Technical Background Document NAPL Calc

Calculations and Software to Determine the Presence of Q-CLC-G-00059
Non-Aqueous Phase Liquids in Environmental Media Revision 0
August 2003 Sheet 1 of 44
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OSR 45-24# (Rev 1-10-2000)
Calculation Cover Sheet
Project Method to Determine and Quantify Non-Aqueous
Phase Liquids in Environmental Media
Calculation Number
Q-CLC-G-00059, Rev. 0
Project Number
NA
Title Method and Software to Determine and Quantify
Non-Aqueous Phase Liquids in Environmental Media
Functional Classification
GS
Sheet 1 of 44
Discipline
PE&CD/Environmental
Preliminary Confirmed
Computer Program No. N/A Version/Release No.
NA
Purpose and Objective
The purpose of this calculation is to document the method and equations for the
determination and quantification of non-aqueous phase liquids in environmental media.
Summary of Conclusion – The calculations were successfully performed by the software for three case
scenarios. The case scenarios were computed with the software and the calculations were hand
checked to verify the results.
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Originator (Print)
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0 Gregory G. Rucker Monique Rabin Thomas Gaughan
Release to Outside Agency – Design Authority (Print) Signature Date
Security Classification of the Calculation

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TABLE OF CONTENTS
LIST OF FIGURES .......................................................................................................................3
LIST OF TABLES.........................................................................................................................3
1.0 INTRODUCTION................................................................................................................4
1.1 NAPL Analytical Models...................................................................................................7
2.0 FOUNDATIONS FOR SOFTWARE CALCULATIONS .............................................11
2.1 Assumptions......................................................................................................................11
2.2 Solubility Limit Theory for NAPL.................................................................................12
2.3 Raoult’s Law ....................................................................................................................13
2.4 Equilibrium Partitioning Theory, Mass Balance and Volume Conservation ............15
2.5 Operational and Computation Order............................................................................20
3.0 INPUTS...............................................................................................................................22
4.0 ANALYTICAL METHODS AND CALCULATIONS ..................................................24
4.1 Equation 1 Molar Fraction (from Chemistry, Moeller et al. 1980)..............................24
4.2 Equation 2 Density of Mixture .......................................................................................25
4.3 Equation 3 Effective Solubility (Raoult’s Law from USEPA 1992 and others).........25
4.4 Equation 4 Effective Vapor Pressure.............................................................................26
4.5 Equation 5 Theoretical Soil Pore-Water Concentration..............................................26
4.6 Equation 6 Soil Saturation Limit (Csat) (from USEPA 1996).....................................27
4.7 Equation 7 Soil Pore-Water Concentration ..................................................................27
4.8 Equation 8 Soil Pore-Vapor Concentration ..................................................................27
4.9 Equation 9 Volumetric Soil Pore-Vapor Concentration ..............................................28
4.10 Equation 10 Soil Sorbed Concentration ........................................................................28
4.11 Equation 11 Contaminant Mass in Soil Pore-Water ....................................................29
4.12 Equation 12 Contaminant Mass in Soil Pore-Air .........................................................29
4.13 Equation 13 Contaminant Mass Sorbed to Soil ............................................................29
4.14 Equation 14 NAPL Concentration for Compound.......................................................30
4.15 Equation 15 NAPL Mass.................................................................................................30
4.16 Equation 16 Mass Balance Equation for Compound ...................................................30
4.17 Equation 17 Total Concentration of NAPL in Sample.................................................31
4.18 Equation 18 Percent Residual NAPL Saturation..........................................................31
4.19 Equation 19 Volume Conservation Equation for Soil Sample (Wet Bulk Density)...31
4.20 Equation 20 Volumetric Content of NAPL in Sample .................................................32
4.21 Equation 21 Volumetric Content of Air in Sample.......................................................32
4.22 Equation 22 Volumetric Content of Water in Sample if Θa = 0..................................32
4.23 Equation 23 Volumetric Content of Soil in Sample......................................................33
5.0 RESULTS ...........................................................................................................................34

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6.0 CONCLUSIONS ................................................................................................................41
7.0 REFERENCES...................................................................................................................44
LIST OF FIGURES
FIGURE 1. DENSE NON-AQUEOUS PHASE LIQUID FROM A GROUNDWATER MONITORING
WELL AT THE SAVANNAH RIVER SITE .....................................................................6
FIGURE 2. EXAMPLE OF RAOULT’S LAW CHANGING A COMPONENT SOIL SATURATION
THRESHOLD...............................................................................................................14
FIGURE 3. GRAPH OF MASS DISTRIBUTION FOR SCENARIO #2.................................................39
FIGURE 4. GRAPH OF VOLUME DISTRIBUTION FOR SCENARIO #2............................................39
FIGURE 5. COMPARISON OF PURE PHASE AQUEOUS SOLUBILITY TO SOLUBILITY OF
COMPONENTS IN A MIXTURE ....................................................................................40
LIST OF TABLES
TABLE 1. COMPARISON OF TWO NAPL MODELS....................................................................8
TABLE 2. GEOLOGIC/CHEMICAL SPECIFIC INPUT PROPERTIES FOR TWO COMPARISON
EXAMPLES .................................................................................................................9
TABLE 3. EXAMPLE 1 - COMPARISON OF NAPLANAL AND NAPLATOR MODEL RESULTS .9
TABLE 4. EXAMPLE 2 - COMPARISON OF NAPLANAL AND NAPLATOR RESULTS...............10
TABLE 5. CHEMICAL PROPERTIES FOR SCENARIO #1, #2 AND #3 ...........................................22
TABLE 6. SCENARIO #1 - SOIL CONCENTRATION AND GEOTECHNICAL INPUTS.....................22
TABLE 7. SCENARIO #2 - SOIL CONCENTRATION AND GEOTECHNICAL INPUTS.....................23
TABLE 8. SCENARIO #3 - SOIL CONCENTRATION AND GEOTECHNICAL INPUTS FOR
SATURATED SAMPLE .................................................................................................23
TABLE 9. SCENARIO #1 SOIL SATURATION AND BULK DENSITY RESULTS .............................34
TABLE 10. SCENARIO #1 MEDIA MASSES...................................................................................34
TABLE 11. SCENARIO #1 MEDIA CONCENTRATIONS .................................................................34
TABLE 12. SCENARIO #1 VOLUME AND RESIDUAL SATURATION RESULTS ..............................35

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1.0 INTRODUCTION
Non-Aqueous Phase Liquid or “NAPL” is a term that most environmental professionals are
familiar with because NAPL is well recognized as a significant source of soil and groundwater
contamination. According to the US Environmental Protection Agency 2004, “Since NAPLs are
only slightly soluble in water, NAPL source zones can persist for many decades and in some
cases for the foreseeable future.”
NAPLs can manifest as either single component liquids or as complex, multi-component
mixtures of organic compounds that are slowly released from environmental media, such as
vadose zone soil, where the contaminants will partition into soil pore vapor, soil pore water, and
soil particles and eventually migrate to groundwater (Figure 1). The identification of NAPL in
the environment is complicated because of inter-media transfer within the soils and because of
the altered physical and chemical properties of complex organic mixtures. Complex multi-
component mixtures distributed in soil air, water, and solids can mask their appearance and
complicate their identification.
Soil analytical results can be compared to a simply calculated NAPL soil threshold value to
determine if a single component NAPL may be present in a soil sample. Conversely,
determination of a multi-component NAPL mixture in soil media from analytical soil data is a
different matter and is complicated by the altered physical and chemical properties of the organic
compounds and phases of environmental media that are present. One of the most important
chemical properties used to determine the presence of a NAPL in environmental media is the
solubility limit, although other major properties are also important including vapor organic
carbon and density. For multi-component mixtures, it is important to comprehend the chemical
properties of a mixture will not be exactly the same as any of the pure phase components. This
fact makes the identification of the NAPL more convoluted and also means the NAPL thresholds
will be much lower than may be assumed.

