Weymouth

Introduction

The Weymouth equation is one of the older equations but is still widely used for distribution and gathering systems. It was originally developed from data taken on small, low to medium pressure pipelines.

When it is used for larger, high-pressure pipelines it is quite conservative, as it predicts values for Q which could be 8-12% low for gas transmission through long pipelines, the Weymouth equation is not recommended. The Weymouth equation is typically used for flow conditions:D>6″,\,Pressure\,\,\,1.5psi\,\,< P_1 < \,\,300psi \~\F=C_fD^{0.1667}

D>6",\,Pressure\,\,\,1.5psi\,\,< P_1 < \,\,300psi \\~\\F=C_fD^{0.1667}

𝐹 − Transmission Factor
𝐶_𝑓 − 11.18
𝐷 − Internal Diameter (in)

Q=C_Q(\frac{T_b}{P_b})D^{2.667}\biggr[ \frac{P_1^2-e^sP_2^2}{GT_fL_eZ} \biggr]^{0.5}

Q=C_Q(\frac{T_b}{P_b})D^{2.667}\biggr[    \frac{P_1^2-e^sP_2^2}{GT_fL_eZ}    \biggr]^{0.5}

𝑄 − Flow Rate (FT³/day)
𝐶_𝑄 − 433.49
𝑇_𝑏 − Temperature Base (°R)
𝑃_𝑏 − Pressure Base (psia)
𝐷 − Internal Diameter (in)
𝑃₁ − Upstream Pressure (psia)
𝑃₂ − Downstream Pressure (psia)
𝐺 − Gas Specific Gravity
𝑍 − Compressibility Factor
𝐿_𝑒 − Pipe Segment Length including Expansion (mi)
𝑇_𝑓 − Gas Flowing Temperature (°R)

s=\frac{C_S\triangle HG}{T_fZ}

s=\frac{C_S\triangle HG}{T_fZ}

𝑠 − Elevation adjustment parameter
𝐶_𝑆 − 0.0375
𝑍 − Compressibility Factor
𝑇_𝑓 − Gas Flowing Temperature (°R)
∆𝐻𝐺 − Change in Elevation (ft)

L_e=\frac{(e^s-1)}{s}

L_e=\frac{(e^s-1)}{s}

𝐿_𝑒 − Pipe Segment Length including Expansion (mi)
𝑠 − Elevation adjustment parameter

V=0.75\frac{Q_h}{D^2P_{avg}}

V=0.75\frac{Q_h}{D^2P_{avg}}

𝑉 − Velocity (ft/sec)
𝑄_ℎ − Volumetric flow rate (scf/hr)
𝐷 − Internal Diameter (in)

For Small Pressure Drop P2 > 0.8 P1:

P_{avg}=\frac{(P_1-P_2)}{2}

P_{avg}=\frac{(P_1-P_2)}{2}

For Large Pressure Drop:

P_{avg}=\frac{2}{3}\biggr[ P_1+P_2-\frac{P_1P_1}{P_1+P_2} \biggr]

P_{avg}=\frac{2}{3}\biggr[  P_1+P_2-\frac{P_1P_1}{P_1+P_2}    \biggr]

Case Guide

Part 1: Create Case

Input Parameter

• Temperature base(°F)
• Pressure base(psia)
• Gas Flowing Temperature(°F)
• Gas Specific Gravity
• Compressibility Factor
• Pipeline Efficiency Factor
• Upstream Pressure(psig)
• Downstream Pressure(psig)
• Flow Rate(MSCFH)
• Internal Pipe Diameter(in)
• Length of Pipeline(mi)
• Upstream Elevation(ft)
• Downstream Elevation(ft)

Downstream Pressure

Flow Rate

Internal Pipe Diameter

Upstream Pressure

Part 2: Outputs/Reports

Results

• Downstream Pressure(psig)
• Flow Rate(MCFD)
• Internal Pipe Diameter(in)
• Upstream Pressure(psig)
• Transmission Factor
• Velocity(ft/sec.)
• Erosional Velocity(ft/sec.)
• Sonic Velocity(ft/sec.)

Downstream Pressure

Flow Rate

Internal Pipe Diameter

Upstream Pressure

References

• McAllister, E. W., “Pipeline Rules of Thumb” Gulf Professional Publishing, Seventh Edition
• Menon, Shahi E., “Gas Pipeline Hydraulics”, Systek Technologies, Inc.
• Carroll, Landon and Hudkins, Weston R., “Advanced Pipeline Design”
• American Gas Association (AGA), “Reference: Eq-17-18, Section 17, GPSA”, Engineering Data Book, Eleventh Edition

FAQ