CALCIUM CARBONATE DISSOLUTION RATE
           IN LIMESTONE CONTACTORS
                      by
             Raymond D.  Letterman
             Syracuse University
           Syracuse, New York 13244
      Cooperative Agreement No.  CR814926
               Project Officer

               Jeffrey Q.  Adams               '•
       Drinking Water Research Division
    Risk Reduction Engineering Laboratory
United States Environmental Protection Agency
            Cincinnati, OH  45268
    RISK REDUCTION ENGINEERING LABORATORY
      OFFICE  OF  RESEARCH  AND  DEVELOPMENT
    U.S.  ENVIRONMENTAL PROTECTION AGENCY
           CINCINNATI, OHIO  45268

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                            DISCLAIMER
     The information in this document has been funded wholly or
in part by the United States Environmental Protection Agency
under Cooperative Agreement Number CR814926 to Syracusp
University.  It has been subject to the Agency's peer £nd
                                                      i
administrative review and it has been approved for publication as
                                                      E
an EPA document.  Mention of trade names or commercial| products
does not constitute endorsement or recommendation for use.

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                             FOREWORD

     Today's rapidly developing and  changing technologies and
industrial products and practices frequently carry with them the
increased generation of materials that, if improperly dealt with,
can threaten both public health and  the environment.  |The U.S.
Environmental Protection Agency is charged by Congress with
protecting the Nation's land, air and water systems.  Under a
mandate of national environmental laws, the agency strives to
formulate and implement action's leading to a compatible balance
between human activities and the ability of natural systems to
support and nurture life.  These laws direct the EPA to perform
research to define our environmental problems, measure the
impacts, and search for solutions.                    !

     The Risk Reduction Engineering Laboratory is responsible for
planning, implementation, and management of research, •
development, and demonstration programs to provide an i
authoritative,  defensible engineering basis in support; of the
policies, programs, and regulations of the EPA with respect to
drinking water, wastewater, pesticides, toxic substancfes,  solid
and hazardous wastes, and Superfund-related activities'.   This
publication is one of the products of that research and provides
a vital communication link between the researcher and £he user
community.                                            j
                                                      i
     Limestone contactors have been shown to be an effective and
economical water treatment device for reducing the tendency of
water to dissolve corrosion by-products,  such as lead, • copper,
and zinc, from surfaces in piping systems.  Models used to design
limestone contactors must predict the effect of a number of
                               111

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factors on the rate of carbonate mineral dissolution from the
stone.  This report describes the results of a study to determine
the effect of limestone composition and water temperature on the
carbonate mineral dissolution rate.                   '•
                              E. Timothy Oppelt,  Director
                              Risk Reduction Engineering
                              Laboratory              '
                                IV

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                             ABSTRACT                 ;
     The rate of carbonate mineral dissolution from limestone was
studied using a rotating disk apparatus and samples ofj limestone
of varied composition. The purpose of this study was to determine
the effect of limestone composition on the kinetics of carbonate
mineral dissolution. The results are needed to improve; the
relationships used to design limestone contactors for (long term
operation.                                            j
     The stone samples with the highest calcite content and
lowest dolomite content had the highest initial rates 'of
dissolution. The magnitude of the overall dissolution irate
constant for fresh stone decreased by approximately 6o'% as the
calcite content of the stone decreased from 0.92 to O.;09 g
CaCO3/g stone.                                         ;
                                                      i
     The overall dissolution rate constant decreased as the
amount of calcium dissolved from the surface of the stone
increased. Analysis of several stone surfaces indicated that a
residue layer of aluminum, silicon and iron formed as ^calcium
dissolved.                                            :
     For a given amount of calcium dissolved per unit [area of
stone surface, the magnitude of the decrease in the dissolution
rate constant increased as the initial amount of iron iand
aluminum in the stone increased. The results suggest that the
effect of sample aging on the rate of dissolution is at a minimum
if the weighted sum of the Fe and Al content of the stone is less
than about 10 mg/g. The weighted sum is equal to the aluminum
content in mg Al/g plus 0.30 times the iron content in mg Fe/g.
                                                      i
     This report was submitted in fulfillment of CR814926 by
Syracuse University under the sponsorship of the U.S. !
Environmental Protection Agency. This report covers a period from
July 1988 to June 1993 and work was completed as of June 30,
1993.                                                 ;

                                v                     :

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VI

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                        TABLE OF  CONTENTS              j
                                                       !
                                                       i
Foreword	!.  .  .  .  iii

Abstract	          v

Figures	'.  .  .     ix

Tables	        xii

Abbreviations, Symbols and Units	!.  .  .  .  xiv

Acknowledgements	'.        xvi

1.   INTRODUCTION	|.          i
     1.1  BACKGROUND	          i
     1.2  PROJECT  PURPOSE  .  .	L  .  .  .    3
     1.3  PROJECT  DESCRIPTION	.......    3

2.   CONCLUSIONS   	    5

3.   RECOMMENDATIONS	:.  .  .  .    9

4.   LITERATURE REVIEW	:.  .       n
     4 . 0  MINERAL  AND LIMESTONE DISSOLUTION KINETICS   |.  .  .  .   11
          4.0.1     Introduction	;.  .       n
          4.0.2     Impurities in-Limestone 	  ....   11
          4.0.3     Mathematical Models of Dissolution:
                    Kinetics	.  .  .  .   12
          4.0.4     Effect of Stone Composition  and    |
                    Crystallography on  Dissolution Kinetics
                       	'.  .  .  .   13
          4.0.5     Effect of Temperature on Dissolution
                    Kinetics	   16
          4.0.6     Effect of Trace Species in Solution on
                    Dissolution Kinetics	  .  .  .   17
     4.1  MODELING CALCITE DISSOLUTION IN LIMESTONE CONTACTORS 17

5.   EXPERIMENTAL  METHODS AND MATERIALS	 .  L  .  .  .   23
     5.0  EXPERIMENTAL MATERIALS	I  ...   23
          5.0.1     Limestone - Physical Characteristics   .  .   23
          5.0.2     Limestone - Chemical Characteristics   .  .   27
          5.0.3     Rotating Disk Solution Characteristics   .   31
     5.1  ROTATING DISK APPARATUS	   31


                               vii

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           5.1.1     Stone Disk Preparation	  .       32
      5.2   EXPERIMENTAL PROCEDURE  .  .  «  .	'.  ..." 34
           5.2.1     "Aging" the Limestone Disk Surface   ...   35
           5.2.2     Calcium and Magnesium Determination  by
                     Atomic Absorption Spectrophotometry  ...   36
           5.2.3     Agreement Between Calculated and  ;
                     Measured Calcium Concentrations .'....   36
           5.2.4     Alkalinity Measurements	'.  .  .  .   37
           5.2.5     Solubility Product Determination   .  .  .  .   37
           5.2.6     Glassware	'.  .  .  .   38

6.    EXPERIMENTAL RESULTS AND DISCUSSION	'.         39
      6.0   DISSOLUTION RATE DETERMINATION	.  .  .  .   39
      6.1   EFFECT OF DOLOMITE CONTENT ON k0   	'..!!'. 42
      6.2   EFFECT OF INSOLUBLE RESIDUE CONTENT ON THE INITIAL
           RATE  OF CALCITE DISSOLUTION	j.         45
      6.3   VARIATION OF k0 WITH THE CaCO3 CONTENT OF THE
           STONE	;.  .  .  .   46
      6.4   EFFECT OF IRON AND ALUMINUM ON THE DISSOLUTION'
           RATE	':....   48
           6.4.1     Residue Layer Resistance  ....'....   51
      6 . 5   EFFECT OF TEMPERATURE ON k0	         62
      6.6   EFFECT OF TEMPERATURE ON kc  AND kL  ....[..'.'.   63
      6.7   APPARENT ACTIVATION ENERGY FOR kL  AND  kc   .  \.  '.'.'.   65

REFERENCES	|.  .  .  .   68

APPENDIX A.  MECHANISM OF HETEROGENOUS REACTIONS  ......   72

APPENDIX B.  CHEMICAL EQUILIBRIUM CALCULATIONS  ...  :.  ...   75

APPENDIX C.  METHYL RED EXPERIMENTS	         79

APPENDIX D.  EQUILIBRIUM MODEL  CALIBRATION	'.         81

APPENDIX E.  SOLUBILITY PRODUCT  DETERMINATION ........   84

APPENDIX F.  CALCIUM ION DIFFUSIVITY	'.         90
                               Vlll

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                             FIGURES


Number                                                i        paqe

4.1.1     Calcium concentration is plotted as a function of
          volume water treated, using data from Haddad  (1986).  21

5.0.1     Photomicrograph of a thin section cut from undissolved
          stone sample WM	.......;....   24

5.0.2     Photomicrograph of a thin section cut from uindissolved
          stone sample SL.   .	:. .  .  .   25

5.0.3     Photomicrograph of a thin section cut from undissolved
          stone sample C	   25

5.0.4     Photomicrograph of a thin section cut from undissolved
          stone sample F	   26

5.0.5     Photomicrograph of a thin section cut from undissolved
          stone sample I	'. .   .  .   26

5.0.6     X-ray diffraction analysis results for undissolved
          stone samples C, F and I	i.         28

5.1..1     Schematic diagram of the rotating disk apparatus   .   33

6.0.1     Calcium concentration in the rotating disk apparatus  as
          a function of time; WM sample  ........ ;. ...   40

6.0.2     pH vs time for the rotating disk experiment of Figure
          6.0.1	   41
                                                      i

6.0.3     Dissolution rate experiment for the WM stone;sample.  43

6.1.1     Calcium,  magnesium and calculated equivalent;calcium
          concentration for a rotating disk experimentiwith stone
          sample J and 600 rpm	I ...   44

6.1.2     Dissolution rate experiment results for stone sample  J.
            	-	i .   .  .   45

6-1.3     Calcium and magnesium concentrations for rotating disk
          experiment with stone sample C at 600 rpm	46
                                                      i

                               ix                     ;

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                        FIGURES  (continued)
Number
6 . 3 .. 1
6.4.1
                                            i       •*- ^"^CT ^^
Effect of the calcite content of the stone sample on
the initial value of the dissolution rate constant.  48

Effect of amount of calcium dissolved on the fractional
decrease in the dissolution rate constant.  ;.        49
6 . 4 .. 2A    Scanning electron micrograph of  freshly prepared WM
          stone sample	:.         52

6.4., 2B    SEM image of WM stone sample after dissolving  6  mg
          Ca/cm2 from the surface of the stone   ...:....   53

6.4.2C    XES map of calcium distribution  in fresh  sample  of the
          WM stone	   54
                                                      i

6.4.3A    Scanning electron micrograph of  the surface 'of a fresh
          SL sample	   55

6.4.3B    XES map of the distribution of calcium on the  fresh SL
          sample	   56
                                                      i

6.4.3C    XES map after dissolving calcium from the surface  of
          fresh SL sample	',.         57

6.4.3D    XES map showing the distribution of silica SL sample
          after calcium was dissolved from the surface.  ...   58
                                                      !

6.4.3E    XES map showing the distribution of aluminum; on  the
          dissolved SL sample	;.  .  .  .   59

6.4.4     Variation in the dissolution rate constant, k0,  with  '
          the amount of calcium dissolved  from the  disk surface61

6.4.5     Plots of ln{(Ceq-C)/Ceq}v/A versus time for SL sample,-
          0.01 meq/L of initial acidity and 600 rpm .'....   63
                                                      i
6.5.1     Plot of ln{(Ceq-C)/(Ceq-Co)}/(V/A)  versus time for 12
          and 18pC and sample B	L  .  .  .   64

6.7.1     Arrhenius plot for the mass transfer (kc)  and surface
          reaction constants (kL)  .	66

1C        pH versus normalized absorbance  for methyl red
          titration in the rotating disk apparatus  used to test
          the rate of response of the pH measuring  system.   .   80

ID        Measured pH versus measured calcium concentrations  for
          the SL stone, w = 600 rpm and initial acidity =0.01
          meq/L	82
                                x

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                       FIGURES  (continued)
Number

2D



IE


2E


3E



4E


5E


IF



2F



3F


4F
Alkalinity calculated from the measured calcium
concentrations plotted against the measured :
alkalinity	   83

Variation of calcium concentration with time1 in open
batch reactor	   85

pH versus time results for the experiments of Figure
IE	'.  . .  .   86

Variation of calcium concentration with time; in the
experiments used to determine the solubility product  of
calcium carbonate in stone samples A, C, F and I.  .   87
                                       1     i
pH measurements from the experiments used to, determine
Ksp for stone samples A, C, F and I.  ...;....   88

Values of pKsp calculated using the calcium
concentration and pH values in Figures 3E and 4E.  .   89

Effect of disk rotational speed on plots of ln{(Ceq-
C)/Ceq}V/A versus time; WM stone sample and initial
acidity of 0.1 meq/L	....'....   91

Effect of disk rotational speed on plots of ln{(Ceq-
C)/Ceq}V/A versus time; WM stone sample and initial
acidity of 0.01 meq/L	 .       92
Inverse of the overall dissolution rate constant versus
    ; WM  stone  and  initial  acidity  =  0.1 meq/L.   .  .  93
p-1/2
Inverse of the overall dissolution rate constant versus
p~1/2; WM  stone  and  initial  acidity  =  0.01  meq/L.    .  94
                                XI

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                              TABLES

Number                                                l        page

5.0,1     Results of stone analysis	         29

5.0.2     Estimated mineral content  of the stone samples   .  .   31

5.2.1     Effective solubility products for calcium carbonate and
          calcium-magnesium carbonate in selected limestone
          samples. Values are for 25pC and infinite dilution.   37

6.0.1     Reported initial rates of  calcite dissolution at 25°C41

6.2.1     Comparison of experimental and corrected overall
          dissolution rate constants for essentially fresh
          limestone disks	:. .  .  .   47

6.4.1     Effect of the iron and aluminum content on the
          fractional decrease in the dissolution rate constant  at
          Cad = 2 mg calcium dissolved per square centimeter of
          limestone surface	   50

6.4.2     Effect of the weighted sum of iron and aluminum in the
          limestone on the fractional decrease in the dissolution
          rate constant at 2 mg calcium per square centimeter of
          limestone surface	|.         51

6.4.3     Residue layer mass transfer coefficient for SL sample61

6.5.1     Effect of temperature on the calculated values of the
          equilibrium calcium concentration and experimental
          values of the dissolution rate constant ..;....   64

6.6.1     Effect of temperature on the calcium ion diffusivity
          and kinematic viscosity	 .  .  .   55

6.6.2     Effect of temperature on the mass transfer coefficient,
          kL/  and the surface  reaction constant,  kc  . j. '.  .  .   66
                                                      !
6.7.1     Apparent activation energies for the limestone
         , dissolution rate constant when dissolution is
          controlled by a)  surface reaction and b)  mass transfer.
            .......	   67

IB        Values of equilibrium constants at 25bC and 1=0 .  .   76

                               xii

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Number

2B


IF


2F
                        TABLES (continued)
Equations used to correct equilibrium constants for
activity	. .  .  76
                                            I

Calcium ion diffusivity, D, and kc for the wm sample
and 25pC	'.  . .  .  95

Calcium ion diffusivity at 25pC	'.  . .  .  95
                              XI11

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                 ABBREVIATIONS, SYMBOLS AND UNITS
Notation
A

a

C

Cad
     Area of  limestone  disk

     Area of  CaCO3 per unit volume of fluid

     Bulk calcium  concentration

     Calcium  dissolved  per  unit area of  disk

Car  Calcium  dissolved  during  an experiment

Cas  Calcium  dissolved  during  storage

Cbo   Calcium  concentration  in  the influent of  a
     contactor

CbL   Calcium  concentration  in  the effluent of  a
     contactor

C0   Initial  calcium concentration

Cs   Calcium  concentration  at  the surface

D    Diffusivity of calcium ion

d    Diameter of limestone  particle

Heq   Equilibrium hydrogen ion  concentration

kc   First order surface reaction rate constant

kf   Residue  layer mass transfer coefficient

kL   Mass transfer rate constant

k0   Overall  dissolution rate  constant

L    Overall  depth of contactor

M    Cumulative mass of calcium dissolved per
     unit area of limestone
Units

cm2 !

cm"1 l

moles/L

mg/cm2

mg

mg


moles/L


molejs/L
    !
mole!s/L

moleis/L

cm2/s

cm  |
    !
mole's/L
    i
cm/s

cm/si

cm/s;

cm/s:
    i
cm  j


mg/cm2
                               xiv

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           ABBREVIATIONS,  SYMBOLS AND UNITS (continued)
Notation



Mre  Modified Reynold's number



ND   Axial dispersion number



     CaCO3 dissolution rate



     Schmidt number



     Superficial velocity of fluid



     Volume of solution



     Depth
r




Sc



Us



V




Z
Greek letters




p    Activity coefficient




p    Thickness of residue layer




pN   Diffusion boundary layer thickness




p    Porosity of limestone particles




pr   Porosity of the residue layer




p    Mean fluid residence time




p    Kinematic viscosity




ps   density of residue solids




pr   Pore length tortuosity




p    Sphericity of limestone particles




p    Angular velocity
Units




dime'nsionless




dimensionless




moles/ (cm2s)




dime|nsionless




cm/s
    i



cm3




dimensionless










dimensionless




cm




cm  ,




dime'nsionless




dimensionless




sec :




cm2/s




mg/cm3




dimensionless




dimensionless




radians/s
                                xv

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                         ACKNOWLEDGEMENTS             !

