Designation: C 1308 – 08

Standard Test Method for

Accelerated Leach Test for Diffusive Releases from
Solidified Waste and a Computer Program to Model
Diffusive, Fractional Leaching from Cylindrical Waste
Forms1
This standard is issued under the fixed designation C 1308; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.

1. Scope calculating diffusive releases that would occur at lower tem-

1.1 This test method provides procedures for measuring the peratures over long times. Tests conducted at high temperatures
leach rates of elements from a solidified matrix material, allow the temperature dependence of the diffusion coefficient
determining if the releases are controlled by mass diffusion, to be determined. They also demonstrate that the diffusion
computing values of diffusion constants based on models, and mechanism is rate-limiting through the measured extent of
verifying projected long-term diffusive releases. This test diffusive release.
method is applicable to any material that does not degrade or 1.2.2 Releases at any temperature can be projected up to the
deform during the test. highest cumulative fractional release value that has been
1.1.1 If mass diffusion is the dominant step in the leaching measured for that material (at any temperature), provided that
mechanism, then the results of this test can be used to calculate the mechanism does not change. The mechanism is considered
diffusion coefficients using mathematical diffusion models. A to remain unchanged over a range of temperatures if the
computer program developed for that purpose is available as a diffusion coefficients show Arrhenius behavior over that range.
companion to this test method (Note 1). NOTE 1—A computer program in which the test results are evaluated
1.1.2 It should be verified that leaching is controlled by using three diffusion models is briefly described in Annex A1 and in the
diffusion by a means other than analysis of the leach test Accelerated Leach Test Method and User’s Guide for the “ALT” Com-
solution data. Analysis of concentration profiles of species of puter Program (2). The data are fit with model equations for diffusion from
interest near the surface of the solid waste form after the test is a semi-infinite solid, diffusion from a finite cylinder, and diffusion with
partitioning of the species of interest to determine effective diffusion
recommended for this purpose. coefficients and quantify the goodness of fit. The User’s Guide contains
1.1.3 Potential effects of partitioning on the test results can several typographical errors; these are identified in Annex A1.
be identified through modeling, although further testing and
1.3 The values stated in SI units are to be regarded as
analyses are required to determine the cause of partitioning (for
standard. No other units of measurement are included in this
example, if it occurs during production of the material or as a
standard.
result of leaching).
1.4 This standard does not purport to address all of the
1.2 The method is a modification of other semi-dynamic
safety concerns, if any, associated with its use. It is the
tests such as the IAEA test (1)2 and the ANS 16.1 Leach Test
wherein elevated temperatures are used to accelerate diffusive responsibility of the user of this standard to establish appro-
release to an extent that would only be reached after very long priate safety and health practices and determine the applica-
times at lower temperatures. This approach provides a mecha- bility of regulatory limitations prior to use.
nistic basis for calculating diffusive releases at repository- 2. Referenced Documents
relevant temperatures over long times, provided that the
2.1 ASTM Standards:3
leaching mechanism does not change with temperature.
C 1220 Test Method for Static Leaching of Monolithic
1.2.1 Tests can be conducted at elevated temperatures to
Waste Forms for Disposal of Radioactive Waste
accelerate diffusive release and provide a mechanistic basis for
D 1193 Specification for Reagent Water
2.2 ANSI/ANS Standard:
1
ANSI 16.1 Measurement of the Leachability of Solidified
This test method is under the jurisdiction of ASTM Committee C26 on Nuclear
Fuel Cycle and is the direct responsibility of Subcommittee C26.07 on Waste
Materials.
3
Current edition approved Dec. 1, 2008. Published January 2009. Originally For referenced ASTM standards, visit the ASTM website, www.astm.org, or
approved in 1995. Last previous edition approved in 2001 as C 1308 – 95 (2001). contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
2
The boldface numbers in parentheses refer to the list of references at the end of Standards volume information, refer to the standard’s Document Summary page on
this standard. the ASTM website.

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 C 1308 – 08
Low-Level Radioactive Wastes by a Short-Term Test scopic measurements of its dimensions by assuming a simple
Procedure4 geometric shape, such as a right circular cylinder.
3.1.17 surface area—for purposes of this test method, the
3. Terminology geometric surface area of a monolithic specimen that is
3.1 Definitions: calculated from macroscopic measurements of its dimensions
3.1.1 cumulative fraction leached—the sum of the fractions by assuming a simple geometric shape, such as a right circular
of a species leached during all sampling intervals prior to and cylinder.
including the present interval divided by the amount of that 3.1.18 waste form—the waste material and any encapsulat-
species in the test specimen before the test. ing or stabilizing matrix in which it is incorporated.
3.1.2 diffusion coeffıcient (diffusivity)—an intrinsic property
4. Summary of Test Method
of a species that relates (1) its concentration gradient to its flux
in a given medium (Fick’s first law), (2) its spatial rate of 4.1 This test method is a semi-dynamic leach test in which
change in the direction of the concentration gradient to the time a cylindrical specimen is immersed in a leachant that is
rate of change in its concentration in a given medium (Fick’s completely replaced after specified intervals. The concentra-
second law), or (3) its mean square displacement to time in a tion of an element of interest in the recovered test solution is
given medium (the Einstein equation). measured after each exchange; this is referred to as the
3.1.3 effective diffusion coeffıcient (De)—the diffusion coef- incremental fraction leached (IFL). The accumulated amount
ficient as modified by other processes (for example, adsorp- of the species of interest in the intervals prior to and including
tion) or physical constraints (for example, tortuosity and the interval of interest is analyzed to determine if the release
constrictivity). from the solid can be described using a mass diffusion model.
3.1.4 finite cylinder (finite medium)—a bounded body for The amount accumulated through a particular test duration is
which Fick’s diffusion equation can be solved. referred to as the cumulative fraction leached (CFL).
3.1.5 incremental fraction leached—the amount of a species 4.2 Tests at a single temperature are adequate to compare
leached during a single sampling interval divided by the the leaching behaviors of different materials.
amount of that species in the test specimen before the test. 4.3 The results of tests at repository-relevant temperatures
3.1.6 leachant—the initial solution with which a solid is can be extrapolated to long times if data from tests run at
contacted and into which the solid dissolves or is leached. elevated temperatures and data from tests run at the reference
3.1.7 leachate—the final solution resulting from a test in temperature (20°C) can be modeled using a diffusion model
which a solid is contacted by a solution and leaches or and the diffusion coefficients show Arrhenius behavior.
dissolves. 4.3.1 Elevated temperatures are used to accelerate the re-
3.1.8 leaching—the preferential loss of components from a lease of a species of interest and collect enough data to show
solid material into solution leaving a residual phase that is that the release is controlled by diffusion and determine the
depleted in those components, but structurally unchanged. value of the diffusion coefficient.
3.1.9 leaching interval—the length of time during which a 4.3.2 Tests must be performed at a minimum of three
given volume of leachant is in contact with a specimen. temperatures to verify that the leaching mechanism does not
3.1.10 leaching mechanism—the set of processes that con- change over that temperature range.
trols the rate of mass transport of a species out of a specimen 4.3.3 By generating data over a range of temperatures, an
during leaching. Arrhenius plot can be produced to interpolate values of the
3.1.11 matrix material—the solid material used to immobi- diffusion coefficient within the temperature range that was
lize the waste or species of interest. tested. Values cannot be extrapolated to temperatures that are
3.1.12 reference leach test—a leach test conducted under higher or lower than the temperature range spanned by the
defined conditions, the results of which are used as a standard tests.
against which the results of other leach tests are compared. In 4.3.4 A computer program that plots the experimental data
this test method, a reference leach test is one that is conducted and a regression curve calculated using a finite cylinder model
at 20°C using demineralized water. (2) is available from ASTM (see Note 1). The program
3.1.13 semi-dynamic leach test—a leach test method in provides the value of the effective diffusion coefficient, the
which the specimen is exposed to fresh leachant on a periodic modeled IFL and CFL values, and a measure of the goodness
schedule. of fit of the model.
3.1.14 semi-infinite medium—a body having a single planar 4.4 If the data from the accelerated tests, the reference test,
surface and extending infinitely in the directions parallel to the and the fit of the modeled curve agree within defined criteria,
surface and in one direction normal to the surface. the leaching mechanism can be taken to be diffusion-controlled
3.1.15 source term—in this test method, the concentration and a diffusion model can be used to calculate releases from
of a species of interest in a specimen prior to leaching. full-scale waste forms for long times.
3.1.16 specimen volume—for purposes of this test method, 4.4.1 The accelerated leach test provides the maximum
the volume of a monolithic specimen calculated from macro- cumulative fractional release to which the modeled data can be
extrapolated. The maximum cumulative fractional release mea-
sured represents the maximum extent of reaction for which the
4
Available from American National Standards Institute (ANSI), 25 W. 43rd St., consistency of the mechanism has been verified for that
4th Floor, New York, NY 10036, http://www.ansi.org. material.

