Learn A Real World Cathodic Protection Calculation

Cathodic protection is a great way to mitigate corrosion. I’m going to go over a simple cathodic protection calculation for a solar farm.

I’ll show you how to calculate the number of required anodes per stanchion. The solar panels will mount to these stanchions.

Before we start though, I’m going to discuss the details of cathodic protection. Because it’s important to understand the science.

Only then, you can better understand and appreciate the cathodic protection calculation.

What is cathodic protection?

corrosion cell schematic

A technique used to control the corrosion of a metal surface. The end goal is to turn the metal you want to protect into a cathode.

When metal becomes a cathode, we prevent metal oxidization. Because oxidation only happens to an anode.

Just as important to know, rust is the result of corroding metal. More specifically, when metal becomes exposed to oxygen and moisture.

Important Note: metals corrode through electron transfer. This leads to the deterioration of the metal. 

The two corrosion processes are oxidation and reduction. 

In oxidation, a metal atom loses electrons. This happens from a chemical reaction between a metal with oxygen. Thus forming the metal oxide. 

While the reduction is the transfer of electrons from a metal to another material. 

Now, let’s define a cathode and anode.

  • Anode (active site): the metal that loses electrons.
  • Cathode (less active site): the metal, liquid, or gas that gains electrons.

Next, the following three things need to be present for corrosion to happen:

  • Two different metals: example is steel and aluminum.
  • An electrolyte: a medium where ions can freely flow. In return, the medium can transport electric charges. Examples of such a medium are seawater and even Earth.
  • An electrical connection between the cathode and anode. This creates a return path for the current flow between the different metals.

Important Note: the two different metals can be separate metals. But also, a single piece of metal with metallurgical differences on the surface will work. 

These can be macroscopic differences, which lead to non-uniformity on the metal surface. Thus, a single pipe can have an anode part and a cathode part.

Or better yet, imagine a pipe that’s half dipped in water with low oxygen concentration. This half becomes the anode. While the other half that’s in a high oxygen concentration becomes the cathode. 

single pipe corrosion schematic

In summary, corrosion can happen when metals come in contact with the following:

  • Water
  • Moist air
  • Moist soil and even moist concrete

How does cathodic protection prevent corrosion?

Cathodic protection prevents corrosion by converting all anodic (active) sites on metal to cathodic (passive) sites. We do this by pumping electrons onto the metal we want to protect.

This metal could be a large steel pipe or the hull of a ship. It doesn’t matter.

What’s more, we can choose between two different cathodic protection methods. Each has its pros and cons in real-world applications.

Method #1: sacrificial anode

sacrificial anode cathodic protection method

The anode is a metal that’s more reactive than the protected metal. When a metal is more reactive, it’ll more easily lose its electrons and form ions.

For example, if we’re protecting iron, we want to use a more reactive metal than iron. A good option would be zinc or magnesium.

Important Note: this additional metal source is also called a sacrificial anode. Because the galvanic anode sacrifices itself to protect another metal from corrosion. 

What now happens is, the sacrificial anode will oxidize in the electrolyte. The electrolyte can be soil or the ocean.

The oxidation of the sacrificial anode then generates electrons.

These electrons then flow to the metal we want to protect. This then forces our metal to become a cathode.

Also, the incoming electrons “heal” our protected metal. The electrons cause any parts of the oxidized cathodic metal to reduce and return to their original state.

The presence of the electrons will cause the ferrous ions to turn back into iron solid.

Important Note: the sacrificial material needs to oxidize before the protected material. Otherwise, cathodic protection will not work. 

Method #2: impressed current protection

impressed current cathodic protection method

This is similar to the sacrificial anode method. Except, we generate the electric current.

We pump electrons onto our protected metal through an alternate power source. For example, using a DC power supply.

We connect the negative end of the DC power supply to our protected metal. This forces the protected metal to become a cathode. As a result, the metal remains protected from oxidation.

The cool thing is, the anode material can be anything. It can even be iron. The only constraint is, the material must be electrically conductive. So you can’t use plastic for instance.

But you’ll have an eternal anode with this approach. Versus with a sacrificial anode, where you need to replace the metal once it’s corroded.

Important Note: a big difference between the two methods is the oxidation.

In the anode of a sacrificial system, the metal oxidizes. Whereas in an impressed current system, the water oxidizes.

Example of cathodic protection with a ship

Think of a large ship that travels through the ocean. The ship sits in an electrolyte solution of saltwater. The ocean.

Our goal is to protect the ship’s steel from corrosion.

So, we drop a zinc anode into the water and connect it electrically to the hull of the ship.

Our reactive metal zinc oxidizes and produces electrons. These electrons are then pumped onto the hull of the ship. This makes the hull of the ship a cathode.

Now assume the ship’s hull’s material is iron (Fe) and it has already started to oxidize.

The anodes’ electrons will reduce the Fe ions and then will form Fe atoms again. This prevents corrosion. Because only Fe ions will bond to other atoms causing corrosion.

