# N.J. Admin. Code 26D app 12

Current through Register Vol. 54, No. 7, April 4, 2022

DERIVATION OF EQUATION EQUIVALENCY USED FOR THE DEVELOPMENT OF SOIL AND INDOOR AIR REMEDIATION STANDARDS

This appendix demonstrates the equivalency between the equations used by the Department in the development of the soil and indoor air remediation standards, and the equations used by the USEPA in the development of soil and indoor air risk-based screening levels. This appendix demonstrates the equivalency for the following Department soil and indoor air remediation standard equations:

* N.J.A.C. 7:26D Appendix 2, Equation 1, Residential Carcinogenic Ingestion-Dermal Human Healthbased Criterion Equation;

* N.J.A.C. 7:26D Appendix 2, Equation 2, Residential Noncarcinogenic Ingestion-Dermal Human Healthbased Criterion Equation;

* N.J.A.C. 7:26D Appendix 2, Equation 3, Nonresidential Carcinogenic Ingestion-Dermal Human Healthbased Criterion Equation;

* N.J.A.C. 7:26D Appendix 2, Equation 4, Nonresidential Noncarcinogenic Ingestion-Dermal Human Health-based Criterion Equation;

* N.J.A.C. 7:26D Appendix 3, Equation 1, Carcinogenic Inhalation Human Health-based Criterion Equation;

* N.J.A.C. 7:26D Appendix 3, Equation 2, Noncarcinogenic Inhalation Human Health-based Criterion Equation;

* N.J.A.C. 7:26D Appendix 5, Equation 1, Carcinogenic Indoor Air Human Health-based Criterion Equation; and

* N.J.A.C. 7:26D Appendix 5, Equation 2, Noncarcinogenic Indoor Air Human Health-based Criterion Equation.

* N.J.A.C. 7:26D Appendix 2, Equation 1-Residential Carcinogenic Ingestion-Dermal Human Health-Based Criterion Equation

The origin of the Department residential soil remediation standard for the ingestion-dermal exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:

Click here to view image

The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:

Click here to view image

The RSLE states that:

Click here to view image

and

Click here to view image

The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:

Click here to view image

And

Click here to view image

Because

Click here to view image

the second equation further simplifies to:

Click here to view image

Starting with the Department-modified base USEPA equation, as described above:

Click here to view image

1. Insert the simplified equations for
SL_{res-soil-ca-ing} and
SL_{res-soil-ca-der} described above into the denominator
of the SL_{res-soil-ca-ing-derm} equation, which then
becomes:

Click here to view image

2. Simplify the reciprocal (in the denominator of the equation
immediately above) containing the equivalent expression of
SL_{res-soil-ca-ing} by multiplying it by the term:

Click here to view image

This is the same as multiplying the reciprocal of the expression by 1.

3. Similarly, simplify the reciprocal containing the equivalent
expression of SL_{res-soil-ca-der} by multiplying it by the
term:

Click here to view image

Again, this is effectively multiplying by 1.

4. This results in the expression:

Click here to view image

5. After separating the common term Click here to view image

from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the expression:

Click here to view image

Performing steps 1 through 5 above results in the following expression:

Click here to view image

This USEPA terminology (immediately above), which is for a residential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

TR | TR | Target cancer risk |

AT_{res} |
AT | Averaging time |

LT | LT | Lifetime |

CSF_{o} |
CSF_{o} |
Oral cancer slope factor |

RBA | None | Relative Bio-availability |

IFS_{res-adj} |
IFS_{adj} |
Age-adjusted soil ingestion rate |

CSF_{d} |
CSFD | Dermal cancer slope factor |

DFS_{res-adj} |
DFS_{adj} |
Age-adjusted soil dermal contact factor |

ABS_{d} |
ABS_{d} |
Dermal absorption fraction |

10^{-6}kg |
10^{-6}kg |
Unit conversion factor |

mg | mg | |

GIABS | GIABS | Gastro-intestinal absorption fraction |

Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:

Click here to view image

Note that the USEPA term
SL_{res-soil-ca-ing-derm} is the equivalent of the
Department term ID_{c}. In addition, there is no Department
RBA parameter because the value is usually 1. Consequently, an RBA parameter
does not appear in the translated equation. The equation presented immediately
above is equivalent to the Department equation presented at N.J.A.C. 7:26D
Appendix 2 as Equation 1 and verifies its equivalence with equations used by
the USEPA.

