EPA-650/2-73-003
July  1973
Environmental  Protection  Technology Series

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                                   EPA-650/2-73-003
        ABSORPTION  OF S02
     BY  ALKALINE  SOLUTIONS
IN  VENTURI  SCRUBBER  SYSTEMS
              C. Y. Wen and S. Uchida

          Department of Chemical Engineering
              West Virginia University
           Morgantown, West Virginia 26505
              Contract No. EHS-D-71-20
               „ Grant No.  800781
             Program Element No. 1A2013

        EPA Project Officer:  Robert H. Borgwardt

             Control Systems Laboratory
         National Environmental Researcn center
      Research Triangle Park, North Carolina  27711

                  Prepared for

           OFFICE OF RESEARCH AND MONITORING
         U. S. ENVIRONMENTAL PROTECTION AGENCY
               WASHINGTON, DC  20460

                   July 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.
                                 11

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                      ABSTRACT

     Studies of S02 absorption from flue gases by water
and alkaline solutions in venturi scrubber processes
which include recycle of the scrubbing liquor are made.
Mathematical models are proposed which describe the
momentum, heat and mass transfer in the processes for
systems of S02-H20, S02-NaOH-H20, S02-CaO-H20, and
S02-CaC03-H20.
     The momentum, heat and mass balances describe the
performance of the processes taking place in the ven-
turi scrubber.  A set of first-order, nonlinear,
ordinary differential equations are generated relating
total pressure, liquid velocity, S0? concentration in
the liquid, etc. along the axial direction.  These
equations are numerically solved to give performance
profiles which are used to examine the effects of the
operating variables such as the liquid flow rate and
the concentration of alkali in the liquid phase on the
absorption rate.
     Data obtained from various sizes of holding tanks
are analyzed and mathematical models for the holding
tanks for the lime and limestone slurry processes are
proposed.

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                                                           11
     Finally these models are combined to simulate the
venturi-holding tank system with closed-loop recycling
of the liquor.  The sensitivities of some operating
variables such as the recycling liquor rate and the
alkali make-up rate on the absorption are examined.
     Practical problems such as oxidation of sulfite
to sulfate and scaling of the solids are qualitatively
discussed.
     The calculated results using these models show
good agreement with experimental data obtained by
several investigators.
     In this investigation it was found that:
     1.  A significantly large amount of heat and mas:;
transfer takes place near the liquid nozzle in the
venturi scrubber.
     2.  The operation of the venturi scrubber is
practically isothermal except in the zone extending a
few centimeters from the liquid injection nozzle.
     3.  The dissolution of lime into weak acid solutions
can be explained by a shrinking core model.
     4.  The performance of the holding tank in the
limestone slurry process can be approximated by an
equilibrium stage model in which the tank is assumed to
be in dynamic equilibrium with the surroundings.

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                                                         iii
                 TABLE OF CONTENTS



Chapter                                            Page

        ABSTRACT . .  . .............     i

        TABLE OF CONTENTS  ...........   Hi

        LIST OF FIGURES  ............   vli

        LIST OF TABLES .............    xi

    I.  INTRODUCTION ..............     1

        A.  Description of Lime/Limestone
            Slurry Scrubbing Process ......     2
        B.  Scope of Investigation

   II.  LITERATURE REVIEW
        A.  Mechanics of Venturi Scrubber
            Operation  .............     ft

            (1)  Pressure drop in a verituri
                 scrubber  ...........     fj
            (2)  Mean diameter of liquid
                 droplets  ...........    12

        B.  Theory of Gas Absorption ......    16

            (1)  Gas absorption without
                 chemical reaction .......    17

            (2)  Gas absorption with chemical
                 reaction  ...........    20

            (3)  Gas absorption in a venturi
                 scrubber  ...........    20
  II J.  THEORETICAL DKVKI-OnvjENT

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                                                    IV
A.  Reaction Mechanism and Thermo-
    dynamics of Various Systems  ....    26

    (1)  S02-H20 system  ........    26

    (2)  SCU-Alkaline solution system   .    2?

    (3)  CC^-Alkaline solution system   .    30

    (4)  SOp-Limestone slurry system .  .    32

B.  Development of Performance Equations.
    for a Venturi Scrubber .......    35

    (1)  Pressure drop .........    36

    (2)  Equation of motion of liquid
         droplet ............    3^
    (3)  Heat and mass transfer in a
         venturi scrubber  .......    1+2

    (4)  Performance equations in
         dimensionless forms ......    44

    (5)  Gas-phase heat and mass
         transfer coefficients .....    46

    (6)  Rate of gas absorption into
         spherical droplet .......    47

C.  Dissolution of Lime and Limestone
    in a Holding Tank  .........    51

    (1)  Properties and behavior of lime
         in acid solution  .......    52

    (2)  Model for dissolution of lime
         in a holding tank .......    54

    (3)  Properties and behavior of lime-
         stone in S02 scrubbing liquor  .    57

    (4)  Model for simulation of a hold-
         ing tank in limestone process  .    64

D.  Overall Operation of Venturi Scrubber
    System with a Closed-Loop               70

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                                                        V
IV.  RESULTS AND DISCUSSION	    76

     A.  Simulation of Performance of
         Venturi Scrubbers  	    76

         (1)  Description of the experiments.    76

         (2)  Pressure drop in a venturi
              scrubber	    #0

         (3)  Momentum, heat and mass
              transfer	    30

     B.  Simulation of the Holding Tank
         Performance	    92

         (1)  Molding tank for the lime
              slurry process  	    92

         (2)  Holding tank for the limestone
              slurry process  	    96

     C.  Performance of Venturi-Holding Tank
         Systems with Closed-Loop Recycle of
         the Scrubbing Slurry 	   100

         (1)  Lime slurry process with a
              closed-loop recycle of the
              scrubbing liquor  	   100

         (2)  Limestone slurry process with
              a closed-loop recycle of the
              scrubbing liquor  	   102

     D.  Scaling and Oxidation in Lime/
         Limestone Processes	   106

 V.  CONCLUSIONS AND RECOMMENDATIONS  ....   114

     NOMENCLATURE 	   119

     BIBLIOGRAPHY 	   129

     APPENDICES

       A.  Enhancement Factor for Gas Absorp-
           tion with Instantaneous Chemical
           Reaction into a Liquid Drop  . . .   137

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                                                  V:L
B.  Derivation of Equation (105)  •  •  •   1A-4

C.  The Rate of Gas Absorption Accom-
    panied by Instantaneous
    Irreversible Reaction in a Liquid
    Droplet in a Venturi Scrubber—
    A Numerical Solution	   H7

D.  Comments on the Physical and Chem-
    ical Properties used in the Mathe-
    matical Models of the Scrubbing
    Processes	   15.1.

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                                                             vii
                   LIST OF FIGURES


Figure                                              Page

   1       Three Basic Process Routes for SOp
           Scrubbing by Lime/Limestone
           Slurry ................     3

           Solubility of S0? in Water vs.
           S02 Partial Pressure
           Comparison of Experimental Data on
           Rate of SOp Absorption with Values
           based on Penetration Theory  .....    29

           Correlation of Instantaneous Unsteady
           State Drag Coefficient with Reynolds
           Number ................    41
           Concentration Profile of S02 in a
                         ,0 System:  constant
                         icentration) 	    49
\S \S 1 1 \s \* 1 i OJ. GLl'-A-VJAi A J
Droplet (SOp-HpO System:  constant
interfacial com
   6       Equilibrium Concentration of Total
           Calcium at 50°C and its concentration
           in Outlet Liquor from Holding Tank
           vs. Liquor pH	    60

   7       Equilibrium Concentration of Total
           Sulfate at 50°C and its Concentration
           in Outlet Liquor from Holding Tank
           vs. Liquor pH	    6l

   &       Equilibrium Concentration of Total
           Sulfite at 50°C and its Concentration
           in Outlet Liquor from Holding Tank
           vs. Liquor pH	    62

   9       Equilibrium Concentration of Total
           Carbonate at 50°C and its Concentra-
           tion in Outlet Liquor from Holding
           Tank vs. Liquor pH	    63

  10       Material Balance Around a Holding
           Tank	    66

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                                                         vlii
11       pH of Limestone Slurry vs. Vapor
         Pressure of C02 at 50°C	    69

12       Mass Transfer Coefficient for C02
         Evolution in the Holding Tank vs.
         Liquor Flow Rate	    71

13.      Venturi-Holding Tank System with
         Closed-Loop	    73

14       (a)  Logic Diagram for Simulation of
         Venturi-Holding Tank Recycling System
         (Lime Slurry Process)	    74
         (b)  Logic Diagram for Simulation of
         Venturi-Holding Tank Recycling System
         (Limestone Slurry Process) 	    75

15       (a)  Dimensions of Venturi Scrubber
         used by Harris et al.
         (b)  Dimensions of Flooded Disc
         Scrubber (FDS) used by Gleason et al  .    77

16       Dimensions of Venturi Scrubber used
         by Johnstone et al	    79

17       Comparison of Calculated Pressure
         Drop in EPA Venturi Scrubber and
         Flooded Disc Scrubber with Experi-
         mental Data	    82

18       Pressure Profile in Venturi Scrubber
         used by Johnstone et al	    83

19       Velocity and Sulfur Concentration Pro-
         files along Axial Distance in EPA
         Venturi Scrubber 	    85
r
20       Temperature Profiles of Gas and Liquid
         along Axial Distance in EPA Venturi
         Scrubber	    87

21       Profiles of Cumulative Absorption
         Rate in Venturi Scrubber (Experiment
         of Johnstone et al)	    88

22       Comparison of SOp Removal Rate in the
         Venturi Scrubber Calculated with
         Experimental Data Obtained by
         Johnstone et al	    89

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                                                           IX
23       Concentration Profile of GCU in a
         Droplet (EPA Venturi:  H20-S02 System),     90

24       Concentration Profiles of SOp and
         NaOII in a Droplet (EPA Venturi:
         NaOH-S00-H90 System)	     9.1
                *-  f^f

25       Comparison of Calculated S0? Removal
         % with Experimental Data .7	     93

26       Comparison of Calculated Concentration
         of Ca(OH)2 in Solution from Holding
         Tank with Data Obtained by Gleason
         et al	     95

27       Comparison of the Valuer of Calculated
         pH of Outlet Liquor from Holding; Tank
         with Experimental Data (Limestone
         Slurry Process)  .  . .	     97

2f>       Comparison of Calculated Value-:;. o(%
         Concentration:.; of Total Calcium and
          Inlfito in Out If I; Liquor from Molding
          funk with Experimental Data (Limestone
         Jlurry Proceed)	     9^'

29       Comparison of Calculated Value:; of
         Concentrations of Total Sul.fate and
         Carbonate in Outlet Liquor from
         Holding Tank with Experimental Data
         (Limestone Slurry Process) 	     99

30       Performance of a Venturi-Holding Tank
         System with a Closed-Loop Recycling of
         Slurry (Lime Slurry Process) 	    101

3"1-       Comparison of Calculated SOp Removal
         "/•> with Experimental Data Obtained by
         Epstein et al. (42) (Limestone Slurry
         Process)	1.04

32       Performance of a Vcnturi-Holding Tank
         System with a Closed-Loop Rocycl Lrig of
         Slurry (Limestone Slurry Process)   .  .    105
A-L      Concentration Profile acorss the Gas-
         Liquid Interface with Instantaneous
         Reaction.  The Dashed Line Indicates
         the Approximate Concentration Gradient
         across the Fluid Film in the absence
         of OheMical Reaction (APPEND!" A)   .  .

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D-l      pll Values of Ca(OH)?  Solution:;  of
         Varying Concentration and  Tempera-
         ture (APPKNDI7 D)

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                                                            xi
                   LIST OF TABLES

Table                                                P.-.u^e

  1        Correlation for Pressure  Drop  in
           Venturi Scrubber  	       II

  2        Empirical Equation:.; for Droplet
           Diameter and Their Applicable
           Ranger;	       13

  3        Experimental Conditions used in
           the Three Experiments	       rfl

  l\.        Experimental Conditions of  Holding
           Tanks used in Four Experiments .  . .       9/i

  D-l      Ionic Velocities  U at Infinite
           Dilution, .1.8°C	      153

  D-2      Solubility of Lime in Water Expressed
           As CaO  or Ca(OII)2 at Different
           Temperatures 	      154

  D-3      pH of Lime Solution at 25°C  ....      156

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                  I .   INTRODUCTION

     In recent years considerable effort has been devoted
to investigating the ever-growing problem of acid gas
and dust pollution of the atmosphere.  Especially the
problem of atmospheric pollution by sulfur dioxide emis-
sion has stimulated a large amount of research and
development of methods for removing the pollutant from
              ' 13' 23' 42' 5°' 7°' 95 ' 98' "' 100'
waste gases
111, 116, 117, 118) ^   Many tvpes of ' processes have been
proposed such as the oxidation or reduction of S02 in a
gas stream to produce sulfuric acid or sulfur, the adsorp-
tion on activated carbon or other adsorbents, the absorp-
tion by various types of solids and liquid followed by
the regeneration of the absorbents, and the absorption
by slurry of lime or limestone followed by discarding
the loaded absorbent.
     Although S02 is not recovered in a useful form in
the lime/limestone processes, these processes have the
outstanding advantages of relative simplicity, lowest
investment, and freedom from the problems of marketing
a by-product.  For these reasons they are being favored
by the electric power industry as one of the best solu-
tions to the S02 emission problem for use in the
immediate future.

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     The application of the lime/limestone slurry scrub-
bing process is not only suitable to the power industry
but also to the other types of plants that emit SOU such
as smelters, refineries, and sulfuric acid plants.
     In this chapter, a general description of the lime/
limestone slurry scrubbing processes and the purpose of
this investigation are given.

     A.  Description of Lime/Limestone Slurry Scrubbing
         Process
     There are three major process routes for SOp scrub-
bing by lime/limestone slurry as shown in Figure 1.  The
advantages and disadvantages of these methods are as
follows:
     Method (a).  Limestone Slurry Process:  This is the
simplest of the lime/limestone processes and seems to be
the one favored by the power industries at present time.
The main drawback is that limestone is not as reactive
as lime and only sparingly soluble in water.  This neces-
sitates both the usage of more limestone than that
required stoichiometrically and large equipment size.
The limestone used must be ground to fine powder in order
to promote high reactivity and better utilization.
     Method (b).  Lime Slurry Process:  Lime, which is
much more reactive and is more alkali than limestone,
                                           t
can be used to improve the scrubbing efficiency.  Although

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           OAS OUT
       OAS IN
            1
               SCRUBBER
                          LMB8TONE
                            I
                               HOLOINO TANK
     Method (a).   Limestone  Slurry Process
                       QAS OUT
                       JL
    UME8TONB
      KIL
     Method (b).  Lime Slurry  Process
                        0A8 OUT
LIMESTONE*
BOKJER

•••
LI
OA
«t
S IN
                        _L
•CRUMB)*
     HOCOIN9 TANK
                                                 SOLID
     Method (c).  Limestone  Injection  to  Boiler  Process
Figure 1.   Three Basic Process  Routes for  S02
             Scrubbing by  Lime/Limestone Slurry

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smaller operating costs are required due to low recir-
culation rate of the lime slurry, the cost of calcina-
tion of limestone to produce lime may be expensive.  Use
of lime may also increase the problem of scale formation
in the scrubber.
     Method (c).  Limestone Injection to Boiler Process:
The cost of calcination of limestone is a major disad-
vantage in lime slurry process.  It can be reduced by
injecting the limestone into the boiler furnace.  The
limestone injected into the boiler is calcined and the
gas then carries the lime into the scrubber.  Boiler
fouling, everburning of limestone, inactivation of the
lime, increased scaling in the scrubber are among the
main problems that endanger this approach.  This method
is not applicable to some plants such as refineries,
sulfuric acid plants or smelters.
     There are several advantages and disadvantages for
each of the methods described.  The best process has to
be selected by an overall consideration of the process
including such factors as the economics of operation,
reliability and availability of lime/limestone.

     B.  Scope of Investigation
     To successfully design processes for the removal of
pollutants from flue gases requires the understanding of
the physical and chemical phenomena taking place in the

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scrubbing equipment.  Although there are many types of



scrubbers and process schemes, the present investigation



is confined to a venturi-type scrubber combined with a



holding tank for recycling the scrubber liquor.  This



combination is similar to Method (a) described above.



     The venturi scrubber was originally developed for



the purpose of dust and mist separation.  It usually



consists of a body, nozzle and diffuser.  When a liquid



is injected into a high velocity gas stream near the



nozzle, the liquid becomes highly dispersed, a large



surface area of the liquid is exposed for gas-phase con-



tacting in the diffuser.  High rates of heat and mass


                                                (^  27
transfer in the atomization zone have been notedv '   '


44, 65, 66, 101, 121)f  This observation led to the devel-




opment of the venturi atomizer which has found important



applications in gas absorption, evaporation and aerosol



collection.  However, the theoretical principles and the



design criteria have not been completely analyzed and



the experimental data available in the literature have



not yet been generalized.



     Due to practical, as well as economical, considera-



tion, most commercial wet scrubbing processes must be



based on a closed-loop system in which the loaded liquor



from the scrubber is regenerated and recycled within the



process and not discharged from the process.  To accom-



plish this, the venturi scrubber is combined with a mixing/

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                                                            6
holding tank which regenerates the degenerated liquor
with fresh feeds of lime or limestone.  (See Figure 13)
     The mechanisms of dissolution of lime or limestone
into acid solutions such as recycling liquor in the lime-
stone process are so complex that they are not fully
understood.  The elucidation of the dissolution mech-
anisms or performance of the holding tank is necessary
for the overall design of a venturi-holding tank scrubber
system.
     The main objective of the study is to understand
the thermodynamics and the kinetics of the system in-
volved, and to elucidate the mechanical and hydrodynamic
characteristics of the system so as to simulate the
performance of heat and mass transfer in the venturi
scrubber and the holding tank for various reaction
systems.
     Various theories of the gas absorption, with and
without chemical reactions, which appear in the literature
(21, 32, 33, 47, 48, 56, 71, 88, 90, 94, 96, 105, 106,
110, 114, 122, 124)are used in interpreting the phenomena
in the venturi scrubber, and based on the experimental
and pilot plant scale operating data ^8' 13' 23' ^2' 5°'
' '    'the rate-controlling mechanism for dissolution
of solid lime and limestone into the recycling slurry is
studied.  The important mathematical models for a venturi
scrubber and a holding tank will be developed and their

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 inter-relationships will be briefly discussed.  These
 models are based  on the phenomenological observation  of
 the actual process  operations with some assumptions to
'simplify the evaluation of the model.
     Finally,  simulations of the venturi-holding tank
 system are performed using the proposed mathematical
 models.  The overall efficiencies of the scrubber-hold-
 ing tank systems  are discussed and sensitivities of
 operating variables on  the S02 removal efficiency are
 also investigated.
     It is hoped  that the information presented here
 can be used to find the best design of these processes.

