and mass transfer
coefficients can be related by means of a penetration theory
model, using equal contact times for both coefficients, we
84
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
-------
find:
1/2
hG _ RT PG CpG kG ' „ 65.0
J~ " RTG Dp (TG) ^
G
where: k_ « 7.3xlQ-5 (cal . /cm2 -sec-°K/cm)
b
The liquid phase heat transfer coefficient is much more
difficult to pin down and, indeed, it will be greatly de-
pendent upon the specific fluid flow system used. As an
approximation of a representative situation we have taken
the heat transfer coefficient predicted for a wetted wall
column and adjusted it through a process of comparison
with experimental mass transfer coefficients.
Upon review of the experimental data for mass transfer
coefficients in wetted wall and packed columns (e.g.,
Norman, 1961, equation 6.34), it appears that "kL" , and
therefore "h", for packed columns depend upon liquid rate
to the 0.75 power. This reflects the influence of liquid
flow rate upon the fraction of packing area which is wetted.
The fraction of area wetted varies as liquid rate to the
0.25 power and the transfer rate varies as the 0.5 power,
so the total influence of liquid rate depends on the 0.75
power.
For the present purpose of exploring the general
characteristics of collection by sheets, we will assume
that the liquid rate is high enough and the geometry such
that the wetted surface area is constant. Thus an equation
such as the following should describe the influence of
liquid rate on transfer rate only.
hL = 0.5 (Vg)1/2 =0.5 (2 (112)
where VB = volumetric liquid flow rate per unit of sheet
width, cm3/sec-cm
Deposition Velocities
In keeping with the previous development for bubbles,
the diffusiophoretic and thermophoretic deposition velo-
cities are as given below. It will be recalled that the
85
A.P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
-------
total particle flux can be computed from the sum of the
individual deposition velocities.
- (Pr - P;)
u n * 0.83 RTr kr — 2 - — cm/sec (113)
pD G G
PBM
C1 yr dT
ur>T = °'25 - ^ cm/sec (114)
P PG TG dx
and, for air/water,
u T = 6.1xl(T3 C1 Tr hp (T. - Tr) cm/sec (115)
pi Vi Vj 1
Li
The centrifugal deposition velocity is given by:
2 r2 p C' v?,
u ~ P_J2 k (cm/sec) (116)
9 u R
and for moist air and p = 1.0(g/cm3):
3.7xlOs rl C1 v'
u r - *- cm/sec (117)
P T R
TG c
In the present model we do not include this effect. For
curved flows it will be used and "R " will be an effective
radius of curvature which will depend on the specific
geometry.
Gravitational settling for Stokes law is defined by:
cos a (118)
m C1 cos a
P ~ t. fi^vi n*
611 u,, r
G p
~C' ^ + ro Pd3"
L rp TG J
where:
m = mass of particle, g
r = the original particle radius before growth, cm
p, = the difference between original particle density and
density of water, g/cm3
86
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
-------
The particle deposition velocity is
Ups = > + UpT + UpG + UPC Cm/SeC
Solution
The relationships given above have been solved by a
finite difference computation on a digital computer. The
results for four computer runs are shown in Table IV and
Figures 16 through 19. All of these predictions were made
for the case where centrifugal (inertial) and gravitational
separation are not active; as would be the case for vertical
plane sheets. Column height was taken as 300 cm for runs
#1 and #2, and as 100 cm for runs #3 and #4. For all runs
the gas flow rate was 0.006 (gmol/cmz-sec) (which corres-
ponds to an air velocity of about 5 ft/sec, depending on
temperature), the liquid rate was 0.03 (gmol/cm2-sec), the
particle radius was 0.33 (ym), and the gas/liquid inter-
facial area was 2.0 (cm2/cm3).
The method of solution was to start from the inlet gas
and outlet liquid values (i.e., from the bottom of the
column) and to compute values of the variables for small
increments of length until the top end of the column is
reached. Figures 16 through 19 are plots of the several
parameters listed below, as a function of distance up the
column. Because different column lengths are used, the
length coordinate is given as fraction of total length.
T_ and TT are given in °C; on "temperature scale"
Pt = fractional penetration; on "normalized scale"
r1 = (r /r ); on normalized scale
S/2 = 1/2 of saturation ratio; on normalized scale
It can be seen that predicted penetrations for these
few conditions are fairly high. Inclusion of centrifugal
deposition would give appreciable improvement in penetration
because the particle size does increase quickly. This
indicates that packed columns would probably be superior to
wetted wall configurations. There would also be the bene-
ficial effect on liquid phase heat transfer coefficient if
packing were used.
87
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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D
o
Table IV
RESULTS OF COMPUTER PREDICTIONS OF COLLECTION BY SHEETS
TJ
O
Cfl
O
m
ra
O
X
m
31
CO
o
oo
oo
Run*
1
2
3
4
In]
TG(°C)
60.
45.
45.
45.
et Conditions
TL(°O
34.7
21.8
22 .5
22 .4
PG(atm)
0.2
0.092
0.092
0.092
n (#/
Pern3)
3,500
3,500
3,500
106
ZCcm)
300.
300.
100.
100.
Outlet Conditions
TG(°C)
34.8
21.9
26.1
26.4
TL(°C)
44.
27.
27.
27.
S
ratio
1.0
1.0
1.04
1.0
Pt(fr)
0.84
0.93
0.94
0.935
rp
(ym)
4.54
4.1
3.96
0.85
Note: The above results were computed for the case of vertical, counter-current
flow of air and water with no centrifugal deposition. Other common
conditions for all runs are as follows:
G = 0.006 (gmol/cm2-sec)
L = 0.03 (gmol/cm2-sec)
r =0.33 (um)
a =2.0 (cm2 contact area/cm3 column vol.)
S,, = critical saturation ratio for condensation =1.0
8
en
o
to
-------
1.0
w
u
C/3
P
w
o
2
0.5
0
100
1.0
100
Pt
u
o
30
20
10
JO
1
0 0.5
FRACTION OF COLUMN LENGTH
u
j
<
u
Q
UU
O
2
0.5 h
0
Pt
50
40
30
20
10
0
u
o
ia
en
3
t-
w
a.
0 0.5 1
FRACTION OF COLUMN LENGTH
Figure 16
Computed predictions
for sheets, Run #1
89
A. P. T. Inc.
Figure 17
Computed prediction
for sheets, Run #2
POST OFFICE BOX 71. RIVERSIDE. CA. 92502
-------
1.0
PJ
,-J
<
u
UD
0
w
Kl
0.5
100
Pt
1.0
u
o
w
(*
ISO g
fr,
S
140 «
50
!0
10
JO
0 1.0
FRACTION OF COLUMN LENGTH
Figure 18
Computed prediction
for sheets, Run #3
W
u
Q
N 0.5
h-H
»-J
o
z
0
Pt
S/2
100
u
o
(A
50 H
n
Du,
40 H
30
20
10
0
0 1.0
FRACTION OF COLUMN LENGTH
Figure 19
Computed prediction
for sheets, Run #4
90
A. P. T. Inc.
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As in the case of transfer from bubbles, the effect
of high particle concentration (see run #4, Figure 19) is
to reduce the water vapor concentration so that diffusio-
phoretic velocity is lower and particle growth is less than
for low particle concentrations. If condensation did not
occur on the particles because the critical saturation
ratio were not reached, the water vapor concentration would
not be depleted and, therefore, the diffusiophoretic
velocity would not be dependent on particle concentration.
When condensation does occur, as in the examples shown
in Table IV, the particle size may increase sufficiently
that collection efficiency by inertial impaction can become
significant. In run #4 the particles grew to 1.7 pm dia-
meter even though the inlet concentration was 106/cm3.
Particles this size can be collected at moderate pressure
drop.
91
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA 92502
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EXPERIMENTAL
Theoretical considerations had indicated that plate-
type scrubbers should be good for FF/C scrubbing on the
basis of their assumed heat and mass transfer character-
istics. It was also clear that the transfer coefficients
were very important in determining particle collection
efficiency, so it was important to verify them by experi-
mental measurements. Thus, the kind of experiment needed
to provide the crucial test of the preliminary theoretical
analysis was defined.
In this section of the report we will describe:
1. Details of the experimental apparatus
2. Experimental procedure
3. Analytical methods
4. Computational methods
5. Results
6. Comparison of experimental results with
predictions .
EXPERIMENTAL APPARATUS
A schematic flow diagram of the experimental apparatus
is shown in Figure 20. The major components were as follows
Test Section: The test section consisted of a 10.2 cm
diameter glass column. A sieve-plate was installed in it,
as the first configuration to be studied for FF/C effects
scrubbing.
The plate was made out of 1.6 mm aluminum sheet and had
an overall diameter of 10.2 cm. It had 30 perforations of
4.8 mm diameter, adding up to 6.6$ free area on the plate.