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The above statements suggest a possibility that NAPL may be more frequently encountered at
contaminated waste sites but its presence may accidentally be overlooked or go unrecognized.
This reason may partially explain why some conventional remedial technologies have failed to
effectively clean up contaminated source zones and groundwater plumes. Some groundwater
clean ups have dragged on for decades and can be traced to previously unrecognized NAPL
source zones. Remedial measures that have been implemented where the presence of NAPL has
gone unrecognized, have resulted in longer than predicted clean-up times and rebounding effects
after the remedies have been implemented because persistent NAPL residuals remain trapped in
the soil, where it acted as a continuing source of contamination to the groundwater.
The dynamic alteration of physical properties of NAPL mixtures may disguise its presence in
environmental media during site characterization and remediation, but this doesn’t need to be the
case because there is a solution. The method and software described in this manuscript are
simple yet powerful tools to determine and quantify NAPL mixtures in environmental media.
The analytical method uses a classic chemistry approach and applies the principals of solubility
limit theory, Raoult’s Law, and equilibrium chemistry to derive an accurate estimation of NAPL
quantity.

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(Note: This is a worst-case example of extraction of free product from an aquifer well
indicating mobile DNAPL from a vadose zone source. This sample consists of
tetrachloroethylene, polychlorinated biphenol, and trichloroethylene in order of molar
fraction composition).
Figure 1. Dense Non-Aqueous Phase Liquid from a Groundwater Monitoring Well at
the Savannah River Site

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1.1 NAPL Analytical Models
A search of relevant literature reveals that there may be only two analytical modeling solutions to
quantify NAPL saturation for complex organic mixtures in a soil sample. The models are called
NAPLANAL (Mariner et al. 1997) and NAPL Calculator. NAPLANAL is a stand-alone model
and estimates NAPL saturation, including media concentrations and masses, as well as
estimations of the volume occupied by NAPL. The analytical method for NAPLANAL uses a
system of equations and constraints to solve for unknowns by an iteration process. The iterations
are bounded by a pre-defined degree of precision. While the residual for the NAPLANAL model
is usually very small (less than 1.0 E-6), the solution is not exact and there is some question of
the model’s accuracy when contaminant masses are low (100 mg/kg or less) using this model.
The second model NAPL calculator (NAPLator) has been developed and is the subject of this
calculation note. Its operation builds upon the NAPLANAL model, but uses a different method
of calculation and estimates additional metrics. NAPLator uses different algorithms to converge
on an exact analytical solution. There are no residuals, not even minor ones. The NAPLator
model uses a classic chemistry approach to sequentially solve a series of equations to compute
the molar fraction, effective solubility, density, effective vapor pressure, soil saturation limit,
NAPL mass, NAPL volume, and residual saturation.
Information outputs of the NAPLator include the soil saturation limit, volumetric soil saturation
limit, concentrations contained in each media, masses within each media, total NAPL mass,
NAPL volume within the soil voids, NAPL density, percent composition of the NAPL, total mass
of each contaminant, effective solubility, total solubility of mixtures, effective vapor pressure,
total vapor pressure of the mixture, and built-in graphing capability to illustrate NAPL physical
and chemical properties. Additionally, there is an extended database of physical properties for
approximately 300 chemicals. The model will estimate concentrations for either saturated or
unsaturated media samples while conserving all mass and volume.
Table 1 compares the features of both NAPLANAL and NAPLator.

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Table 1. Comparison of Two NAPL Models
Feature NAPLANAL NAPLator
Operating Platform Stand alone MS Excel©
Calculates NAPL Saturation Yes Yes
Calculates NAPL Volume Yes Yes
Calculates Total NAPL Concentration No, by compound only Yes, by compound and
total
Calculates NAPL Density Yes Yes
Calculates Media Masses No Yes
Calculates Media Concentrations Yes Yes
Calculates Media Volumes Yes Yes
Built-in Data Base of Chemical
Properties
Yes Yes, but huge and more
comprehensive
Calculates Soil Saturation Limit No Yes
Calculates Effective Solubility No Yes
Calculates Effective Vapor Pressure No Yes
Calculates Mixture Properties No Yes
Calculates Volumetric Air
Concentration
No Yes
Provides Graphic Output No Yes
Numerical Accuracy Almost exact with errors at
low concentrations
Exact
Mass Balance for each Compound No Yes
Volumetric Balance Displayed Output Yes Yes
Table 2 lists the input parameters for the comparison examples shown in Table 3 and Table 4.
These tables show examples that compare the accuracy and type of results derived from both
models. In both examples, all the input parameters are kept the same so the models can be
equally compared.

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Table 2. Geologic/Chemical Specific Input Properties for Two Comparison Examples
Input Parameter
Tetrachloroethylene
(PCE)
Trichloroethylene
(TCE)
Molecular Weight (g/mol) 165.85 131.29
Aqueous Solubility (mg/L) 200.0 1100.0
Vapor Pressure (mmHg) 18.47 74.31
Henry’s Law Constant (unitless) 0.943 0.3649
Carbon Partitioning Coefficient (L/kg) 364.0 126.0
Density (kg/L) 1.63 1.46
Fraction Organic Carbon (decimal fraction) 0.0001 .0001
Total Porosity (decimal fraction) 0.40 0.40
Moisture Content (decimal fraction) 0.20 0.20
Contaminant Mass Example 1 (mg/kg) 100.0 100.0
Contaminant Mass Example 2 (mg/kg) 400.0 900.0
Table 3. Example 1 - Comparison of NAPLANAL and NAPLator Model Results
NAPLANAL NAPLator
Parameter PCE TCE PCE TCE
Soil Saturation Limit (mg/kg) Not Calculated Not Calculated 22.39 101.34
NAPL Saturation (%) 0.0288 0.0226
Total NAPL Concentration (mg/kg) 68.60 32.45 77.60 0.0
NAPL Present in Sample Yes Yes Yes No
Mole Fraction (%) 0.6260 0.3740 0.4418 0.5582
Effective Solubility (mg/L) Not Calculated Not Calculated 88.37 613.97
Effective Vapor Pressure (mmHg) Not Calculated Not Calculated 8.16 41.48
NAPL Density (kg/L) 1.57 1.54
NAPL Volume (%) 0.000115 0.00009
Air Volume (%) 0.1999 0.1999
Bulk Density (kg/L) 1.79 1.79
Volumetric Air Concentration
(ppmv@20C)
Not Calculated Not Calculated 12,086.67 40,502.99
Solubility of Mixture (mg/L) Not Calculated 702.34
Vapor Pressure of Mixture (mmHg) Not Calculated 49.64
Pore Water Concentration (mg/L) 125.2 411.41 88.37 605.81

