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MEMORANDUM – DERIVATION OF STACK TEST METHOD AND EFFECTIVE 

FACILITY-WIDE DESTRUCTION AND REMOVAL EFFICIENCY EQUATIONS FOR 

SUBPART I 2012 PROPOSED AMENDMENTS

To: Docket EPA-HQ-OAR-2011-0028

From: Alexis McKittrick, EPA/Climate Change 

Date: September 11, 2012

Subject: Derivation of subpart I stack test method equations in 40 CFR part 98.93(i) and 

effective facility-wide destruction or removal efficiency equations in 40 CFR part 

98.96(r). 

1.0 Introduction

In this memorandum, we present the derivation of equations for the periodic stack test method in 

proposed 40 CFR part 98.93(i)(3). Specifically, we show the derivation for proposed Equations 

I-17, I-19, I-21, I-23, and I-24 in subpart I, which would be used by reporters to calculate annual 

emissions of fluorinated greenhouse gases (F-GHGs) for stack systems that are tested in an 

electronics manufacturing fab. We do not show the derivation of equations which apply to byproduct F-GHGs (e.g., proposed Equations I-18, I-20, I-22 in subpart I); however, the same 

derivation methodology presented in this memorandum applies to the by-product F-GHG 

equations.1For more information regarding the use of the stack test method in proposed 40 CFR 

98.96, see “Technical Support for the Stack Test Option for Estimating Fluorinated Greenhouse 

Gas Emissions from Electronics Manufacturing Facilities Under Subpart I,” Docket ID No. EPAHQ-OAR-2011-0028. 

We also present the derivation of equations used to calculate an effective facility-wide 

destruction or removal efficiency (DRE) that all facilities would be required to provide in 

proposed 40 CFR 98.96(r). 

2.0 Derivation of Stack Test Method Equations

To calculate annual F-GHG emissions for a fab using the periodic stack test method in proposed 

amendments to subpart I, reporters would perform stack testing of all stack systems2that do not 

 

1

Proposed Equations I-18, I-20, and I-22 apply specifically to by-product F-GHGs. These by-product equations 

apply to F-GHGs which are not input gases and are created during electronics manufacturing production processes 

or in abatement systems and F-GHGs which are input gases whose emissions exceed consumption because such 

gases are generated as by-products of other input gases. 

2 EPA is proposing to define “stack system” to mean “one or more stacks that are connected by a common header or 

manifold, through which a fluorinated GHG-containing gas stream originating from one or more fab processes is, or 

has the potential to be, released to the atmosphere. For purposes of this subpart, stack systems do not include 

emergency vents or bypass stacks through which emissions are not usually vented under typical operating 

conditions.”
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meet the criteria3in proposed 40 CFR 98.93(i)(2) while concurrently monitoring the F-GHG

consumption of the tools exhausting to those stack systems and the abatement system downtime 

in the fab for a sampling period (e.g., 8 hours). Reporters would then calculate fab-specific 

emission factors using the collected data. Reporters would use the fab-specific emission factors, 

along with activity data for the reporting year, to calculate annual F-GHG emissions for all nonexempt stack systems in the fab. The following is an explanation and derivation of equations 

used in the stack test method. 

Reporters would calculate the total F-GHG input gas i emitted during the sampling period using 

proposed Equation I-17 in subpart I. Proposed Equation I-17 in subpart I requires reporters to 

determine the average hourly concentration of F-GHG input gas in the effluent of the stack 

system. The concentration of the gas is integrated over time (represented by the summation of 

“Xism*∆tm”) and then multiplied by the flow rate of the stack system (with the appropriate 

conversions) to obtain the mass of F-GHG input gas i emitted over the sampling period. 

m

N

m

ism

is i s

t

X

SV

E  MW Q   *

10

*

10

1

*

1

* *

3 1 6 (Eq. I-17 in subpart I)

Where:

Eis = Total fluorinated GHG input gas i, emitted from stack system s, 

during the sampling period (kg).

Xism = Average concentration of fluorinated GHG input gas i in stack system 

s, during the time interval m (ppmv).