It had two straight weirs, 8.1 cm long and 9.5 mm high, for
the liquid inlet and outlet on the plate. As the plate was
to be used to study FF/C effects scrubbing, the additional
design criteria used were:
92
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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WATER
AIR
AIR GAS WATER
Legend:
1. Valves
2. Pressure Regulator
3. Rotameters
4. Water Cooler
5. Air Prefliter
6. Air Blower
7. Air Cooler
8. Venturi-meter
9. Air Heater
10. "Absolute" Filters
TO DRAIN
11. Particle Charge Neutralizer
12. Gas Mixing Section
13. Boiler
14. Steam Entrainment Separator
15. Pressure Indicator
16. Air Filter
17. Pressure Indicator
18. Collison Atomizer
19. Impactor
20. Evaporation-Condensation Columns
21. Sieve-plate Scrubber
Figure 20 - Experimental apparatus
93
A. P. T. Inc.
POST OFFICE BOX 71. RIVERSIDE. CA 92502
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1. Very low weir height. Since the major portion
of the collection is expected to take place
during a bubble rise of a few bubble diameters,
a large foam height is not needed.
2. Large perforation diameter and low gas velocity
in the perforations, since it was desired for
experimental purposes to maintain a low collection
efficiency during bubble formation.
3. Large weir length, since it will ensure good
liquid distribution and thus a constant liquid
temperature on the plate.
The operating characteristics of the plate are shown in
Figure 21.
The water was introduced £rom the top to the sieve-
plate behind the inlet weir, through a downcomer tube. An
outlet downcomer tube located behind the outlet weir re-
moved the water from the plate. A sampling valve was pro-
vided in the outlet water flow. The flow rate of water
through the test section was measured by a set of rotameters
on the inlet line. Water temperature was maintained by
distributing the inlet water flow between a cooler and a
bypass line before it was introduced in the test section.
The inlet and outlet water temperatures were measured by
iron-constantan thermocouples located in the respective
downcomers.
The air stream, under controlled conditions of tempera-
ture, humidity and particle concentration flowed upwards
through the perforations in the sieve-plate. The inlet and
outlet temperature and humidity were measured by wet and dry
bulb thermometers located in the respective lines. Sampling
probes for particle concentration and size distribution
measurements, together with static pressure taps for measur-
ing the pressure drops, were also provided in the air lines
at the inlet and outlet to the test section. A variable
height probe was provided in the test section. It could be
adjusted to obtain air samples and static pressure readings
within the test section, at any height over the sieve-plate.
Ample height was provided over the sieve-plate in the test
section, to prevent entrainment of water drops in the outlet
air stream.
94
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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£
u
2
O L=0.985,liters/min
Q L=1.9, liters/min
Weep
O
0.2 0.5 0.9
GAS FLOWRATE, CmVmin)*
e
u
ex,
—L = 2.50, liters/min
— L = 2.96, liters/min
0.3
aP
Weep
I
I
0.5 0.8
GAS FLOWRATE, (ms/min)*
20°C, 1 atm
Figure 21 - Operating characteristics of the
sieve plate.
A. P. T. Inc.
95
POST OFFICE BOX 71, RIVERSIDE. CA. 92502
-------
Air Flow System
A 1/2 HP Rotron "Cyclonair" blower supplied the air
flow, which was prefiltered. The air flow-rate was
measured by a calibrated venturi meter. A finned-tube
heat exchanger in the air line, cooled the air flow by
means of ice water to 18°C and a heater using three
electrical elements could heat the air if desired. The
air was then passed through an "Ultra Aire" absolute
filter made by Mine Safety Appliances Company. The
filter is rated at 99.97% efficiency of retention for
0.3 ym particles by the manufacturer, and was regularly
checked by measuring the particle concentration in the
filtered air.
A controlled flow of aerosol from the particle
generator was introduced into the air stream. The air
stream then passed through a charge-neutralizer utilizing
ten Polonium 210 elements, with radioactivity of 500 pc
each, mounted on the wall of a 76.2 cm section of 3.8 cm
diameter glass pipe. At the maximum air flow-rate of
0.71 (m3/min) with particle concentration of 10s particles/
cm3, the residence time of 0.1 sec in the charge neutral-
izer is considered sufficient, due to^the high energy of
disintegration [5.4 Mev) for the Pozl alpha particles.
A controlled quantity of steam was then added to the
air stream to obtain the desired moisture content in the
air. The steam passed through an entrainment separator
column packed with bronze wool, and then through an
absolute filter similar to the filter used in the air
line, before it was introduced into the air stream. The
humidified aerosol then entered the sieve-plate column
following a mixing section.
Particle Generator
The major components of the particle generator assembly
were: (1) a 3-orifice Collison atomizer (CA). (2) an
impactor with a cut-off diameter of 2 um, and (3) an
evaporation-condensation (E-C) aerosol generator. The
particle generator set-up is shown in Figure 22.
Dibutyl-phthalate (DBP), with 0.01% by weight of anthra-
cene as nucleating agent, was used as aerosol material in
the CA. Filtered air at 40 psig was fed to the CA for gene-
rating a DBP spray. Particles larger than 2 vim diameter
96
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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Compressed air
@ 40 psig
Filter
r~\
3-Orifice
Collision
atomizer
L\
Impactor
2 ym cut-off
(\
Charge Neutralizer
Vent
®
Figure 22 - Particle generator assembly
97
P. T. Inc.
POST OFFICE BOX 71. RIVERSIDE, CA. 92502
-------
were then removed by the impactor following the CA.
The particles then entered the bottom of the first E-C
column, a 2.54 cm O.D. glass tube, 94 cm long with heat-ing
tapes wrapped around the tube at top and bottom to serve as
evaporation zones. Axial baffles were provided near the
entrance to the tube to promote mixing and better heat
transfer area in the first evaporating zone. The particles
then flowed into the top of the second E-C column. The
upper section of the column was a 48 cm long, 2.2 cm O.D.
Vigeraux column and the lower section was plain pyrex tubing
30.5 cm long and 2.2 cm O.D. The second E-C column had one
evaporation zone located at the top near the entrance to
the column.
The particle characteristics were studied for various
values of voltages applied to the three heating tapes and
various pressures in the compressed air line. The values
of 40 psig pressure in the air line and 65V applied to each
of the heating tapes were found to give particles with a
mass mean diameter, d = 0.7 pm and a geometric standard
deviation, a = 1.215, measured by the eight stage, non-
viable Anderson sampler. As this aerosol was suitable for
our purposes, the particle generator was routinely operated
at these settings.
Particulate Sampling System
This system consisted of three major components:
(1) Filter sampling system to measure the particle
concentration in the inlet and outlet air
streams.
(2) The Climet CI-201 particle analyzer to measure
the particle concentration and size distribution
in the inlet and outlet air streams, and
(3) The eight stage, non-viable Anderson sampler to
measure the particle size distribution in the
inlet and outlet air streams.
Both the inlet and outlet sampling lines consisted of
insulated 6.4 mm aluminum tubing. The sampling probes were
located near the center of the air pipes, bent to face the
air stream in the direction of flow. Since the particle
98
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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sizes in the air stream were small (d = 0-7 vim, a = 1.215),
no consideration need be given for isoKinetic sampling. Two
lines were drawn from each of the sampling probes, one going
to- the Climet particle analyzer and the other to the Anderson
sampler and the filter sampling systems. The sampling sys-
tem was so designed, as to keep the sampling lines as short
as possible. A schematic diagram of the sampling system is
shown in Figure 23.
EXPERIMENTAL PROCEDURE
The experiment was started by bringing the particle
generator to the operating conditions. When an aerosol
stream containing particles in the range of 0.4 urn <_ d < 2ym
is illuminated by a beam of white light, the light scattering
by the particles produce angular spectra, known as the high-
er-order Tyndall spectra. The spectra exhibits different
colors depending on the angle of observation. The satura-
tion and brightness of the colors increase with uniformity
of particle size. This phenomenon was used to determine
whether the particle generator was producing nearly mono-
disperse aerosol. After an iron-constantan thermocouple
located in the E-C column indicated that the temperature
had reached a steady state, the aerosol was observed with
forward-scattered light from a flashlight until a bright
orange color was seen due to the higher order Tyndall
Spectra. This normally took 10 to 15 minutes and indicated
that the generator was ready.
Before the particles were introduced into the air
stream, the air and water flow-rates were brought to the
operating values. When a saturated or unsaturated air
flow was desired, the temperature of the air was set by
either operating the heater or the cooler, the particle
concentration was measured in the filtered air using the
particle analyzer and then steam was added to reach the
operating values of temperature and humidity. Supersaturated
air flow was attained by first adding the required amount
of steam into heated air flow so that the gas remained un-
saturated. The heat was then gradually reduced to reach
the desired values of temperature and supersaturation in
gas.
After the steady state was reached, which took from
thirty to sixty minutes, the flow-rate conditions, foam
height, pressure drop across the plate, the inlet and outlet
air wet and dry bulb temperatures and the water inlet and
outlet temperatures were noted. When the air was
99
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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D
o
s
CO
o
m
03
O
X
m
CO
O
CO
rvj
en
O
ro
o
o
Water
in
Thermometers
Dryer
Cold trap
Climet particle analyzer
with dilution system
Water to drain.
Figure 23 - Sampling system.