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               II.  LITERATURE REVIEW





     Despite the many industrial applications of atomi-



zation techniques, little quantitative information on



the performance of venturi scrubbers can be found in the



literature.  In designing and controlling of the per-



formance of a wet scrubber, it is necessary to know the



mechanism of atomization, to estimate the total pressure



drop across the venturi scrubber, and to evaluate the



amount of heat and mass transferred between the liquid



droplets and the gas in the venturi scrubber.  The aux-



iliary equipment associated with the wet scrubber such



as the holding tank etc. must also be designed.  The



following is a review of the literature pertaining to



the pressure drop in a venturi scrubber, atomization, gas



absorption and the efficiency of venturi atomizers as



gas absorbers.





     A.  Mechanics of Venturi Scrubber Operation



     (1)  Pressure drop in a venturi scrubber



     The overall pressure drop across the venturi scrub-



ber is an important practical factor which must be con-



sidered in the design of the scrubber since moct of the



operating costs are associated with the power consumed



in overcoming the venturi's relatively high pressure drop.

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The pressure drop for a gas flowing through a venturi
scrubber can be estimated by considering the effects of
friction along the wall of venturi scrubber and the accel-
eration of the injected liquid.  Frictional losses depend
largely upon the geometry to the scrubber and must be
determined experimentally.  Acceleration losses which are
frequently predominant in the scrubber pressure drop, are
fairly insensitive to the scrubber geometry and in most
cases are predictable theoretically^
     Several correlations for the pressure drop in a
venturi scrubber available in the literature are sum-
marized in Table 1.
     Some of experimental data on the pressure drop in
venturi scrubbers have been reported    '   ' ^ '   '   '
50, 62, 125) Matrozov's correlation ^2^ is probably the
first to appear in the form of an equation.  In 1963,
Gieseke *  ' performed experiments with a small scale
venturi scrubber and found that the experimental data
could be correlated by a plot of two quantities:  that
is, the product of the Euler number and the ratio of the
volume flow rate of liquid to that of gas versus the axial
distance divided by the product of the drop diameter and
the square root of the Reynolds number.  The computed
pressure drops were about ten percent lower than the
experimental values.  This seems to be caused by neglect-
ing the friction loss at the wall of the venturi scrubber.

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                                                             10
               (12)
     Boothroyd    ' also measured the pressure drop of
gaseous suspensions of fine particles flowing through a
duct and found that the total pressure drop could be
represented by the summation of several individual losses
as shown in Table 1.
     Recently Volgin et al.     ' presented an empirical
correlation consisting of only one term which tends to
zero in a dry venturi scrubber.  Gleason and McKenna    '
also presented an empirical correlation for pressure drop
in a flooded disc scrubber using a sodium carbonate
solution.
                                   i
     Most of the pressure drop correlations discussed
above were experimentally obtained on relatively small
scale equipment.  Therefore they are not applicable to
different types or sizes of venturi scrubbers unless the
values of the coefficients or the powers involved in
these correlations are adjusted.
     Calvert ^  ' and Boll      developed equations which
seem to be applicable to a general type of venturi scrub-
ber.  Calvert derived a pressure drop equation by apply-
ing Newton's law to obtain the force required to change
the momentum of the liquid flowing at a given rate.  This
equation does not contain a term accounting for the
frictional losses at the wall of the venturi scrubber;
however, this term becomes negligibly small at a high
liquid rate in comparison with the term associated with

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  Table 1.  Correlation for Pressure Drop in Venturi Scrubber
  Investigator
                         Correlation
Matrozov
         (82)
Geiseke
        (49)
Boothroyd
          (12)
Volgin et al.





Calvert (24)





Gleason et al.
              (125)
(50)
Boll
     (11)
             = 2.22 x
             = 4 x 10~7v 2q

           ^            o
AP,  = 5.23 x 10~9v 2(0.264F+73.S)
  *+•               o

             p    2
   &p     v  — v       r t
     oz    co   c .   m
                             g
                                                            fv
                                               dt
                                                  dz

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                                                            .1.2
the acceleration losses.  Boll's equation is substan-
tially the same as Gieseke's correlation except that
the former takes the wall friction into consideration.
This equation has been derived by taking a momentum
balance on the gas and the liquid in a venturi scrubber
and gives the pressure distribution within the venturi
scrubber.

     (2)  Mean diameter of liquid droplets
     Various correlations are available in the litera-
     (51, 59, 68, 72, 81, 84, 89, 127, 129) +.    4. •   4.
ture v' '   '   '   '   '   '   '    '    ' to estimate
the mean diameter of liquid droplets from various types
of atomizers under different operating conditions.  These
correlations are applicable only to the specified type
of atomizers within a certain range of operating con-
ditions and fluid properties.  These conditions include
such variables as the volume ratio of gas and liquid,
relative velocity of the gas and the liquid, type of noz-
zle, surface tension, viscosity of the liquid etc.  There-
fore, the number of correlations for droplet size appli-
cable to a specific type of venturi atomizer is rather
limited.  These correlations are summarized in Table 2.
In using one of these correlations to estimate the droplet
diameter, it is important to select a proper correlation
which takes those factors into consideration.  Applica-
bilities of various correlations in terms of the range

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Table.2.  Empirical Equations for Droplet
  Dia;meter and Their Applicable Ranges
INVESTIGATOR
Nukiyama
and
Tanasawa
(89)
Mugele
(84)
Gretzinger
and
Marshall
(5D
EQUATION*
r, -rd- rnn J °"
V-/^L
^T 0.45 L
+597 (T=-) ' (1000— J1'5
* J L o
D32 _ ,(Dr,-PLvr B/Lvr C
"„ A r " '
(A, B, C,; constants)
D -" 600r(^L)-(DnVg0>Pg)]0-4
m M it
g ^g
APPLICABLE RANGE
v [cm/sec]
10,000 to
sonic
velocity
10,000 to
sonic
velocity
10,000 to
sonic
velocity
(Mg/ML)[ - ]
1.8 to
15
1.8 to
15
1 to
15
/'LCpoise]
0.01 to
0.46
—
0.01 to
0.30

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Table 2.  (continued)
INVESTIGATOR
i
Wigg
(129)
Kim and
Marshall
(68)
EQUATION*
/L * 0.1
D =20,000 (— ) 'M,
111 fJ J_j
•^ J_J
j., n 0.1 0.2
n^Li Dn &
CD _/ cr T* /"^
o ^
APPLICABLE RANGE
v [cm/secj
8
0.411x0.32
O~ y T
f) -C -| Of) , ' J-i
01 (v2 P )°'57S °-36DO.l6
+"i & oonf 	 ^ 1 f V
FT ®" 0.54 1'1-r
J L v L
ro
m - -1 for M^^T < 3
o -1
m = -0.5 for K^My > 3
o — '
,000 to
35,000
7,500
to
sonic
Velocity
(Mg/ML)[ - ]
0.5 to
20.2
0.06 to
40
^Lfpoise]
0.032 to
0.45
0.01 to
0.50
                    all units are in c.  g.  s.  unit;

-------
 of mass ratio of gas and liquid,  relative velocity of



 gas and liquid, and the viscosity of liquid, which are



 considered to be among the most important factors, are



 also indicated in Table 2.



      Among these correlations,  probably the best known



 and the most widely used is that  of Nukiyama and



 Tanasawa     .  Analysis of this  equation shows that for



 a ratio of Qa/Q-L greater than 5,000, the second term has



 only a slight influence on droplet size.  Also, in this



 correlation the size is determined by the relative velo-



"'city of the gas and liquid, the liquid density and sur-



 face tension; the nozzle dimensions do not enter the



 correlation.  This correlation  is suitable for flows of



 high relative velocity and of large mass ratio of gas



 and liquid.


             (127)
      Wetzel v   ' studied venturi atomization of a molten



 wax and a molten metal alloy with room temperature air.



 His data indicated an inverse variation of the spray



 particle size with the air-to-liquid mass ratio.  The



 droplet size decreased from 110 to 30 /*• when air-to-



 liquid mass ratio increased from  100 to 300.



      Mugele ^  ' attempted to develop an expression for



 the maximum and mean droplet size by dimensional analysis.



 His correlation covers almost the same range as that of



 Nukiyama and Tanasawa.  A similar correlation was sub-



 sequently derived by Gretzinger and Marshall      which

-------
consists of dimensionless groups having the same ranges



of applicability as those for Nukiyama and Tanasawa's



correlation.


                        (129)
     Wigg's correlation v    ,  which was proposed to



explain wax spray experiments,  .covers a wide range of



relative velocity and mass ratfo of gas and liquid;



however, the viscosity of the wax was substantially



higher than that of water and /aqueous solutions used in



this study.



     Kim and Marshall      recently developed a correla-



tion which covers wide ranges of the operating variables.



Their correlation has a form similar to that of Nukiyama



and'^Tanasawa,  but predicts smaller droplet sizes under



similar operating, conditions/. .  However, .Nukiyama and •



Tanasawa's equation was based on the data obtained by a



physical sampling technique which probably introduced



some-errors due to evaporation and the target effect



resulting .from the presence of the .sample collecting



device.  Kim and Marshall    \  also,reported that a modi-



fied form of their correlation can be used to correlate


                        (127)
Wetzel's drop-size data     ' obtained by venturi



atomization.






     B.  Theory of Gas Absorption



     Since gas absorption is one of the most common unit



operations in the chemical industry, there are voluminous

-------
publications by numerous researchers on the theory of
diffusion in counter-current equipment and on the per-
formance of packed towers and other devices used in gas
absorption.  Only a brief review of this field is given
in this section.
     (1)  Gas absorption without chemical reaction
     Historically the best known theory of physical
absorption, the two-film theory, was proposed by Lewis
            (73)
and Whitman v' •" in 1923.  This theory has proved to be
of great use in understanding the process of diffusion
between two fluids, although there appears to be no
tangible evidence of an appreciable diffusional resis-
tance at the actual interface of the fluids, or of tin1
validity in the assumption that equilibrium exists at
the interface of the two fluids in contact.  In the case
of mass transfer between gas and liquid, the concentra-
tion and the partial pressure of solute component A at
the interface are assumed to be related by the equi-
librium condition.  Thus,

                     CAi-»APAi                    ^
     Under the steady-state operation, the solute gas A
is absorbed into a liquid stream at a rate given by:

           NA •= kG  -" RL ^Ai-V           (2)
This equation,  based on the two-film model, gives rise to
the so-called "additivLty of resistance::," .  Using the
relation (1) P.. and C.. are eliminated and we obtain:

-------
        NA = KG (PA-A} = KL '
where
                             _1 = HA   1_
                          '   KL~^   kL

           CI = VA      '    CA = Vl

     The values of mass transfer coefficients must be
estimated for a given type of contacting device and a
given operating condition.  Kinetic theories of gas are
sufficiently well established to the point that mass
transfer coefficients for most gases can be estimated
              (. i 7 }
theoretically Vt'''.  There are also many experimental
correlation, available ">«•  88' *• 106 • ^ i21-'.
     For the mass transfer coefficient in the liquid
phase, two cases must be considered; gas absorption with
and without a chemical reaction in the liquid phase.
There are many theories to explain the complex diffusion
processes in the liquid phase even for physical absorp-
tion since the two-film theory was first proposed.
     In 1935 » Higbie    ' proposed the penetration theory
to explain gas absorption into quiescent liquid under
unsteady state conditions.  The average rate of gas
absorption and the mass transfer coefficient in time
o ~ t are functions of time  and expressed as follows:

-------
                                                            1-9
                 NA • 2
The exposure time t is determined by the hydrodynamic



conditions within the system and is the only parameter



required to account for their effect on the mass transfer



coefficient kj..



     Applications of the Higbie's penetration theory to



gas absorption into agitated liquids where the dissolved



gas is transported from the surface to the bulk of a



liquid phase by convective motion has been made by



Danckwerts^31), Harriott^52), and others ^33' 114' 12/f^.



     Higbie's model specifies the same time of exposure



for all the elements of the surface.  However, Danckwerts


( 31)
     assumes that the probability of an element of the



surface being replaced by fresh liquid is independent of



the length of time for which it has been exposed.  That



is to say, a stationary distribution of the surface ages



is assumed in which the fraction of the surface has been



exposed to the surface for times between  6 and (6+ d0)


     — ° &
is se ° d9.  Here s is the fraction of the area of surface



which is replaced with fresh liquid in unit time.  The



average rate of absorption by this model, and its mas:.;



transfer coefficient arc:




                  NA  ' ^Ai

-------
                                                            20
Here again, the hydrodynamic conditions within the system,



so far as they affect k,.., are accounted for by a single



parameter s which has the dimensions of reciprocal time.



     Some surface-age distributions other than those of


                                                       (11
Higbie and Danckwerts have been discussed by Danckwerts



     (2)  Gas absorption with chemical reaction



     When gas absorption is accompanied by a chemical



reaction, its rate is accelerated to  a  certain degree



depending upon the type of the reaction.  The kinetic



theories of simultaneous diffusion and chemical reaction



in the liquid phase were first developed by Hatta^ ">j>',



followed by many investigators.  There are a number of



theories which have been developed and are associated with



different types of reactions and hydrodynamic condition:.;.



Many cases with complicated chemical reactions have been



numerically solved (l6' 17' 18' 19' 22' 6>> 79' 97).



The case of gas absorption with an instantaneous second-



order chemical reaction is discussed in Appendix A.



The details of other models can be found in the litera-



ture cited (33' 6°' 9°' 94> io6' ^.



     (3)  Gas absorption in a venturi scrubber


                    (27)
     Comings et al.      found good heat transfer from



gas to liquid, with a subsequent rapid vaporization of



the liquid when the liquid was introduced in the form



of a simple jet into a high-velocity gas streams.  Using



a venturi atomizer, a smoke cloud was created by

-------
                                                            21
vaporizing oil with subsequent condensation to form very


small drops.  They found that the hot gas was cooled


rapidly and very high heat transfer rate was achieved in


this type of atomizer.  This type of scrubber was con-


sidered most suitable when the gas film controls the


rate because of stagnant conditions existing within the


drops.  Pigford et al.     'on the other hand proved


that this type of equipment can also be used even when


the liquid film resistance controls the rate such as in


the desorption of oxygen from water.


     Johnstore and Roberta      measured the overall


efficiency of a venturi scrubber as a gas absorber and


obtained an equation for the efficiency of absorption.


     Tassler (m), Feild ^4\ and Johnstone et al/6^


studied the absorption of sulfur dioxide in alkaline


solutions using a venturi scrubber and measured experi-


mentally the amount of sulfur dioxide absorbed at various


distances from the point of liquid injection.  They found


that the average volumetric gas film coefficient, K a,
                                                   LI

increased with the liquid feed rate and the gas velocity


at a given position in the venturi scrubber, and decreased


at a constant liquid rate and gas velocity with increasing


distance from the point of liquid injection.


     Tassler ^   ' also studied the performance of a


venturi scrubber for the desorption of carbon dioxide

-------
from water.  The overall transfer coefficient, Kra,



was calculated from the experimental data.  The values



of KLa are higher than those obtained in packed towers



under countercurrent operation.  However, the values of



K,-a are smaller than those obtained for the absorption



of sulfur dioxide in the same venturi scrubber.


                            (3)
     Anderson and Johnstone ^Jl studied the absorption



and subsequent liquid-phase reaction of catalyzed sodium



sulfite solutions and the simultaneous absorption of



atmospheric oxygen with nitrogen dioxide and with sulfur



dioxide by water.  They found that in the case of oxygen



absorption by sodium sulfite solutions containing 0.01M



CoSO,  as a catalyst, the values of K^a close to the liquid



injection point are nearly 100 times higher than those



for oxygen absorption by pure water.  The K.a values



decrease rapidly with distance and are nearly equal to



those for pure water at 1 inch from the liquid injection



point.



     Kuznetsov and Oratovskii      obtained equations



for the rate of gas absorption with chemical reaction; Ln



the throat and the divergent section of a venturi scrub-



ber, relating the number of transfer units and the degree



of absorption to the principal operating and design para-



meters of the apparatus.  They, also, showed that the liquid



to gas ratio had an optimum value, while an increase in



the gas velocity could lead either to an increase or to a

-------
                                                            23
decrease in the degree of absorption depending on the



region in which the process was being conducted, that



is, chemical reaction controlling, diffusion controlling
or the intermediate region.  The equations obtained by



                                                 ; in <


                                                 (14)
Kuznetsovot al.    'forthe number of transfer units in a
venturi absorber were investigated by Boyadzhiev



The optimal conditions for gas absorption with various



types of chemical reactions were also determined by


                    M 12)
Sazkin and Matrozov '   '.



     Markant et al.      studied the absorption of S02



from dilute gas streams by magnesium bisulfite solution



and obtained a correlation for the vapor pressure of S02



over the magnesium bisulfite-magnesium rnonosulfitc solu-



tion for their experimental ranges of temperature and



acid composition.  A correlation for the effects of



magnesium monosulfite concentration, acid strength, and



acid temperature on SO? absorption efficiency of the



venturi scrubber was obtained.



     Elenkov and Boyadzhiev ^ ' obtained experimental



data on the absorption of 302 in water and aqueous solu-



tion:; of surfactant.'.; in a nozzleless venturi scrubber in



the range  of NR = (1.44 ~ 3-27) x 10  and a gas throat



velocity of 40 ~ 120 m/ sec.



     Volgin et al.       studied absorption of SOp by



ammonium sulfite-bisulfite solution in a venturi scrub-



ber which had a throat with either rectangular (10 x 15 mm)

-------
                                                            21,
cross section and a length of 13 mm, or cylindrical (20



mm diameter) cross section and a length of 10 mm.  They



demonstrated that absorption in multi-stage venturi



scrubbers are competitive with conventional scrubbers



such as packed towers and bubble towers with respect to



the pressure drop and the consumption of the electric



power and that there is an optimum condition of venturi



operation with respect to the pressure loss and the extent



of absorption.


             (123)
     Tillman v  " recently studied the performance of



a venturi scrubber analytically.  The mechanism of par-



ticulate collection by water droplets in a venturi scrub-



ber was investigated and the effect of water drop size



on collection efficiency, the importance of water flow



rate, and the best point for injection of the water have



been shown.



