ASTM C1733-21

Standard Test Method for Distribution Coefficients of Inorganic Species by Batch Method

SIGNIFICANCE AND USE
4.1 The distribution coefficient, Kd, is an experimentally determined ratio quantifying the distribution of a chemical species between a given fluid and solid material sample under certain conditions, including the attainment of constant aqueous concentrations of the species of interest. The Kd concept is used in mass transport modeling, for example, to assess the degree to which the movement of a species will be delayed by interactions with the local geomedium as the solution migrates through the geosphere under a given set of underground geochemical conditions (pH, temperature, ionic strength, etc.). The retardation factor (Rf) is the ratio of the velocity of the groundwater divided by the velocity of the contaminant, which can be expressed as:
   where:  
  ρb  =  bulk density of the porous medium (mass/length3), and    ηe  =  effective porosity of the medium (unitless) expressed as a decimal.    
4.2 Because of the sensitivity of Kd to site specific conditions and materials, the use of literature derived  Kd values is strongly discouraged. For applications other than transport modeling, batch Kd measurements also may be used, for example, for parametric studies of the effects of changing chemical conditions and of mechanisms related to the interactions of fluids with solid material.
SCOPE
1.1 This test method covers the determination of distribution coefficients, Kd, of chemical species to quantify uptake onto solid materials by a batch sorption technique. It is a laboratory method primarily intended to assess sorption of dissolved ionic species subject to migration through pores and interstices of site specific geomedia, or other solid material. It may also be applied to other materials such as manufactured adsorption media and construction materials. Application of the results to long-term field behavior is not addressed in this method. Kd for radionuclides in selected geomedia or other solid materials are commonly determined for the purpose of assessing potential migratory behavior of contaminants in the subsurface of contaminated sites and out of a waste form and in the surface of waste disposal facilities. This test method is also applicable to studies for parametric studies of the variables and mechanisms which contribute to the measured Kd.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Jan-2021
• ICS: 13.080.99 - Other standards related to soil quality
• ICS: 71.040.40 - Chemical analysis
• Technical Committee: C26 - Nuclear Fuel Cycle
• Drafting Committee: C26.13 - Spent Fuel and High Level Waste

Relations

• Refers: ASTM C859-24 - Standard Terminology Relating to Nuclear Materials
• Effective Date: 01-Jan-2024
• Refers: ASTM D4448-01(2019) - Standard Guide for Sampling Ground-Water Monitoring Wells
• Effective Date: 01-Feb-2019
• Refers: ASTM D2488-17 - Standard Practice for Description and Identification of Soils (Visual-Manual Procedures)
• Effective Date: 15-Jul-2017
• Refers: ASTM C859-14a - Standard Terminology Relating to Nuclear Materials
• Effective Date: 15-Jun-2014
• Refers: ASTM E177-14 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• Effective Date: 01-May-2014
• Refers: ASTM C859-14 - Standard Terminology Relating to Nuclear Materials
• Effective Date: 15-Jan-2014
• Refers: ASTM C859-13a - Standard Terminology Relating to Nuclear Materials
• Effective Date: 01-Jun-2013
• Refers: ASTM E691-13 - Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
• Effective Date: 01-May-2013
• Refers: ASTM E177-13 - Standard Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• Effective Date: 01-May-2013
• Refers: ASTM C859-13 - Standard Terminology Relating to Nuclear Materials
• Effective Date: 01-May-2013
• Refers: ASTM D4448-01(2013) - Standard Guide for Sampling Ground-Water Monitoring Wells
• Effective Date: 01-Apr-2013
• Refers: ASTM D1293-12 - Standard Test Methods for pH of Water
• Effective Date: 01-Jan-2012
• Refers: ASTM E691-11 - Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
• Effective Date: 01-Nov-2011
• Refers: ASTM D3370-10 - Standard Practices for Sampling Water from Closed Conduits
• Effective Date: 01-Dec-2010
• Refers: ASTM C859-10b - Standard Terminology Relating to Nuclear Materials
• Effective Date: 01-Nov-2010

Overview

ASTM C1733-21: Standard Test Method for Distribution Coefficients of Inorganic Species by Batch Method provides a laboratory procedure to determine the distribution coefficient (Kd) of chemical species. The Kd measures the distribution of a chemical between a fluid and a solid, reflecting uptake onto solid materials by a batch sorption technique. This test method plays a crucial role in evaluating how dissolved inorganic species-like ions and radionuclides-migrate through geomedia or other porous materials under specific geochemical conditions such as pH, temperature, and ionic strength.

Determining Kd is especially significant for environmental management, groundwater modeling, nuclear waste disposal, and contaminant transport assessment. The batch method provides empirical data essential for mass transport modeling and for understanding contaminant retardation as fluids move through soils, rocks, or engineered barriers.