     The author acknowledges the support and guidance of Jeffrey
Q. Adams the USEPA Drinking Water Research Division project
officer. The assistance of David A. Hopkins, geologist for the
J.E. Baker Company, York, PA, and Professor Donald I. Siegel,
Department of Earth Sciences, Syracuse University, is sincerely
appz-eciated.                                          '
                               xvi

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                             CHAPTER I                  \
                           INTRODUCTION                i
 1.1 BACKGROUND
     A  limestone  contactor  is  a  treatment  device  in which water
 flows through and dissolves  carbonate  minerals  (typically calcium
 carbonate)  from a packed bed of  crushed  limestone.  Dissolution of
 calcium carbonate (under a  closed-to-atmospheric-carbon  dioxide
 condition)  increases  the pH, alkalinity  and dissolved 'inorganic
 carbon  concentration  of the  water  and  depletes  the  amount of
 calcium carbonate in  the bed.  Limestone  contactors  are: simple,
 low-cost devices,  which usually  require  minimal maintenance and
 are, therefore, especially  suitable  for  small water supplies.  In
 an earlier  study  sponsored by  the  United States Environmental
 Protection  Agency (USEPA),  it  was  shown  that limestone' contactors
 can effectively reduce the dissolution of  corrosion byf-products,
 such as lead, copper  and zinc, from  surfaces in pipingi systems
 (Letterman  et al., 1987).                              ;
     The results  of the USEPA  sponsored  study  (Letterman  et al.,
 1987)  were  used to derive and  test a mathematical model  for
                                                       i
 designing limestone contactors.  The model  relates the  depth of
 limestone required in a contactor to the desired effluent water
 chemistry,  influent water chemistry, limestone  particle  size and
 shape,   limestone  bed porosity,  and .water temperature and
 superficial velocity. The model  assumes that the kinetics of
 calcium carbonate dissolution  is determined by  a heterogeneous
 reaction,  the rate of which is determined by a  calcium] ion mass
transfer resistance and a surface reaction acting in series
 (Letterman et al., 1991).                              :
     In a study that followed the USEPA sponsored investigation,
Haddad  (1986) monitored the long-term operation of  a contactor
containing a somewhat impure, high-calcium limestone. liaddad' s

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steady-state model predicted the initial performance of the
column when the limestone was fresh, however, as the unit was
operated for a period of several months the effluent p'H,
alkalinity and calcium ion concentration decreased below the
initial values.
     Haddad (1986) used a scanning electron microscope, with an
attachment for x-ray energy spectroscopy to analyze the surfaces
of particles of limestone from the contactor employed ;in the
long-term study. He found that the dissolution of calcium
carbonate significantly increased the amounts of aluminum,
silicon and iron at the limestone surface.  He concluded that as
calcium carbonate dissolved from the stone the rate of
dissolution decreased because relatively insoluble impurities
such as silica,  alumino-silicates and aluminum and iron
oxides/hydroxides remained on the surface and formed a "residue
layer". As the residue layer increased in thickness, it tended to
decrease the rate of transport of calcium ion from the calcium
carbonate surface to the bulk solution and this caused the
performance of the contactor to decrease with time.   <
     Field experiments have shown (Letterman et al., 1*987) that
the temperature of the water flowing through a limestone
contactor can affect its performance. For a given set ;of design
and operating conditions, contactor performance decreased with
decreasing temperature.                               ••
     In rotating disk experiments conducted by Sjoberg and
Rickard (1983)  and Lund  (1975), the rate of calcite dissolution
decreased with decreasing temperature. The extent to which a
given temperature change affected the rate of dissolution varied
with the rate limiting step in the dissolution process. At low pH
(2 to 4) where the dissolution rate was mass transfer Icontrolled,
the effect of temperature was less than at high pH where the rate
was apparently controlled by a combination of transport and
surface reaction resistances. Relationships are available for
correcting mass transfer coefficients for temperature, however,
the effect of temperature on the surface reaction rate constant

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for calcite dissolving from limestone is not known. This  limits
the usefulness of Haddad's contactor design model.    '

1.2 PROJECT PURPOSE
     The purpose of this study was to: 1) determine the effect of
limestone composition, especially the dolomite and impurity
content of the stone, on the kinetics of carbonate mineral
dissolution, and 2) determine the effect of temperature on the
rate of dissolution of calcite from limestone. The results are
needed to improve relationships used in computer programs for
designing limestone contactors.                       ;
                                                      I
1.3 PROJECT DESCRIPTION
                                                      i
     The dissolution rate experiments were conducted with a 2-
liter, temperature-controlled batch reactor and rotating disk
apparatus.  Samples of solution were withdrawn from the reactor as
carbonate minerals dissolved from the disk surface. The calcium
and magnesium concentrations in the samples were used ;to
determine dissolution rate constants as a function of Jthe
composition of the stone sample, the amount of carbonate mineral
dissolved from the sample,  and the temperature of the 'solution.
Between dissolution rate experiments, the stone samples were
"aged" by controlled dissolution in dilute acid solutions. The
limesstone ranged in composition from a white, calcitic Vermont
marble with a significant amount of insoluble silica to
sedimentary limestones that consisted of approximately 100
percent calcite (CaC03) to  essentially pure  dolomite  (CaMg (C03) 2) .
The aluminum and iron content of the sedimentary stoneis was a
variable.                                             ;
     The rotating disk apparatus was used in these experiments
instead of limestone contactors because it is difficult to
economically study the effect of the amount of mineral dissolved
on dissolution kinetics using a continuous-flow,  packed-bed
device. Given the objectives of this study,  contactor operation
would have required a significant number of contactors, large

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quantities of water and long operational periods to obtain
meaningful results.

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                            CHAPTER 2
                           CONCLUSIONS

1.   The heterogeneous reaction model of Rickard and Sjoberg
     (1983)  explained the dissolution rate data for all samples
     except the two with the highest dolomite  (CaMg (C03) 2)
     content. The heterogeneous reaction model assumes that the
     rate of carbonate mineral dissolution is controlled by a
     cation mass transfer resistance and a surface reaction
                                                      I
     acting in series. For calcite (CaC03)  and the  experimental
     conditions of this study, the surface reaction rate was
     relatively large and the rate of dissolution was .essentially
     mass transfer controlled.                        I

2.   According to the literature and the results of this study, a
     calcium ion diffusivity of 0.8 x 10~5 cm2/s (at 25^0  can be
     used to predict the mass transfer resistance in the
     heterogenous reaction rate model. This value is now being
     used in the contactor design program DESCON.     !
                                                      !
3.   The stone samples with the highest calcite content and
     lowest dolomite content had the highest initial rates of
     dissolution. The magnitude of the overall dissolution rate
     constant for fresh stone decreased by approximately 60% as
     the calcite content of the stone decreased from 0.92 to 0.09
     g CaC03/g stone.

4.   When the high dolomite content samples were fresh, it
                                                      :
     appeared that the calcium carbonate component of -the
     dolomite dissolved faster than the magnesium carbonate
     component. This phenomenon has been reported by p'lummer and
                                5                     :

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     Busenberg  (1982). The rate of dissolution of magnesium was
     negligible in all samples except the high dolomite content
     samples  (93 and 100 mass percent dolomite).      ;

5.   The rate of dissolution of stones with high amounts of
     dolomite may be enhanced by the presence of small amounts of
     calcite. For example, the stone that was essentially pure
     dolomite had a value of the initial overall dissolution rate
     constant that was 66% less than the value for another
     dolomitic stone with approximately 9% calcite.   j

6.   The overall dissolution rate constant decreased as the
     amount of calcium dissolved from the surface of the stone
     increased. Analysis of several stone surfaces by 'scanning
     electron microscopy and x-ray energy spectroscopy indicated
     that the density of calcium atoms on the surface lof the
     stone decreased and the density of aluminum, silicon and
     iron increased as calcium dissolved.

7 .   For a given amount of calcium dissolved per unit .area of
     stone surface,  the magnitude of the decrease in the overall
     dissolution rate constant increased as the amount1 of iron
     and aluminum in the stone increased. For a stone with less
     than 8 mg Fe/g and 2 mg Al/g,  the decrease for 2 mg Ca
     dissolved/cm2 was  about  10% while the  decrease  was  over  70%
     for a stone with 160 mg Fe/g and 50 mg Al/g. The approximate
     iron content of the thirteen stone samples used in the study-
     ranged from 15 to 377 mg Fe/lOOg and the approximate
     aluminum content from 1 to 134 mg Al/lOOg.       ;

8.   The results suggest that the effect of sample aging on the
     rate of dissolution is a minimum if the weighted sum of the
     Fe and Al content of the stone is less than about 10 mg/g.
     The weighted sum is equal to the aluminum content in mg Al/g
                                                      i
     plus 0.30 times the iron content in mg Fe/g. To minimize the

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     negative effect of mineral dissolution and residue-layer
     build-up on the performance of a limestone contactor during
     long-term operation, the iron and aluminum content should be
     less than this weighted sum.                     -

9.   The presence of silica as the principal impurity ,in the
     white marble sample (35 mass percent silica)  did ;not appear
     to cause a reduction in the dissolution rate of the calcite
     surface. It simply reduced the effective surface area of the
     calcite in proportion to the mass of silica in the sample.
                                                      i
     The contactor design program DESCON reduces the carbonate
     mineral surface area according to the amount (mass percent)
     of silica in the stone.                          ',

10.  The effect of temperature on the rate of dissolution of
     calcite was studied in the range of 5° to 25°C using one of
     the purer calcitic stone (94.5% CaC03) .  The dissolution  rate
     decreased with decreasing temperature. The overall
     dissolution rate constant at 5°C was 0.38 x 10~3 cm/s and
     2.80 x 10~3 cm/s at 25°C.                         :

11.  The heterogeneous reaction model was used with the overall
     dissolution rate constant versus temperature data to
     determine the apparent activation energy (Ea) for; the
     surface reaction rate constant. The value determined,  Ea =
                                                      i
     101 kJ/mol,  is significantly greater than values iin the
     literature (30 to 60 kJ/mol).  The exact reason for this
     discrepancy is not known but could be attributed to
     compositional and crystallographic differences between the
     stones used in the studies compared.

12.  The effective solubility product for calcium carbonate in
     limestone is an important parameter in the design program
     DESCON. Values of this parameter were determined |using a
     number of the stone samples and a set of open-tor-
                                7                     ;

-------
atmospheric-C02,  batch-reactor dissolution experiments. The
results ranged from Ksp =  1.5  x  10~9 to 6.3 x 10~9 ,(1=0,
T=25°C) or pKsp =  8.20 to  8.81.  In  the solubility! product
experiments the final concentrations  of magnesium were
always significantly less than the  final  concentrations of
calcium, even for the stones  with the  highest dolomite
content. It is not known exactly why this occurred but it
may be associated with the small amount of  calcium dissolved
per unit area of stone at equilibrium  (~  0.5 mg  Ga/cm2) .  The
incongruent dissolution of calcium  from the dolomite
surfaces may have been a factor.  The  magnitude  of Ksp for
calcite did not seem to be affected by the  amount of
dolomite in the stone.                           ;

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                            CHAPTER 3
                         RECOMMENDATIONS

1.   It is not known to what extent, if any, biological films on
     the stone packing affect the performance of a limestone
     contactor. Limited data from laboratory and field
     investigations do not support a conclusion that biological
     films are a significant factor. Future study should examine
     the effect of biological film formation on the kinetics of
     mineral dissolution. Recent work sponsored by the American
     Water Works Association Research Foundation on bio-films in
     water treatment systems could provide a starting point.

2.   It is well known that compounds such as orthophpsphate
     adsorb on calcium carbonate surfaces and reduce the rate of
     mineral dissolution. Future study should determine if this
     phenomenon is an important consideration in limestone
     contactor design and operation.

3.   While effective methods,  such as the computer program
     DESCON, are available for limestone contactor design, the
     chemical and physical quantities needed as input to the
     program are sometimes difficult for potential users such as
     the officials of small communities and some state regulatory
     officials to determine. Also, some potential users do not
     have a personal computer. A future investigation -might use
     the more detailed and exact design tools (such as DESCON)
     and practical ranges of input parameters (raw water
     chemistry, stone characteristics,  etc.) to develop simple,
     conservative methods for contactor design.        :

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4.   Orthophosphate has been shown to be an effective :additive
     for corrosion control in water distribution and home
     plumbing systems. Packed-bed contactors filled with slightly
     soluble phosphate-containing minerals should be investigated
     as devices for orthophosphate addition at small water supply
     systems.                                          ;

5.   Contactor treatment has the potential to be combined in one
     unit with other treatment processes such as slow ;sand
     filtration or packed-beds of metal oxides that adsorb
     natural organics. This is an interesting avenue for future
     research.                                        :

6.   It is generally assumed that limestone contactor 'treatment
     is very cheap,  however,  accurate cost analyses have not been
     prepared. Future research should consider this.
                               10

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                            CHAPTER 4
                        LITERATURE  REVIEW

4.0 MINERAL AND LIMESTONE DISSOLUTION KINETICS

4.0,. 1 Introduction                                    I
     Limestone dissolution kinetics is important in understanding
problems such as geochemical weathering  (Plummer and Wigley,
1976; Berner and Morse, 1974), the distribution of carbonate
sediments in marine environments (Berner and Morse, 1974), flue
gas desulfurization (Chan and Rochelle, 1982), the liming of
acidified natural waters  (Bjerle and Rochelle, 1982) and the
design of limestone contactors.  Limestone or calcite :dissolution
has been studied using rotating disks  (Plummer et al. / 1978;
Sjoberg and Rickard, 1983), rotating cylinders (Wallin and
Bjerle, 1989a; Schott et al., 1989), and agitated batch reactors
containing crushed limestone particles (Plummer and Wigley,
1976) .
     The rate of carbonate mineral dissolution is determined by
the physical and chemical characteristics of the stone, including
the type and amount of impurities and the mineral     >
crystallography. The chemistry and temperature of the solution
are also important.

4 . 0 ,. 2 Impurities in Limestone                         {
     Natural limestones contain varying amounts of impurities
(Boynton, 1980) . Impurities can be classified as either
homogeneous or heterogeneous. Homogeneous impurities are usually
silt, sand or clay  (or other forms of silica such as g.uartz) that
entered the stone when it was first deposited and are ;therefore
uniformly distributed throughout the formation. Heterogeneous
                                                      i
                                11

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impurities are contaminants that have accumulated between the
strata or are loosely embedded in the stone.
     The most common impurities in limestone are silicon and
                                                      !
aluminum followed by iron. Silicon is usually present 'as silica
or with aluminum in alumino-silicate minerals. Aluminum may also
be present as alumina. Iron may exist as an iron carbonate or
iron oxide, distributed heterogeneously from minerals such as
pyrite or limonite. Other, usually much less significant,
contaminants include manganese, copper, titanium, sodium and
               .                                       i
potassium  (Boynton, 1980) .
     Murray et al.  (1954) analyzed 45 high-calcium limestone
samples and found measurable amounts of silica, alumina, and
magnesium oxide in each of them. Potassium, sodium and sulfur
were detected in some samples. A spectrographic analysis of 25 of
the 45 samples indicated that iron, barium, strontium ;and tin
were also present.                                    \
     Relatively pure limestones tend to develop a thin, light-
cove;red crust when weathered.  Impure varieties, especially those
containing iron, weather yellowish or brown, and if there is much
clay or sand, an obvious crust is formed. According to; North
(1930) , weathering involves the removal to solution of! the
                                                      (
calcium carbonate fraction of the stone and, if much insoluble
material is present, it tends to remain behind, forming a
superficial layer usually different in color from the unweathered
rock.