-------
supersaturated, a sample was drawn from the air line and
heated to determine the humidity with wet and dry bulb
thermometers. This enabled the determination of the
amount of steam lost due to condensation on the walls when
the air temperature was reduced.
The particles were then introduced into the air
stream. The particle concentration was controlled to
obtain approximately 5 mg of sample on the outlet filter
in 30 minutes. In the meantime, the Anderson sampler and
the filters were prepared and heated in the oven to the
inlet gas temperature. The sample lines were heated by
drawing air through them. The filter holders were then
connected in the respective lines and the sampling lines
were checked for possible leakage.
The inlet and outlet filter sampling was started. The
sampling time was approximately 30 minutes and the flow rate
was approximately 5.1 litres/min (@ 20°C, 1 atm) . All the
operating conditions were rechecked while the filter samp-
ling was going on.
Upon completion of the filter sampling, sampling for
the particle size distribution in the inlet gas was started
using the Anderson sampler. Again, the same precautions
were taken against condensation and leakages in the
sampling lines as taken earlier for filter sampling. The
sampling time was approximately 45 minutes and the flow rate
28.3 (litres/min).
After the sampling using the Anderson sampler was com-
pleted, the particle size distribution and concentration in
the inlet and outlet air lines were measured using the
particle analyzer. This was done by connecting the sampling
lines to the particle analyzer and reading the particle con-
centrations for successively larger particle sizes, using
the potentiometer connected to the analyzer.
The inlet valve from the particle generator to the air
line was then shut off. The experimental conditions of gas
flow rate, etc. were then recorded without the particles, as
done earlier, prior to the introduction of the particles.
The filter papers and the Anderson sampler plates were
weighed immediately upon the completion of sampling on an
analytical balance (Sartorius Model 2443; ±0.05 mg precision)
101
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE, CA. 92502
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These were then left to dry in a desiccator and reweighed
after at least 20 hours. At this point the run is com-
pleted.
The experimental conditions were found to stay very
stable, once the steady state was reached. The conditions
were checked at the start of each sampling run for the
filter sample and the Anderson Sampler. They were rechecked
at least once while the sampling was going on and then
again at the end of the sampling run. The water and steam
flow-rates were significantly affected by variations in the
inlet pressures. Pressure regulators and throttle valves
on these lines enabled the maintenance of constant flow-
rates. The particle generator had been repeatedly tested
for consistency in particle size distribution and particle
concentration in its output over a period of time. These
parameters were found to remain significantly constant at
least for a period of up to four hours. For all the experi-
mental runs reported, the temperature conditions for the
experiment varied within ±0.5°C during the experimental
period.
METHODS OF ANALYSIS AND CALCULATION
As mentioned previously, three sampling methods were
used to determine the particle concentration and size
distribution. These were: (a) filter sampling, (b)
Climet CI-201 particle analyzer and (c) Anderson sampler.
Details of each of these methods are given below.
(a) Filter Sampling
47 mm glass fibre filter papers (Type E, made by
Gelman Instruments Company) were used in the filter sampling
system. The sampling flow-rates were measured by rotameters
on each line and were controlled by needle valves. Upstream
from the rotameter the line pressures were measured by Dwyer
"Magnehelic" pressure gauges and the temperature by iron-
constantan thermocouples. Cold traps and dryers were used
in the sampling lines to prevent condensation in the rota-
meters .
The DBF used to generate aerosol was rated by the manu-
facturer to have a boiling point of 172°C-174°C @ 5mm of Hg.
A substantial change in the particle concentration was ob-
served when the gas temperature was changed. This is
attributed to the evaporation of some of the aerosol material,
DBF. It was decided to maintain the inlet gas temperature
102
A. P. T. InC POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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below 50°C in order to keep the fraction of DBF in the
vapor phase at a low, controllable level. Also, the
temperature of both the inlet and outlet filter holders
were maintained at the inlet gas temperature, by placing
them in an oven. This eliminated any biased effect of
gas temperature (due to vaporization) on the particle con-
centration during the sampling. The inlet and outlet
filter sampling were done simultaneously under identical
conditions.
The particle mass concentration was calculated as:
_ (weight gain on the filter, at inlet gas temperature)
P (sampling flow-rate,Std. conditions) x (sampling time)
(g/cm3)
where, c = particle mass concentration. Note that the
P particle mass concentration can change with the
gas temperature due to the evaporation loss of
DBF. The concentration expressed here is at
the inlet gas temperature.
The overall penetration (Ft) in the test section was
calculated as:
c
Pt = -E°
°pi
where "c " and "c ." are calculated for the same conditions
of temperature and pressure.
As the inlet and outlet filter samples were collected
with the sample gas heated to the inlet gas temperature in
both the lines, and as the line pressures in both the lines
were almost same, the maximum difference being less than
12 cm W.G.; "Pt" can be expressed as:
pt _ weight gain on the outlet filter
weight gain on the inlet filter
At least two samples were taken for each set of condi-
tions to test for reproducibility.
(b) Climet CI-201 Particle Analyzer
The Climet CI-201 particle analyzer operates on
103
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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the total light-scattering principle, which permits direct
characterization of the particles as to their size distri-
bution and concentration. The instrument measures the
particle concentrations in the range from 3.5X101* to
3.5xl09 particles/m3 with the help of the 100/1 dilution
system (Model 0294-1) . It was modified with a potentio-
meter so that the counting size threshold could be varied
continuously in the range from 0.3 ym to 3 ym diameter
instead of being restricted to several fixed sizes. A
dryer was placed in the line connecting the particle
analyzer to the diluter system to prevent condensation
in the optical sensor.
To determine the particle number concentration
(n , #/cm3) , the potentiometer and the particle size
selector switch were set to read the concentration of
particles greater than 0.3 ym diameter. Because particle
size distribution measured with the Anderson sampler had
shown that 1001 particles were >0.3 ym, this setting on
the instrument indicated the total number of particles per
unit sample volume. The inlet and outlet sample lines were
connected, in turn, to the instrument and the concentrations
were read off the dial.
To determine the particle size distribution, the sample
line was connected to the instrument and the potentiometer
was set at successively larger values of particle diameters.
From these data, the geometric standard deviation (a ) and
the number mean diameter (d ) were determined.
(c) The Anderson Sampler
The Anderson Sampler is an eight-stage cascade
impactor. The perforations in each stage are designed to
provide successively smaller cut-off diameters. Thus, when
an aerosol is passed through it, successively smaller dia-
meter particles are collected on the stages and the particle
size distribution is determined on a weight basis, by
measuring the weight gain on each stage. The cut-off
diameters depend on the flow rate through the sampler and
a preliminary check of the manufacturer's rated values
using an optical microscope was found to be approximately
correct. An absolute filter was used after the final stage
of the sampler to capture all the particles that escape
collection in the sampler.
104
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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The flow rate through the sampler was maintained at
approximately 28.3 (liters/min) and measured by a cali-
brated dry gas meter. The sample flow line pressure was
measured by a mercury U-tube manometer and the line temp-
erature was measured by an iron-constantan thermocouple
before it entered the dry gas meter. As with the filter
sampling system, the temperature of the Anderson sampler
was maintained at the inlet gas temperature in the oven.
The plates were weighed before and immediately after
the sampling, and again after they were dried in a desic-
cator for over 20 hours, on the Sartorius analytical bal-
ance. They were then washed with soap and rinsed success-
ively with de-mineralized water, ethanol and acetone.
Then they were placed back in the sampler and the sampler
sealed off until the next run.
The geometric standard deviation (0 ) and the mass
mean diameter (dpg) of the aerosol were Determined from
the weight of particles collected on the plates in
different stages with known cut-off diameters. The
particle mass concentration was also determined as:
(weight gain on sampler and filter,at inlet gas temp.)
C "" ~LI
p (sampling flow-rate,std. conditions) x (sampling time)
(g/cm3)
This value was then checked against the value determined
from filter sampling.
Air Supersaturation
A direct determination of the saturation ratio (S)
using the wet and dry bulb thermometers is not possible when
the air is supersaturated. Since it was desired to obtain
data for different values of Tdi < 50°C, the inlet air was
cooled prior to the introduction of steam. When steam was
introduced in the air flow, it was found that a part of it
condensed in the line. Assuming that the air line was well
insulated and there was no heat loss through the pipe, we
calculated "S" in the following way:
(a) The air was heated to a temperature higher than
T^ and steam was^introduced at a rate such
that the desired y was attained, under unsatura-
ted conditions.
105
A. P.T. Inc. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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(b) The heaters were turned off and the air
temperature was allowed to reach a lower
steady state value, Tdg, keeping the same
rate of introduction of steam as in (a).
(c) The mole ratio, and hence S, were calculated
from an enthalpy balance. First, the increase
in air temperature due to the sensible heat of
steam was calculated and then the amount of
steam condensed in step (b) was determined.
Thus, the partial pressure of vapor, pfi, was
determined and S was calculated from:
S =
Saturated vapor pressure at T^
Transfer Coefficients
The transfer coefficients needed for predicting theoret-
ical values of penetration at the experimental conditions
are: h, , k,,, and hr. The values of these transfer coeffi-
L u b
cients were determined individually for each run.