Key Topics

• Distribution Coefficient (Kd): Quantifies the ratio of a substance adsorbed on a solid to that remaining in solution under equilibrium conditions. Expressed typically in units of mL/g, it summarizes the collective effect of sorption processes including adsorption, ion exchange, and precipitation.
• Batch Sorption Technique: Involves mixing a known mass of solid and a defined volume of contaminant solution, allowing interaction, and measuring concentrations after equilibrium is reached.
• Site-Specific Relevance: Kd values are highly dependent on the specific materials and conditions tested. Using literature values for Kd is discouraged; direct laboratory determination for each site or material is essential for accuracy.
• Influencing Factors: Sorption and distribution are strongly affected by parameters like pH, redox conditions, ionic strength, mineralogy, organic content, and particle size of the solid medium.
• Retardation Factor (Rf): Kd values inform the calculation of the retardation factor, which quantifies the extent to which contaminants move slower than groundwater due to interactions with the geomedia.

Applications

• Contaminant Transport Modeling: Used to predict the movement and retardation of inorganic species, including radionuclides, through groundwater and geological formations.
• Nuclear Waste Management: Provides data to assess the potential migration of radionuclides from spent fuel or waste forms into the environment, supporting safety assessments for disposal facilities.
• Site Remediation: Informs decision-making for remediation of contaminated sites by evaluating how site-specific soils or rocks affect contaminant mobility.
• Material Evaluation: Used to test manufactured adsorption media and construction materials for their sorption capacity and behavior when exposed to contaminant-bearing fluids.
• Parametric and Mechanistic Studies: Supports studies examining the effects of changing geochemical parameters and the mechanisms driving sorption processes under varying laboratory conditions.

Related Standards

Several referenced ASTM standards may be relevant when conducting Kd determinations under ASTM C1733-21, including:

• ASTM C859: Terminology Relating to Nuclear Materials
• ASTM D1293: Test Methods for pH of Water
• ASTM D2217: Practice for Wet Preparation of Soil Samples for Particle-Size Analysis and Determination of Soil Constants
• ASTM D2488: Practice for Description and Identification of Soils (Visual-Manual Procedures)
• ASTM D3370: Practices for Sampling Water from Flowing Process Streams
• ASTM D4448: Guide for Sampling Ground-Water Monitoring Wells
• ASTM E177: Practice for Use of the Terms Precision and Bias in ASTM Test Methods
• ASTM E691: Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method