     Gleason and McKenna      performed experiments on



SOp absorption by sodium carbonate, calcium oxide, and



calcium carbonate solutions in a flooded disc scrubber



which is a type of venturi scrubber.  They obtained



extensive data on the S02 removal efficiency, pressure



drop etc.  Princiotta and Epstein *   ' recently pre-



sented the data on the S02 removal efficiency and pres-



sure drop obtained from their commerical size plant.

-------
            III.  THEORETICAL DEVELOPMENT





     Despite many important applications of venturi



atomization in various fields of industries, only a few



theoretical studies can be found in the literature.



Most of these are however restricted to the experimental



studies of the efficiency of the particle removal from



the gas or on the pressure drop, heat and mass transfer



in a venturi scrubber of relatively small size.  There-



fore, the results do not cover all ranges of the operating



conditions which may be encountered in practice.



     In this chapter, some theoretical models are



developed for purposes of simulation and design of a



venturi-holding tank system as a gas absorber.  First,



reaction kinetics of several systems treated in this



study, mechanics of a venturi scrubber operation, and heat



and mass transfer taking place in the process are dis-



cussed in the following sections.  The performance



equations describing a venturi scrubber operation aro



thf.-n derived and are used to simulate the SO- gas absorp-



tion both for open-loop and close-loop operations.  Fin-



ally, the dissolution of lime and limestone are investi-



gated and :: i mul.-jt ion mode: Is ore proposed for hold in,";



tank:; ,-iiifJ I.he simulation of the venturi-scrubber combined



with a holding tank  is  discussed.

-------
     A.  Reaction Mechanism and Thermodynamics of

         Various Systems



     In this section, the reaction mechanisms and the



thermodynamics for the systems in this study, namely,



(1) S02 - H20 system, (2) S02 - alkaline solution



system, (3) C02 - alkaline solution system and (4) S02 -



limestone system are discussed.



     (1)  S02 - H20 system



     When sulfur dioxide is absorbed into water, the



following reactions occur in the liquid phase:




       302 + II20 5=s H2S03 ^= II+ + HSO~            (9)




                HSO~ == H+ + SO"                   (10)




The equilibrium constants for reactions (9) and (10)



at 25°C are Kg = 1.7 x 10~2 g-mole/1 and KIO = 6.2xlO~7



g-mole/1, respectively ^   .  Therefore, the latter



reaction can be neglected under normal conditions.  The



forward and backward reaction rate constants for reaction
(9) with respect to S02  and H  and IISO^  arc kf = 3-4x.l.O)

   	 I                 d                / (YJ \

sec   and k,  = 2 x 10  l./g-mole " sec ^   .  In the light


                                    (78)              (92)
of the data obtained by Lynn et al. v   , Onda et al. v


                  (57)
and Hikita et al.    ' it appears that the rate of hydrol-



ysis reaction of S02 in water is rapid relative to the



diffusion process and that the surface of the water film



is instantly saturated at the equilibrium concentration



upon exposure to gaseous S02.  Therefore, the absorption

-------
of GOo in water may be treated as o physical phenomenon.



The equilibrium relation of this system .Is given in



Figure 2.  The SOo absorption rater/, obt.lined by i.wo typos



of contacting devices, are compared with the theoretical.



rate using the equilibrium relation as shovm in Figure 3-



Good agreement in the comparison tends to validate the



mechanism presented above.



     (2)  SOp - Alkaline solution system



     In the case of the absorption of S02 by alkaline



solutions, two additional reactions may occur,




            S02 (aq) + OH" ^=t HSO~                 (11)




            HSO~+ OH~ -=£ 30^ -t- H20                (12)




and the equilibrium constants for reactions (11) and



(12) are Kn = 1.7 x 1012 1/g-mole and K±2 = 6.2 x 106



1/g-mole, respectively.



     Experimental data obtained by S02 absorption into


                                          (92)
sodium hydroxide solutions by Onda et al. ^  ' and Hikita

       (57)

et al. v  ' have been correlated in the present study by



the penetration theory based on an assumption that the



reaction is instantaneous and irreversible as shown in



Figure 3.  The fact that the rate of 302 absorption inl.o



the sodium hydroxide solution can be represented by the



penetration theory with an instantaneous reaction allows



these two reactions to be considered as occurriing instan-



taneously.  Thus, from the values of equilibrium constants

-------
0.012

    '0        0.5         1.0        1.5        2.0
           S02 partial  pressure,  atm x I0~9
 Figure 2.  Solubility  of  302 in Water vu. SO-
                  Partial  Pressure \')'

-------
~  8

i  6


1  4
«
•5
    8
    6
    4
 5  2
  KT
                                     T-tt-r
             I   I  I  I      I   ft I      I   I   I  I      I
           	 O  H20
           	V  01938 N NoOH
           	 A  1.0 N NdOH (with  surface  octfve ogent)
           	 0  2.0 N NoOH
                         2(CA
                                                                 I I
short  contact  time  by  .  %
liquid  jet, Hikito  et oL<57)
long contact  time by
stop  cock, Ondo  etot@2)
                               I
                                           t	I
                                                I
   2
K>~7S
8  ^
          KT3   2     4   6  8K>-2   2" 2     468K)3    2     4   68 10
                                contact  time,  t (sec)
  'igure  3.   Comparison of Experimental Data on Rate  of S02 Absorption  with
             Values based on penetration Theory

-------
                                                             30
for these reactions S02 can be considered bo react with the;
hydroxyl ion irreversibly with the overall  reaction
scheme represented by:
             S02 + 20H~ —- S03=+ H20                (13)
This reaction has the stoichiometric factor (number  of
OH  ions reacting with one molecule of 302(aq))  of two.
     (3)  C02 - Alkaline solution system
     The kinetics of the reactions involved in the
industrially important processes of the absorption of
C02 by alkaline solutions are in general rather  simple
and fairly well understood ^' 2i*' 33' 35f  U' g6' 10^'
    .  Three reactions may occur when C02 is absorbed
by aqueous alkaline solution.
                C02 t- OH" ^^ IICO"                   (.14)
                C02 »- H20 *= IICO" > II1"              (15)
                HCO ~ + OH~ ^=±  CO-T + II00             (16)
                   3             32
     Equilibrium constants for reactions (14),  (15)» arid
(16) are K.J,  = 6.1 x 107 1/g-mole, K15 - 4.5 x. 10~7
1/g-mole, and K,/- = 5-9 x 10  1/g-mole ^->-J»  *''  respec-
tively.  Reaction (14) is second-order and  its rate  con-
stant at 20°C and at infinite dilution is about  6000
1/g-mole • sec      .  Reaction (15) is first-order with
roupect to the concentration of C02 in the  :;olution, with
a rate-constant of about 0.02 :.:ec  " at 20  C

-------
in any solution in which the concentration of OH  is



greater than 10   g-ion/1  (pH>10), the rate of reaction



of COp by reaction (14) will be greater than 0.6 see" .



This is more than 30 times as fast as the rate of re-



action by (15). V/hen the pH value of the solution is less



than 10, reaction (15) becomes important from the re-



action rate point of view.  However, even in the case of



COp absorption in the solution whose pH is lower than 10,



from the equilibrium constant for this reaction (15) and



experimental data for absorption of COp in water obtained



by many investigators, ^ '    '   ' the hydrolysis



reaction (15) has no effect on the absorption of COp in



weak alkaline or weak acid solutions.  That is, the



absorption of COp in such solutions can be treated by a



physical mechanism.  Therefore, reaction (15) is normally



neglected in determining the rate of absorption of COp.



     In a solution of alkali hydroxide such as sodium



hydroxide and calcium hydroxide (lime), reaction (14)



is followed instantaneously by reaction (16).  Thus the



overall reaction is:




                 C02 + 20H" —-  C03= + H20          (1?)




     This reaction is generally treated as a second-



order reaction with respect to COp and OH~ and may bo



considered  Irreversible as Ion/1; a:.; the solution .i.:j an



alkaline sol.ution.  The :;toichiomctric factor for Uiiu

-------
reaction is two.




     (4)  S0? - Limestone slurry system



     Although limestone slurry processes have been often



encountered in the industry, very  few  data are avail-



able for the reaction kinetics of SCU.  Possible reaction



mechanisms for flue gases containing C02 and SOp were



       rop<


       (9)
                                 (95)
first proposed by Pearson et al. vy" and Beuschlein
et al.



     In spite of some apparent disagreements recent works



by various investigators have clarified the situation



somewhat in regard to the nature and extent of reaction:;



occurring in the limestone slurry process.  In this sec-



tion, the mechanisms of this system are reviewed and



discussed in more detail.



     The absorption of S02 from flue gases by a lime-



stone slurry generally constitutes a three-phase system



involving gas, liquid and solid.  When D02 is absorbed



into the limestone slurry, the following chemical react-



ions take place in the scrubber and the holding tank.

        02 + Il^O *=* II2S03 5=£ \\+ + 1130 ~            (iii)



       H30~ ^ II"*" -i- S03=                            (19)



       II2303 + HCO~—  HSO 3~ + H2C03                 (20)
       CaCO-(s) *=s CaCO,(aq) *=* Ca"*"4" + CO.,         (21)
           J            :>                   :>
       CaC03(aq) + n2c03 —" Ca(HC03)2               (22)



               )2^^ Ca++ + 2HCOJ                   (23)

-------
                                                             33
       C02 + H20 5=± H2C03*=* H* + HCO"            (24)



       HCO~ i=± H* + C03=                             (25)



       Ca++ •*• S03=— * CaS03                          (26)
       CaS03 + .VH20 -~  CaS03' >H20 1                 (2?)



       CaS00 + s00 — - CaSO.                         (28)
           J     t         4


       CaS04 + 2H20 — * CaS04 • 2H2Oi                 (29)




     Gaseous S02 from the flue gas is absorbed into  the



liquid phase, where it is partially ionized according



to reactions (IS) and  (19).  Solid calcium carbonate  is



dissolved by the solution in which it undergoes a rever-



sible reaction with the weakly ionized carbonic acid to



form fairly soluble calcium bicarbonate, as shown in



reactions (2L), (22), and (23).  The formation of r:a l.c.i urn



bicarbonate is favored by the high partial pressure  of



carbon dioxide in the flue gas according to reaction



(24).  If the concentration of IICO.T ions is high enougli



in the liquid phase as in the case of limestone slurry



process, reaction (20) between S02(aq) and bicarbonate



ion is considered as  one of the possible reactions.



This reaction is an exchange reaction between a strong



acid and a weak acid.  It has been suggested by Bjerle



et al.    ' and Nilsson et al. ^    that the key reaction



of the S00 scrubbing  mechanism is this type of react Lori.



For this roue I, i on (20), the equilibrium constant, K, at,



50°C; is given a:.; ^  K •= 7.0 x !
-------
has been proved      that the rate  of absorption  of 30,,



into limestone slurry can be explained  by  tho  irreversible



and instantaneous reaction between  dissolved 502  and



HCO.T presenting in the liquid.  Dissociation reactions



(21) and (25) are not considered significant in the lime-



stone slurry since the dissociation constants  are very



small.  Bisulfite ions produced by  reaction  (20)  react



as reactions (19) and (26), and some parts  of calcium



sulfite, then, react with oxygen dissolved in  the liquid



phase.  As the result, calcium sulfite  and calcium sul-



fate combined with water molecules  precipitate out of



the liquid.



    Therefore, the following reaction represents  an



overall reaction between SOp and limestone slurry:


                          -|  O             -y

     CaC03(s) + S02(g) 4- (2+?°<) H20(l) + 2 °2(g)




        —»• (1-oOCaSO., ' -Hl00(s) +«Ca30. •  2H90(s)
                     J     *•            M-    <•



           + C02(g)                                  (30)




where oC is a fraction of calcium sulfite oxidized to



calcium sulfate.  According to the  stoichiometric rela-



tion, for every mole of S02 absorbed, one  mole of lime-



stone is dissolved in the liquid phase, and one mole of



calcium salt (calcium sulfite and calcium  sulfate)  pre-



cipi.tate:; out of tho liquid phase,  and  consequently one



rno I e <>!' (10.,  i:: evolved I'rotn l,h<:  IL(juor.  I'lxpc.-f i HKMil.a I

-------
data from the overall system including a scrubber and o


holding tank should satisfy these stoichiometric


relations.


     Equilibrium relations among the dissolved com-


ponents in the liquid phase, coexisting solids, and the


partial pressures of S02 and C00 over the limestone

                                       (qq\
slurry have been calculated by Philips v  ' and


Berkowitz et al. ^ '



     B.  Development of Performance Equations for a
         Venturi Scrubber


     When a liquid is injected into a high velocity gas


stream in a venturi scrubber, it is atomized by the


formation and subsequent shattering of attenuated,


twisted filaments and thin cuplike films.  These ini-


tial filaments and films provide extremely large sur-


face areas for heat and mass transfer.  Later, nearly


spherical droplets are formed which have less surface


area per unit volume of liquid than do the attenuated


films and filaments.


     Although the actual process of the atomization of


the liquid is very complex, the following representa-


tions of atomization are realistic enough so that the-


oretical treatment can be applied.


     (a)  Every droplet formed at the point of liquid


injection will have a nuiari diameter that can be calcu-


lated by a correlation.  Practically no change in the

-------
droplet diameter takes place while passing through the



venturi scrubber that may be caused by coalescence or



shattering of the droplets.



     (b)  The shape of the droplet is nearly spherical



and internal circulation of liquid in the droplet can



be neglected so the droplet can be represented by a



rigid sphere ^  '.



     (c)  Effect of gas compressibility can be neglected.



     (d)  Deposition or reentrainment of the liquid or



from the wall of the scrubber vessel can be neglected.



     (e)  The variation in gas flow rate due to liquid



vaporization is negligibly small.



     (f)  The amount of SOp absorbed is so small corn-



pared to the amount of liquor, heat generated due to



reaction and solution is negligible.



     (g)  Sensible  heat exchange takes place between gas



and liquid streams.  However, temperatures within a



single liquid droplet is assumed uniform.



     (h)  Heat loss through the wall of the venturi



scrubber is negligible.



     (i)  There is  no dissolution of lime or limestone



in the venturi scrubber.





     (1)  Pressure  drop



     A differential equation for pressure drop in a ven-



turi scrubber with  respect to the axial distance is

-------
                                                            37
derived by making a momentum balance in an incremental
section of the scrubber ^  '.
 d(Mgvg) +  d(MLvL) + Sgcdpf
         + Sgcdp = 0
                                                    (3D
Using the relationships:
Mg =
M  = S
equation (31) is reduced to the following form:
                                 constant
                                    ^constant
               c               c
This is a nonlinear, first-order, ordinary differential
equation for pressure loss with respect to axial dis-
tance of the venturi scrubber.
     The last term on the right hand side of equation
(32) relates to the friction loss which is generally
expressed by the following form under turbulent flow
conditions.              o
                                                    (33)
where f is a friction factor which depends on the rough-
ness of the wall of the venturi scrubber and the Reynold:
                  / do \
number of the gas     .
     In the case of a venturi-type scrubber such a.o the
flooded disc scrubber (FDS) in which there is a sudden

-------
expansion or contraction of the gas, an additional



pressure loss term is added to equation (32).  Pres-



sure losses due to the contraction and the expansion,



AP , and AP  can be calculated by the following
  C        C
equations, respectively



                             2
                          v

                  = 0.5    &L-                      (34)
                    P(v  -v  )2

                            R1                       (35)
     Total pressure drop in the venturi scrubber is



therefore obtained as the summation of these losses.



That is:




               AP = AP  + AP- + AP  4- AP            (36)
                      a     f     c     e           \> /




where AP0 is the acceleration loss calculated by the
        a


first and the second terms in the right hand side of



equation ( 3^ ) .




     (2)  Equation of motion of liquid droplet



     Assuming that the liquid atomizes instantly into



the droplet form with a constant mean diameter at the



point of entry to the high velocity gas stream, the



force balance for a vertically moving droplet yield :j:
                                                    (j/)

-------
                                                            39
where C, is the drag coefficient, defined as





           P    	drag

            d                  j> (v -vLJ2           (38)

                (frontal area)( " A"	)

                                    C




     In general, the dimensional analysis shows that



the drag coefficient is a function of various dimen-



sionless groups as follows:




          C  — f (N   N   N   N
           d       Re, Su,  Wt, Ac




The analysis of the droplet motion is so complicated by



the gas-liquid droplets interactions particularly in



the acceleration region as well as the nature of the



droplet that it is practically impossible to obtain a



complete trajectory except under rather idealized con-



ditions.  For steady motion of solid spheres, C, becomes



a function of Reynolds number alone.  The studies on



the effects of acceleration, distoration, oscillation



and internal motion in the liquid droplets have been



summarized by Hughes and Gilliland     .  According to


                                        (2)          (29)
the experimental data obtained by Allen   ' and Cook



the drag coefficients in their study are always higher

                                               ((") \

than those for steady motion.  Recently Ingebo



studied the drag coefficients for droplets and solids



in cloud accelerating in airstreams.  Diameter and velo-



city data for individual droplets and solid spheres were

-------
                                                             40
obtained with a high-speed camera.  An analysis  of  the
data for unsteady momentum transfer from airstreams to
clouds of solid spheres, nonevaporating droplets and
evaporating droplets gave the following correlation for
the drag coefficient.

                          °-84                       (40)
Equation (40) is said to be applicable for a  Reynolds
number range of 6 to 400 and a sphere diameter  range
of 20 to 120 microns.  Rapid variation in acceleration
and velocity difference with time gave instantaneous
drag coefficients between Stokes1 law and steady state
values.  These results are summarized in Figure 4 with
the lines obtained from the literature ^  ' .
     If the droplet is flowing in the gas-phase under
normal pressure the second term on the right  hand :;.i.de
of Equation (37) is usually negligible in comparison  to
the other terms.  For vertical motion, equation (37)
can be reduced to:
                          PL        VL
     If the motion is in the horizontal  direction,  the
term due to gravity can be eliminated and  the  relatiori-
.v.hip ir; :;impl L.I' Led to:
        d v .    .. (J . o  ( v -v ,  ) |v -v i I
                ^li ti:   K  '-  ' i:   '•'                 (it;i)
                ^ Pi,      vl,

-------
                                                         /I I
                       Fixed  Solid Spheres
                         (Steady State)
Free Falling
          lets
      Stokes' Law

        C<«24/NRe
Water Dro
         Ingebo's  Correlation
0.1
Figure /,..  Correlation of  Instantaneous Unsteady
           State Dra/j; Coo IT latent with Reynold.".