N.J.A.C. 7:26D Appendix 2, Equation 1 is:

Click here to view image

N.J.A.C. 7:26D Appendix 2, Equation 2-Residential Noncarcinogenic Ingestion-Dermal Human Health-Based Criteria Equation

The origin of the Department residential soil remediation standard for the ingestion-dermal exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:

Click here to view image

The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:

Click here to view image

The Department calculation of the residential noncarcinogenic ingestion-dermal criterion is based on a child exposure scenario. As such, the RSLE states that:

Click here to view image

and

Click here to view image

The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:

Click here to view image

and

Click here to view image

Because

Click here to view image

the second equation further simplifies to:

Click here to view image

Starting with the Department-modified base USEPA equation, as described above:

Click here to view image

1. Insert the simplified equations for
SL_{res-soil-nc-ing-c} and
SL_{res-soil-nc-der-c} described above into the denominator
of the SL_{res-soil-nc-ing-der-c} equation, which then
becomes:

Click here to view image

2. Simplify the reciprocals in the denominator of the equation immediately above (similar to what was done in the derivation of N.J.A.C. 7:26D Appendix 2, Equation 1 above) using the respective terms:

Click here to view image

and

Click here to view image

Again, this is the same as multiplying each of the reciprocals in the equation denominator by 1.

3. This results in the following:

Click here to view image

4. After separating out the common terms

Click here to view image

and

Click here to view image

from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the expression:

Click here to view image

Performing steps 1 through 4 above results in the following expression:

Click here to view image

This USEPA terminology (immediately above), which is for a residential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

THQ | THQ | Target hazard quotient |

AT_{res-c} |
AT | Averaging time |

EF_{res-c} |
EF | Exposure frequency-child |

BW_{res-c} |
BW | Body weight - child |

ED_{res-c} |
ED | Exposure duration - child |

RBA | None | Relative Bio-availability |

RfD_{o} |
RfD_{o} |
Oral reference dose |

IRS | IR | Soil ingestion rate - child |

RfDD | RfD_{D} |
Dermal reference dose |

SA_{res-c} |
SA | Skin surface area - child |

AF_{res-c} |
AF | Soil adherence factor - child |

ABS_{d} |
ABS_{d} |
Dermal absorption fraction |

10^{-6}kg mg |
10^{-6}kg mg |
Unit conversion factor |

GIABS | GIABS | Gastro-intestinal absorption fraction |

Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:

Click here to view image

Note that the USEPA term
SL_{res-soil-nc-ing-der-c} is the equivalent of the
Department term ID_{nc}. In addition, there is no
Department RBA parameter because the value is usually 1. Consequently, an RBA
parameter does not appear in the translated equation. The equation presented
immediately above is equivalent to the Department equation presented in
N.J.A.C. 7:26D Appendix 2 as Equation 2 and verifies its equivalence with
equations used by the USEPA.

N.J.A.C. 7:26D Appendix 2, Equation 2 is:

Click here to view image

N.J.A.C. 7:26D Appendix 2, Equation 3-Nonresidential Carcinogenic Ingestion-Dermal Human Health-Based Criteria

The origin of the Department nonresidential soil remediation standard for the ingestion-dermal exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:

Click here to view image

The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:

Click here to view image

The Department calculation of the nonresidential carcinogenic ingestion-dermal criterion is based on an adult outdoor worker exposure scenario.

As such, the RSLE states:

Click here to view image

and

Click here to view image

The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:

Click here to view image

And

Click here to view image

Because

Click here to view image

the second equation further simplifies to:

Click here to view image

Starting with the Department-modified base USEPA equation, as described above:

Click here to view image

1. Insert the simplified equations for
SL_{ow-soil-ca-ing} and
SL_{ow-soil-ca-der} described above into the denominator of
the SL_{ow-soil-ca-ing-der} equation, which then
becomes:

Click here to view image

2. Simplify the reciprocals in the equation denominator immediately above (similar to what was done in the derivation of N.J.A.C. 7:26D Appendix 2, Equation 1 above) using the respective terms:

Click here to view image

and

Click here to view image

Again, this is the same as multiplying the reciprocals in the equation denominator by 1.

3. This results in the following:

Click here to view image

4. After separating out the common terms
(EF_{OW} x ED_{OW}) and

Click here to view image

from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the expression:

Click here to view image

Performing steps 1 through 4 above results in the following expression:

Click here to view image

This USEPA terminology (immediately above), which is for a nonresidential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

TR | TR | Target cancer risk |

AT_{ow} |
AT | Averaging time - outdoor worker |

LT | LT | Lifetime |

CSF_{o} |
CSF_{o} |
Oral cancer slope factor |

RBA | None | Relative Bio-availability |

IR_{ow} |
IR | Soil ingestion rate-outdoor worker |

CSF_{d} |
CSFD | Dermal cancer slope factor |

AF_{ow} |
AF | Soil adherence factor-outdoor worker |

ABS_{d} |
ABS_{d} |
Dermal absorption fraction |

10^{-6}kg mg |
10^{-6}kg mg |
Unit conversion factor |

GIABS | GIABS | Gastro-intestinal absorption fraction |

Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:

Click here to view image

Note that the USEPA term
SL_{ow-soil-ca-ing-der} is the equivalent of the Department
term ID_{c}. In addition, there is no Department RBA
parameter because the value is usually 1. Consequently, an RBA parameter does
not appear in the translated equation. The equation presented immediately above
is equivalent to the Department equation presented in N.J.A.C. 7:26D Appendix 2
as Equation 3 and verifies its equivalence with equations used by the
USEPA.

