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Wave Speed in Pipelines

Contents

Introduction

The equation for wave speed can be expressed in this general form.

a = \frac{\sqrt{\frac{K_S}{\rho}}}{\sqrt{1 + \left(\frac{K_S}{E}\right)\left(\frac{D}{t}\right) m}}

a = \frac{\sqrt{\frac{K_S}{\rho}}}{\sqrt{1 + \left(\frac{K_S}{E}\right)\left(\frac{D}{t}\right) m}}

Where:
π‘Ž βˆ’ Wave Speed
πΎπ‘ βˆ’Adiabatic Bulk Modulus of fluid
𝜌 βˆ’ Density of fluid
𝐸 βˆ’ Modulus of Elasticity for Steel Pipe (psi)
𝐷 βˆ’ Pipe Diameter (in)
𝑑 βˆ’ Pipe Wall Thickness (in)
πœ‡ βˆ’ Poisson’s Ratio (0.30 for Steel)
π‘š βˆ’ Coefficient for type of pipe support

  • Pipe anchorage only at the upstream end = (5/4βˆ’πœ‡)
  • Pull pipe restraint from axial movement = (1βˆ’πœ‡2)
  • Longitudinal expansion joints along the pipeline = (1.0)

K_s = A + B(P) – C(\sqrt{T}) – D(AP I) – E(AP I^2) + F(T)(AP I)

K_s = A + B(P) - C(\sqrt{T}) - D(AP I) - E(AP I^2) + F(T)(AP I)

Where:
𝐾𝑠 βˆ’ Adiabatic Bulk Modulus
𝑃 βˆ’ Pressure (psig)
𝑇 βˆ’ Temperature (°𝑅) = (℉+460)
𝐴𝑃𝐼 βˆ’ API gravity of liquid @ 60℉
𝐴 = 1.286×106
𝐡 = 13.55
𝐢 = 4.122×104
𝐷 = 4.53×103
𝐸 = 10.59
𝐹 = 3.228

K_s = (1.286 \times 10^6) + (13.55\times P) – (4.122 \times 10^4 \times\sqrt{T}) – (4.53 \times 10^3\times A) – (10.59\times A^2) + (3.228 \times T \times A)

K_s = (1.286 \times 10^6) + (13.55\times P) - (4.122 \times 10^4 \times\sqrt{T}) - (4.53 \times 10^3\times A) - (10.59\times A^2) + (3.228 \times T \times A)

Case Guide

Part 1: Create Case

  1. Select the Wave Speed in Pipelines application from the PLTB Misc. Module
  2. To create a new case, click the β€œAdd Case” button
  3. Enter Case Name, Location, Date and any necessary notes.
  4. Fill out all required Parameters.
  5. Make sure the values you are inputting are in the correct units.
  6. Click the CALCULATE button to overview results.

Input Parameters

  • Pipe Type
  • Nominal Pipe Diameter (in)
  • Outside Pipe Diameter (in)
  • Nominal Wall Thickness (in)
  • Reduced Wall Thickness (in)
  • Internal Pipe Diameter (in)
  • Liquid Temperature (Β°F)
  • Product Type
  • Liquid Specific Gravity
  • Pressure (psi)

Part 2: Outputs/Reports

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

Results

  • Adiabatic Bulk Modulus (psi)
  • Wave Speed in Pipeline (ft/sec)

References

  • Hydraulics for Pipeliners – C.B. Lester
  • API standard 2540 Manual of Petroleum Measurement Standards, Chapter 11.1-Volume Correction Factors, Volume X – Background, Development, and Program Documentation.
  • API RP 1117 Movement of In-Service Pipeline
Updated on January 4, 2024
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