           Number

-------
                                                               1,2
     The  average gas velocity at any  point in the ven-

turi scrubber is calculated by the following relation:


                   vg = ^                            (43)

where £ is  a  voidage in the scrubber  and is related by

the following relationship to the velocity of the

droplet.
                          LQ

                   VL = TTTeTS                        (U)


     (3)  Heat and mass transfer in a venturi scrubber

     The  heat and mass balances for gas arid liquid

stream in an  incremental section of a venturi scrubber

are:
                                 CPLdtL
                                                       U5)
                              dv
                           = aNAdV  =  -(G|/p)dpA       (47)
U.-ring  the  relationships, x " C./K,   dV -  odz,  N. -

and a  -  f>(l-6)/d  and riof, I cct in/-;  d I.,  in oc|iial. i on:j

ari(J (/i//)  i.n <:oni|)ar i ::(.)ii willi (.lie oLhcr l.crni:;, t,ln-

-------
                                                            '.3
following set of differential equations are obtained:


    dtT
    dtg     hQa
    dz    (Gn/S)Cpg      g
     Lm
    dz  ~ " (G/S)   A
              m
    dCA
And from VT = dz/dt,
          L
                dt _ 1
                dz   v,
                    (tT-t )                         (50)
             apky
                                                    (52)
                                                    (53)

-------
     (4)  Performance equations in dimensionless forme



     The above differential equations (32), (4-0, and



(49) ~ (55) can be written in dimensionless forms by



introducing the following dimensionless variables and



coefficients:
t

_

t
        go
            P=£_
                    C

                   ~~~
                    go
                                           v  =
                               gO
                                     L
                                 /    rn
                                                 gO
                                      mo
         Bo
                                            Ao
                                      C  G
10
                               ha5i
                            '    11

-------
Then,


                      V
  dz
                  _  L
          e dz    2  L  dz     3 2
dT
dP.
 dZ
                         v(57)
       g                  L
  o-
_e =. (TT-T  )                                  (59)
 dz     «   L e
dL'

-------
  dv    .

  — =^i2 (yWi-yw) p                              (63)
   dZ
  dT   !                                            /, v
  — = —                                           (64)

  dZ   VL






     This set of differential equations is numerically



solved by Runge-Kutta-Gill method, which saves computer



memories, using given initial condition:: at the noK:••,'!.c-



point.  The heat and mass transfer coefficients and



equilibrium relations needed to solve the above :\r.\; of



equations are estimated as discussed be Low.





     (5)  Gas-phase heat and mass transfer coefficients



     Gas-phase heat and mass transfer to or from a single



sphere placed in a moving fluid has been studied by many



investigators   f '    '     .  A correlation having the



same form as the Ranz-Marshall equation obtained by



Steinberger and Treybal     ' can be used to calculate



the gas-phase heat and mass transfer coefficients of the



individual droplet in a venturi scrubber:
    NSh • NSh,o * °'»7 (NRe- Ns)'                (65)
where
    N,,,    = 2 + 0.569 (Nr - Nn )0'250 for (N  - N  .
     on , o               lir   oC             ur   ^c

-------
      o
        = 2
           0.0254 (N
                               1


                               J,
                       Qr
The applicable ranges of this correlation are:






      1 < NRe < 30,000




    0.6 < NS(, <  3,000





     Equation (65) is also used to compute the mass



transfer coefficient of water vapor from the  surface



of a liquid drop into the gas-phase.





     (6)  Rate of gas absorption into spherical,  droplet



     The rate of gas absorption arid the mass  transfer-



coefficient in a stagnant liquid drop for physical, ab-



sorption can be obtained by solving the following



partial, differential equation expressing the  material



balance in the drop.






              'J A    s^   --1 Cr^-1 ft
        9t
   .1 .0.    :   t  • 0,   0 < r < r




   B.C.I.  :   r = 0,   t > 0
B.C. 11. :
                   r  ,
                        t>0
                                               , .
                                               A :L

-------
This partial differential equation  can  be  solved ana-


lytically as follows.  By introducing a change  of


variables, u = C.r, the above equation  with  initial


and boundary conditions are rewritten to:

     I.C.    :   t = 0,    0  <; r  < rQ    :    u  = 0



     B.C.I.  :   r = 0,    t>0         :    u  = 0
     B.C.II  :   r=r0    t > 0         :    u =
The solution of this set of a partial  differential


equation with modified initial and boundary  conditions


ic given by:


              2r C    oo  / , vm       „          D.m2;r21
                o Ai v—  v-1)    .   ,m7trx      ,    A
                                 .   ,.      ,          .
   u = rC., + 	 2_, 	  sm  (	)  exp (	«	)
                     	1   ITI         I'             y, ~
                     m-1              o            r0
or,
  P         ^r»   «>      m                   r\  *~  *~


  -^  = 1 + j^- C i~- sin  (!1II)  exp  (-  JL.	)   (70)

   Ai         r m i   m         rQ            r
The concentration profiles of the dissolved  gas in the


droplet along the radial direction  is  chown  in Figure 'j


with (D.t/r '") a:; a pararnctt.-r.

-------
                                                             49
 '0         02        0.4        0.6        Ot8
         dlmensionlei) depth from surface, I- (r/r0)
1.0
Figure  5.   Concentration Profile  of 302 in a  Droplet

            (S00-H00 System : constant interfacial
                                    \ (91)
                     rnnront.r.Thi nn ) x  '

-------
     From the definition of the flux of the dissolved
gas A at the interface in a unit time, we have,
                   3C
         NA =  DA (_)                             (7D
          H     H  9r r = r
                            o
Differentiating equation (70) with respect to r, the
equation for rate of absorption into the spherical drop
at time t is obtained as;
              2D.C..   *         Dm22
         "A
                 o    m=l
Thus the mass transfer coefficient at time t is given
by;
         kLp= T~
                o  m=l
     For gas absorption into a stagnant liquid drop
with an irreversible, instantaneous reaction such as
absorption of 302 into alkaline solution, the liquid-
phase mass transfer coefficient is given as follows:
Assuming both the diffusivities of the gas and the re-
actant in the liquid are nearly the same (see APPENDIX
A ) , we have
                       Q
                                                    (74)
where C... is the interfacial concentration calculated
by:

-------
                                                            5.
      CAi
               - CBoR
where the ratio of the resistance in gas-phase to that

in liquid-phase, that is R = k» H./k .

     The rate of absorption in this case will be:
      NA=kLCAl = VACA                           (76)
     When the interfacial concentration, C... , changes

considerably, or the diffusivities of the gas and the

reactant cannot be approximated to have same values,

this approach will produce some errors.  In that case,

a  set of partial differential equations obtained from

the material balance within a droplet has to be solved

numerically  (see APPENDIX C).  However, in most cases

of SOp absorption by lime or limestone slurry in a

venturi scrubber, the above approach is sufficiently

accurate.


     C.   Dissolution of Lime  and Limestone  in a  Holding
                          Tank

     A clear understanding of the  dissolution mechanisms

of lime  and limestone into a  weak  acid  solution  that is

recycled in the SOp scrubbing process ic essential  in

development and efficient operation of  the  wet scrubbing

system.

-------
     In this section, studies on the properties and be-

haviors of lime and limestone in the solution are pre-

sented and their reactions and the dissolution into the

recycling liquor are analyzed.  Based on these analyses,

mathematical models which can be used to predict per-

formance of a holding tank are proposed.

     For more information on the physical and chemical

properties of lime and limestone, see APPENDIX D.

     (1)  Properties and behavior of lime in acid
          solution

     Lime's effectiveness as an alkali scrubbing liquor

largely depends upon its ultimate solubility and the

rate of dissolution.  Some of the previous studies on

the dissolution of lime into various solutions, have

revealed the following  (1' 15' 25' 54^.

          i.  The initial rate of the dissolution is

directly proportional to the ultimate solubility of

lime.

          ii.  Particle size exerts some influence over

the rate of dissolution.  The increase in rate of dis-

solution is proportional to the increase in the con-

tact area between the solid lime and the solution.

          iii.  If the lime reacts with an acid that forms

a soluble lime salt, the rate of dissolution is increased,

the increase over the rate in water being directly pro-

portional to the concentration of acid.

-------
          iv.  If the lime reacts with an excess of acid



that forms an insoluble salt, the particles of lime are



crusted over with this insoluble coating (blinding), so



that the rate of dissolution decreases.



     When lime is dissolved into water, the following



reactions take place:





        CaO + H20  ^=s  Ca(OH)2                     (77)





         Ca(OH)2  ^±  Ca++ + 20H~                   (7#)





Since reaction (7$) is an ionic reaction, it may be



considered as a rapid reaction.  The previous study on



the rate of dissolution of lime ^•>^' shows that the



hydrolysis reaction (77) is also very fast and the dis-



solution process into water may be controlled by the



diffusion of the product from the lime particle.  Thus,



when a solid lime is placed in contact with a liquid,



the liquid-solid interface can be considered to be



covered by the saturated solution.  The solute diffuses



from the solid surface through the film of liquid sur-



rounding the solid particle into the main body of the



liquid where it is uniformly distributed by the con-



vection currents.



     If the excess acid such as sulfuric acid is present



in the solution, the following reaction occurs in the



liquid film surrounding the particle.

-------
        Ca (OH)2 + H2303 —-  CaSC>3 J  + H20           (79)

     (2)  Model for dissolution of lime in a holding
          tank
     In order to develop a model for dissolution of lime
in a holding tank, the following assumptions are made:
          i.  The concentration of Ca(OH)2 at interface
is considered to reach the saturated concentration
immediately.
          ii.  The dissolution reactions take place only
from the surface of the particle rather than from within
the particle.
          iii.  As the dissolution proceeds, the size of
the particle shrinks.
          iv.  All particles are nearly spherical in
shape and can be represented by a mean diameter when it
is present in the tank.
                                                (71)
     Applying the particle size shrinking model    ' to
the particles in the holding tank, the following equation
may be written on the rate of the dissolution:
              1     dNR
          - —2 • TT = ks (CBS-CBO>               <*»
            47lrp2
Introducing the molar density of the solid, f^^t into
this relation, wo obtain;
            d r     k.
          _ 	[1 .- 	''_ (r  -c  }                     (,i! i }
             -'•    A,,
-------
     If the diffusion process in the film  around  the



particle is the controlling step and the relative



velocity between the solid and the liquid  is  small,



the following relation is applicable:



               Nc,  = 2.0                             (82)
that is,

                    Dn

                                                     (83)
                    r
                     P
When the excess acid present.?, in the solution,  k_.  :Lu
                                                 *~*


approximated by    ':
Then the equation (8l) can be integrated as
             -R

              P       °B
             P


Therefore, the radius of the solid particle  at  time  t



i:j given by:
                      d    a  i [-,   /-,   \  .             / ,»/ \
             r  -  / JC - 	  (Cn -Cn  ;  t             (06;
              ~    / P   P     Bs  Bo
                         /MB
The time required for the complete dissolution,



is given by:
                                                             55

-------
     From the relation of the radius of the particle



and the fraction of the dissolution, we have:
                                      Ttr     r
   volume of particle left    ,     _ 3  P  _ (_E\3


   total volume of particle          4,^ 3    Rp
Combining equations (£6) and (88), we obtain:
     If the holding tank can be considered as a complete



mixing tank, the exit age distribution function is given



by:
              E(t) =~e  ""•                       (90)

                     t




where



              t - 60 V^/F                           (91)





Thus, the fraction of solid dissolved in the tank has the



following relation with the tank characteristics:




           -     f"
       1 - XB =   (l-XB)E(t)dt
            B   ^    B



                      fr     2DR                  /~


                  o    1   D "" O     ^^  ^^   '

                Rp3t  J0       /MB


                                                    (V2)



     From the material balance of Ca(OII)0 around the hold-



ing tank, tho following additional relation can be

-------
                                                             57
obtained:






          MXB^60L0 (GBo - CBi)                     (93)





These equations (37),  (92), and (93) are solved to



obtain the outlet concentration of Ca(OH)p in the



solution.




     (3)  Properties and behavior of limestone in S02

          scrubbing liquor



     Similar to the case of lime, in order to provide a



model for simulation of the dissolution mechanism of



limestone into acid solutions such as the recycling



liquor in the limestone - S02 scrubbing system, experi-



mental data taken under the conditions similar to the



field plants are needed.  However, only a few studies



on the dissolution rate of limestone into several acid


                             (^7  "\&  Q$}
solutions have been reported v^ ' * '   '.  These data



were obtained under limited conditions different from



the conditions of practical interest.  Therefore.it is



questionable that these results are useful to simulate



the holding tank in the limestone slurry process.



     To develop a kinetic model to estimate the rate of



dissolution of limestone, it is necessary to know the



key reactions contributing to the dissolution as well as



to find the ultimate solubility of limestone into the



slurry.  In the case of limestone, however, not only a



number of reactions are taking place simultaneously but

-------
also its solubility is strongly dependent upon the


partial pressure of CO- over the solution or the con-


centration of carbonate ions in the solution ^ ''*'  ' "•* .


     In pure distilled water in which there is no dis-


solved COp and which is exposed to a COp - free atmos-


phere, limestone is virtually insoluble.  With an in-


crease in partial pressure of COp, the solubility increases


steadily to a point where it might be characterized as


sparingly soluble.  A number of measurements have been


made by many researchers   ^'      on solubilities under


varied conditions, such as temperature, partial pressure


of COo  and in aqueous solutions which contain other
     *• >

soluble salts.  Many of the results do not agree with


each other, but this is believed to be due to different    '


laboratory procedures, conditions of test, and the quality


of the limestone.


     Chemical reactions involved in the dissolution of


limestone into S02 scrubbing liquor are discussed in


Section A of this chapter.  Besides the complexity of


the reaction mechanism, reactions seem to interact with


each other making it practically impossible Lo Limit


the number of reactions us rate-doterrnin.i rig step:.;.


     There is, however, a considerable amount of data


on the total concentrations of the key components such


as sulfate, suLfite, calcium, and carbonate in the re-


cycling liquor obtained from various SOp scrubbing

-------
plants ^6' 13' 23>     .   It is believed that these



components play main roles in the overall reaction in



SOp - limestone system.  This was already discussed in



Section A in this chapter.  In Figure 6 ~ 9> comparisons



of the outlet concentrations of such components with the



equilibrium values calculated by computer programs


                                 (99)
originally developed by Phillips V77'> and revised later

                    / rt \

by Berkowitz et al.     are shown against the pH of the



liquor leaving the holding tank.



     From these figures,  we can observe the following



facts:  In spite oT the significant difI'eroncer; Ln the



operating conditions and the design of the holding tank



such as residence time and area exposed to the atmos-



phere, the data seem to indicate that concentrations of



each component in the liquor are very close to the



equilibrium values.  Effect of magnesium components on



the equilibrium relations seems significant.  Since



MgSOo and MgSOy are both soluble (18 and 50 g/1, respec-


       (J 3)
tively v  ') the magnesium fed with the limestone will



inexorably build up in the scrubber liquor.  As seen



from the figures, most of magnesium in the liquor pre-



sents in the form of MgSO,.  The rate of building up of



magnesium depends upon the operating time, quality of



limestone, etc.

-------
                                                                     f>0
    4


    2
8
6

4
i  8
    6
  KT1
    6
    6
            O
            A
            G
  Equilibrium concentration (50°C, Mg=0)

  Equilibrium concentration (50°C, Mg= 30 mg-mole/1)

  Borgwardt ^ 3^ (43 °C, Mg * 35 mg- mole/I)

  Burklln  and  Phillips(23)(50°C,Mg= I~6mg-mole/l)

  Skloss  et al.(|l7H500C,Mg=25^32mg-mole/l)
    4.5
5.0
                        55
                                 PH
6.0
70
  Figure 6.   Equilibrium Concentration of  Total
               Calcium at  50°C and its  Concentration
               in Outlet  Liquor  from Holding Tank  v:;,
               Liquor p!I.

-------
r°
 8
 6

 4
6   6
S   2
  KT1
    8
    6
           O
           A
           Q
Equilibrium concentration (500C, Mg=0)

Equilibrium concentration (50°C,Mg=30ma-mole/l)
Borgwardt(l3) (43°C, Mgi 3 3 mg-mole/1)

Burklin and Phllilp8(23)(50°C,Mg= I~6mg-mol«/l)

SKI088 et al.(ll7)(500C,Mg=25~32mg-mol«/l)
                AA
                                          A
                                  PH
                                       6.0
                                             7.0
 Figure ?.   Equilibrium  Concentration of  Total  Su.lfate
              at  >0°C and  itr;  Concentration in Outlet
              [.iquor from  lloldinf, Tank v::.  T.iquor pll.

-------
  icr'
   8
   6
   4
  IOT'
   8
   6
 I
  10*
•HP*
 W  6
 1  4
          O
          A
          0
          Equilibrium concentration (50°C, Mg=0)
          Equilibrium concentration (50°C,Mg=30mg-mole/l)
          Borgwardt(' 3> (43 °C, Mg* 35 mg-mole/l)
          Burklin and  Phillipe(23)(50°C,Mg= I~6mg-mole/l)
          Skloss et al.("7)(50°C,Mg=25~32mg-mole/l)
 X
_ X
               5.0
                      5.5
                                PH
70
  Figure 8.   Equilibrium  Concentration  of Total LJulfito
               at 50°C and  its Concentration  in Outlet
               Liquor from  Holding Tank  vz. Liquor  pll.

-------
icr'
  8
  6
      O
       A
       G)
  Equillibrium concentration (50°C, Mg=0)

  Equilibrium concentration (50eC,Mg-30mg-mole/l)
  Borgwardttl3)(43°C, Mg* 35 mg-mole/l)

  Burklin and Phillips <23)(500C,Mg= I~ 6mg-mole/l)

  Skloss et al.tll7)(500C,Mg = 25-32mg-mole/l)
  i
.5
5.0
5.5
                               PH
6X)
7.0
Figure 9.   Equilibrium Concentration of  Total Car-
             bonate at  50°C and its  Concentration in
             Outlet Liquor from Holding  Tank vs.
             TAquor pll.

-------
     (4)  Model for simulation of a holding tank in
          limestone process

     As mentioned in the previous section, the disso-

lution mechanism of limestone into SOp scrubbing liquor

which may contain various salts and ions in addition to

dissolved CO- is rather complex and cannot be completely

explained by the available data at the present time.