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Table 4. Example 2 - Comparison of NAPLANAL and NAPLator Results
NAPLANAL NAPLator
Parameter PCE TCE PCE TCE
Soil Saturation Limit (mg/kg) Not Calculated Not Calculated 13.18 134.19
Total NAPL Saturation (%) 0.3427 0.3433
NAPL Concentration (mg/kg) 385.82 770.97 386.82 765.82
NAPL Present in Sample Yes Yes Yes Yes
Mole Fraction (%) 28.37 71.63 26.03 73.97
Effective Solubility (mg/L) Not Calculated Not Calculated 52.05 813.71
Effective Vapor Pressure (mmHg) Not Calculated Not Calculated 4.81 54.97
NAPL Density (kg/L) 1.51 1.50
NAPL Volume (%) 0.00137 0.00137
Air Volume (%) 0.19863 0.19863
Bulk Density (kg/L) 1.79 1.79
Volumetric Air Concentration
(ppmv@20C)
Not Calculated Not Calculated 7119.47 54,402.96
Solubility of Mixture (mg/L) Not Calculated 865.76
Vapor Pressure of Mixture (mmHg) Not Calculated 59.78
Pore Water Concentration (mg/L) 56.75 787.88 52.05 813.71
Table 3 indicates the occurrence of an inaccuracy in the NAPLANAL model algorithms at soil
concentrations less than or equal to 100 mg/kg for PCE and TCE. NAPLANAL overestimates
NAPL mass in the sample because the mole fractions deviate by approximately 20% and are
calculated incorrectly by the NAPLANAL model. NAPLANAL predicts a TCE NAPL when
none can occur. NAPL mass cannot exist for TCE in Example 1 because the estimated pore-
water concentration (411 mg/L) in the soil sample never exceeds the effective solubility (614
mg/L) for TCE (see Section 2.2). Analysis of the reason for the overestimation cannot occur
because sufficient documentation of the numerical process does not exist in the NAPLANAL
program to facilitate further evaluation. However, the inaccurate results reported by the
NAPLANAL model would lead investigators to incorrectly conclude a TCE/PCE NAPL mixture
was present at this waste site when, in fact, only PCE NAPL was present in the sample. The
NAPLANAL model would also lead to over-estimation of the magnitude of NAPL
contamination present at the site.

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In the second example, NAPL saturation, NAPL mass, and NAPL volume are almost identical
between both software packages and the differences are probably statistically insignificant.
However, NAPLANAL still slightly overestimates mole fractions by 1 to 3% and is responsible
for the minor deviations in the calculated values. These inconsistencies may be due to the
differences in computational methods used in the models; however, sufficient documentation
does not exist for the NAPLANAL model to permit evaluation. By contrast, NAPLator
calculates exact solutions and reports metrics not reported in the NAPLANAL model. These
additional metrics (soil saturation limit, effective solubility, effective vapor pressure, mixture
solubility, mixture vapor pressure, volumetric vapor concentration, and mass balance for each
compound) are important for characterization and understanding of the source for remedial
activities. NAPLator provides a more useful and robust information output which is inherently
easier to understand.
2.0 FOUNDATIONS FOR SOFTWARE CALCULATIONS
The calculations performed by the NAPLator model are based on a set of definitions that are
derived from a number of scientific theories and laws. These are discussed in the following
paragraphs as are the governing equations used to arrive at the solutions and the operational steps
of the software.
2.1 Assumptions
• The NAPL mixture will behave as an ideal solution. An ideal solution will obey Raoult’s
Law. The effects of co-solvency are not considered.
• All mass and volume is conserved. There is no loss of mass or volume due to
volatilization, degradation, evaporation, photolysis, etc. or other physical-chemical
processes. At the end of the calculation, final mass and volume will equal the initial mass
and volume.
• Contaminants are uniformly distributed throughout the contaminated media.

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• Equilibrium partitioning is instantaneous and linear for vapor, aqueous, solid and NAPL
phases.
• All NAPL or NAPL mixtures are liquids at ambient temperatures.
• Environmental media has three phases: soil particles, soil pore-air, and soil pore-water.
• Mass is composed of four states: solid, vapor, aqueous, and NAPL.
• In a saturated sample, there is no air-filled porosity.
• Soil temperature is assumed to be a constant 20° C.
2.2 Solubility Limit Theory for NAPL
Solubility limit theory for NAPL states that if the concentration of an organic chemical dissolved
in water exceeds its pure-phase aqueous solubility limit, then NAPL is present in the sample.
The most fundamental quantitative test for NAPL is conducted by comparing the solubility limit
of an organic compound to its dissolved equilibrium concentration in water. By application of
equilibrium partitioning theory, theoretical upper bound, solubility-saturation related
concentrations can be similarly calculated for other phases of media such as soil-vapor and
sorbed-soil concentrations. In its simplest form, the definition for a NAPL can be expressed as:
For a single component, NAPL exists when Cw > S
or
For a component of a multi-component mixture when Cwi > SE
i
Where:
Cw = Chemical dissolved concentration in water
S = Pure phase aqueous solubility limit of the chemical
Cwi = Component i water concentration
SE
i = Effective solubility limit of the organic compound i in a mixture
The following example illustrates the concept of this definition:

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TCE was detected in a groundwater sample at a concentration of 2000.0 mg/L (Cw). A
comparison of the measured groundwater analytical result (2000.0 mg/L) with that of the
aqueous solubility limit for TCE (1100.0 mg/L) (S) indicated that NAPL was present in the
groundwater sample because the concentration in the sample had exceeded the pure phase
aqueous solubility limit for TCE, i.e., Cw > S. There is approximately 900 mg/L of TCE in free-
phase (NAPL) in this sample.
This is the simplest example of how the solubility limit theory is applied to determine the
presence and concentration of a NAPL in a groundwater sample. However, real world examples
are seldom this straight forward. This example can become significantly more complicated if
multiple organic compounds are in a mixture, and the compounds have partitioned between soil
particles, soil-pore air, and soil-pore water phases. In practice, NAPL at a waste site is often
detected as a mixture of organic compounds, not as a single organic compound, and in soil
media, as well as groundwater. Think about the following example:
The analysis of a vadose zone soil sample measured 100.0 mg/kg of TCE and 100.0 mg/kg of
PCE.
Is NAPL present in this soil sample? What compound(s) are NAPL and what concentration of
NAPL is present in this sample if there is NAPL? Is the soil concentration for each compound
compared to its pure-phase solubility limit or does some other method need to be applied? What
if there were three, four or more compounds in this mixture? The answer to some of the above
questions requires the application of Raoult’s Law.
2.3 Raoult’s Law
Raoult’s Law must first be applied to answer some of the questions above by calculating the
molar fraction of each component in a multi-component organic mixture. The molar fraction is
then used to calculate the solubility for each component. Raoult’s Law states the effective
solubility of a compound is equal to the molar fraction of the compound in the mixture
multiplied by its pure-phase solubility.