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 C 1308 – 08
4.4.2 Because the cumulative fraction leached is a function 5.3.3 Extrapolations in time and scale are limited to values
of the specimen surface area-to-volume ratio, the results of that correspond to the maximum CFL value obtained in an
tests with the small-scale specimens used in the ALT directly accelerated test.
represent leaching from large-scale waste forms having the 5.3.4 The mechanism must be the same at all temperatures
same aspect ratio. used in the extrapolation. The same model that describes the
4.4.3 The effective diffusion coefficient can be used to results of tests conducted at elevated temperatures must also
calculate diffusive releases from waste forms with other describe the results of tests run at the reference temperature of
shapes. 20°C.
4.5 If the diffusion model does not fit the data within defined
criteria, no extrapolation can be made in time or specimen size. 6. Apparatus
However, other models can be applied to the data to evaluate 6.1 A forced-air environmental chamber or a circulating
the leaching process. water bath capable of controlling leachant temperatures to
4.5.1 A model including diffusion with partitioning of the within 1°C of the target test temperature shall be used.
species of interest between phases having different release 6.2 Balance—The balance shall be accurate to 0.1 % of the
behaviors is included in the computer program (2). test load.
4.5.2 The possibility of a solubility-limit to the release of
the species of interest is addressed in the computer program 7. Reagents and Materials
(2).
4.6 If the data cannot be fit with a diffusion model within the 7.1 Leachant—The leachant can be selected with regard to
defined criterion, then graphical comparisons of the data are the material being tested and the information that is desired.
recommended for added insight: For example, a plot of the Demineralized water, synthetic or actual groundwaters, or
cumulative fraction leached (CFL) from ALT conducted at an chemical solutions can be used. The effects of the leachant
elevated temperature against the CFL from ALT conducted at solution on the species of interest (that is, the species for which
the reference temperature can be used to verify that the the diffusion coefficient is to be measured) and the solid must
accelerated data are consistent with the reference data and that be considered. For example, the leachant should not degrade
the accelerated test appropriately accelerates the release, even the host solid. In general, the leachant should be devoid of the
though the release is not diffusion-limited. species of interest to minimize solution feedback and solubility
limit effects. If the leachant does contain a non-negligible
5. Significance and Use amount of the species of interest, blank tests should be
5.1 This test method can be used to measure the release of conducted to provide background concentrations to calculate
a component from a cylindrical solidified waste form into the amounts released from the solid by using the concentrations
water at the reference temperature of 20°C and at elevated measured in the tests. If demineralized water is used, it must
temperatures that accelerate the rate and extent of leaching meet or exceed the standards for types II or III reagent water
relative to the values measured at 20°C. specified in Specification D 1193.
5.2 This test method can be used to: 7.2 Leaching Containers—Leaching containers shall be
5.2.1 Compare releases of waste components from various made of a material that does not react with the leachant,
types of solidification agents and formulations. leachate, or specimen. It is particularly important to select
5.2.2 Determine the diffusion coefficients for the release of materials that are not susceptible to plate-out of species of
waste components from waste forms at a specific temperature. interest from solution. High density polyethylene has been
5.2.3 Promote greater extents of reaction than can be found to be a suitable container material. The top of the
achieved under expected service conditions within a laboratory container shall fit tightly to minimize evaporation. The mass of
time frame to provide greater confidence in modeled diffusive the vessel must be checked before sampling to verify that
releases. evaporative losses are less than 1 % of the leachant mass (or
5.2.4 Determine the temperature dependence of diffusive volume) over every test interval.
release. 7.3 Specimen Supports—Supports for the specimens shall
5.3 Fitting the experimental results with a mechanistic be made of a material that does not react with the leachant,
model allows diffusive releases to be extrapolated to long times leachate, or specimen and is not susceptible to plate-out. The
and to full-scale waste forms under the following constraints: method of support should not impede leaching by contacting
5.3.1 Results of this test method address an intrinsic prop- more than 1 % of the surface area of the specimen. Moreover,
erty of a material and should not be presumed to represent the support should not interfere with the removal and replace-
releases in specific disposal environments. Tests can be con- ment of the leachate.
ducted under conditions that represent a specific disposal 7.3.1 It is often convenient to suspend the waste form from
environment (for example, by using a representative ground- the cover of the leaching container using monofilament string.
water) to determine an effective diffusion coefficient for those 7.3.2 Alternatively, samples can be placed on perforated or
conditions. mesh stands.
5.3.2 Projections of releases over long times requires that 7.4 Sample Containers—Containers to hold aliquots of
the waste form matrix remain stable, which may be demon- leachate for storage prior to analysis should not be susceptible
strated by the behavior of the specimen in ALTs at elevated to plate-out of radionuclides. The container must allow for
temperatures. adequate preservation of the leachate and specimen.