     In order to develop a model for simulation of a

holding tank in limestone slurry process, the following

assumptions are made:

          i.  The tank is operated under steady state

condition and is completely mixed.

          ii.  The tank is operated very closely as an

equilibrium stage, that is, the outlet concentrations

of each component are in "dynamic equilibrium" with

the gas-phase.

          iii.  There is an evolution of C02 from the

liquid in the tank to the gas-phase.

          iv.  There is no heat transferred between tank

and surrounding:.;, and heat of dissolution can be neglected.

     With the above assumptions, a schematic flow dia-

gram of a holding tank can be shown as figure 10.

     Taking the material balance around the tank for

each component, we obtain:

-------
     X-L + T! = S-L                                       (94)




where




     Tls  Yl + Zl     and      Sls  xl + Yi + zi



     X2 + T2 = S2                                       (95)




where



     T2 a  Y2 + Z2     and      S2 a  X2 + Y2 + Z2




     W  = M                                              (96)



     X3 + T3= M                                         (97)




where



    T  s Y  +7
     13   Y3 + Z3




     F  [Ca]j  + S± + M = F [CaJ2 +  S2 + M               (98)




     F  [SJ-L i- T.j_      = F [SJ2 + T2 + T3               (99)




where



     [S]-,3  rSO.J.+CSO, L  and  ^SJ9^ [SO,]0+rsO. J0
        i     J 1    4-L>        ^      j 
-------
Non  g-mole/min
 \S\Js}

                  g-mole/i


                J- g-mole/4
            [SO. L g-mole/*
               4 -L

                J1 g-mole/1
                                                      g-mole/min
                                   [CaJ2  g-mole/J2


                                       ]2 g-mole/0


                                       J   g-mole/JZ
                      g-mole/rain
        )-,)T g-mole/rain     X-,-(CaC07),  g-mole/min      X0=(CaC00)0 g-mole/min
          -i-                 -»       -'**                  
-------
            [S]2 = f2  (pH)                            (103)

            [C0312 = f2  (pH)                          (104)

     Thus, there are nine unknowns;  [CaL   [s]0  [C00]0
                                         C. ,     £ ,     J £. ,
S-j  T,  TO X,  X.,  and pH, and  nine  equations;  (95), and
 < t  *• t  J 1 £. i  J i
(97) ~ (104).  Theoretically  it is possible to solve this
set of equations but it  will  require a  trial and  error
method.
     It is easier to find the pH of  the liquor by using
the following relation.  The  derivation of  this equation
is shown in APPENDIX B.  The  pH of the  leaving liquor
should satisfy:

       ACa - AS - AC03 + NCO  /F - 0                   (10!;)

where
       ACa =  fCa.l-i - [CaL
                 -L       f^,
       Aq  =  fq]  - fsl
       tiO     I.. OJ-i   U "J J p

       AcOo = Ceo,]., - Cco3J2

     The rate of C02 evolution  from  the holding tank may
be approximated by:
N,,n  :i.r; a .('unction of  pi I,  operating condition:.; and Hie
 (j\)rj
design of the  tank.  Once;  the  value of k^aV,  which i.:j a

function of the operating  conditions and the  design of

-------
the tank, is known, every term in equation (105) becomes


a function of pH only.  Therefore the pH of the leaving


liquor from the tank can be calculated by this equation.


     The equilibrium partial pressure of CO- over the


limestone slurry is shown in Figure 11 against the pH


of the liquor.  The partial pressure of COp is a strong


function of pH of the liquor and also the concentration


of magnesium.  When pH is less than 6, which is often


encountered in the scrubber operation, the equilibrium


partial pressure of COp is much higher than the partial


pressure of C0? in the scrubbing gas.  This means that


COp may evolve in the scrubber in the limestone slurry


process rather than being absorbed.  When the pH of the


liquor increases above 6, the partial pressure of COp


decreases sharply so that the rate of COp evolved from


the tank which is represented by equation (106) is re-


duced if k'aV remains constant.  Therefore, it is dif-


ficult to increase the pH higher than a certain value


under normal operating or design conditions.


     To find the pH of the outlet liquor by solving


equation (105), k~a has to be estimated.  From the experi-


mental data obtained from the various investigations ^  '

23, 11?)^ k^a is calculated:


                                    F
       k'a - (ACu-ASO-j-ASO. -ACOj 	v	            (.1.07)
        °            343  V

-------
   1.2
   1.0
 .08
8"
§0.6
I
50.4
                            Mg°0
Mga6mg-mole/l
                            PH
                                   6
               8
   Figure  11.   pH  of Limestone Slurry vs. Vapor
               Pressure of C02 at 50°C

-------
                                                             70
where pCQ  is the equilibrium pressure of C02 with the
pH of the outlet liquor.  The calculated results are
shown in Figure 12 versus liquor flow rate.  The mass
transfer coefficient for CO- evolution from the holding
tank in limestone slurry process, k!,a, slightly increases
with the liquor flow rate.  The following correlation for
k~a can be used to approximate the CO- evolution rate in
the holding tank.

             k'a = 0.000211F0'263                    (lOtf)
     D.  Overall Operation of Venturi Scrubber
              System with a Closed - Loop

     From the practical point of view, most commercial

wot .scrubbing processes must be based on a c Losod-.l.oop

system in which the loaded liquor from the scrubber is

regenerated in a holding tank and recycled within the

process and not discharged from the process.  Removed

sulfur from the scrubbing gas is withdrawn as solid cal-

cium salts from the process.

     In this section a procedure of simulation of over-

all operation of a venturi scrubber with a holding tank

and some other auxiliary equipment as shown in Figure

13 is discussed.

     Prior to tho discussion, the following assumptions

are imposed on the venturi-holding tank system.

-------
  10"
   8
   6
E  8
!  4
o

t  2
  I0r»
   8
   6
    2


  ICT4
           0  Borgwordt^13)
           A  Burklin and Phillips^23)

           Q  Skloss et al.(|l7)
i  .  I
6  810*
                     J_
    10
iw     2     4   6  810*
liquid  flow  rate, r ,  l/min.
  Figure  12.  Mass Transfer Coefficient for  C0?
               Evolution  in the  Holding Tank  vsf
               Liquor Flow Rate.

-------
                                                             72
          i.  There is no dissolution of lime or lime-
stone except in the holding tank.
          ii.  The holding tank is considered to be com-
pletely mixed.
          iii.  Solid deposit and undissolved solid lime
or limestone are removed from the clarifier.
          iv.  Make-up water is either not required or
can be added without significant effect on the process
performance,  since the loss of the water due to evapo-
ration in scrubber or with solid deposit from the system
is negligibly small.
          v.  The system is under steady-state condition.
          vi.  Heat is exchanged between the gas-phaso
and the liquid-phase only in the venturi .scrubber.  Heat
loss from the system through the auxiliary equipment and
heat of dissolution of lime or limestone is negligible.
     Hence, with the knowledge of given conditions such
as the flow rate of recycling liquor, the amount of gas
scrubbed, the sulfur-alkali ratio, etc., the steady-
state operating conditions in the system can be found as
shown in Figure 14(a) and I/,.(b).

-------
                                                          73
     Flue Gas In
                                         Solid
                                  Lime or
                                  Limestone
                                   1
                                      Holding Tank
Figure  .1.3.   Venturi-Holding Tank  System with
             Closed-Loop

-------
   Read  G0, L0,  M , tgo
         yAo,etc.
            J.
  Assume liq. temp, to venturi, tLO
        outlet liq. temp, from
          venturi, t^
    Assume  inlet  alkali
        cone., C0Q	
            ±
     Calc.  XB by Eq.(92)
    Calc. performance of
    venturi by Eq(56)~(64)
             _L
    Calc.  X0 byEq.(93)
I.oi_r, i.c:  Diagram  i'or' .j'i mul ation ol
Vont',ur i.-IIol clin^  Tank  '{ccycl. \.\\\\
:'Jy:.;i,'Mn  (l.inif! .'jlur-i-y  Pr't^M•:;:•.)

-------
                Read   G0 ,  L0 , M, tgo
                         1
              Assume liq. temp, to venturi, tLO
                 Gate, outlet liq. temp, from
                     venturi, tu>
pH=pH+ApH
                 Assume pH of outlet
                  liq. from Holding tank
                 Cote. NCOJ by Eq.(l06)
                     and equilibrium cone.
                 Cola performance  of
                 venturi by Eq.(56)^(64)
                  Calc. SQz  absorbed, NSOa
        (h).    U)/r,Lr:  Diagram  for :; Lmi.iiu1.ioi)  of
                Vonturi-Holdin^  Tonk  Re; eye'I-i 11,3
                Sy:.-.tem  (T,.i.mei;torio ."-lurry  Pro^o:;

-------
              IV.  RESULTS AND DISCUSSION





     In order to verify the mathematical models developed



in the last chapter, a series of simulations of various



venturi scrubbers and holding tanks are performed and



the results are compared with experimental data.  These



simulations are conducted independently for venturi



scrubbers and holding tanks, and then an overall simu-



lation of a venturi-holding tank in which the scrubbing



liquor is recycled is conducted.  The sensitivity of the



scrubbing efficiency on several operating variables is



also investigated.





     A.  Simulation of Performance of Venturi Scrubbers



     In this section, simulations of the experiments of



SOp absorption by various solutions in several venturi



scrubbers conducted by Harris et al. ^ } '  J  , Gl.euson
et al.     ,  and Johnstone et al. ^^' Jj>' are discussed.



    (1)  Description of the experiments



     Harris et al. ^ ^'     studied S02 absorption by



water and NaOH solution in a venturi ,s;crubber whose



dimensions are shown in Figure 15-(a) (EPA venturi scrub-



ber).  The liquid was injected to the convergent section



of the venturi scrubber where it was immediately atomized



into small liquid droplets.  The pressure drop across tin;

-------
               (a)
Figure 15.   (a)
            (b)
Dimensions of Venturi Scrubber
used by Harris et al. (53» °5)
(EPA Venturi Scrubber)

Dimensions of Flooded Disc
Scrubber (FDS) used by Gleasor.
et al. (50)

-------
venturi scrubber and the difference in partial pressures



of SO- at inlet- and outlet- points were measured.



     Gleason et al.      investigated the absorption of


SOp .by water and lime and limestone slurries in a flooded
  ^'    i


disc scrubber (FDS).  The FDS has a movable disc near the



throat   •  'as shown in Figure 15-(b).  Vertical move-



ment of the disc in the converging throat provides a



means for varying the area of the annulus.  This allows



flexibility with respect to maintaining a fixed pressure



drop under varying process operating conditions dut; to


scaling, change in gas flow rate, etc.  Also the move-able



disc can be adjusted to give a desired efficiency with



varying the velocity at the throat.  Gleason et al.



also used a flooded disc scrubber in combination with a


packed tower connected through a holding tank.  The con-



centration of SOp in the scrubbing gas at the inlet and


outlet of the FDS, pressure drop across the FDS and the



pH at several points in the system were measured.


  ;.  The last case of SOp absorption in a venturi scrubber



is a series of experiments conducted by Johnstone et al..


\\-LV, )J>f  'f]-ie dimensions of their scrubber are shown in



Figure 16.  As mentioned in CHAPTER II, they measured



the total pressure and the rate of absorption at several


points along the length of the venturi scrubber for water-



SOp and NaOH solution - SOp systems.

-------
                             Pressure  taps
                                                              Sampling  position
            •Fluid  inlet pipe: 0.24 cm ID
Figure  16.  Dimensions  of Venturi Scrubber used bv Johnstone
             et  3.1. (^,  65)   (in  crr,.)

-------
                                                              rto
     The operating conditions in these  experiments  are



summarized in Table 3-



    '(2)  Pressure drop in a venturi scrubber



     In Figures 1? and 1$, the calculated pressure  drops



are compared with experimental data, showing good agree-



ment between the two.  Application of the pressure  drop



correlations for venturi-type scrubbers listed  in Table



1 to the experiment.?, described above shows that none  of



the correlations could predict the pressure drop without



changing the coefficients or powers in  the equations



except Calvert's equation and Boll's equation.   Calvcrt's



and Boll's equations are basically the  same as  equation



(32).  Calvert's equation predicted the pressure drop



fairly accurately in the case of the flooded disc scrub-



ber, while it gave higher values for the venturi scrubber



used by Harris et al. ^53' ^.



     The change in the static pressure  along the venturi



scrubber was predicted closely by equation (32) for the



venturi scrubber used by Johnstone et al. as shown  in



Figure 18.  It is advantageous to use equation  (32) since



it can*predict accurately the pressure  profile  within a



venturi scrubber.



     (3)  Momentum, heat and mass transfer



  "•fe Figure:;  19 through 2k are example:; of calculated



rc:;ul.t::; for venturi. :;crubbor:; of llarrl:; ^ '^' .-.ind .li>lm::U>n<:



et al. ^/l'/"    .  The velocity profile:; of the;  g;i:;  and

-------
Table 3«   Experimental Conditions used in the Three  Experiments
Experiment
Gas rate, rrr/rcin
(Gas rate, ACH-i)
Licuid rate, /rr.in
(Liquid rate, GPK)
Gas velocity,
m/sec
Inlet gas temo °C
Outlet gas terr:p°C
Pressure drop
cm-H20
502 inlet cone.
ppm
S02 removal %
Solution
Harris et al.
(53,85)
25.5 ~ 34.0
900 —1,200
3S and 57
(10 and 15)
60 — 70
120 — 160
25
20 — 30
2,000
32 ~ 64
11 (for H20)
K20,
IlaOH soln.
Gleason et al.
(50)
25.5
(900)
30 ~ 60
(8 - 16)
30 ~ 43
180 ~ 190
49
13- 25
1,000 ~ 2,000
40 — 50
14 (for H20)
'r> 0
"2L
CaO slurry
Johnstone et al.
"(44,65)
7.1 — 13.6
250 ~ 4^0
0.11 ~ 1.14
(0.03 ~ 0.30)
100 ~ 200
	
	
1,520'
1.5~ 15
- NaOH'soln. .

-------
  50
JUo
Q.
   30
9
CO
i
  20
o
u
   10
A  Harri8(t93)(EPAv«nturi tcrubbtr)
            O
            o°cpf£(S>
         10        20        30        40       50
         experimental  pressure  drop,  AP (cm-H20)
   Figure  17.   Comparison of Calculated Pressure Drop
               in  EPA  Venturi  Scrubber and Flooded
               Disc  Scrubber with Experimental Data

-------
          Gas  velocity  at throat* 152 m/sec
          	 calculated  value

            O   experimental  data  obtained
                by  Fei1d(44)
              02         0.4         0.6         0.6
            dimensionless  distance from  nozzle ,Z
1.0
Figure  18.   Pressure  Profile in  Venturi Scrubber
 *                                       (f i   A t~ i
             used by Johnstone et al. ^+^'   }'

-------
the liquid, the concentration profile  of  sulfur dioxide
absorbed in the liquid-phase and the temperature profiles
in the' gas and liquid along the axial  direction in the'
EPA venturi scrubber are presented  in  Figures 19 and 20.
The operating conditions and experimental.data covered
are:
        Gas flow rate = 30.3 mVmin
        Liquid rate = 37-35  /min
        Inlet gas temperature = 1$4°C
        Outlet gas temperature = 43 C
        Inlet SOp concentration = 2000 ppm
        Outlet SOp concentration =  1160 ppm
        Pressure drop = 21 cm HpO

     Figure 19 shows that in the EPA venturi,  the velo-
city of the liquid reaches its maximum value  after the
throat of tho venturi while the; gas velocity  reaches
    /
maximum In the throat sect.ion.  The liquid velocity
exceeds,, tho gas velocity when the gas  velocity decrease:.;
   '*'
sharply due to the expansion of the venturi duct after
the throat.  The contraction and the expansion of the ven-
turi duct seems to be desirable not only  for  atomization
of the ?liquid but also for heat and mass  transfer between
the gas and the liquid as the result of the high relative
velocity induced.
     I'Yom tho concent,ration profil.o:; of .  :u.ll.'u.r dioxide
absorbed in Uie  liquid plia:'.e  i I,  i:.;  :;een l.lial.  ,j lai1;1^1
amount of absorption take:.: pi.ace near  the point, of I.IK;

-------
                              liquid velocity
                              gas  velocity

                       	sulfur  concentration in liquid
                       Inlet  gas  velocity, 15.7 m/sec
                       Inlet concentration of NaOH, 0.03M
             0.2         0-4        Q6         0.8
             dlmensionless   distance  from  nozzle, Z
Figure  19.  Velocity and Sulfur  Concentration
             Profiles along Axial Distance ifi
             EPA Venturi  Scrubber (53)

-------
liquid injection.  This is principally due to the follow-



ing three factors in this region:  the small transfer



resistances, large concentration difference, and rela-



tively long residence time of the liquid droplets.



     The temperature profiles of the gas and the liquid



shown in Figure 20 indicate that the temperatures of both



the liquid and the gas approach the same value rather



quickly.  Thus venturi scrubbers can be considered to be



highly efficient heat transfer devices.



     The performance of the FDS can be seen to be nearly



the same as the EPA venturi scrubber.



     Figures 21 and 22 are comparisons of calculated



values of the absorption rate along the venturi as a



function of the liquid rate based on the experimental
data obtained by Johnstone et al.    '   J' .   The cumu-



lative absorption rate in Figure 21 and botal absorption



rate in Figure 22 increases with liquid rate almost pro-



portionally.  The calculated values show satisfactory



agreement.



     Figures 23 and 24 show the concentration profiles



of S02 and alkali within a liquid drop in two typical



cases with the distance from the point of the liquid in-



jection as a parameter.  For the SOp - H~0 system, the



concentration of 502 within the liquid drop is almost in



equilibrium at the outlet point as shown in Figure 23.



In Figure 24 the concentrations of iJCU and NaOlI within

-------
  1.0
o
  0.8
*
|0.6


"5

g


{04
(0
0)

|02
=6
I
I


I
I
 I
 I

 \
  \
   «
   \
                           liquid  temperature

                           gas temperature
                          Inlet  gas temperature, 154 °C
              0.04       008        0.12        OI6       0.20

               dimensionless distance from nozzle, 2
 Figure 20.   Temperature  Profiles of Oar;  and Liquid

              along Axial.  Distance in KPA  Venturi

              ,'jcrubher (')!>)

-------
o  8
o
x
•i 6
E
i
O
.8
I 2
s
a

u
 O  Experimental  data  of Johnstone  et al.(44>65)

—  Calculated  values
                                                           0.507  l/min.
                         10          6         20
                          distance  from  nozzle,    cm
                                              25
30
35
    Figure 21.   Profiles of Cumulative  Absorption Rate  in Venturi Scrubber

                 (Experiment of Johnstor.e et al.)  (^t,  6?)

