UNITED STATES ENVIRONMENTAL PROTECTION AGENCY WASHINGTON, D.C. 20460

OFFICE OF AIR AND RADIATION



### Petroleum and Natural Gas Systems (Subpart W) of the Greenhouse Gas Reporting Rule Docket: EPA-HQ-OAR-2011-0512

Title: Development of New Equations for Estimating Emissions from Acid Gas Removal (AGR) Units

Summary: EPA is replacing Equation W-4 w ith Equations W-4A and W-4B. These new equations, which will be under Calcul ation Methodology 3 in 40 CFR 98.233 (d)(3) for calculating emissions from acid gas remova l (AGR) units, seek to improve reporting accuracy while not increasing the level of burden on reporters. This memo explains the derivation of the two new equations that replace the earlie r equation for W-4.

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### Development of New Equations for Estima ting Emissions from Acid Gas Removal (AGR) Units

EPA is replacing Equation W-4 with Equati ons W-4A and W-4B. These new equations, which will be under Calculation Methodology 3 in 40 CFR 98.233 (d)(3) for calculating emissions from acid gas removal (AGR) un its, improve reporting accuracy while not increasing the level of burden on reporters. The inputs to these equations are the same as in the November 2010 final rule and Se ptember 2011 rule proposal; however, the equations are more accurate in their approxi mation among all equations considered thus far. This memorandum provides a derivation of the new equations, describes the analysis conducted to test the new equations, and confir ms that they are more accurate than those suggested by commenters to the September 2011 proposal.

Background AGR units are one of the emission sources li sted under Subpart W of 40 CFR Part 98 for onshore petroleum and natural gas production and onshore natural gas processing industry segments. Under paragraph 98.233( d) there are four listed calculation methodologies that reporters can use to dete rmine emissions from AGRs. Calculation Methodology 1 uses a continuous emissions monitoring system (CEMS), Calculation Methodology 2 uses a flow meter on the vent stack, Calculation Methodology 3 uses a flow meter on either the inlet or the ou tlet of the AGR, and Ca lculation Methodology 4 uses a simulation software package. Calc ulation Methodology 3 and Equation W-4 were added in the November 2010 final rule as per comments received on the April 2010 proposed rule. This equation was revised in the September 2011 proposed rule because of a question submitted by a reporter to the EPA. The reporter provided a numerical analysis that showed condition under which the N ovember 2010 equation was inaccurate. EPA received further comments on Equation W-4 during the public commenting period for the September 2011 proposed rule. EPA notes that under certain conditions, the equations both in the November 2010 rule and in the September 2011 proposed rule could severely misrepresent emissions from AGRs. Theref ore, EPA is revising the equation to more accurately characterize emissions from AGRs.

Earlier Equations Calculation Methodology 3 uses Equation W- 4 to estimate emissions from AGR units. The equations in both the November 2010 final rule and September 2011 proposal require reporters to monitor either the inlet or outlet gas flow rate for the AGR. This data, along with the CO 2 

### concentration in both the inlet and outlet streams is then used to estimate CO 2 

### emissions. In the November 2010 rule, Equation W-4 was as shown below.

E = 

## ( V + α * 

## ( V * 

## ( Vol

− Vol 

## ))) * 

## ( Vol

− Vol O 

## )

a , CO 2 I O I 

### (Eq. W-4)

Where:

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### E a,CO2 

### = Annual volumetric CO 2 

### emissions at actual c ondition, in cubic feet

per year. V = Total annual volume of natural gas flow through the AGR unit in cubic feet per year at actual c ondition as determined using methods specified in paragraph (d )(5) of this section.

