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
-------
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.
-------
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
-------
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
-------
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 :
-------
VI
-------
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
-------
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
-------
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 ;
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
quantities of water and long operational periods to obtain
meaningful results.
-------
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 :
-------
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
-------
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. ;
-------
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. :
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
Limestone. Second Edition. John Wiley and Sons,1 1980.
16. Murray, J.A., et al. J. Am. Ceram. Soc. 37:323-3-28, 1954.
17. North, F.J. Limestones: Their Origin, Distribution, and
Uses. Thomas Murby & Co., London, 1930.
18. Sjoberg, E.L. A fundamental equation for calcite
dissolution kinetics. Geochemica et Cosmochemica Acta. 40:
441-447, 1976. ;
19. Plummer, L.N., Wigley, T.M., Parkhurst, D.L. Critical
review of the kinetics of calcite dissolution and
precipitation. Amer. Chem. Soc. Symp. Ser. 93: 537-S73/
1979. :
20. Bjerle, I., and Rochelle, G. Limestone dissolution from a
plane surface. Chem. Enq. Sci. 39: 183-185, 1984.
21. King, C.V., and Liu, C.L. The rate of solution of marble in
dilute acids. J. Amer. Chem. Soc. 55: 1928-1940|, 1933.
22. Tominaga, H., Azumi, H., and Isobe, T. The viscosity effect
on the rate of solution of calcium carbonate in hydrochloric
acid. Chem. Soc. of Japan. 14: 248-252, 1939. ;
23. Kaye, C.A. The effect of solvent motion on limestone
solution. J. Geol. 65: 34-36, 1957. [
24. Weyl, P.K. The solution kinetics of calcite. J. Geol. 66:
163-176, 1958.
25. Nierode, D.E., and Williams, B.B. Characteristics of acid
reaction in limestone formation. Soc. Petrol. Jour. Trans.
251: 406-418, 1971. :
26. Sjoberg, E.L., and Rickard, D. Temperature dependence of
calcite dissolution kinetics between 1 and 62PC at pH 2.7 to
8.4 in aqueous solutions. Geochemica et Cosmochemica Acta.
48: 485-493, 1984a. ' i
69 ;
-------
27. Sjoberg, E.L., and Rickard, D. Calcite dissolution
kinetics: Surface speciation and the origin of variable p.H
dependence. Chem. Geol. 42: 119-136, 1984b. '
28. Sjoberg, E.L., and Richard, D. The effect of added
dissolved calcium on calcite dissolution kinetics in aqueous
solutions at 25°C. Chem. Geol. 49: 405-413, 1985.
29. Compton, R.G., and Daly, P.J. The Dissolution kinetics of
Iceland spar single crystals. J. Colloid Interface Sci.
101: 159-166, 1984.
30. Holdren, G.R., Jr., and Berner, R.A. Mechanism of feldspar
weathering: I. Experimental studies. Geochemica et
Cosmochemica Acta. 43: 1161-1171, 1979. :
31. Schott, J., Berner, R.A., and Sjoberg, E.L. Mechanism of
pyroxene and amphibole weathering: I. Experimental studies
of iron-free minerals. Geochemica et Cosmochemida Acta.
45: 2123-2135, 1981.
32. Berner, R.A., and Schott, J. Mechanism of pyroxene and
amphibole weathering: II. Observations of soil grains..
Amer. J. Sci. 282: 1214-1231, 1982. ;
33. Schnoor, J.L. Kinetics of chemical weathering: A comparison
of laboratory and field weathering rates. In; Aquatic
Chemical Kinetics: Reaction Rates of Processes in Natural
Waters. John Wiley and Sons, New York. 1989. pp. 475-503.
34. Chou, L., and Wollast, R. Study of the weathering of
albite at room temperature and pressure with a fluidized bed
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.
Royal Soc. London Philos. Trans. A-265: 299-358,, 1951.
37. Compton, R.G., and Daly, P.J. The dissolution of Iceland
spar crystals: The effect of surface morphology. • J. Colloid
Interface Sci. 113: 12-20, 1986. ' :
38. Holdren, G.R., Jr., and Speyer P.M. Reaction rate-surface
area relationships during the early stages of weathering: I.
Initial observations. Geochemica et Cosmochemicai Acta. 49:
675-681, 1985.
70
-------
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
rate. Water Resour. Res. 13: 381-394, 1977. ;
.41. Palmer, A.N. Origin and morphology of limestone caves.
Geol. Soc. of Amer. Bull. 103: 1-25, 1991.
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
calcite dissolution rates. Amer. J. Sci. 283: '815-830,
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
-------
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 ;
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
-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
-------
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
-------
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
-------
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
-------
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
------- |