4.0.3 Mathematical Models of Dissolution Kinetics
     A number of models have been developed for predicting the
rate of calcium carbonate dissolution in aqueous systems. Some of
these are entirely empirical (Sjoberg, 1976),  and some have a
partial basis in fundamental principles (Plummer et al'., 1979;
Bjerle and Rochelle, 1984).  The potential for transport control
of calcite dissolution has been recognized by many investigators
(King and Liu,  1933; Tominaga et al., 1939; Kaye, 1957:; Weyl,
1958;  Nierode and Williams,  1971;  Berner and Morse,  1974; Lund et
                               "12                     i

-------
al.,r  1975; Plummer  and Wigley,  1976;  Bjerle  and Rochelle,  1984;
Chan  and Rochelle,  1982; Wallin and Bjerle,  1989b;  Haddad,  1986).
There is some  agreement that  in neutral to alkaline solutions  the
dissolution of calcite is  controlled  by mixed  kinetics  in  which
the rate depends on both a surface chemical  reaction and the
transport of reactants and/or products to or from the :reaction
sites (Sjoberg and  Rickard, 1983, 1984a,b, 1985; Berner and
Morse, 1974; Plummer et al.,  1978; Compton and Daly,  1984).
Haddad  (1986)  concluded that  predicting the  rate of calcitic
limestone dissolution in a packed-bed contactor requires
knowledge of both the hydrodynamic mass transport properties of
the mineral-water system and  the kinetics of the heterogenous
reaction at the calcite surface.
      Most existing  models  of  calcite  dissolution are  based  on
results obtained using large  crystals of essentially  pure
calcite. For example, a number  of studies have  been do'ne with
Iceland spar.  The direct application  of these  results 'to the
dissolution of calcite crystals in limestone is questionable.
Differences between limestone and pure calcite  that may affect
dissolution kinetics include: (a) impurities in the  limestone
such  as silica, aluminum and  iron, (b) crystal  growth histories
and defects,  and (c) crystal  grain sizes.             !
                                                      i
4.0.4 Effect of Stone Composition and Crystallography ion
     Dissolution Kinetics                             ;
      The effect of impurities on the dissolution rate !of
limestone has not been studied extensively.  Research on silicate
weathering has revealed the existence of a surface  leached layer
(Holdren and Berner, 1979;   Schott et al.,  1981; Berner and
Schott,  1982; Schnoor,  1989). Studies of feldspar weathering by
Chou and Wollast (1984)  show the formation of a residue layer
consisting mainly of aluminum and silica at the mineral surface.
The rate of weathering of  feldspar was found to be  controlled by
the existence and properties of the residue layer.  As jthe layer
increased in thickness,  the rate of dissolution decreased rapidly
                                13

-------
until it reached a quasi-steady state value. The quasi-steady
state condition, it was suggested, is due to a balance between
the rate of dissolution of the fresh feldspar  (which depends on
the diffusion of reactants and products through the residue
layer) and the rate of dissolution of the residue layer. Schnoor
(1989) has called this phenomenon "initial incongruent
dissolution".                                         ;
     Weathering experiments by Sverdrup  (1990) indicated that the
dissolution rate of minerals containing aluminum, like feldspar,
biotite and anorthite, is affected by the presence of ialuminum if
the solution aluminum concentration is greater than sdme limiting
value. According to Sverdrup (1990), when aluminum is produced by
chemical reaction at the mineral surface this rate is 'determined
by the aluminum concentration gradient from the particle surface
to the bulk solution. Sverdrup (1990)  suggests that a .similar
mechanism could apply to cations such as Ca, Mg, K, Na, Fe, and
Si that are released from the mineral surface during dissolution.
     Differences in surface defect density, kink and step
density, and the number of edges and corners per unit ivolume of a
mineral can all combine to bring about significant differences in
dissolution kinetics  (Burton et al., 1951) . For calcite this
                                                      \
problem was addressed by Schott et al. (1989)  who studied the
dissolution of Iceland spar (high purity calcite) using rotating
cylinders strained to a high defect density. They proposed that
dissolution occurs preferentially at active sites such as lattice
defects. Minerals with greater defect densities dissolve faster
since their effective surface areas are greater than more perfect
specimens of the same compound.
     Compton and Daly (1984)  found the rate of dissolution of
Iceland spar was sensitive to the method of surface preparation.
Surfaces obtained by misorienting the crystal face provided more
sites at which dissolution could occur and thus dissolved faster
than surfaces with ordinary cleavage planes.          !
     Compton,  Daly and House (1986)  have shown that the
dissolution rate of Iceland spar is influenced by surface
                               14                     '

-------
morphology and the method used to prepare the surfaceiof the
stone sample. Freshly cleaved crystals were essentially
                                                      i
unreactive, but surfaces obtained by misorienting the crystal
faces dissolved faster than the ordinary cleavage planes because,
it was assumed, these provide more terrace sites at which
dissolution can occur.                                ;
     The relationship between dissolution rate and particle grain
size for alkali feldspars was studied by Holdren and Speyer
(1985, 1987) . They observed that the dissolution rate ;increased
linearly with decreasing grain size down to a critical range
(approximately 50-100 |U,m) . In this range, they hypothesized, the
grain size and distance between adjacent reactive sites become
roughly equivalent. For grain sizes below the critical region,
rate and reactant surface area were not related, however, the
rates for larger grain size minerals were reported as ;rates per
unit area, where rate and area had a linear relationship.
     The dissolution of dolomitic limestones  (CaMg(C03)2) was
studied by Plummer and Busenberg (1982) in C02-H20-acid systems
using a temperature range of 1.5 to 65°C. Their results show that
in the early stages of dissolution the CaC03  component; of
                                                      1
dolomite dissolves faster than the MgC03  component,  forming a Mg-
enriched surface. After the initial period of enhanced CaC03
dissolution,  Ca and Mg ions were released stoichiometrically.
     Pure dolomite dissolves more slowly than pure calcite  (Rauch
and White, 1977; Palmer, 1991). In stones that are a mixture of
CaC03 and dolomite,  the  dissolution  rate  has  been shown  to
decrease in a regular way with increasing dolomite content of the
rock (Rauch and White, 1977) .                          ;
     Herman and White (1985)  studied the dissolution of dolomite
samples and concluded that the dissolution rate increases with
decreasing grain size. However, the difference between the
initial rate of dissolution for a large single rhomb of dolomite
and a microcrystalline rock was only a factor of 1.5. ;
                                15

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4.0.5 Effect of Temperature on Dissolution Kinetics   -
     The effect of temperature on the dissolution kinetics of
limestones has received limited study. Rickard and Sjoberg  (1983)
showed that the experimentally observed rate constant ; for the
dissolution of calcite in aqueous solutions is controlled by a
surface reaction and a mass transfer resistance that act in
series. They therefore concluded that the overall dissolution
rate constant is likely to be a complex function of the
temperature.                 .                          ;
     The temperature dependence of rate constants for
heterogeneous reactions is usually quantified using tlie Arrhenius
equation, i.e.,                                       .

          Ink = Ea/RT + InA                           ;  (1)

where Ea is the apparent  activation  energy,  R is  the  gas constant
(8.314 J mol^K"1) ,  k  is the  dissolution  rate  constant  at the
absolute temperature, T,  and A is a constant.         .
     The apparent activation energies for heterogeneous reactions
have been used to discriminate between reactions showing
transport control, surface chemical reaction control or mixed
kinetics. The magnitude of Ea  for  reactions  controlled; by
transport processes is typically much less than values for
surface and homogeneous chemical reactions,  e.g., 10 to 20 kJ/mol
versus 30 to 100 kJ/mol.                               :
     Rickard and Sjoberg (1983)  concluded that at 25°G the rate
of calcite dissolution in the H+-dependent regime is  controlled
by mass transfer, which they assumed to be the diffusion of H+
from the bulk solution through the mass transfer boundary layer
to the stone surface. In the H+-independent  regime the; surface
chemical reaction controls and in the transition region between
these limits the kinetics is a function of both the surface
reaction and mass transfer. Lower temperatures cause tine surface
chemical reaction rate constant to become smaller and :the extent
                                                      i
of the transition region expands into the H+-dependenti region.
                                16                     i

-------
     Lund et al.,  (1975) used a rotating cylinder to Study the
rate of dissolution of calcite in hydrochloric acid. The
dissolution rate was limited by mass transfer at 25°C, even at
high cylinder rotational speeds. At -15.6°C both mass ;transfer
and surface reaction resistances were important.      :

4.0.. 6 Effect of Trace Species in Solution on Dissolution Kinetics
     Another important factor that may affect the dissolution
rate of calcite is the presence of trace species in solution that
adsorb on the mineral surface. Inhibition can occur at! very low
levels of trace species as demonstrated by the strong ^retarding
effect on calcite dissolution of micromolar concentrations of
dissolved Sc+4  (Terjesen et al./ 1961) and orthophosphate  (Berner
and Morse, 1974) . While modeling limestone dissolution in soils/
Warfvinge and Sverdrup  (1989) found that the rate of deactivation
due to adsorbed impurities on the limestone surface had a
significant influence on the model calculations. Fresh calcite
was coated with rust colored precipitates when exposed to soil
solutions or surface waters containing iron and dissolved organic
carbon.
                                                      I
                                                      i
4.1 MODELING CALCITE DISSOLUTION IN LIMESTONE CONTACTORS
     Haddad (1986) described the dissolution of calcite in
limestone contactors by adapting the rate model derived by
                                                      i
Rickard and Sjoberg  (1983). Rickard and Sjoberg's model assumes
that the dissolution of calcium carbonate in acidic splutions is
controlled by a heterogenous reaction (see Appendix A), the rate
of which is determined by a mass transfer resistance and a
surface reaction acting in series. According to this assumption/
the rate of calcium carbonate dissolution, r, is given by,

               r = k0 a (Ceq - C)                       ;  (2)

where Ceq and C  are the  equilibrium and bulk  fluid calcium ion
concentrations, respectively, and a is the interfacial area of
                                17

-------
calcium  carbonate  per unit volume of fluid. k0 is the overall
dissolution  rate constant and is given by,

                k0 =  [(l/kL) + (1/kjr1                 I  (3)
                                                       i
where kL is the mass transfer rate constant for the  calcium ion
and kc is the first order  surface reaction rate constant.
     For a limestone  contactor  Ceq is a function of the  chemistry
and temperature of the untreated water.  In this study [it was
calculated using the  chemical equilibrium model described in
Appendix B,  Equations  7B-9B.  The quantity a is the interfacial
                                                       i
area of calcium carbonate per unit volume of interstitial water
and, for a limestone  contactor  with  stone that is essentially 100
percent CaC03,  is given by,                            '

                a = 6(l-e)/(dexF)                        ;  (4)
                                                       |
where d and *F are the  volume-mean diameter and sphericity of
limestone particles and e  is  the bed porosity.        ',
     According  to Haddad  (Haddad, 1986;  Letterman et al.,  1991),
for a packed bed of crushed limestone, the magnitude o|f kL can  be
determined using equations derived by Chu et al. (19531)  . Equation
5 was used for  values  of  the  modified Reynold's number  (MRe)  in
the range 1 < MRe £ 30,                                j
                                                       i
                kL = 5.7 Us (MRe)-°-87  (Sc)-2/3,            ;  (5)

and Equation 6 was used for values in the range 30 < MRe <,
10,000,                                                 .;

               kL = 1.8 Us (MRe)-°-44  (Sc)-2/3    .         ,  (6)

     The modified Reynold's number is given by,        I

               MRe = dUs / (v(l-e))                      ; (7)
                                18                      ;

-------
and the Schmidt number,  Sc,  by,

               Sc  =v/D                                 ! (8)

where V is the kinematic viscosity,  D is the calcium ion
diffusivity and Us is the superficial velocity  of  the  fluid.
     Haddad  (1986) assumed that  the  magnitude of kc  is' determined
by the chemistry of  the  solution at  the CaC03 surface  land used
data from Sjoberg  and Rickard (1984)  to derive  the following
empirical relationship,                                |

               kc  (cm/s)  = 1.6 x 1014  {Heq}1-7            ; (9)

where {Heq} is the  interfacial (equilibrium)  hydrogen ion
activity. In this  study  the  magnitude of {Heq} was calculated
with the chemical  equilibrium model  (Appendix B,  Equations 7B-9B)
and is related to  the equilibrium  calcium ion concentration
(Ceq) .
     Haddad  (1986) used  the  following version of the continuity
equation to model  the limestone  dissolution  process  iri a
contactor operating  at steady-state,
                                                       !

               ND d2C/dZ2 - e  dC/dZ +  r© = 0            '! (10)
                                                       i
where ND  is  the  dimensionless axial dispersion  number, ; C  is the
calcium ion concentration, Z  is  the  dimensionless  depth,  @ is the
mean fluid residence time and r  is the  calcium  dissolution rate
expression.  Equation 2 was substituted  for r into  Equation 10 and
the resulting expression was  integrated over the depth of the
column to obtain,                                      ;

     (Ceq-CbL) / (Ceq-Cbo) = exp{-k0aL8/Us  +  (k0aLe/Us)2  ND}  j (11)
                                                       r
where Cbo and CbL  are  the  influent and effluent calqiumj
concentrations and L is the  overall depth of the cpntactpr.  This
                                19                     •

-------
equation assumes that the rate of dissolution at any point in the
bed is constant with time and, therefore, factors such as residue
layer formation and limestone particle shrinkage are  i
insignificant. Haddad  (1986) derived the following approximate
equation for ND using data from a tracer response study,

               ND = 2(d/L) .                            ! (12)

     Equations 3 through 9 and 11 and 12 effectively predict the
initial performance of a contactor filled with fresh limestone
(Letterman et al., 1991). However, when an experimental contactor
filled with limestone from Boonville, New York (the quarry where
the SL sample of this study was taken)  was operated continuously
for several months, Haddad  (1986) observed that the effluent pH
and calcium ion concentration decreased with time (see! Figure
4.1.1) .  Curve A was obtained using the steady state mo'del, curve
B is the simulation of non-steady-state when the stone diameter
decreases and curve C is the simulation when stone diameter
decreases and residue layer forms. The discrepancy between the
values predicted by the steady-state model and the measured
values increased with time.
                                                      i
     Haddad (1986) used the steady-state model (Equations 3-9 and
11-12) to develop a time-step simulation program for predicting
the performance of contactors during the non-steady-stiate
behavior of long term operation. In this program the operational
period is divided into short time intervals and the contactor bed
is divided into thin layers. The steady-state model predicts the
amount of calcium dissolved from each layer during each interval
of time. After each interval, a new stone diameter is calculated
for each of the layers using the amount of calcium dissolved. The
results obtained from this simulation program showed that
shrinkage of the limestone particles explained some but not all
of the decrease in performance observed by Haddad in his long
term column experiment (Curve B, Figure 4.1.1) .
                                                      !
     Haddad (1986) used x-ray energy spectroscopy to analyze the
                                20                     ;

-------
          8
        20        40        BO         80
    Volume of water treated Ccublc meters}
                                                             100
Figure 4.1.1
Calcium concentration is plotted as a function of
volume water treated, using data from Haddad
(1986) .
surface of limestone particles from the contactor used in the
long term experiment. He observed that the surface density of
aluminum, silica and iron had increased during the experiment and
concluded that a "residue layer" had formed as the CaC03
dissolved from the limestone matrix. As the residue layer
                                                      i
increased in thickness, he assumed, it limited the transport of
calcium ion away from the surface of the limestone and slowed the
rate of dissolution.                                  ;
     The transport of calcium ions across the residue ; layer was
modeled using,                                        i
               kf = Der/ (8tr)
                                         (13)
                                21

-------
where kf is the residue layer mass transfer coefficient, er and 8
are the porosity and thickness  of the  residue  layer,  D is  the
dif fusivity of the calcium  ion  in the  bulk  solution,  and Tr is
the pore length  (tortuosity)  factor. An  expression  for 8 was
derived by assuming that the  thickness of the  residue 'layer was
much less than the diameter of  the particle and that  it increased
                                                       i
as calcium dissolved from the surface  of the limestone,  i.e.,

               8=  [M(l-fi)  is the mass fraction of CaC03 in the stone, ps is  the
mass density of the residue solids and f is the fraction of the
total residue solids that remains on the stone surface'.
                                                       i
     The following equation for kf is obtained by substituting
Equation 14 into Equation 13,

               kf = 0.4BDK/[M(1-B) ] .                    ; (15)