MWi = Molecular weight of fluorinated GHG input gas i (g/g-mole).

Qs = Flow rate of the stack system s, during the sampling period (m3/min).

SV = Standard molar volume of gas (0.02240 m3/g-mole at 68°F and 1 

atm).

∆tm = Length of time interval m (minutes). Each time interval in the 

sampling period must be less than or equal to 60 minutes (for example 

an 8 hour sampling period would consist of at least 8 time intervals).

1/103= Conversion factor (1 kilogram/1,000 grams).

106= Conversion factor for Xism from ppmv to fractional volume.

i = Fluorinated GHG input gas.

s = Stack system.

 

3 EPA is proposing that a fab would not be required to test a certain stack system if 1) the sum of the F-GHG 

emissions from all combined stack systems in the fab that are not tested is less than 10,000 metric CO2e (mtCO2e) 

per year; 2) each of the stack systems that are not tested are within the fab’s lowest F-GHG emitting stack systems 

that together emit 15 percent or less of total fab F-GHG CO2e emissions; and 3) the F-GHG emissions from each of 

the stack systems that are not tested can be attributed to only one particular collection of process tools during the 

test.
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N = Total number of time intervals m in sampling period.

m = Time interval. 

Reporters would also calculate “UTf,” the total uptime of abatement systems that are vented to 

the stack systems being tested during the sampling period using proposed Equation I-23 in 

subpart I. Reporters would evaluate the terms “Tdpf” and “UTpf” for the sampling period, instead 

of the reporting year, when developing fab-specific F-GHG emission factors. The terms “Tdpf” 

and “UTpf” would be evaluated for the reporting year for all abatement systems in the fab when 

determining fab emissions as required in proposed Equation I-21 in subpart I.

(Eq. I-23 in subpart I)

Where:

UTf = The total uptime of all abatement systems, for fab f (expressed as a 

decimal fraction).

Tdpf = The total time, in minutes, that abatement system p, connected to 

process tool(s) in fab f, is not in operational mode as defined in the 

current 40 CFR 98.98. 

UTpf = Total time, in minutes per year, in which the tool(s) connected at any

point during the year to abatement system p, in fab f could be in 

operation. For determining the amount of tool operating time, a 

facility could assume that tools that were installed for the whole of the 

year were operated for 525,600 minutes per year. For tools that were 

installed or uninstalled during the year, a facility would have to

prorate the operating time to account for the days in which the tool 

was not installed; and treat any partial day that a tool was installed as 

a full day (1,440 minutes) of tool operation. For an abatement system 

that has more than one connected tool, the tool operating time would 

be 525,600 minutes per year if there was at least one tool installed at 

all times throughout the year. If a facility had tools that are idle with 

no gas flow through the tool, they could calculate total tool time using 

the actual time that gas is flowing through the tool.

f = Fab.

p = Abatement system.

Proposed Equation I-23 makes a simplifying assumption that abatement systems for F-GHG are 

almost always “point-of-use” abatement systems with only one tool per system, and that a 

system would rarely, if ever, have more than one tool connected at a time. This assumption is 

consistent with typical fab configurations. Otherwise, for abatement systems connected to 

multiple tools, both Tdpf and UTpf would need to be multiplied by the number of tools connected 

to the abatement system to ensure that system was properly weighted in the calculation.
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Additionally, reporters would calculate “dif,” the average consumption-weighted fraction of FGHG input gas i destroyed or removed in point-of-use abatement systems in fab f, using 

proposed Equation I-24 in subpart I. 

(Eq. I-24 in subpart I)

Where:

dif = The average weighted fraction of fluorinated GHG input gas i 

destroyed or removed in abatement systems in fab f (expressed as a 

decimal fraction).

Cijf = The amount of fluorinated GHG input gas i consumed for process 

type j fed into abatement systems in fab f (kg).4

DREij = Destruction or removal efficiency for fluorinated GHG input gas i in 

abatement systems connected to process tools where process type j is 

used (expressed as a decimal fraction) determined according to 

proposed amendments 40 CFR 98.94(f).

f = fab.

i = Fluorinated GHG input gas.

j = Process type.