-------
  12
  10-
8
e



«
o
 0   Experimental data of Johnstone et

	 Calculated  values
              0.2         0.4        0.6

                      liquid  rate,   l/min.
                                       0.8
1.0
   Figure  22.   Comparison of 30? Removal Rate  in thr

                Vonturi  Scrubber Calculated with Expori-

                monta.l Data Obtainod  by John:;toiU! ot al..

-------
                                                                90
                           distance from nozzle 73cm
            02         0.4        O6        03
          dimensionless  depth  from surface, l-(r/r0)
Figuro  :.'.'
Concentration  Profile  oJ' 30?  in a
Droplet (KPA Vc.-nturi :   ll,,0 -  :.)0?

-------
 1.0
0.8
                   '2.5cm
                /
               /

             / 19cm
                                 /dlitonc*  from noult

                               / 38 cm
                      /       /
                     /       /
                     /       /
                  	S0t conotntrotion

                  	OH* concentration
              0.2         0.4        0.6        0.8

           dimensionless depth from  surface, l-ir/rj
                                             I JO
Figure  2/f.
Concentration  Profiles of

in a  Droplet  (EPA Ventura

M20 System)
)2 and  NaOH

 Naon -  :;o2

-------
                                                             92
a liquid drop are shown in a case of the SO- - NaOH -
HpO system.
     Finally the calculated S02 removal percentages are
summarized and compared in Figure 25 with the experi-
mental data obtained from different venturi scrubbers
under different experimental conditions.  The agreement
between the calculated values and the data is quite
satisfactory.

     B.  Simulation of the Holding Tank Performance
     In this section, the simulation of the holding tank:.;
for the l.irnc and the Limestone slurry processor; will bo
be discussed.  On l.y a few data on the performance of
holding tanks for the lime and the limestone slurry pro-
cesses are available.  The operating conditions under
which these data were taken are summarized in Table 4.
     (1)  Holding tank for the lime slurry process
     Only one series of experiments performed by Gleason
et al. ^  ' fed lime directly to the mixing/holding tank.
They measured the values of pll at the inl.ct and outlet
points of the holding tank.  The value of pll is related
to the concentration of Ca(OH)? in the solution as shown
in Figure D-l in APPENDIX D.  The model for the disso-
lution of lime proposed in the last chapter has been used
to simulate the holding tank used by Gleason et al.  The
results are compared with experimental data in Figure 26,
showing good agreement.

-------
                                                               93
  100
   80
i  eo
o"
CO
I
o

o
u
  40
   20
         O   Harrisl5%F* vwrturilNaOH-SCVH^O)
A  GleasonJ^FDS: CaO-SOf Hp)

A  Glea8on<50)(FD§;soL-H/))

G  Johnstone et al.(44,6&)

            (NaOH-SOrHtO)
              20        40         60         80

                experimental  S0t  removal  %
                                                100
          25.  Comparison  of Calculated SO,-,  Removal.

               % with  Kxperimental Data

-------
Table 4*  Experimental Conditions of Holding
    Tanks Used in Four Experiments
Experiment
alkali
volume , i
(volume, gallon)
liquid rate, ^/rdn
(liquid rate, GPM)
residence time,min
liquid temp. C
Gleason^50^
lime
1900-5600
(500-1500)
30—60
(B - 16)
30 - 150
40 - 50
Borgwardt^1-*'
limestone
1,300
(350)
32.2
(8.5)
4-40
43
Burklin and
Phillips(23)
limestone
22,700
(6,000)
570-1,540
(150-485)
12—40
50
Skloss et al.
(117)
limestone
2,350
(620)
435
(115)
5.4
50

-------
   1.8
b
x 1.6
 ©
•5
 £
   1.4
3
   12
| 1.0
3
 o
 o
   0.
      8
  1.0         1.2         1.4          1.6
experimental concentration of Ca(OH)2,g«mole/l  XIO"2
1.8
   Firure 26.   Comparison  of Calculated Concentration
     *^            _  _  t	_\   .   _.  •.  _•    ,.     ¥*ii*    m
                                                Holding Tank
  of  Ca(OII)2  in Solution .1'rom
  with Data Obtained  by Glea^on et a.l.
  (50)

-------
                                                             96
     (2)  Holding tank for the limestone slurry process



     The amount of data available on the performance of



holding tanks in the limestone slurry processes is sub-



stantially greater than that available on the holding



tanks in the lime slurry processes.  The holding tanks



in the limestone slurry processes are simulated based on
the data obtained by Borgwardt v J ,  Burklin and Phillips


(23)                    (117)
v JJ ,  and Skloss et al. v     .  The comparisons of calcu-



lated results with the experimental data arc shown in



Figures 2?, 2#, and 29.



     In Figure 27, the values of the pH of the outlet



liquor are shown.  Although some scatter of the points



is seen, the agreement between the experimental and cal-



culated outlet pH is satisfactory within the errors of



the data.



     In Figures 28 and 29, the calculated concentrations



of the key components in the outlet solutions, such as



total calcium, total sulfite, total sulfate, and total



carbonate, are compared with the measured values.  Total



sulfite and carbonate concentrations arc somewhat scat-



tered but the calculated and experimental, values arc



within the same order of magnitude.  The experimental



and calculated total calcium and total sulfite concen-



trations are in good agreement.



     In the above simulations of the holding tank in the



limestone slurry process,  it is assumed that the holding

-------
  7.5
  7.0
  6.5
a
u
  6.0
  50
         A  Burklin  and Phillips(23)

         D  Skloss et al(ll7)
    5.0
55         60         6.5
        pH, experimental
70
75
   Figure 27.
  Comparison  of the Valuer, of Calculated
  pH of Outlet Liquor  from Holding'Tank
  with KxperJ mental Data.   (fArncutorK:
  blurry Proce:::;)

-------
   IO'1
    8

    6

    4
JB
o
I*
Total  calcium
O
A Burklln and  Philllps(23)
O Skloss et al.«17)

Total  sulflte
9 Borgwardt('3)
A Burklin and
   Skloss et
              I        466  I0~*
              total Cd**or S0| experimental,
                                2       4
                                g -mole /I
6   8ICT1
  Figure ?.&.
     Comparison  of Calculated  Values of Con-
     centrations of Total Calcium and  oulfit
     in  Outlet  Liquor  .from Holding Tank with
     Experimental Data (Limestone Slurry
     Process)

-------
                                                                   99
  10-'
    8

    6
£
 o
 E
 o>
  io"
1  •
"10  6
8
 S  4

If

I  .
Total sulfote
O  Borgwardt(|3)
A  Burklln  and Phillips^23)
Q  Skloss et al.("7)

Totol carbonate
© Borgwardt('3)
A Burklln and Phillips(23>
Q Skloss et al.(|l7)
  w-£j
10"
             2        4    6   8 10'*      2       4
               total SO^or CO^  experimental, g-mole/l
                                              6  6  10"'
 Figure 29.
      Comparison of Calculated Values of Con-
      centrations: of  Total Sulfate and Carbon-
      ate in Outlet Liquor from Holding Tank
      with Experimental Data  (r,ime:;tone Dlurry
      Process)

-------
                                                          100
tank is an equilibrium stage.  Based on the favorable

comparison of tho calculated pH and concentrations of

key components with the experimental data, this assump-

tion appears to be vc.ry reasonable.  A model based on

the equilibrium stagn assumption will be used to simu-

late the holding tank of a scrubber-holding tank system

in which the scrubbing liquor is recycled.

     C.  Performance of Venturi-Holding Tank Systems
         with Closed-Loop Recycle of the Scrubbing Slurry

     In this section the calculated results for venturi-

holding tank systems based on the conditions described in

Section D of CHAPTER III are discussed and the sensi-

tivities of operating variables are investigated.  For

more detailed information see the references ^ "h ' ^ ' "   .

     (1)  Lime slurry process with a closed-loop recycle
          of the scrubbing liquor.

     The momentum, heat and mass balances describing tho

lime slurry process based on Gleason's experiment ^ '

were solved.  The dependence of the alkali efficiency

(defined as the percentage of consumed alkali to rnake-up

alkali), and the SOp removal percentage on the liquid flow

rate and the alkali feed rate is shown in Figure 30.  From

this figure, the following can be concluded:

     1.  At low alkali feed rate, the percent S02 removal

increases proportionally with the alkali feed rate.

     2.  An increase in the liquid flow rate reduces GOp

removal arid alkali efficiency since the residence time in

-------
                                                                 101
                                       liquid rott « I
                                         (l/Mn)
                    SO* removal %
                              liquid rote =20
                                   (l/min)
          6os flow rote = 700 ACFM
          Volume of tank = 500 gallons
          Inlet SOg cone.»2220 ppm
          Inlet gas temp. & 365 °F
          Gas velocity at throat» 98 ft/sec
                         80
                     moM-up
                rate,
  120
g-CaO/mln
Figure 30.
Performance  of a Venturi-Holding Tank
System with  a Closed-Loop  Recycling of
Slurry (Lime Slurry Process)

-------
                                                          102
the holding tank under the constant volume condition de-

creases.  An increase in liquid flow rate also produces

in a larger diameter droplet resulting in more alkali

in the outlet liquid.

     3.  The pressure drop (which is not in this figure)

increases with the liquid flow rate from 17 cm-H20 at

50 1/min of liquid rcte to 47 cm-H20 at 200 1/min.

     4.  At low liquid rates, and the alkali feed rates

above 80 [g-CaO/min], the percentage of S02 removal does

not improve as rapidly with increase in alkali flow rate

as in the case where the alkali feed rate is less than

$0 [g-CaO/min.].  The rear:on for this is that at this flow

rate the .solubility -limit of CaO in the recycling liquor

is reached.  Therefore, the alkali efficiency goe.-j down

rapidly from this po:int.

     f>.  Taking into consideration the pressure drop,

S02 removal % and alkali efficiency, there will be an

optimum operating condition for this lime slurry process.


     (2)  Limestone r.lurry process with a closed-loop
          recycle of the scrubbing liquor

     An overall simu.lation of a scrubber-holding tank

system is based on the experimental conditions used by

Princiotta and Epstein ^2> Wl^ .

     In addition to 1-he assumptions made in Section D

of Chapter III, the following assumptions are made in

this calculation.

-------
                                                           103
     a)  Alkali sulfur ratio (mole ratio of alkali to


sulfur dioxide in the scrubbinggas) is high enough so


that the liquor leaving the holding tank is in cquili-


grium with solid limestone present in the liquid phase.


     b)  From the relation of the overall reaction (30),


one mole of SOp absorbed produces one mole of CO^.  The


amount of COp evolved in i,he holding tank is equal to


the amount of S02 absorbed in the scrubber.


     The calculated results in typical cases are shown

                                    f/ 2}
and compared with experimental data  v ' in Figure y.l.


The agreement between the calculated values and tho data


seems quite fair.


     The dependence of SO., removal percentage arid tho pll


of the liquor in the holding tank on the flow rato of


the recycling liquor is shown in Figure 32.  Some other


operating conditions are listed in the same figure.  Exam-


ination of this figure reveals the following:


     1.  The SOp removal percentage increases with the


liquid rate and the decrease in pH of the inlet liquor


to the scrubber has Dittlo effect on the absorption


efficiency.


     2.  An increase in the liquor flow rate causer, a


decrease in pll of the liquor leaving the holding tank


since C02 evolution per unit of liquor from the holding


tank decreases with the liquor rate.  The pll of the

-------
                                                           lO/,
        Gas flow rate = 15,000-30,000 ACFM
        Liquid flow rote » 300-600 GPM
        Inlet SOg cone. • 2400-2600 ppm
        inlet gas temp • 295-318 *F
           10       20      30      40       50
            experimental  S02  removal  %
Figure  31«   Comparison of Calculated SOp Removal '/.
             with Experimental Data  Obtained by
             Kpst(in  et al. (^2)  (Limestone Slurry
             Process)

-------
                                                                   105
  60
  50
  40-
  30
CO
  20
   10
	S02 removal % calculated by proposed model
	pH of liquor in tank calculated by proposed model
     Empirical  correlation of Epstein  et al.
          removal
             \
              ^
    Gos flow rote ° 15,000 ACFM
    Volume, of tank = 36,000 gallons
    Inlet SOg cone. = 2500 ppm
    Inlet gas temp.° 305°F
    Gas velocity at throat»100 ft/sec
               780
                                                   6.44
 440
                                                   ase
                                                   628
-6£4
                                          30OO
                      liquid  rate, F ,  l/min
 Figure  32.   Performance of  a Venturi-Holding Tank
                System with a Closed-Loop  Recycling  of
                Slurry (Limestone Slurry Process)

-------
                                                            106
recycling liquor increases with the C02 evolution.


     3.  The calculated SOp removal percentages are


compared with the values calculated by the correlation

                           /i 2)
obtained by Epstein et al. v   .   Two show similar


trends with respect to the change in liquid flow rate.




     D.  Scaling and Oxidation in Lime/Limestone Processes


     Some of the problems encountered in the practical


operation of a lime/]imestone process are scaling,


erosion, corrosion arid pH instability.  Of these scaling


in the scrubber and other parts of the scrubber-holding


tank system is one of the major problems encountered in


removing SO^ from acid, gases by a lime or limestone


scrubbing process.  This has consistantly been the main


problem in the operation of lime/limestone scrubbing


systems starting from the ICI-Howden work ^' ' '•*' in


England in the 1930' t; to the current pilot plant tests.


     Hence, the study of the mechanism of scale formation


and related problems has been an active area of research


since the I930's 
-------
                                                            107
recycling liquor is usually near saturation or above
saturation with respect to the concentrations of calcium
sulfite and calcium sulfate.  Therefore, the production
of these compounds resulting from SOp absorption in the
scrubber increases the tendency for crystallization of
calcium salts to take place on exposed surfaces, not
only on crystals already present in the slurry but also
on the scrubber walls and packing.
    The mechanism of scaling in a scrubber system
appears to be much more complex than for scaling in
boilers and desalination equipments.  Factors related
to scaling are:
      (i)  degree of oxidation in the scrubber
     (ii)  pH levels at various points in the scrubber
    (iii)  type of the scrubber
     (iv)  type of alkali
      (v)  amount of 30p absorbed per unit of slurry
     (vi)  concentration of calcium sulfite and calcium
           sulfate crystals (seeds) in the recirculated
           slurry.
    When SOp is absorbed in lime or limestone slurry,
crystalline CaSO^'aiUQ is produced in the system.  If
oxygen is present in the gas, as it is in most situations,
oxygen is alno absorbed simultaneously with SOp.  The
oxygen absorbed will be partially consumed in the

-------
oxidation of sulfite or bisulfite existing in the
solution to sulfate.
    There is evidence that the degree of sulfite oxi-
dation in the system has an important effect on absorp-
tion, scaling (or precipitation of calcium salts), and
corrosion.  Since there are several offsetting consid-
erations, it is not yet clear whether oxidation should
be promoted, inhibited, or left alone.  There are several
ways for either promoting or inhibiting oxidation but
their relative merits have not been studied adequately.
    There are both advantages and disadvantages of
sulfite oxidation.  The following presents a few of the
major advantages and disadvantages ^10^' 1IIf 11^t 119'.
    1.  Under upset scrubber conditions, which promotes
low pH, and an increased sulfite concentration in the
solution (see Figure 3), sulfite crystallization on
limestone surfaces may occur.  This process is called
blinding.  An increase in the oxidation rate could reduce
the sulfite content, which perhaps would decrease the
blinding effect.
    2.  The degree of oxidation in scrubber and its
supporting system increase the sulfate to sulfite ratio
in the solid phase.  This ratio is important in solid
settling since the sulfate crystals grow larger and thus
settle better.

-------
                                                             109
    3.  Oxidation of sulfite throughout the scrubber



system, including the waste pond, reduces the possibility



of water pollution by sulfite.



    4.  If a recovery process were operated with CaO-CaCO-



as the absorbent, oxidation of the sulfite to sulfate



would not be desirable because it is more difficult to



thermally regenerate calcium oxide from the sulfate than



to regenerate CaO from CaSO.,.



    In what is to follow some of the conclusions reached



in kinetic studies of the sulfite oxidation reaction is



reviewed.



    The sulfite oxidation reaction which is thought to



take place in the liquid phase is





               SO.T + -k 0? —" SO, =                  (109)
                 J       *•      H-



                                               (33)
This reaction has been investigated since 1697      and



a chain reaction mechanism with typical radical inter-



mediates has been suggested.



    Reaction (109) can be accelerated by a trace of heavy



metal ions such as cuprous, nickel and cobaltous ions



and retarded strongly by the addition or organic metals



such as carbohydrates, and benzoic, phthalic and


              (33)
glycolic acid     .  The sulfite oxidation reaction is



also affected by several other factors such as tempera-



ture, light intensity, solute concentration, pH value,

-------
                                                             110
etc.  The reaction has also very complex kinetics *•'•'';
for instance when the reaction is catalyzed by cobalt,
it is zero-th order with respect to 02 for sulfite con-
centrations of 0.06 g-mole/1, Ist-order for sulfite con-
centrations of 0.25 g-mole/1, and 2nd-order with respect
to Op for sulfite concentration between 0.25 and 1.0
                                  (if\ \
g-mole/1.  Linek and Mayrhoferova ^  ' do not recommend
taking the rate data for the reaction from the literature
because the quoted rate constants may depend strongly
                                              (70
on the purity of the sulfite solution.  Linek ^'Jl
showed the effect of impurities using the experimental
data.
    There are many other studies on the absorption of
oxygen into a sulfite solution and suggested reaction
mechanisms <26' 3°« *> ^' 6?' 7^> 75' ?6' 13°> including
an experimental study by Anderson and Johnstone *•*' in
which a venturi scrubber was used in the presence of a
copper or cobalt catalyst and considerable oxidation
was observed.  A study reported by Yagi and Inoue \ ' I
shows that the absorption rate of oxygen into sulfite
solution without catalyst may be represented by the
absorption of 02 into the liquid phase accompanied by
rapid, 2nd-order reaction.
    The situation in regard to the various promoters
(fly ash, N02, limestone constituents) and inhibitors

-------
                                                            Ill
(phenolics, etc.) is somewhat confused     .  More work
must be done before the relative importance of these
factors can be determined.
     The type of the scrubber is an important consid-
eration when scaling is prevalent.  Scrubber types differ
in the amount of slurry hold up.  Unfortunately, those
with the largest hold up appear to be the ones most
subject to scaling:  packed beds of the standard type,
for example, give good hold up, but the fixed packing
expecially if it has horizontal surfaces where solids
can settle and convert to adherent sulfite or sulfate,
is more likely to scale than a moving bed, spray tower,
turbulent bed contactor, or venturi scrubber.  The ven-
turi scrubber is mechanically simple and thus it is easy
to clean even if solid scale deposits on the equipment.
Therefore, venturi scrubbers are considered to be
superior in scaling resistance even though S02 removal
efficiency in venturi scrubbers may be lower than some
other scrubbers and therefore are suitable for scrubbing
high SOp content gases.  Although scaling in the main
body of the venturi scrubber can be avoided, at the wet-
dry interface, such as at the nozzle where liquid may
stagnant, a "mud" tends to collect and stick to the
surfaces.  Careful design with regard to the irrigation
of the surfaces with slurry or a special spray, or

-------
                                                            112
soot blowers at critical points will probably be re-



quired at the wet-dry interface to prevent scale build



up.