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 C 1308 – 08
7.5 Stirrers—Stirrers are used to homogenize the leachate 9. Procedure
solution prior to removing aliquots for analysis. 9.1 The dimensions of each specimen shall be measured
7.6 Filtration Equipment—If filtration of visible particu- with a calibrated device (for example, digital calipers) to the
lates in the leachate is required, the filter medium should be nearest 0.01 cm. At least two measurements of the diameter
capable of removing particulates that are 0.45 µm in diameter shall be made at the top and bottom of the specimen and two
or larger. Disposable syringe filters are recommended. Tests measurements of the height at diametrically opposite locations.
must be conducted to determine if the filter and the filtration The geometric surface area and volume are calculated by
apparatus adsorb a significant amount of the species of interest. modeling the specimen as a right circular cylinder and using
It may be necessary to pre-condition each filter with a the arithmetic averages of the measured diameters and heights.
sacrificial volume of the leachate solution to saturate sorption 9.1.1 The surface area and volume of the specimen are used
sites in the filter. to calculate the diffusion coefficient (see A1.3.2.1).
8. Specimens 9.1.2 The uncertainty in the surface area and volume of the
8.1 Right circular cylindrical specimens shall be used with a specimens contribute to the uncertainty in the diffusion con-
diameter-to-height ratio between 1:1 and 1:2. This shape is stant and should be quantified, for example, by using the
used to facilitate modeling the test results. A convenient size is propagation of errors method or, preferably, that developed by
2.5 cm diameter by 2.5 cm height. Smaller specimen sizes the International Committee for Weights and Measured
should not be used to avoid producing nonhomogeneous (CIPM) and promulgated by NIST (3); see Annex A2.
samples. 9.1.3 The surface area and volume used to model the results
8.2 To the extent possible, the specimens should be prepared can be adjusted to take into account deviations in the specimen
using the same techniques as those used to produce full-scale shape from an ideal right circular cylinder based on additional
waste forms. For example, the curing conditions used to measurements and geometric calculations.
prepare laboratory-scale specimens should match those used 9.2 Leachant Volume—The leachant volume is selected
for actual waste forms as closely as possible, especially the based on the specimen surface area and an estimate of the leach
temperatures experienced by the large waste forms. rate. The volume must be low enough that the solution
8.3 Specimens shall be representative of the full-scale concentrations that are generated during the test can be
solidified waste form. Particular attention should be paid to analyzed, but high enough that solution feedback effects on
ensuring that the species of interest is homogeneously distrib- leaching are negligible (that is, so that the chemical gradient
uted in the material being tested. Test specimens can be cut between the solid and solution remains nearly constant). The
from a larger sample or cast individually. solution mass can be measured and used to calculate the
8.4 Many solids prepared by casting form a skin on the volume if the solution density is known.
outer surface during preparation that has different characteris- 9.2.1 The solution volume is not used directly in the
tics than the bulk material. The effect of the skin must be calculation of the diffusion constant, but is used to calculate the
determined and differentiated from the bulk property. This can mass of the species of interest from the measured solution
be done by conducting separate tests using samples with concentration.
surfaces that are representative of the structure of surfaces of 9.2.2 The specimen surface area-to-solution volume must
large waste forms, such as surfaces that are cast against remain the same for all test intervals in an ALT to ensure that
container walls, and tests with samples having cut or polished any impacts of solution feedback and solubility limitation are
surfaces that expose the bulk material to the leachant. The similar during each test interval.
effect of the skin can be determined from differences in the 9.2.3 The specimen size and solution volume must be
derived diffusion coefficients for materials with and without the selected by compromising the benefits of using a large speci-
skin. men (ease of fabrication, uniformity of specimens, ease of
8.5 A minimum of three replicate tests should be conducted sampling reacted materials, etc.) with the complications of
at each temperature if results are to be used to predict large solution volumes (handling, analytical limitations, waste
long-term behavior. disposal, etc.).
8.6 The dimensions, weight, composition, curing history, 9.2.4 The effects of solution feedback and solubility limits
and other pertinent information that could affect performance can be identified (or mitigated) by conducting tests at different
shall be recorded for each specimen. specimen surface area-to-leachant volume ratios. Solution
8.7 Accurate determination of the amount of the species of feedback effects are expected to be more significant at higher
interest in the specimen at the start of the leach test shall be temperatures and surface area-to-leachant volume ratios.
made and recorded. 9.2.5 For example, to replicate the standard conditions in
8.8 If a specimen is prepared in a mold, any excess material the Test Method C 1220 static leach test, the leachant volume
should be removed from the specimen prior to weighing it. (in cm3) used for each interval must be 103 the surface area of
8.8.1 If the quantity of the species of interest in the the specimen (in cm2) as calculated below:
specimen (that is, the source term) was determined before the
Specimen surface area ~cm2! 1 cm2
specimen was removed from the mold, the amount of that 3 [ 5 0.1 cm–1 (1)
Leachant volume ~cm ! 10 cm3
species that remained in the mold (plus material removed as
excess) shall be determined and the amount accounted to be in 9.2.5.1 This ratio requires a very large volume of water for
the specimen adjusted. specimens of even moderate size. For example, a 2.5 3 2.5 cm

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 C 1308 – 08
cylindrical specimen having a surface area of 29.45 cm2 would and place it on a new container with the appropriate volume (or
require 294.5 mL of solution for each of the 11 test durations. mass) of fresh leachant. The new leachant may be pre-heated to
Specimens that are much larger than this and tests at lower the test temperature (if practical). The new container can be
surface area-to-leachant volume ratios will require volumes of sealed and placed into the temperature-controlled environment
water that need sophisticated means of wastewater handling immediately. During leachant changes, the specimen should be
(such as peristaltic pumps for draining the containers), since exposed to air for as short a time as possible. Rinsing the
large volumes may be too unwieldy for pouring. sample prior to transfer is not necessary.
9.2.6 Large volumes of leachant can make analysis chal- 9.4.2 If the specimen is at the bottom of the test container,
lenging, even for major constituents of the specimen, and the leachate can be decanted into a collection container and the
present unnecessary waste disposal costs. Under these circum- sample recovered with forceps and placed immediately into
stances, higher specimen surface area-to-leachant volume ratio another test container with pre-heated leachant (is not neces-
may be used. The leach rates of some waste form materials sary to rinse the specimen). The new test container can be
may be low enough that a specimen surface area-to-leachant sealed and placed into the controlled-temperature device.
volume ratio higher than 0.1 cm–1 must be used to generate 9.4.3 The mass of the assembled vessel shall be measured
measurable solution concentrations. before the vessel is placed in the controlled-temperature device
9.2.7 The user must verify that solution feed-back effects or at the start of a test interval and when the vessel is removed at
solubility limits do not affect the results. Solution feedback the end of the test interval. The difference in mass provides a
effects (or solubility limits) are considered negligible if the measure of the loss of leachate solution due to evaporation (see
same value of De, within experimental uncertainty, is obtained 7.2).
for tests conducted at different specimen surface area-to- 9.5 Acid Strip—At least one vessel bottom shall be sub-
leachant volume ratios. jected to an acid strip at the end of a test interval to verify that
9.3 Temperature—For materials and formulations that have the species of interest is not sorbing to the vessel. If the amount
not been tested previously, leach tests shall be conducted at a sorbed is not negligible, the vessel shall be acid-stripped after
minimum of three temperatures to establish that the leach rate every sampling, and the amount of the species of interest
increases systematically with higher temperatures. One tem- recovered in the acid strip shall be added to the amount in the
perature must be 20°C. The other temperatures should be leachate.
selected based on knowledge of the material being tested. For 9.5.1 Discard any remaining leachate solution from the
example, the recommended maximum temperature is 50°C for vessel and rinse with demineralized water.
cementatious materials, which is below the threshold of 9.5.2 Fill vessel with an amount of demineralized water
anomalous releases observed previously (3). Temperatures equal to or greater than the amount of leachate that was
above 50°C can be used if it is demonstrated that the leaching removed.
mechanism does not change. 9.5.3 Add the appropriate amount of concentrated ultrapure
9.3.1 The controlled-temperature device must maintain a nitric acid to produce a 2 volume% acid solution.
temperature within 1°C of the desired temperature throughout 9.5.4 Cap the container and agitate, then let settle for several
the test (except for short-term perturbations with the vessels are minutes.
removed for sampling). The temperature shall be recorded
9.5.5 Collect a sample of the acid strip solution for analysis.
either before the vessel is placed in the device at the beginning
of a test interval or before it is removed at the end of a test 9.6 Leachate Sampling—Immediately after opening the
interval. vessel, the old leachate should be stirred thoroughly and
sampled quickly to minimize any artifacts that could occur
9.3.2 The time required for the device to return to the set
during cooling (for example, precipitation). Several aliquots
temperature after it is opened (for example, to emplace or
may be required at each sampling for desired analyses.
remove a test vessel) should be noted, even though the vessel
may not have attained that temperature. The time required to 9.6.1 If the specimen is suspended from the vessel lid, place
heat the specimen to relatively high test temperatures may be the lid on the vessel with fresh water and initiate the next test
a significant fraction of the first two test intervals (2 and 5 interval before removing aliquots of the leachate for analysis.
hours). 9.6.2 If the specimen is placed on a stand at the bottom of
9.4 Leachant Replacement—Leachant replacements shall the vessel, stir solution and remove aliquots of the leachate for
take place at the following time intervals: 2 hours, 5 hours, 17 analysis before initiating the next test interval.
hours, and 24 hours, and then daily for the next 10 days, for a 9.6.3 The solution aliquots should be collected and pre-
total test duration of 11 days. The times at which the specimen served in ways appropriate for the analytical technique(s) to be
is removed from the leachate and placed in the fresh leachant employed.
should be noted to the nearest minute. The times at which the 9.6.4 If particulates are visible in the leachate, it is neces-
vessel is removed from and emplaced in the controlled- sary to account for the quantity of the species of interest
temperature devise should be noted to the nearest minute. The associated with them.
use of an electric clock or a watch is adequate. 9.6.4.1 If the particulates form by spalling from the speci-
9.4.1 If the specimen is suspended from the top of the men, they should be removed prior to analyzing the solution
container, the most convenient method for changing the and the species of interest associated with the spalled material
leachant is to lift off the cover (with the specimen still attached) should be excluded from the amount released.