The coefficient K in Equation 15 includes all  the parameters  that
Haddad  (1986)  could not measure experimentally and  is igiven by,
               K = p,(l-er) (er)/[(f) (Tr)] .              !  (16)
                                                      1
     The residue layer mass transfer coefficient, kf, was
included in the calculation of the  overall dissolution  rate
constant by expanding Equation 3 as follows,          :
               k0 = [(l/kL)  +  (l/kc) +  (1/kf)]-1.       -  (17)

     Haddad calibrated the non-steady-state simulation program
(with the residue layer resistance) by finding that K |=  0,6  gave
                                                      i
good agreement between the measured and model  predicted  effluent
calcium concentrations. This value of K was in reasonable
agreement with a value of K calculated using rough estimates of
the magnitudes of the parameters in Equation 16.      [
                                22

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                            CHAPTER  5
                EXPERIMENTAL METHODS AND MATERIALS    :

5.0 EXPERIMENTAL MATERIALS                            i
     The study was conducted using 13  samples  of  limestone
including a white marble  (sample WM) from  a quarry  in proctor,
Vermont, a sedimentary limestone  (sample SL) from a qu|arry near
Boonville, New York, Black River limestone (sample  BR)I  from  a
quarry near Watertown, New York and  10  samples  (sample's A-J) from
a dolomite quarry near York, Pennsylvania.
     The SL stone was selected for the  study because it is from
the quarry where Haddad  (Haddad, 1984,  1986; Letter-man  et al.,
1991.) obtained his samples. The Vermont marble sample ;(sample WM)
was used to compare the behavior of marble with that of
sedimentary limestones. The Black River limestone was iselected
because of its unusual black color. A black color in limestone is
usually caused by small amounts of organic material (Boynton,
1980). The 10 samples from the dolomite quarry in Pennsylvania
were selected to study the effect of the dolomite content on
dissolution kinetics. The dolomite content of these stones ranged
from essentially zero to 100 percent. Their physical and chemical
                                                      i
characteristics are discussed below.                  ;

5.0.1 Limestone - Physical Characteristics
     A qualitative assessment of the mineral content of five of
the limestone samples (samples WM, SL,  C,  F and I) wa-sl made by
observing thin sections of stone under polarized light using a
Zeiss petrographic microscope. The thin sections were prepared by
gluing samples of stone to a glass slide and then cutting and
grinding them to a thickness of about 3 microns. Photomicrographs
                                23

-------
of the sections are shown in Figures 5.0.1-5.0.5. According to
this analysis the WM sample consisted of coarse grains of calcium
carbonate and included about 20% quartz. The SL sample was gray
in color and fine-grained. The photomicrograph of the ;SL sample
(Figure 5.0.2)  shows that this stone was derived from Calcareous
mud called micrite (microcrystalline calcite).  Some fossil debris
and small quartz grains are evident in the sample.    '
     Figure 5.0.3 shows that stone I is a high magnesium calcite
dolomicrite. It is finely crystalline and brecciated and consists
of angular fragments up to 50 mm wide separated by thin calcite
cemented fractures. In sample C (Figure 5.0.4)  calcite has
cemented and replaced dolomicrite breccia. This sample is similar
to sample I except that calcite has replaced dolomite;in large
areas as well as in the fractures. Sample F  (Figure 5;0.5) is a
low magnesium limestone. It ha,s finely crystalline micrite with
Figure 5.0.1
Photomicrograph of a thin section cut from
undissolved stone sample WM.          ',
                                24

-------
Figure 5.0.2
Photomicrograph of a thin section cut from
undissolved stone sample SL.     "     ;
Figure 5.0.3
Photomicrograph of a thin section cut from
undissolved stone sample C.

                 25           •          !

-------
Figure 5.0..4
Photomicrograph of a thin section cut from
undissolved stone sample F.      "      :
Figure 5.0.5
Photomicrograph of a thin section cut from
undissolved stone sample I. '
                               26

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fossil forminifera and some blocky secondary calcite. :X-ray
diffraction analysis was done on stones samples I, C and F using
a Philips APD 3520 x-ray diffraction apparatus. According to the
results in Figure 5.0.6, the 20 angle for calcite is 29.55
degrees for samples C and F and 29.5 degrees for sample I. The
dolomites are ordered and the 20 angle is 31.5 degrees for
samples C and F and 31.1 for sample I. According to Figure 5.0.6,
stone I is essentially dolomite, stone C is dolomicrite and stone
F is low magnesium calcite.

5.0.2 Limestone - Chemical Characteristics
     Samples of each of the stones  (BR, SL, WM  and A-J) were
powdered using a mortar and pestle. The stone samples were core
sections that had been located next to the wafers cut for the
rotating disk apparatus. A 0.1 g quantity of each powdered sample
was dissolved in concentrated hydrochloric acid overnight. For a
number of the samples some translucent material, probably quartz,
remained after 2 days of dissolution. The acidified samples were
then diluted to 50 mL using DI water. After 2 days, 1 |mL of the
sample solution was diluted to 50 mL with DI and duplicates of
both the diluted and undiluted samples were analyzed with a
Perkin Elmer Model PE 3030B atomic absorption spectrophotometer
(AAS). The calcium, magnesium, iron and aluminum content of the
samples was determined by averaging the duplicate measurements
for the diluted samples. The results are listed in Table 5.0.1.
     The atomic absorption spectrophotometer was calibrated using
1000 ppm Ca, Mg, Al and Fe reference solutions  (certified Fisher
Scientific atomic absorption standards).  For Ca and Mg,
interference from phosphates, silica, and aluminum was minimized
by adding 1% lanthanum chloride  (1 mL LaCl2 solution tb 10 mL
soliition) to the standards and samples. The AAS was operated
using a wavelength of 422.7 nm and a slit width of 7 nm  (normal).
     The Ca, Mg, Fe and Al results for samples A-J  (Table 5.0.1)
were compared with measurements made by the quarry in sYork, PA
that had sent the cores. The quarry's results and the ;values
                                27                    !

-------
                                                     O

                                                     CO
                                                     (1)
                                                     rH
                                                     S-
                                                     CO
                                                     C!
                                                     O
                                                     4-1
                                                     CO
                                                     0)
                                                     O
                                                     CO
                                                     CO
                                                    •H
                                                    -d
                                                     a
                                                     13
                                                     CO
                                                     CO
                                                     CO
                                                    -H
                                                     CO
                                                    a
                                                    o
                                                    •H
                                                    4J
                                                    O
28
                                                    (ti
                                                    X M
o


LO


 0)



 I
-H

-------
              Table 5.0.1  RESULTS OF STONE ANALYSIS
Limestone
Stone ID Ca
WM 25.6
SL 37.5
BR 40.0
A 39.0
B 37.8
C 21.2
D 35.4
E 34.6
F 37.5
G 22.0
H 26.8
I 23.6
J 19.4
Composition
Mg
0.09
0.49
0.23
2.1
0.58
8.9
2.3
3.8
1.1
7.8
7.0
12.2
13.6
(g/100g)
Fe
0.071
0.101
0.019
0.024
0.029
0.189
0.040
0.041
0.015
0.294
0.154
0.377
0.189

Al
0.034
0.114
• 0.044
: 0.012
! 0.001
; 0.093
; 0.037
' 0.025
; o.oos
: 0.129
, 0.134
1 0.032
; o.oio
listed in Table 5.0.1 were compared using the mean relative
difference parameter  (MRD), Z{ (| Qi-sJ ) / [ (QJ.+SJ.)/2] },  where Qj.  is
the quarry's result for a given element and a given  sample and Si
is the corresponding value from Table  5.0.1. The MRD values were
10% for calcium, 45% for magnesium, 56% for iron and 1'36% for
aluminum. It could not be determined if the quarry's analytical
samples were from the same location in each core as  the ones
sent, therefore, it is likely that the higher values of the MRD
for Al and Fe, and to a certain extent for Mg, reflect^ spatial
differences in the Al, Fe, and Mg content of the stone;.
                                                      \
     The analytical results listed in  Table 5.0.1 were; used to
estimate the calcite, dolomite and insoluble residue content  of
the samples. In these calculations the magnesium was assumed,
based on the x-ray diffraction and thin-section photomicrography
results, to be associated only with dolomite. The dolomite
                                29                     ;

-------
content in grams per 100 grams was calculated using  the  magnesium
concentration from Table 5.0.1, CMg,  and              !

          dolomite content = CMg x  (184.3/24.3)        ;  (18)
                                                      I
     The calcite content was determined by  subtracting the
calculated amount of calcium in the  dolomite from the Itotal
amount of calcium in the sample, CCa,  listed in  Table 5.0.1,
i.e.,,                                                 ;

     calcite fraction =  [ (CCa -  (CMg x 40/24.3)]  x (100/40)   (19)

     The insoluble residue was assumed  to be the mass fraction of
the stone not attributable to either  calcite or dolomite,

     insoluble residue =  lOOg/lOOg  - (calcite + dolomite)   (20)

     The results of these calculations  are  listed in Table 5.0.2.
In several cases, as a result of measurement error,  the  sum of
the calcite and dolomite fractions is greater than lOQg/lOOg  of
stone. In these cases the insoluble  residue content  wa!s  set equal
to zero.                                               !
     The results in Tables 5.0.1 and  5.0.2  indicate  that samples
WM, SL and BR as well as a number of  the samples from ithe York,
Pennsylvania dolomite quarry (samples A, B, D, E and F)  are high
calcium limestones. A number of the York samples  (samples C,  G,
H, and I)  are predominately dolomite  and sample J is essentially
pure dolomite.                                        ;
     The WM sample had the highest insoluble residue content  (36
g/lOOg) but relatively low amounts of iron  and aluminum  (34 mg
Al/lOOg and 71 mg Fe/lOOg of stone). It is likely that
insoluble residue in this sample is quartz. Sample  I,
Pennsylvania, had the highest amount of iron  (377 mg Fe/lOOg)  and
sample H had the highest amount of aluminum  (134 mg Al/lOOg).
                                30
 the
from York,

-------
   Table 5.0.2  ESTIMATED MINERAL  CONTENT  OF  THE  STONE  SAMPLES

   	Major Stone Constituents  (g/lOOg)	
    Stone  ID	Calcite	Dolomite	Insoluble
       WM               64                1             j   35
       SL               92                4             i   4
                                                      j
       BR               99                2             :   0
A
B
C
D
E
F
G
H
I
J
5.0. .3 Rotating Disk
89
92
17
79
7.1
89
23
38
9
0
Solution
16
4
68
18
29
9
59
53
93
100
Characteristics
0
4
' 15
i
: 3
i 0
: 2
; 18
i 9
0
! 0
!
     All solutions used in the rotating disk experiments were
made with distilled and deionized  (DI) water that had been boiled
for a few minutes, several hours before use, to remove carbon
dioxide. Fisher analytical grade  (ACS Certified) chemicals were
used (KC1, N/10 HC1) . The background electrolyte was Oj.079 M KC1.

5.1 ROTATING DISK APPARATUS                           ,
                                                      f
     Transport to or from a rotating disk in a batch reactor is
affected by the disk diameter, the vessel size and gepmetry, and
the disk rotational speed. According to Riddiford  (196^6) , the
disk radius, r0,  should be much greater than the thickness of the
diffusion boundary layer at the face of the disk, i.e,'
                                31

-------
                (2.8/r0) (V/CO)1/2 < 0.03
(21)
where  v is the kinematic viscosity in cm2/sec and 0) is the
angular velocity in radians/sec.
     The condition expressed by Equation 21 was met in all
experiments by choosing a disk diameter of 4.45 cm.   ;
     According to Riddiford  (1966) the effect of the vessel walls
on fluid motion at the disk is minimized if the minimum distance
between the rotating disk and the walls of the reactor is greater
than 0.5 cm. In this apparatus the reactor diameter was 14 cm and
the clearance between the disk and the walls of the vessel was
greater than 4 cm. The disk was centered about 3 cm above the
bottom of the vessel (see Figure 5.1.1).
                                                      i
     The disk was rotated by an adjustable-speed, DC motor. A
bench tachometer  (Amtek Model 1723) was used to set arid monitor
the rotational speed which was varied over the range 200 to 1200
rpm.
     The reactor was constructed with double glass walls. A Haake.
Model A80 water bath was used to circulate water betwe'en the
walls to maintain the reactor contents at preselected
temperatures in the range 4 to 25 ± 0.2°C. The plexiglass cover
on the reactor had holes for the insertion of the rotating shaft,
pH electrode and wetted nitrogen inlet tube. Additional holes
were provided for measuring the temperature and pipetting samples
for the calcium measurement.
     The pH was measured using a Ross "Sure-Flow111?" combination pH
electrode (Orion)  connected to an Orion Expandable lori Analyzer,
Model EA940. The bulb of the pH electrode was located •!.5 cm from
                                                      i
the rotating disk and 3 cm above the bottom of the vessel. To
monitor the pH measurements, the ion analyzer was interfaced with
a microcomputer.                                       '

5 .1., 1 Stone Disk Preparation
     The SL sample was prepared by cutting a 3.10 cm diameter,
cylindrical core from a piece of rock collected at the quarry.
The WM and BR samples were cut from existing 3.68 cm and 2.45 cm
                                32

-------
                                Drive shaft
                     Teflon-coated
                     disk holdei=-v
                                            Wato- jacsetsd reactor
Figxire 5.1.1    Schematic diagram of the rotating disk Apparatus



diameter  cores,  respectively.  The ten samples from  the;  York,
                                                        i
Pennsylvania  quarry were cut  from existing 3.65 cm  dia'meter

cores. Each core was cut into  a  number of 3 mm thick  4isks using

a rock saw. The disk faces were  smoothed and polished [on a

lapwheel  using 400 (38 micron) and then 600  (25 microri)  grit size

                                 33                     '

-------
silicon carbide.                                      ;
     The back face and edge of the disks were coated with plastic
so that only the polished face was available for dissolution.
Each disk was mounted in a teflon-coated brass holder |as shown in
Figure 5.1.1. The WM sample and samples A-J were glued, as is, in
the 3.7 cm diameter x 4 mm deep well in the bottom of the holder.
For the 3.1 cm diameter SL and the 2.45 cm diameter BR samples, 3
mm thick plexiglass rings were used as fillers to center the
stone disks in the holder.                            ;

5.2 EXPERIMENTAL PROCEDURE                            ;
     A free-drift method, in which the pH was allowed !to increase
as the carbonate minerals dissolved from the stone, was used in
all experiments. Each experimental solution (600 mL)  was prepared
as needed by adding KC1 and the required volume of acid to boiled
wate;r and then transferring this to the reactor.      '
     Ultra-pure nitrogen gas, saturated with water vapor, was
bubbled continuously through the solution for a few minutes
before the experiment was started. During the experiment,
humidified nitrogen flowed through the headspace above: the
solution to minimize exchange of C02  with  the  atmosphere.  The
nitrogen flowrate was approximately 1 L/min. Sjoberg and Rickard
(1983)  have shown that the use of low C02  nitrogen  gas I in this
way causes negligible loss of dissolved inorganic carbpn from the
                                                      i
reactor during the dissolution experiment, apparently because of
the low rate of gas-solution exchange of C02.          !
     The pH measurement was standardized with Fisher™ pH 4 and 7
buffer solutions that had been adjusted to the temperature of the
reactant solution. A series of experiments (described in Appendix
C) was conducted using methyl red dye and a fiber optic probe
colorimeter to verify that the solution in the vessel was well
mixed and that the response time of the pH electrode w|as not
                                                      i
affecting the accurate measurement of the time-varying pH.
     Each experiment was started by raising the vessel^ and
solution into place beneath the rotating disk and against the
                               34

-------
plexiglass cover. Samples of solution  (either 2 or 5 ml volume)
were withdrawn from the vessel at 6 or  9 minute internals for a
period of 1.5 hours using a Finnpipette  (1-5 ml). The ^samples
were stored in polyurethane disposable test tubes at 4°C for no
longer than 2 days before the ion concentrations were ;measured by
AAS,,
     The total calcium and magnesium ion concentration's in each
sample were measured with a Perkin Elmer Model PE 3030 atomic
absorption spectrophotometer. After a run, the disk was either
rinsed with DI water and stored in a known volume of DI water or
the surface of the disk was "aged" with an acidic solution. The
aging procedure is discussed below.                   |
     In the experiments on the effect of temperature, /the disk
holder and the disk were brought to the temperature of the
solution by wrapping the disk holder in Saran plastic ;wrap and
immersing it in the water bath before it was attached 'to the
drive shaft and inserted in the solution for the rate experiment.