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The law is expressed mathematically as
SE
i = xi * Si
Where:
SE
i = Effective solubility of compound i in a mixture (mg/L)
xi = Molar fraction of compound i in a mixture (%, unitless)
Si = Pure phase solubility of the compound i (mg/L)
(This is an often overlooked factor of NAPL determination. The more components present in the
mixture, the lower the NAPL threshold becomes for all the components in the mixture. This is due to the
effective solubility of the components becoming a linearized fraction of their pure-phase solubility and is
also the same reason why NAPL is persistent in the environment.)
Figure 2. Example of Raoult’s Law Changing a Component Soil Saturation Threshold
The molar fraction is determined by dividing the molecular weight of compound i by the sum of
molecular weights of all the compounds in the mixture. Therefore, the sum of the molar
fractions is equal to one. Assuming an ideal solution, Raoult’s Law is applicable, and the
resulting solubility of the mixture is equal to the sum of the effective solubilities. Like solubility,

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density and vapor pressure for a mixture may be similarly calculated for a mixture. These
calculations are stated in detail later in this calculation note.
2.4 Equilibrium Partitioning Theory, Mass Balance and Volume Conservation
Because of the assumption of conservation of mass, the partitioning of a compound into each of
the four separate phases must mass balance with the total mass for each compound within the
mixture. Likewise, each of the chemical concentrations must then mass balance with the total
contaminant mass in the sample. This mass balance is expressed by the following equations:
Mti = Mai + Mwi + Msi + MNAPLi
Where:
Mti = Total mass of compound i in sample (mg)
Mai = Mass of compound i in soil pore air (mg)
Mwi = Mass of compound i in soil pore-water (mg)
Msi = Mass of compound i sorbed on soil particles (mg)
MNAPLi = Mass of compound i as NAPL (mg)
Then:
Mt = ΣMti
Therefore:
Where:
Ct = Total soil chemical concentration (mg/kg)
Mt = Total mass of contaminants in the sample (mg)
Equilibrium partitioning theory assumes that a compound will partition (distribute) linearly
between four separate phases in environmental media. The four phases include the aqueous

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phase, e.g., dissolved in groundwater or soil-pore water; the solid phase, e.g., sorbed on soil
particles; vapor phase, e.g., vapor in the soil pore-air; and NAPL, as free phase, if any NAPL is
present in the sample. The explicit partitioning equations will be stated mathematically in the
next section.
Application of the equilibrium partitioning calculations and mass conservation equations will
permit estimation of the concentrations and masses for each of the chemical compounds in each
of the four phases. This assumes that an organic compound will partition into the media
according to a water-soil (Kd) and a water-vapor (H’ Henry’s Law Constant) distribution
coefficient.
All equilibrium calculations use the soil pore-water concentration as the basis for all subsequent
equilibrium calculations. The soil pore-water will be one of three permutations in the model:
• the aqueous solubility limit for a single compound NAPL,
• the effective solubility limit for a mixture of compounds, or
• an estimated pore-water concentration if there is no NAPL in the sample.
The model uses logic arguments to determine which permutation will be used for the equilibrium
calculations. Once the pore-water concentration is solved, partitioning calculations are
performed to distribute soil pore vapor, sorbed soil, and NAPL concentrations. The mass present
in each phase is then calculated after concentrations have been determined.
The Soil Saturation Limit or Csat is a very important partitioning equation because it determines
the NAPL threshold concentration or limit. Csat is a theoretical upper-bound soil limit that
partitions contaminants in three phases only, e.g., soil particles, soil pore air, and soil pore water.
It is a threshold concentration that identifies the saturation point for a contaminant sorbed to soil
particles, dissolved contaminant in pore-water, and saturation of pore-air with contaminant
vapor. For a single chemical compound, NAPL will be present at concentrations exceeding Csat

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(Brost et al. 2000). The software will always calculate Csat using either the pure-phase solubility
limit or the effective solubility limit.
The partitioning equation for determining the soil saturation limit is expressed as:
Csat = (SE
i/Pb) x (Kd x Pb + θw + H’ x θa)
Where:
Csat = Soil Saturation Limit (mg/Kg)
Si or (SE
i) = Solubility limit of compound in water (mg/L)
Pb = Bulk density (kg/L)
Kd = Soil-water partitioning coefficient (L/kg)
θw = Water filled soil porosity (fraction, %)
H’ = Henry’s Law Constant (dimensionless)
θa = Air-filled porosity (fraction, %)
Partitioning in the saturated zone is managed in a slightly different manner by the software.
Since the model assumes there is no air-filled porosity in the saturated zone (all the pore spaces
are filled with water), a compound in a saturated sample cannot partition into the vapor phase.
Therefore, there can be no Ca in a water saturated sample; hence, Ma is deleted from the mass
balance equation for saturated samples. In this case, the software will solve for three phases
instead of four phases.
A reversible partitioning coefficient is used to describe the sorption of the compound from water
to organic carbon in the soil. A form of the Freundlich equation (USEPA 1996) is used as a
linear isotherm with respect to sorption onto soil. The dimensionless form of Henry’s Law
Constant is used to describe the partitioning of a compound from the water phase to the vapor
phase at a constant 20 degrees C.

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In order to determine the volumes occupied by each phase in a sample, the compounds must first
be partitioned into the vapor, aqueous, soil, and NAPL phases (if present) of the sample. The
volume conservation equation is
Vt = Va + Vw + Vs + Vn
Where:
Vt = Total volume of sample
Va = Volume of soil-pore air
Vw = Volume of soil-pore water
Vs = Volume of soil particles
Vn = Volume of NAPL
Also, where nt is the total porosity:
nt = θa + θw
For saturated samples:
nt = θw and θa = 0
As explained previously, the Csat value represents the chemical-physical saturation limits in soil
based on the chemical characteristics of the compound. The value of Csat is the contaminant
concentration in soil at which soil-pore vapor and pore water are saturated with the chemical and
the sorptive limits of the soil particles have been reached. Above this threshold the contaminant
may be present in free-phase.

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Therefore, the mathematical expression used to determine the concentration of NAPL for
compound i within the sample is
NAPLi = Cti – Csati
Where:
NAPLi = NAPL concentration in soil for compound i (mg/kg)
Cti = Measured concentration for compound i in soil sample (mg/kg)
Csati = Soil Saturation Limit for compound i (mg/kg)
If Cti < Csati, there is no NAPL in the sample.
Because the volume of a sample is composed of solids (soil particles) and void space (porosity),
the NAPL must occupy physical space within a sample. NAPL saturation (Sr) is a calculated
value that expresses the percentage of porosity occupied by NAPL within a soil sample.
Therefore the residual saturation is defined as the volume fraction of pore space occupied by
NAPL. Residual saturation is a useful measurement to understand the magnitude of NAPL
volume in the subsurface. The residual saturation is an important parameter to estimate the
potential volume of contaminated media at a waste site for design of a remediation system and as
a contaminant baseline against which to measure remediation system performance. Residual
saturation is also important to estimate NAPL mobility in the subsurface (Brost et al. 2000).
The residual NAPL saturation equation is
Sr = Nv/nt
Where:
Sr = Residual NAPL saturation in soils, (%, L/L)
Nv = NAPL volumetric content (NAPLt * Pb)/PNAPL, (%, L/L)

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NAPLt = ΣNAPLi, (mg/kg)
PNAPL = Density of the NAPL mixture, (mg/L)
Pb = Bulk density of soil, (kg/L)
nt = Total volumetric soil porosity, (%,L/L)
2.5 Operational and Computation Order
The determination of NAPL in a soil sample requires an orderly series of computational steps to
be performed. These steps are referred to as an “operational order.” As indicated by the name, a
series of computations must be performed in a specific order to arrive at a solution. Some
computations in the model are iterative, such as the bulk density, but most are not. However, this
does require the “Calculation” option in Excel to be set to “On” to enable iteration a maximum of
five times for the model. Use of this feature also enables elimination of “Circular References.”
in the calculations.
The operational order for the computations in the model is listed below:
1. The organic chemicals to be evaluated are selected.
2. The concentrations (mass per mass; mg/kg) from the analytical results of the soil
sample are entered. The units must be in mg/kg.
3. The total porosity, air-filled porosity, water-filled porosity, and fraction of organic
carbon representative of the soil sample are entered. The units for these values
should be entered as decimal fractions. As an example, 40% total porosity equals
0.40. These are the last user-supplied inputs. All physical parameter values are
automatically entered by the software from the built-in database.
4. The mole fraction for each compound is calculated.
5. The density of the mixture is calculated.