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 C 1308 – 08
9.6.4.2 If the particulates formed after the species of interest obtain the average fraction released per area per time. This
were leached, two approaches can be used. One requires allows comparisons of tests conducted with samples having
filtration of the leachate and subsequent analysis of both the different surface areas.
filtrate and the particulate material on the filter. The other is to 10.2 Cumulative Fraction Leached—The cumulative frac-
acidify the leachate to dissolve the particulates and thereby tion of species i leached through the jth interval (CFLj) is
include the associated species of interest in the analyzed calculated by using Eq 3:
solution. One or both methods can be used (for example, j
analyze filtered and unfiltered solutions), depending on the ( i an
n51
j
information desired. CFLj 5
iA0
5 ( IFLj
n51
(3)
9.7 Analysis and Standards—Analysis of the leachate for
the species of interest shall be conducted by standard methods NOTE 2—The indices for the species and interval are excluded for
and using appropriate calibration standards. If necessary, stan- convenience hereafter.
dards should be prepared to match the matrix elements in the 10.2.1 Plotting the CFL value for each interval against the
samples. For radioactive specimens, a series of waste reference cumulative time provides a graphical comparison of data from
solutions can be prepared by diluting an aliquot of the original various tests with each other and with modeling results. An
solution (or waste) that was used to make the specimens for example of this type of plot is shown in Fig. 1.
comparative analysis. The analytical results for the test 10.3 Effective Diffusion Coeffıcient—The results of this test
samples can then be compared directly to analytical results for method can be used to determine the effective diffusion
these reference solutions to calculate fractional releases with- coefficient (De) for the release of the species of interest based
out the need for absolute standards, detector efficiencies, or on a model. A computer program has been developed at
decay corrections. Brookhaven National Laboratory to calculate a best fit effective
9.8 Standard Test—One or more ALTs with an equivalent diffusion coefficient (De) based on the equations for diffusion
specimen shall be conducted at 20°C for use as a standard for from a semi-infinite medium or from a finite cylinder (4). The
comparison with ALTs conducted at other temperatures and ALT computer program also evaluates the possible influence of
ALTs conducted with other materials. Triplicate standard tests partitioning and solubility limits on the diffusive release. That
at 20°C are required if the results will be used to project program is available from ASTM for use with this test method
releases to long durations or larger waste forms. (2); see also (5, 6). The computer program determines the value
9.9 Blank Test—Depending on the species of interest, a of the effective diffusion coefficient by regressing analytical
blank test with either no specimen or with a specimen that does expressions for diffusion from a semi-infinite solid and from a
not contain the species of interest is recommended to provide finite cylinder to the CFL determined from the test results. The
background solutions to help detect contamination that may analytical expressions are provided in Annex A1. The uncer-
occur during the procedure or provide background levels for tainty in the diffusion coefficient can be calculated using the
leachants that contain the species of interest. formula for diffusion from a semi-infinite solid.
10.4 Agreement with Models—The CFL values calculated
10. Calculations using values of De determined from the data using the diffusion
10.1 Incremental Fraction Leached—The incremental frac- models can be compared with the CFL values calculated from
tion of species i leached (IFL) during test interval n is the test data by plotting both against the cumulative test
calculated by using Eq 2: duration. If the CFL values calculated with the model agree
with the measured values within a designated “goodness of fit”
ian
IFL 5 A (2) (which is related to the uncertainty in the regression; see
i 0
10.4.1), then it can be concluded that diffusion is the rate-
where: determining step in the leaching mechanism and the effective
ian = the quantity of species i measured in the leachate diffusion coefficient is the regressed value of De. If this is the
from the nth test interval, and case, then the diffusion model can be used to calculate releases
iA0 = the quantity of species i in the specimen at the over long times at that temperature. The use of the diffusion
beginning of the test. model requires that the waste form remains intact and the
In the case of radionuclide i, both terms must be corrected leaching mechanism does not change with time. Demonstrating
for radioactive decay to the beginning of the test. that the same mechanism is operative at 20°C and at elevated
10.1.1 It may be necessary to calculate the value of ian from temperatures provides confidence that it will not change over
the measured solution concentration using the leachant vol- long times at intermediate temperatures, at least up to the
ume. In that case, the uncertainty in the measured concentra- extent represented by the maximum CFL value measured in a
tion and the uncertainty in the leachant and leachate volumes test.
must be taken into account. (See Annex A2.) 10.4.1 The percent relative error in the fit of the model to the
10.1.2 The average rate of release for any interval can be data (ER2) is determined by dividing the sum of the squares of
calculated by dividing IFL by the duration of that interval. The the residuals between the CFL value of the optimized model
rate can then be divided by the surface area of the specimen to curve and the measured value by the CFL value of the

