### Under the proposed rule for Mandatory Reporting of Greenhouse Gases: Additional Sources of Fluorinated GHGs, facilities interested in pursuing the mass
-balance approach to estimate their fluorinated GHG emissions from fluorinated GHG production would have to be able to demonstrate that their process measurements and calculations passed an error test (75 FR 18652, April 12, 2010). Calculations for the test are included in the proposed rule. The workbook entitled “Example Mass Balance Error Calculation.xls” illustrates how the error calculation might work with one well
-known production process. This workbook was developed as a "proof of concept," not an actual calculation tool. If EPA finalizes the error test for the mass
-balance approach, the Agency will provide a more user
friendly tool that will include instructions and background. Nevertheless, by working through the spreadsheets and referring to the corresponding equations in the proposed subpart L regulatory text, one can see how the error test could be implemented. There are four

spreadsheets in the workbook. The first one containsthe cal culations of interest. The second and third

provide background on the reaction and ensure that the masses will actuall y balance. A facility

wouldn't need the second spreadsheet to calculate the error for an actual process because the relevant values would be measured rather than calculated.The fourth displays errors associated with various values for process variability (RSD) and sampling frequenc y based on t

he student’s t distribution. (This spreadsheet was integrated into a previous version of the workbook but has not y et been integrated into this one.) To see how the first spreadsheet works , spreadsheet users should refer to the equations in the proposed regulatory text whose numbers appear in the heading of each group of columns. In general, the equations appear in the sheet in the order that a facility would solve them to calculate its emissions. Within each equation, the columns on the left side are t he inputs, and the last column is the output. The values that are calculated using the mass
-bal ance equations (and error propagation equations) appear in purple. (Since the spreadsheet is just a model, it also calculates some of the input values that appear in black, but they would be measured in an actual process.) The calculations proceed from left to right and down. The outputs of some equations are used as the inputs for the next, both for the emissions calculation and for the error calculation. The values for the percentages of products and by-products in various streams are hypothetical. Users of the spreadsheet can adjust these, but they should take care to ensure that they are accounting for all masses and flows (e.g., make sure the percentages of the by
-product going to the various process streams don't add up to more than 100%). One important note: the spreadsheet uses the example of HCFC
- 22 with HFC
-23 as the b yproduct because this is a widely known reaction. The workbook calculates both HCFC
- 22 emissions (the product) and HFC
- 23 emissions (the by
-product). However, HCFC
- 22 production is actually covered b y subpart O rather than subpart L, and only the HFC
- 23 emissions, not the HCFC
- 22 emissions, are covered by subpart O. Nevertheless , the basic math and logic should be the same for the processes covered by subpart L.Percent reactant in waste stream 1%

Percent waste stream composed of reactant 10% Percent product in waste stream 1% Percent waste stream composed of product 10% Percent product emitted through equipment leaks 2% Percent byproduct in waste stream 10% Percent waste stream composed of byproduct 20% Percent byproduct emitted through equipment leaks 1% Percent byproduct recaptured 89% Destruction efficiency 99% Equation Variable DE F-GHG c F-GHG Sj Pj DE F-GHG c F-GHG Sj Bkj c FC Sj Rdj c Bkl Sl Bkl Value 99% 10% 839.05 83.07 99% 20% 105 20.79 10% 410.10 41.01 80% 233.63 186.9 Relative Error 0.00% 10% 0.20% 10.0% 0.00% 10% 0.20% 10.0% 10% 0.20% 10% 10% 0.20% 10% 83.905 21 41.0101 186.9 Equation Variable Pj MFF P Bkj Bkl MFF Bk Rdj MFF Rd F D Value 83.07 0.44 20.79 186.9 0.81 41.01 0.95 244.57 Relative Error 0.10 0.0 0.10 0.10002 0.0 0.10 0 7% Equation Variable Rd MFF Rd P MFF P F D E F check F emission rate Value 4101.01 0.95 8138.785 0.44 244.57 75.97 75.9696 1.97% Relative Error 0.20% 0 0.20% 0 7% 25% L-9 ( Destroyed reactant non- L-10 (Recaptured by-product)

L-7 (Total mass fluorine in destroyed or recaptured streams)

L-6 (Total mass of fluorine emitted) L-8 (Destroyed F-GHG product) L-8 (Destroyed F-GHG by-product)Reactant Product Byproduct

moles 100 97 3 2HF + CHCl3 = 2HCl + CHClF2 Chemical CHCl3 HCFC-22 HFC-23 MW 119.5 86.5 70 100 moles chloroform should make 100 moles 22; if 3 go into 23 instead, will make 97 moles 22 Mass 11950 8390.5 210

Reactant Product Byproduct moles 203 97 3 Chemical HF HCFC-22 HFC-23 MW 20 86.5 70 Mass 4060 8390.5 210
102 8780
Check Reactants 22 and 23 HCl Products 16010 8601 7410 16010

2.5% Please note: Production of HCFC-22 is covered by subpart O, not subpart L, and only HFC-23 emissions, not HCFC-22 emissions, are covered by subpart O. This process is used here only as a well-known example.carbon fluorine chlorine hydrogen Molecular weight MFF carbon fluorine chlorine hydrogen HF 1 1 20 0.95 12 19 35.5 1 HCFC-22 1 2 1 1 86.5 0.44 HFC-23 1 3 1 70 0.81 CHCl3 1 0 3 1 119.5 0 HCl 1 1 36.5 0

2HF + CHCl3 = 2HCl + CHClF2Monthly sampling
tolerable error square roott value RSD RSD Number of samples square

root t value for

n=12, v=11 error 0.3 1.732051 4.3 0.120841 100% 12 3.46 2.2 64% 0.5 1.732051 4.3 0.201401 50% 12 3.46 2.2 32% 0.4 1.732051 4.3 0.161121 40% 12 3.46 2.2 25% 0.35 1.732051 4.3 0.140981 30% 12 3.46 2.2 19% 0.2 2.44949 2.57 0.190622 20% 12 3.46 2.2 13% 0.209839621 2.44949 2.57 0.2 15% 12 3.46 2.2 10%

0.3 2 3.18 0.188679 10% 12 3.46 2.2 6% 5% 12 3.46 2.2 3% Biw eekly sampling
RSD Number of

samples square

root t value for

n=26, v=25 error 100% 26 5.10 2.06 40% 50% 26 5.10 2.06 20% 40% 26 5.10 2.06 16% 30% 26 5.10 2.06 12% 20% 26 5.10 2.06 8% 15% 26 5.10 2.06 6% 10% 26 5.10 2.06 4% 5% 26 5.10 2.06 2% Weekly sampling
RSD Number of

samples square

root t value for

n=30, v=29 error 100% 52 7.21 2.045 28% 50% 52 7.21 2.045 14% 40% 52 7.21 2.045 11% 30% 52 7.21 2.045 9% 20% 52 7.21 2.045 6% 15% 52 7.21 2.045 4% 10% 52 7.21 2.045 3% 5% 52 7.21 2.045 1% 

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