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 with Equations 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) 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 earlier equation for W-4. 

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Development of New Equations for Estimating Emissions from Acid Gas Removal 

(AGR) Units 

EPA is replacing Equation W-4 with Equations 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) units, 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 September 2011 rule proposal; however, the 

equations are more accurate in their approximation 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 confirms that they are more accurate than those 

suggested by commenters to the September 2011 proposal. 

Background 

AGR units are one of the emission sources listed 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 determine 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 outlet of the AGR, and Calculation Methodology 4 

uses a simulation software package. Calculation 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 November 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. Therefore, 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 CO2 concentration in both the inlet and outlet streams is then used to 

estimate CO2 emissions. In the November 2010 rule, Equation W-4 was as shown 

below. 

E = (V +α * (V * (Vol −Vol )))* (Vol −VolO ) a,CO 2 I O I (Eq. W-4) 

Where: 

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Ea,CO2 = Annual volumetric CO2 emissions at actual condition, in cubic feet 

per year. 

V = Total annual volume of natural gas flow through the AGR unit in 

cubic feet per year at actual condition as determined using methods 

specified in paragraph (d)(5) of this section. 

α = Factor is 1 if the outlet stream flow is measured. Factor is 0 if the 

inlet stream flow is measured. 

VolI = Volume fraction of CO2 content in natural gas into the AGR unit as 

determined in paragraph (d)(7) of this section. 

VolO = Volume fraction of CO2 content in natural gas out of the AGR unit 

as determined in paragraph (d)(8) of this section. 

The largest source of error in the November 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*(VolI – VolO) underestimates the volume 

removed in the contactor. When the inlet gas 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 outlet gas is used. 

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

⎡ V ⎤ Ea,CO2 = ⎢ ⎥ * (VolI −VolO ) (Eq. W-4) 

⎣1 − (VolI −VolO )⎦

Where: 

Ea,CO2 = Annual volumetric CO2 emissions at actual condition, in cubic feet 

per year. 

V = Total annual volume of natural gas flow into or out of the AGR unit 

at actual conditions, in cubic feet per year. 

VolI = Volume fraction of CO2 content in natural gas flowing into the 

AGR unit. 

VolO = Volume fraction of CO2 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 with the term 1/(1 – (VolI – VolO)) 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 resulted in the smallest possible error while 

maintaining the same level of burden on reporters. Therefore, a mass balance approach 

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was used to develop two new equations, proposed as Equations W-4A and W-4B, to 

better estimate emissions from AGR units. Equation W-4A would be for when the inlet 

gas flow rate is known, and Equation W-4B would be for when the outlet gas flow rate is 

known. The derivation of these two equations is shown below. 

Ea,EM = Volume of emissions
 

VolEM = Mole fraction of CO2 in Emissions 

emissions stream Stream Ea,CO2 = Volume of CO2 emissions 

Ea,CO2 = Ea,EM * VolEM 

Outlet Stream 

AGR 

Unit 

(Sour Gas) 

(Sweet Gas) 

Vout = Volume of gas leaving AGR 

VolO = Mole fraction of CO2 in outlet 

stream 

Inlet Stream 

Vin = Volume of gas into AGR 

VolI = Mole fraction of CO2 in 

inlet stream
 

Overall Mole Balance: 

V in out a = V + E ,EM 

CO2 Mole Balance: 

V ×Vol = V ×Vol + E ×Vol in I out O a,EM EM 

If Vout 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 −VolI ) out I O a,EM EM 

⎡ VolI −VolO ⎤ E a,EM out =V ⎢ ⎥ Vol −Vol ⎣ EM I ⎦

If Vin 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 −VolO ) in I O a,EM EM 

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⎡ VolI −VolO ⎤ E a,EM in =V ⎢ ⎥ Vol −Vol ⎣ EM O ⎦

Assumptions: 

VolEM =1 

Therefore: 

E a,CO2 = Ea,EM 

Final Equations: 

⎡VolI −VolO ⎤ Ea,CO2 = Vin ∗ ⎢ ⎥ (Eq. W-4A) 1−Vol ⎣ O ⎦

⎡VolI −VolO ⎤ Ea,CO2 = Vout ∗ ⎢ ⎥ (Eq. W-4B) 1−Vol ⎣ I ⎦

Where: 

Ea,CO2 = Annual volumetric CO2 emissions at actual condition, in cubic feet 

per year. 

Vin = Total annual volume of natural gas flow into the AGR unit at 

actual conditions, in cubic feet per year. 

Vout = Total annual volume of natural gas flow out of the AGR unit at 

actual conditions, in cubic feet per year. 

VolI = Volume fraction of CO2 content in natural gas flowing into the 

AGR unit. 

