DEVELOPING A KINETIC LEACHING MODEL FOR
SOLIDIFIED/STABILIZED HAZARDOUS WASTES
KUANG YE CHENG
PAUL L. BISHOP
Department of Civil and Environmental Engineering
University of Cincinnati
INTRODUCTION
Chemical stabilization/solidification is common practice in the
disposal of radioactive waste. In recent years this method has been
applied to treatment of hazardous materials.
Several generic treatment systems have been used. The pozzolan- or
Portland cement-based treatment systems show potentially useful
application for wastes containing heavy metals. The mixing of
pozzolanic-based binders with wastes converts heavy metals in the
waste to insoluble hydroxides and silicates which are entrapped
within the solid paste. It also is believed that some metals may
be physically bound to the paste lattice. Permeability coefficients
of the solidified waste .matrices have been comparable to those of
clay, ranging from 10~5 to 10~7 cm/sec .
The potential impact on the environment of solid wastes disposed
on land is most frequently assessed and predicted using bench scale
laboratory leaching tests. In order to do this effectively,
predictive mathematical models must be used.
Short term leachability studies of solidified low-level radioactive
wastes2 and solidified hazardous wastes show diffusion to be the
dominant factor governing leaching rate. A semi-infinite medium
diffusion model with uniform initial concentration and zero surface
concentration~; can be used to interpret the kinetic data generated
from seriai?;batch leaching tests2. The equatidn takes the form
(1)
w
where an = contaminant loss during leaching period n (mg)
A = initial amount of contaminant present in the
specimen (mg)
V = volume of specimen (cm )
S = surface area of specimen (cm )
tn = time to end of leaching period n (sec)
-------
De — effective diffusion coefficient (cm2/sec)
Leachate generation is an extremely complex process. The free
alkalinity present in the pozzolanic-based paste maintains a hicjh
pH environment and limits the metal leachability of fixed wastes .
Calcium hydroxide, which is produced by the hydration reactions of
binder, provides most of the buffering capacity. The leaching
model shown above, however, does not include the factor of acid
strength of the leachant and cannot describe the distance of
leaching front into the waste solid.
This paper shows the relationship of the hydrogen ion in the
leachant, the distance of leaching front, and the alkalinity
leached from the solid matrix. Using these results, kinetic
leaching models are developed.
METHOD AND MATERIAL
Six binder combinations were prepared by mixing three different
pozzolanic-based binders at two different water/binder ratios
according to ANSI/ASTM Standards. Samples were cast as 23.5mm
diameter by 25.6mm height cylinders. Sample types are summarized
on the table below. In the rest of discussion, samples will be
referred as the sample numbers shown on the table.
Binder
Type
Cement Kiln
Dust
50% Lime, Type N*
50% Fly Ash?J Type F
«",&=,„..
*t
Type I Portland
Cement
Water/Binder
Ratio
0.50
0.65
0.35
0.50
* .
0.33
0.45
Leachant
Strength
(meq/g)
15
5
15
5
15
5
15
5
15
5
15
5
Sample
Number
KD50-15
KD50-5
KD65-15
KD65-5
LF35-15
LF35-5
LF50-15
LF50-5
PC33-15
PC33-5
PC45-15
PC45-5
Dolomitic hydrated lime.
Dynamic leaching test procedures were followed. A 20 to 1 leachant/
2
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solid ratio was used. Five specimens of each binder combination
were leached at each of two different strengths of acetic acid
solution, 5 and 15 milliequivalents per gram of dry sample. The
leachants were renewed at 25, 45, 70, 91, and 117 hrs for the
cement kiln dust and lime - fly ash samples; 26, 104, 340, 531, and
681 hrs for the portland cement samples. Calcium hardness titration
and pH measurement were determined for each contacted solution.
Physical measurements included the dimensions and the wet and dry
weights of each sample before leaching as well as after contact
with leachant. One sample was removed.for physical measurement at
each renew schedule. During each contact, an outer layer of friable
leached product with distinct texture/color difference was observed
on each specimen. The kernel, which is the unfriable part of
specimen, was obtained by physically scrubbing; off the friable
outer layer. Physical measurements include weighing before and
after drying and measuring the dimensions of the oven dried kernel
with a micrometer gauge.
