Cathodic Protection Module Attenuation Calculation

Introduction

Where long distances are covered by impressed current systems, voltage drops occur along the structure in a reduction fashion of voltages and currents. Reductions can be significant depending on the current demand and voltage drops. This may require additional cathodic protection for the pipeline system.

R_L=\frac{\rho}{A_w}\,or \,R_L =4L\frac{\rho}{\pi(D_o-D_i)}\~\R_T=\frac{R_0}{\pi D_o}\~\R_K=\sqrt{R_LR_T}\~\\alpha=\sqrt{\frac{R_L}{R_T}}

R_L=\frac{\rho}{A_w}\,or \,R_L =4L\frac{\rho}{\pi(D_o-D_i)}\\~\\R_T=\frac{R_0}{\pi D_o}\\~\\R_K=\sqrt{R_LR_T}\\~\\\alpha=\sqrt{\frac{R_L}{R_T}}

E_x=E_0 \sinh \alpha X-R_KI_0\sinh \alpha X \~\ E_0=E_x \sinh \alpha X-R_KI_x\sinh \alpha X\~\ I_x=I_o \cosh \alpha X-\frac{E_0}{R_K}\sinh \alpha X \~\ I_0=I_x \cosh \alpha X-\frac{E_x}{R_K}\sinh \alpha X

E_x=E_0 \sinh \alpha X-R_KI_0\sinh \alpha X \\~\\ E_0=E_x \sinh \alpha X-R_KI_x\sinh \alpha X\\~\\ I_x=I_o \cosh \alpha X-\frac{E_0}{R_K}\sinh \alpha X \\~\\ I_0=I_x \cosh \alpha X-\frac{E_x}{R_K}\sinh \alpha X

Where:

𝑅_𝐿 — Linear Electrical Resistance of the Section of the Pipeline(ohm/m)
𝑅_𝑇 — Leakage or Transverse Resistance of the Section of the Pipeline(ohm/m)
𝑅_𝐾 — Characteristic Resistance of the Section of the Pipeline(Ohms)
𝛼 — Attenuation Constant of the Section of the Pipeline(Ohms)
𝑅₀ — Pipe to Electrolyte Insulation Resistance(Ohms)
𝜌 — Specific Resistance of the Pipeline Material(Ohms)
𝐿 — Half Distance between Drain Points(anodes)(m)
𝐷_𝑜 — External Diameter of the Pipeline(m)
𝐷_𝑖 — Internal Diameter of the Pipeline(m)
𝐴_𝑤 — Pipe Cross Sectional Area(in-2)
𝐸₀ — Pipe to Electrolyte Potential at the Drain Point(Anode)(V)
𝐸_𝑥 — Pipe to Electrolyte Potential at the Distance of X from the Drain Point(V)
𝐼₀ — Current Flowing onto the Pipe at the Drain Point(Anode)(amp)
𝐼_𝑥 — Current Flowing onto the Pipe at Distance X from the Drain Point(Anode)(amp)

For typical pipeline with multiple drain points (anodes) with uniform spacing of 2L the potential and current are given: E_x=E_0 \frac{\cosh\alpha (L-X)}{\sinh \alpha L}\~\I_x=I_0 \frac{\sinh\alpha (L-X)}{\sinh \alpha L}

E_x=E_0 \frac{\cosh\alpha (L-X)}{\sinh \alpha L}\\~\\I_x=I_0 \frac{\sinh\alpha (L-X)}{\sinh \alpha L}

Case Guide

Part 1: Create Case

Input Parameters

• Pipe Outside Diameter (in)
• Pipe Wall Thickness (in)
• Half Distance between Drain Points (Anodes) (ft)
• Specific Resistance of Pipeline Material (m-ohm-cm)
• Pipe-to-Electrolyte Insulation Resistance (ohm-ft²)
• Pipe-to-Electrolyte Potential at the Drain Point (volt)
• X – Distance from the Drain Point (Anode) (ft)

Part 2: Outputs/Reports

Results

• Linear Electrical Resistance of the Pipeline Section (ohm/ft)
• Leakage/Transverse Resistance of the Pipeline Section (ohm-ft)
• Characteristic Resistance of the Pipeline Section (ohm)
• Attenuation Constant of the Pipeline Section (1/ft)
• Pipe-to-Electrolyte Potential at the Distance of X from the Drain Point (volt)

References

• NACE Standard Practices 0169 – Latest Edition “Control of Corrosion on Underground or Submerged Metallic Piping Systems”
• Uhlig’s Corrosion Handbook (2nd Edition) Edited by: Revie, R. Winston © 2000 John Wiley & Sons
• ISO 15589-2 Petroleum and Natural gas Industries Cathodic Protection Pipeline Transportation Systems
• Pipeline Corrosion and Cathodic Protection, Third Edition, Gulf Publishing Company

FAQ