The Math Behind Corrosion Rates NACE SP0775
Corrosion coupons are in common use in the oilfield and many of us use the formula from NACE SP0775 daily to calculate corrosion rates by mass loss, but have you ever stopped to think how this formula was derived? How is it that we report “mils per year” (mpy) but there are no “mils” anywhere in the formula nor are there any years? If you are as dense as I am (pun intended) you may be inclined to think of this like you do “miles per hour” which is very clear to me that the miles are in the numerator and hours in the denominator (m/h). Likewise, I would expect to see mils in the numerator and years in the denominator in the formula for mils per year (m/y) but alas no mils and no years can be found. What gives? Let’s break this down and see if we can figure out what is going on here.
I would like to dedicate this to my high school chemistry teacher Ms. Adams. I am sorry I was a poor student, I did not pay attention during unit conversions and for all the times I asked “when are we ever going to use this in real life?”. How could I know I would one day be tasked with saving the planet one corrosion coupon at a time.
The Formula from NACE SP0775 2.4.1. is:
CR = 22270 x W
(ATD)
where:
CR = average corrosion rate, mils per year (mpy)
W = mass loss, grams (g)
A = initial exposed surface area of coupon, square inches
T = exposure time, days
D = density of coupon metal, grams per cubic centimeter
What is a mil per year anyway?
A “mil” is simply industry jargon for one thousandth of an inch or 0.001 inches. The term “mil” comes from an abbreviation of the word “milli-inch” and is primarily in use in the US. This potential for confusion is why I prefer using thousandths of an inch, in most machine shops in the United States you will hear “thou” in reference to a thousandth of an inch and “tenths” in reference to a ten-thousandth of an inch. I suppose that “a thousandth of an inch per year” was a little too wordy but this is exactly what is meant by mpy. Normally we associate these Latin prefixes with SI units, so it does seem out of place, but the term Mil is in common use especially as a thickness measurement for paper and plastic films. You may recall the last time you purchased a trash bag it may have been labeled 1-mil, 2-mil, or maybe even 4-mil if it was hefty, which just tells you how many thousandths of an inch thick the plastic is. This is all of course derived from the Latin prefix Milli which is why the Roman numeral for 1,000 is M and it is likely no coincidence that a Million (MM) is one thousand thousands, although it would be cool to be a “Meganaire”.
To put a fine point on it when we say the corrosion rate is 1 mil per year or 1 mpy we simply mean that we expect the material loss from the inside of the pipe to be 1 thousandth of an inch over the course of a year. This is of course an estimate, and the realized material loss will be different based on many variables beyond the scope of this article.
“Wait!” you say, “1 thousandth of an inch is a measure of distance how do we end up with depth loss when our input is weight loss of the corrosion coupon in grams”. Answer: Follow the math. Let’s break down the equation starting with the conversion factor of 22270. The first version of the formula gives us some clues:
CR = W x 365 x 1000
ATD x (2.54)^3
365 you may recognize as the days in a year, remember we want the corrosion rate in a year. 1,000 or 1 X 10^3 in scientific notation moves the decimal three places to convert from inches to thousandths of an inch. Without this factor we would be reporting 0.001 inches per year for example. Lastly 2.54^3 converts the density in g/cm^3 to inches; there are 2.54 cm in an inch. Combining and simplifying these terms we get the constant or K factor 22270. By the way if you are looking for corrosion rate in millimeters per year (mmy) you can use the formula from NACE SP0775 2.4.1.1 or use the proper K factor from ASTM G1.
Now how do we get inches in the numerator? We are given surface area in square inches and density in grams per cubic centimeter which we will convert to inches as part of our K factor. The formula for area is Length X Width and the formula for density is mass/volume or mass / Length X Width X Height (depth). Multiplying these two terms we get:
Area X Density = L(in) X W(in) X Mass(g)
L(in) X W(in) X Depth(in)
You may remember if you ever studied unit conversions that the length and width in inches will cancel each other and we will be left with grams over the third dimension of volume “depth” in inches which are the units we want to report. Through the magic of math, we have found the units we want to report and isolated the third demission height or “depth”. You can imagine this as a graduated cylinder, when we measure volume in a cylinder, we have fixed the length and width so all changes in volume are attributed to changes in depth. Similarly, all changes in the mass of the corrosion coupon are attributed to changes in material lost as depth. At this point the equation looks something like:
Weight(g) X 22270
T(days) X Mass(g)/Depth(in)
We have a fraction in the denominator, and you may remember when you divide by a fraction you multiply by the reciprocal (inverse) so:
Weight(g) X 22270 = Weight(g) X22270 X Depth(in) = Weight(g) X 22270 X Depth(in)
T(days) X Mass(g)/Depth(in) T(days) Mass(g) T(days) X Mass(g)
Once again, the grams cancel, and we are left inches and days as the only units. The conversion to Years as mentioned previously is built in the constant 22270.
So this is how we get the corrosion rate of a corrosion coupon in mils per year beginning with no units called mils or years. I hope you enjoyed this fun math problem. Some of this is difficult to describe in word form so I have included photos to hopefully add clarity.
If you have any questions, please contact me and we can break out the scratch paper together!
Will Ritter Pacific Sensor 972-242-5750 will.ritter@pacificsensor.com
