From a corrosion probe to remaining wall
LPR measurementlinear polarization resistancecorrosion rate from Icorrremaining life calculation
Turning a polarization resistance reading into a corrosion current, a penetration rate in mm per year, and the years of wall left.
Polarization Resistance
The slope of potential against current at the corrosion potential: apply a few millivolts, measure the current that flows, divide. The measurement that feeds the Stern-Geary equation.
Tafel Equation for Overpotential
Julius Tafel's 1905 observation, still the backbone of electrode kinetics: the overpotential driving an electrode reaction rises with the logarithm of the current density, in a straight line whose slope is the Tafel slope.
Stern-Geary Corrosion Current
Stern and Geary's 1957 result: the corrosion current is the Stern-Geary constant divided by the polarization resistance. The equation that made an instantaneous corrosion rate a field measurement rather than a laboratory exercise.
Penetration Rate from Corrosion Current Density
Faraday's law applied to a corroding metal: a corrosion current density converted into the thickness of metal it removes per year, through the equivalent weight and the density.
Wall Penetration and Remaining Life
How many years of wall are left: the metal above the retirement thickness divided by the penetration rate. The number that turns a corrosion rate into an inspection interval.
How they fit together
This is the inspection chain rather than the design chain: an instrument reading at one end, a date on a replacement schedule at the other. Polarization resistance is the measurement itself, a small applied potential shift divided by the current it produces. Small is load-bearing. The linear approximation holds within roughly ±10 to 20 mV of the free corrosion potential; push harder for a cleaner signal and the relationship stops being linear, the number stops meaning what the next formula assumes, and the reading comes out optimistic.
Stern-Geary converts Rp into corrosion current, and it needs the B constant that the Tafel equation supplies through the anodic and cathodic slopes. Here is the honest weakness of the whole method, and it is better stated than hidden: those slopes are rarely measured. Practitioners assume B ≈ 0.026 V and move on. That assumption is usually within a factor of two and occasionally out by three, so an LPR corrosion rate is a good trend instrument and a mediocre absolute one. Two readings a month apart on the same probe with the same assumed B will tell you truthfully that things got worse; a single reading will not tell you truthfully what the rate is.
Penetration rate from current density is Faraday's law wearing work clothes, and it is the step where the metal's own identity enters through molar mass, valence and density. The same current density eats very different depths of steel, copper and aluminium, so a rate quoted without naming the alloy is not a rate. Remaining life then divides the wall you have above retirement thickness by that rate, and carries the largest caveat in the set: it describes general corrosion only. Pitting removes the same mass from a hundredth of the area and perforates a vessel while the average wall loss still reads comfortable. If the damage mechanism is pitting, crevice attack or cracking, this number is not conservative — it is irrelevant, and the inspection has to be a thickness survey rather than an average.