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6. The total solubility of the mixture and the effective solubility of each compound
in the mixture is calculated. If there is a single compound in the sample, the pure-
phase aqueous solubility limit is used instead.
7. The total vapor pressure of the mixture and the effective vapor pressure of each
compound in the mixture is calculated.
8. A theoretical pore-water concentration (ICwi) is calculated. This value is
compared to the effective solubility (SE
i) or the solubility limit (S). The software
selects the lesser of the effective solubility, solubility limit, or the pore-water
concentration to calculate media phase concentrations and masses.
9. Csat is calculated using the effective solubility, solubility limit, or pore-water
concentration for each compound.
10. The equilibrium concentration for each compound is calculated for soil pore-water
and soil pore-vapor with either the effective solubility limit, or the theoretical
pore-water concentration of each compound (Cwi). The software automatically
uses a logic function to select the lower of the values S, SE
i or Cwi..
11. The mass per unit volume (Mti) for each compound is calculated for soil pore-
water, soil pore-vapor, soil pore-water, and NAPL, if any, based upon the Cwi
(determined in the preceding step).
12. The mass balance calculations are performed. This equation assumes the form of
(Cti-Csati), with the NAPL concentration being summed for all compounds.
13. The “Percent Residual NAPL Saturation” (Sr) is calculated. This is in the form of
a volumetric calculation of either the volume of NAPL occupying porosity in
unsaturated samples or the volume of NAPL occupying total porosity for saturated
samples. A logic equation is automatically used to determine which.
14. The volume conservation equation is completed to account for all compound mass
per volume in the sample, which culminates in a wet bulk density value in units of
kg/L. This is an iterative equation and calculates the mass per discrete unit

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volume for NAPL volume, air-filled porosity volume, water-filled porosity
volume, soil volume, and, finally, wet bulk density for the sample.
15. Automatic graphing functions are built-in, including the molar fraction for each
compound in the NAPL mixture, the effective solubility for each compound in the
NAPL mixture, and the effective vapor pressure for each compound in the NAPL
mixture.
3.0 INPUTS
Inputs will be used to operate the software and to check the validity and accuracy of the output.
Two separate simulations with different inputs will be used to verify the solutions and ensure
software operation. The inputs for the case scenarios are included in Tables 5, 6, 7, and 8.
Table 5. Chemical Properties for Scenario #1, #2 and #3
Chemical
Molecular
Weight
(MWi)
(g/mol)
Solubility
Limit
(Si)
(mg/L)
Vapor
Pressure
(VPi)
(mmHg)
Henry’s
Law
Constant
(Hi’)
(unitless)
Organic
Carbon
Coefficient
(Koci)
(L/kg)
Density
(di)
(kg/L)
Trichloroethylene 1.31E+02 1.10E+03 7.43E+01 3.65E-01 1.26E+02 1.46E+00
Tetrachloroethylene 1.66E+02 2.00E+02 1.85E+01 9.43E-01 3.64E+02 1.63E+00
Arochlor 1260 3.72E+02 1.44E-02 1.10E-05 1.03E-02 6.70E+06 1.57E+00
1,3,5-
Trinitrobenzene
2.13E+02 3.85E+02 3.03E-06 9.10E-08 2.00E+01 1.50E+00
2,4,6-
Trichlorophenol
1.97E+02 4.34E+02 1.20E-02 1.98E-04 2.00E+03 1.50E+00
Benzo(a)pyrene 2.52E+02 5.00E-05 5.60E-09 1.53E-03 5.50E+06 9.00E-01
Table 6. Scenario #1 - Soil Concentration and Geotechnical Inputs
Chemical
Mass of
Contaminant
In Sample
(Cti, mg/Kg)
Total
Porosity
(nt, fraction)
Volumetric
Water
Content
(θw, fraction)
Volumetric
Air Content
(θa, fraction)
Fraction
Organic
Carbon
(foc, fraction)
Trichloroethylene 100 0.40 0.30 0.1 0.0001
Tetrachloroethylene 15 0.40 0.30 0.1 0.0001
Arochlor 1260 60 0.40 0.30 0.1 0.0001
1,3,5-Trinitrobenzene 3 0.40 0.30 0.1 0.0001
2,4,6-Trichlorophenol 2 0.40 0.30 0.1 0.0001
Benzo(a)pyrene 1 0.40 0.30 0.1 0.0001

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Table 7. Scenario #2 - Soil Concentration and Geotechnical Inputs
Chemical
Mass of
Contaminant
(Cti, mg/Kg)
Total
Porosity
(nt, fraction)
Volumetric
Water
Content
(θw, fraction)
Volumetric
Air Content
(θa, fraction)
Fraction
Organic
Carbon
(foc, fraction)
Arochlor 1260 4000 0.42 0.22 0.2 0.01
1,3,5-Trinitrobenzene 10000 0.42 0.22 0.2 0.01
2,4,6-Trichlorophenol 5000 0.42 0.22 0.2 0.01
Benzo(a)pyrene 2500 0.42 0.22 0.2 0.01
Table 8. Scenario #3 - Soil Concentration and Geotechnical Inputs for Saturated
Sample
Chemical
Mass of
Contaminant
(Cti, mg/kg)
Total
Porosity
(nt, fraction)
Volumetric
Water
Content
(θw, fraction)
Volumetric
Air Content
(θa, fraction)
Fraction
Organic
Carbon
(foc, fraction)

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4.0 ANALYTICAL METHODS AND CALCULATIONS
4.1 Equation 1 Molar Fraction (from Chemistry, Moeller et al. 1980)
Equation 1a Percent Mass
Wti = Cti/Mt
Where:
Wti = % Mass for compound i (mg/mg)
Cti = Measured soil contaminant mass for compound i (mg/kg)
Mt = ΣCti, Sum of contaminant masses for all compounds in the sample (mg/kg)
Equation 1b Moles/Gram
Mci = Wti/MWi
Where:
Mci = Molar Mass or Moles/Gram for compound i (mol/g)
Wti = % Mass for compound i (g/g)
MWi = Molecular Weight for compound i (g/mol)
Equation 1c Mole Fraction
Xi = Mci/ΣMci
Where:
Xi = Mole Fraction for compound i (%)
Mci = % Molar Mass for compound i (mol/g)