α = Factor is 1 if the outlet stream fl ow is measured. Factor is 0 if the inlet stream flow is measured. Vol I 

### = Volume fraction of CO 2 

### content in natural gas into the AGR unit as determined in paragraph (d)(7) of this section. Vol O 

### = Volume fraction of CO 2 

### content in natural ga s out of the AGR unit as determined in paragra ph (d)(8) of this section.

The largest source of error in the Novemb er 2010 equation is how it factors in a volumetric change between the inlet and outlet stream when gas is removed in the AGR. When the outlet gas is known, the term V*(Vol I 

### – Vol O 

### ) underestimates the volume removed in the contactor. When the inlet ga s is known, the equation does not take into account any change between the inlet and outlet volume. The emissions are underestimated regardless of whether the inlet or outle t gas is used.

Equation W-4 in the September 2011 proposed rule is shown below.

⎡ V ⎤ E

a , CO 2 

### = ⎢ ⎥ * 

## ( Vol I 

### − Vol O 

## ) (Eq. W-4) ⎣ 1

− ( Vol I 

### − Vol O 

### ) ⎦



### Where:
E a,CO2 

### = Annual volumetric CO 2 

### emissions at actual c ondition, in cubic feet

per year. V = Total annual volume of natural ga s flow into or out of the AGR unit at actual conditions, in cubic feet per year. Vol I 

### = Volume fraction of CO 2 

### content in natural gas flowing into the AGR unit. Vol O 

### = Volume fraction of CO 2 

### content in natural gas flowing out of the AGR unit.

The September 2011 equation has shortcomings similar to the November 2010 equation. The proposed equation also does not take into account any change between the inlet and outlet volume when the inlet gas is known. The current equation also inaccurately scales up the known outlet flow w ith the term 1/(1 – (Vol I 

### – Vol O 

### )) to account for gas removed in the contactor. Here again, the emissions are underestimated regardless of whether the inlet or outlet gas is used.

Development of Revised Equation EPA sought to revise Equation W-4 so it resu lted in the smallest possible error while maintaining the same level of burden on repor ters. Therefore, a mass balance approach

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### was used to develop two new equations, pr oposed as Equations W-4A and W-4B, to better estimate emissions from AGR units. E quation W-4A would be for when the inlet gas flow rate is known, and Equation W-4B woul d be for when the outlet gas flow rate is known. The derivation of these tw o equations is shown below.

E a,EM = Volume of emissions Vol EM = Mole fraction of CO 2 in Emissions emissions stream Stream E a,CO2 = Volume of CO 2 emissions

E a,CO2 = E a,EM * Vol EM

Outlet Stream



### AGR Unit

(Sour Gas) ( Sweet Gas )

V out = Volume of gas leaving AGR Vol O = Mole fraction of CO 2 in outlet

stream

Inlet Stream

V in = Volume of gas into AGR Vol I = Mole fraction of CO 2 in inlet stream



### Overall Mole Balance:
V = V + E

in out a

, EM



### CO 2 

### Mole Balance:
V × Vol = V × Vol + E × Vol

in I out O a

, EM EM



### If V out 

### is known: 

# ( V + E 

# ) × Vol = V × Vol + E × Vol

out a , EM I out O a

, EM EM 

### V × Vol + E × Vol = V × Vol + E × Vol

out I a

, EM I out O a

, EM EM 

### V × Vol

− V × Vol = E × Vol

− E × Vol

out I out O a

, EM EM a

, EM I 

### V × 

## ( Vol

− Vol 

## )

= E × 

## ( Vol

− Vol I 

## )

out I O a

, EM EM 

### ⎡ Vol I 

### − Vol O 

### ⎤ E = V

a , EM out 

### ⎢ ⎥ Vol

− Vol ⎣ EM I 

### ⎦

If V in 

### is known:
V × Vol = 

# ( V

− E 

# ) × Vol + E × Vol in I in a

, EM O a

, EM EM 

### V × Vol = V × Vol

− E × Vol + E × Vol

in I in O a

, EM O a

, EM EM 

### V × Vol

− V × Vol = E × Vol

− E × Vol

in I in O a

, EM EM a

, EM O 

### V × 

## ( Vol

− Vol 

## )

= E × 

## ( Vol

− Vol O 

## )

in I O a

, EM EM

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### ⎡ Vol I 

### − Vol O 

### ⎤ E = V

a , EM in 

### ⎢ ⎥ Vol

− Vol ⎣ EM O 

### ⎦

Assumptions: 

