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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-2009-0923 

Title: Change to Equation W-7: Time to Vent Gas 

Summary: The purpose of this analysis is to appropriately account for the duration of 

time required for wells to expel the natural gas contained within the casing at shut-in 

pressure, so that the prescribed monitoring methodology under §98.233(f) does not 

double count emissions during that period. 
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Change to Rule Equation W-7: Time to Vent Gas from Well Liquids Unloading 

The purpose of this analysis is to appropriately account for the duration of time required 

for wells to expel the natural gas contained within the casing at shut-in pressure, so that 

the prescribed monitoring methodology under §98.233(f) does not double count 

emissions during that period. Additionally, it develops appropriate engineering equations 

to be used for wells equipped with plunger lifts and the time to expel the natural gas 

contained in the tubing above the plunger lift. 

Background 

In mature gas wells, the accumulation of fluids in the well tubing can impede and 

eventually halt gas production. One barrel of water will stand 260 feet in a 2 inch inside 

diameter tubing, exerting 130 psi back pressure in addition to the sales line pressure on 

the reservoir. Hence a few barrels of water can choke a well flow altogether. As the water 

accumulates in the tubing, and the back pressure increases, gas flow into the well from 

the reservoir slows and reservoir pressure at the well perforations rises, eventually to near 

shut-in pressure when accumulated liquids virtually stop gas flow. The well casing at this 

point will be pressured up to near shut-in pressure, just the same as if the well were shutin at the well head. Some operators remove accumulated fluids through the use of a beam 

pump or remedial treatments, such as swabbing, soaping, or venting the well to 

atmospheric pressure (referred to as “blowing down” the well). This latter method, 

blowing wells to the atmosphere, while least expensive, expels large volumes of natural 

gas and methane to the atmosphere. This is a common practice1

. However, one Natural 

Gas STAR Partner company2 reported a study of the effectiveness of this well “blow 

down” technique for removing accumulated water. They found that the practice expelled 

a low amount of the accumulated water. This is because the water “plates-out” on the 

tubing walls and allows the gas to bypass it. After blowing off the high pressure (shut-in 

pressure) bubble of gas in the well casing, the well returns to normal flowing velocity 

which allows the water to drains back down the tubing. 

The most effective period for expelling liquids is the maximum gas flow up the tubing. 

This will occur when the sales line is shut-in and the high-pressure bubble of gas in the 

casing is vented to atmospheric back pressure. The volume of this gas can be estimated 

by the well depth, shut-in pressure and casing inside diameter. This is the method in 

subpart W, §98.233 Calculating GHG emissions, section (f) equation W-7 alternative to 

metering the well venting flow, as described in the Natural Gas STAR Lessons Learned 

study on plunger lifts3

. 

Some operators may allow their wells to vent to atmosphere longer than necessary to 

expell this casing gas bubble, which is analgous to producing the well to the atmosphere. 

This may be conservatively approximated by the sales flow rate. Total emissions from the 

well blowdown can be approximated by the sum of the volume of natural gas contained 

 

1 http://epa.gov/gasstar/documents/workshops/2008-tech-transfer/denver3.pdf

2

 http://www.epa.gov/gasstar/documents/desaulniers.pdf 3

 http://www.epa.gov/gasstar/documents/ll_plungerlift.pdf 
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within the well casing at shut-in pressure and the additional volume of gas that is 

produced to the atmosphere after the casing volume is expelled but before the vent is 

closed so that the gas is produced to the sales line. Equation W-7 in Section §98.233(f) 

of the proposed rule accounted for the time operators may leave their wells producing to 

the atmosphere, which commenters correctly pointed out could double account for the 

time the casing gas is vented down to production pressure. Therefore the time of venting 

needed to be adjusted for the time to blow down the higher pressure casing gas. 

Commenters also correctly pointed out that the proposed equation did not account for the 

much more efficient liquids unloading using a plunger lift. The plunger acts like a swab 

or “pig” to use the higher pressure gas accumulated in the casing to efficiently push the 

plunger and liquid column up the tubing, minimizing liquid flow back on the tubing walls 

and gas bypass of the liquid column. Whether with a mechanical timer, “smart 

automation” programmable logic controlled timer or manual venting, a plunger lift 

properly operated will vent considerably less gas to the atmosphere: minimally the tubing 

volume at sales line pressure. As with well blowdown without a plunger lift, if the well 

is left open longer than the time it takes the plunger to rise to the wellhead, excessive gas 

will vent to the atmosphere. Although this gas flowrate will be higher than normal 

production rate, a conservative estimate of the gas flow, not requiring measurement or 

simulation, would be the average sales flow rate. Then the time of venting needs to be 

adjusted for the amount of time it takes to push the plunger from the bottom catcher to 

the wellhead. Plunger operation is tuned to a maximum plunger velocity to avoid damage 

to the plunger catcher at the well head. Therefore, the minimum time to vent the tubing 

gas from a well with a plunger lift is determined by the recommended speed of the 

plunger traveling up the well tubing. 