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ΣMci = Sum of molar masses (mol/g)
Equation 1d Sum of Mole Fractions
ΣXi = 1
4.2 Equation 2 Density of Mixture
d = Σ(Xi * di)
Where:
d = Density of the mixture (kg/L)
Xi = Mole Fraction (%)
di = Density for compound i (kg/L)
4.3 Equation 3 Effective Solubility (Raoult’s Law from USEPA 1992 and others)
Where:
SE
i = Effective Solubility for compound i in mixture (mg/L)
Xi = Mole Fraction for compound i (%)
Si = Pure-Phase Aqueous Phase Solubility for compound i (mg/L)
Equation 3a Solubility of Mixture
St = ΣSE
i
Where:
St = Solubility of the Mixture (mg/L)

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4.4 Equation 4 Effective Vapor Pressure
VPE
i = (Xi * VPi)
Where:
VPE
i = Effective Vapor Pressure for compound i in mixture (mmHg)
Xi = Mole Fraction (%)
VPi = Pure-Phase Vapor Pressure for compound i (mmHg)
Equation 4a Vapor Pressure of Mixture
VPt = ΣVPE
i
Where:
VPt = Total vapor pressure for the mixture (mmHg)
4.5 Equation 5 Theoretical Soil Pore-Water Concentration (Feenstra et al. 1991 and
Mariner et al. 1997)
Cwi = (Cti * Pb)/(Kdi * Pb + θw + H’i * θa)
Where:
Cwi = Theoretical Soil Pore-Water Concentration for compound i (mg/L)
Cti = Total contaminant concentration i in soil sample (mg/kg)
Pb = Wet Bulk Density (kg/L)
Kdi = Soil-water partitioning coefficient (foc x Koci) (L/kg)
Koc = Soil organic carbon/water partitioning coefficient (L/kg)
θw = Water filled soil porosity (decimal fraction, L/L)
H’i = Henry’s Law Constant for compound i (dimensionless)
θa = Air filled soil porosity (decimal fraction, L/L)

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4.6 Equation 6 Soil Saturation Limit (Csat) (from USEPA 1996)
Csati = (SE
i/Pb) * (Kdi * Pb + θw + H’i * θa)
Where:
Csati = Soil Saturation Limit for compound i (mg/kg)
SE
i = Effective solubility limit for compound i (mg/L)
Pb = Wet soil bulk density (kg/L)
Kdi = Soil-water partitioning coefficient (L/kg)
θw = Water-filled soil porosity (decimal fraction, L/L)
θa = Air-filled soil porosity (decimal fraction, L/L)
4.7 Equation 7 Soil Pore-Water Concentration
Cwi =Either Cwi or Si or SE
i
Where:
Cwi = Theoretical Soil Pore-Water Concentration for compound i (mg/L) or
SE
i = Effective Solubility for compound i (mg/L) or
Si = Solubility Limit for compound i (mg/L)
Cwi = is determined from logic tests. For example if Xi = 1, Si will be selected as the soil
pore-water concentration. If Cwi >= SE
i then SE
i will be selected as the soil pore-water
concentration.
4.8 Equation 8 Soil Pore-Vapor Concentration
Cai = Cwi * H’i

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Where:
Cai = Soil pore-vapor concentration for compound i (mg/L)
Cwi = Soil pore-water concentration for compound i (mg/L)
4.9 Equation 9 Volumetric Soil Pore-Vapor Concentration
Cavi = Cai * R * CF * T/(P * MWi)
Where:
Cavi = Volumetric soil pore-air concentration for compound i (ppmv)
Cai = Soil pore-vapor concentration (mg/L)
R = Universal Gas Constant (8.31451 Pa m3
)/(K*mole)
CF = Conversion factor (1E+6 mg/L)
T = Temperature (293.15 K)
P = Pressure (101325 Pa)
MWi = Molecular weight for compound i (g/mol)
4.10 Equation 10 Soil Sorbed Concentration (Freundlich Isotherm from USEPA 1996
and others)
Csi = Cwi * Kdi
Where:
Csi = Soil sorbed concentration for compound i (mg/kg)
Kdi = Soil-water partitioning coefficient for compound i (L/kg)
Cwi = Pore-water concentration for compound i (%, mg/L)

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4.11 Equation 11 Contaminant Mass in Soil Pore-Water
Mwi = Cwi* θw
Where:
Mwi = Mass in soil pore water for compound i (mg)
θw = Water filled soil porosity (decimal fraction, L/L)
4.12 Equation 12 Contaminant Mass in Soil Pore-Air
Mai = Cwi*H’i*θa
Where:
Mai = Mass in soil pore-air for compound i (mg)
4.13 Equation 13 Contaminant Mass Sorbed to Soil
Msi = Cwi*Kdi*Pb
Where:
Msi = Mass sorbed to soil for compound i (mg)
Cwi = Soil pore-water concentration for compound i (mg/kg)
Kdi = Soil-water partitioning coefficient for compound i (L/kg)
Pb = Wet bulk density (kg/L)

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4.14 Equation 14 NAPL Concentration for Compound
NAPLi = Cti - Csati, if Cti>Csati
Where:
NAPLi = NAPL concentration in soil sample for compound i (mg/kg)
Cti = Soil concentration for compound i (mg/kg)
Csati = Soil Screening Limit for compound i (mg/kg)
4.15 Equation 15 NAPL Mass
MNAPLi = NAPLi * Pb
Where:
MNAPLi = Mass of NAPL for compound i (mg)
4.16 Equation 16 Mass Balance Equation for Compound
Mti = (Mai + Mwi + Msi + MNAPLi)
Therefore,
Mt = ΣMti
Where:
Mti = Total contaminant mass of compound i (mg)
Mai = Mass in soil pore-air for compound i (mg)
Mwi = Mass in soil pore water for compound i (mg)
Msi = Mass sorbed to soil for compound i (mg)
NAPLi = Mass of NAPL for compound i (mg)
Mt = Total contaminant mass for all compounds in a mixture (mg)

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4.17 Equation 17 Total Concentration of NAPL in Sample
NAPLt = ΣNAPLi
Where:
NAPLt = Total concentration of NAPL in soil sample (mg/kg)
NAPLi = Concentration of NAPL for compound i (mg/kg)
4.18 Equation 18 Percent Residual NAPL Saturation
Sr = (NAPLt*Pb/d)/nt
Where:
Sr = Percent Residual NAPL Saturation (%)
nt = Total soil porosity (%, L/L)
d = Density of NAPL mixture (mg/L)
4.19 Equation 19 Volume Conservation Equation for Soil Sample (Wet Bulk Density)
Pb = (Wv * dw) + (Av * da) + (Sv * ds) + (Nv * d)
Where:
Wv = Volume of soil pore-water (%, L/L)
dw = Density of water (1.0 kg/L)
Av = Volume of soil pore-air volume (%, L/L)
da = Density of air (0.0013 kg/L)

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Sv = Volume of soil (%, L/L)
ds = Density of soil (2.65 kg/L)
Nv = Volume NAPL (%, L/L)
d = Density of NAPL mixture (kg/L)
4.20 Equation 20 Volumetric Content of NAPL in Sample
Nv = (NAPLt * Pb)/Pnapl
Where:
Nv = NAPL volume (%, L/L)
Pb = Wet bulk soil density (kg/L)
Pnapl = Density of NAPL mixture (mg/L)
4.21 Equation 21 Volumetric Content of Air in Sample
Av = θa-Nv
Where:
Av = Volume of air in sample (%, L/L)
4.22 Equation 22 Volumetric Content of Water in Sample if θa = 0
Vw = θw – Nv
Where:
Vw = Volume of water in sample (%, L/L)