### Vol EM 

### = 1

Therefore:
E = E

a , CO 2 a , EM



### Final Equations: 

### ⎡ Vol I 

### − Vol O 

### ⎤ E

a , CO 2 

### = V in 

### ∗ ⎢ ⎥ (Eq. W-4A) 

### 1

− Vol ⎣ O 

### ⎦ ⎡ Vol I 

### − Vol O 

### ⎤ E

a , CO 2 

### = V
out 

### ∗ ⎢ ⎥ (Eq. W-4B) 

### 1

− Vol ⎣ I 

### ⎦

Where:
E a,CO2 

### = Annual volumetric CO 2 

### emissions at actual c ondition, in cubic feet

per year. V in 

### = Total annual volume of natura l gas flow into the AGR unit at actual conditions, in cubic feet per year.
V out 

### = Total annual volume of natural gas flow out of the AGR unit at actual conditions, in cubic feet per year. Vol I 

### = Volume fraction of CO 2 

### content in natural gas flowing into the AGR unit. Vol O 

### = Volume fraction of CO 2 

### content in natural gas flowing out of the AGR unit.

As stated, these two equations were developed using a mass balance on the AGR unit. It was also assumed that 100% of the gas be ing removed from the feed stream was CO 2 

### . As a result, the accuracy of the emission estim ate diminishes when the composition of the vent stream deviates from unity (i.e. it is not a pure CO 2 

### stream).

Results To compare the error rates associated w ith the different equations, the calculated emissions from each equation were compared to the actual emissions from the AGR unit as if the removed gas was measured directly (for both flow rate and CO 2 

### composition). Firstly, the outlet flow rate of gas and the outlet CO 2 

### composition were fixed. Furthermore, a value was assumed for the actual emissions, both flow rate and CO 2 

### composition. By picking an inlet CO 2 

### concentration, the inlet fl ow rate could be back calculated from the data already assumed. With the inlet and outlet flow rates and CO 2 

### compositions now known, the equations could be used to calculate the emissions. To determine the percent error, the calculated emissions were then compared to actual emissions established in the beginning of the analysis.

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### The equations were tested under various c onditions to see what percent error they produced. The outlet stream flow rate was held constant at 1000 Msc f. Both the inlet CO 2 

### concentration and the emissions stream CO 2 

### concentration were varied, from 7% to 15% and from 95% to 100%, respectiv ely. Three different outlet CO 2 

### concentrations (5%, 3% and 1%) were used as well. The resu lts are shown in Tables 1 through 5. Table 1: AGR Unit Emissions Comparison #1 Assumptions: Vol out = 1000 Mscf gas
CO 2 mol % in = 7%