Practical Value

ASTM C1733-21 is an essential standard for laboratories, environmental consultants, and nuclear waste managers requiring robust, reproducible testing of distribution coefficients for inorganic species. Reliable Kd data support accurate environmental risk models, compliance with regulatory expectations, and development of site-specific mitigation strategies. The test's strong emphasis on real-site materials and conditions ensures that results are scientifically defensible and practically relevant for environmental and engineering applications.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: C1733 − 21
Standard Test Method for
Distribution Coefficients of Inorganic Species by Batch
Method
This standard is issued under the fixed designation C1733; 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.
INTRODUCTION
As an aqueous fluid migrates through geologic media or contacts an engineered material, certain
reactions occur that are dependent upon the chemistry of the fluid itself and upon the chemistry and
geochemistry of other fluids and solid phases with which it comes in contact. These chemical and
geochemicalinteractionsaffecttherelativeratesatwhichchemicalspeciesinthemigratingfluid(such
as ions) travel with respect to the advancing front of water. Processes of potential importance in
retarding the transport of chemical species in the migrating fluid (movement of species at velocities
less than the ground-water velocity) include ion exchange, adsorption, complex formation, precipi-
2+ 2+
tation (or coprecipitation, for example Ba and Ra co-precipitating as a sulfate), redox reactions,
and precipitate filtration. Partitioning may be caused by processes that include adsorption,
precipitation, and coprecipitation that cannot be described easily by equations and, furthermore, these
solute removal mechanisms may not instantaneously respond to changes in prevailing conditions and
may not be entirely reversible.
An empirical ratio known as the distribution coeffıcient (K ) is defined as the mass of the solute on
d
the solid phase per unit mass of solid phase divided by the mass of solute in solution per unit volume
of the liquid phase (Eq 1).This ratio has been used to quantify the collective effects of these processes
for the purpose of modeling (usually, but not solely, applied to ionic species). K is used to assess the
d
degreetowhichachemicalspecieswillberemovedfromsolution(permanentlyortemporarily)asthe
fluidmigratesthroughthegeologicmediumorcontactsasolidmaterial;thatis, K isusedtocalculate
d
the retardation factor that quantifies how rapidly an ion can move relative to the rate of ground-water
movement.
This test method is for the laboratory determination of the K , which may be used by qualified
d
experts for estimating the retardation of contaminants for given underground geochemical conditions
based on a knowledge and understanding of important site-specific factors. It is beyond the scope of
this test method to define the expert qualifications required, or to justify the application of laboratory
data for modeling or predictive purposes. Rather, this test method is considered as simply a
measurement technique for determining the degree of partitioning between liquid and solid, under a
certain set of conditions, for the species of interest.
Justification for the K concept is generally acknowledged to be based on expediency in
d
modeling-averaging the effects of attenuation reactions. In reference to partitioning in soils,
equilibrium is assumed although it is known that this may not be a valid assumption in many cases.
The K for a specific chemical species may be defined as the ratio of the mass sorbed per unit of
d
solid phase to the mass remaining per unit of solution, as expressed in the above equation. The usual
units of K are mL/g (obtained by dividing g solute/g solid by g solute/mL solution, using
d
concentrations obtained in accordance with this test method).
Major difficulties exist in the interpretation, application, and meaning of laboratory-determined K
d
values relative to a real system of aqueous fluid migrating through geologic media (1). The K
d
concept is based on an equilibrium condition for given reactions, which may not be attained in the
natural situation because of the time-dependence or kinetics of specific reactions involved. Also,
migrating solutions always follow the more permeable paths of least resistance, such as joints and
fractures, and larger sediment grain zones.This tends to allow less time for reactions to occur and less
sediment surface exposure to the migrating solution, and may preclude the attainment of local
chemical equilibrium.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1733 − 21
Sorption phenomena also can be strongly dependent upon the concentration of the species of
interest in solution. Therefore, experiments performed using only one concentration of a particular
chemical species may not be representative of actual in situ conditions or of other conditions of
primary interest. Similarly, experimental techniques should consider all ionic species anticipated to be
present in a migrating solution, in order to address competing ion and ion complexation effects, which
may strongly influence the sorption of a particular species.
Sorption can be strongly controlled by pH.Therefore, in situ pH, especially of groundwater, should
be considered in determinations of K . Values of pH must be determined, preferably in the field when
d
materials are sampled and must be carefully determined in the laboratory procedure. Other in situ
conditions (for example, ionic strength, anoxic conditions, or temperature) could likewise have
considerable effect on the K and need to be considered for each situation.
d
Site-specific materials must be used in the measurement of K . This is because the determined K
d d
values are dependent upon rock and soil properties such as the mineralogy (surface charge and
energy), particle size distribution (surface area), and biological conditions (for example, bacterial
growth and organic matter). Special precautions may be necessary to assure that the site-specific
materials are not significantly changed prior to laboratory testing. This may require refrigeration or
freezing of both soil and water samples. Chemical means of preservation (such as addition of acid to
groundwater) will cause changes in sample chemistry and must be avoided.
The choice of fluid composition for the test may be difficult for certain contaminant transport
studies. In field situations, the contaminant solution moves from the source through the porous
medium.As it moves, it displaces the original ground water, with some mixing caused by dispersion.
If the contaminant of interest has a K of any significant magnitude, the front of the zone containing