VolO = Volume fraction of CO2 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 being removed from the feed stream was CO2. As 

a result, the accuracy of the emission estimate diminishes when the composition of the 

vent stream deviates from unity (i.e. it is not a pure CO2 stream). 

Results 

To compare the error rates associated with 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 CO2 composition). 

Firstly, the outlet flow rate of gas and the outlet CO2 composition were fixed. 

Furthermore, a value was assumed for the actual emissions, both flow rate and CO2 

composition. By picking an inlet CO2 concentration, the inlet flow rate could be back 

calculated from the data already assumed. With the inlet and outlet flow rates and CO2 

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 conditions to see what percent error they 

produced. The outlet stream flow rate was held constant at 1000 Mscf. Both the inlet CO2
 

concentration and the emissions stream CO2 concentration were varied, from 7% to 15% 

and from 95% to 100%, respectively. Three different outlet CO2 concentrations (5%, 3% 

and 1%) were used as well. The results are shown in Tables 1 through 5. 

Table 1: AGR Unit Emissions Comparison #1 

Assumptions: 

Vol out = 1000 Mscf gas 

CO2 mol % in = 7% 

CO2 mol % emitted = 100% 

CO2 mol % out = 

Vol in = 

Actual Emissions = 

Case 1 

5.0% mol % CO2

1022 Mscf gas 

21.51 Mscf CO2

Case 2 

3.0% mol % CO2

1043 Mscf gas 

 43.01 Mscf CO2

Case 3 

1.0% mol % CO2 

1065 Mscf gas 

 64.52 Mscf CO2 

November 2010 Equation 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

20.40 Mscf CO2

5.14% 

20.43 Mscf CO2

5.00% 

 41.60 Mscf CO2

3.28% 

 41.72 Mscf CO2

3.00% 

 63.60 Mscf CO2 

1.42% 

 63.87 Mscf CO2 

1.00% 

September 2011 Equation 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

20.41 Mscf CO2

5.10% 

20.43 Mscf CO2

5.00% 

 41.67 Mscf CO2

3.13% 

 41.72 Mscf CO2

3.00% 

 63.83 Mscf CO2 

1.06% 

 63.87 Mscf CO2 

1.00% 

Revised Equations 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

21.51 Mscf CO2

0.00% 

21.51 Mscf CO2

0.00% 

 43.01 Mscf CO2

0.00% 

 43.01 Mscf CO2

0.00% 

 64.52 Mscf CO2 

0.00% 

 64.52 Mscf CO2 

0.00% 

Table 2: AGR Unit Emissions Comparison #2 

Assumptions: 

Vol out = 1000 Mscf gas 

CO2 mol % in = 7% 

CO2 mol % emitted = 98% 

CO2 mol % out = 

Vol in = 

Actual Emissions = 

Case 1 

5.0% mol % CO2

1022 Mscf gas 

21.51 Mscf CO2

Case 2 

3.0% mol % CO2

1044 Mscf gas 

 43.96 Mscf CO2

Case 3 

1.0% mol % CO2 

1066 Mscf gas 

 65.93 Mscf CO2 

November 2010 Equation 

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Emissions Using Vol out 20.40 Mscf CO2 41.60 Mscf CO2 63.60 Mscf CO2 

Percent Error 5.29% 3.43% 1.57% 

Emissions Using Vol in 20.44 Mscf CO2 41.76 Mscf CO2 63.96 Mscf CO2 

Percent Error 5.10% 3.06% 1.02% 

September 2011 Equation 

Emissions Using Vol out 20.41 Mscf CO2 41.67 Mscf CO2 63.83 Mscf CO2 

Percent Error 5.25% 3.27% 1.22% 

Emissions Using Vol in 20.44 Mscf CO2 41.76 Mscf CO2 63.96 Mscf CO2 

Percent Error 5.10% 3.06% 1.02% 

Revised Equations 

Emissions Using Vol out 21.51 Mscf CO2 43.01 Mscf CO2 64.52 Mscf CO2 

Percent Error 0.15% 0.15% 0.15% 

Emissions Using Vol in 21.52 Mscf CO2 43.05 Mscf CO2 64.60 Mscf CO2 

Percent Error 0.11% 0.06% 0.02% 

Table 3: AGR Unit Emission Comparison #3 

Assumptions: 