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 C 1308 – 08

FIG. 1 Plotted Results of Test 1, Test 2, and Test 3 with

Model Fits

experimental data of the longest duration. For a total of N This could indicate that the release is not controlled by
measured CFL values, the percent relative error for the ALT is diffusion or that the testing conditions are not appropriate to
defined as: measure the diffusion coefficient. The Solubility Model pro-
N vides the relative standard deviation in the IFL values of the
( ~CFLi,model – CFLi,measured!2
i51
1-day test intervals as the relative variance (VR) defined as:
ER3 5 100 · CFLN,measured (4)
standard deviation
VR 5 100 · mean IFL (5)
10.4.1.1 A goodness of fit value of ER2 equal to or less than
0.5 % is taken to mean that the diffusion model accurately 10.5.2.1 Relative variances of 10 % or less indicate that the
represents the data. The residuals for points furthest from the release is constant, within analytical uncertainties, and not
mean duration are typically the highest, so the value of ER2 is diffusion-limited.
not conservative for the data set. Although it is not statistically
10.6 Relationship of Temperature to Leaching—The accel-
unique, ER2 provides a convenient empirical benchmark for the
goodness of fit in tests conducted for similar total durations. erated leach test relies on elevated temperature as the primary
10.5 In addition to the two diffusion models, the computer means of increasing the rate of mass transport from specimens.
program provides an indication of whether processes that The temperature dependence of an activated process (in this
complicate or mask simple diffusive release may be occurring case leaching as expressed by the diffusion coefficient De) is
in the ALT by using the Partition Model and Solubility Model. usually described using the Arrhenius equation:
10.5.1 The Partition Model divides the source term for the
species of interest into separate leachable and unleachable
k
De 5 A exp RT S D (6)
fractions. It then uses the diffusion models to analyze release of
the leachable fraction by varying the partition factor until an where:
De (T) = the effective diffusion coefficient measured at
acceptable model fit is obtained. The Partition Model provides
temperature T (Kelvin),
an effective diffusion constant, partition constant, and a mea-
A and k = constants, and
sure of the relative error in the fit. An acceptable fit by the R = the gas constant.
Partition Model indicates that diffusion controls the release
kinetics, but that the release is complicated by an additional 10.6.1 To apply Eq 6, the logarithms of the diffusion
constraint. The species of interest may not be homogeneously coefficients determined from experiments (De) conducted at
distributed in the specimen or homogenously released to several temperatures are plotted against k/T. A linear plot
solution. It may indicate an error in the surface-to-volume ratio indicates that the increase in leaching is proportional to the
that was used for the specimen in the calculation, or other increase in temperature and means that:
discrepancy. (1) The leaching mechanism, as well as the structural
10.5.2 The Solubility Model is used to determine if solubil- controls on leaching (for example, tortuosity, porosity), are
ity constraints are limiting the release of the species of interest. unchanged by increasing temperature; and

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 C 1308 – 08
(2) Effective diffusion coefficients can be calculated for 11. Precision and Bias
temperatures between those tested.
11.1 The precision of this test method will vary depending
10.7 The relationship between leaching and temperature
on the solid waste being tested, the temperature, and the
must be determined using at least three temperatures. To
species of interest being leached. Factors affecting the test
project the results from short-term tests at elevated tempera-
precision include the condition of the sample surface (rough-
tures to long times at lower temperatures using this test
ness, the presence of skin, fracturing, porosity, etc.), estimation
method, it must be demonstrated that a linear relationship
of the geometric surface area and volume of the specimen, time
exists between log De and the inverse absolute temperature
at temperature, and analysis of the solutions.
over that temperature range. The range of temperatures over
which the relationship is linear defines the range for which 11.2 No standard reference materials exist that would allow
application of the model is mechanistically justifiable. The the accuracy of this test method to be determined. Determina-
minimum temperature is expected to be the ALT reference tion of the precision of values discussed in this standard
temperature of 20°C. The maximum temperature will likely be (expressed as the combined standard uncertainty) is discussed
determined by the thermal stability of the host solid. For in Annex A2.
example, some organic matrix materials become unstable 11.3 Results from replicate ALTs are shown in Table 1 as
above 50°C. examples. The CFL values are plotted in Fig. 1 along with the
10.7.1 If the value of De at the temperature of interest is fitted curves generated by the ALT computer model. The
known (by measurement or interpolation), the CFL can be Diffusion Model fits for Tests 1, 2 and 3 and the Partition
calculated for long times, up to the time when the maximum Model fit for Test 1 are shown. The Partition Model provides a
CFL value measured in an ALT with that material is attained visibly better fit than the Diffusion Model for Test 1. The sums
(regardless of the time or temperature at which the maximum of the squared residuals are 3.28 3 10–3 and 1.81 3 10–4 for
CFL value was measured). Values of CFL projected beyond the Diffusion and Partition Model fits to Test 1, respectively,
those measured in an ALT should be considered unreliable due and 5.62 3 10–5 for the Diffusion Model fit to Test 2. The
to possible changes in the mechanism at an extent of reaction Diffusion Model gives ER2 values of 0.565 % and 0.011 % for
greater than measured in a test. Test 1 and Test 2, respectively, and 0.06 % for Test 3. The
10.7.2 An ALT conducted at the high temperature extreme Diffusion Model is not acceptable for the Test 1 results, based
can be continued for longer durations (additional 1-day inter- on the criterion of ER2 < 0.5, but the Partition Model gives an
vals) to attain higher CFL values. acceptable ER2 value of 0.032 for Test 1. The Diffusion Model
10.8 Empirical Correlation—If the mechanistically-based is acceptable for the Test 2 and Test 3 results and the values of
diffusion models do not provide a good fit, diffusion may not be De are 4.98 3 10–10 m/s and 6.35 3 10–10 m/s. The improved
the rate-limiting process in the leaching mechanism. Empirical fit for Test 1 that is obtained with the Partition Model may
approaches can be taken to compare releases from the accel- indicate that the value of the source term used in the Diffusion
erated test with releases from the reference test. Model was too high. This could be an indication that the
10.8.1 The effect of temperature on the release can be species of interest is not homogeneously distributed in the
evaluated by plotting CFL values from the accelerated test on solid, a defect exists in the sample used in Test 1, contamina-
the y-axis of a graph and CFL values from the reference test tion of an early sampling occurred in Test 1, etc. The value of
(for the same test interval) on the x-axis. If this scatter plot De for Test 1 from the Partition Model is 2.07 3 10–9 m/s for
shows a linear relationship, the data from the two tests can be a partition factor of 0.70. Fig. 2 shows the results of Test 1
compared and the results of the accelerated test can be said to plotted against the results of Test 2. The diagonal line in Fig. 2
accurately reflect the data from the reference test. The slope of shows the ideal correlation for replicate tests. In the calculated
the correlation provides insight regarding the effective activa- CFL value, the effect of the source term cannot be distin-
tion energy for release. However, such empirical correlations guished from the effect of the surface area-to-volume ratio of
do not confirm a diffusion-controlled mechanism and cannot be the test sample. By itself, the partition factor of 0.70 could
used to extrapolate the data to long times. indicate that the S/V ratio of the specimen used in the

TABLE 1 Example ALT Test Results

Time Test 1 Test 2 Test 3
(days) IFL CFL IFL CFL IFL CFL
0.083 6.12E-02 6.12E-02 6.06E-02 6.06E-02 6.09E-02 6.09E-02
0.29 5.82E-02 1.19E-01 4.13E-02 1.02E-01 3.96E-02 1.01E-01
1.0 1.04E-01 2.23E-01 7.43E-02 1.76E-01 8.90E-02 1.90E-01
2.0 8.27E-02 3.06E-01 6.61E-02 2.42E-01 7.45E-02 2.64E-01
3.0 5.51E-02 3.61E-01 4.68E-02 2.89E-01 6.10E-02 3.25E-01
4.0 3.98E-02 4.01E-01 3.85E-02 3.28E-01 3.95E-02 3.65E-01
5.0 3.37E-02 4.35E-01 3.58E-02 3.63E-01 3.45E-02 3.99E-01
6.0 2.45E-02 4.59E-01 2.48E-02 3.88E-01 2.45E-02 4.24E-01
7.0 2.45E-02 4.84E-01 2.48E-02 4.13E-01 2.50E-02 4.49E-01
8.0 2.14E-02 5.05E-01 2.20E-02 4.35E-01 2.65E-02 4.75E-01
9.0 1.84E-02 5.23E-01 2.20E-02 4.57E-01 2.00E-02 4.95E-01
10.0 1.53E-02 5.39E-01 1.93E-02 4.76E-01 2.25E-02 5.18E-01
11.0 1.53E-02 5.54E-01 1.93E-02 4.95E-01 1.70E-02 5.35E-01

