Theoretical Concepts, Calculations, and Attenuation
Core theory
Cathodic protection depends on shifting the structure potential to the protection criterion by supplying cathodic current. Key concepts: electrochemical potential, polarization (activation and concentration), IR drop, and the difference between 'on' and 'instant-off' potentials. The 100 mV polarization criterion and −0.85 V vs Cu/CuSO4 criterion are references; IR drop must be removed for accurate assessment.
Resistance and current
Anode resistance to remote earth uses Dwight's equation for vertical rods: R = (ρ/2πL)[ln(4L/a) − 1], where ρ is resistivity, L length, a radius. Parallel anodes: 1/R_total = Σ1/R_i (with spacing factor). Current output I = ΔE/R_total via Ohm's law.
Attenuation
On long coated structures (pipelines), current and potential attenuate with distance from the drain point. Attenuation is governed by coating conductance (leakage) and pipe longitudinal resistance. The attenuation equation: E(x) = E0·exp(−αx), where α = √(g/r), g = coating conductance per unit length, r = pipe resistance per unit length. Higher coating quality (lower g) gives longer attenuation length and better current throw. This is a frequent calculation and conceptual trap: better coating = longer protected length.
Common traps
Confusing attenuation length with anode spacing; using 'on' potential including IR drop; forgetting temperature and resistivity effects on groundbed resistance; and misapplying Dwight's equation with wrong units. Also watch sign conventions and reference electrode calibration.
Worked rule of thumb
For a coated pipeline, halving coating conductance increases attenuation length by √2. Always remove IR drop (instant-off) before judging protection.