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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Elevation Difference		m
Inlet pressure		106N/m2
Outlet pressure		106N/m2
Pressure, std. condition		106N/m2
Temperature, std. condition		° C
Mean temperature of line		° C
Inside diameter		mm
Pipe length		km
Gas relative density
Mean gas compressibility
Pipeline efficiency

Optional Data

Pipe effective roughness		10-6mm
Mean gas viscosity		cp

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OUTPUT   VARIABLES   &   GRAPHS

Gas Flow Equation	Uphill/Downhill Flowrate m3/day	"Horizontal" Flowrate m3/day	Computed Friction factor
♦  Weymouth
♦  Panhandle A
♦  Panhandle B
♦  AGA
♦  Ohirhian

Flow Of Compressible Gas In An Inclined Pipeline

For a slightly inclined pipeline, flow rate predictions are obtained by the modification of the horizontal gas pipleline flow equations. The elevation change (positive uphill, negative downhill) is compensated for by adding the static head of gas column to the pressure loss calculation.

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

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. ƒ_m is the friction factor (also called the Moody friction factor) that is commonly tabulated in the Moody Charts. Quite often the Fanning Friction factor ƒ_f is used: ƒ_f = ƒ_m/4.

The equations for each method is given below with the e^S and L_e terms accounting for elevation change :

 -  Panhandle A:

 -  Panhandle B:

 -  AGA (fully turbulent):

 -  Ohirhian:

Where:

   q_sc = gas rate at standard condition, scf/d
   P₁ = inlet pressure, psia
   P₂ = outlet pressure, psia
   P_sc = pressure at standard condition, psia
   T_sc = temperature at standard condition, °R
   T_m = mean temperature of line, °R
   T_g = ground temperature, °R
   μ = mean gas viscosity, cp
   γ = mean gas relative density (air = 1)
   Z_m= mean gas compressibility factor

   d = inside diameter of pipe, inches
   L = pipe length, miles
   L_e = effective pipe length, miles
  ΔH = Change in elevation between inlet & outlet (ft)
   E = pipeline efficiency
  ƒ_m = Moody friction factor
  ƒ_f = Fanning friction factor
  F_t = transmission factor (√[1/ƒ_f ])
  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:

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.
• Tian S. & Adewusi M.A.; Development of analytical design equation for gas pipelines; Paper SPE-24861, Soc. of Petroleum Eng., Richardson, Texas, 1992.
• 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.