Freeman

12-06-2008, 11:25 PM

Flow Of Compressible Gas In A Horizontal Pipeline

The four commonly-used equations for long-distance gas pipeline are:

- Weymouth Equation

- Panhandle A

- Panhandle B

- AGA (American Gas Association)

Another equation was recently derived by Ohirhian via the manipulation of three basic equations : Weymouth, Colebrook and Reynold's number.

Each of the above five gasflow equations is based on some assumed expression for Friction factor ƒ , a dimensionless correlating function. ƒm is the friction factor (also called the Moody friction factor) that is commonly tabulated in the Moody Charts. Quite often the Fanning Friction factor ƒf is used: ƒf = ƒm/4.

The equations for each method is given below:

- Weymouth Equation:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%37%75%34%2d%5 3%5a%79%49%2f%41%41%41%41%41%41%41%41%41%5a%38%2f% 52%77%46%6b%50%4f%61%53%4b%5f%63%2f%73%31%36%30%30 %2d%68%2f%57%65%79%6d%6f%75%74%68%2e%67%69%66)

- Panhandle A:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%37%39%6f%2d%5 3%5a%7a%49%2f%41%41%41%41%41%41%41%41%41%61%45%2f% 53%58%64%6b%58%75%45%58%52%4c%34%2f%73%31%36%30%30 %2d%68%2f%50%61%6e%68%61%6e%64%6c%65%2e%67%69%66)

- Panhandle B:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%38%4b%6f%2d%5 3%5a%30%49%2f%41%41%41%41%41%41%41%41%41%61%4d%2f% 43%57%36%67%30%65%41%67%56%6c%4d%2f%73%31%36%30%30 %2d%68%2f%50%61%6e%68%61%6e%64%6c%65%42%2e%67%69%6 6)

- AGA (fully turbulent):

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%38%68%6f%2d%5 3%5a%31%49%2f%41%41%41%41%41%41%41%41%41%61%55%2f% 6c%37%4b%6a%39%52%56%55%54%78%73%2f%73%31%36%30%30 %2d%68%2f%41%47%41%2e%67%69%66)

- Ohirhian:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%38%73%6f%2d%5 3%5a%32%49%2f%41%41%41%41%41%41%41%41%41%61%63%2f% 73%52%4b%39%69%7a%72%61%41%55%77%2f%73%31%36%30%30 %2d%68%2f%4f%68%69%72%68%69%61%6e%2e%67%69%66)

Where:

qsc = gas rate at standard condition, scf/d

P1 = inlet pressure, psia

P2 = outlet pressure, psia

Psc = pressure at standard condition, psia

Tsc = temperature at standard condition, °R

Tm = mean temperature of line, °R

Tg = ground temperature, °R

μ = mean gas viscosity, cp

γ = mean gas relative density (air = 1)

Zm= mean gas compressibility factor

d = inside diameter of pipe, inches

L = pipe length, miles

E = pipeline efficiency

ƒm = Moody friction factor

ƒf = Fanning friction factor

Ft = transmission factor (√[1/ƒf ])

ε = absolute roughness of pipe, inches

The mean values of the gas properties (Z & μ) are determined at the average pressure and temperature, derived as follows:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%2d%71%6f%2d%5 3%5a%33%49%2f%41%41%41%41%41%41%41%41%41%61%6b%2f% 64%72%37%51%70%59%6d%4f%7a%49%38%2f%73%31%36%30%30 %2d%68%2f%4d%65%61%6e%73%2e%67%69%66)

BIBLIOGRAPHY

Maddox R.N. & Lilly L.L.; Gas Conditioning & Processing, Volumes 2 & 3; Campbell Petroleum Series, Norman, Oklahoma, 1990.

Katz D.L. & Lee R.L.; Natural Gas Engineering - Production & Storage; McGraw-Hill Publ. Co., New York, 1990, chap. 6.

Ohirhian P.U.; Direct calculation of the gas volumetric flow rate in horizontal and inclined pipes; Paper SPE-37394, Soc. of Petroleum Eng., Richardson, Texas, 2002.