The conditions for the gas and liquid flow rates,
temperatures and moisture contents were such that the net
heat and mass transfer were always from the gas phase to
the liquid phase. Under such conditions, the transfer
coefficients can be determined using Mickley's method,
described by A. S. Foust et al. (I960) and many others.
However, the conventional graphical approach is not suffi-
ciently accurate due to the curvature in the enthalpy-
temperature saturation curve in this range of gas and liquid
conditions.
A computer program was developed to evaluate coeffic-
ients for the experimental runs. The approach used was
essentially the same as the Mickley's method, except that
heat and mass transfer in the gas-phase were used separately
instead of being combined into gas-phase enthalpy transfer.
Also, instead of setting the Lewis number;
k' C
N = bG Pm
"
106
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
-------
equal to one, which is not valid when the water vapor con-
centration is high, the ratio ^G/\G was assumed to remain
constant for a run. This ratio was calculated from the
penetration theory correlation,
V*
(121)
kbG 1 1
hxr R Tr \P,
bG G ' i
DG
G« f ™-r*
pG G
cal
where, k = thermal conductivity of gas,
b sec-cm-°K;'
For the experimental conditions, this ratio changes by a
maximum of 5.26% (from 0.144 to 0.152 for Run No.'s 7 and 8)
for the inlet and exit conditions respectively. Thus, an
average value can be used for the ratio during a run, with-
out appreciable error.
After the value of k'/h. is determined from the method
ti LI
discussed above, h. is computed from a heat balance on the
LI
liquid bulk. "kup" and "h, .-," were then determined from
the values of h, , k/r/hT , and k' /h/r.
This approach incorporates the following assumptions:
1. The gas bubbles are spherical and are of a
constant diameter throughout the foam.
2. The bubbles are perfectly mixed internally.
3. The foam density is constant throughout the
foam layer on the plate.
4. The liquid bulk temperature is constant throughout
the foam, and is taken as the average temperature
between the liquid inlet and outlet stream.
5. All of the bubble surface area is available for
transfer mechanisms and this area lends itself
equally for both, heat and mass transfer.
6. The penetration theory adequately predicts the
ratio of the gas-phase mass transfer coefficient
to the heat transfer coefficient.
Note that the ratio is independent of the surface
renewal time.
107
A. P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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Accuracy of Measurements
1. Determining Overall Penetration:
The overall penetration, Pt was determined as:
rr _ weight gain on the outlet filter n??1
weight gain on the inlet filter
The analytical balance used has a precision of ±0.05 mg
W
Pt - °
Pt ~ W7
i
where, W is the weight gain on the filter.
d_Ft _ d WQ d w.
Pt W W.
o i
As the absolute values for the error are small compared
to the actual weights, we can say that,
A_P~t _ A WQ A W.
Ft w w.
o i
For calculating maximum error, the error terms are
considered to be additive. Thus,
_ AW AW.
Maximum error, Pt = + -
W W.
o i
The precision of the balance is ±0.05 mg.
the maximum values for AW = A W. = 0.1 me
o i 6
Minimum values for W = W. = 5 mg.
Maximum error, Pt = ± ^-^- = ±4%.
O
In the range of experimental conditions, the maximum
error in determining Pt is ±4$.
108
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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2. Determining Particle Characteristics:
The particle characteristics determined were:
(a) particle concentration, (b) particle size distribu-
tion.
(a) The particle concentrations were measured from
the weight gain during filter sampling. The
analytical balance used to weigh the filter
paper had a precision of ±0.05 mg. Most runs
lasted 30 minutes out of which the end effects
did not take more than 0.08 minutes, or 0.27%
of the sampling time. The rotameters are
rated for accuracy in flow measurement at
±5% the maximum error expected in determining
the particle mass concentration is ±12.27% for
a 5.0 mg sample on the filter.
(b) During the experimentation, the size distri-
bution measured was; d = 0.7 ym, a = 1.22
pg S
by the Anderson sampler. An analysis of the
Anderson sampler performance for determining
size distribution of nearly monodisperse
aerosols has shown that the "a " value indi-
cated by the sampler would be higher than the
actual "a " of the aerosol. The actual "a "
8 g
value es expected to be between 1.0 and 1.22.
Particle size data taken with the Climet instrument are
not included in this report because they were not suffic-
iently reproducible. Operating problems with the counter
and the sample dilution apparatus required that the instru-
ment be sent back to the manufacturer several times for
repairs. During the time the instrument was operable the
data obtained were not consistent. Therefore, major re-
liance had to be placed on sizing with the cascade impactor.
3. Air Flow Rate:
The air flow rate was determined by a venturi-
meter. The venturi-meter was calibrated using a pitot tube.
The maximum error in the flow rate calibration is expected
to be ±5% as rated by the manufacturer.
4. Water Flow Rate:
The water flow rate was measured by rotameters in
109
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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the line. These were calibrated in the laboratory and the
maximum error is expected to be II of the maximum flow
rate.
EXPERIMENTAL RESULTS
The experimental conditions and results are shown in
Table V. It was desired to use a high liquid to gas flow-
rate ratio (L/G) so as to maintain a low liquid temperature
on the sieve plate which permits a high driving force for
vapor condensation on the bubble wall. An average (L/G)
ratio of 7.7 (£/m3) was maintained for runs 1 to 6. This
was the highest (L/G) value that could be employed without
entering the weeping and raining regions of the sieve-
plate. The (L/G) ratio was decreased to an average value
of 3.53 (Jl/m3) for runs 7 and 8.
Two sampling runs were made for each set of experi-
mental conditions. The air was maintained unsaturated
for runs 1 and 2. The air temperature was then decreased
keeping the humidity unchanged for runs 3 and 4. The
effect of increasing the humidity at the original air
temperature was studied in runs 5 and 6. Runs 7 and 8
were for a different set of experimental conditions.
Discussion
Collection Mechanisms: The experimental Ft values are
the ratios of outlet to inlet particle mass concentrations
as determined from weight gains on sampling filters, as
explained earlier. For the experimental conditions, the
collection can be attributed to the combined effects of:
impaction during bubble formation, diffusiophoresis, thermo-
phoresis, diffusion, and particle growth due to condensa-
tion resulting in a higher centrifugal force. Thus, Pt
can be expressed as:
Ft = Ftp x PtD x PtT x PtBD x Ptc (123)
For runs 1 to 6, where the flow conditions are approximately
identical, the following observations can be made:
1. Ptp will be the same for these runs and was
calculated at 963.
2. For these runs, the temperature gradients were
not substantially different and were quite small.
Thus Pt™ was high and nearly the same for all
the runs.
110
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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Table V
EXPERIMENTAL CONDITIONS AND RESULTS
Run
Mo.
1
2
3
4
S
6
7
8
Air*
Flow-
Rate
(m'/min)
x 10
3.60
3.60
3.66
3.66
3.66
3.66
5.10
5.10
Water
Flow-
Rate
(liters/
mm)
2.92
2.92
2.88
2.88
2.62
2.62
2.35
2.46
Particle
Concen-
tration
xlO'5
(»/cc)
2.3
2.4
1.9
2.3
4 .6
4.4
4.7
4.0
Gas Conditions
Inlet
T ,.
di
CC)
41
41
33
33
41
41
47
42
*i
0.059
0.064
0.057
0.059
0.095
0.095
0.111
0.111
Exit
Tde
(°C)
24
25
24
24
28
28
29
29
ye
0.031
0.032
0.031
0.031
0.039
0.039
0.042
0.042
Water Temps .
TLi
(8C)
17.9
17.9
17.9
17.9
17.8
17.8
16.0
16.8
TLO
(°C3
19.1
19.1
19.0
19.0
20.0
20.0
21.5
19.0
S
0.73
0.78
1.09
1.12
1.13
1.13
0.93
1.21
y . -y
7 i ' e
0.028
0.032
0.026
0.028
0.056
0.056
0.069
0.069
Pt
exp
(*}
89.0
86.6
86.4
82.2
72.9
69.1
84.4
81.9
Pttheo
(%)
94.0
90.8
88.3
87.0
84.7
84.7
84.8
74.2
hexp
Ccm)
5.0
5.0
4.7
4.7
4.8
4.8
6.4
7.6
htheo
Ccm]
7.6
9.2
7.2
7.6
8.4
8.1
10.2
9.7
* a 20°C, 1 atm.
_ g-mole vapor
g-mole dry air
A. P. T. Inc.
111
POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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3. For the particle s:i_ze used, in the range of
0.5 ym to 1.0 urn, PtgD was insignificant and
can be neelected.
can be neglected.
4. It is possible that Ftp was nearly the same
for all the runs and quite high, as the DBF
particles are not highly wettable and would
require a saturation ratio larger than per-
haps 1.9 in order for water to condense on
them. The saturation ratio in the bulk of
the gas phase did not go much higher than
1.0.
The results indicate that diffusiophoresis is the major
contributor to particle collection efficiency for a single
p_late. The contributions of the rest of the phenomena to
Ft will remain approximately the same for all the runs.