     The type of alkali affects the degree of scaling.



Lime gives more scaling than limestone, but no conclu-



sive reasons for this observation have been found.  The



generally lower pH in limestone system appear to be a



factor, at least with regard to sulfite scaling.  At the



present level of development, lime system must be



operated with recycle liquor diluted by adding water,



or the stoichiometric amount of lime must be reduced



to maintain a lower pH.  It appears possible, in a



venturi scrubber system, to use slightly higher stoichi-



ometric ratios of lime to compensate for the relatively



lower SOp absorption efficiency of the venturi scrubber.



     In order to have adequate SOo removal, in closed-



loop scrubbing operation with limestone, the slurry



circulation rate and slurry solids content must be much



higher for limestone scrubbing process than for lime



scrubbing process.  Since this operating condition should



also reduce scaling, the limestone process may be



superior to lime process with regard to scaling.  However,



in the venturi scrubber where scaling poses no serious



problems and the pressure drop is relatively high, lime



is a better absorbent for SOp removal with a low liquor



rate.

-------
                                                            113
     As mentioned above the scaling mechanisms are not



simple and it is impossible to draw any definite con-



clusions about the process of scaling based on the



present information concerning scaling.  However, it



can be concluded that the venturi scrubber presents



less scaling problems than other types of conventional



scrubbers.  More studies are required to avoid this



problem completely in the lime/limestone slurry



processes.

-------
                                                            1H
         V.  CONCLUSIONS AND RECOMMENDATIONS





     The mechanism of sulfur dioxide absorption into



water and various alkaline solutions in a venturi-



holding tank system have been investigated.  The data



in the literature on the reaction kinetics accompanying



sulfur dioxide absorption in alkaline solutions and



water serve as the foundation to build a mathematical



model for the mechanical and hydrodynamic character-



istics of the venturi scrubber as well as heat and mass



transfers.  The model of the venturi scrubber developed



can predict performances that compare favorably with



the experimental data for the S02~H20 and the S02~NaOH



systems.



     For lime or limestone slurry scrubber systems,



the dissolution mechanisms of lime and limestone into



a weak acid solution such as the recycle liquor become



important.  It was possible to explain these mechanisms



by a kinetic model based on the dissolution of lime,



and an equilibrium model in the limestone slurry process



for the performance of the holding tank.  These models



are used to simulate the performances of the holding



tanks and compared with the available experimental data.



     Finally, the model for S02 absorption in a venturi



scrubber has been combined with the model for the holding

-------
                                                            115
tank to simulate a closed-loop operation in which the



scrubbing liquor is recycled.  This combined model for



a venturi-holding tank system has been used to inves-



tigate the sensitivity of the operating variables on



the SOp removal efficiency in lime and limestone slurry



process.



     In addition, practical problems such as scaling



and oxidation were briefly discussed.



     In developing mathematical equations for simulation,



assumptions and simplification were made to reduce



mathematical difficulties and to provide realistic but



convenient and practical models.  In spite of the sim-



plification, the comparison between the calculated



results based on the model and the experimental data



shows good agreement.



     The specific conclusions and recommendations



resulting from this study are as follows:




     Conclusions



     (1)  A significantly large amount of mass and heat



transfer takes place near the liquid nozzle in the ven-



turi scrubber.  This is primarily due to small transfer



resistances, large driving forces, and relatively long



residence time of the liquid droplets in this region.



     (2)  The operation of the venturi scrubber is prac-



tically isothermal except in the zone extending a few

-------
                                                             116
centimeters from the liquid injection nozzle.
     (3)  Liquid-phase SC>2 concentration is observed to
be close to the equilibrium concentration in the case
of the SOp-HpO system at the exit of the scrubber.
     (4)  The dissolution mechanism of lime into a weak
acid solution can be explained by a kinetic model which
expresses the rate of dissolution of lime by the shrink-
ing core model.
     (5)  The performance of a holding tank in the
limestone slurry process can be approximated by the
"equilibrium stage model" in which the holding tank
liquor is assumed to be in a "dynamic equilibrium" with
the gaseous phase above the tank.  The rate of CCU evo-
lution in the holding tank plays an important role in
the dissolution process and may control the attainable
pH value of the limestone slurry in the holding tank.

     Re commendat ion s
     (1)  The  effect  of the solid phase in a liquid
on the absorption rate of a gas may be negligible in
the venturi-type scrubber.  This is because the resi-
dence time of the liquid is so short that very little
dissolution can take place.  However, the presence of a
solid phase affects the rate of dissolution of limestone
in the holding tank and in scrubbers which have a rela-
tively long residence time.  It is necessary, therefore,

-------
                                                             117
to have a better understanding of the mechanisms of the
dissolution of limestone into acid solutions.  More
fundamental studies on the mechanism of the limestone
dissolution are required.
     (2)  The formation of the scale, particularly
around the nozzle mouth, during the scrubbing operation
affects the diameter of the droplet, and is one of the
major causes for the decrease in absorption efficiencies
in the venturi scrubbers.  Studies to elucidate the
cause of scale formation and to develop a means of
reducing scale are needed.
     (3)  The reaction kinetics of oxidation of sulfite
to sulfate in the liquid phase must be studied.  The
effects of oxidation on absorption, equilibrium between
gas and liquid, scaling and corrosion, must be investi-
gated in more detail.  Oxidation may be important in
improving the settling rate of calcium salts and in
increasing the efficiency of the lime or limestone
scrubbing processes.
     (4)  The effects of the presence of magnesium species
in the liquid phase on the equilibrium relation appear
to be very important.  To use the equilibrium stage model
for a holding tank successfully, an accurate estimate of
the concentration of magnesium components accumulating
in the liquid phase is needed.

-------
                                                            118
     (5)  To improve the mathematical models proposed
in this study, more accurate information on the total
concentrations of the key components and pH values of
the liquor at various points in the scrubber process
should be developed.

-------
                                                             119
                    NOMENCLATURE


A          component of gas absorbed
                                           p    Q
a          contact area per unit volume, cm /cnr

B          reactant in liquid-phase

C.         concentration of component A in liquid-phase,

           g-mole/cnr

[Ca] .      total concentration of calcium in liquid-

           phase of recycling liquor, i = 1~3, g-tnole/1

"C.         mean concentration of component A in liquid-

           phase with respect to radial direction in

           venturi scrubber, g-mole/cnr

7J),         dimensionless mean concentration of  component

           A in liquid-phase with respect to radial

           direction in venturi scrubber, -

C..        concentration of component A at interface,
                    o
           g-mole/cnr

C.         concentration of component A at t=0  or in

           bulk liquid-phase, g-mole/cnr
  *
C.         concentration of component A in equilibrium

           with partial pressure of gas A in bulk gas-
                           *3
           phase, g-mole/cm
^\
C.         concentration of component A defined by

           equation (A-12), g-mole/cnr

Cg         concentration of component B in liquid-phase,

           g-mole/cnr

-------
                                                            120
Cg.       concentration of component B in inlet liquor



          to holding tank, g-mole/crrr



Cg        concentration of component B at t=0 or in hulk

                                 T

          liquid-pha.;e, g-mole/crrr



Cnc,       concentration of component B at liquid-solid
 D o
                              n

          interface, g-mole/cm



CPQ .      concentration of CO^ at gas-liquid interface,

   ii               o

          g-mole/crrr



C,        drag coefficient defined by equation (3#)



Cp        concentration of component F in liquid-phase,



          g-mole/cnr



[CO^]      total concentration of carbonate in liquid-

   * i

          phase of rocycling liquor, i = 1~3»  g-mole/1



CQU       concentration of hydroxyl ion in liquid-phase,



          g-mole/cnr



cpp.       specific hoat of gas, cal/g-mole • °C



Cpj       specific hoat of liquid, cal/g-mole • °C



Cq^ .      concentration of SO? at gas-liquid interface,



          g-mole/cm^



D         mean diffu.sivity of gas and reactant in

                          o

          liquid-phar.je, cm /sec



D.        diffusivity of component A in liquid-phase,


            2/
          cm /sec


D         diffur.Lvity of component B in Liquid-phase,

-------
                                                           121
                                                     o

D.        diffusivity of component A in gas-phase, cm /sec
 A§


D-  d     effective diameter, cm
 c f  G


D         mass median diameter of droplet, micron



D         diameter of nozzle, cm



d         diameter of liquid droplet, cm



dp.£.       differential pressure drop due to friction, atm



dV        differential volume of venturi scrubber, cm



Dop       surface-volume mean diameter of liquid drop-



          let, micron



E         enhancement factor for gas absorption with



          chemical reaction



E^        enhancement factor for gas absorption with



          instantaneous reaction



E(t)      exit age distribution function



F         volumetric liquid flow rate, 1/min



f         friction factor



G         component of gas absorbed

                                             P

g         acceleration due to gravity, cm/sec

                                       p

g         unit conversion factor, g/sec 'cm-atm or
 c
                  p

          g*cm/sec -G



G         molar flow rate of gas, g-mole/sec



G         volumetric gas flow rate, crrr/sec



H.        Henry's law constant for component A, g-molc/


            3
          cnr *atm



hu        heat transfer coefficient in gas-phase,
 u


          cal/cm -sec* C

-------
                                                           122
k         thermal conductivity, cal/cnrsec'°C



KG        overall macs transfer coefficient,

                   P

          g-mole/cm . sec • atm



RG        mass transfer coefficient in gas phase,



          g-mole/cm • tec • atm



k'a       mass transfer coefficient for COp evolution,



          g-mole/1 *m:i n • atm
~
          mass transfer coefficient for H20 evaporation,

                   2

          g-mole/cm • sec • atm
KJ        overal]. mass transfer coefficient, cm/sec



kj        mass transfer coefficient in liquid-phase, cm/sec



k,.0       mass transfer coefficient in liquid-phase



          without reaction, cm/sec



kT        instantaneous mass transfer coefficient in
 bp


          liquid-phase, cm/sec



k^        mass transfer coefficient for solid disso-
 o


          lution, cm/sec



k^.        mass transfer coefficient for solid disso-
 o


          lution with reaction, cm/sec



kp  kp    reaction rate constant for second-order reaction,



          l/g-mole*sec



L         length of throat, mm




L         molar liquid flow rate, g-mole/sec



L'         dimensionless molar liquid flow rate, -



L         volumetric liquid flow rate, cm /sec

-------
                                                             123
M          make up rate of lime or limestone, g-mole/min



M          mass flow rate of gas, g/sec
 o

ML         mass flow rate of liquid, g/sec



m          liquor to gas mass ratio, g-liquid/g-gas

                                          q

m          specific wetting,  1 -liquid/ m -gas



N.         rate of absorption of component A, g-mole/



           cm *sec



N.°        rate of absorption of component A without
 'A
                              p

           reaction, g-mole/cm -sec
N.         acceleration group, (d /v "


N,,         number of moles of component B, g-mole
 D


NGr        Grashof number, gdp3(/)L-j|) Jg//^2, -



 COp       rate of C0? evolution, g-mole/min


Nn         Reynolds number,


M          Schmidt number, _,--, r „.
                            5  & Ag,

Nsh        Sherwood number, d k^RT'/DA  or d h^,

                                            O

NSu        surface tension group, gc<*dpfi//jr  » -


Nwt        gravity group, dp[4g^(/^-/) )/3/^-  ]    , -


P          dimensionless total pressure, -


p          total pressure, atm


PA         dimensionless partial pressure of gas  A in


           gas-phase, -


p.         partial pressure of gas A in gas-phase, atm


p...        partial pressure of gas A at gas-liquid inter-


           face , atm

-------
                                                          124
PCQ       equilibrium partial pressure of CCU at gas-


          liquid interface, atm

  o
PCQ       partial pressure of C02 in bulk gas-phase,


          atm


q         liquid to gas ratio, liter-liquid/m -gas


R         gas constant, = $2.06 cmv£-mole-°K


R         radius of .solid particle, cm


r         distance from center of droplet, cm


r.        rate of reaction expressed by equation (A-7),


r         radius of Liquid droplet, cm


r         radius of .".olid particle, cm

                                             2
3         cros^-sect-Lonal area of venturi, cm


Sj_        flow rate uf solid with recycling liquor,


          i = 1~2, g-mole/min


[sj.      total concontration of sulfur in liquid-phase


          of recycling liquor, i=l~3» g-mole/1


[SO^J.    total concentration of sulfite in liquid-


          phase of recycling liquor, i=l~3» g-molc/1


CSO,]^    total  concentration of sulfate in liquid-


          phaso of recycling liquor, i=l~3» g-mole/1

                                         2
5         flow area for atomizing air, cm


T         dimen.'jionloss time, -


t         time, sec


t"         mean residence time, sec


T         dimensionless gas temperature, -
 «_*

T'        gas temperature, °K
 o

-------
                                                            12'
T^         flow rate of solid calcium salts with


           recycling Liquor, i = 1~3, g-mole/min


t          gas temperature, °C
 5

Tr         dimensionless liquid temperature, -


tr         liquid temperature, °C


v          velocity, cm/sec


V          dimensionless gas velocity, -
 &

v          gas velocity, cm/sec
 6

v          gas velocity at nozzle, cm/sec
 c«

v -,        gas velocity at entrance to venturi or at


           downstream,  cm/sec


v 2        Sas velocity at exit from venturi, cm/sec


Vj         liquid velocity or velocity of liquid drop,


           cm/sec


v          relative velocity of gas and liquid, cm/sec


v          relative velocity of gas and liquid at throat,


           cm/sec


Vy         dimensionless velocity of liquid droplet, -


V,         volume of holding tank, 1
  v

w          gas velocity at throat, m/sec


x          mole fraction of component A in liquid-pharjc, -


7R         fraction of dicsolution of solid particle, -


Y...         mean fraction of dissolution of solid, -


X.         flow rate of solid limestone with recycling


           liquor, i = l~3» g-mole/min

-------
                                                             126
Y-          flow   rate   of  solid calcium sulfite in



           recycling Liquor, i = l~3> g-mole/min



y          mole fraction of H^O in gas-phase, -



ywi        mole fraction of HpO at gas-liquid interface, -



Z          dimensionless distance from nozzle in venturi, -



Z-         flow   rato   of solid calcium sulfate in



           recycling liquor, i = l —3, g-mole/min



z          distance from nozzle along axial direction



           of venturi, cm
                    Greek Letters





  £         heat of vaporization, cal/g-mole



  f         stoichiometric factor, -



AC.        driving force for gas absorption, g-mole/cirr



AC!!        dimensionless driving force for gas



           absorption, -



AMj        difference of mass flow rate at entrance and



           at exit of venturi, g/sec



Ap         total pressure drop across venturi scrubber,



           atm



AP         pressure drop due to acceleration of liquid,
  3.
  ag
           atm



           precrjure drop due to acceleration of gas, cm-H00
                                                         2

-------
                                                             .1.2?
AP o       pressure drop due to acceleration of solid,



           cm-H20



AP         pressure drop due to contraction, atm
  c
                                             o

AP,        pressure drop due to friction, N/m



AP         pressure drop due to expansion, atm
  C


AP,.        pressure drop due to friction, atm



AP         measured pressure drop across test section,
  m


           cm-H20



AP         pressure drop at generalized position, cm-HpO



Ap         pressure drop across test section due to gas
  J^o


           and gravity, cm-HpO



Ap         pressure drop across test section due to



           solids and gravity, cm-HpO



Ap         pressure drop due to composite fluid friction,
  w


           cm-H20

                                            o

Ap         pressure drop across venturi, N/m



Ap         pressure drop across venturi, mm I-UO



AP         pressure drop across venturi, in H20



AP,         pressure drop across flooded disc scrubber,



           in H20



Av         difference of gas velocity at entrance and at

  o


           exit of scrubber, cm/sec



AvT        difference of liquid velocity at entrance and
  J_j


           at exit of scrubber, cm/sec



 £         void fraction in venturi scrubber, -

-------
 9         time


 U         viscosity of gas, poise
' o

M         viscosity of liquid, poise


 ^         stoichiometric factor, -


£•         dimensionloss coefficient, i = l~12, -


 p         density of gas, g/cnr
 O
 ft         density of liquid,
                                              •^
 fi»         molar density oT liquid, g-mole/cm-3


^g        molar density of solid particle, g-mole/crrr


 P         mean density of gas mixed with liquid, g/cirr


 C-         surface tension, dyne/cm


 f         time required for complete dissolution,  sec

-------
                                                             129
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                                                            137
                     APPENDIX A


        Enhancement Factor for Gas Absorption
        with Instantaneous Chemical Reaction
                 into a Liquid Drop


     When mass transfer is accompanied by a chemical

reaction, its rate is accelerated and becomes faster

than that without the chemical reaction.  This effect

may be expressed in terms of an enhancement factor,

defined as follows:

                      E -   b                       (A-l)
where, kJ3 = mass transfer coefficient without reaction

       kj- = mass transfer coefficient with chemical
            reaction

     If a gas A and a reactant B in the liquid phase

react very rapidly according to the following stoichi-

ometric equation,

                  A +  tfB — -  Product               (A-2)

the liquid film at the phase boundary is rapidly de-

pleted of reactant s A and B.  Thus, the reaction can

proceed only as fast as the reactants can diffuse to

the reaction surface.  A diffuses from the interface

to the reaction surface and B diffuses from the bulk of

the liquid to this surface.  A semiquantitative plot of

the concentration profiles in and around the liquid film

is shown in Figure A-L.  The dashed line indicates an

-------
                                                           138
Gas
Gas Film
Liquid Film
Liquid
                                       CBO
                                        CAL
                     \
                      Reaction Zone
                                        Distance
 Figure A-l:  Concentration Profile Across the Gas-
              Liquid Interface with Instantaneous
              Reaction.  The Dashed Line  Indicates
              the Approximate Concentration Gradient
              across the -Fluid Film in  the Absence
              of Chemical Reaction.