5.2.1 "Aging" the Limestone Disk Surface              j
     A special procedure was used to dissolve controlled amounts
of calcium and,  for some dolomitic stones, magnesium f;rom the
disks between rotating disk experiments. This is refer'red to as
"aging" the disk surface. Each disk and its holder was! placed in
a beaker containing a measured volume of acidified solution (0.1
meq/L acid,  initial pH=4). The solution was stirred continuously
with a magnetic stirrer. At the conclusion of this procedure,  a
sample was taken for determining the calcium and magnesium
concentrations and the volume of the solution was recorded. The
measured calcium concentration was used with the volume of this
solution to determine the mass of calcium dissolved (Cas) .  The
remaining solution was discarded,  the disk was placed in fresh pH
4 solution,  and the process was repeated until the desired mass
of calcium had been dissolved from the disk.          '
     The total mass of calcium dissolved per unit area: of the
disk surface,  Cad,  was  obtained by dividing the  sum  of j the  mass
                               35

-------
of calcium dissolved during  aging  (2Cas) and the mass of calcium
dissolved during all the earlier rate  experiments  (2Car) by the
surface area of the disk  (A).                         :

               Cad = (ECas  +  ZCar)/A                   !  (22)  '
5.2 ,.2  Calcium and Magnesium Determination by Atomic Absorption
       Spectrophotometrv
                                                      !
     The standards used to calibrate the AAS were made by
diluting 1000 ppm calcium reference solution  (certified Fisher
Scientific atomic absorption standard) with background
electrolyte solution  (0.079 M KC1). The calcium concentrations in
the standards ranged  from 0.5 to 5 ppm. To minimize interference
from phosphates, silica and aluminum, 1% lanthanum chloride was
added to the standards and samples using 1 mL LaCl2 solution to
10 mL solution. The AAS was operated using a wavelength of 422.7
nm and a slit width of 7 nm (normal).                 •
     The standards were used to obtain a linear calibration curve
of cibsorbance versus the calcium concentration. The standards
were then run as samples to verify the calibration. After this
                                                      i
verification step, the AAS was calibrated again and the samples
were analyzed a second time. The difference between the first and
second measurement was always less than 4 percent.    ;

5.2.3  Agreement Between Calculated and Measured Calcibm
       Concentrations                                 ;
     To check for consistency between the measured pH and the
measured calcium ion concentration, Equation 11B in Appendix B
was used to calculate the theoretical amount of calcium dissolved
as a. function of the measured pH. Good agreement was obtained
between the measured and calculated calcium concentrations when
it was assumed that the solution contained 1.28 x 10~5 !moles/L of
initial dissolved inorganic carbon (see Appendix D). This
suggests that the procedures used to minimize the amount of
                                                      !
                                36                     •-

-------
carbon dioxide in the rotating disk solutions were not entirely
effective.                                            ;

5.2.4 Alkalinity Measurements
     Alkalinity measurements were used occasionally as an
                                                      t
approximate check of the measured calcium concentrations (see
Appendix D).  The alkalinity was determined using strong acid
titration to an equivalent endpoint determined by Gran plot
analysis. A 75 ml sample was titrated to a pH of 3.2 using 0.1 N
HC1 and a computer controlled Metrohm Dosimat 655 automatic
titrator. Two DI water blanks were analyzed before titrating the
samples. The error in duplicates analyzed was less than 0.3%.

5.2.5 Solubility Product Determination                i
     A set of long duration experiments was performed'to estimate
the solubility product of the calcium carbonate in the limestone
samples. The calcium and magnesium concentrations and1the pH and
alkalinity at the end of the experiment were used with the
relationships presented in Appendix E to calculate the solubility
product. Effective solubility products for calcite anql calcite
combined with dolomite were determined for samples WM, SL,  A, C,
F, and I.  The results are listed in Table 5.2.1.     ;

Table 5.2.1  EFFECTIVE SOLUBILITY PRODUCTS FOR CALCIUM CARBONATE
             AND CALCIUM-MAGNESIUM CARBONATE IN SELECTED
             LIMESTONE SAMPLES. VALUES ARE FOR 25°C AND INFINITE
             DILUTION.                                :(
                                                      i'
         Stone sample ID          Negative log of theieffective
                                        solubility product
WM
SL
A
C
F
I
8
8
8
8
8
8
.20
.35
.76
.72
.88
.89
± 0.07
± 0.06
± 0.09
± O.Q7
± O.,05
± 0.04
                                37

-------
5.2.6 Glassware
     All glassware used in sampling and the preparation of
standards was soaked overnight in 1 N HC1 and then rinsed three
times with DI water. The glassware was then soaked in-DI water
for a day and rinsed with fresh DI water before use.
                               38

-------
                             CHAPTER 6
               EXPERIMENTAL  RESULTS AND  DISCUSSION   !

6.0 DISSOLUTION RATE DETERMINATION                    •
     The calcium concentration  and  pH  change  with time  in a
typical rotating disk experimental  run are  shown  in Figures 6.0.1
and 6.0.2. In this example,  the WM  stone sample was used,  the
rotational speed was 600 rpm and the initial  acidity was  0.01
                                                      i
meq/L. At the end of the experiment the  pH  was 9.04 and the
calcium concentration was  1.71  mg/L. For an initial acidity of
0.01 meq/L and with no calcium  in the  solution at t = iO,  the
calculated equilibrium calcium  concentration  is 11.6 mg/L and the
calculated equilibrium pH  is 10.02  (see  pKsp for sample  WM, Table
5.2,,1, and Equations 7B-9B, Appendix B) .
     The initial rate of dissolution in  this  study ranged from 8
x 10~10 moles Ca/cm2s to  1 x 10~9 moles Ca/cm2s. These values lie
within the range of values  (1 x 10~10 moles  Ca/cm2s to 2  x 10~9
moles Ca/cm2s)  reported in  the literature (see Table  61.0.1).
     The overall dissolution rate constant, k0, was determined
for each experimental run using the measured  calcium
concentrations and, in some  cases,  the measured magnesium
concentrations. For the stones  that released  negligible amounts
of magnesium, the calcium concentrations  (Ct)  were  substituted  in
the relationship,

               Ln/a - In { (Ceq - Ct)  / (Ceq  - C0)  } (Vt/A)  ;  (23)

where Ceq and C0 are the equilibrium and initial calcium
concentrations, respectively, and A is the  surface area of the
stone sample disk exposed to the solution.  C0 was   zero; in all
experiments. Vt is  the  volume of the solution in the rotating
                                39

-------
           2,5

           2.0
          c
          0
          r5
          +j
          o>
          C 1,0
          o
          u
          E
          U 0.5
           0.0$
             0,0   0,2   0.4   O.B    0,8    1,0
                             Time Choirs}
1,2   1.4
Figure 6.0.1  Calcium concentration in the rotating disk
              apparatus  as  a  function of time;  WM sample; w = 600
              rpm and initial acidity of 0.01 meq/L.  \
                                                       \

disk apparatus. For sample  WM and samples A-J the limestone disk
was 3.6 cm in diameter and, therefore,  A was 10.17 cm2;.  For the
3.1 cm diameter SL sample and the 2.5 cm diameter BR s,amplef A
was 7.91 cm2 and 4.71 cm2, respectively.               ;
     The magnitude of Ceq was  determined for each experimental
run using the equilibrium model  described by Equations 7B-9B in
Appendix B and the effective  solubility products listed in Table
5.2., 1. For the stone samples  that were not included in the
solubility product experiments,  i.e.,  samples B, D, E,i G, H and
J, the average value of  the effective solubility products for the
samples from the same quarry  (pKsp = 8.81) was used. pKsp  =  8.35
was used for sample BR because of its similarity to sample SL.
     As samples were withdrawn during an experiment, the
                                40

-------
        10.0
        9.0 -
        8.0 -
        7.0 -
        6.0 -
        5.0
          0,0     0,2    0,4    0,6     0.8    1.0    1.2    1,4    1.6
                              Time Chours}
Figure  6.0.2    pH vs time for the rotating disk  experiment of
                Figure 6.0.1.
  Table 6.0.1   REPORTED INITIAL RATES OF CALCITE  DISSOLUTION AT
                25°C                                     ;
         Reference
 Type  of  System
       Used
Rate x 1010 moles
     Ca/cm2s
 Wallin and Bjerle
 (1989a)

 Sjoberg and Rickard
 (1983)

 Plummer et al.  (1978)
Rotating
Cylinder

Rotating Disk
Stirred
Suspensions
     1 to 5
     5 to 20
    10 to 20
magnitude of Vt decreased. A value  of Vt was  calculated for each
value of Ct using the relationship,                     ',
                                 41

-------
               Vt = V0 - nv                            i  (24)

where V0 is the volume  of  the solution in the reactor jat the
start of the experiment, v is the volume of each sample withdrawn
                                                      i
for the calcium and magnesium measurements and n is the total
number of samples withdrawn from the reactor up to that sample.
In the dissolution rate experiments, V0 was 600 mL and v was
either 2 or 5 mL.                                     ;
     A straight line was fitted to the Ln/a versus time points
using the method of least squares. The negative slope jof this
line is equal to the overall dissolution rate constant, k0.
     Figure 6.0.3 is a Ln/a versus time plot for a fresh sample
of WM stone. In this experiment the disk rotational speed  was 600
rpm, the water temperature was 25°C and the initial acidity was
0.01 meq/L. The negative slope of the least squares line in
Figure 6.0.3 yields an overall dissolution rate constant of 3.3 x
10"3 cm/s.

6.1 EFFECT OF DOLOMITE CONTENT ON k0                  |
     Significant amounts of magnesium were dissolved from  the
high dolomite content stones  (samples I and J with approximately
93 and 100 percent dolomite, respectively) during the !rate
experiments and during the batch aging process and the solubility
product experiments of Appendix E. The average calcium to
magnesium mass ratios for each of the solutions used in the batch
aging process was 0.51 for stone I and 0.54 for stone |J. For the
stoichiometric dissolution of pure dolomite the theoretical Mg/Ca
mass ratio is 0.61.
     For stone samples I and J, an effective value of jk0 was
determined using an "equivalent" calcium concentration, C't, in
place of Ct in  Equation  23.  The magnitude of C't was calculated
for each sample from the reactor by adding the measured
concentrations of calcium and magnesium  (expressed in (equivalents
per liter) and then multiplying this sum by the equivalent weight
of calcium.
                                42

-------
       9
       o
       w
       cd
       ^
         -10 -
         -12
           0.0
                 0,2    0.4    0.6     D.B    1.0
                               Time  £hours}
1.2
      1.4
            1.6
Figure 6.0.3   Dissolution rate experiment  for  the  WM ;stone
               sample. Initial acidity  =0.01 meq/L and w = 600
               rpm.  In this example, k0 = 0.0033 cm/s.

     Figure 6.1.1 shows the calcium and magnesium concentrations
and the calculated equivalent calcium concentrations plotted
versus time for an experiment with sample J. The Ln/a versus time
points (calculated using the equivalent calcium concentrations)
are plotted in Figure 6.1.2. An "effective" equilibrium calcium
concentration of 6.48 mg/L was used in  place of Ceq  inequation
23. This value was calculated using an  effective solubility
product of pKsp =8.81 and the equilibrium relationships
described in Appendix B.                              (
     A significant y-axis intercept for the line fitted to the
Ln/a versus time data (see Figure 6.1.2) was typical for the
first rate experiments conducted with new disks of  stones I and
J. B'or fresh samples of stones I and J, there was always an
initial period with a high rate of dissolution. This period is
apparently the cause of the significant y-axis  intercept of the
                                43

-------
      0.8
      o.o»
        0.0
0.2    0.4    0.6    O.B    1.0
             Time CHours}
1.2
1.4
1.6
Figure 6.1.1   Calcium, magnesium and calculated  equivalent
               calcium concentration for a rotating  disk
               experiment with stone sample J  and 600  rpm.

least-squares fitted line.                            j
     The high initial rate of dissolution for  stones I  and J is
consistent with the observations of Plummer and Busenb'erg  (1982)
who, in their study of dolomite dissolution, observed ;that
initially the calcium carbonate component of dolomite :dissolved
faster than the magnesium carbonate component, forming a Mg-
enriched surface on the disk. After this initial  period the
dissolution of Ca and Mg became slower and more consistent
(stoichiometrically) with the composition of the  solid.
     For all stone samples except I and J, the highest
concentration of magnesium measured during a rate experiment was
always less than 0.03 mg/L. Figure 6.1.3 shows the calcium and
magnesium concentrations plotted versus time for  s,tone  sample C.
                                44

-------
         0,0$
        -1.0
        -2.D
       E-3,0
       cd
        -4.0
        -5.0
        -B.O
        -7.0
           0.0
                               I
                                     _l_
                 D.2
                        0.4
0,6    0.8
  Time
                                           1,0
                                                 1.2   i 1 .4
                                                             1.6
Figure 6.1.2
               Dissolution rate experiment  results for stone
               sample J.  Ln/a calculated using the equivalent
               calcium concentrations  in  Figure 6.1.1.
Sample C had 17% calcite and  68%  dolomite.            ;

6.2  EFFECT OF INSOLUBLE RESIDUE  CONTENT  ON THE INITIAL RATE OF
     CALCITE DISSOLUTION                              !
                                                      I
     It was observed that the overall  dissolution rate  constant
for fresh calcitic stones  (stones with low  dolomite content)
tended to decrease as the estimated amount  of insoluble residue
in the stone increased. It  is reasonable  to conclude tihat the
insoluble impurities reduce the area of calcite exposed to the
solution. To test this hypothesis,  it  was assumed that  the area
qf exposed calcite is proportional to  the mass percent  of calcite
in the stone. The rate constants  were  "corrected" for; the residue
content by dividing them by the mass percent of calcite in the
                                45

-------
        2.0
        1.5

      o
      o
      o
        1.0
       D.5
       0.0&
                                       -7*
-X-
X
         0.0    0.2    0,4     0.6    O.B     1.0
                              Time Chours}
     1.2
 1.4
                  1,5
Figure 6.1.3   Calcium and magnesium concentrations for rotating
               disk experiment  with stone sample C at i600 rpm.

stone. The results of this calculation,  listed in the right-hand
column of Table 6.2.1, show  that  this correction reduces the
effect of the residue content on  k0.                   I
     The corrected overall dissolution rate constant for the
coarse-grained WM sample  (3.12  x  10~3 cm/s)  is somewhat less than
the values of  3.51 x 10~3 and 3.75 x 10~3 cm/s for the .fine-
grained SL and BR samples. This difference  is consistent with the
observation of Holdren and Speyer (1985)  that stones With smaller
grain size have higher rates of dissolution.
                                                       I
6.3  VARIATION OF k0 WITH THE CaC03 CONTENT OF THE STONE
     In Figure 6.3.1 the  experimental values  of k0  for!the  fresh
stone samples, koi, are plotted  versus the approximate ;calcite
                                46

-------
Table 6.2.1  COMPARISON OF EXPERIMENTAL AND  CORRECTED -OVERALL
             DISSOLUTION RATE CONSTANTS FOR  ESSENTIALLY  FRESH
             LIMESTONE DISKS                          \
(Small amounts of calcium had been dissolved from  samples  WM,  SL
and BR before the first rate constants were  determined).