Ptn depends on the amount of vapor condensed, which can be
expressed as (y. - y ), or the gmole of vapor condensed
per gmole of dry air. Figure 24 is a plot_of Ft vs.
(y. - y ) for runs 1 to 6, and also shows Ftp due to im-
paction during bubble formation, under the experimental
conditions .
Comparing Ft values for runs 1 and 2 with runs 3
and 4, we see that for approximately the same water vapor
concentrations, the penetration is lower for the lower gas
temperatures. This is also observed by comparing run 7
with run 8. Comparing runs 1 and 2 with runs 5 and 6 shows
that the penetration is lower when the water vapor concentra-
tion is increased at the same temperature. It is also
evident from Table V that the penetration decreases as the
saturation ratio, S, increases.
However, further experimental studies under wider
ranges of operating conditions are needed before the trend
of Ft with any of the parameters can be generalized.
Comparison of results with predictions
The model for collection in a sieve plate scrubber,
described earlier was used to predict the theoretical
penetration, Pttueo> for the experimental conditions. It
was found that the model will satisfactorily predict the
112
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE. CA. 92502
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0.01
0.02
0.03
0.04
0.05
0.06
g-mol vapor condensed
' g-mol dry air
Figure 24 - Particle penetration versus water
vapor condensed.
A. P. T. Inc.
113
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general form and magnitude of experimental results if the
proper heat and mass transfer coefficients are used. The
heat and mass transfer coefficients, h., k/G and h,-,, were
determined individually for each run. The calculation pro-
cedure is shown in an earlier section and the resulting
coefficients are shown in Table VI.
The results for runs 2 to 8 are comparable to the
values predicted by the penetration theory for k/r and
hbG; 1.6xlO-VpBM and 2.2xlO-2//TG respectively. The
values for "h," are approximately 10~2 times the corres-
ponding value predicted by the penetration theory, 0.31.
This indicates that the assumptions regarding the bubble
area available for transfer, the bubble diameter, liquid
temperature, liquid surface renewal time, and the consis-
tency of the foam density may be in error. The resolution
of this question will require additional experimental and
computational work.
Pt , values were then calculated for the experimen-
tal runs, using the corresponding experimental values of
transfer coefficients. The Pt . values, together with
the foam height, h , , indicated by the model to reach
the exit gas temperature, are listed in Table V with the
corresponding experimental conditions. The difference in
^exo ant* ^theo va-'-ues indicate that the assumptions re-
garding the bubble diameter area available for transfer
and the consistency of the foam density may be in error.
These questions could only be resolved by experimentation
under highly controlled conditions as indicated earlier.
Pttheo is Plotted against Pt on Figure 25. Except
for run 8, Pit . was higher than Pt
theo & exp
To check if the difference between Pt.,, and Ft
theo exp
was only due to statistical scatter in the data, the follow-
ing assumptions were made:
1. Pttheo values correctly and uniquely represent
the penetration for any set of experimental
conditions examined. The experimental conditions
dp not change during an experimental run. Thus,
Pttheo rePresent th-e mean of Pt values for any
set of experimental conditions.
114
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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1.0
0.9
0.8
u
HH
E-
O
w
0.6
0.5
00
0.5 0.6 0.7 0.8 0.9 1.0
EXPERIMENTAL Pt
Figure 25 - Theoretical versus experimental
penetration.
115
A. P. T. Inc.
POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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Table VI
TRANSFER COEFFICIENTS DETERMINED BY
MICKLEY'S METHOD
Run
No.
1
2
3
4
5
6
7
8
h.xlO3
L
1.84
2.09
2.56
2.52
2.54
2.54
3.57
3.57
kbGXl°"
14.72
2.09
2.04
2.02
2.54
2.54
2.50
2.50
hbG/T^x
16.72
2.48
2.32
2.29
2.95
2.95
3.00
3.00
116
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2. Pt values are normally distributed about
C A L/ ^^_
the mean (or pttheo) for any set of experi-
mental conditions.
Thus, the standard error between Pttheo and
6.6%. As this error is higher than the maximum experimental
error, 4%, our assumption that Pt,, is the true mean of
Pt values is incorrect.
exp
Noting that Pt values are normally distributed, the
GXp
probability of obtaining less than two observations on the
negative side of the mean, in a sample of eight observations,
is 0.035. The lowjjrobability indicates that there is a
positive bias for Pt values, when compared to P~ttu
More experimental data are needed if the statistical rela-
tion between Pt., and Pt is to be studied more
theo exp
rigorously.
Overall, the comparison of experimental data with
predictions based on our mathematical model shows that the
model is capable of giving useful and realistic results.
While additional refinement, as discussed above, is needed,
the model can account for what is observed experimentally
and gives us a good tool for interpreting what we see and
utilizing this knowledge for engineering design of practical
equipment.
117
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ECONOMIC FEASIBILITY
The technological feasibility of FF/C scrubbing has
been discussed in previous sections and it is clear that
fine particles can be collected with high efficiency by
this means. Both diffusiophoresis and particle growth by
condensation are practically insensitive to particle size
and they are the most important factors in FF/C scrubbing.
What remains to be shown is whether the cost is low enough.
The following section deals with the question of economic
feasibility, with the object of determining some broad
outlines of the cost picture. Two specific cases of in-
dustrial applications for FF/C scrubbing were studied and
preliminary process designs and cost estimates are des-
cribed .
Before getting into the details of case studies it is
instructive to consider some general features of FF/C
scrubbing. Both the theoretical and experimental results
indicate that it should require a minimum of about 0.1 or
0.15 g water condensed/g dry gas in order to grow particles
to about 2.0 ym diameter if the concentration is about
107/cm3. The experimental data show a penetration of about
70% at a steam condensation of about 0.035 g/g for
n - 105 entering one sieve plate.
The computer runs show the effect of steam condensing
on the liquid as well as the particles, which raises the
steam consumption for a given increase in particle size.
These runs indicate that steam condensation of about
0.06 g/g would cause growth to r = 0.85 urn for n = 106/cm3
(see run #4 for sheets, Table IVj and about 0.14 g/g would
cause growth to r 1.4 um for n = 107/cm3 (see run #17
for plates, Table III). In contrast, we may note that if
all the steam condensed on the particles, it would take
0.033 g/g condensed to grow 107 particles/cm3 to r = 1.0 ym.
For illustrative purposes, we may take 0.15 g/g as rep-
resenting a low practical steam condensation rate. If steam
costs $1.32/1,000 Kg ($0.60/1,000 Ib), FF/C scrubbing would
cost $0.20/1,000 Kg ($0.24/1,000 m3) of dry gas for steam
alone. A venturi scrubber which had a performance capabil-
ity of 80% efficiency on 0.5 ym diameter particles with
118
A. P. T. InC POST OFFICE BOX 71. RIVERSIDE, CA. 92502
-------
density of 1.0 g/cm3 would require a pressure drop of about
450 cm W.C. (see S.H.B. Figure 5.3.6-9). The scrubbing
power cost for this pressure drop would be about
$0.24/1,000 m3 if electricity cost l.Of/K.W.H. Thus, the
costs for FF/C and high-energy scrubbing are fairly close
for this example and will be more favorable for FF/C scrub-
bing as the collection efficiency requirement becomes more
stringent.
It is clear from the above example that FF/C scrubbing
might or might not afford to pay for steam, depending on the
particle size and concentration, and the required perform-
ance. The next question is whether cooling water costs are
acceptable. There is a wide range of cooling water costs
given in the literature; from about 0.25^/m3 to 3.9
-------
in this report. Heat and mass transfer coefficient and the
critical saturation values required for nucleation were
either based on experimental data or calculated and checked
against similar coefficients for similar cases.
The capital and especially the operating costs of the
FF/C scrubber vary according to geographical location,
availability of cold water and climatic conditions. Our
estimations are based on the availability of water at 20°C.
The calculations were made for large industrial plants
and this assumes that one could satisfactorily scale-up
processes which have been studied only in the laboratory.
Accepted scale-up methods were used to extrapolate the
laboratory results to the industrial scale.
BASIC OXYGEN FURNACE EMISSION CONTROL
In recent years the use of the Basic Oxygen Furnace
(B.O.F.) is increasing among the various steelmaking pro-
cesses. The major reason for its wide acceptance is its
short cycle which lasts about 50 minutes. The Basic Oxygen
Furnaces vary in size from less than 50 ton/heat to over 400
ton/heat with 200-250 ton/heat being a common size. During
about twenty minutes of each cycle oxygen is blown into the
bath and that is when the flue gas reaches a temperature of
over 1,480°C. The reason for this high temperature lies in
the high CO content of the flue gas.
Because of the low fuel value and hazardous properties
of CO, in most U.S. plants air is permitted to leak into the
systems at the hood inlet in order to burn the CO to CO-.
In most foreign countries the CO is used either for its heat
value or for chemical synthesis. This is done in one of two
ways: 1. The gases containing the CO are cleaned and then
transferred for further use. 2. The CO is burned to C02 as
in most U.S. processes but the heat recovered in a waste
heat boiler.