With the results of Equations I-17, I-23, and I-24, total emissions from fab f would be calculated 

for the sampling period using the simplified formula presented in Equation A of this 

memorandum.

(Eq. A)

The left side of Equation A represents the summation of the mass of F-GHG input gas i emitted

from all stack systems tested in the fab. 

The first set of terms on the right side of Equation A (EFif * UTf * Activityif) represent emissions 

during the time that abatement systems are in an operational mode.

5

The term “EFif” is the 

 

4

In proposed Equation I-24 in subpart I, the ratio formed as a result of the multiplication and subsequent division by 

the term “Cijf” is an approximation of the ratio of input gas i fed to abatement systems in process type j since 

proposed Equation I-24 does not account for the utilization of input gas i in process type j.

5 As proposed in subpart I, the revised definition of “operational mode” would mean “the time in which an 

abatement system is properly installed, maintained, and operated according to manufacturers’ specifications as 

required in proposed 40 CFR 98.93(f)(1). This includes being properly operated within the range of parameters in 

the operations manual provided by the system manufacturer.”
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emission factor for F-GHG input gas i in fab f if all abatement systems are operating. The term

“Activityif” represents the consumption of F-GHG input gas i in fab f during the sampling period. 

The product of the emission factor and the consumption represents emissions from fab f of FGHG input gas i if all abatement systems are operating; however, abatement systems may not be 

in operation for the entire duration of the evaluation period, therefore, the consumption is 

multiplied by the uptime factor to calculate the amount of F-GHG input gas i consumed during

the sampling period while the abatement systems are in operation. 

The second set of terms on the right side of Equation A represent emissions during the time that 

abatement systems are not in operation. The first term, “EFif,” is divided by “(1-aif*dif)” to yield 

an emission factor which does not include abatement (i.e., these are emissions from the tools 

before abatement). The term “aif” represents the fraction of F-GHG input gas i used in fab f in 

tools with abatement systems. The term “dif” represents the DRE of F-GHG input gas i for the 

abatement systems connected to those tools in fab f. The second term “(1- UTf)” is the total time 

for which abatement systems are not operating, for fab f, expressed as a decimal fraction. 

Multiplication of the terms results in emissions from the stack system when abatement systems 

are not in an operational mode. The addition of the terms on the left and right sides of the plus 

sign represent the total emissions of F-GHG input gas i from all stacks in the fab.

All terms in Equation A are known except “EFif.” Equation A can be rearranged to solve for 

“EFif,” first by grouping similar terms:

(Eq. A1)

Then, a simple rearrangement yields proposed Equation I-19 in subpart I:

(Eq. I-19 in subpart I)

Where:

EFif = Emission factor for fluorinated GHG input gas i, from fab f, 

representing 100 percent abatement system uptime (kg emitted/kg 

input gas consumed).

Eis = Mass emission of fluorinated GHG input gas i from stack system s, 

during the sampling period (kg emitted).

Activityif = Consumption of fluorinated GHG input gas i, for fab f, in the tools 

vented to the stack systems being tested, during the sampling period, 

as determined following the procedures specified proposed 40 CFR 

98.94(j)(3) (kg consumed).

UTf = The total uptime of all abatement systems for fab f, during the 

sampling period, as calculated in proposed Equation I-23 in subpart I
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(expressed as decimal fraction). If the stack system does not have 

abatement systems on the tools vented to the stack system, the value 

of this parameter is zero.

aif = Fraction of fluorinated GHG input gas i used in fab f in tools with 

abatement systems (expressed as a decimal fraction).

dif = Fraction of fluorinated GHG input gas i destroyed or removed in 

abatement systems connected to process tools in fab f, as calculated in 

proposed Equation I-24 in subpart I (expressed as decimal fraction). If 

the stack system does not have abatement systems on the tools vented 

to the stack system, the value of this parameter is zero.

f = Fab.

i = Fluorinated GHG input gas.

s = Stack system.