  Stone      Mass %     Experimental k0 x  103  Corrected k0 x 103
            Calcite             (cm/s)                (cm/s)
Cad =
WM
SL
BR
Cad «
B
F
0.2 mg Ca/cm2
64
92
100
0 mg Ca/cm2
92
89

1
3
3

4
3

.99
.26
.75

.39
.46

3
3
3
!
4
3

.12
.51
.75

.77
.89
content of the stone  (CAL) in grams of CaC03 per 100 grams of
stone  (see Table 5.0.2). The magnitude of CAL ranges from  92
g/100 g for sample B to 0 g/lOOg for the essentially pure
                                                      i
dolomite stone (sample J).
     According to the results plotted in Figure  6.3.1,. the
magnitude of koi for fresh stone decreases by  approximately 60%
as the calcite content of the stone decreases from  92 ;to 9 g
CaC03/100  g.  The  y-axis intercept  of the line fitted to these
points by the method of least-squares is an extrapolated value of
koi for pure dolomite  (CAL=0). The value of  this  intercept  for
the data plotted in Figure 6.3.1 is 2.58 x  10~3 cm/s, which is
significantly greater than the observed value of koi (koi = 0.93 x
10~~3 cm/s) for the fresh sample of pure dolomite. This^result
suggests that the presence of calcite in stones  with high
dolomite content enhances the rate of dolomite dissolution. Since
the Mg concentrations measured in the rate  experiments were
negligible for all stone samples except I and J, it appears that
                                47

-------
       0)
       (0
       0
       +J
       (0
       cr 2
       c
       o
       — 1
       O
       0)
       0)
       5
                     _L
       Rate constant  for essentially pure dolomite
                          J_
                    20         40         60         BO   \
                   Calcfte ContentJ  CAL C9/100g stone}
                                              100
Figure 6.3.1
Effect of the calcite content of the  stone  sample
on the initial value of the dissolution  rate
constant.                               '••
the dissolution of dolomite  in  all but  the  essentially: pure
dolomite samples occurred, as observed  by Plummer and Busenberg
(1982), by the dissolution of calcium and carbonate from the
dolomite fraction of the stone.
6.4 EFFECT OF IRON AND ALUMINUM ON THE DISSOLUTION RATE
     It was observed that the extent to  which  the  dissolution of
calcium from the stone surface reduces the  overall dissolution
rate constant depends on the aluminum and iron content of the
stone.                                                 !
     Figure 6.4.1 shows the normalized overall dissolution rate
                                48

-------
             1.2
           r\
             0.0
                0         2         4         6        8
                  Ca dissolved per  unit area of disk 09/sq
Figure 6,4.1
Effect of amount of calcium  dissolved oh the
fractional decrease in the overall  dissolution
rate constant.
constant  (i.e., the measured  value  divided by the initial, fresh
stone, value, k0/koi) plotted  versus the  amount of calcium
dissolved from the  surface  of the stone,  Cad,  for stones  A-D,  F,
G, I and J  (see Equation  22).  For stones D,  G and I, k0 decreased
by more than 60 percent as  the amount of calcium dissolved
increased from 0 to 4 mg  Ca/cm2. For  stones F,  B  and J the
decrease was less than 30 percent.
     Values of k0/koi were interpolated from Figure 6.4*. 1  at Cad =
2 mg Ca/cm2 and then listed in Table  6.4.1 in  rank order,  from
the highest  (k0/koi =0.90 for stone F) to the  lowest (k0/koi =
0.23 for stone G).  The stones with  the highest aluminum content
(> 25 mg Al/lOOg of stone)  had the  greatest  decrease in k0 for
                                                       i
                                49                     :

-------
Table  6.4.1  EFFECT  OF  THE IRON AND ALUMINUM CONTENT ON THE
             FRACTIONAL DECREASE IN THE OVERALL DISSOLUTION RATE
             CONSTANT AT Cad =  2 mg  CALCIUM  DISSOLVED  PER SQUARE
             CENTIMETER OF LIMESTONE SURFACE.
Stone
ID
F
A
B
J
E
D
C
I
H
G
Calcite
88.9
88.9
92.1
0
70.7
78.9
16.5
8.8
38.3
22.9
k0 x 103*
(cm/s)
3.5
4.7
4.4
0.9
3.3
4.2
2.7
2.8
3.3
3.2
*./**
0.90
0.74
0.73
0.70
0.65
0.61
0.43
0.36
0.35
0.23
Fe
(mg Fe/lOOg)
15
24
29
189
41
40
189
377
154
294
Al
(mg Al/lOOg)
5
12
: 1
: 10
25
37
93
32
134
, 129
^interpolated from Figure  6.4.1  at  Cad = 2 mg Ca/cm2.  :

this amount of calcium dissolved. For several  stones,  especially
stone I with k0/koi = 0.36, the iron content  seemed to  be an
additional factor.
     Since both the iron and  aluminum content  of the stone seem
to determine how sample aging affects the  overall dissolution
rate constant, a composite parameter  that  includes a weighted
combination of the iron and aluminum  concentrations (aCA1 + bCPe)
was derived, where CA1 is the  aluminum concentration in mg Al/100
g and CFe is the iron concentration  in mg Fe/100 g.. The highest
linear correlation between k0/koi and  the parameter (r2'= 0.92)
was obtained with weighting factors a =  1  and  b = 0.37: i.e.,  (CA1
+ 0.30 CFe) ,  The quantity  k0/koi  and corresponding values of (CA1
+ 0.30 CFe) are listed in Table  6.4.2.
     According to the results in Table 6.4.2,  the effect of iron
and aluminum on the overall dissolution  rate constant  will be
minimized if the quantity CA1  +  0.30 CFe for the stone is less
                                                       i
                                so                      ;

-------
Table 6.4.2    EFFECT OF THE WEIGHTED SUM OF IRON AND ALUMINUM IN
               THE LIMESTONE ON THE FRACTIONAL DECREASE IN THE
               OVERALL DISSOLUTION RATE CONSTANT AT 2 mg CALCIUM
               PER SQUARE CENTIMETER OF LIMESTONE SURFACE
Stone ID k0/koi
F , 0.90
A 0.74
B 0.73
J 0.70
E 0.65
D 0.61
C 0.43
I 0.36
H 0.35
J 0.23
cA1 + o;.3o cFe
(mg/lOOg)
io
19
10
67
37
49
149
145
180
217
than about 10 mg/lOOg.                                :

6.4.1 Residue Layer Resistance                        ;
     Haddad  (1986)  assumed that when limestone contains
impurities such as alumino-silicates, iron and aluminum, the
dissolution of calcium carbonate from the limestone matrix leads
to the formation of a residue layer on the exposed limestone
surface. With a significant residue layer resistance, ;the overall
dissolution rate constant can be assumed to be given by Equation
17. When the residue layer is negligible and kf is large,
Equation 3 is used to calculate the overall dissolution rate
constant.                                              ;
     Scanning electron micrographs of the surfaces of ;the WM and
SL stones are shown in Figures 6.4.2A-6.4.2C and  6.4.3A-6.4.3E.
These electron micrographs show that the appearance of the disk
                                                      i
surface changed significantly due to dissolution. According to
Figure 6.4.2A, freshly polished WM stone is relatively smooth and
                                51                     ;

-------
Figure 6.4.2A
Scanning electron micrograph of freshly prepared
WM stone sample.
                                52

-------
Figure 6.4.2B
SEM image of WM stone sample after dissolving 6
mg Ca/cm2 from the surface of the stone.
Undissolved elevated regions are silica.
                                53

-------
Figure 6.4.2C   XES map of calcium distribution in fresh -sample
                of the WM stone.                      ;
                                54

-------
Figure 6.4.3A   Scanning electron micrograph of the surface of a
                fresh SL sample.                      '
                                55

-------
Figure 6.4.3B   XES map of the distribution of calcium on the
                fresh SL sample.
                                56

-------
Figure 6.4.3C
XES map after dissolving calcium from the surface
of fresh SL sample.  The abundance of calcium has
decreased significantly compared to Figure
6..4.3B.
                                57

-------
Figure 6.4.3D   XES'map showing the distribution of silica SL
                sample after calcium was dissolved from the
                surface.
                               58

-------
Figure 6.4.3E   XES map showing the distribution of aluminum on
                the dissolved SL sample.             .  ;
                               59

-------
 featureless. Analysis  of  the  surface by an x-ray energy
 spectrometer  (XES)  indicated  that  it was mostly calcium and
 silica  (see Figure  6.4.2B). As  CaC03 was dissolved, significant
 pitting  and roughening of the surface became apparent.; Areas of
 silica remained -and formed plateau-like structures on ^the surface
 of the disk  (Figure 6.4.2C).                           ;
     For the SL stone,  dissolution of CaCO3 produced  a'brownish-
 white residue  layer on the surface.  The SEM/XES analysis
 indicated that this layer consisted of aluminum,  silica and iron
 (Figures 6.4.3D and 6.4.3E).  The impurities  measured  in the SL
 sample  (Table  5.0.2) are  consistent  with these  observations.
     Values of k0 plotted as a function of Cad,  the mass of
 calcium  dissolved per  unit area of stone (in mg/cm2) ,   are shown
 in Figure 6.4.4 for the SL, WM and BR samples.  kf values for
 different amounts of calcium  dissolved from  the surface  of  the SL
 stone are given in  Table  6.4.3.
     To  calculate kf, experimentally determined values; of k0/  kL
 and kc were substituted in Equation 17. As increasing amounts of
 calcium  are dissolved,  kf becomes  smaller and, eventually
 controlling. Also included in Table  6.4.3  are the  kf values
 calculated using the empirical equation (Equation  13)  derived by
 Haddad (1986) for his  non-steady-state  simulation  model.
                                                       !
     The WM stone contains less calcium than  the SL and  BR  stones
 (Table 5.0.2) . It also  contains the  greatest  amount of, silica (as
 indicated by the analysis  of thin  sections).  This  stone  provides
 limited  evidence that  the  silica content does not by  itself
 establish that a residue  layer will be  formed.  Repeated
 experiments with the same WM stone did  not produce a  significant
 decrease in the dissolution rate.   Even  after  Cad was 5.7 mgCa/cm2
 the dissolution rate was  essentially equal to the  initial value.
     SL  stone,  on the  other hand,   is 93% CaC03  (see Table 5.0.2)
but it also contains more  of the elements  (aluminum and  iron)
that seem to be critical  for the formation of a residue  layer,
 (CA1 + 0.3 CFe)  = 114 mg/lOOg.  As calcium was  dissolved ;from the
 surface of the SL stone the overall dissolution rate  constant
                                60

-------
               o.oo:-
               0.004
               DOD3
               o.ooa
               0,001
               o.ooo
                                 SL
                                             BR
                        -•=»	
                             -H—
                                     . Haddad's calculations
                             I
                             2          4          B
                      Mass of calcium dissolved Cmg Ca/sq.cm^
Figure  6.4.4   Variation in the overall dissolution  rate
                constant,  k0/  with the amount of calcium  dissolved
                from the disk surface.   The dashed  line curve is
                the relationship used by Haddad  (1986)  ;in his
                simulation program.


Table 6.4.3  RESIDUE  LAYER MASS TRANSFER COEFFICIENT FOR SL
              SAMPLE                                      ;
Calcium
dissolved
(mg Ca/cm2)
0.00
0.19
0.56
0.80
1.96
2.69
3.80
4.00
k0 x 103
Experimental
(cm/sec)
3.95
3.51
2.65
3.13
2.04
2.02»
1.41
0.68
kf x 103
From exp . k0
(cm/sec)
—
—
640.57
—
8.74
8.38
2.99
0.91
kf x 1Q3
Haddad
(cm/sec)
; —
: 169
: 57
; 40
• 16
! 12
, 8.4
,8.0
decreased,  from 3.50 x  10 3 cm/s at  Cad=0.2  to 0.68 x  10~3 cm/s at

                                  61                      '

-------
Cad=4.0  mgCa/cm2.                                      ;
     BR stone has the highest calcium content  (99% Ca003, Table
5.0.2) and small amounts of aluminum and iron  (CA1  +  OJ3  CPe = 50
mg/lOOg).  The dissolution rate decreased slightly  from 3.75  x  10"
3  to  3.39  x  10~3 cm/s as the amount of calcium dissolved  increased
from Cad = 0.2 to Cad =  6.2 mg Ca/cm2. The BR stone was;
essentially black in color, possibly from the presence' of  trace
amounts of organic matter.
     The residue layer that formed on the SL disk was ;scraped
into concentrated nitric acid, ultrasonicated and the ^solution
was analyzed for total soluble aluminum. The soluble aluminum
expressed as the amount per area of disk was 0.97 |4,moles/cm2 (26
jig/cm2) . The scraped residue  did not dissolve completely in acid
suggesting the presence of alumino-silicates. The overall
dissolution rate constant for SL stone increased to  90%  of its
original value when the residue layer was removed by scraping  the
disk surface  (see Figure 6.4.5).
                                                      !
6.5 EFFECT OF TEMPERATURE ON k0
     The effect of temperature on the rate of calcite dissolution
was studied by conducting rotating disk experiments  at 5,  12,  18
and 25°C.  Stone sample B was used for these experiments  because
it had a high calcite content and low amounts of impurjities  (CM
+ 0.3 CFe =  10 mg/lOOg). The background electrolyte wa§ 0.079 M
KC1,  the disk rotational speed was 600 rpm and the initial
acidity was 0.01 meq/L.                               i
     Figure 6.5.1 shows plots of Ln/a versus time for 12°C and
18°C. The equilibrium calcium concentration, Ceq, used. ;to
calculate values of Ln/a was determined for each temperature
using the chemical equilibrium model described in Appendix B and
an effective solubility product of 1.55 x 10~9  (pKsp = 8.81).  The
procedure used to estimate the effective solubility  product  is
described in Appendix E. Table 6.5.1 lists the calculated  values
of Ceq and the experimental values of k0 for each temperature.
                                62

-------
         u
         id
         X.
           -10 -
           -15 -
             0.0
                                                            1.6
Figure 6.4.5
  Plots of ln{(Ceq-C)/Ceq}V/A versus  time; for  SL
  sample; 0.01 meq/L of initial acidity  and 600  rpm.
  Curve A and C are for 0.2 and 3.8 mg/cm2 of
  calcium dissolved from the surface  of  SL sample.
  Curve B was obtained after scraping the residue.
6.6 EFFECT OF TEMPERATURE ON kc  AND kL
     The experimental values of k0 listed in Table 6.5ll were
used to determine the effect of temperature  on  the  surface
reaction rate constant, kc,  for stone B and on the mass transfer
constant, kL,  for the calcium ion. For heterogeneous reactions,
the overall dissolution rate constant  is  related to  kL;and kc by,
k0 = kL kc/(kL
                             kc)
(25)
     The magnitude of kL for the surface of a rotating: disk is
                                63

-------
           D.D
                                                             1.6
Figure 6.5.1   Plot of ln{(Ceq-C)/(Ceq-Co)}/(V/A)  versus time for
               12 and 18°C and  sample  B.   Initial  acidity is 0.01
               meq/L and rotational  speed is  600 rpm.
Table 6.5.1
EFFECT OF TEMPERATURE ON THE CALCULATED  VALUES  OF
THE EQUILIBRIUM CALCIUM CONCENTRATION AND
EXPERIMENTAL VALUES OF THE DISSOLUTION RATE
CONSTANT
Temperature
°C
5
12
18
25
25
c *
^eq
mg/L
6.04
6.16
6.00
6.60
6.60
k0 x 103
(cm/s)
0.38
0.;84
1:.3
2.8
2.83
 *based on pKsp = 8.81  at  25°C
                                64

-------
             kL = 0.62 D2/3 V~1/6 OF1'2                     (26)

given by the theoretical  expression,  where D is the diffusivity
of the calcium ion, v is  the  kinematic viscosity and CO is the
rotational velocity of the disk.  The  assumed magnitude of D at
25°C  (D25 = 0.8 x  10~5  cm2/s, See Appendix F)  was used with
Equation 27 to calculate  values of D  for the other temperatures,
i.e.,                                                  :

          Dr   =   (D25 V25/298)  x  [(T+273)/VT) ]           ' (27)

where T is the temperature in degrees Celsius.  Solving; Equation
25 for kc yields,

          kc  = k0  kL/(kL - k0) .                          ; (28)

     Equations 26 and 28  were used with the values of D and V
listed in Table 6.6.1 to  calculate the values of kL and kg  listed
in Table 6.6.2.                                        '
Table 6.6.1   EFFECT OF  TEMPERATURE ON THE CALCIUM ION
              DIFFUSIVITY AND  KINEMATIC VISCOSITY
Temperature
°C
5
12
18
25
D x 105
(cm2/s)
0.44
0.55
0.65
0.80
V
1.521
1.238
1.061
0S694
6.7 APPARENT ACTIVATION ENERGY FOR kL AND  kc           ;
     Values of the  apparent activation energy (Ea)  were
determined for kc and kL by plotting the natural log of the
quantities listed in  Table 6.6.2 versus the reciprocal of the
absolute temperature  (see Figure 6.7.1). The slopes of the

                                 65

-------
TABLE  6.6.2   EFFECT OF TEMPERATURE ON THE MASS  TRANSFER
               COEFFICIENT,  kL, AND  THE SURFACE REACTION  CONSTANT,
               kr
      Temperature
           °C
                 kL x 103
                  (cm/s)
kc k 10
 (cm/s)
           5

           12

           18

           25

           25
                   2.63

                   3.17

                   3.65

                   4.26

                   4.26
  0.144

  1:14

  2,02

  8.<17

  8.43
           -4.5
           -5.0
           -5 5
         •D -B.O

          K5

         tf-6.5
           -7.0
           -7.5
           -B.O
                      I
                             I
                                                  I
3.30    3.35    3.40    3.45    3.50

                     1000/T C1/
                                                 3.55
                                                        3. BO
                                                               3. 55
Figure  6.7.1    Arrhenius plot  for  the mass transfer  (kp and
                surface reaction  constants (kL) .         :


straight  lines  fitted to these points are equal to Ea/R where  R.
is the  gas  law  constant, 8.314 J/mol°K.  The correlation
coefficients  (r2)  for  the lines fitted to  points in Figure  6.7.1
                                 66

-------
are greater than 0.98.