The gas stream leaving the B.O.F. during the first part
of the cycle contain less dust, mainly kish, and is at a
lower temperature. During the period when oxygen is blown
the flue gas is hot and its dust load is as high as 45-90
grams per standard cubic meter of dry gas. The dust con-
sists mainly of iron oxides, slag and other metallic oxide
fumes.
120
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Present Control Methods
Venturi scrubbers and electrostatic precipitators are
presently used to control B.O.F. emission. Both have their
advantages and disadvantages and one is not preferred over
the other. When electrostatic precipitators are used the
hot gases are first cooled to 320°C in an evaporation
chamber or a spark box. The evaporation chamber is fol-
lowed by a drop-out box where the larger dust particles
settle. In the spark box excess water is sprayed and the
large dust particles settle together with the excess
water and are removed from the system. The dirty gases
now at 320°C enter the electrostatic precipitator, are
drawn by the fan and sent out through the stack.
When high energy venturi scrubbers are used to clean
the gas, the gas is also first cooled by water injection.
Concurrently the large particles are removed from the gas
and the water sludge is drained. The gas then enters a
venturi scrubber followed by an entrainment separator. In
most cases the gas is further cooled in a cooling section
to increase its density and as a result the fan efficiency.
The cold gases enter the fan that emit them through a stack
to the atmosphere.
Background Data
Information regarding the B.O.F. process, dust load
and particle size distribution were collected from the
following sources: Battelle report to NAPCA on the Iron and
Steel Industry (1969), an article by H. C. Henschen (1968),
M.R.I, report on particulate emissions (1971) and SRI Manual
of Electrostatic Precipitators Technology (1970).
The dust load coming out of the B.O.F. ranges from
45-90 grams/standard dry cubic meter of gas. Most air pol-
lution control agencies require that the dust concentration
in the outlet gas not exceed 0.115 gram/standard dry cubic
meter of gas (which is practically invisible). Thus a col-
lection efficiency of 99.741 to 99.87$ is required. The
dust particle size distribution is reported by M.R.I, to
have a mass median diameter of 0.095 ym and a geometric
standard deviation of a = 2.3. The dust composition and
properties were also taken from the M.R.I, report.
121
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For design purposes we shall consider a shop which con-
sists of two 250 ton vessels, one of which is assumed to be
in operation while the other is assumed to be shut down for
relining. Such a shop makes about 30 heats of steel a day
or one every 48 minutes. During about 20 minutes of each
cycle oxygen is blown into the bath at a rate of
710.0 mVmin (25,000 CFM) . About 3.75 ton of dust, mostly
oxides of iron, are discharged from the vessel during the
blowing period. During the majority of the blowing period
the gas discharging from the furnace mouth is at =1,500°C
and contains 90% CO and 10$ CO,. Upon combustion with the
theoretical quantity of air a temperature in excess of
2,000°C can be developed at the furnace mouth. For calcu-
lation purposes we assumed the gas temperature when enter-
ing quenchers to be constant at =1,500°C during the hot
part of the cycle. (We shall consider later the beginning
and end of the cycle when the gas temperature is lower.) At
this temperature the gas flow rate is 29,400 actual cubic
meter per minute (1.04xl06 ACFM).
Steam addition is beneficial for efficient operation of
the FF/C scrubber if it can increase the saturation ratio
above 1.0. For this example we will assume that it can be
done .
An alternative approach would be to saturate the gas
by direct contact with water sprays and dispense with the
steam generation and storage apparatus. This may be
superior economically and it might also be that the specific
nature of the particulates makes it impossible to sustain a
saturation ratio higher than 1,0 so that the indirect gener-
ation of steam for addition to the gas would have no benefit,
The sensible heat of the flue gases will be utilized in
three ways: a. A steam production in a waste heat boiler.
b. Air reheat at the tail end of the process to prevent
steam plume and give the gas additional buoyancy, c. Gas
saturation with water vapor by spraying water into the gas
in a saturation chamber.
From these operating conditions and with the use of
material and energy balances the process flowsheet illustra-
ted schematically in Figure 26 was calculated. The calcu-
lation method we have developed for a FF/C spray tower
scrubber could now be used to calculate the scrubber perform-
ance. Particle growth was calculated based on a critical
supersaturation of one.
122
A. P. T. InC. POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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I
WATER
WATER
WATER
TO STACK
I
FROM
B.O.F.
t . tv
1
V
••^•^•B
o
o
o
_y
S
>
. rv
7 L
\ V
SATURATOR
e
u
c
»-
^~
O
L
f
*
7
STEAM
ACCUMULATOR
9
OUJT JUJ\'
SATURATOR
i
-------
A heat balance shows that enough steam is produced
during the high temperature part of the cycle to supply the
needs of the whole cycle. Steam accumulators are required
to store the excess steam which is generated during the hot
period. The clean, cool gas now enters the fan which trans-
fers it through a reheater and a stack to the atmosphere.
The reheater was calculated based on the TVA experiments
that warming the flue gases by 50°F is enough to prevent
visible steam condensation when the ambient temperature
ranges between 50°F and 80°F.
Since the purpose of this study is to show how FF/C
scrubber compares with other control equipment a common
ground for comparison was sought. No attempt was made to
optimize the system and the only changes made were those
necessary for the FF/C scrubber to work adequately.
Capital cost information came from the following
sources: Battelle report (1969), Swindell and Dressier
study (1969), A.P.T. Scrubber Handbook (1972), Cost
Engineering i.n the Process Industries (1960) and Modern
Cost Engineering Techniques (1970) . The method used to
calculate the capital costs is the one described in: "Data
Techniques for Preliminary Capital Cost Estimating" by
K. M. Guthrie, Modern Cost Engineering Techniques! The
method is based on calculating the F.O.B. equipment cost
and the multiplying by various factors for materials,
labor, indirect costs, contingency, and fee. The capital
cost was then adjusted to a common time base. The Chemical
Engineering Plant Cost Index was used to account for cost
changes with time.
Cost of FF/C System
Equipment for the system shown schematically in
Figure 27 and discussed above was selected and sized for
the purpose of cost estimation. A summary of the results
of- this process design and cost estimation are as
follows:
124
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Capital Cost:
Tubular Membrane Hood (estimated from
the cost of waste heat boilers) $690,000
Steam Accumulators, 3 vessels, 1.0 m
dia. x 25.0 m long 513,000
Saturator 4.6m dia x 30.0m long 53,000
Spray Tower (3.0 m high) 218,000
Reheater (300 m2 area) 96,000
Blower (1,300 HP) 100,000
Subtotal $1,670,000
Piping 8 91 of total 150,000
Total $1,820,000
Annual Operating Costs:
Maintenance @4I of capital cost $ 73,000
Capital expenses and depreciation
@20% of capital cost 364,000
Plant O.H. @ $0.10/ACFM-year 50,000
Power @$0.011/hw-hr 104,000
Water: 247 gpm @ $.40/Mgal 47,500
2000 gpm 9 $.lS/Mgal 144,000
Labor: 8000 hrs @ $5/hr 40,000
TOTAL $ 822,500
There is no charge for steam in the operating costs
since the gas sensible heat is used for steam production.
The water and boiler costs are included in their proper
places.
125
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TABLE VII
B.O.F. CONTROL SYSTEM COSTS
Item
Electrostatic
Precipitator
Capital Cost
Annual Cost
Fabric Filter
Capital Cost
Annual Cost
High Energy
Scrubber
Capital Cost
Annual Cost
M.R.I.
Report
$4,900,000
1,660,000
4,500,000
1,260,000
6,000,000
2,360,000
Swindell-
Dressier
Report
$4,150,000
1,520,000
3,200,000
1,160,000
3,800,000
1,850,000
S.R.I.
Report
$5,000,000
FF/C Scrubber Costs by A.P.T., Inc.
Capital Cost $1,820,000
Annual Cost $ 822,500
126
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POST OFFICE BOX 71. RIVERSIDE, CA. 92502
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For comparison, the costs presented by Midwest Research
Institute, Swindell-Dressier and Southern Research Institute
are given in Table VII. The costs quoted can be reduced by
various manipulations, such as assuming two B.O.F. furnaces
operating at staggered intervals, etc. However, to obtain
a comparison between the three alternatives the same condi-
tions were assumed for all three control equipments, which
would not necessarily lead to the lowest conceivable costs.
KRAFT RECOVERY FURNACE CONTROL
Characteristic air-pollution problems of the pulp in-
dustry are associated with the release of malodorous sulfur
compounds and particulate matter. Pulp is made by either
the sulfate (kraft), sulfite, semichemical, soda, or by a
mechanical process. Most of the pulp produced in the
United States is made by the kraft process. In the follow-
ing we shall examine the economics of using a FF/C scrubber
to control the fine particles emitted from the recovery
furnace in the kraft process.
The chemical pulping process known as Kraft pulping,
employs a cooking liquor whose main ingredients are sodium
sulfide and sodium hydroxide in solution.