-------
                                                            139
approximate concentration across the liquid film in


the case of physical absorption.  It can be noted that


with the chemical reaction, the concentration gradient


of A is steeper.  Thus, the enhancement factor, E,


should be greater than 1.


     Hatta ^ •5' first derived an expression for E. based


on the assumption of a completely stagnant fluid film


and found:


                   E. = 1 + J^Bo                  (A_3)

                    1       O^Ai


Of course, the assumption of a stagnant fluid film with


an abrupt transition to the bulk of the liquid is not


very realistic, but equation (A-3) fits many experi-


mental data very well.


     Two other theories for predicting E- for very fast


reaction lead to similar results.  Higbie's penetration


theory, ^  ' which is based on unsteady state diffusion


into a laminar fluid stream, leads to the following


expression ^^' for the enhancement factor:


                                  D
               E  =
This differs from equation (A-3) only by the factor
,/D./DB  which is often nearly unity.  A derivation based


on the boundary layer theory results in the expression


(45, 79, 102,
                         DC     D
               r-  - i i _L   B Bo\ /  A\                /A  r\
               E  ~ ^ l+     — ) ^^                (A-5)
                                  B

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                                                            140
     If the diffusivities of components A and B are
equal, equations (A-3), (A-4) and (A-5) become:
                             Q
                   E  = 1 H-  JZ                    (A-6)
                    1
     The above expression for the enhancement factor is for
gas absorption into semi-infinite plane of liquid.  The
following is a demonstration that for gas absorption into
a droplet with an instantaneous reaction, the enhance-
ment factor always reduces to equation (A-6) if the
diffusivities of the gas and the reactant in the liquid
                (21)
phase are equal     .
     Suppose that the  reaction rate for reaction (A-2)
can be expressed as a  function of the concentration of
A and B as follows:
                   rA  = k2r CCA.CB>                 
Then, equations of continuity for the two components are
generally given as:
          9C                7
              + WCA  = DA V2CA - k2f (CA,CB)       (A-«)
                      = DB ? CB - * k2f (CA,CB>     
If D. = DB = D, the above set of equations can be simpli-
fied.  Multiplying equation (A-3) by "ft and subtracting
equation (A-9) from this product gives:
       X P  P
                         -CB) = DV2UCA-CB)        (A-10)

-------
                                                            HI
or
                                                    (A-ll)
where,
                                      Ai
                                                    (A-12)
The boundary conditions for equations (A-#)  and (A-9)
are:
          t = o,  r >  o     :
          r = o,  t >  o
          r = rQ,  t >  o
CA = o
ar^   u  '  3r
CA = Cfl, ,
                    (A-13)
                                 'A ~ "Ai '    ar
When these conditions are substituted into equation
(A-12), the following initial and boundary conditions
on C. result:
          t = o ,  r >  o
          r = o ,  t >  o
          r = r   t >  o
               o >
C  -o
                                 9r
                   (A-H)
     The rate of gas absorption from the gas phase to the
liquid phase is obtained as the product of the  diffusivity
of the gas and its concentration gradient at the  inter-
face.  That is,
                NA =  D

     Since equation (A-ll)  does not contain the reaction
term, this equation expresses the gas absorption without
chemical reaction, i.e.,  physical absorption.   The rate

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                                                            142
of physical absorption will be expressed as follows:
                         ^
     For equal diffusivities of A and B, the enhance-
ment factor is reduced to the ratio of the concentration
gradient of C. at interface.
                   NA  ,9C A
              Ei =
     Taking the derivative of equation (B-12) with re-
spect to r,
                     P       r   *^ P       "\ P      -«
        (_Ji)    -    Ai     [n—)    (  B)    1
          "    "   ^CAi+CBo  L    9 r r=rr,  9 r r=r-. J
Applying boundary condition (A-13), (3CB/9r)r_r =  o,  gives
             A,        *CAi    ,3CA,
                      "           I^=
                                            r
Therefore, from equations (A-l?) and (A-19), the en-
hancement factor for gas absorption with an instantaneous
chemical reaction into a droplet is also given by the
same equation as equation (A-6).  That is:

                     E  = I
     When a second gas whose diffusivity is the same as
that of the first gas is absorbed and reacts with the
same liquid component, B, irreversibly and instantane-
ously according to the following chemical reaction,

-------
                   G + $B — ^  Product              (A-21)
it can be shown also that the enhancement factors for
both gases are equal to:      '
                              Q
                  E  := I  +      °                   (A"22)
     If a gas which contains S02 and CCU is treated with
an alkaline solution, the rates of absorption of these
two gases will be accelerated by the factor:
                                                    (A-23)
                                                            143

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                                                             144
                     APPENDIX  B
            Derivation  of  Equation  (105)
     As discussed in Section  (4) of CHAPTER III, if
the holding tank can be considered as an equilibrium
stage, the following set of nine simultaneous equations
is obtained from the material balance.

      X2+T2 = S2                                   (B-l)
      X3+T.= M                                     (B-2)
           = X2/S2                                  (B-3)
      F[Ca]1+S1-Hy[ = F[Cal2+S2+M                     (B-4)
      FEsJ-L+T-L = F[SJ2+T2+T3                        (B-5)
      FECO,]+X.,+M = F[CO,]4-X9+X,+Npn               (B-6)
          j 1  -L         j 2. £  j   UUp
      [CaJ2 = fx(pH)                                (B-7)
      [S]2 = f2(pH)                                 (B-S)
      [C03J2 = f3(pH)                               (B-9)
     It will be shown that the pH of the liquor in  the
holding tank must satisfy a consistency condition and that
the pH can be calculated without solving the entire  set
of equations.
     Assume that the pH of the liquor leaving the tank
is known.  Then [Cal2  Cs]2 and [C03J2 are given by
equations (B-7), (B-8), and (B-9).  Substituting these
relations into the rest of the equation, we obtain:
      S2 = FJCCal-L-CCaJ^+S-L                         (B-10)

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                                                            145
           = M
      X2+T2 = S,
                 - o
Equation (B-ll) through (B-14) can be written:
(B-ll)
(B-12)
(B-13)
(B-14)
(B-15)
                                                    (B-16)
                                 3b2                (B-17)
                                                    (B-18)
                                                    (B-19)
       •**      «w    *«•  »-p
The augmented coefficient matrix of the above set of the
equations is given as:
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
b
b
b
b
1
2
3
4

=


1
0
0
0
1
1
0
-1
0
1
1
0
0 b1
0 b..
i b2
1 b,-b1
I
0
0
0
0
i
0
0
-1
1
1
1
0
0
1
1
b
b
2
4~b:
3
L+b3
     Therefore, in order for equations (B-l) through (B-9)
to be consistent and have a solution,

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                                                             146
              b0 = b. - bn + b-
               *•    4    J-    }
or in terms of the definitions of the b's,
          FAC03+X1+M-NCO  = S-p-FAS-T^+M

Substituting equation (B-10) and S^ = X-^ + 7^ into the
above equation gives
           AC  - AS - AGO. + Npn /F = 0              (B-20)
             a           j    L«UO
This is the condition for the existence of a solution to
equations (B-l) through (B-9).

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                                                            147
                     APPENDIX C

       The Rate of Gars Absorption Accompanied
        by  Instantaneous Irreversible Reactions
      in a Liquid Droplet in a Venturi Scrubber—
                A Numerical Solution
     As discussed in Section A of CHAPTER III, absorption
of SCL (and COp) by alkaline solutions and limestone
slurries may be treated as gas absorption accompanied
by an instantaneous reaction.  Numerical methods have
been used by many investigators to solve the equations
describing mass transfer under similar situations.
                  (97)
Perry and Pigford v    numerically solved the simul-
taneous partial differential equations for the pene-
tration model of gas absorption into a liquid accompanied
                                                     (19)
by a second-order reversible reaction.  Brian et al.
also solved the penetration model for an irreversible
chemical reaction and presented results for a wide range
of parameters.
     In this appendix, the equations describing gas
absorption into a spherical"liquid drop with instan-
taneous irreversible reaction in the liquid phase are
presented.  Also the equations describing mass transfer
in the gas phase surrounding the liquid sphere are given
along with the initial and boundary conditions appro-
priate for the description of gas absorption in a venturi
scrubber.

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     When S02 (and C02) is absorbed into a liquid drop
which contains an alkali reactant, instantaneous
reactions such as reactions (A-2) and (A-21) in APPENDIX
A will take place.  Material balances on the absorbed
gases and alkali reactant in the liquid sphere yield the
following set of partial differential equations.
  2C       ^C       9C
            2
           3
            2
           3 CG
I.C.   : t=0 ,  r>0;  CA = 0   ,   CB = CBQ> CQ = 0
                      3CA         3CB     '?
B.C. I : r=0 ,  t > 0;  -r = 0   ,   — =0 ,
B.C. II : r=ro> t>0;  CA=CAI   ,  — = 0
In the derivation of these equations it is assumed that
the reactions taking place in liquid are all second-
order reactions.
     The concentrations of the absorbed gases at the gas
liquid interface are not constant but change with posi-
tion in the venturi scrubber.  Usually the interfacial
concentration of G. Cr, •   which is carbon dioxide in
                     (ji,

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                                                           149
this case can be approximated by a constant  since  its
solubility is much lower than sulfur  dioxide and its
partial pressure in the gas-phase is  nearly  constant.
     If the resistance to mass transfer  in the gaseous
phase around the liquid drop is not negligible, boundary
condition II has to bo replaced by:
   B.C. II'     :      r = r        t >  0;
and the rate of absorption of species  A  into  the  liquid
is given by:

            NA • VirrWo                          (c-6>

     The set of partial differential equations, equations
(C-l) through (C-3),  combined with appropriate boundary
conditions can be solved numerically as  described below.
     Equations (C-l)  through (C-3), boundary  conditions
(C-4) or (C-5), and equation (C-6) were  approximated  by
an explicit finite difference discretization  of these
equations utilizing forward differences  to  approximate
the time derivatives and the central differences  to
approximate space derivatives.  By choosing k~ — *-oo
and k — » oo   , equations (C-l) through (C-3)  are  made

-------
                                                            150
to represent the case of instantaneous, irreversible
reactions occurring in the liquid.  For the case of con-
stant interfacial concentration, C. .=C,, .=constant,
analytical solutions are available and the numerical
solution can be checked against them.  It was soon
discovered, through trial and error,  that an exceedingly
small "net" size v/as necessary to ensure convergence of
the numerical method to the correct solution.

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                                                             .1.51
                      APPENDIX   D
        Comments on the Physical and Chemical
         Properties used  in  the Mathematical
         Models of the Scrubbing Processes
     The values of physical and  chemical properties used

in the  simulation of the processes described  in this

study were evaluated as follows.

     The density and viscosity of the gas and  liquid

phases, surface tension of liquid, thermal  conductivity

of the  ga:;, dirfusiviU.es of 302 and COp in the gas arid

the  liquid phases were approximated by the  values for

air  in  the case of the gas phase and water  in  the case

of the  liquid phase.  This is reasonable since the tem-

perature and the pressure in the system are moderate

and  the concentration of dissolved components  in the

liquid  phase are dilute.  The data on these properties

are  quoted from standard correlations which appear in the

literature (4' *>*• **' 12Z'}.

     Some of the other important properties in mass

transfer processes are shown below:

     Diffusivities of NaOH, Ca(OH)p, and HCO?"

     The diffusion of an electrolyte is complicated by

the  dissociation of the molecule into ions.   Conduc-

.tivity  measurements indicate that the various  ions have

-------
                                                            152
different mobilities, and consequently, it might be


expected that the various ions might diffuse at dif-


ferent rates.  This would lead, however, to high local


concentrations of positively and negatively charged


ions, and the resulting electro-static forces would


slow down the fast ions and increase the speed of slow


ions.  As a result, the ions actually diffuse at equal


speeds, and. the solution remains electrically neutral.


Since the ions are smaller than the undissociated mole-


cules, they diffuse at a greater rate.


     In this study, d if fusivities of NaOII, CaCOHK, and


HCO^" (approximated by H?CO^) are calculated by Nernst's
   j   .   •              <••  j

equation ^  *' as follows:
                 U  + U   Z""   Z



where U  and U~ = absolute velocity of the cation and



                  anion, respectively, cm/sec, under a



                  force of 1 dyne at infinite dilution.



      Z  and Z  = values of the cation and anion,



                  respectively.

                                              n
             R  = the gas constant, &.3-U- * 10


                  erg3/g-mole °K.



             D  - diffusivity at infinite dilution,

                    p

                  cm ,/sec



             T  = temperature, °K

-------
                                                            153
                      Table D-l



  Ionic Velocities U at Infinite Dilution, 1#°C
Cation or anion
U* or IT
Na+
46.6
H+
337
i _ ++
tCa
55.7
OH~
18?
1
ico3"
64.5
     In the actual absorption calculations, the liquid



phase diffusivities of the absorbed gases and the alkali



reactant were assumed to be the same and equal to the



mean value of the individual diffusivities.




     The properties of solid lime are also important for



the simulation of the holding tank in a lime slurry



process.



     Solubility of lirne



     The solubility of lime in water has been measured



in many investigations and the values of the solubility



are in reasonably good agreement *   .   The following



table provides solubility data in tabular form expressed



as CaO equivalent or as Ca(OH)2:

-------
                      Tab.1e D-2
       Solubility of Lime in Water Expressed   /,r\
  as CaO or Ca(OH)2 at Different Temperatures  ^  J'
temperature, °C
0
20
40
60
80
100
CaO, g/1
0 . 140
0.125
1.106
0.088
0.070
0.054
Ca(OII)2, g/1
0.185
0.165
0 . 140
0.116
0.092
0.071
     pH of Lime Solut Ion


     The pi! of Ca(OII)? solutions at 25°C has  been

         Mr)         '           '
measured v '' and thi.3 pH as a function of  CaO  equiva-


lent is shown in Figure D-l.  The data arc  also pre-


sented in tabular form below in Table D-3-

-------
  131
  12
0.11
  10
              O.2        0.4        0.6         0.8         1.0
                   concentration of  CaO in  solution ,  g/l
1.2
L4
.-inure  D-l.   oH Values of Ca(OH)2  Solutions of Varying Concentration ar.c
              merr:Derature  •

-------
                                                             156
                      Table D-3
           pH of Lime Solution at 25°C
Concentration of CaO, g/1
0.06
0.122
0.271
0.680
0.975
1.160
pH of the solution
11.27
11.54
11. .89
12.29
12.44
12.53
     Examination of this table reveals that the lime in
the solution is almost completely dissociated into it:.;
ionic forms.  The lines for 50°C and 53°C in Figure D-.1.
are calculated from the ion product of water at these
temperatures.

-------
  ,r L" r-RAPHIC DATA
  i  El
                   1. Report No.
                     EPA-650/2-73-QQ3
,4. Tiilc and Subtitle
 Absorption of SO2 by Alkaline Solutions  in Venturi
      Scrubber Systems
                                                              	157

                                                              3. Recipient'.-; Accession Ni
                                                              5- Kcpori Drue
                                                                  July 1973
                                                              6.
7. Author(s)
 C.Y. Wen and S. Uchida
                                                              8. Performing Or^nnizuiiun Kepi.
                                                                No.
9. Performing Organiiiai ion Name and Address
Department of Chemical Engineering
West Virginia University
Morgantown, West Virginia   26505
                                                              10. I'roiect/Task/Work Unit N,:
                                                              11. Contract/dram No.
                                                              Grant No. 800781
12. Sponsoring Organi/.aiion Name .ind Address
EPA, Office of Research and Development
NERC-RTP, Control Systems Laboratory
Research Triangle Park, North Carolina 27711
                                                              13. Type ol Keport & Period
                                                                 Covered

                                                                    Final
                                                              14.
15. Supplementary Notes
16.
             repOrt describes studies of  SO2 absorption from flue gases by water
and alkaline solutions in venturi scrubber processes,  including recycle of the scrub-
bing liquor. It  proposes mathematical models describing the process momentum,
heat, and mass  transfer for SO2-H2O, SO2-NaOH-H2O, SO2-CaO-H2O, and SO2-
CaCO3-H2O systems. The momentum, heat, and mass balances describe the  perform-
ance of the  processes taking place in the venturi scrubber.  It generates a set of first-
order ,  nonlinear , ordinary differential equations , relating  total pressure , liquid
velocity, SO2 concentration  in the liquid, etc. along the axial direction. It solves
these equations  numerically for performance profiles ,  used to examine the effects of
such operating variables as  liquid flow rate and the concentration of alkali in the
liquid phase on the absorption rate. It analyzes data  from various size holding tanks
and proposes mathematical models for the lime/limestone slurry process  holding
                                             tanks.  Finally, it combines these models
                                             to simulate the venturi/holding-tank
                                             system with closed-loop recycling of the
                                             liquor.  It examines  the sensitivities of
                                             such operating variables as the  recycling
                                            liquor rate and the alkali makeup rate on
                                             the absorption. It qualitatively discusses
                                             such practical problems as oxidation of
                                             sulfite  to sulfate and scaling of the
                                             solids.  The calculated results using
17. Key Words ami Document Analysis. 17o. Deseripturs
Air Pollution
Sulfur Dioxide
Absorption
Washing
Flue Gases
Water
Circulation
Mathematical Models
Sodium Hydroxide
1 7b. Idcnt il ir r.s , Open- hndrd I"e. mis
Air Pollution Control
Stationary Sources
Alkaline Solutions
Venturi Scrubbers
                Calcium Oxides
                Calcium Carbonates
                Limestone
                Slurries
                Scaling
                Oxidation
                                             these models show good agreement with
                                             experimental data obtained by several
                                             investigators.
I7c •
         F,..|.l/C.r.,..n   13B ,  7A , 7B
18. A vui I ;ilii I it y Si.it
CORM NT! U- 33 («£V. 3 • 7 .i I
                  Unlimited
                                                    19. Si-, in ii y <  l.i-.-. .'I In-
                                                      R.-p.MI )
                                                   20. Sri niily ( la.s.s (Tin:
                                                      P..*.-
                                                        IIN( I.ASSII-'II-.I)
                                                                       21. No
                                                                          J--7
                                                                       '11. V

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I OHM N1IV.I9 U.I V.  I /.'>                                                                                     "••< "MM '»  '«""-' '''

-------