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θw = Water filled soil porosity (decimal fraction, L/L)*
Nv = NAPL volume (%, L/L),
*If θa = 0, model assumes a saturated sample, θw = nt
4.23 Equation 23 Volumetric Content of Soil in Sample
Sv = 1-(θw + θa + Nv)
Where:
Sv = Volume of soil (%, L/L)
θw = Water filled soil porosity (%, L/L)

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5.0 RESULTS
Tables 9 through 20 show the results for scenarios #1, #2, and #3.
Table 9. Scenario #1 Soil Saturation and Bulk Density Results
Analyte
Pb
(kg/L)
Csat-Wet
(mg/kg)
Pd
(kg/L)
Csat-Dry
(mg/kg)
Trichloroethene 1.89E+00 1.53E+02 1.59E+00 1.80E+02
Tetrachloroethene 1.89E+00 4.25E+00 1.59E+00 4.94E+00
Aroclor 1260 1.89E+00 1.49E+00 1.59E+00 1.49E+00
1,3,5-Trinitrobenzene 1.89E+00 8.36E-01 1.59E+00 9.92E-01
2,4,6-Trichlorophenol 1.89E+00 1.51E+00 1.59E+00 1.64E+00
Benzo(a)pyrene 1.89E+00 1.05E-04 1.59E+00 1.05E-04
Table 10. Scenario #1 Media Masses
Analyte
Ma
(mg)
Mw
(mg)
Ms
(mg)
NAPL
(mg)
Mt
(mg)
Trichloroethene 1.91E+01 1.57E+02 1.25E+01 0 1.89E+02
Tetrachloroethene 1.64E+00 5.21E+00 1.19E+00 2.03E+01 2.84E+01
Aroclor 1260 2.29E-06 6.69E-04 2.82E+00 1.11E+02 1.13E+02
1,3,5-Trinitrobenzene 4.71E-08 1.56E+00 1.97E-02 4.09E+00 5.67E+00
2,4,6-Trichlorophenol 8.34E-05 1.27E+00 1.60E+00 9.19E-01 3.78E+00
Benzo(a)pyrene 2.90E-11 5.71E-08 1.98E-04 1.89E+00 1.89E+00
TOTAL 2.08E+01 1.65E+02 1.81E+01 1.38E+02 3.42E+02
Table 11. Scenario #1 Media Concentrations
Analyte
Cav
(ppmv)
Ca
(mg/L)
Cw
(mg/L)
NAPL
(mg/kg)
Cs
(mg/kg)
Trichloroethene 3.51E+04 1.91E+02 5.25E+02 0 6.61E+00
Tetrachloroethene 2.38E+03 1.64E+01 1.74E+01 1.07E+01 6.32E-01
Aroclor 1260 1.48E-03 2.29E-05 2.23E-03 5.85E+01 1.49E+00
1,3,5-Trinitrobenzene 5.32E-05 4.71E-07 5.20E+00 2.16E+00 1.04E-02
2,4,6-Trichlorophenol 1.02E-01 8.34E-04 4.22E+00 4.86E-01 8.44E-01
Benzo(a)pyrene 2.77E-08 2.90E-10 1.90E-07 1.00E+00 1.05E-04

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Table 12. Scenario #1 Volume and Residual Saturation Results
TOTAL NAPL
SATURATION
d= 1.49E+00 kg/L Density of NAPL Mixture (kg/L)
NAPLt= 7.29E+01 mg/kg Total NAPL Concentration
Pnapl= 1.49E+06 mg/L Density of NAPL Mixture (mg/L)
Sr= 2.31E-04 Fraction NAPL Saturation
%Sr 0.02% % Residual NAPL Saturation*
*% Total porosity occupied by NAPL
VOLUME
Nv= 9.25E-05 L/L NAPL Volume
Av= 9.99E-02 L/L Air Volume (Oa)
Wv= 3.00E-01 L/L Water Volume
Sv= 6.00E-01 L/L Soil Volume
V= 4.00E-01 L/L Total Porosity (nt)
Pb= 1.89E+00 kg/L Wet Bulk Density
Pd= 1.59E+00 kg/L Dry Bulk Density

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Analyte
Pb
(kg/L)
Csat-Wet
(mg/kg)
Pd
(kg/L)
Csat-Dry
(mg/kg)
Aroclor 1260 1.84E+00 4.09E+01 1.54E+00 4.09E+01
1,3,5-Trinitrobenzene 1.84E+00 2.28E+01 1.54E+00 2.45E+01
2,4,6-Trichlorophenol 1.84E+00 8.72E+02 1.54E+00 8.73E+02
Benzo(a)pyrene 1.84E+00 1.08E-01 1.54E+00 1.08E-01
Analyte
Ma
(mg)
Mw
(mg)
Ms
(mg)
NAPL
(mg)
Mt
(mg)
Trichloroethene 2.41E+01 7.27E+01 7.65E+02 1.75E+04 1.84E+04
Aroclor 1260 1.25E-06 1.34E-04 7.52E+01 7.28E+03 7.35E+03
1,3,5-Trinitrobenzene 1.29E-06 1.57E+01 2.62E+01 1.83E+04 1.84E+04
2,4,6-Trichlorophenol 1.71E-03 9.54E+00 1.59E+03 7.59E+03 9.19E+03
Benzo(a)pyrene 5.97E-10 4.30E-07 1.98E-01 4.59E+03 4.59E+03
TOTAL 3.67E+01 1.13E+02 2.91E+03 8.06E+04 8.36E+04
Analyte
Cav
(ppmv)
Ca
(mg/L)
Cw
(mg/L)
NAPL
(mg/kg)
Cs
(mg/kg)
Aroclor 1260 4.05E-04 6.26E-06 6.11E-04 3.96E+03 4.09E+01
1,3,5-Trinitrobenzene 7.29E-04 6.46E-06 7.13E+01 9.98E+03 1.43E+01
2,4,6-Trichlorophenol 1.04E+00 8.57E-03 4.34E+01 4.13E+03 8.67E+02
Benzo(a)pyrene 2.85E-07 2.98E-09 1.96E-06 2.50E+03 1.08E-01

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TOTAL NAPL
SATURATION
d= 1.51E+00 kg/L Density of NAPL Mixture (kg/L)
NAPLt= 4.38E+04 mg/kg Total NAPL Concentration
Pnapl= 1.51E+06 mg/L Density of NAPL Mixture (mg/L)
Sr= 1.27E-01 fraction NAPL Saturation
%Sr 12.70% % Residual NAPL Saturation*
*% Total porosity occupied by NAPL
VOLUME
Nv= 5.33E-02 L/L NAPL Volume
Av= 1.47E-01 L/L Air Volume (Oa)
Wv= 2.20E-01 L/L Water Volume
Sv= 5.80E-01 L/L Soil Volume
V= 4.20E-01 L/L Total Porosity (nt)
Pb= 1.84E+00 kg/L Wet Bulk Density
Pd= 1.54E+00 kg/L Dry Bulk Density