Replacement of the term “Activityif” in equation A of this memo, which represents the 

consumption of F-GHG input gas i in fab f during the sampling period, with the term “Cif” which 

represents the consumption of F-GHG input gas i in fab f during the reporting year, yields 

proposed Equation I-21 in subpart I. Proposed Equation I-21 in subpart I is used to calculate 

annual fab-level emissions. Note that the value of the term “UTf,” would be determined for the 

reporting year, instead of the sampling period when using proposed Equation I-21 in subpart I.

 

  if f

if if

if

if if if f C UT

a d

EF

E EF C UT 



  * * 1

1 ( * )

* * (Eq. I-21 in subpart I)

Where:

Eif = Annual emissions of fluorinated GHG input gas i (kg/year) from the 

stack systems that are tested for fab f.

EFif = Emission factor for fluorinated GHG input gas i emitted from fab f, as 

calculated in proposed Equation I-19 in subpart I (kg emitted/kg input 

gas consumed).

Cif = Total consumption of fluorinated GHG input gas i in tools that are 

vented to stack systems that are tested, for fab f, for the reporting 

year, as calculated using Equation I-13 in subpart I (kg/year).

UTf = The total uptime of all abatement systems for fab f, during the 

reporting year, as calculated using proposed Equation I-23 in subpart 

I(expressed as a decimal fraction).

aif = Fraction of fluorinated GHG input gas i used in fab f in tools with 

abatement systems (expressed as a decimal fraction).

dif = Fraction of fluorinated GHG input gas i destroyed or removed in 

abatement systems connected to process tools in fab f that are 
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included in the stack testing option, as calculated in proposed 

Equation I-24 in subpart I (expressed as decimal fraction).

f = Fab.

i = Fluorinated GHG input gas.

3.0 Derivation of Facility-Wide Destruction or Removal Efficiency

In order to determine the extent to which GHG emissions from electronics manufacturing are 

being abated, EPA is proposing to include in 40 CFR 98.96(r) a requirement for each facility to 

calculate and report an effective facility-wide DRE. This factor would be calculated as one 

minus the ratio of actual reported emissions to the emissions that would occur if there were no 

abatement. EPA has developed three equations, Equations I-26, I-27, and I-28 of the proposed 

subpart I, to support this calculation. These equations would not require reporters to collect any

additional data, but instead rely on data already collected to calculate and report GHG emissions 

from a facility. 

Reporters would use proposed Equation I-26 in subpart I to calculate an effective facility-wide 

DRE as follows:





















  



 



 

j

N O, j N O, j N O

j

j N O

i

i i

FAC UAFGHG SFGHG C * ( U )* GWP

FGHG * GWP N O *GWP

DRE

2 2 2

2 2

1

1 (Eq. I-26)

Where:

DREFAC = Facility-wide effective destruction or removal efficiency value, 

expressed as a decimal fraction.

FGHGi = Total emissions of each fluorinated GHG i emitted from electronics 

manufacturing processes in the facility, calculated according to the 

procedures specified in proposed 40 CFR 98.93. 

N2Oj = Emissions of N2O from each N2O-emitting electronics manufacturing 

process j in the facility, expressed in metric ton CO2 equivalents, 

calculated according to the procedures in proposed 40 CFR 98.93.

UAFGHG = Total unabated emissions of fluorinated GHG emitted from 

electronics manufacturing processes in the facility, expressed in 

metric ton CO2 equivalents as calculated in proposed Equation I-27 of 

subpart I.

SFGHG = Total unabated emissions of fluorinated GHG emitted from 

electronics manufacturing processes in the facility, expressed in 

metric ton CO2 equivalents, as calculated in proposed Equation I-28 

of subpart I. 
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CN2O,j = Consumption of N2O in each N2O emitting process j, expressed in 

metric ton CO2 equivalents.

1-UN2O,j = N2O emission factor for each N2O emitting process j from proposed 

Table I-8 of subpart I.

GWPi = GWP of emitted fluorinated GHG i from Table A-1 of 40 CFR part 

98, subpart A. For those fluorinated GHGs for which Table A-1 of 40 

CFR part 98, subpart A does not define a GWP value, a facility would 

use a GWP value of 2,000.