     For kc,  Figure 6.7.1 yields Ea  =  101  ±  8  kJ/mol,  a value

that is significantly larger than the  literature values  listed in

Table 6.7.1 for surface reaction controlled kinetics.  For  kL, Ea

= 17 ±0.3 kJ/mol was obtained. This quantity,  as  expected,  is in

good agreement with the values  listed  in  Table  6.7.1  for mass
transfer controlled kinetics.
TABLE 6.7.1
         APPARENT ACTIVATION  ENERGIES  FOR THE LIMESTONE
         Overall dissolution  rate  constant WHEN DISSOLUTION
         IS CONTROLLED BY  a)  SURFACE REACTION AND' b)  MASS
         TRANSFER.                                :
   Predominant
     Mineral
                   Stone
             Characteristics
  Apparent
 Activation
 Energy,  Ea
Reference
 a)   surface reaction control
 b)
     Calcite
     Calcite

     Dolomite
               Iceland spar
              Carrara marble

                 Coarsely
               crystalline
Calcite       Vermont marble

mass transfer control
     Calcite


     Calcite

     Calcite
               Iceland spar
               and Carrara
                  marble

                Limestone

               Iceland spar
46 ± 4 kJ/mol
54 ± 4 kJ/mol

  62 kJ/mol
  63 kJ/mol


  13 kJ/mol



  15 kJ/mol

  41 kJ/mol
   (1)
   (1)

   (2)


   (3)


   (1)


   (4)

   (5)
 (1)  Sjoberg and Rickard  (1984) , Rotating disk experiments
     conducted at constant pH

 (2)  Lund et al.  (1973), Rotating disk experiments with pH free-
     drift                                            i

 (3)  Lund et al.  (1975), Rotating disk experiments with pH free-
     drift                                            !

 (4)  Barton and Vatanatham  (1976)

 (5)  Plummer,  Wigley and Parkhurst  (1978)             i
                                67

-------
                            REFERENCES                i
                                                      !

1.   Letterman, R.D., Driscoll, C.T., Haddad, M., and Hsu, H.A.
     Limestone bed contactors for control of corrosion, at small
     water utilities.  A Report for the Water Engineering
     Research Laboratory, Office of Research and Develbpment-
     USEPA, 1987.                                     :

2.   Letterman, R D., Haddad, M., and Driscoll, C.T.  Limestone
     contactors-steady-state design relationships, J. Env. Enq.,
     ASCE, 117: 339-358, 1991.                        :

3.   Haddad,  M.  Modeling of limestone dissolution in packed bed
     contactors treating dilute acidic water. Ph.D. Dissertation,
     Department of Civil Engineering, Syracuse University, 1986.

4.   Sjoberg,  E.L., and Richard, D. The influence of experimental
     design on the rate of calcite dissolution. Geochemica et
     Cosmochemica Acta. 47:  2281-2285, 1983.         , -

5.   Lund, K., Fogler, H.S., McCune, C.C., and Ault, J,.W.
     Acidization - II. The dissolution of calcite in hydrochloric
     acid. Chem. Eng. Sci. 30:  825-835, 1975.        :

6.   Plummer,  L.N., and Busenberg, E.  The kinetics of:
     dissolution of dolomite in C02-H20 systems at 1.5 to  65°C
     and 0 to 1 ATM PC02.  Amer. Jour, of Sci. 282:  45-78, 1982.

7.   Plummer,  L.N., and Wigley, T.M.  The dissolution pf calcite
     in C02 saturated solutions at 25°C and 1.0 atm. total
     pressure.  Geochemica et Cosmochemica Acta.  40:  191-202,
     1976.

8.   Berner,  R.A., and Morse, J.W.  Dissolution kinetics of
     calcium carbonate in sea water: IV. Theory of calcite
     dissolution. Am. J. Sci.  274:  108-134, 1974.

9.   Chan, P.K., and Rochelle, G.T.  Limestone dissolution:
     Effects  of pH, C02,  and buffers modeled  by mass transfer.
     ACS Symposium Series.  188:  75-97, 1982.

10.  Bjerle,  I., and Rochelle, G.  Limestone dissolution in acid
     lakes.  Vatten.  38:  156-163, 1982.
                                                      i
11.  Plummer,  L.N., Wigley, T.M., and Parkhurst, D.L. ' The
     kinetics of calcite dissolution in C02 water systems at  5°C
     to 60°C and 0.0 to 1.0 Atm.  C02.  Amer.  J. Sci.  278:  179-
     216,  1978.

12.  Wallin M., and Bjerle, I.  A mass transfer model for
     limestone dissolution from a rotating cylinder.  Chem. Enq.

                                68

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     Sci.  44:  61-67, 1989a.                         !

13.  Wallin M., and Bjerle, I.  Rate models for limestone
     dissolution: A comparison.  Geochemica et Cosmochemica Acta.
     53:  1171-1176, 1989b.

14.  Schott,  J., Brantley, S., Crerar, D., Guy, C., Borscik, M.,
     and Williame, C.  Dissolution kinetics of straine;d calcite.
     Geochemica et Cosmochemica Acta.  53:  373-382, 1^989.

15.  Boynton, R.S.  Chemistry and Technology of Lime and
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16.  Murray,  J.A., et al.   J. Am. Ceram. Soc. 37:323-3-28, 1954.

17.  North, F.J.  Limestones: Their Origin, Distribution, and
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18.  Sjoberg, E.L.  A fundamental equation for calcite
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     441-447, 1976.                                   ;

19.  Plummer, L.N., Wigley, T.M., Parkhurst, D.L.  Critical
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     1979.                                            :

20.  Bjerle,  I., and Rochelle, G.  Limestone dissolution from a
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21.  King, C.V., and Liu,  C.L.  The rate of solution of marble in
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22.  Tominaga, H., Azumi,  H., and Isobe, T.  The viscosity effect
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23.  Kaye, C.A.  The effect of solvent motion on limestone
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24.  Weyl, P.K.  The solution kinetics of calcite.  J. Geol.  66:
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25.  Nierode, D.E., and Williams, B.B.  Characteristics of acid
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26.  Sjoberg, E.L., and Rickard, D.  Temperature dependence of
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                                69                     ;

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27.  Sjoberg, E.L., and Rickard, D.  Calcite dissolution
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28.  Sjoberg, E.L., and Richard, D.  The effect of added
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29.  Compton, R.G., and Daly, P.J.  The Dissolution kinetics of
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30.  Holdren, G.R., Jr., and Berner, R.A.  Mechanism of feldspar
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31.  Schott,  J., Berner, R.A., and Sjoberg, E.L.  Mechanism of
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32.  Berner,  R.A.,  and Schott, J.  Mechanism of pyroxene and
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33.  Schnoor, J.L.   Kinetics of chemical weathering: A comparison
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34.  Chou, L., and Wollast, R.   Study of the weathering of
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     reactor.  Geochemica et Cosmochemica Acta  48:  2205-2217,
     1984.

35.  Sverdrup, H.U.  The Kinetics of Base Cation Release due to
     Chemical Weathering.  Lund University Press,  Lund, Sweden.
     1990.

36.  Burton,  W.K.,  Cabrera, N., and Frank, F.C.  The growth of
     crystals and the equilibrium structure of their surfaces.
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37.  Compton, R.G., and Daly, P.J.  The dissolution of Iceland
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38.  Holdren, G.R., Jr., and Speyer P.M.  Reaction rate-surface
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                                70

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39.  Holdren, G.R., Jr., and Speyer, P.M.  Reaction rate-surface
     area relationships during the early stages of weathering:
     II, Data on eight additional feldspars.  Geochemica et
     Cosmochemica Acta.  51:  2311-2318, 1987.

40.  Rauch, H.W., and White, W.B.   Dissolution kinetics of
     carbonate rocks. 1. Effects of lithology on dissolution
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.41.  Palmer, A.N.  Origin and morphology of limestone caves.
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42.  Herman, J.S., and White, W.B.  Dissolution kinetics of
     dolomite:  Effects of lithology and fluid flow velocity.
     Geochemica et Cosmochemica Acta.  49:  2017-2026,, 1985.

43.  Rickard, D., and Sjoberg, E.L.  Mixed kinetic control of
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     1983.

44.  Terjesen, S.G., Erga, 0., Thorsen,  G., and Ve, A.   Phase
     boundary processes as rate determining steps in reactions
     between solids and liquids.  Chem.  Enq. Sci.  14:  248-252,
     1961.                                            ;

45.  Warfvinge, P,. and Sverdrup, H.  Modeling limestone
     dissolution in soils.  Soil Sci. Am. J.  53:  44-51, 1989.

46.  Chu, I., Kaill, J., and Wetteroth,  W.A.  Mass transfer in
     fluidized beds.  Chem. Enq. Prog.  49:  141-149,  1953.

47.  Riddiford, A.C.  The rotating disk system.  In:  P. Delahay
     (ed.), Advances in Electrochemistry and Electrochemical
     Engineering, Electrochemistry.  Vol. 4., 1966. pp.  47-116.

48.  Lund, K., Fogler, H.S., and McCune, C.C.  Chem. Enqr. Sci.
     28:  691, 1976.

49.  Barton, P., and Vatanatham, T.   Kinetics of limestone
     neutralization of acid waters.  Envirn. Sci. and Tech.  10:
     262-266, 1976.

50.  Snoeyink, N., and Jenkins, D.  Water Chemistry.  iJohn Wiley
     and Sons, New York, 1980.                        ;
                                71

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                            Appendix A                :
               MECHANISM OF HETEROGENOUS REACTIONS

     Heterogenous reactions, which include mineral dissolution in
aqueous systems, involve several steps  (Stumm and Morgan, 1981),
    1.   mass transport of dissolved reactants from the; bulk
        solution to the mineral surface,              :
    2.   adsorption of solutes,                        '
    3.   interlattice transfer of reacting species,
    4.   chemical reactions,
    5.   detachment of reactants from the surface, and
    6.   mass transport into the bulk solution.
    The net rate of the heterogenous reaction process is
determined by the combined effects of its separate stages. The
rate of the entire process is governed by the slowest step if one
step> is significantly slower than the others. In cases- where the
slow step involves the introduction or removal of reactants, the
reaction is said to be diffusion controlled and is governed by
the laws of diffusion kinetics. If, on the other hand, the
chemical or physical transformation constitutes the slow step,
the rate of the reaction is determined by the kinetics, of these
processes.
    The overall  rate of reaction can be  characterized as being
either transport controlled, surface chemical reaction: controlled
or a  combination of effects, i.e., mixed-kinetics controlled.

Transport Control/Diffusion Kinetics
    The transport of a solute in a moving liquid is  governed by
two quite different mechanisms,                       ;
    1.   molecular diffusion as a result of concentration
        differences, and,
    2.   transport of entrained solute particles by the moving
        liquid.                                        ;
    The combination of these mechanisms  is called convective

                                72                     ;

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diffusion of solute in a  liquid. A simple  example of qonvective
diffusion is mass transfer  in  a  system where a heterogenous
reaction occurs at the surface of  an  infinite rotating disk.
    When the surface chemical  reaction rate  is  larger  than  the
rate of introduction or removal  of ions  from the reaction
surface, the reaction is  said  to be transport-controlled. All
species approaching the surface  react instantaneously.. The
overall rate of the heterogenous reaction  is determined by the
slower rate of mass transfer.  The  rate of  the transport-
controlled reaction is a  function  of  the bulk solution flow
                                                       i
velocity.                                              ;
    Nernst (1904)  assumed that all heterogenous  reactions were
transport controlled and  their rates  could be described by,
                                                       i
    dC/dt|T = D(A/V) (CS-C)/6N                           ( (1A)

where D is the molecular  diffusion coefficient,  Cs and;C the
concentration at the surface and in the  bulk respectively,  V  the
volume of solution, A is  the surface  area  exposed to the
solution, 5N the thickness of the fluid layer attached to the
surface through which molecular diffusion  is the major, mass
transport process. This is  also called the diffusion boundary
layer (DEL) . For the rotating  disk 8N is given by  (Pleskov  and
Filinovski,  1976) .

    8N = 1. 6D1/3V1/60)-1/2                                   '. (2A)

where v is the kinematic  viscosity and CO the rotational  velocity
of the disk. The transport  rate constant kL is given by
                                                       i
    kL = D/8N = D/(1.6D1/3V1/6CO-1/2)                        \ (3A)

The transport rate is

    dC/dt|T = kLA(Cs-C)/V                                i (4A)
                                73                      !

-------
Surface Chemical Reaction Control
    When chemical transformations constitute the slow step, the
rate of the reaction is controlled by the  kinetics  of these
processes. Since the rate of mass transfer is  large, the
concentration of the entire solution is  constant.     '
    For dissolution reactions the rate of the first order surface
chemical reaction is proportional to the chemical potential
difference between the concentration of  the dissolving  solute at
the solid-liquid interface, Cs,  and the concentration of the
solute in equilibrium with the solid, Ceq,

    dC/dt|c = kcA(Ceq-CJ/V                             ;  (5A)

where k0 is  the rate constant for chemical reaction.

Mixeid Kinetic Control
    When the rates of transfer of the reactants and of:the
chemical reaction are comparable, the reaction  is said  to
controlled by mixed kinetics.
    For steady-state,  the diffusion rate must balance the
chemical reaction rate,                               ':

    dC/dt|T = dC/dt|c                                    (6A)

Solving Equation 6A for Cs and substituting it into either
Equation 4A or Equation 5A yields the general rate  equation,
                                                      i
    dC/dt =  k0(A/V) (Ceq-C)                                (7A)
                                                      I
which reduces to Equation 4A for kL«kc and-to  Equation  5A for
kc«kll. In Equation 7A, k0 is the overall rate constant, given  by,


    k0 =  kLkc/ (kL + kc)                                   (8A)
                                74

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                            Appendix B                 \
                CHEMICAL EQUILIBRIUM CALCULATIONS     :

     In all the equations described below the concentrations of
the species in the  carbonate  system,  including carbon dioxide,
bicarbonate and carbonate,  are given in terms of the total
inorganic carbon  concentration,  CT/ and ionization fractions,
i.e.,

    [H2C03] = CT a0                                     ;  (IB)

    [HC03~] = CT at                                     ;  (2B)

    [C03=] = CT CC2                                         (3B)

where,

    ao  =   l/{l+(K1/[H+]) + (K1K2/[H+]2) }                    ;  (4B)
                                                       I

    Cd  =   l/{l+([H+]/Kx) + (K2/[H+]) }                      I  (5B)

    a2  =   l/{l+([H+]/K2) + ([H+]2/K1K2}                     :  (6B)

    K!  and K2 are  the temperature and  activity corrected values of
the first and second ionization constants for carbonic' acid.
Values of equilibrium constants at  25°C were taken from Snoeyink
and Jenkins (1980)  (see  Table IB).  The Davies equation: was used
to calculate activity coefficients  for correcting the 
-------
    TABLE IB   VALUES OF  EQUILIBRIUM CONSTANTS AT  25 °C  AND 1=0

 First ionization  constant for carbonic acid,  Kx    ig-s.ss
 Second ionization constant for carbonic  acid,  K2   ]_o"10-33
 Ion Product of  water,  Kw                           10~14
 Henry's Law constant,  KH                           10~1-47

TABLE 2B    EQUATIONS USED TO CORRECT EQUILIBRIUM CONSTANTS FOR
            ACTIVITY                                    |

 Activity coefficients  were calculated using the Davis  equation,
 i.e.,
  log(fi)   = -0.5z2{ [IV (H-I*) ]-0.2I}
 where,
        z  - charge of the  ion                          '.
        I  - ionic strength  in moles/L
       fx  - activity coefficient  for  charge of +/- one
       f2  - activity coefficient  for  charge of +/- two,
 The activity corrected equilibrium constants  given by:
       Kx  = ^/(fj2                                    ;
       K2  = K2/(f2)                                     I
      Ksp  = Ksp/(f2)2
__ Kw  = Kw/(f1)2 _ j

remain constant .  The equilibrium pH and calcium ion concentration
can be determined with the following equations,        !
        acidity  = CT (oc^oj + [H+] -Kw/ [H+]                 (7B)

         (alkalinity - Ca)  = CT (ax+2a2) +KW/ [H+] - [H+] -2 [Ca]  (8B)

         [Ca]  = Ksp/(a2CT)                                 (9B)

where CT is in moles per liter and Kw is  the ion product of

                                 76                     i

-------
water. Ksp  is  the  solubility product for CaC03.
        For known amounts  of initial  acidity,  initial alkalinity
and initial calcium ion concentrations,  Equations 7B, 8B and 9B
are solved simultaneously  to calculate  the equilibrium pH.
Equation 9B gives the equilibrium  calcium concentration.