Method – Liquid Unloading Wihout a Plunger Lift 

The time for a well to blowdown its casing volume without a plunger lift was estimated 

by dividing the volume of the casing gas, Vc, from Equation 1 below, into increments and 

calculating the pressure in the casing as each increment of volume flowed up the tubing 

string, summing the time increments until the casing pressure dropped to normal flowing 

pressure (approximated by sales line pressure). The flow rate of gas up the tubing string 

was estimated using the Weymouth equation from the Pipeline Rules of Thumb 

Handbook4

. This analysis ignores the gas vented from the tubing string above the liquid 

in the tubing because relative to the gas in the casing it is negligible. The volume of the 

gas inside the well casing is calculated in Equation 1 below. 

( ) Vc Dc LPs

3 2 0.37 10− = × Equation 1 

where, 

 

4 Pipe Line Rules of Thumb Handbook, Fourth Edition, Gulf Publishing Company, Houston, Texas, 1998. 
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Vc = volume of the well casing gas at shut-in pressure, cubic feet 

0.37×10-3 = {pi(3.14)/4}/{(14.7*144) psia converted to pounds per square feet} 

Ps = Shut-in pressure (psig). 

Dc = inner diameter of the well casing, assumed to average 5 inches 

L = well depth, feet 

The Weymouth formula, shown below, is used to calculated the flow rate of gas through 

a pipeline and assumes the gas is at 60 degrees Farenheit and has a specific gravity of 

0.60. For the purposes of this analysis it was assumed that the Weymouth formula would 

provide an adequate approximation. 

24

871 2

2

2

1

8 / 3

×

× × − = LD P P

Q Equation 2 

where, 

Q = cubic feet of gas per hour 

D = inner diameter of the pipeline, inches

P1 = inlet pressure (psig) 

P2 = outlet pressure (psig) 

L = well depth, miles 

871 = constant 

24 = hours per day 

The flow rate of gas from the casing through the tubing is mostly dependent on the well 

depth, casing diameter, and the pressure gradient as the column of liquid moves up and 

out of the well. 

As the casing gas is vented, the well casing pressure decreases, approaching the well’s 

down hole normal production pressure. The decremented casing pressures can be used to 

estimate the increments of casing volume as gas flows up the tubing to the atmosphere. 

To calculate the total time needed to vent the casing gas during a well blowdown, the 

pressure drop from shut-in pressure, Ps, to normal flowing pressure, assumed to be the 

sales line pressure, PSL, was divided into ten intervals for which the flow rate, Q, was 

calculated using Equation 2 above. The volume of gas in the well casing at each interval 

decreases from the total casing gas volume at shut-in pressure, Vc, proportionately with 

the pressure of the casing at each interval, Pi. The difference in the casing gas volume 

between interval i and the previous interval, i-1, is the volume of gas vented during that 

interval, Vi. This is shown below in Equations 3 and 4. 
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n

P P P P s SL

i i

− = −1 − , P0 = Ps Equation 3

( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟ − ⎠

⎞ ⎜

⎝

⎛ = − = −

∑

1 1

1

i

i

i

v

i c i v P

P V V V Equation 4

where, 

Pi = the casing pressure at each interval n, pounds per square inch 

Pi-1 = the casing pressure at the previous interval before Pi

P0 = the initial casing pressure, equal to the shut-in pressure, pounds per 

square inch 

Ps = Shut-in pressure, pounds per square inch 

PSL = sales line pressure, pounds per square inch 

Vi = the volume of casing gas vented per interval i, cubic feet 

Vc = volume of the well casing gas at shut-in pressure, cubic feet see 

Equation 1 

n = the total number of intervals; selected 10 for this analysis 

i = the current interval 

The casing gas vented at each interval, Vi, was divided by the calculated flow rate at each 

interval to give the venting time for that interval. Although some of the standing liquid is 

unloaded at the surface, most of it is assumed to remains along the tubing wall. 

Therefore, an eighth-inch was subtracted from the average 2-inch tubing diameter to 

estimate the flow rate, Q. The sum of the venting times from each interval gives the total 

time to vent the entire casing. This summation is shown below in Equation 5. 

∑ ∑ = = −

= =

n

i T i A

i n

i

i

D P P

V L

t t

1

2 2 3

8

1 871

5280 24

Equation 5

where, 

t = Hours needed to vent the entire casing volume 

ti = Hours needed to vent Vi 

n = the total number of intervals; selected 10 for this analysis 

DT = inner diameter of the well tubing adjusted for an 1/8 inch of water 

running along the tubing wall, assumed to be 1.875 inches 

Pi = the casing pressure at each interval n, pounds per square inch 

PA = atmospheric pressure, 14.7 pounds per square inch 

L = well depth, feet 

871 = constant 

24 = hours per day 
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5280 = feet per mile 

Method – Liquid Unloading With a Plunger Lift 

EPA’s expert opinion is that plunger lifts are operated such that the plunger travels at no 

faster than 700 feet per minute to avoid damaging the well head. The time to vent the 

tubing gas with a plunger lift is dependent on the speed of the plunger traveling up the 

well tubing. The speed of the plunger depends on the amount of liquids accumulated 

above the plunger, shut-in pressure of the well, and the well depth. Operators are 

assumed to use historical well unloading experience to determine the plunger travel time, 

and from that the travel velocity, and from these the time increment between well 

venting. Smart Automation timers use this information, along with casing pressure and 

sales line back pressure to optimize the plunger launch frequency. 