d
this contaminant will be considerably retarded. This means that the granular medium encountered by
the contaminant has had many pore volumes of the contaminant source water pass through it. The
exchange sites achieve a different population status and this new population status can control the
partitioningthatoccurswhentheretardedcontaminantreachesthepointofinterest.Itisrecommended
that ground water representative of the test zone (but containing added tracers) be used as contact
liquid in this test, or a carefully prepared simulated (site-specific) groundwater; concentrations of
potential contaminants of interest used in the contact liquid should be judiciously chosen. For studies
of interactions with intrusion waters, the site-specific ground water may be substituted by liquids of
other compositions.
TheK foragivenchemicalspeciesgenerallyassumesadifferentvaluewhenconditionsarealtered.
d
Clearly, a very thorough understanding of the site-specific conditions that determine their values is
required if one is to confidently apply the K concept to migration evaluation and prediction.
d
The most convenient method of determining K is probably the batch method (this test method), in
d
which concentrations of the chemical species in solid and liquid phases, which are in contact with one
another, are measured. Other methods include dynamic column flow-through methods using
continuous input of tracer or pulsed input. In the field, a dual tracer test can be conducted using a
conservative(non-sorbing)tracerandonethatdoessorb;fromthedifferenceintraveltimesofthetwo
tracers, K can be calculated.
d
In summary, the distribution coefficient, K , is affected by many variables, some of which may not
d
be adequately controlled or measured by the batch method determination. The application of
experimentally determined K values for predictive purposes must be done judiciously by qualified
d
experts with a knowledge and understanding of the important site-specific factors. However, when
properly combined with knowledge of the behavior of chemical species under varying physicochemi-
cal conditions of the solid surface (or geomedia) and the migrating fluid, K can be used for assessing
d
the rate of migration of chemical species through a saturated geomedium.
This test method is under the jurisdiction of ASTM Committee C26 on Nuclear Fuel Cycle and is the direct responsibility of Subcommittee C26.13 on Spent Fuel and
High Level Waste.
Current edition approved Feb. 1, 2021. Published March 2021. Originally approved in 2010. Last previous edition approved in 2017 as C1733 – 17a. DOI:
10.1520/C1733-21.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
C1733 − 21
1. Scope E691 Practice for Conducting an Interlaboratory Study to
Determine the Precision of a Test Method
1.1 This test method covers the determination of distribu-
tion coefficients, K , of chemical species to quantify uptake
d
3. Terminology
onto solid materials by a batch sorption technique. It is a
laboratory method primarily intended to assess sorption of 3.1 Definitions:
3.1.1 Please refer to Terminology C859 for additional ter-
dissolved ionic species subject to migration through pores and
interstices of site specific geomedia, or other solid material. It minology which may not be listed below.
3.2 Definitions of Terms Specific to This Standard:
may also be applied to other materials such as manufactured
adsorption media and construction materials. Application of 3.2.1 distribution coeffıcient, K,n—the concentration of a
d
species sorbed on a solid material, divided by its concentration
the results to long-term field behavior is not addressed in this
method. K for radionuclides in selected geomedia or other in solution in contact with the solid material, under constant
d
concentration conditions, as follows:
solid materials are commonly determined for the purpose of
assessing potential migratory behavior of contaminants in the
mass of solute on the solid phase per unit mass of solid phase
K 5
subsurface of contaminated sites and out of a waste form and d
mass of solute in solution per unit volume of the liquid phase
in the surface of waste disposal facilities. This test method is
(1)
alsoapplicabletostudiesforparametricstudiesofthevariables
3.2.1.1 Discussion—By constant concentration conditions,
and mechanisms which contribute to the measured K .
d
it is meant that the K values obtained for samples exposed to
d
1.2 The values stated in SI units are to be regarded as
the contact liquid for two different time periods (at least one
standard. No other units of measurement are included in this day apart), other conditions remaining constant, shall differ by
standard.
not more than the expected precision for this test method. It is
convenienttoexpressK inunitsofmL(orcm )ofsolutionper
d
1.3 This standard does not purport to address all of the
gram of solid material.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro- 3.2.2 species, n—specific form of an element defined as to
priate safety, health, and environmental practices and deter-
isotopic composition, electronic or oxidation state, complex or
mine the applicability of regulatory limitations prior to use. molecular structure, or combinations thereof (2).
1.4 This international standard was developed in accor-
3.2.3 tracer, n—an identifiable substance, such as a dye or
dance with internationally recognized principles on standard-
radioactive isotope, that can be followed through the course of
ization established in the Decision on Principles for the
a mechanical, chemical, or biological process.
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
4. Significance and Use
Barriers to Trade (TBT) Committee.
4.1 The distribution coefficient, K , is an experimentally
d
determined ratio quantifying the distribution of a chemical
2. Referenced Documents
species between a given fluid and solid material sample under
2.1 ASTM Standards:
certain conditions, including the attainment of constant aque-
C859 Terminology Relating to Nuclear Materials
ous concentrations of the species of interest. The K concept is
d
D422 Test Method for Particle-SizeAnalysis of Soils (With-
used in mass transport modeling, for example, to assess the
drawn 2016)
degree to which the movement of a species will be delayed by
D1293 Test Methods for pH of Water
interactions with the local geomedium as the solution migrates
D2217 Practice for Wet Preparation of Soil Samples for
through the geosphere under a given set of underground
Particle-Size Analysis and Determination of Soil Con-
geochemical conditions (pH, temperature, ionic strength, etc.).
stants
The retardation factor (R) is the ratio of the velocity of the
f
D2488 Practice for Description and Identification of Soils