Intermediate  Calcium Ion Concentration                 ;
        For dilute acidic  water with  dissolving CaC03 the charge
balance relationship is,

        (2S + alk0)  = (CTO+S) (a1+2a2)+Kw/[H+]-[H+]         (10B)

where S is the molar concentration of calcium  carbonate
dissolved,  CTo is  the initial concentration of  the dissolved
inorganic carbon  (DIG) . Equation 10B  is  based  on the assumption
that the dissolution of 1  eq/L of  calcium carbonate increases the
alkalinity by 1 eq/L and increases the  dissolved inorganic  carbon
concentration by  1 mole/L.                             ':
        Equation  10B is solved for S  for a given pH by
substituting  known values  of initial  alkalinity and DIG.

Open-to-Atmosphere Equilibrium pH  and Calcium  Concentration
        The following equations are used to calculate the
equilibrium pH and equilibrium calcium  concentration when calcium
carbonate dissolves in a solution  that  is in equilibrium with
atmospheric carbon dioxide.
        2[Ca] + Cc + [H+]  =  KHPco2 (Oi + 202) /OCo + Kw/ [H+] + Ca

        [Ca] = Kspa0/ (a2KHPc02)                          !  (12B)
                                                      i

Cc and Ca are the  influent concentrations  in equivalents per
liter of cations excluding  hydrogen, and  anions  excluding
inorganic carbon species  and hydroxide, respectively. KH is the
Henry's Law constant in mols/L  atm and Pco  is the partial

                                77                    ;

-------
pressure of carbon dioxide in atmospheres. Equation 11B and
Equation 12B are solved numerically for the equilibrium calcium
ion concentration and the pH using known values of Ksp.
                                78

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                           Appendix  C
                      METHYL  RED  EXPERIMENTS

    A series  of experiments was performed using methyl red dye to
check if the solution in the reaction vessel was well-mixed and
if the response time of the pH electrode had an adverse affect on
the recorded results. The dye was prepared by dissolving 1 g of
the sodium salt of methyl red in 1 L of DI water. A 1 mL quantity
of this solution was added to 600 mL of experimental solution in
the reaction vessel. Methyl red is red at low pH (pH<4) and
becomes yellow as the pH is increased above approximately 7.
    A Brinkman dipping probe  colorimeter (Model PC800)  equipped
with a red (545 nanometer wavelength) filter was used to measure
the absorbance of the solution in the reactor. The colorimeter
probe tip was positioned in the vessel in the same position as
the bulb of the pH electrode but on the opposite side of the
rotating disk. During each run the absorbance readings were
recorded on a high speed, strip chart recorder while the pH
readings were logged on a personal computer.          ;
    A calibration curve of normalized absorbance versus pH was
first prepared by stepwise titrating the experimental solution
(initial pH=4 and ionic strength of 0.079M) with 0.0IN KOH. The
experimental solution was stirred using a magnetic stirrer.
Approximately 0.2 mL of base was added each step. The pH and
absorbance were recorded after each increment of base had been
added and the readings had stabilized.
    A second  calibration curve was prepared using the above
procedure. However, the solution was stirred by the rotating disk
operating at 400 rpm. The disk was covered with plastic wrap so
that the limestone was not in contact with the solution. A 1 mL
volume of dye was rapidly injected into the stirred solution. The
absorbance reading stabilized almost instantaneously  (< 1 s)
indicating that the solution was well mixed. The solution was
then titrated with 0.01 N KOH, as described above, and the pH and
absorbance recorded.
                               79                    :

-------
    Two free drift experiments, using initial pH values of 4 arid
5, were conducted with disks of WM stone dissolving  in  the
solution and with methyl red dye present. The pH valuers recorded
with time were used with the pH versus absorbance  calibration
curve  (described above) to prepare a plot of absorbance versus
time. This was compared with the absorbance versus time curve
measured during the experiment. The curves obtained  with  slow
stepwise titration with strong base and the curves obtained  with
dissolving stone are in good agreement  (see Figure 1C). This
indicates that the response time of the pH electrode i's not  a
significant factor in the free drift experiments.
         n:
         Q.
            0.0
A

B

•;
- — (:#•- •
n
                   0,2
                           0.4
                                  0.5
                               ABS/ABSo
                                         O.B
                                                 1.0
                                                        1.2
Figure 1C   pH versus normalized absorbance for methyl1 red
            titration in the rotating disk apparatus used to  test
            the rate of response of the pH measuring system.
            Curve A and B are for base addition by  reagent
            dispenser with mixing by magnetic stirrer  and inert
            rotating disk.  Curve C and D are for calcium
            carbonate dissolution from the WM stone with an
            initial acidity of 0.1 meq/L and 0.01 meq/L
             respectively.
                                80

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                            Appendix D
                  EQUILIBRIUM MODEL CALIBRATION       '

    The pH values measured during a rotating disk experiment were
substituted in the charge balance equation  (Equation 10B,
Appendix B) to calculate corresponding values of the theoretical
amount of calcium dissolved. In Figure ID, pH is plotted as a
function of calcium ion concentration calculated for different
amounts of initial dissolved inorganic carbon concentration  (DIG)
and calcium ion concentration measured by the AAS. For
experiments with 0.01 meq/L of initial acidity, good agreement
was obtained by solving the charge balance equation with some
amount of initial DIG. In all such experiments the solution seems
to be in equilibrium with atmospheric C02.  The experimental
solution was boiled to remove C02 but the solution  could have
dissolved C02  when it  was  being transferred to the  reactor. The.
bubbling of the solution by nitrogen before beginning the
experiment could have also dissolved some carbon dioxide. Once
the experiment was started no further exchange of C02  took  place.
This is evident from the good agreement obtained between the
measured calcium and calcium concentrations calculated by solving
the charge balance equation. The charge balance equation is
written for a closed system with no exchange of atmospheric C02.
For the experiments with 0.1 meq/L of initial acidity, the
mineral acidity is much greater than the carbon dioxide acidity,
therefore, DIG is still present but it has a minimal effect on
the calculated calcium ion concentrations.
    The calcium measurements by the AAS  were verified  by
measuring the alkalinity in some experiments. Figure 2D, in which
the alkalinity calculated from calcium measurements is, plotted
against the measured alkalinity, shows that the calcium dissolved
contributed to all the acid neutralizing capacity meas.ured in the
experimental solution.
                                81

-------
          u
          w
                              Data points are measured pH vs Ca
                        Assumed Initial DIG concentration
                           CTC=D
CTC=1.72E-5
  — — —— g
                                           CTC=1.28E-5
             0.0      D.5      1.0      1.5      2.0      2.5
                       Calcium concentration  Cmg  Ca/l_}
                             3.0
Figure  ID    Measured pH versus measured calcium concentrations
             for the SL stone,  w = 600 rpm and initial acidity =
             0.01 meq/L.  The  three theoretical curves were
             determined using  the measured pH,  the equilibrium
             model discussed in Appendix B and several assumed
             values of the  initial dissolved  inorganic carbon
             concentrations  (CTC)  in the rotating disk reactor
             solution.
                                 82

-------
         SOD
      '- 300
      CO
      .V

      CCS  200
         100
                                I
                                                   I
                     1OO       20O
                      Measured  a
       300
ka I I n I ty
                                                  400
                                                            soo
Figure 2D   Alkalinity calculated from the measured calcium
            concentrations plotted against the measured
            alkalinity.  All experimental points are close to  1:1
            line indicating that essentially all the calcium is
            derived from the dissolution of calcium carbonate.
                                83

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                           Appendix  E
                 SOLUBILITY PRODUCT DETERMINATION

    The  solubility product of the calcium carbonate in the WM,
SL, A,  C, F and I stone samples was determined by equilibrating
samples of the stone with quantities of acidified solution in
open beakers.  Samples of stone were broken into coarse granules
(approximately 0.5 cm in diameter) using a mortar and pestle. The
granules were rinsed with DI water and air dried. The surface
area of the granules was approximately 14 cm2.         ;
    Four solutions were used  in the  experiment.  Two solutions had
mineral acidities of 0.01 and two had acidities of 0,10 meq/L.
The background electrolyte was 0.079 M KC1. The solutions were
stirred with a magnetic stirrer under an open-to-the-a'tmosphere
condition. The temperature was 25 ± 1°C.              ,
    The  calcium concentration and pH were measured with time as
shown in Figures IE to 4E. The temperature was recorded each time
samples were collected for pH and calcium measurement.; The volume
of the samples used to determine the calcium concentration was
1.5 mL.  Each sample was centrifuged for 15 minutes at 15,000xg
and then 1 mL of centrifugate was withdrawn with an automatic
pipette. The calcium ion concentration was determined :by AAS.
    At  about 600 hours  of stirring the  pH had been essentially
constant for approximately 50 hours. At this point several
samples were taken for measuring the alkalinity. The alkalinity
was determined using 75 mL of solution made by diluting 2 mL of
centrifugate to 100 mL with distilled water.
    The  measured pH and alkalinity were used to calculate the
carbonate ion concentration with the expression,      i

    [C03=] = {0.833[alk+[H+]-KH/[H+] }/{l+(2K2/[H+]) }       :  (IE)

where alk is the alkalinity in equivalents per liter and K2 is
the second ionization constant of carbonic acid. The .molar

                                84

-------
      ti
       CD
       8
       E
a
         •40
         35
   25
      —  2D
         15
              &
                   S-to ne samp I e C I n 111 a I  ac I d I ty.,  meq/
                       WMCP.'O WM eg,. 013 SL CO.i:iSL CA-0
                       200
                                    400
                                                EDO
                                                             BOO
                              T I me
Figure IE   Variation  of  calcium concentration with time in open
            batch reactor.   Used to determine the apparent
            solubility product of calcium carbonate in the SL and
            WM stone samples.

concentrations of calcium and carbonate ion were then used in the
following equation to  determine the solubility product,
    Ksp = Y++Y=[Ca++] [C03-]
                                                  (2E)
where y++  and y_, the activity  coefficients for the calcium and
carbonate ions, were calculated using the Debye-Htickel; equation
and I = 0.079.  Representative  results (pKsp versus time,)  are
plotted in Figure  5E.  The last 10 or so pKsp values were  averaged
for the samples analyzed and the results are listed in Table
5.2.1.                                                 ;
    The charge balance equation  for  a system open-to-atmospheric
carbon dioxide  was used  with the solubility product equation to
                                 85

-------
          S.B
          8,6
        X
        P- 8.4
          8.2
                                                    '**
                     Stone sample C initial acidity,  meq/LO
                        WM CO. 13 WM CO.013 SL C0.1:-SL CD.013
                        200          400
                               Time C hours}
                                                BOO
                                                            800
Figure 2E   pH versus time results  for the experiments of  Figure
            IE.

check the values of Ksp determined using Equation 2E .  The
expressions used are,                                  ;
2[Ca+]
= (KHPCo2/a0)
Kw/
                                                          (3E)
and
    [Ca*]  = Ksp{a0/(a2
                   (4E)
where KH is Henry's  law constant and Pco is the  atmospheric
partial pressure of carbon dioxide,  a0,  air and  a2 are the
ionization fractions for the  carbonate system (see Appendix C)
and  [Cl~]   is the  strong acid anion concentration. The ion product
 (Kw)  of water and the  ionization constants for carbonic acid used
                                 86

-------
         30
      r\
      •M
      c
      0)
      y
      8
         25
       c
       O 20
         10
       o
                 4 «
                       Sample I Sample F Sample
                          s\    —k4—   --
-------
                          Stone I Stone F Stone (', Stone A
                                         I
                                             J_
                                   _L
                                                        I
                                                             I
50    100   150
                             2DD  250  300  350

                               Time Chours;}
                                   400   450   500   550
Figure  4E   pH measurements  from the  experiments  used ,to
             determine Ksp  for stone samples A, C,  F and I.
                                   88

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         11
         10
      a

      ^2
      a
                                        i
                                              i
                                                    i
                                                         _1_
           50    100    150   200   250    300    350   400   450    500


                               Time Chours}
Figure 5E    Values of pKsp  calculated using the  calcium

             concentration and pH values in Figures  3E and 4E.
                                 89

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                            Appendix F                 '
                     CALCIUM  ION  DIFFUSIVITY          ;

    A set of rotating disk experiments was used  to  determine the
calcium ion diffusivity  at  25°C.  Rearranging Equation >8A in
Appendix A and substituting Equation 3A for  kL yields,

        l/k0 =  1.61V1/6D-2/3c«r1/2  +  l/k0.                   : (IF)

    According to Equation IF,  if  l/k0 is plotted as a function of
Qj-i/2 the  slope,  S,  of the straight line fitted to these points is
equal to 1.61v1/6D"2/3 and  the intercept,  I, is equal to ;l/kc. The
magnitude of D and  kc can, therefore, be  determined using,

        D = 2.04 V1/4 S~3/2                                (2F)
and
        kc = I'1                                        : (3F)

    Experiments were performed  at 25°C using the WM stone and
initial acidities of 0.1  and  0.01 meq/L.  The rotational speed was
varied from 400 to  1200  rpm.  A  systematic increase in k0  with
increasing rotational  speed is  shown in Figures IF and 2F for
constant experimental  conditions.
     Values of l/k0  from Figures  IF  and 2F are plotted as a
function of Ctr1/2 in Figures 3F and 4F, respectively.  The  values
of  D and kc obtained from the slopes  and  intercepts in Figures  3F
and 4F are listed in Table  IF.  The  magnitude of D is 0.93 x 10"5
cm2/s for an initial acidity  of 0.1  meq/L and 0.50  x  10~5 cm2/s
for an initial acidity of 0.01  meq/L. While  these values differ
by  a factor of approximately  2,  this difference is not
statistically  significant at  a  95%  confidence level.
                                 90

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          -10  -
        o
        w

        td
        ^.
-15  -
                   220 rpm 400 rpm BOO rpir.  BOO rpm  1000 rpm 1200 rpm

                    —0—   —X—   --<:>•-•   —X—    —X—    —X—
          -20  -
          -25  -
          -3D
            0.0
                                                                 1.6
Figure  IF   Effect  of disk rotational speed on plots  of ln{(Ceq

             -C)/Ceq}V/A versus  time; WM  stone sample  and initial

             acidity of 0.1 meq/L.
                                   91

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        id
        ^
                                   B00,rpm 1DDD rpm  120Drpm
          -10 -
          -12 -
          -14 -
          -1B
            0.0
                  0.2
                                                                1.15
Figure  2F    Effect of disk  rotational speed  on plots of

            ln{(Ceq-C)/Ceq}V/A versus time; WM stone sample and

            initial acidity  of 0.01 meq/L.
                                  92

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           500
                                                              0.20
Figure 3F    Inverse  of the overall dissolution rate  constant
             versus C0"1/2; WM stone  and  initial acidity = 0.1
             meq/L.
                                 93

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           BOO
             0.00
                          0.05
                                      0.10
                                                   0.15
                                                               O.EiO
Figure 4F    Inverse of the  overall dissolution  rate constant
             versus co"1/2/  WM stone and  initial acidity =0.01
             meq/L.
                                  94

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TABLE IF   CALCIUM ION DIFFUSIVITY,  D, AND  kc FOR THE WM SAMPLE
           AND 25°C.                                  ;


    Initial Acidity            D x 10s               kc x 103
        (meg/L)	(cm2/sec)	(cm/sec)	

         0.10                  0.93                  1.38

         0.01                  0.50                  0.02
     The values of D from this  study are in general agreement

with those from the literature  (see  Table 2F).  The values of D

listed in Table 2F were  averaged and this quantity (D = 0.8 x

10~5 cm2/s at 25°C) was used in  the analysis of  results.


            TABLE 2F.   CALCIUM  ION DIFFUSIVITY AT  25 °C
           Reference             Ionic    Calcium ion diffusivity
                                Strength       x 105 at 25°C
          	(cm2/s)	

 This study                      0.079              0.50
                                                    0.93

 Sjoberg and Richard  (1984a)      0.7               0.84
                                  0.7               0.8.5
                                  0.7               0.74
                                  0.1               0.79

 Wallin and Bjerle  (1989)         0.1               0.79

 Hodes  (1972)                     0.05              0.85
                                  0.5               0.75
                                 95

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