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Page 1 of 11 **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 1 1 , 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). Specificall y, we show the derivation for proposed Equation s 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 gas es (F - GHG s ) for stack sy stems that are tested in an electronics manufacturing fab. We do not show the derivation of equations which appl y 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. 1 For more information regarding the use of the stack test method in propose d 40 CFR 98.96, see “Technical Support for the Stack Test Option for Estimating F luorinated 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 , rep orters would perform stack testing of all stack sy stems 2 that 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 “s tack 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. ”**DRAFT DO NOT CITE OR QUOTE** 

Page 2 of 11 meet the criteria 3 in proposed 40 CFR 98.93(i)(2) while concurrentl y monitoring the F - GHG consumption of the tools exhausting to those stack sy stems 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 sy stems in the fab. The following is an explanation and derivation of equations used in the stack test method. Report er s would calculate the total F - GHG input gas i emitted during the sampling period using propose d Equation I - 17 in subpart I . Proposed Equation I - 17 in subpart I require s reporters to determine the av erage hourly concentration of F - GHG input gas in the effluent of the stack sy stem . The concentration of the gas is integrated over time (represented by the summation of “ X ism * ∆ t m ”) and then multiplied by the flow rate of the stac k s ys tem (with the appropriate conversions ) to obtain the mass of F - GHG input gas i emitted over the sampling period.

m N m ism s i is 

### t X SV Q MW E   

# 

 

### * 10 * 10 1 * 1 * * 1 6

3 (Eq. I - 17 in subpart I) Where: E is = Total fluorinated GH G input gas i, emitted from stack s ys tem s, during the sampling period (kg). X ism = Average concentration of fluorinated GHG input gas i in stack system s, during the time interval m (ppmv). MW i = Molecular weight of fluorinated GHG input gas i (g/g - mole). Q s = Flow rate of the stack s ys tem s, during the sampling period (m 3 /min). SV = Standard molar volume of gas (0.02240 m 3 /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). 1/10 3 = Conversion factor (1 kilogram/1,000 grams). 10 6 = Conversion factor for X ism from ppmv to fractional volume. i = Fluorinated GHG input gas. s = Stack sy stem. 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 CO 2 e (mtCO 2 e) per year; 2) each of the stack systems that are not tested are within the fab’s lowe st F - GHG emitting stack systems that together emit 15 percent or less of total fab F - GHG CO 2 e emissions; and 3) the F - GHG emiss 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.**DRAFT DO NOT CITE OR QUOTE** 

Page 3 of 11 N = Total number of time intervals m in sampling period. m = Time interval. Reporters would also calculate “ UT f , ” the total uptime of abatement s ys tems that are vented to the stack s ys tems being tested during the sampling period using proposed Equation I - 23 in subpart I. Reporters would evaluate th e terms “Td p f ” and “UTpf

” for the sampling period , instead of the reporting ye ar , when deve loping fab - specific F - GHG emission factors . The terms “Td p f ” and “UTpf

” would be evaluated for the reporting year for all abatement s ys tems in the fab when determining fab emissions as required in proposed Equation I - 21 in subpart I . (Eq. I - 23 in subpart I) Where: UT f = The total uptime of all abatement systems, for fab f (expressed as a decimal fraction). Td pf = The total time, in minutes, that abatement s ys tem 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 ye ar to abatement sy stem p, in fab f could be in operation. For determining the amount of tool operating time, a facility could ass ume that tools that were installed for the whole of the ye ar were operated for 525,600 minutes per year. For tools that were installed or uninstalled during the ye ar, a facility would have to prorate the operating time to account for the day s 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 s ys tem that has more than one connected tool, the tool operating time would be 525,600 minutes per year if there w as 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 sy stem. Proposed Equation I - 23 makes a simplifying assumption that abatement systems for F - GHG are almost always “point - of

- use” abatement s ys tems with only one tool per s ystem, and that a sy stem would rarel y, if ever, have more than one tool connected at a time . This assumption is consistent with ty

pical fab con f

igurations. Otherwise, for abatement s ys tems connected to multiple tools, both Td pf and UTpf would need to be multiplied by the number of tools connected to the abatement s ys tem to ensure that s ystem was properl y weighted in the calculation.**DRAFT DO NOT CITE OR QUOTE** 

Page 4 of 11 Additionally , reporters would calculate “ d if ,” the average consumption - weighted fraction of F GHG input gas i destro ye d or removed in point - of - use abatement s ys tems 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 s ys tems in fab f (expressed as a decimal fraction). C ijf = The amount of fluorinated GHG input gas i consumed for process ty pe j fed into abatement systems in fab f (kg). 4 DRE ij = Destruction or removal efficiency for fluorinated GHG input gas i in abatement s ys tems connected to process tools where process ty pe j is used (expressed as a decimal fractio n) determined according to proposed amendments 40 CFR 98.94(f). f = fab. i = Fluorinated GHG input gas. j = Process ty pe. With the results of Equations I - 17, I - 23, and I - 24, total emissions from fab f w ould 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 s ys tems tested in the fab. The first set of terms on the right side of Equation A ( EF if * UT f * Activity if