groundwater divided by the velocity of the contaminant, which
(Visual-Manual Procedures)
can be expressed as:
D3370 Practices for Sampling Water from Flowing Process
R 5 11 ρ /η K (2)
~ !
Streams f b e d
D4448 Guide for Sampling Ground-Water MonitoringWells
where:
D5730 Guide for Site Characterization for Environmental
ρ = bulk density of the porous medium (mass/length ), and
b
Purposes With Emphasis on Soil, Rock, the Vadose Zone
and Groundwater (Withdrawn 2013)
η = effective porosity of the medium (unitless) expressed as
e
E177 Practice for Use of the Terms Precision and Bias in
a decimal.
ASTM Test Methods
4.2 Because of the sensitivity of K to site specific condi-
d
tions and materials, the use of literature derived K values is
d
strongly discouraged. For applications other than transport
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
modeling, batch K measurements also may be used, for
d
Standards volume information, refer to the standard’s Document Summary page on
example, for parametric studies of the effects of changing
the ASTM website.
chemical conditions and of mechanisms related to the interac-
The last approved version of this historical standard is referenced on
www.astm.org. tions of fluids with solid material.
C1733 − 21
NOTE 1—It is recognized that sampling is likely to be a major problem.
5. Apparatus
Materials (or fractures) that the contaminants pass through are likely to be
5.1 Laboratory Ware (plastic bottles, centrifuge tubes, open
themostdifficultpartofthegeologicsectiontosample.Inaddition,proper
dishes, pipettes), cleaned in a manner consistent with the
sampling entails determining the path of groundwater flow so that the
critical materials can be sampled. This determination is seldom accom-
analyses to be performed and the required precision. Where
plished in sufficient detail in normal geologic site exploration programs,
plateout may have significant effect on the measurement,
and, if it is attempted in some cases, the exploration program may become
certain porous plastics should be avoided and the use of
unacceptably expensive. Specific guidelines are beyond the scope of this
fluorinated ethylene propylene (FEP) or tetrafluoroethylene
test method, however, it is recommended that geologic and water
(TFE) containers is recommended. sampling procedures be carefully considered by the personnel involved in
the site examination.
5.2 Centrifuge, capable of attaining 1400 g, or filtering
apparatus.
7. Procedure
5.3 Filters, filtration apparatus, including syringe filters,
7.1 This test method can be applied directly to unconsoli-
capableofremovingparticlesof≥0.45µm.Filtermediashould
datedmaterialsamplesortodisaggregatedportionsofsamples.
be selected to not sorb species of interest under the experiment
If necessary, ultrasonic methods may be used, although it
conditions. Sorption has been observed on filter media com-
should be noted that the effect of ultrasonics on the microstruc-
posed of certain materials (3).
ture of the material may lead to higher sorption values in
5.4 Laboratory Shaker/Rotator, ultrasonic cleaner (op- certain cases. Chemical dispersants shall not be used.
NOTE 2—A significant source of error with regard to how well the
tional).
experimental environment represents natural conditions may be intro-
5.5 Environmental Monitoring Instruments, a pH meter,
duced by disaggregating the sample in a batch test in that (a) disaggre-
conductance meter, and thermometer. gation can mask a preferred flow path (either horizontal or vertical), (b)
disaggregation can destroy the effect of preferred flow paths caused by
5.6 Analytical Balance capable of measuring to 0.01 g.
fracturesorperhapsthinsandstringers,and (c)disaggregationwilltendto
increase the available surface area of the geologic materials. It is for the
5.7 Appropriate Equipment, necessary to replicate in situ
purpose of achieving uniformity of application, however, that disaggre-
conditions within the laboratory apparatus.
gation is recommended for this test method. It should be realized by
persons applying results from this method that inclusion of the disaggre-
5.8 Analytical Instrumentation, appropriate for determina-
gatingoperationsmayforthesereasonstendtomaximizethevaluesofthe
tion of the concentration of major constituents (cations and
K obtained from this test method. It may be useful to do replicate tests
d
anions) and of the species of interest (for which K is being
d
using as-received and disaggregated samples.
determined) in the contact solutions (and, optionally, in the
7.2 Using standard analytical procedures, characterize the
solid material samples).
solidspecimenasconsideredappropriate(forgeologicsamples
see Guide D5730).
6. Sampling
7.2.1 Analysis of the solid may include percent elemental
6.1 The solid samples of soil, rock, sediment, or other
composition, mineralogy, carbonate content, specific surface
materialsshallbeconsideredtoberepresentativeofthestratum
area (m /g), total organic carbon, and cation and anion ex-
from which it was obtained by an appropriately accepted or
change capacity (at specified pHs).
standard procedure (for example, methods outlined in Guide
7.2.2 Similarly, characterize the contact liquid obtained
D5730) and based on expert judgment.
from the test zone as appropriate for interpreting the results.
Chemical analysis of the liquid should include macro
6.2 The sample shall be carefully identified as to origin in
constituents, pH of the contact liquid (Test Method D1293), as
accordance with Practice D2488.
well as the concentration (if present) of the chemical species of
6.3 When using site specific materials, a geological descrip-
interest.Ifthespeciesofinterestmayexistinthecontactliquid
tion shall be given of the core material used for the K
d
in a variety of valence or chemical states (for example, with
measurement. This may include particle-size analysis (Test
studies of actinides), care with maintaining chemical condi-
Method D422) for unconsolidated material, depth of sample,
tions to preserve speciation is especially important.
and boring location.
7.3 Before completing the actual K determinations, ascer-
d
6.4 Field collected solid phase geomedium samples should
tain the time required for the tracer/solid system to achieve
not be dried. Freezing is recommended for storage of solid
constant solution concentrations for each species of interest.
samples.
This is best done by doing a preliminary K batch experiment
d
6.5 Samplingofrepresentativegroundwaterinthetestzone that is sampled over several time intervals to determine the
for use as the contact liquid in this test method shall be time required to attain constant so
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: C1733 − 20 C1733 − 21
Standard Test Method for
Distribution Coefficients of Inorganic Species by Batch