N.J.A.C. 7:26D Appendix 2, Equation 3 is:

Click here to view image

N.J.A.C. 7:26D Appendix 2, Equation 4--Nonresidential Noncarcinogenic Ingestion-Dermal Human HealthBased Criteria

The origin of the Department nonresidential soil remediation standard for the ingestion-dermal exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

Click here to view image

Click here to view image

The Department calculation of the nonresidential noncarcinogenic ingestion-dermal criterion is based on an adult outdoor worker exposure scenario. As such, the RSLE states:

Click here to view image

and

Click here to view image

Click here to view image

and

Click here to view image

Because

Click here to view image

the second equation further simplifies to:

Click here to view image

Starting with the Department-modified base USEPA equation, as described above:

1. Insert the simplified equations for
SL_{ow-soil-nc-ing} and
SL_{ow-soil-nc-der} described above into the denominator of
the SL_{ow-soil-nc-ing-der} equation which then
becomes:

Click here to view image

2. Simplify the reciprocals in the equation denominator immediately above (similar to what was done in the derivation of N.J.A.C. 7:26D Appendix 2, Equation 1 above) using the respective terms:

Click here to view image

and

Click here to view image

Again, this is the same as multiplying each of the reciprocals in the equation denominator by 1.

3. This results in the following:

Click here to view image

4. After separating out the common terms

Click here to view image

and Click here to view image

from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the term:

Click here to view image

Performing steps 1 through 4 above results in the following expression:

Click here to view image

This USEPA terminology (immediately above), which is for a nonresidential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

THQ | THQ | Target hazard quotient |

AT_{ow} |
T | Averaging time-outdoor worker |

EF_{ow} |
EF | Exposure frequency-outdoor worker |

BW_{ow} |
BW | Body weight-outdoor worker |

ED_{ow} |
ED | Exposure duration-outdoor worker |

RBA | None | Relative Bio-availability |

RfD_{o} |
RfD_{o} |
Oral reference dose |

IR_{ow} |
IR | Soil ingestion rate-outdoor worker |

RfD_{D} |
RfDD | Dermal reference dose |

SA_{ow} |
SA | Skin surface area-outdoor worker |

AF_{ow} |
AF | Soil adherence factor-outdoor worker |

ABS_{d} |
ABS_{d} |
Dermal absorption fraction |

10^{-6}kg mg |
10^{-6}kg mg |
Unit conversion factor |

GIABS | GIABS | Gastro-intestinal absorption fraction |

Click here to view image

Note that the USEPA term
SL_{ow-soil-nc-ing-der} is the equivalent if the Department
term ID_{nc.} In addition, there is no Department RBA
parameter because the value is usually 1. Consequently, an RBA parameter does
not appear in the translated equation. The equation presented immediately above
is equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 2
as Equation 4 and verifies its equivalence with equations used by the
USEPA.

N.J.A.C. 7:26D Appendix 2, Equation 4 is:

Click here to view image

N.J.A.C. 7:26D Appendix 3, Equation 1--Carcinogenic Inhalation Human Health-Based Criteria

The Department addresses both residential and nonresidential land uses in calculating the carcinogenicbased inhalation exposure pathway soil criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.

The origin of the Department residential soil remediation standard for the inhalation exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by isolating the inhalation related screening level term:

Click here to view image

The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the inhalation aspect, which is designated:

Click here to view image

The RSLE states that:

Click here to view image

The above equation includes the units for the listed input parameters. Deleting the units simplifies the equation to:

Click here to view image

This USEPA terminology, which is for a residential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

TR | TR | Target cancer risk |

AT_{res} |
AT | Averaging time - residential |

LT | LT | Lifetime |

IUR | IUR | Inhalation unit risk factor |

EF_{res} |
EF | Exposure frequency - residential |

VF_{ulim} |
VF | Soil-to-air volatilization factor |

PEF | PEF | Particulate emission factor |

ED_{res} |
ED | Exposure duration - residential |

ET_{res} |
ET | Exposure time - residential |

1000 ug /mg | 1000 ug/ mg | Unit conversion factor |

1 day/24 hours | 1 day/24 hours | Unit conversion factor |

Click here to view image

As the USEPA term SL res-soil-ca-inh is the equivalent of the
Department term Inh_{c}, the equation presented above is
equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 3 as
Equation 1 and verifies its equivalence with equations used by the
USEPA.