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 C 1308 – 08

FIG. 2 Plot of the Results of Test 1 versus the Results of Test 2

calculation is 43 % too low, perhaps due to an error in the 11.4 The results of early samplings are more heavily
measured dimensions, the presence of micro cracks, etc. weighted in the determination of the diffusion coefficient than
However, the observation in Fig. 2 that the differences in later samplings because the cumulative release fraction after
corresponding samplings in Test 1 and Test 2 are not linear each interval is used. Any error (or contamination) in a
with time or time1/2 suggests a real difference in the value of sampled concentration will be propagated to all subsequent
De. This suggests a difference in the surfaces of the two CFL values and affect the value of De that is calculated.
specimens, perhaps due to the presence of a casting film. 11.5 Other data and modeling results using the ALT are
Finally, as an example of the Solubility Model, the relative available (3, 6, 7).
variances for samplings of Tests 1, 2 and 3 after 1 day intervals
are 64.7 %, 47.4 %, and 45.0 %, respectively, which indicate 12. Keywords
that the releases in these tests are not solubility-controlled. 12.1 accelerated; diffusion; leach; waste

ANNEXES

(Mandatory Information)

A1. COMPUTER PROGRAM FOR THE ACCELERATED LEACH TEST

A1.1 Scope A1.2 Equipment

A1.1.1 This Annex contains a brief outline of the ALT A1.2.1 The computer program that is available for analyz-
computer program that was developed to accompany the ing data from this test method is a compiled version and runs
accelerated leach test. The program serves a variety of func- on IBM or IBM compatible personal computers. A math
tions including: co-processor is desirable to decrease the computation time. A
A1.1.1.1 Comparing experimental data to curves generated graphics board is required to generate plots and can be a CGA,
by four models, EGA, VGA, or a Hercules color or monocolor board. In the
absence of a compatible graphics board, the program will
A1.1.1.2 Calculating incremental and cumulative fractional perform all calculations and list the results.
releases, and
A1.1.1.3 Storing data in a form compatible with Lotus A1.3 Approach
1-2-3. A1.3.1 The release of components by mass transport
A1.1.2 The Accelerated Leach Test computer program and a through a solid is modeled based on the diffusion rate being
detailed Users’ Guide (2) are available from: ASTM, 100 Barr proportional to the concentration gradient, as formulated in
Harbor Drive, West Conshohocken, PA 19428-2959. Fick’s second law (Eq A1.1):

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 C 1308 – 08
]C 2
]t 5 –Deπ C (A1.1) (an S Det
CFL 5 A 5 2 V p
0
F G 1/2
(A1.2)

where: where:
C = the concentration of the species of interest, an = the total amount of the species of interest released in
t = time, all leaching intervals through time t,
De = the effective diffusion coefficient, and A0 = the initial amount of the species of interest in the
π2C = the spatial rate of change in the direction of the specimen (that is, the source term),
concentration gradient. S = the surface area of the specimen,
A1.3.2 The ALT computer program contains four math- V = the specimen volume, and
ematical models that can be used to represent the data and De = the effective diffusion coefficient.
determine the value of the effective diffusion coefficient. The A1.3.2.2 Diffusion through a finite cylinder
leaching mechanisms described by these models are diffusion This model takes into account depletion of the solid due to
through a semi-infinite medium, diffusion through a finite leaching and is usually appropriate for materials that give high
cylinder, diffusion plus partitioning of the species of interest,
CFL values in the ALT (for example, CFL > 0.2). The
and solubility-limited leaching (dissolution). As illustrated in
mathematical solution is based on diffusion from a cylindrical
the logic flow diagram in Fig. A1.1, an iterative method is used
solid of height H and radius R. In the finite cylinder model, the
to optimize the fit to the entire data set. The data are first fit
diffusive fractional cumulative release is calculated as a double
using the semi-infinite solid medium model to obtain an initial
series expression:
value of De. If this does not give an acceptable fit, the other
models are applied to the data to obtain better fits.
A1.3.2.1 Diffusion through a semi-infinite medium
(an 32
S
CFL 5 A 5 1 – 2 Sp~t! Sc~t!
0 p D (A1.3)

This model is usually appropriate for porous materials that

with the series:
give low CFL values in the ALT (for example, CFL < 0.2). It
is the simplest model and provides an initial value of De for use
in other models. The CFL is calculated in the semi-infinite Sp~t! 5
`
(
SF
exp –
~2n – 1!p
H G D
2
Det
(A1.4)
solid model as: n51 ~2n – 1!2

and the series:

Sc~t! 5 (
`
bm
exp – R SF G D 2
Det
(A1.5)
n51 bm2

where the parameter bm represents the mth zero of the zeroth

order cylindrical Bessel function. Values of the bm for m = 1 to
20 are provided in Table A1.1. In the ALT program, an ad hoc
term is added to Eq A1.3 to account for the non-zero
y-intercept typical in experimental results. The numerical
convergence for these open series is extremely slow, and
analytical closed forms expressions have been developed (4).
The closed forms include separate terms to represent the closed
series and the maximum absolute error introduced by truncat-
ing the open series. The equations developed by Pescatore (4)
are given here for completeness.
For the Sp (t) series:
Sp~t! 5 Sp,N~t! 1 Ep,N~t! (A1.6)
N21 2 2
exp~ –~2n – 1! g ~t!!
Sp,N~t! 5 (
n51 ~2n – 1!2

1
N
~2N – 1!2
exp@ –~ 2N – 1 !2 2
g ~ t !# – S D
p1/2
2 g~t! erfc@~2N – 1! g~t!#
(A1.7)

with:
p~Det!1/2
g~t! 5 H (A1.8)

and the error term:

FIG. A1.1 A Flow Chart of the Major Functions of the Accelerated

0 , Ep,N~t! ,
1
6~2N – 1! F
g2~t! 1
2
~2N – 1!2 G
exp@ –~2N – 1!2 g2~t!#
Leach Test Computer Program (A1.9)

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 C 1308 – 08
TABLE A1.1 Values of the Parameters bm for m = 1 to 20A
m bm m bm m bm m bm
1 2.4048255577 6 18.0710639679 11 33.7758202136 16 49.4826098974
2 5.5200781103 7 21.2116366299 12 36.9170983537 17 52.6240518411
3 8.6537279129 8 24.3524715308 13 40.0584257646 18 55.7655107550
4 11.7915344391 9 27.4934791320 14 43.1997917132 19 58.9069839261
5 14.9309177086 10 30.6346064684 15 46.3411883717 20 62.0484691902
A
These parameters satisfy the equation Jo(bm) = 0, with Jo(x) the zeroth order cylindrical Bessel function.