GWPN2O = GWP of N2O from Table A-1 of 40 CFR part 98, subpart A.

i = Fluorinated GHG.

j = Process Type.

The fraction on the right side of proposed Equation I-26 in subpart I represents the actual 

reported total GHG emissions from a facility divided by the total GHG emissions that would 

occur if there were no abatement. In the numerator, the terms “FGHGi” and “N2Oj” represent the 

actual reported emissions, in metric tons of all F-GHG and N2O respectively, that facilities 

would report under proposed 40 CFR 98.96(c). The terms for each F-GHG and for N2O in the 

numerator are multiplied by the appropriate global warming potential (GWP) from Table A-1 of 

40 CFR part 98, subpart A to convert to mtCO2e. Note that these CO2e emissions are already 

calculated as part of the total, facility-wide CO2e emissions reported under §98.3(c)(4)(i). In the 

denominator, the terms “UAFGHG” and “SFGHG” represent the total unabated emissions, in 

mtCO2e, of all F-GHG emitted from electronics manufacturing processes whose emissions of FGHG were calculated by the default utilization and by-product formation rate procedures in 

proposed 40 CFR 98.93(a) or 98.93(i)(4) and according to the stack testing procedures in 

proposed 40 CFR 98.93(i)(3), respectively. The far right term in the denominator represents the 

total unabated emissions of N2O, calculated by summing the product of N2O consumption and 

utilization across each process type (in addition to multiplying by the appropriate GWP to 

convert to mtCO2e). 

Note that the Equation I-26 is calculated on a facility-wide basis, not on a fab basis. If a facility

reporting under subpart I has more than one fab, then data and emissions from all the fabs at a 

facility must be aggregated to perform this facility-wide calculation.

The term “UAFGHG” is calculated using proposed Equation I-27 in subpart I. The term 

“UAFGHG” represents unabated emission of F-GHGs whose emissions were calculated and 

reported according to proposed 40 CFR 98.93(a) or 98.93(i)(4), based on default emission 

factors. Unabated emissions of input gases are calculated by summing the product of the 

consumption of input gas i for process type j and one minus the utilization of input gas i for 

process type j for all input gases and process types (multiplied by the appropriate GWP). 

Unabated emissions of by-products are calculated by summing the product of the consumption of 

input gas i for process type j and the by-product formation rate of by-product k, from input gas i, 

for process type j across all input gases and process types (multiplied by the appropriate GWP).

The values Cij, (1-Uij), Cij, and Bijk are the same as those used in Equations I-8 and I-9.
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    

i j

ij ijk k

i j

UAFGHG Cij* (1 Uij )* GWPi C * B * GWP (Eq. I-27)

Where:

UAFGHG = Total unabated emissions of fluorinated GHG i emitted from 

electronics manufacturing processes in the facility, expressed in 

metric ton CO2e for which the facility calculated total emissions

according to the procedures in proposed 40 CFR 98.93(a) or 

98.93(i)(4).

Cij = Total consumption of fluorinated GHG i, apportioned to process j, 

expressed in metric ton CO2e which the facility used to calculate total 

emissions according to the procedures in proposed 40 CFR 98.93(a) 

or 98.93(i)(4).

Uij = Process utilization rate for fluorinated GHG i, process type j, which 

the facility used to calculate total emissions according to the 

procedures in proposed 40 CFR 98.93(a) or 98.93(i)(4).

GWPi = GWP of emitted fluorinated GHG i from Table A-1 of 40 CFR part 

98, subpart A. For those fluorinated GHGs for which Table A-1 of 40 

CFR part 98, subpart A does not define a GWP value, a facility would 

use a GWP value of 2,000.

GWPk = GWP of emitted fluorinated GHG by-product k, from Table A-1 of 40 

CFR part 98, subpart A. For those fluorinated GHGs for which Table 

A-1 of 40 CFR part 98, subpart A does not define a GWP value, a 

facility would use a GWP value of 2,000.