CO 2 mol % emitted = 100%

CO 2 mol % out =
Vol in =

Actual Emissions = Case 1
5.0% mol % CO 2 1022 Mscf gas

21.51 Mscf CO 2 Case 2
3.0% mol % CO 2 1043 Mscf gas

43.01 Mscf CO 2 Case 3
1.0% mol % CO 2 1065 Mscf gas

64.52 Mscf CO 2 November 2010 Equation Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 20.40 Mscf CO 2 5.14%

20.43 Mscf CO 2 5.00% 41.60 Mscf CO 2 3.28%

41.72 Mscf CO 2 3.00% 63.60 Mscf CO 2 1.42%

63.87 Mscf CO 2 1.00% September 2011 Equation Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 20.41 Mscf CO 2 5.10%

20.43 Mscf CO 2 5.00% 41.67 Mscf CO 2 3.13%

41.72 Mscf CO 2 3.00% 63.83 Mscf CO 2 1.06%

63.87 Mscf CO 2 1.00% Revised Equations Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 21.51 Mscf CO 2 0.00%

21.51 Mscf CO 2 0.00% 43.01 Mscf CO 2 0.00%

43.01 Mscf CO 2 0.00% 64.52 Mscf CO 2 0.00%

64.52 Mscf CO 2 0.00%



### Table 2: AGR Unit Emissions Comparison #2 Assumptions: Vol out = 1000 Mscf gas
CO 2 mol % in = 7%

CO 2 mol % emitted = 98%

CO 2 mol % out =
Vol in =

Actual Emissions = Case 1
5.0% mol % CO 2 1022 Mscf gas

21.51 Mscf CO 2 Case 2
3.0% mol % CO 2 1044 Mscf gas

43.96 Mscf CO 2 Case 3
1.0% mol % CO 2 1066 Mscf gas

65.93 Mscf CO 2 November 2010 Equation

Page 6 of 9Emissions Using Vol out 20.40 Mscf CO 2 41.60 Mscf CO 2 63.60 Mscf CO 2 Percent Error 5.29% 3.43% 1.57%

Emissions Using Vol in 20.44 Mscf CO 2 41.76 Mscf CO 2 63.96 Mscf CO 2 Percent Error 5.10% 3.06% 1.02% September 2011 Equation Emissions Using Vol out 20.41 Mscf CO 2 41.67 Mscf CO 2 63.83 Mscf CO 2 Percent Error 5.25% 3.27% 1.22%

Emissions Using Vol in 20.44 Mscf CO 2 41.76 Mscf CO 2 63.96 Mscf CO 2 Percent Error 5.10% 3.06% 1.02% Revised Equations Emissions Using Vol out 21.51 Mscf CO 2 43.01 Mscf CO 2 64.52 Mscf CO 2 Percent Error 0.15% 0.15% 0.15%

Emissions Using Vol in 21.52 Mscf CO 2 43.05 Mscf CO 2 64.60 Mscf CO 2 Percent Error 0.11% 0.06% 0.02%



### Table 3: AGR Unit Emission Comparison #3 Assumptions: Vol out = 1000 Mscf gas
CO 2 mol % in = 7%

CO 2 mol % emitted = 95%

CO 2 mol % out =
Vol in =

Actual Emissions = Case 1
5.0% mol % CO 2 1023 Mscf gas

22.73 Mscf CO 2 Case 2
3.0% mol % CO 2 1045 Mscf gas

45.45 Mscf CO 2 Case 3
1.0% mol % CO 2 1068 Mscf gas

68.18 Mscf CO 2 November 2010 Equation Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 20.40 Mscf CO 2 5.52%

20.45 Mscf CO 2 5.26% 41.60 Mscf CO 2 3.66%

41.82 Mscf CO 2 3.16% 63.60 Mscf CO 2 1.81%

64.09 Mscf CO 2 1.05% September 2011 Equation Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 20.41 Mscf CO 2 5.48%

20.45 Mscf CO 2 5.26% 41.67 Mscf CO 2 3.51%

41.82 Mscf CO 2 3.16% 63.83 Mscf CO 2 1.46%

64.09 Mscf CO 2 1.05% Revised Equations Emissions Using Vol out

Percent Error 21.51 Mscf CO 2 0.40% 43.01 Mscf CO 2 0.40% 64.52 Mscf CO 2 0.40%

Page 7 of 9Emissions Using Vol in 21.53 Mscf CO 2 43.11 Mscf CO 2 64.74 Mscf CO 2 Percent Error 0.28% 0.16% 0.05%