Important Note: Zinc anode oxidation: Zn \rightarrow Zn^{2+}(aq) + 2e^{-}

Now, assume some iron has oxidized on the ship’s hull.

The below chemical reaction shows the Fe ions grabbing the two electrons from zinc. In return, we have solid iron again. This is what we want!

Reduction: Fe^{2+} + 2e^{-} \rightarrow Fe(s)

Now, let’s assume iron hasn’t oxidized on the ship’s hull.  Instead of reducing Fe ions back to Fe solid, a different reaction occurs. We reduce water and oxygen into OH^{-} with the addition of the electrons. Because the electrons need to go somewhere. 

Reduction: O_{2}(aq) + 2H_{2}O(l) + 4e^{-} \rightarrow 4OH^{-}(aq)

Your water heater and submarines

This is exactly how your water heater works in your home. Let’s go over a quick and easy water heater hack.

Replace your sacrificial anode every couple of years in your water heater.  Your water heater will then last you a long time, saving you a lot of money.

What’s more, submarines use cathodic protection. It’s how these large engineering marvels can safely stay underwater for so long.

In short, you use cathodic protection when the environment around metal acts as an electrical conductor.

Cathodic protection calculation for a solar farm

Finally, let’s do our calculation for an embedded steel structure in the soil.

We want to install 378 steel stanchions for our solar farm. We need to protect these stanchions from corrosion.

First, we calculate how much current we need to output from each anode. Or as we learned, the number of electrons that’ll flow out from an anode.

The required current output for the protection of embedded steel structures we define as:

i_{m} = \dfrac{(S_{cm})(f)(Y)}{\rho}

Where,
S_{cm} = factor for uncoated steel = 150,000
f = anode factor = 1.90 for 42lb long shape 3″ x 3″ x 72″ magnesium anode
Y = structure to soil potential correction factor for standard -0.85 volt differential = 1.0
\rho = soil resistivity in ohm-centimeters = 1951 ohm-centimeters for this location (per test report)
i_{m} =curent output in milliamperes

i_{m} = \dfrac{(150,000)(1.0)(1.90)}{1951} = 146.08 milliamps output per anode

Our location is in low resistivity (high corrosion) soil. In our case, a current of 15 milliamperes/ft^{2} of surface is required.

Now, the total embedded surface area for 378 stanchions is 1,669,920 in^{2} or 11,597 ft^{2}

Thus, (11,597 ft^{2}) x (15 x 10^{-3} Amps/ft^{2}) = 173.95 Amps

I = 173.95 Amps (total current requirement) = 173,950 milliamps

Based on a 10-year life, the total weight of anodes is given by the following equation:

W = \dfrac{L_{m} \times I }{42.81}

Where,
W = weight of anodes
L_{m} = projected life in years
I = total current required in milliamps

W = \dfrac{10 \times 173,950 }{42.81} = 40,633 pounds of magnesium anodes

Now, we calculate the number of anodes required:

\dfrac{W}{weight \: per \: anode} = \dfrac{40,633}{42} = 967.5 anodes

Next, we calculate the number of anodes per stanchion:

\dfrac{967.5}{378} = 2.56

With 3 anodes per stanchion = 3 x 378 = 1134 total anodes

L_{m} = \dfrac{42.81(1134 \times 42)}{173,950} = 11.72 years anticipated life

Important Note: anodes are 3-inch x 3-inch x 72-inch.

Anodes installed in 6-inch diameter by 72-inch length hole with backfill. Also, anodes installed approximately 10-feet from the stanchion they’re protecting. 

General rules of thumb with sacrificial anode system designs

Let’s further simplify matters.

I = \dfrac{V}{R} drives the amount of electric current an anode can discharge.

Yes, Ohms Law!

Where,
I = flow of current in amps
R = circuit resistance
V = voltage difference between the anode and cathode

In application, the current is high at first. Because the voltage difference between the anode and cathode is great.

But, over time the potential difference drops. This happens as the current travels from the anode to the cathode. Then eventually, the current decreases with the polarization of the cathode.

Finally, for the circuit resistance, let’s refer to our ship example. The path through the saltwater and metal and any connected cables make up the resistance.

Important Note: as a general rule of thumb with anodes:

  • An anode’s length determines the amount of generated current. In return, determines the area of metal you can protect.
  • An anode’s cross-sectional area determines for how long you can protect a metal. The cross-section is a function of the anode’s weight. 

Cathodic protection calculation wrap up

Without cathodic protection, the world we live in today would be much different.

Because we install metals in corrosive environments all the time. Then there are the ships that endlessly travel across seas and oceans.

Without a doubt, cathodic protection has contributed greatly to modern world advancements.

So much more goes into every installation job than the eye can see. A real-world cathodic protection calculation and installation is a project in itself.

What are your thoughts on the cathodic protection calculation? Which type of cathodic protection do you most commonly see installed? 

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