Method
This standard is issued under the fixed designation C1733; 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.
INTRODUCTION
As an aqueous fluid migrates through geologic media or contacts an engineered material, certain
reactions occur that are dependent upon the chemistry of the fluid itself and upon the chemistry and
geochemistry of other fluids and solid phases with which it comes in contact. These chemical and
geochemical interactions affect the relative rates at which chemical species in the migrating fluid (such
as ions) travel with respect to the advancing front of water. Processes of potential importance in
retarding the transport of chemical species in the migrating fluid (movement of species at velocities
less than the ground-water velocity) include ion exchange, adsorption, complex formation, precipi-
2+ 2+
tation (or coprecipitation, for example Ba and Ra co-precipitating as a sulfate), redox reactions,
and precipitate filtration. Partitioning may be caused by processes that include adsorption,
precipitation, and coprecipitation that cannot be described easily by equations and, furthermore, these
solute removal mechanisms may not instantaneously respond to changes in prevailing conditions and
may not be entirely reversible.
An empirical ratio known as the distribution coeffıcient (K ) is defined as the mass of the solute on
d
the solid phase per unit mass of solid phase divided by the mass of solute in solution per unit volume
of the liquid phase (Eq 1). This ratio has been used to quantify the collective effects of these processes
for the purpose of modeling (usually, but not solely, applied to ionic species). K is used to assess the
d
degree to which a chemical species will be removed from solution (permanently or temporarily) as the
fluid migrates through the geologic medium or contacts a solid material; that is, K is used to calculate
d
the retardation factor that quantifies how rapidly an ion can move relative to the rate of ground-water
movement.
This test method is for the laboratory determination of the K , which may be used by qualified
d
experts for estimating the retardation of contaminants for given underground geochemical conditions
based on a knowledge and understanding of important site-specific factors. It is beyond the scope of
this test method to define the expert qualifications required, or to justify the application of laboratory
data for modeling or predictive purposes. Rather, this test method is considered as simply a
measurement technique for determining the degree of partitioning between liquid and solid, under a
certain set of conditions, for the species of interest.
Justification for the K concept is generally acknowledged to be based on expediency in
d
modeling-averaging the effects of attenuation reactions. In reference to partitioning in soils,
equilibrium is assumed although it is known that this may not be a valid assumption in many cases.
The K for a specific chemical species may be defined as the ratio of the mass sorbed per unit of
d
solid phase to the mass remaining per unit of solution, as expressed in the above equation. The usual
units of K are mL/g (obtained by dividing g solute/g solid by g solute/mL solution, using
d
concentrations obtained in accordance with this test method).
This test method is under the jurisdiction of ASTM Committee C26 on Nuclear Fuel Cycle and is the direct responsibility of Subcommittee C26.13 on Spent Fuel and
High Level Waste.
Current edition approved Feb. 1, 2020Feb. 1, 2021. Published April 2020March 2021. Originally approved in 2010. Last previous edition approved in 2017 as C1733 – 17a.
DOI: 10.1520/C1733-20.10.1520/C1733-21.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1733 − 21
Major difficulties exist in the interpretation, application, and meaning of laboratory-determined K
d
values relative to a real system of aqueous fluid migrating through geologic media (1)). . The K
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concept is based on an equilibrium condition for given reactions, which may not be attained in the
natural situation because of the time-dependence or kinetics of specific reactions involved. Also,
migrating solutions always follow the more permeable paths of least resistance, such as joints and
fractures, and larger sediment grain zones. This tends to allow less time for reactions to occur and less
sediment surface exposure to the migrating solution, and may preclude the attainment of local
chemical equilibrium.
Sorption phenomena also can be strongly dependent upon the concentration of the species of
interest in solution. Therefore, experiments performed using only one concentration of a particular
chemical species may not be representative of actual in situ conditions or of other conditions of
primary interest. Similarly, experimental techniques should consider all ionic species anticipated to be
present in a migrating solution, in order to address competing ion and ion complexation effects, which
may strongly influence the sorption of a particular species.
Sorption can be strongly controlled by pH. Therefore, in situ pH, especially of groundwater, should
be considered in determinations of K . Values of pH must be determined, preferably in the field when
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materials are sampled and must be carefully determined in the laboratory procedure. Other in situ
conditions (for example, ionic strength, anoxic conditions, or temperature) could likewise have
considerable effect on the K and need to be considered for each situation.
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Site-specific materials must be used in the measurement of K . This is because the determined K
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values are dependent upon rock and soil properties such as the mineralogy (surface charge and
energy), particle size distribution (surface area), and biological conditions (for example, bacterial
growth and organic matter). Special precautions may be necessary to assure that the site-specific
materials are not significantly changed prior to laboratory testing. This may require refrigeration or
freezing of both soil and water samples. Chemical means of preservation (such as addition of acid to
groundwater) will cause changes in sample chemistry and must be avoided.
The choice of fluid composition for the test may be difficult for certain contaminant transport
studies. In field situations, the contaminant solution moves from the source through the porous
medium. As it moves, it displaces the original ground water, with some mixing caused by dispersion.
If the contaminant of interest has a K of any significant magnitude, the front of the zone containing