The spent cooking liquor is black from the lignin,
waste fibers, and dissolved sulfide salts--hence called
"black liquor". Vitally important to the economics of the
kraft process is the recovery and recycle of inorganic
chemicals in the black liquor. To accomplish chemical
recovery, black liquor is concentrated by evaporation and
burned in recovery furnaces. Most of the organic and in-
organic sulfur is reduced in the lower oxygen-poor region
of the furnace to form an ash or smelt of molten chemicals,
primarily sodium sulfide and carbonate.
Recovery furnaces also produce valuable process steam
from the heat of the burning black liquor. Hot gases from
the combustion zone relinquish most of their heat energy in
passing over boiler tubes and heat economizers. Steam may
be used elsewhere in the pulp-making process or sent to
turbines for electrical power generation. Additional
utilization of the furnace heat is accomplished by the use
of a direct contact evaporator. Such an evaporator util-
izes the heat of the flue gases to further evaporate black
liquor just prior to its firing in the recovery furnace.
127
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Direct contact evaporation has one serious drawback,
however, from an air-pollution standpoint--the stripping
of hydrogen sulfide which occurs when acidic flue gases
contact the black liquor. Following the direct contact
evaporator, furnace gases pass through collectors (such as
electrostatic precipitators and scrubbers) to remove par-
ticulate matter consisting of sodium salts and carbon
particles. Exhaust gases containing the remaining par-
ticulates, plus the malodorous sulfur compounds, then pass
to the atmosphere.
When the black liquor is burned in the furnace, an
appreciable quantity of particulate is liberated. Chemical
content of the solids entrained in the recovery furnace
flue gases is a function of furnace operating conditions
and feed liquor composition. Usually Na2SO., Na-CO.., and
NaCl in the fume can vary greatly from mill to mill. For
example, NaCl is present in measurable quantities when logs
have been stored in salt water before chipping; inland mills
have less NaCl passing through the recovery system. The
SRI Manual of Electrostatic Precipitator Technology (1972) •
presents size distribution data obtained from electron
microscope pictures. The mass median particle diameter
is 1.94 urn and the geometric standard deviation is 2.06.
All the particles emitted from the recovery furnace
are soluble and do not require supersaturation for growth.
They will even grow when the saturation ratio is less than
1.0 (=80% of the particles are Na^SO. which will start grow-
ing at a relative humidity of =901).
To use a condensation scrubber advantageously, the size
of the waste heat boiler is increased and the exit tempera-
ture of the flue gases is reduced to =120°C. The gases then
flow through a waste heat recovery venturi evaporator and
into the condensation scrubber system as shown in Figure 27.
A surface condenser (heat exchanger) was selected to con-
dense most of the water vapor from the gas stream leaving
the cyclone separator following the venturi evaporator. The
purpose of this condenser is to isolate the condensate liquid
which contains dissolved salts so that it can be recycled to
the process without requiring concentration and so that the
cooling water can be kept clean. An alternative approach
would be to use a direct contact condenser and circulate the
condenser coolant liquid through the tubes of an evaporative
type cooler.
128
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28.2 m3/min
Cool ing
Water
TJ
O
CO
O
-n
Tl
O
X
-j
Reco ve ry
Furnace
Gas
Stream Am3
1
^-
i
Venturi
k
1 4
fc
^>s
Cyclone
^
Concentrated V
Liquid J
/mm T °C
1 14,000 121
2 12,700 74
3 9,900 60
4 9 , 800 60
Condenser
^
J
-^
-*•
1
Spray
Scrubber
3
r
+
Sump
1
r
-O
4 To
Re cycle
Liquid
Recycle
Liquid
m
3)
CA
O
m
O
Figure 27 - Flowsheet for FF/C scrubber on
Kraft liquor recovery furnace.
to
ro
in
o
-------
Spray scrubber liquid would recirculate at nearly
constant temperature and with makeup liquid flow rate
being equal to the rate of blow-down liquid flow back to
the process. Particle collection efficiency in the spray
scrubber would be 95% for the design shown; in order to
be comparable to one of the alternatives given by Hendrick
son et al. (see below). Because the major collection mech-
anism active in the scrubber would be inertial impaction
of the grown particles, the scrubber penetration could be
decreased by increasing liquid rate or contact length, or
by appropriately changing other factors. It would be
possible to decrease penetration from 5.01 to 0.25% by
doubling scrubber length, for example.
Much information regarding emission control in the
wood pulping industry is found in the report "Control of
Atmospheric Emissions in the Wood Pulping Industry",
E. R. Hendrickson et al., (1970). In that study, they
presented the economics for several processes for up-
grading the performance of existing Kraft furnace air
pollution control systems. Costs for two of these
processes will be compared with costs for the FF/C scrub-
bing system described above. Inlet gas flow rates,
temperatures, particulate loadings and other pulping
process conditions are the same for the FF/C system and
the two alternatives listed below:
1. Increase the collection efficiency of an
existing system by converting an existing
venturi scrubber to a low efficiency
(about 50%) venturi/cyclone evaporator
and adding a 99% efficiency electrostatic
precipitator.
2. Make the same change as in No. 1, except
add a 971 efficiency second stage venturi
rather than the electrostatic precipitator.
The FF/C system is also based on the change to a
venturi/cyclone evaporator. Costs for the FF/C system
were computed to be as follows:
130
A. P. T. Inc. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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Capital Investment
Condenser (7,500 m2 area) $400,000
Spray Scrubber (4m high, concrete
lined) 160,000
Pumps (4x7.5 m'/min) 40,000
Stack 11,600
(piping costs are included above)
Total $611,000
Annual Costs
Capital cost and depreciation $121,500
Cooling water @ 1.25
-------
It can be seen that within the accuracy of this kind
of estimate the venturi and the FF/C add-on systems are
about even. If high efficiency were required, however, the
FF/C system could decidedly surpass either of the other
two systems because the major additional expense required
would be for another scrubber increment. Thus the addition-
al capital investment would be about $160,000 and the
additional annual operating cost would be perhaps $40,000.
132
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FUTURE RESEARCH RECOMMENDATION
The primary objective of investigating the feasibility
of FF/C scrubbing has been achieved with a clearly affirma-
tive result. It has been shown in the present program that
FF/C scrubbing can remove fine particles at high efficiency
and that, within some limitations, it is more economical
than other means of particle collection. Mathematical
modeling of the many simultaneous phenomena taking place
in an FF/C scrubber has been accomplished for some important
unit mechanisms, although several coefficients remain to be
fitted to experimental data.
In accordance with the original objective of selecting
and performing a brief exploratory experiment of significant
nature, our experimental work extended over a narrow range
of conditions. Within this range the agreement between
theoretical predictions and experimental results for parti-
cle collection is fairly good, once the heat and mass
transfer coefficients are evaluated from experimental data.
However, despite the good agreement, theoretical predictions
of collection efficiency for plates are consistently higher
than the experimental results. This, along with the dis-
crepancy between computed and predicted liquid phase heat
transfer coefficients, indicates that the mathematical
model for bubbles should be revised.
To achieve the objective of building a working FF/C
scrubber, development work will be required in three main
areas:
1. Complete the experimental evaluations and
development of the theoretical models for
bubbles, sheets, and drops.
2. Define and develop an optimal FF/C scrubber,
based on the improved design methods.
3. Build a pilot plant scale unit of the proposed
optimum FF/C scrubber. Test the pilot unit in
the laboratory and under actual operating
conditions in the field.
The rest of this section will be devoted to a detailed
discussion of these three topics.
133
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EVALUATION OF THEORETICAL MODELS
Our present model for hubbies (i.e., plate type
devices), when compared to experimental results, presents
two major questions:
A. Why is the computed liquid phase heat
transfer coefficient so low in comparison
to the predicted coefficient?
B. Why is the predicted particle penetration
higher than the experimental?
Possible explanations to these questions may be:
1. Incorrect estimate of the heat and mass
transfer area.
2. Low estimate of liquid surface temperature,
if co-current flow of liquid with rising
bubbles is significant.
3. Unusual sieve plate design and operating
conditions have caused a significant
departure from customary behavior.
4, Different bubble shape and gas dynamics
cause different transfer rates and particle
deposition by centrifugal force.
5. Measurement problems may introduce errors.
In order to resolve the questions raised up to this
point, it will be necessary to perform experiments which
provide the following features:
1. Particles used for tests should have a range of
surface properties and high enough vapor pressure
that gas temperature of 80°C will cause negligible
vaporization.
2. Wettable particles should be used in some runs
so that the effect of growth can be clearly
identified. These runs should be at relatively
low saturations, such as were used for D.B.P.
aerosol in the runs reported here.
134
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3. Large water vapor concentration gradients
should be used under conditions such that
saturation is low enough to avoid condensation
on particles. This could be achieved through
the use of high gas and liquid temperatures
with non-wettable particles.
4. Sieve plates with more customary dimensions
as for mass transfer, should be used and
operated at usual gas velocities.
5. Packed columns should be used to validate the
"liquid sheets" model. The more defineable
transfer surface area and liquid renewal time
for packings as compared to plates will enable
a less equivocal interpretation of particle
penetration and transport rate data.
We consider this extension of the work on bubbles and
sheets important since it will test the assumptions made
in deriving the theoretical model. Once they are either
proven or modified so as to be valid, the concepts from
these models can be used to derive unit mechanism equations
for other geometries.