The four commonly-used equations for long-distance gas pipeline are:

- Weymouth Equation

- Panhandle A

- Panhandle B

- AGA (American Gas Association)

Another equation was recently derived by Ohirhian via the manipulation of three basic equations : Weymouth, Colebrook and Reynold's number.

Each of the above five gasflow equations is based on some assumed expression for Friction factor ƒ , a dimensionless correlating function. ƒm is the friction factor (also called the Moody friction factor) that is commonly tabulated in the Moody Charts. Quite often the Fanning Friction factor ƒf is used: ƒf = ƒm/4.

The equations for each method is given below:

- Weymouth Equation:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%37%75%34%2d%5 3%5a%79%49%2f%41%41%41%41%41%41%41%41%41%5a%38%2f% 52%77%46%6b%50%4f%61%53%4b%5f%63%2f%73%31%36%30%30 %2d%68%2f%57%65%79%6d%6f%75%74%68%2e%67%69%66)

- Panhandle A:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%37%39%6f%2d%5 3%5a%7a%49%2f%41%41%41%41%41%41%41%41%41%61%45%2f% 53%58%64%6b%58%75%45%58%52%4c%34%2f%73%31%36%30%30 %2d%68%2f%50%61%6e%68%61%6e%64%6c%65%2e%67%69%66)

- Panhandle B:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%38%4b%6f%2d%5 3%5a%30%49%2f%41%41%41%41%41%41%41%41%41%61%4d%2f% 43%57%36%67%30%65%41%67%56%6c%4d%2f%73%31%36%30%30 %2d%68%2f%50%61%6e%68%61%6e%64%6c%65%42%2e%67%69%6 6)

- AGA (fully turbulent):

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%38%68%6f%2d%5 3%5a%31%49%2f%41%41%41%41%41%41%41%41%41%61%55%2f% 6c%37%4b%6a%39%52%56%55%54%78%73%2f%73%31%36%30%30 %2d%68%2f%41%47%41%2e%67%69%66)

- Ohirhian:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%38%73%6f%2d%5 3%5a%32%49%2f%41%41%41%41%41%41%41%41%41%61%63%2f% 73%52%4b%39%69%7a%72%61%41%55%77%2f%73%31%36%30%30 %2d%68%2f%4f%68%69%72%68%69%61%6e%2e%67%69%66)

Where:

qsc = gas rate at standard condition, scf/d

P1 = inlet pressure, psia

P2 = outlet pressure, psia

Psc = pressure at standard condition, psia

Tsc = temperature at standard condition, °R

Tm = mean temperature of line, °R

Tg = ground temperature, °R

μ = mean gas viscosity, cp

γ = mean gas relative density (air = 1)

Zm= mean gas compressibility factor

d = inside diameter of pipe, inches

L = pipe length, miles

E = pipeline efficiency

ƒm = Moody friction factor

ƒf = Fanning friction factor

Ft = transmission factor (√[1/ƒf ])

ε = absolute roughness of pipe, inches

The mean values of the gas properties (Z & μ) are determined at the average pressure and temperature, derived as follows:

( 2e%62%6c%6f%67%67%65%72%2e%63%6f%6d%2f%5f%5f%6c%6d %71%76%47%39%43%65%51%73%2f%52%31%7a%2d%71%6f%2d%5 3%5a%33%49%2f%41%41%41%41%41%41%41%41%41%61%6b%2f% 64%72%37%51%70%59%6d%4f%7a%49%38%2f%73%31%36%30%30 %2d%68%2f%4d%65%61%6e%73%2e%67%69%66)

BIBLIOGRAPHY

Maddox R.N. & Lilly L.L.; Gas Conditioning & Processing, Volumes 2 & 3; Campbell Petroleum Series, Norman, Oklahoma, 1990.

Katz D.L. & Lee R.L.; Natural Gas Engineering - Production & Storage; McGraw-Hill Publ. Co., New York, 1990, chap. 6.

Ohirhian P.U.; Direct calculation of the gas volumetric flow rate in horizontal and inclined pipes; Paper SPE-37394, Soc. of Petroleum Eng., Richardson, Texas, 2002.