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this contaminant will be considerably retarded. This means that the granular medium encountered by
the contaminant has had many pore volumes of the contaminant source water pass through it. The
exchange sites achieve a different population status and this new population status can control the
partitioning that occurs when the retarded contaminant reaches the point of interest. It is recommended
that ground water representative of the test zone (but containing added tracers) be used as contact
liquid in this test, or a carefully prepared simulated (site-specific) groundwater; concentrations of
potential contaminants of interest used in the contact liquid should be judiciously chosen. For studies
of interactions with intrusion waters, the site-specific ground water may be substituted by liquids of
other compositions.
The K for a given chemical species generally assumes a different value when conditions are altered.
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Clearly, a very thorough understanding of the site-specific conditions that determine their values is
required if one is to confidently apply the K concept to migration evaluation and prediction.
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The most convenient method of determining K is probably the batch method (this test method), in
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which concentrations of the chemical species in solid and liquid phases, which are in contact with one
another, are measured. Other methods include dynamic column flow-through methods using
continuous input of tracer or pulsed input. In the field, a dual tracer test can be conducted using a
conservative (non-sorbing) tracer and one that does sorb; from the difference in travel times of the two
tracers, K can be calculated.
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In summary, the distribution coefficient, K , is affected by many variables, some of which may not
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be adequately controlled or measured by the batch method determination. The application of
experimentally determined K values for predictive purposes must be done judiciously by qualified
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experts with a knowledge and understanding of the important site-specific factors. However, when
properly combined with knowledge of the behavior of chemical species under varying physicochemi-
cal conditions of the solid surface (or geomedia) and the migrating fluid, K can be used for assessing
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the rate of migration of chemical species through a saturated geomedium.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
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1. Scope
1.1 This test method covers the determination of distribution coefficients, K , of chemical species to quantify uptake onto solid
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materials by a batch sorption technique. It is a laboratory method primarily intended to assess sorption of dissolved ionic species
subject to migration through pores and interstices of site specific geomedia, or other solid material. It may also be applied to other
materials such as manufactured adsorption media and construction materials. Application of the results to long-term field behavior
is not addressed in this method. K for radionuclides in selected geomedia or other solid materials are commonly determined for
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the purpose of assessing potential migratory behavior of contaminants in the subsurface of contaminated sites and out of a waste
form and in the surface of waste disposal facilities. This test method is also applicable to studies for parametric studies of the
variables and mechanisms which contribute to the measured K .
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1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
C859 Terminology Relating to Nuclear Materials
D422 Test Method for Particle-Size Analysis of Soils (Withdrawn 2016)
D1293 Test Methods for pH of Water
D2217 Practice for Wet Preparation of Soil Samples for Particle-Size Analysis and Determination of Soil Constants
D2488 Practice for Description and Identification of Soils (Visual-Manual Procedures)
D3370 Practices for Sampling Water from Flowing Process Streams
D4448 Guide for Sampling Ground-Water Monitoring Wells
D5730 Guide for Site Characterization for Environmental Purposes With Emphasis on Soil, Rock, the Vadose Zone and
Groundwater (Withdrawn 2013)
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method
3. Terminology
3.1 Definitions:
3.1.1 Please refer to Terminology C859 for additional terminology which may not be listed below.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 distribution coeffıcient, K , n—the concentration of a species sorbed on a solid material, divided by its concentration in
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solution in contact with the solid material, under constant concentration conditions, as follows:
mass of solute on the solid phase per unit mass of solid phase
K 5 (1)
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mass of solute in solution per unit volume of the liquid phase
3.2.1.1 Discussion—
By constant concentration conditions, it is meant that the K values obtained for samples exposed to the contact liquid for two
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different time periods (at least one day apart), other conditions remaining constant, shall differ by not more than the expected
precision for this test method. It is convenient to express K in units of mL (or cm ) of solution per gram of solid material.
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3.2.2 species, n—specific form of an element defined as to isotopic composition, electronic or oxidation state, complex or
molecular structure, or combinations thereof (2).
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
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3.2.3 tracer, n—an identifiable substance, such as a dye or radioactive isotope, that can be followed through the course of a
mechanical, chemical, or biological process.
4. Significance and Use
4.1 The distribution coefficient, K , is an experimentally determined ratio quantifying the distribution of a chemical species
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between a given fluid and solid material sample under certain conditions, including the attainment of constant aqueous
concentrations of the species of interest. The K concept is used in mass transport modeling, for example, to assess the degree to