) represent emissions during the time that abatement systems are in an operational mode . 5 The term “EF if ” is the 4 In proposed Equation I - 24 in subpart I, the ratio formed as a result of the multiplication and subsequent divisi on by the term “C ijf

” 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 def inition 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 5 of 11 emission factor for F - GHG input gas i in fab f if all abatement s ys tems are operating . The term “ Activity if ” 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 rep resents emissions from fab f of F GHG input gas i i f 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 s ys tems are in operation. The second set of terms on the right side of Equation A represent emissions during the time that abatement s ys tems are not in operation . The first term, “EF if , ” is divided by “ ( 1 - a if*d if ) ” to yield an emission factor which does not include abatement (i.e., these are emissions from the tools before abatement) . The term “ a if ” represents the fraction of F - GHG input gas i used in fab f in tools with abatement sy stems. The term “ d if ” represents the DRE of F - GHG input gas i for the abatement s ys tems connected to those tools in fab f. The second term “( 1 - UT f )” is the total time for which abatement s ys tems are not operating, for fab f, expressed as a decimal fraction. Multiplication of the terms results in emissions from the stack sy stem when abatement s ys tems 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. A ll terms in Equation A are known except “EF if . ” E quation A can be rearranged to solve for “EF if , ” first by group ing similar terms: (Eq. A1 ) Then, a simple rearrangement yi elds proposed Equation I - 19 in subpart I : (Eq. I - 19 in subpart I) Where: EF if = Emission factor for f luorinated GHG input gas i, from fab f, representing 100 percent abatement s ys tem uptime (kg emitted/kg input gas consumed). E is = Mass emission of fluorinated GHG input gas i from stack sy stem s, during the sampling period (kg emitted). Activity

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

vented to the stack s ys tems being tested, during the sampling period, as determined following the procedures specified proposed 40 CFR 9 8.94(j)(3) (kg consumed). UT f = The total uptime of all a batement systems for fab f, during the sampling period, as calculated in proposed Equation I - 23 in subpart I**DRAFT DO NOT CITE OR QUOTE** 

Page 6 of 11 (expressed as decimal fraction). If the stack system does not have abatement s ys tems on the tools vented to the stack sy stem, the value of this parameter is zero. aif = Fraction of fluorinated GHG input gas i used in fab f in tools with abatement s ys tems (expressed as a decimal fraction). dif = Fraction of fluorinated GHG input gas i destroyed or removed in abatement s ys tems connected to process tool s in fab f, as calculated in proposed Equation I - 24 in subpart I (expressed as decimal fraction). If the stack s ys tem does not have abatement s ys tems on the tools vented to the stack sy stem, the value of this parameter is zero. f = Fab. i = Fluorinated GHG input gas. s = Stack sy stem. Replacement of the term “ Activity if ” 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 “ C if ” which represents the consumption of F - GHG input g as i in fab f during the reporting year, yi elds 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 “ UT f ,” would be determined for the reporting year, ins tead of the sampling period when using proposed Equation I - 21 in subpart I. 

#     f if if if if f if if if UT C d a EF UT C EF E



   1 * * ) * ( 1 * * (Eq. I - 21 in subpart I) Where: E if = Annual emissions of fluorinated GHG input gas i (kg/ye ar) from the stack sy stems that are tested for fab f. EF if = Emi ssion 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). C if = Total consumption of fluorinated GHG input gas i in tools that are vented to stack s ys tems that are tested, for fab f, for the reporting ye ar, as calculated using Equation I - 13 in subpart I (kg/year). UT f = 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 s ys tems (expressed as a decimal fraction). dif = Fraction of fluorinated GHG input gas i destroyed or removed in abatement s ys tems connected to pro cess tools in fab f that are**DRAFT DO NOT CITE OR QUOTE** 

Page 7 of 11 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 o**  **r Removal Efficie**  **ncy** 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 rel y 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 effectiv e facility- wide DRE as follows:          

   

  

##  



j O N j , O N j , O N j O N j i i

i FAC GW P * ) U ( * C SFGHG UAFGHG GW P * O N GW P * FGHG DRE 2 2 2 2

2 1 1 (Eq. I - 26) Where: DRE FAC = Facility- wide effective destruction or removal efficiency value, expressed as a decimal fraction. FGHG i = 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. N 2 O j = Emissions of N 2 O from each N 2 O - emitting electronics manufacturing

process j in the facility , expressed in m etric ton CO 2 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 CO 2 equivalents as c alculated 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 CO 2 equivalents, as calculated in proposed Equation I - 28 of s ubp art I .**DRAFT DO NOT CITE OR QUOTE** 