Results – Without Plunger Lifts 

Equation 5 above was solved for shut-in pressures ranging from 300 to 1,000 psia at well 

depths of 12,000, 6,000, and 2,000 feet. The HPDI database, which collects well 

information from states, indicates that in the U.S. the average well depth is 6,000 feet 

with a maximum around 12,000 feet and a minimum around 2,000 feet. The results for 

each permutation of well depth and shut-in pressure is displayed in the Figure 1. 

Figure 1. Time to vent the casing gas at shut-in pressures ranging from 300 psi to 

1000 psi at well depths of 12,000 feet, 6,000 feet, and 2,000 feet. 

Time for Well Liquids Unloading

0

200

400

600

800

1000

1200

‐ 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Time to Vent (hours)

Shut‐In Pressure (psi)

12000 feet 6000 feet 2000 feet

The average well depth of 6,000 feet with a casing of 5 inches requires an average of 0.5 

hours to unload its liquids. The maximum, 12,000-foot well, with a 5-inch casing requires 
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about 1.25 hours to unload its liquids. The minimum, 2,000-foot well, with a 5-inch 

casing requires about 0.1 hours to unload its liquids. One hour was selected as a 

conservative estimate for the amount of time a well without a plunger lift would take to 

vent its casing gas. Since the well flow rate to the atmosphere will approach average sales 

flow, to the extent that this venting time is too short or too long will only result in that 

difference being accounted for at average sales flow rate. 

Equation W-7 in Section §98.233(f)(ii) of the Final Subpart W Rule was adjusted using 

this estimate to avoid double counting vented emissions from well liquids unloading at 

the sales production rate. The adjusted equation is shown below. 

 Es,n = {(0.37×10-3)*CD2

*WD*SP*Nv}+{SFR*(HR-1.0)*Z} (Eq. W-8) 

 

where: 

Es,n = Annual natural gas emissions at standard conditions, in cubic 

feet/year. 

0.37×10-3 = {pi(3.14)/4}/{(14.7*144) psia converted to pounds per square feet} 

CD = Casing diameter (inches). 

WD = Well depth (feet). 

SP = Shut-in pressure (psig). 

Nv = Number of vents per year. 

V = Number of vents per year. 

SFR = Sales flow rate of gas well in cubic feet per hour. 

HR = Hours that the well was left open to the atmosphere during unloading. 

1 = Hours for average well to blowdown casing volume. 

Z = If HR is less than 1.0 then Z is equal to 0, otherwise Z is equal to 1. 

Results – With Plunger Lifts

This analysis assumes plungers travel on average 700 feet per minute up the tubing based 

on EPA’s expert information. For wells with depths of 12,000, 6,000, and 2,000 feet it 

would take 20, 10, and 3 minutes respectively for the plunger to reach the surface and 

vent the tubing gas. Because the plunger maximum velocity is an upper limit, and EPA 

assumes operators will deviate on the safe side (lower velocity) the rule assumes half an 

hour as a conservative estimate for the time to vent the tubing gas above the plunger. If 

the well is left open to the atmosphere longer, it is assumed that the well is venting at the 

sales flow rate, which is also very conservative given the casing pressure would be near 

shut-in pressure during most of the excess venting. 

Equation W-8 in Section §98.233(f) of the Final Subpart W Rule was added to account 

for these wells separately while avoiding double counting vented emissions from well 

liquids unloading at the sales production rate. The additional equation is shown below. 

 Ea,n = {(0.37×10-3)*TD2

*WD*SP*Nv}+{SFR*(HR-0.5)*Z} (Eq. W-9) 

where: 
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Ea,n = Annual natural gas emissions at actual conditions, in cubic feet/year. 

0.37×10-3 = {3.14 (pi)/4}/(14.7*144) psia converted to pounds per square feet 

TD = Tubing diameter (inches). 

WD = Tubing depth (feet). 

SP = Sales line pressure (psia). 

Nv = Number of vents per year. 

V = Number of vents per year. 

SFR = Average sales flow rate of gas well in cubic feet per hour. 

HR = Hours that the well was left open to the atmosphere during unloading. 

0.5 = Hours for average well to blowdown tubing volume. 

Z = If HR is less than 0.5 then Z is equal to 0. If HR is greater than or 

equal to 0.5 then Z is equal to 1.