Vol out = 1000 Mscf gas 

CO2 mol % in = 7% 

CO2 mol % emitted = 95% 

CO2 mol % out = 

Vol in = 

Actual Emissions = 

Case 1 

5.0% mol % CO2

1023 Mscf gas 

22.73 Mscf CO2

Case 2 

3.0% mol % CO2

1045 Mscf gas 

 45.45 Mscf CO2

Case 3 

1.0% mol % CO2 

1068 Mscf gas 

 68.18 Mscf CO2 

November 2010 Equation 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

20.40 Mscf CO2

5.52% 

20.45 Mscf CO2

5.26% 

 41.60 Mscf CO2

3.66% 

 41.82 Mscf CO2

3.16% 

 63.60 Mscf CO2 

1.81% 

 64.09 Mscf CO2 

1.05% 

September 2011 Equation 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

20.41 Mscf CO2

5.48% 

20.45 Mscf CO2

5.26% 

 41.67 Mscf CO2

3.51% 

 41.82 Mscf CO2

3.16% 

 63.83 Mscf CO2 

1.46% 

 64.09 Mscf CO2 

1.05% 

Revised Equations 

Emissions Using Vol out 

Percent Error 

21.51 Mscf CO2

0.40% 

 43.01 Mscf CO2

0.40% 

 64.52 Mscf CO2 

0.40% 

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Emissions Using Vol in 21.53 Mscf CO2 43.11 Mscf CO2 64.74 Mscf CO2 

Percent Error 0.28% 0.16% 0.05% 

Table 4: AGR Unit Emission Comparison #4 

Assumptions: 

Vol out = 1000 Mscf gas 

CO2 mol % in = 10% 

CO2 mol % emitted = 95% 

CO2 mol % out = 

Vol in = 

Actual Emissions = 

Case 1 

5.0% mol % CO2

1059 Mscf gas 

58.82 Mscf CO2

Case 2 

3.0% mol % CO2

1082 Mscf gas 

 82.35 Mscf CO2

Case 3 

1.0% mol % CO2 

1106 Mscf gas 

 105.88 Mscf CO2 

November 2010 Equation 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

52.50 Mscf CO2

6.05% 

52.94 Mscf CO2

5.26% 

 74.90 Mscf CO2

4.26% 

 75.76 Mscf CO2

3.16% 

 98.10 Mscf CO2 

2.47% 

 99.53 Mscf CO2 

1.05% 

September 2011 Equation 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

52.63 Mscf CO2

5.82% 

52.94 Mscf CO2

5.26% 

 75.27 Mscf CO2

3.79% 

 75.76 Mscf CO2

3.16% 

 98.90 Mscf CO2 

1.68% 

 99.53 Mscf CO2 

1.05% 

Revised Equations 

Emissions Using Vol out 

Percent Error 

Emissions Using Vol in 

Percent Error 

55.56 Mscf CO2

0.58% 

55.73 Mscf CO2

0.28% 

 77.78 Mscf CO2

0.58% 

 78.11 Mscf CO2

0.16% 

 100.00 Mscf CO2 

0.58% 

 100.53 Mscf CO2 

0.05% 

Table 5: AGR Unit Emission Comparison #5 

Assumptions: 

Vol out = 1000 Mscf gas 

CO2 mol % in = 15% 

CO2 mol % emitted = 95% 

CO2 mol % out = 

Vol in = 

Actual Emissions = 

Case 1 

5.0% mol % CO2

1125 Mscf gas 

125.00 Mscf CO2

Case 2 

3.0% mol % CO2

1150 Mscf gas 

 150.00 Mscf CO2

Case 3 

1.0% mol % CO2 

1175 Mscf gas 

 175.00 Mscf CO2 

November 2010 Equation 

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Emissions Using Vol out 110.00 Mscf CO2 134.40 Mscf CO2 159.60 Mscf CO2 

Percent Error 7.37% 5.68% 4.00% 

Emissions Using Vol in 112.50 Mscf CO2 138.00 Mscf CO2 164.50 Mscf CO2 

Percent Error 5.26% 3.16% 1.05% 

September 2011 Equation 

Emissions Using Vol out 111.11 Mscf CO2 136.36 Mscf CO2 162.79 Mscf CO2 

Percent Error 6.43% 4.31% 2.08% 

Emissions Using Vol in 112.50 Mscf CO2 138.00 Mscf CO2 164.50 Mscf CO2 

Percent Error 5.26% 3.16% 1.05% 

Revised Equations 

Emissions Using Vol out 117.65 Mscf CO2 141.18 Mscf CO2 164.71 Mscf CO2 

Percent Error 0.93% 0.93% 0.93% 

Emissions Using Vol in 118.42 Mscf CO2 142.27 Mscf CO2 166.16 Mscf CO2 

Percent Error 0.28% 0.16% 0.05% 

In all cases tested, the December 2011 final 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 never 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 CO2 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 for the current rule resulted in less error than either of the 

two previously proposed equations. Therefore, 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 cases tested, the newly finalized Equations W-4A and W-4B, 

while still underestimating emissions, reduce the error in the 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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