RESULTS AND DISCUSSION
Acid attacks pozzolanic-based paste through permeation of pore
structure and dissolution of ions that must diffuse back through
a chemically altered layer to enter solution. Acid consumes most
of the calcium hydroxide in the leached layer and leaves a highly
porous structure. Diffusion across this layer can be considered as
a steady-state process. At the leaching front, diffusion of
hydrogen ions proceeds as if the medium is infinite and dissolution
reactions occur simultaneously in the pores. Proton transfer
reactions are usually very fast with half-lives less than milli-
seconds5. Hence, the dissolution reactions can be treated as
diffusion-controlled fast reactions. The whole process then can be
described as steady-state diffusion across the leached layer and
unsteady-state diffusion controlled fast reactions in the porous
leaching front.
Figures 1 through 3 show the cumulative amount of calcium hardness
leached from solidified/stabilized samples plotted versus the
square root of time for cement kiln dust, lime - fly ash, and
Portland cement binder systems, respectively. Figures 4 through 6
show the penetration distance of the leaching front versus the
square roofe; of time for the same samples.
Two acetic acid strengths were used as the leachants - 5 and 15 meq
acetic acid per gram of solids leached. Figures 1 through 3 show
that the 15 meq/g leachant leached considerably more hardness than
the 5 meq/g leachant. The figures also show that the lower
water/binder ratio samples leached less in a given acid strength
leachant than ones with a higher water/binder ratio. These results
are as expected. Figures 4 through 6 show that the distance of
penetration of the leaching front is highly dependent on the
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leachant acid strength. The leachant with 15 meq acidity/g solids
advanced into the solids • much more rapidly than did the weaker
leachant. Water/binder ratio had little or no effect on penetration
distance or rate of penetration. This indicates that acid
penetrating into the solids and metal leaching from the solids are
controlled by different mechanisms.
Figure 7 shows predicted ratios based on least square regression
of calcium hardness leached at 5 meq/g and 15 meq/g based, and
figure 8 ratios of penetration distance at the two acid strengths
for each time interval. Figure 7 shows that the 15 meq/g leachant
consistently leaches approximately 1.65 times as much hardness as
the 5 meq/g leachant, for all binders and at all water/binder
ratio. Figure 8 indicates that the penetration distance for the 15
meq/g leachant is approximately 2.0 times that for the weaker
leachant.
At this moment a numerical solution to the problem of combined acid
penetration and resultant metal leaching seems premature.
Appropriate assumptions need be made to approach the answer. For
gas-solid systems, a steady state diffusion across the product
layer with chemical reactions at the boundary is often assumed. The
pseudo-steady state assumption, however, is only valid in gas-
solid systems when the gas density is about thousandth of the
solid density. For liquid-solid systems this assumption may be in
error6.
When non-porous solid dissolves in acid, the dissolution can be
idealized as three sequential steps. In the first step, acid and
other reagents diffuse to the surface; in the second, they react
with the surface; in the third, the dissolved solid diffuses away
from the surface. The overall dissolution rate depends on the sum
of the resistances of diffusion and of reaction. However, the
pozzolanic-based paste is a porous material and the dissolution is
more complicated than that of non-porous solids because diffusion
and reactions occur simultaneously within the whole leaching zone .
It is. the authors' opinion that the phenomenon can be simplified
as "unsteady diffusion with fast chemical reactions" at the early
stage of leaching when the friable layer is fairly thin. Further
work should, be done to find the limitations. Following is a
discussion ."of. the model.
'• • ,*
Unsteady—State Diffusion
The solution of the problem of diffusion from a solid, the surface
concentration of which is maintained constant, into a semi-
infinite medium, having zero initial concentration, involves only
the single dimensionless parameter
z
-------
where z is the penetration distance.