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Analyte
Pb
(kg/L)
Csat-Wet
(mg/kg)
Pd
(kg/L)
Csat-Dry
(mg/kg)
Analyte
Ma
(mg)
Mw
(mg)
Ms
(mg)
NAPL
(mg)
Mt
(mg)
TOTAL 0.00E+00 1.06E+02 1.54E+01 1.94E+03 2.06E+03
Analyte
Cav
(ppmv)
Ca
(mg/L)
Cw
(mg/L)
NAPL
(mg/kg)
Cs
(mg/kg)
Trichloroethene 7.80E+01 4.24E+01 9.82E-01
Tetrachloroethene 1.86E+02 9.33E+02 6.76E+00

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Figure 3. Graph of Mass Distribution for Scenario #2
Figure 4. Graph of Volume Distribution for Scenario #2

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Figure 5. Effect of Raoult’s Law on the Total Aqueous Solubility of a Mixture

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6.0 CONCLUSIONS
The three case scenarios have demonstrated the robust type and quantity of information generated
in the software output. The scenarios determined if NAPL was present in a soil sample, and if it
was present, the residual saturation, NAPL mass, and NAPL volume were calculated.
The first output calculated the mole fraction for each compound in the chemical mixture. The
mole fraction determines the effective solubility for each compound in the mixture as well as the
effective vapor pressure and density. The mole fractions balanced accordingly (Xi = 1). The
effective solubility, theoretical groundwater concentration, or aqueous solubility limit is the first
key piece of data for determining if NAPL is present in a mixture of organic compounds.
In a sequential series of calculations, the theoretical pore water concentration was estimated. The
theoretical pore water concentration was compared to the effective solubility or solubility of a
compound. If the theoretical pore water concentration was less than the effective solubility, the
result indicated there was no NAPL for that compound. In this case, mass and concentration
were calculated for three phases of soil media: soil, aqueous, and vapor. If the theoretical pore
water concentration was greater than the effective solubility, the result indicated NAPL was
present in the sample. In this case, mass and concentration was calculated for four phases of soil
media: soil, aqueous, vapor, and NAPL.
The solubility limit (or effective solubility in the case of a mixture) is used to calculate Csat. Csat
is a theoretical limit that indicates the contaminant concentration in soil-pore air and soil pore
water are saturated and the sorptive limits of the soil particles have been reached. Above this
theoretical limit, the contaminant is present as free-product. Therefore, Csat is the fundamental
parameter used to determine the mass of NAPL in the sample because it is used to perform the
mass balance equation. Any contaminant mass above the Csat value is NAPL by definition (Cti –
Csati = NAPLi, if Cti>=Csati).

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The software next calculated the equilibrium concentrations for pore water, air and soil media
using either the smaller of the solubility, effective solubility, or the theoretical pore water
concentration as the theoretical upper boundary. The organic compounds were partitioned to
three phases of soil media: air, water and solid. Partitioning is derived from a linear isotherm
using the Freundlich equation.
The soil pore water concentration was next used to calculate the mass of each compound in each
media according to equilibrium partitioning theory also. In the preceding step, Csat was used to
determine the mass of NAPL in the sample. The phase masses for each compound were
summed, including the NAPL mass (if NAPL was in the sample), using the mass conservation
equation. Therefore, mass was calculated and balanced for four phases (if NAPL was present).
The summed phase masses were equal to the initial measured mass from the soil sample, so the
equation balanced precisely (Cti = Mti) with no residuals.
The total NAPL mass in the sample was then converted into a volume and then reported as a
volume fraction. Since volume conservation law applies in this model, the NAPL volume
fraction is subtracted from the air-filled porosity volume fraction for unsaturated samples because
the NAPL must occupy available space (porosity) within the sample. The volume conservation
equation balanced precisely (Nv + Av + Wv + Sv= Vt) for porosity in the sample and (Vs = 1 – Nv
+ Av +Wv) for solids in the sample. For saturated samples (Oa = 0), the NAPL volume fraction is
subtracted from the water-filled porosity volume fraction, (Nv + Wv + Sv= Vt) and (Vs = 1 – Nv +
Wv).
This software and calculation method can be extremely powerful for environmental professionals
who must determine if NAPL is present in any phase of environment media by evaluating
environmental analytical samples. The software is flexible enough to determine NAPL
thresholds in any sample from any phase concentration. For example, soil vapor concentrations
can also be used to indicate the presence of NAPL in a sample. If soil vapor sampling is being
performed, the soil vapor results (in units of either mg/L or ppmv) can be compared to the air
concentrations on the spreadsheet by entering theoretical soil concentrations into the model.

RDP 1377.doc
Next, if the soil vapor equals or exceeds the calculated soil vapor concentration, Cai, where Cwi =
Si or SE
i then it may be assumed that the sample indicates NAPL. The total concentration of the
compound in soil (Cti) can be adjusted to match the concentration of any phase detected in the
field with analytical data. The total compound concentrations can then be compared to determine
relative compound concentrations in any phase.
The software was also useful to quantify the volume of NAPL (Sr) contamination which is
widely used as a measure of the quantity present in the environment. NAPL saturation has
become more or less a standard used by the scientific community. Residual saturation may also
be to assess whether the NAPL may be mobile (Brost et al. 2000). The volume and density
results provide investigators with a number of useful parameters to help estimate the chemical
characteristics of contaminated media at a waste site. Likewise, the parameters generated by the
software can provide essential data for remedial system design.
The method used by the software is extremely powerful to determine and quantify if NAPL is
present in environmental media using commonly available analytical soil or groundwater results.
It is extremely important to use the model early in the site characterization to interpret and assess
the extent of impacted soils and groundwater at a waste site. The information provided by the
model can guide additional phases of characterization and the output is also of particular
relevance for remedial design engineering. The results of the model provide a reasonable
estimate of the extent and magnitude of subsurface contamination which is necessary to develop
an appropriate remedial response for NAPL contamination in soils such as electrical resistance
heating, dynamic underground stripping, soil flushing, or excavation among others.

RDP 1377.doc
7.0 REFERENCES
Brost, E. J., George E. DeVaull, 2000. “Non-Aqueous Phase Liquid (NAPL) Mobility in Soil,”
American Petroleum Institute, GRI, No.9
Feenstra, Stan, D. M. Mckay, and J. A. Cherry, Spring 1991. “A Method for Assessing Residual
NAPL Based on Organic Chemical Concentrations in Soil Samples,” Ground Water Monitoring
Review, pages 128-136
Mariner, P.E., M. Jin, and R. E. Jackson, 1997. “An Algorithm for the Estimation of NAPL
Saturation and Composition from Typical Soil Chemical Analyses,” Ground Water Monitoring
and Remediation, 17, 1:122-129
Moeller, T., J. Bailar, Jr., J. Kleinberg, C. Guss, M. Castellion, C. Metz, 1980. Chemistry,
Academic Press, New York, NY
USEPA, 1992. “Estimating Potential for Occurrence of DNAPLs at Superfund Sites,” United
States Environmental Protection Agency, Office of Solid Waste and Emergency Response, R. S.
Kerr, Environmental Research Laboratory, Pub. 9355.4-07FS
USEPA, 1996. Soil Screening Guidance: Technical Background Document, United States
Environmental Protection Agency, EPA/540/R-95/128

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