The values n and N represent the series term and the number than 0.5 %, then the model can be taken to represent the
of terms included in the sum. leaching mechanism and can be used to calculate releases over
For the Sc (t) series: long times and scaled to calculate releases from full size
Sc~t! 5 Sc,M~t! 1 Ec,M~t! (A1.10) cylinders. If the value of ER is greater than 0.5 %, then the
model cannot be used to make reliable projections in time or
M21
exp~ –bm2u2~t!! scale.
Sc,M~t! 5 (
m51 bm2 A1.3.3.3 Diffusion Plus Partitioning of the Species of
1
F
1 b f 1
M M
1
2bM2
exp@ –b M
2 2
u G
~ t !# –
p1/2 u~t!
fM erfc@bM u~t!#
Interest—This is an empirical model in which a fraction of the
species of interest is not available for release to solution
(A1.11) because of adsorption, sequestration in an alteration phase,
with: sequestration into a more durable phase, etc. The effect of the
1 partitioning is to decrease the amount of the species of interest
fM 5 p – , M .. 1 (A1.12) in the source term (Ao) by a source term partitioning factor P,
8pM2
where 0 < P < 1. The partitioned fraction may be leached at a
~Det!1/2 lower rate, although this is not modeled.
u~t! 5 R (A1.13)

and the error term:

(an
CFL 5 P · A 5 2 V p
o
F G
S Det 1/2
(A1.15)
fM
Ec,M~t! , 6b
M
F u2~t! 1
1
bM2 G
exp@ –bM2 u2~t!# (A1.14) The Partition Model allows uncertainty in the concentration
and distribution of the species of interest in the test material
The values m and M represent the series term and the number itself (that is, the source term) to be identified and taken into
of terms included in the sum. Only the first 10 values of bm are account. That is, the appearance of partitioning in the test
used in the computer program. results may actually indicate an error in the source term value
A1.3.3 The computer program provides plots of the experi- or an artifact in the test sample. From Eq A1.15, the linear
mental data and a curve calculated from the model that best fits impact of P on CFL can also arise due to errors in the values
the data. This is done through an iterative method that of S or V.
optimizes the fit to the entire data curve (see logic flow diagram A1.3.3.4 Solubility-Limited Leaching (Dissolution)—This
in Fig. A1.1). Data sets are evaluated using several models model accounts for systems in which diffusion is affected by
sequentially and the results provided to the user. the limited solubility of the species of interest, which may be
A1.3.3.1 Diffusion Through a Semi-Infinite Cylinder—The established by a phase within the solid or an alteration phase
semi-infinite solid model is used if CFL values are less than formed during the test. The Solubility Model is based on the
0.2. It is also used to determine the value of the ad hoc term concept that the incremental fractions leached will be the same
used to take into account the non-zero y-intercept commonly at the end of each 1-day sampling interval if the solution
seen in diffusion tests. concentration of the species of interest is solubility-limited.
A1.3.3.2 Diffusion through a Finite Cylinder—This model Although solubility-limited release should be apparent in plots
is used for CFL > 0.2. The solution to the finite cylinder of CFL versus time and IFL versus time, the model quantifies
equation that is used in the program was developed by the likelihood. The mean and standard deviation of the incre-
Pescatore (4, 9). This method is particularly attractive because mental releases are calculated and the coefficient of variation is
it becomes asymptotic at high fractional releases while using expressed as a percentage of the mean using the following
relatively little computer time. The program calculates model equation:
CFL values for the experimental test durations using various
values of De. The optimum value of De is determined by
minimizing the sum of the squared residuals of the measured
100
VR 5 –
x
Œ( ~n – 3!
–
~IFL – x !2
(A1.16)
and modeled CFL values. The relative error in fit (that is, the
goodness of fit) is calculated by normalizing the sum by the where the sum is over the samplings intervals beyond the
squared residual of the longest-duration data point and pre- second, IFL is the incremental fraction leached during an
sented as the percentage value ER2. The value of has no interval, and –x is the mean of the n-2 IFL values that are
statistical significance, but provides a relative measure of included in the sum. Solubility is considered to limit the
confidence for extrapolation. In general, if the “goodness of fit” measured release if the coefficient of variation is less than 10 %
between the data curve and the model gives an ER2 value less of the mean.

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 C 1308 – 08
A1.3.4 These processes were observed in studies with A1.4.2.6 Default Times (standard ALT)—The default times
various materials during development of the test method (3, 8). are 2, 5, 17, and 24 hours for the first four intervals and the 1.0
Theoretical background for each mechanism is given in Ap- days for the next 10 intervals, for a total test duration of 11
pendix A of the Users’ Guide (2). days.
A1.3.5 The results of the ALT program are presented in A1.4.2.7 Sample Diameter (cm)—Diameter of the specimen
several forms. Tables of data and associated parameters (for that was leached.
example, the values of the IFL, CFL, variance, and relative A1.4.2.8 Sample Height (cm)—Height of the specimen that
error in the fit, ER2) are displayed on the screen and can be was leached.
printed. Graphs of CFL plotted as a function of time are A1.4.2.9 Counting Sample Volume (mL)—The volume of
generated on screen and contain both experimental data points the aliquot used for radionuclide counting.
and the curve produced by the model. In addition, graphs are A1.4.2.10 Source Term Multiplication Factor—The factor
available in which the experimental data are plotted on the by which the original source solution was diluted to make the
x-axis and model-generated values are plotted on the y-axis. counting standard. For example, 3 mL of tracer were added to
This type of plot allows easy comparison of the relationship a specimen when it was made and 1 mL of that solution was
between the data and the model results. If the test has been run diluted 1000-fold to produce the standard that was counted.
at three or more temperatures, the activation energy (k) can be The multiplication factor would be 3000 (regardless of the total
determined by the program. Projections of future releases and volume of source solution that was made).
for full-scale waste forms can be made if diffusion is found to A1.4.2.11 Detailed instructions, in a screen-by-screen for-
be the rate-limiting step in the leaching mechanism. mat, are given in the User’s Guide (2).
A1.5 Errata in the Users’ Guide (2)
A1.4 Running the Program
NOTE A1.1—Based on comparison with reference (4), there are several
A1.4.1 The program starts by giving the user eight options, typographical errors in the User’s Guide for Accelerated Leach Test
including entering new (raw) data, entering data in the form of Computer Program (2). The following refer to equations in Appendix A of
CFL, retrieving data from files, or editing data. Key F1 the User’s Guide (2).
provides explanations of these choices. A1.5.1 The first term in Eq. 5 should be:
A1.4.1.1 Some prompts in this program have default an-
exp~ –~2n – 1!2g2~t!!
N21
swers that appear in brackets. Pressing “ENTER” will select Sp,N~t! 5 (
n51 ~2n – 1!2
the default choice.
A1.4.2 Inputs required by various portions of the program
are explained in A1.4.2.1-A1.4.2.10.
1
N
~2N – 1!
2 2
2 exp@ –~2N – 1 ! g ~t !# –
p1/2
S D
2 g~t! erfc@~2N – 1! g~t!#
(A1.17)
A1.4.2.1 Multiple Source Term Data—Some data require a
new value for the source term for each interval. This would be A1.5.1.1 There are 2 errors in the User’s Guide: The first
necessary for a very short half-life radionuclide. The source term in exponent of the first term on the right hand side (2n-1)2
term value that is input here is the number of counts from a is incorrectly written as (2-1)2 in the User Manual. The
standard. Corrections for dilutions are made automatically. The complimentary error function erfc is incorrectly written as efrc
standard counts are separated by a comma from the leachate in the User Manual.
counts. A1.5.2 The first term in Eq. 6 should be:
A1.4.2.2 Single Source Term Data—Some data require only exp~ –bm2u2~t!!
M21

