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).  

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 by-product 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. For 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. EPA-HQ-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 systems that do not meet the criteria in
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 non-exempt stack systems in the fab. The
following is an explanation and derivation of equations used in the
stack test method. 

∆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. 

 	(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).儍ॳऽ汆睯爠瑡⁥景琠敨猠慴正猠獹整⁭ⱳ搠
牵湩⁧桴⁥慳灭楬杮瀠牥潩⁤洨⼳業⥮മ噓㴉匉慴摮牡
⁤潭慬⁲潶畬敭漠⁦慧⁳〨〮㈲〴洠⼳ⵧ潭敬愠⁴㠶䚰
愠摮ㄠ愠浴⸩

∆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.

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.

Additionally, reporters would calculate “dif,” the average
consumption-weighted fraction of F-GHG 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).

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. The term “EFif” is the 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 F-GHG
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
(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.

 	(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 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: 

 	(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. 

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 F-GHG 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.

 	(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
by-product 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-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.

	

 	(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). 

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.

 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.   

 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.”

…

†

#

$

H

h

À

É

Ë

Ó

„

…

†

‰

摧䯇

h

搒Ǡ摧䐛@

摧⌁<

h

h

h

(ions from each of the stack systems that are not tested can be
attributed to only one particular collection of process tools during the
test.

 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.

 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.”

DRAFT

DO NOT CITE OR QUOTE

Page   PAGE  11  of   NUMPAGES   11 