Bijk = By-product formation rate of fluorinated GHG k created as a byproduct per amount of fluorinated GHG input gas i (kg) consumed by 

process type j (kg).

i = Fluorinated GHG.

j = Process Type.

k = Fluorinated GHG by-product.

The term “SFGHG,” is calculated by using proposed Equation I-28 in subpart I. The term 

“SFGHG” represents unabated F-GHG emissions for all fabs within a facility whose emissions 

were calculated and reported according to the proposed 40 CFR 98.93(i)(3), based on stack 

testing. The first term in brackets (“[ ]”) on the right side of proposed Equation I-28 in subpart I 

represents unabated emission of input gases. The term, “EFif,” is divided by “(1-aif*dif)” to yield 

an emission factor which does not include abatement. The term “aif” represents the fraction of F-
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GHG input gas i used in fab f in tools with abatement systems. The term “dif” represents the 

DRE of F-GHG input gas i for the abatement systems connected to those tools in fab f. A similar 

division is performed for the by-product emission factor in the second term in brackets on the 

right side of the equation. The “unabated” emission factors are multiplied by consumption and 

the appropriate GWP value and summed across input gases and by-products for all fabs to 

calculate unabated input gas and by-product emissions for the facility, respectively, whose 

emissions were calculated and reported according the proposed 40 CFR 98.93(i)(3). The values 

EFif and EFkf are the same as those calculated using Equations I-19 and I-20, respectively, and 

the values Cif, aif, dif, akf, and dkf are the same as those used in Equations I-21 and I-22.

         







































k f

k

i

if

k f kf

kf

i f

if i

if if

if * C *GWP

a * d

EF

*C *GWP

a * d

EF

SFGHG

1 1

(Eq. I-28)

Where:

SFGHG = Total unabated emissions of fluorinated GHG i emitted from 

electronics manufacturing processes in the facility, expressed in 

metric ton CO2e for which a facility calculated total emission 

according to the procedures in proposed 40 CFR 98.93(i)(3).

EFif = Emission factor for fluorinated GHG input gas i, emitted from fab f, 

as calculated in proposed Equation I-19 of subpart I (kg emitted/kg 

input gas consumed). 

aif = Fraction of fluorinated GHG input gas i used in fab f in tools with 

abatement systems (expressed as a decimal fraction). 

dif = Fraction of fluorinated GHG i destroyed or removed in abatement 

systems connected to process tools in fab f, which a facility used to 

calculate total emissions according to the procedures in proposed 40 

CFR 98.93(i)(3) (expressed as a decimal fraction). 

Cif = Total consumption of fluorinated GHG input gas i, of tools vented to 

stack systems that are tested, for fab f, for the reporting year, 

expressed in metric ton CO2e which a facility used to calculate total 

emissions according to the procedures in proposed 40 CFR

98.93(i)(3) (expressed as a decimal fraction). 

EFkf = Emission factor for fluorinated GHG by-product gas k, emitted from 

fab f, as calculated in proposed Equation I-20 of subpart I (kg 

emitted/kg of all input gas consumed in tools vented to stack systems 

that are tested).

akf = Fraction of all input gas used in fab f in tools with abatement systems 

(expressed as a decimal fraction). 
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dkf = Fraction of fluorinated GHG by-product k destroyed or removed in 

abatement systems connected to process tools in fab f, which a facility

used to calculate total emissions according to the procedures in

proposed 40 CFR 98.93(i)(3) (expressed as a decimal fraction).

GWPi = GWP of emitted fluorinated GHG i from Table A-1 of 40 CFR part 

98, subpart A. For those fluorinated GHGs for which Table A-1 of 40 

CFR part 98, subpart A does not define a GWP value, a facility would 

use a GWP value of 2,000.

GWPk = GWP of emitted fluorinated GHG by-product k, from Table A-1 of 40 

CFR part 98, subpart A. For those fluorinated GHGs for which Table 

A-1 of 40 CFR part 98, subpart A does not define a GWP value, a 

facility would use a GWP value of 2,000.

i = Fluorinated GHG.

j = Process Type.

k = Fluorinated GHG by-product.