a single value for the source term throughout the entire

Sc,M~t! 5 (
m51 bm2
experiment. This can be in the form of counts per minute
(CPM) or as concentration (for stable elements). For some
1
F
1 b f 1
M M
1
2bM G 2 2
2 exp@ –bM u ~t !# –
p1/2 u~t!
fM erfc@bM u~t!#
specimens that are radioactive, liquid standards may not be (A1.18)
available. In this case, the activity in the specimen should be A1.5.2.1 There are 3 errors in the User’s Guide: The first
calculated. This value can be input as “concentration” in the term in exponent of the first term on the right hand side
single source term option. exp(-bm2u2(t)) is incorrectly written as exp(-bmu2(t)). Brackets
A1.4.2.3 Number of Sampling Increments—This is the num-
ber of samplings in the experiment. The default value is 13 for @
around the second term 1 / bMfM 1 1 2bM2 are missing. / #
the standard ALT sampling times. The pre-exponential in the far right term incorrectly takes the
square root of u(t).
A1.4.2.4 Number of Species—This input is the number of
A1.5.3 The last term in Eq. 6 (the error term) should be:
elements or radionuclides analyzed in each set of leachate
samples that need to be addressed by the program. A maximum
of eight species is allowed in each data file.
fM
Ec,M~t! , 6b
M
F u2~t! 1
1
bM2Gexp@ –bM2 u2~t!# (A1.19)

A1.4.2.5 Leachate Volume—This is the volume of leachate A1.5.3.1 There is 1 error in the User’s Guide: The numera-
used during each sampling interval. The test method recom- tor of the pre-exponential term is incorrectly written as p rather
mends 3 litres. than fM.

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 C 1308 – 08

A2. UNCERTAINTY

A2.1 It is recommended that the contributions of the A2.2.1 For example, the surface area of a 2.5 3 2.5 cm right
parameters used to calculate a value of interest (for example, cylinder is 29.45 cm2. If the diameter and height are measured
CFL, De, Ea) be combined to estimate the uncertainty in the to a precision of 0.01 cm, then the standard uncertainty in the
calculated value following the recommendations in (9). surface area is 0.176 cm2, and the relative standard deviation is
A2.1.1 Each component used in a calculation contributes a 0.596 %.
standard uncertainty ui to the result. The uncertainty in a
parameter may be due to a single measurement or the propa- A2.3 The combined standard uncertainty can be multiplied
gation of the uncertainties in several measurements. by a coverage factor, k, to represent an uncertainty range at a
A2.1.2 The parameters contributing to various values cal- given confidence level. The value of k varies with the confi-
culated within this standard are summarized in Table A2.1. The dence level; for example, k=2 represents the 95.45 % confi-
variables used to represent the parameters in this standard are dence level. The product of k and uc (y) gives the expanded
included for convenience. Values of ui, are usually represented uncertainty U about the measurand y, such that any measured
as a relative standard deviation and are assigned by the user value Y is expected to lie within the range y–U # Y # y+U at
based on experimental variables. the confidence level used to calculate U.

A2.2 The estimated standard deviation of a result y is A2.4 The combined standard uncertainty does not include
represented by the combined standard uncertainties of the systematic uncertainties such as laboratory or operator bias. It
measurements that contribute to the result uc. The combined may be possible to estimate systematic uncertainties based on
standard uncertainty in the measurand y, uc (y), is calculated by previous measurements in the same or other laboratory, expe-
propagating the uncertainties using the root-sum-of-squares rience with the behavior of similar materials, literature reports,
method. and manufacturer’s specifications.

TABLE A2.1 Contributions to Uncertainties in Parameters and Calculated Values

Parameter Variable ui Main Contributors to Uncertainty
Source term in specimen Ao Analytical uncertainty, homogeneity of source material
Specimen radius R Measured dimensions (half of measured diameter)
Specimen height H Measured dimensions
Specimen surface area S Measured dimensions (diameter and height); geometry
Volume of specimen V Measured dimensions (diameter and height); geometry
Concentration in sample ai Analytical uncertainty
Volume of leachant — Density (if leachant volume determined by weight)
Mass of leachant — Measurement accuracy (if leachant volume determined by weight)
Volume or mass of counting sample — Measurement accuracy
Source term multiplication factor — Measurement accuracy, analytical uncertainty
Incremental fraction leached IFL Measured concentration in leachate, volume leachate, volume analytical sample, source term
Cumulative fraction leached CFL Uncertainty in contributing IFL
Time (interval or cumulative) t Precision of interval time; fraction of time at temperature
Effective diffusion coefficient (at temperature) De(T) CFL values, regression of CFL values, permitted deviation in regression
Temperature T Thermometer reading, thermocouple calibration
Activation energy Ea Regression of De(T), measured T

REFERENCES

(1) Hespe, E. D., “Leach Testing of Immobilized Radioactive Waste (5) Dougherty, D. R., Pietrzak, R. F., Fuhrmann, M., and Colombo, P., “An
Solids, A Proposal for a Standard Method,” Atomic Energy Review, Experimental Survey of Factors that Affect Leaching from Low-Level
Vol 9, No. 1, pp. 195–207, April, 1971. Radioactive Waste Forms,” Topical Report, BNL-52125, Brookhaven
(2) Fuhrmann, M., Heiser, J., Pietrzak, R. F., Franz, E. M., and Colombo, National Laboratory, Upton, NY, September 1988.
P., “Accelerated Leach Test Method and Users’ Guide for the “ALT” (6) Fuhrmann, M., Pietrzak, R. F., Heiser, J., Franz, E. M., and Colombo,
Computer Program,” BNL-52267, Brookhaven National Laboratory, P., Accelerated Leach Test Development Program, BNL-52270,
Upton, NY, October 1990. Brookhaven National Laboratory, Upton, NY, October 1990.
(3) Fuhrmann, M., Pietrzak, R. F., Franz, E. M., Heiser, J. H., and (7) Fuhrmann, M., and Kalb, P. D., “Leaching Behavior of Polyethylene
Colombo, P., “Optimization of the Factors that Accelerated Leaching,” Encapsulated Nitrate Waste,” Stabilization and Solidification of Haz-
Topical Report, BNL-52204, Brookhaven National Laboratory, Upton, ardous, Radioactive and Mixed Wastes, STP 1240, T. M. Gilliam and
NY, March 1989. C. C. Wiles, Eds. American Society for Testing and Materials,
(4) Pescatore, C., “Improved Expressions of Modeling Diffusive, Frac- Philadelphia, 1993.
tional Cumulative Leaching from Finite Size Waste Forms,” Waste (8) Fuhrmann, M., Pietrzak, R. F., Heiser, J., Franz, E. M., and Colombo,
Management, Vol 10, 1990, pp. 155–159. P., “The Effects of Temperature on the Leaching Behavior of Cement

Copyright by ASTM Int'l (all rights reserved); Thu Apr 16 08:52:09 EDT 2009 13
Downloaded/printed by
Laurentian University pursuant to License Agreement. No further reproductions authorized.
 C 1308 – 08
Waste Forms—The Cement/Sodium Sulfate System,” Scientific Basis (9) NIST Guidelines for Evaluating and Expressing the Uncertainty of
for Nuclear Waste Management XIII, Materials Research Society NIST Measurement Results, NIST Technical Note 1297 (1994).
Symposium Proceedings, Vol 176, 1990, pp. 75–80.

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