Page 8 of 11 C N2O,j = Consumption of N 2 O in each N 2 O emitting process j, expressed in metric ton CO 2 equivalents. 1 - UN2O,j = N 2 O emission factor for each N 2 O emitting process j from proposed Table I - 8 of s ubpart I . GWP i = 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. GWP N2O = GWP of N 2 O from Table A - 1 of 40 CFR part 98, subpart A . i = Fluorinated GHG. j = Process Ty pe. 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 “FGHG i ” and “ N 2 O j ” represent the actual reported emissions, in metric tons of all F - GHG and N 2 O respectively , that facilities would report under proposed 40 CFR 98.96(c). The terms for each F - GHG and for N 2 O 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 mtCO 2 e. Note that these CO 2 e emissions are already calculated as part of the total, facility- wide CO 2 e emissions reported under §98.3(c)(4 )(i). In the denominator, the terms “ UAFGHG” and “SFGHG ” represent the total unabated emissions, in mtCO 2 e, of all F - GHG emitted from electronics manufacturing processes whose emissions of F GHG were calculated b y the default utilization and by- product fo rmation 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), respectivel y. The far right term in the denominator represents the total unabated emissions of N 2 O, calculated by summing the product of N 2 O consumption and utilization across each process ty pe (in addition to multiplying by the appropriate GWP to convert to mtCO 2 e). Note that the E quation I - 26 is calculated on a facility- wide basis, not on a fab basis. If a facil ity 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 typ e 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 pro duct of the consumption of input gas i for process type j and the b y- product formation rate of by- product k, from input gas i, for process ty

pe j across all input gases and process ty pes (multiplied by

the appropriate GWP ). The values C ij , (1 - U ij ), C ij , an d B ijk are the same as those used in Equations I - 8 and I - 9.**DRAFT DO NOT CITE OR QUOTE** 

Page 9 of 11 

##     

  i j k ijk ij i j i ij ij GWP * B * C GWP * ) U ( * C UAFGHG 1 (Eq. I - 27) Where: UAFGHG = Total unabated emissions of fluorinated GHG i emitted from electronics manufacturing processes in the facility, expressed in metric ton CO 2 e fo r which the facility calculated total emission s according to the procedures in proposed 40 CFR 98.93(a) or 98.93(i)(4). C ij = Total consumption of fluorinated GHG i, apportioned to process j, expressed in metric ton CO 2 e which the facility used to calculate total emissions according to the procedures in proposed 40 CFR 98.93(a) or 98.93(i)(4). U ij = Process utilization rate for fluorinated GHG i, process ty pe j, which the facility used to calculate total emissions according to the procedures in proposed 4 0 CFR 98.93(a) or 98.93(i)(4). GWP i = 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. GWP k = GWP of emitted fluorinated GHG b y- 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. B ij k = By-product formation rate of fluorinated GHG k created as a byproduct per amount of fluorinated GHG input gas i (kg) consumed b y process type j (kg) . i = Fluorinated GHG. j = Process Ty pe. k = Fluorinated GHG b y-product. The term “SFGHG ,” is calculat ed b y 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 firs t term in brackets ( “ [ ]”) on the right side of proposed Equation I - 28 in subpart I represents unabated emission of input gases. The term, “EF if , ” is divided by “( 1 - a if*d if )” to yield an emission factor which does not include abatement. The term “ a if ” represents the fraction of F -**DRAFT DO NOT CITE OR QUOTE** 

Page 10 of 11 GHG input gas i used in fab f in tools with abatement sy stems. The term “ d if ” 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 b y- products for all fabs to calculate unabated in

put gas and by-product emissions for the facility , respectivel y , whose emissions were calculated and reported according the proposed 40 CFR 98.93(i) (3) . The values EF if and EF kf are the same as those calculated using Equations I - 19 and I - 20, respectivel y, and the values C if

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

#     

#  

            

         

  k f k i if kf f k kf i f i if if if if GWP * C * d * a EF GWP * C * d * a EF SFGHG 1

1 ( Eq. I - 28) Where: SFGHG = Total unabated emissions of fluorinated GHG i emitted from electronics manufacturing processes in the faci lity, expressed in metric ton CO 2 e for which a facility calculated total emission according to the procedures in proposed 40 CFR 98.93(i)(3). EF if = Emission factor for fluorinated GHG input gas i, emitted from fab f, as calculated in proposed Equation I - 1 9 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 s ys tems (expressed as a decimal fraction). dif = Fraction of fluorinated GHG i destroyed or removed in abatement sy stem s connec ted 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). C if = Total consumption of fluorinated GHG input gas i, of tools vente d to stack sy stems that are tested, for fab f, for the reporting year, expressed in metric ton CO 2 e 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). EF kf = Em ission factor for fluorinated GHG b y- 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 s ys tems that are tested). akf = Fraction of all input gas used in fab f in tools with abatement s ys tems (expressed as a decimal fraction).**DRAFT DO NOT CITE OR QUOTE** 

Page 11 of 11 dkf = Fraction of fluorinated GHG by- product k destroyed or removed in abatement s ys tems connected to process tools in fab f, which a facility used to calculate total emissions acco rding to the procedures in proposed 40 CFR 98.93(i)(3) (expressed as a decimal fraction). GWP i = 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. GWP k = GWP of emitted fluorinated GHG b y- 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 Ty pe. k = Fluorinated GHG b y-product.