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

-------
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

-------
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.

-------
o _
tO tO CD CD
aaaa
                                                      q

                                                      in
                                                        Ld
                                                     .  o
                                                         O
                                                         O
                                       a
                                       CO
 o
 o
 o
 o
O
O
O
o
CN
o
o
o
o
                                                      .0
                                                        •

                                                      o
                     SS3NGHVH
                                                             (D

                                                             E
                                                             o
                                                             o
                                                             a
                                                             13

                                                             CT
                                                             CO



                                                             CO*
                                           •a
                                            0)
                                           _c
                                            o
                                            o
                                            
                                           — CO
                                                              CO
                                                              o  c

                                                             ^S
                                                               .  o

                                                              E.L.
                                                              13  O
                                                              O

                                                              U.
                          10

-------
                                         03
                                         E
                                 .   O
X
X
X
X
X
•t a
• o
• a
• o
• o
+
•+
>
>
4*
' -U;x, ••>?;" • • ' .
'•&.-,. ^"
T;-. ".-•'* ..
»,- V '". »
1 1 1 1 1 " f I I J
O
O
o
o


-
m


"
"
o
! t i 1 1 I 1 1 1 J 1 1 t I I 1 1 J 1 1 »««•»«' Q
Oo°
0 S
° 2
o o
                                  o
                                 id
                                    o
                                    00
01
(£00°0
 SS3NQHVH
o
o
                                         03

                                         D
                                         13
                                         CT
                                         CO
                                         CO
-a
 0)
-C
 o
 o
_C£


 CO
 CO
 0)
 C
                                            CO
                                         o  o
                                         5 E
                                         ID *~"
                                         CM
 01
 ZD
 o
 lo-

-------
                                    03
                                    E
 FT
o
o
o
o
CO
1  1  t  1  i  1  t  1 1  I  i  1
                o
                o
                o
                o
                                                           o

                                                           0
                             o
                             o
                                                             Ld
                               U_
                               O
                               o
                               o
                             o<
                            •»-3
                               O
                               CO
                                    o
                                    o
                                    D

                                    3
                                    CT
                                    W



                                    OT
                                     0)
                                    JC
                                     u
                                     D
                                     0)
                                     CO
                                        ^
                                        cu
                                     D  0.

                                     E^
                                     ZJ  O
                            .0
                              «

                             o
      o
      o
      o
      o
      CJ
                                                                   bJ
                                                                   (T
                                                                   ID
                                                                   O

                                                                   U.
12

-------
 I  I  I   I
oomm
LO m co co
QQQQ
Xl
X
X
X
X


I [ 1 1 \ \ 1 1 1
o
O
•
•*
0 +T
D >
D +
n ^
o 41
.6

1 | j 1 1 1 1 1 1 1 I J 1 1 11 1 I I 1 » 1 » » • » » » « ' '
§ § S S
* ^
ro CN *- <

••
_

-
_
0
0
D
3
D



q
in
*—



0
o
v_

0)
D
. 3
cr
CO
                                                          Ld
                                                          L.
                                                          O


                                                          fe
                                                          O
Ld
                                                          CO
      (LUUU) 30NV1S1Q
                                                               CO
     o

     D
     0) -M
     — CO
O C
(** (D

§E
                                                               C O

                                                                 s""
                                                               0)

                                                               C
     «^-

     LU


     ID
     O

     Lu
                           13

-------
          in   m
        lO-r-iO*-
        I   1  I  I
        mmoo
        roromm
        Lj_LuLj_Li>





ITT1
. X
X
X
X
X
1 1 1 1





rr
a
a
a
a
o
TT
4i
+
+
•jp
+
\






                                                                o
                                                                o

                                                         o

                                                         •«"     £

                                                         """     o

                                                                cr
                                                                m


                                                                m

                                                           x-\   ^
                                                           CM
                                                         O «-   -C

                                                         •o«  -8
                                                           1,1   Q
                                             o
                                             o
                                             IT
O
O
O
o
o
C3
o
o
o
o
             (tutu) 30NVISIQ  NOLLVH13hQd
                                    -3 05

                                    •D °


                                    03 ^

                                    OH-

                                    C „


                                    £ C
                                    07 *•—
                                                                c  o

                                                                2s"
                                                                ^  03
                                                                03 -+->
                                                                C
                                                                Q3 H-
                                                                a.  °
IT)


LJ
CC
O
CD
                               14

-------
                                                          o
                                                          o

11} i t nun n n n i i i i 1111111
                                                   o
                                                   n
                                                  L   o

                                                      &
                                                      o
                                                      QL
                                                    0<


                                                   .*"a
                                                      CO
                                        .o
                                          *
                                         o
 o
 o
 in
o
o
                     o
o
q
cs
o
o
o
o
           (tutu) 30NVJS1Q NOLLV*LGN3d
                                              a?

                                              o
                                              13
                                              CT
                                                          CO



                                                          CP


                                                         *^
                                                         . o
                                                          o
                                                 c
                                               cncu


                                              '5 ®
                                              ^ o
                                              •I-
                                                          ^o'

                                                          IM
                                                          O
                                                          i_
                                                          -*-*,
                                                          0)
                                                          C
CD


Ld
ct:

Z5
O
                            15

-------
                          o
                          o
 nm.-.-inin
  I  i "?"? !  I
                    o
                    o
                     *
                    o
                      c
                     o
                     ,q
                     d
                     n
                     .00


                     *fc
                       O
                       IT

                       LJ
O3HOV31 SS3NQHVH
    o

JO  OLLVH
                          cr
                          co


                          CO
                                                •o
                                                0?
                                                .c
                                                0
                                                o
                                                 CO
                                                 CO

                                                 c


                                                 o
                                                 o
                                                o
                           o
                           Lil
                           o:
                           z>
                           o
                           L_
16

-------
                  «2|£inin^_



                  _^_^ ^i_  I  1 r^S ^^^
o
to
o
o

fO
o
t
o

°.
cs
o
m
o
a
                                           T"

                                            o
                                                    o
                                                    ,o
                                                     o
                                                    .0
                                                    -OO
                                                      .
                                                       O
                                                       a:
                                             o
                                             o
                                                       ui


                                                       f
                                                       —•*
                                                       °
                                                     o
                                                    •o
o
o

d
                                                             o
                                                             o
                                                             03


                                                             O
                                                             Z3

                                                             cr
                                                              O3
                                                      05
                                                      O

                                                      c

                                                      o

                                                      CO

                                                      T3


                                                      C

                                                      O
                                                      0)
                                                      c
                                                      QJ
                                                      a.
                                                              o
                                                              u
        30NViSia NOaVHlHhGd  dO  OLLVH
                                                       o
                                                      a:
                         00


                         UJ

                         DC
                             17

-------