### Table 4: AGR Unit Emission Comparison #4 Assumptions: Vol out = 1000 Mscf gas
CO 2 mol % in = 10%

CO 2 mol % emitted = 95%

CO 2 mol % out =
Vol in =

Actual Emissions = Case 1
5.0% mol % CO 2 1059 Mscf gas

58.82 Mscf CO 2 Case 2
3.0% mol % CO 2 1082 Mscf gas

82.35 Mscf CO 2 Case 3
1.0% mol % CO 2 1106 Mscf gas

105.88 Mscf CO 2 November 2010 Equation Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 52.50 Mscf CO 2 6.05%

52.94 Mscf CO 2 5.26% 74.90 Mscf CO 2 4.26%

75.76 Mscf CO 2 3.16% 98.10 Mscf CO 2 2.47%

99.53 Mscf CO 2 1.05% September 2011 Equation Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 52.63 Mscf CO 2 5.82%

52.94 Mscf CO 2 5.26% 75.27 Mscf CO 2 3.79%

75.76 Mscf CO 2 3.16% 98.90 Mscf CO 2 1.68%

99.53 Mscf CO 2 1.05% Revised Equations Emissions Using Vol out

Percent Error

Emissions Using Vol in

Percent Error 55.56 Mscf CO 2 0.58%

55.73 Mscf CO 2 0.28% 77.78 Mscf CO 2 0.58%

78.11 Mscf CO 2 0.16% 100.00 Mscf CO 2 0.58%

100.53 Mscf CO 2 0.05%



### Table 5: AGR Unit Emission Comparison #5 Assumptions: Vol out = 1000 Mscf gas
CO 2 mol % in = 15%

CO 2 mol % emitted = 95%

CO 2 mol % out =
Vol in =

Actual Emissions = Case 1
5.0% mol % CO 2 1125 Mscf gas

125.00 Mscf CO 2 Case 2
3.0% mol % CO 2 1150 Mscf gas

150.00 Mscf CO 2 Case 3
1.0% mol % CO 2 1175 Mscf gas

175.00 Mscf CO 2 November 2010 Equation

Page 8 of 9Emissions Using Vol out 110.00 Mscf CO 2 134.40 Mscf CO 2 159.60 Mscf CO 2 Percent Error 7.37% 5.68% 4.00%

Emissions Using Vol in 112.50 Mscf CO 2 138.00 Mscf CO 2 164.50 Mscf CO 2 Percent Error 5.26% 3.16% 1.05% September 2011 Equation Emissions Using Vol out 111.11 Mscf CO 2 136.36 Mscf CO 2 162.79 Mscf CO 2 Percent Error 6.43% 4.31% 2.08%

Emissions Using Vol in 112.50 Mscf CO 2 138.00 Mscf CO 2 164.50 Mscf CO 2 Percent Error 5.26% 3.16% 1.05% Revised Equations Emissions Using Vol out 117.65 Mscf CO 2 141.18 Mscf CO 2 164.71 Mscf CO 2 Percent Error 0.93% 0.93% 0.93%

Emissions Using Vol in 118.42 Mscf CO 2 142.27 Mscf CO 2 166.16 Mscf CO 2 Percent Error 0.28% 0.16% 0.05%



### In all cases tested, the December 2011 fina l rule equations W- 4A and W-4B more accurately estimate the emissions than the other equations considered thus far. Under the conditions tested here, the new equations neve r give an error greater than 1%, while the previously considered equations never give an error less than 1%. EPA also performed a much wider case study varying the CO 2 

### concentration in the inlet from 3% to 50%, the outlet from 1% to 30%, and in the emissions stream from 90% to 100%. In every case tested the equations proposed fo r the current rule resulted in less error than either of the two previously proposed equations. Theref ore, the new equations more accurately characterize the emissions from AGR units. As expected, the largest source of error in these equations occurs when the composition of the vent stack deviates from unity.

Conclusions Equation W-4, in its previous forms in the rule, tends to underestimate emissions by a substantial amount. In all cas es tested, the newly finalized Equations W-4A and W-4B, while still underestimating em issions, reduce the error in th e estimation. Therefore, EPA is replacing Equation W-4 with Equation W- 4A and Equation W-4B . These equations will place no additional burden on reporters while simultaneously improving reporting

accuracy.

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