DEFINE AND DEVELOP AN OPTIMAL FF/C SCRUBBER
To design an efficient and economical FF/C scrubber
one should attempt to optimize the geometric configurations,
the method by which the desired saturation ratio is achieved
and the combination of collectors to achieve various stages
of particle separation.
In the work done to date, various unit mechanism equa-
tions were derived. The next step is to integrate these
equations so that they describe a scrubber. For example,
the unit mechanism equation for the collection of particles
by drops can be integrated into a venturi type design, a
spray column, an ejector venturi, part of a wet cyclone, an
impingement and entrainment scrubber or a moving bed scrub-
ber. Collection by sheets can be integrated into packed
bed scrubbers, baffle and secondary flow scrubbers or
similar designs. Similarly, the bubble model is the basis
for various plate type devices. Devices which combine
several unit mechanisms can also be explored through mathe-
matical modeling. Only after this is done can we say which
135
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device best utilizes the FF/C effects and is most efficient
and economical.
It follows from our present models that saturation and
particle growth are very important. The economics of the
scrubber may depend in the final analysis, on our ability
to obtain the required saturation ratio in a large enough
fraction of the aerosol, to permit nucleation and growth
of almost all the particles.
Several ways to achieve the required degree of satura-
tion have been described previously. All possible ways
should be checked for each device until the method most
suitable is found. It is quite probable that no single
method would be best in all cases and different methods will
better suit different aerosols. Approaches such as the
alteration of particle wettability by means of a pre-
treatment in which there is some absorption of a surface
conditioning should be explored.
Once a scrubber geometry most suitable for particle
collection and the formation of the desired saturation
ratio has been defined, it becomes a straight-forward
matter to build the scrubber. This scrubber should then
be tested in the laboratory under controlled conditions in
order to determine whether theoretical predictions and
experimental findings agree. It could be expected that
during these tests further modifications will make the
scrubber a more efficient one.
FIELD TESTS OF PILOT SCALE FF/C SCRUBBER
The efficiency and economics of FF/C scrubbers are
much more sensitive to the properties of the dust being
removed and to the presence of small condensation nuclei
than most other scrubbers. For this reason field tests on
various dusts emanating from different sources are necessary,
A good way to obtain these results is to build a mobile FF/C
scrubber and test it on various industrial sources. These
field tests will give us valuable information on the be-
havior and economics of FF/C scrubbers when the dust is
neither uniform nor monodisperse. Further, the effects of
trace components, process variations, and other practical
complications will become known.
An important adjunct of the field tests should be the
development and proving-out of analytical methods for the
136
A.P. T. InC. POST OFFICE BOX 71, RIVERSIDE. CA. 92502
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definition of all significant properties of the source.
For example, it is of special importance that we be able
to measure the particle number concentration, the critical
saturation ratio, and the number of condensation nuclei;
in addition to the usual size distribution, etc. The
ultimate aim should be to eliminate the need for pilot test
ing in order to determine FF/C scrubbing feasibility.
Another round of process design and economic evalua-
tion should be performed after the pilot study information
has been obtained and assimilated. The accuracy of cost
estimates is highly dependent on the amount of process
detail available and o'n the specificity of equipment defi-
nition. Items such as cooling towers, water treatment,
and large (and cheap) heat exchangers are very significant
in the FF/C process economics and should be studied in
detail.
It should be noted that the program reported here did
not stop with the termination of the contract period of
performance. Additional work to answer some of the ques-
tions discussed here has been funded under another contract,
137
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,3
GLOSSARY
a - constant defined by equation (12)
a, - specific surface area of bubble, cm"1
A - area of plate, cm2
b - constant defined by equation (13)
B - dimensionless parameter defined by equation 4-38
c - mass concentration Kg/m3 or g/cm3
c. - molar concentration, gmol/cnr
CT - Cunningham correction factor, dimensionless
C - specific heat, kcal/kg-°C or cal/g-°C
C - temperature jump coefficient, = 2.3, dimensionless
C - isothermal slip coefficient, = 1.25, dimensionless
d - diameter, m or cm
D - diffusivity, cm2/sec
D - particle diffusivity for Brownian diffusion, cm2/sec
F - fraction of the total condensing vapor which condense
on the drops.
F - f]ux force in "x" direction, dynes
.A
F - foam density, ratio of clear liquid height to total
foam height.
G - gas flow rate, gmol/cm2-sec
Gp - dimensionless quantity defined by equation (14), (18)
or (24)
h - heat transfer coefficient, cal/sec-cm2-°C
I - integral defined by equation 4-40
i - Van't Hoff factor
144
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J - dimensionless parameter defined by equation 4-45
k. - thermal conductivity of substance A, cal/sec-cm-°C
k1 - mass transfer coefficient, gmol/cm2-sec-atm
KD - diffusiophoresis constant defined by equation (94)
Kp - overall gas phase transfer coefficient gmol/sec-atm-cm2
K - inertia parameter defined by equation (24)
K - particle flux coefficient for Brownian diffusion,
p cm/sec
KT - thermophoresis constant defined by equation (99)
L - liquid mass flowrate, kg/sec or g/sec
L,. - latent heat of vaporization cal/g
m - mass, kg or g
m - moles of solute in a drop, gmol/drop
M - molecular weight, kg/kgmol or g/gmol
n - particle number concentration, no./cm3
N - mass flux, kg/m2-sec or g/cm2-sec
N - particle flux, no./cm2-sec or g/cm2-sec
N B - particle flux due to Brownian diffusion, no./cmz-sec
p - partial pressure of solute, mbar or atm
p M - mean partial pressure of non-transferring gas, atm
Pt - penetration (one minus efficiency), fraction or
percent
Ptc, Ptn, and PtT are defined in equations (42), (43) and (44)
q - mass vapor condensed per mass particles, g/g
Q - volumetric flow rate, mVsec, cm3/sec or JL/sec
145
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Q - heat transferred per unit cross-section area of
column, cal/cm2
r - radius, cm or ym
r' - dimensionless particle radius Ln equation
R - ideal gas law constant
R - effective radius of curvature
c
s - distance from jet nozzle to plate, cm
S - saturation ratio, atm/atm
t - time, sec
T - temperature, °K (or °C, where specified)
T' - dimensionless temperature in equation (89)
u - velocity, m/sec or cm/sec
v - velocity, cm/sec
v_ - liquid flow rate per unit width, cm3/sec-cm
V - volume, m3 or cm3
W - jet width, cm
W - weight gain on filter
x - distance in "x" direction, cm
X - dimensionless distance in "x" direction
y - mole fraction, gmol/gmol
Y - distance in "Y" direction
z - height of foam, cm
Z - distance in "Z" direction
Z1 - thermophoretic parameter
146
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Dimensionless Numbers
N UF
FD = — , Flux deposition number
o
h'd
N^, = , y , Nusselt number
Nc = 1V/ Po D_, Schmidt number
oC U
u
Npr = C p/k, Prandtl number
Np = du/D, Peclet number
NRe = pdu/y, Reynolds number
NKn E */r > Knudsen number
Greek
a - contact angle of a drop on a solid surface, degrees
a - fraction of particle mass increase as predicted
theoretically, used in equation (40)
6 - dimensionless jet spacing = 2 s/w
6 - boundary layer thickness, cm or ym
e - volume fraction voids in scrubber
0 - contact time, sec
n - efficiency due to a unit mechanism, fraction or
percent
A - mean free path of gas molecules, cm or \im
p - density, kg/m3 or g/cm3
147
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a - geometric standard deviation
&
o - diffusion slip factor in equation 6, dimensionless
T - relaxation time, sec
p - viscosity, g/cm-sec
v - kinematic viscosity = y/p, cm2/sec
Subscripts
b
BD -
C
d
D
d
e
exp -
F
F
F
G
i
i
i
L
m
M
P
bubble
Brownian diffusion
centrifugal
drop
diffusiophoretic
difference
exit
experimental
foam
impaction during bubble formation
flux force
gas phase
interface
in
increment
liquid phase
mixture
molal quantity
particle
148
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pa - aerodynamic
pB - particle, Brownian diffusion
pD - particle, diffusiophoresis
pn - particle, number mean
pT - particle, thermophoresis
pi - particle, inertial
s - surface
s - sum of
t - terminal velocity
tg - tangential
theo - theoretical
T - turbulent layer
T - thermophoretic
v - vapor
x - in the "x" direction
y - in the "y" direction
o - original condition
oo - for plane surface
Superscripts
* - in equilibrium
- film
dimensionless quantity
— - overall or average
149
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BIBLIOGRAPHIC DATA
SHEET
1. Report No.
EPA-650/2-73-036
3. Recipient's Accession No.
4. I ulc and Subtitle
Feasibility of Flux Force/Condensation Scrubbing for Fine
Particle Collection
5' Report Date
October 197-3
6.
7. Amhor(s)
Seymour Calvert. Jhuda Goldshmid, David Leith. Nikhil Jhave
&• Performing Organization Kept.
No.
Performing Organization Nnmc.' find A72
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