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which the movement of a species will be delayed by interactions with the local geomedium as the solution migrates through the
geosphere under a given set of underground geochemical conditions (pH, temperature, ionic strength, etc.). The retardation factor
(R ) is the ratio of the velocity of the groundwater divided by the velocity of the contaminant, which can be expressed as:
f
R 5 11~ρ /η ! K (2)
f b e d
where:
ρ = bulk density of the porous medium (mass/length ), and
b
η = effective porosity of the medium (unitless) expressed as a decimal.
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4.2 Because of the sensitivity of K to site specific conditions and materials, the use of literature derived K values is strongly
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discouraged. For applications other than transport modeling, batch K measurements also may be used, for example, for parametric
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studies of the effects of changing chemical conditions and of mechanisms related to the interactions of fluids with solid material.
5. Apparatus
5.1 Laboratory Ware (plastic bottles, centrifuge tubes, open dishes, pipettes),cleaned in a manner consistent with the analyses to
be performed and the required precision. Where plateout may have significant effect on the measurement, certain porous plastics
should be avoided and the use of fluorinated ethylene propylene (FEP) or tetrafluoroethylene (TFE) containers is recommended.
5.2 Centrifuge, capable of attaining 1400 g, or filtering apparatus.
5.3 Filters, filtration apparatus, including syringe filters, capable of removing particles of ≥0.45 μm. Filter media should be
selected to not sorb species of interest under the experiment conditions. Sorption has been observed on filter media composed of
certain materials (3).
5.4 Laboratory Shaker/Rotator, ultrasonic cleaner (optional).
5.5 Environmental Monitoring Instruments, a pH meter, conductance meter, and thermometer.
5.6 Analytical Balance capable of measuring to 0.01 g.
5.7 Appropriate Equipment, necessary to replicate in situ conditions within the laboratory apparatus.
5.8 Analytical Instrumentation, appropriate for determination of the concentration of major constituents (cations and anions) and
of the species of interest (for which K is being determined) in the contact solutions (and, optionally, in the solid material samples).
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6. Sampling
6.1 The solid samples of soil, rock, sediment, or other materials shall be considered to be representative of the stratum from which
it was obtained by an appropriately accepted or standard procedure (for example, methods outlined in Guide D5730) and based
on expert judgment.
6.2 The sample shall be carefully identified as to origin in accordance with Practice D2488.
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6.3 When using site specific materials, a geological description shall be given of the core material used for the K measurement.
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This may include particle-size analysis (Test Method D422) for unconsolidated material, depth of sample, and boring location.
6.4 Field collected solid phase geomedium samples should not be dried. Freezing is recommended for storage of solid samples.
6.5 Sampling of representative ground water in the test zone for use as the contact liquid in this test method shall be accomplished
in accordance with Practices D4448 and D3370, using sampling devices that will not change the quality or environmental
conditions of the waters to be tested. Proper precautions should be taken to preserve the integrity of in situ conditions of the
sampled water, and in particular to protect against oxidation-reduction, exposure to light for extended periods, and temperature
variations. Chemical methods of preservation, such as acidification, shall not be used.
NOTE 1—It is recognized that sampling is likely to be a major problem. Materials (or fractures) that the contaminants pass through are likely to be the
most difficult part of the geologic section to sample. In addition, proper sampling entails determining the path of groundwater flow so that the critical
materials can be sampled. This determination is seldom accomplished in sufficient detail in normal geologic site exploration programs, and, if it is
attempted in some cases, the exploration program may become unacceptably expensive. Specific guidelines are beyond the scope of this test method,
however, it is recommended that geologic and water sampling procedures be carefully considered by the personnel involved in the site examination.
7. Procedure
7.1 This test method can be applied directly to unconsolidated material samples or to disaggregated portions of samples. If
necessary, ultrasonic methods may be used, although it should be noted that the effect of ultrasonics on the microstructure of the
material may lead to higher sorption values in certain cases. Chemical dispersants shall not be used.
NOTE 2—A significant source of error with regard to how well the experimental environment represents natural conditions may be introduced by
disaggregating the sample in a batch test in that (a) disaggregation can mask a preferred flow path (either horizontal or vertical), (b) disaggregation can
destroy the effect of preferred flow paths caused by fractures or perhaps thin sand stringers, and (c) disaggregation will tend to increase the available
surface area of the geologic materials. It is for the purpose of achieving uniformity of application, however, that disaggregation is recommended for this
test method. It should be realized by persons applying results from this method that inclusion of the disaggregating operations may for these reasons tend
to maximize the values of the K obtained from this test method. It may be useful to do replicate tests using as-received and disaggregated samples.
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7.2 Using standard analytical procedures, characterize the solid specimen as considered appropriate (for geologic samples see
Guide D5730).
7.2.1 Analysis of the solid may include percent elemental composition, mineralogy, carbonate content, specific surface area
(m /g), total organic carbon, and cation and anion exchange capacity (at specified pHs).
7.2.2 Similarly, characterize the contact liquid obtained from the test zone as appropriate for interpreting the results. Chemical
analysis of the liquid should include macro constituents, pH of the contact liquid (Test Method D1293), as well as the concentration
(if present) of the chemical species of interest. If the species of interest may exist in the contact liquid in a variety of valence or
chemical states (for ex
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