Gas Pipeline Blowdown - Semiemperical Model - Report No. 87-2

Based on SW Research Report calculations for the blowdown time and mass of gas vented to atmosphere to a piping system. Accurate to within a few percent. Blowdown time is impacted through constricting valve changes from sonic (choked) flow to subsonic. This is because of the pressure ratio across the valve is unknown.

Where

𝑉_𝑜 − Total Volume[ft³]

𝑉_𝑠𝑦𝑠 − Volume of system[ft³]

   
 

𝑉_𝑃 − Volume of Mainline Pipe[ft³]

𝐿_𝑝 − Mainline Pipe Length[in]

𝐷_𝑝𝑖 − Mainline Pipe Internal Diameter[in]

 
 

𝑉_𝑠(𝑖) − Volume of individual pipes[ft³]

𝐷_𝑠(𝑖) − Diameter of individual pipes[in]

𝑤𝑡_𝑠(𝑖) − Wall Thickness of individual pipes[in]

𝐿_𝑠(𝑖) − Length of individual pipes[mi]

 
 

𝑓 − Friction Factor(Sum of flow friction through all diameters of blowdown piping)

𝐿 − Blowdown Pipe Length[ft]

𝑑_𝑖 − Internal Diameter of Blowdown Pipe[in]

 
 

𝐴_𝑟 − Cross−Sectional Area of Choke[in²]

𝐷_𝑟 − Diameter of Choked Flow Point[in]

 
 

𝐴_𝑝 − Cross−Sectional Area of Blowdown Pipe[in²]

𝑑_𝑖 − Internal Diameter of Blowdown Pipe[in]

 

𝑅_𝐴 − Ratio of Choked Flow Area to Pipe Flow Area

𝑐_𝑓 − Coefficient of Blowdown Loss(Sum of loss for 𝑅_𝐴/𝑓𝑙_𝑑)

 
 
 
 

𝑃_𝑠𝑖 − Initial Subsonic Pressure[psi]

𝑃_𝑖𝑛 − Initial Pressure[psi]

𝑃_𝑓 − Final Pressure[psi]

𝑃_𝑏 − Base Pressure[psi]

𝑃_{𝑐𝑎𝑣𝑔} − Average Sonic Pressure[psi]

𝑃_{𝑠𝑎𝑣𝑔} − Average Subsonic Pressure[psi]

 
  From the SWRI – SIMPLIFIED BLOWDOWN CALCULATIONS FOR PRESSURIZED GAS SYSTEMS Technical Report you can find tables and equations to complete many of the remaining calculations in this module.

𝛾 − Can be found in table I of the SWRI Technical report mentioned above.

𝑅 − Universal gas constant (𝑈𝑟 = 1545)divided by the molecular weight 𝑀_𝑤

𝐴_𝑐 − Acoustic Velocity[ft/sec]

𝐴_𝑐𝑐 − Sonic Acoustic Velocity[ft/sec]

𝐴_𝑐𝑠 − Subsonic Acoustic Velocity[ft/sec]

𝑔 − gravitational constant, 32.2

𝑍 − Compressibility Factor

𝑇 − Absolute Temperature of the gas[°R]

   
𝑐𝑒 − Isentropic Compression Exponent  
 


𝑀_𝑢𝑐 & 𝑀_𝑢𝑠 − Thermodynamic multiplier to account for compressibility, Table II(choked and subsonic)

 
 
𝑇_𝑐 − Choked Blowdown Time[sec]


     
𝑇_𝑠 − Subsonic Blowdown Time[sec]
 
 
 
𝑇_{𝑇𝑜𝑡𝑎𝑙} − Total Blowdown Time[min]
 
 
 

∆𝑀_𝑐 − Mass Loss[lbs]

𝑉_{𝐿𝑜𝑠𝑠} − Gas Volume Lost[MSCF]

 
 

Input Parameters

1. To create a new case, click the “Add Case” button
2. Select the Gas Pipeline Blowdown – Semiempirical Model – Report No. 87-2 application from the Pipeline Testing module.
3. Enter Case Name, Location, Date and any necessary notes.
4. Fill out all required fields.
5. Make sure the values you are inputting are in the correct units.
6. Click the CALCULATE button.

• Pb – Base Pressure(psia)
• Pi – Initial Pressure(psig)
• Pf – Final Pressure(psig)
• Lo – Main Line Pipe Length(ft)
• do – Main Line Pipe Internal Diameter(in)
• L – Blowdown Pipe Length(ft)
• d – Internal Diameter of Blowdown(in)
• dr – Diameter at Choke Flow Point(in)

 

Outputs/Reports

1. View the results.
2. If an input parameter needs to be edited be sure to hit the CALCULATE button after the change.
3. To SAVE, fill out all required case details then click the SAVE button.
4. To rename an existing file, click the SAVE As button. Provide all case info then click SAVE.
5. To generate a REPORT, click the REPORT button.
6. The user may export the Case/Report by clicking the Export to Excel/PowerPoint icon.
7. To delete a case, click the DELETE icon near the top of the widget.

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