N.J.A.C. 7:26D Appendix 3, Equation 1 is:

Click here to view image

N.J.A.C. 7:26D Appendix 3, Equation 2--Noncarcinogenic Inhalation Human Health-Based Criteria

The Department addresses both residential and nonresidential land uses in calculating the noncarcinogenicbased inhalation exposure pathway soil criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.

The origin of the Department residential soil remediation standard for the inhalation exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by isolating the inhalation related screening level term:

Click here to view image

The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the inhalation aspect, which is designated:

Click here to view image

The RSLE states that:

Click here to view image

The above equation includes the units for the listed input parameters. Deleting the units simplifies the equation to:

Click here to view image

This USEPA terminology, which is for a residential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

THQ | THQ | Target hazard quotient |

AT_{res-a} |
AT | Averaging time-residential adult |

EF_{res-a} |
EF | Exposure frequency-residential adult |

ED_{res-a} |
ED | Exposure duration-residential adult |

ET_{res-a} |
ET | Exposure time - residential adult |

RfC | RfC | Reference concentration |

VF_{ulim} |
VF | Soil-to-air volatilization factor |

PEF | PEF | Particulate emission factor |

1 day/24 hours | 1 day/24 hours | Unit conversion factor |

Click here to view image

As the USEPA term SL res-soil-nc-inh is the equivalent of the
Department term Inh_{nc}, the equation presented above is
equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 3 as
Equation 2 and verifies its equivalence with equations used by the
USEPA.

N.J.A.C. 7:26D Appendix 3, Equation 2 is:

Click here to view image

N.J.A.C. 7:26D Appendix 5, Equation 1--Carcinogenic Indoor Air Human Health-Based Criteria

The Department addresses both residential and nonresidential land uses in calculating the carcinogenic indoor air human health-based criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.

The origin of the Department residential indoor air remediation standard for the vapor intrusion exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

The above equation includes the units for the listed input parameters. Deleting the units simplifies the equation to:

Click here to view image

This USEPA terminology, which is for a residential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

TR | TR | Target cancer risk |

AT_{res} |
AT | Averaging time - residential |

LT | LT | Lifetime |

IUR | IUR | Inhalation unit risk factor |

EF_{res} |
EF | Exposure frequency - residential |

ED_{res} |
ED | Exposure duration - residential |

ET_{res} |
ET | Exposure time - residential |

1 day/24 hours | 1 day/24 hours | Unit conversion factor |

Click here to view image

As the USEPA term SL_{res-air-ca} is the
equivalent of the Department term IA_{c}, the equation
presented above is equivalent to the Department equation presented at N.J.A.C.
7:26D Appendix 5 as Equation 1 and verifies its equivalence with equations used
by the USEPA.

N.J.A.C. 7:26D Appendix 5, Equation 1 is:

Click here to view image

N.J.A.C. 7:26D Appendix 5, Equation 2--Noncarcinogenic Indoor Air Human Health-Based Criteria

The Department addresses both residential and nonresidential land uses in calculating the noncarcinogenic indoor air human health-based criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.

The origin of the Department residential indoor air remediation standard for the vapor intrusion exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):

Click here to view image

The above equation includes the units for the listed input parameters. Deleting these units simplifies the equation to:

Click here to view image

This USEPA terminology, which is for a residential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:

USEPA Term | Department Term | USEPA Definition |

THQ | THQ | Target hazard quotient |

AT_{res-a} |
AT | Averaging time-residential adult |

EF_{res} |
EF | Exposure frequency-residential adult |

ED_{res} |
ED | Exposure duration-residential adult |

ET_{res} |
ET | Exposure time - residential adult |

RfC | RfC | Reference concentration |

1000 ug/ mg | 1000 ug/ mg | Unit conversion factor |

1 day/24 hours | 1 day/24 hours | Unit conversion factor |

Click here to view image

As the USEPA term SL_{res-air-nc} is the
equivalent of the Department term IA_{nc}, the equation
presented above

is equivalent to the equation presented at N.J.A.C. 7:26D Appendix 5 as Equation 2 and verifies its equivalence with equations used by the USEPA.

N.J.A.C. 7:26D Appendix 5, Equation 2 is:

Click here to view image

References

USEPA (2018) Regional Screening Levels (RSLs)--Equations (November 2018)

http://www.epa.gov/risk/regional-screening-levels-rsls-equations

TECHNICAL REQUIREMENTS FOR SITE REMEDIATION

### Notes

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