It follows from this that
1. the distance of penetration of any .given concentration
is proportional to the square root of time;
2. the amount of diffusing substance entering the medium
through unit area of its surface varies as the square
root of time8.
The concentration of diffusing substance C(z,t) and the diffusing
flux J(z,t) are given by
C(z,t) = C0 [1 - erf (z/74Det) ] (2)
J(z,t) = C0 (yDg/TTt) exp(-z2/4Det) (3)
where erf is the error function and C0 the initial bulk
concentration of the diffusing substance.
Ionization of Weak Acid
The free hydrogen ions available in the leachant^may be the most,
important factor governing leaching rate because H* has a diffusion
coefficient which is approximately one order of magnitude higher
than the other species. Acetic acid is considered a weak acid and
is not completely ionized in dilute solutions. The ionization
reaction of acetic acid can be illustrated as
HAc ^ H+ + Ac"
[H+] [Ac"]/[HAc] » KA = 1.75 x 10"5 ' at 25°C
where Ac" is used to designate the acetate ion and HAc the acetie
acid. K. is the ionization constant. If Cp is the initial molar
concentration of acetic acid in the solution and x is the molar
concentration of the acetic acid ionized to form H* and Ac" ions,
then
^:... ; [HAc] = (C0 - x) mole/1
"Tife- ' [H*] = [Ac"] = x mole/1
'*r- -V K. = [H*] [AC"]/[HAC] = (X) (x)/(CQ-X)
ir n 9
At room temperature, the value of x is very small compared to the
value of C and the ionization constant KA can be approximated as
KA « (x) (x)/(C0)
X « /(KA) (C0) . (4)
Equation 4 shows that the hydrogen ion concentration is
• • 5
-------
proportional to the square root of initial acetic acid
concentration. For the two acetic acid strengths used in this
research, 15 meq/g and__5_meq/g, the ratio of hydrogen ion
concentration becomes /(15/5), which is approximately 1.73. This
suggests that the concentration of free hydrogen ions in the
aqueous solution controls the penetration of the reaction front and
can be considered an independent variable for the leaching
mechanism9. Figure 7 shows that the amount of calcium leached in
the 15 meq/g leachant was 1.7 times greater than in the 5 meq/g
leachant. This is in complete agreement with the above discussion.
Based on the experiment results presented earlier, the distance of
penetration and the accumulative hardness leached do follow linear
relationships versus square root of time. Penetration distance is
obtained from averaging original dimension and height minus kernel
dimension and height. The penetration distance vs. square root of
time can be interpreted as representing the free hydrogen ions
diffusing into the solid matrix, and the accumulative hardness vs.
square root of time as the dissolved metal ions diffusing out of
the solid matrix.
Acid Neutralization Capacity
.Acid neutralization capacity (ANC) is determined by conducting
separate extractions of several predried, crushed, waste samples
with leaching solutions of varying levels of acidity . ANC can be
defined as the amount of acidity neutralized by a given quantity
of sample to a certain pH range with the unit mole/mass, and can
be obtained by running the ANC test . It has been used to determine
the buffering capacity of the stabilized/ solidified waste form.
For cement-based wastes, the ANC is generally about 15 meq/g to
bring the pH down from 12.5 to 912.
Simplified Mathematical Model
A mathematical equation can be derived to describe the penetration
distance r by combining equation 3 and the concept of acid
neutralization capacity. To do this, we first write a mass balance
on a thin liayer AZ, located at some arbitrary position z within the
semi-infinite medium with .constant cross section area A. The mass
balance of hydrogen ions in this layer is
Hydrogen ion = H* diffusion in + amount produced
accumulation minus that out by chemical reactions
In mathematical terms, this is
(AAZCH)/ t = A(J|Z - J|^2) -«- r^z • (5)
-------
where C, denotes the concentration of hydrogen ions, J| and JJ^
the f lux of hydrogen ions at z and z+Az, respectively. The net rate
of hydrogen ions produced per volume, r., can be explaxned as the
hvdroaen ions produced by ionization of weak acid minus the
^i^^^^^:^^
clplcit? chSged, ->ef o, z = o, q, = ca
z - «, q, * o
the solution is
CjCz/t) - C0 [1 - erf(z7(l+eK)/y4Det)] (9)
J(Zft) - Ca [/De(l+eK)/Tt] exp[-z2{l+eK)/4D,t] (10)
The concentration of hydrogen ions at any give distance and given
7 . .
-------
time can be obtained by solving equation 9. The pH profile along
the penetration distance Can then be established.
SUMMARY
It is concluded that the leaching mechanisms in the pozzolanic-
based solid matrix are controlled by the free hydrogen ions
available in the leachant. Alkalinity leached is the consequence
of the penetration of hydrogen ions. Hydrogen ions diffuse into the
solid matrix and neutralize the alkalinity provided by the binder
in the leach front. pH decreases after the acid neutralization
capacity is consumed. The metals precipitated previously in high
pH environment are dissolved again and diffuse outward into the
leachant. A friable, silica-rich leached layer has been formed and
moves deeper into the solid matrix with time. At early stages of
leaching, an "unsteady diffusion with fast chemical reaction" model
can be used to predict the acid penetration in the pozzolanic-
based paste.
ACKNOWLEDGEMENTS
The authors would like to thank Steve Liatti who did the
experimental work. Also, thanks to Jerry Isenberg who designed the
experiments and provided valuable opinions during the course of the
research. The paper described herein was in partial fulfillment of
Work Assignment #2-7, Contract No. 68-03-3379 to the University of
Cincinnati, Department of Civil and Environmental Engineering. The
work was done under the sponsorship of the Waste Minimization,
Destruction and Disposal Research Division of the U.S. EPA Risk
Reduction Engineering Laboratory, Cincinnati, Ohio.
-------
REFERENCES
1. Van der Sloot, H.A. and Wijstra, J., "Short and Long Term
Effects in the Leaching of Trace Elements from Stabilized Waste
Products", 5th International Ocean Disposal Symposium, Corvallis,
Oregon, 1984.
2. Godbee, H.W. , D.S. Joy, "Assessment of the Loss of Radioactive
Isotopes from Waste Solids to the Environment. Part I: Background
and Theory.", Oak Ridge National Laboratory, ORNL-TM-4333, 1974.
3. Bishop, P., "Prediction of Heavy Metal Leaching Rates from
Stabilized/Solidified Hazardous Wastes.", 18th Mid-Atlantic
Industrial Waste Conference, Blacksburg, Virginia, 1986.
4. Shively, W., "The Chemistry and Binding Mechanisms Involved
with Leaching Tests of Heavy Metals Solidified and Stabilized with
Portland Cement.", Master thesis, U. of New Hampshire, 1984.
5. • Stumm, W. and J. Morgan, "Aquatic Chemistry", 2nd.ed., Wiley-
Interscience, New York, N.Y., 1981,
6. Bischof f, K., "Accuracy of the Pseudo Steady State
Approximation for Moving Boundary Diffusion Problems ",, Chemical
Engrg. Science, Vol. 18, 1963.
7. Cussler, E,, "Diffusion: Mass Transfer in Fluid System",
Cambridge University Press, Cambridge, 1984.
8. Crank, -J., "The Mathematics of Diffusion", 2nd edition, Oxford
University Press, New York, 1975.
9. Cote, P., "Contaminant Leaching from Cement-Based Waste Forms
Under Acidic Conditions", Ph. D. Thesis, McMaster University, 1986.
10. "Stabilization/Solidification of CERCLA and RCRA Wastes", U.S.
EPA Contract No. 68-03-3413, 1989.
11. "Acid- Neutralization Capacity", Test Methods for Solidified
Waste Characterization, Environment Canada and Alberta
Environmental. Center, 1986. e
12. Cote, P., and T. Bridle, "Long-Term Leaching Scenarios for
Cement-Based Waste Forms", Waste Management & Research, Vol 5,
1987.
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