Rules of thumb
Evan Zabawski | TLT From the Editor March 2021
Thumbtimes they work, and thumbtimes they don’t.
All scientific disciplines have rules of thumb for doing back-of-the-envelope calculations, but occasionally some are used beyond their qualifications or even to the point as to be taken as fact. With lubricants, that might be the case with the statement that “the rate of oil oxidation doubles with every 10 C rise in temperature.”
Often when this statement is made, it is qualified as being based on the Arrhenius equation, an equation proposed by Swedish scientist Svante Arrhenius in 1889. The equation is a formula for the temperature dependence of the rate of reaction, and what it can show is the relationship between the activation energy (a term Arrhenius introduced) and the rate of reaction.
The activation energy can be imagined as a speed bump in front of a stationary vehicle, and that it would take a certain amount of energy to push the vehicle forward to roll it up and over the speed bump, but once the vehicle is past the speed bump, it will take less energy to keep pushing it forward. In an endothermic reaction, picture the road surface on the other side of the speed bump as being higher than the starting road surface, meaning some of the energy put into the vehicle is absorbed or not recovered. In an exothermic reaction, picture the road surface on the other side as being lower than the starting side, meaning some of the energy already in the vehicle is released.
When a match is struck, the friction provides the activation energy to start a combustion reaction of the match head, and since the combustion is exothermic, the match will continue to release enough energy to continue reacting. However, we know that typically matches will not spontaneously combust—they need the activation energy to get started. Oil oxidation is not all that different.
Some of the more complete references to the aforementioned rule of thumb qualify that the rate becomes significant above 70 C (~160 F), a value that also appears in a regreasing interval rule of thumb (shorten the interval by half for every 10-15 C increase above 70 C). What they are hinting at is that the activation energy requirements will be lower at higher temperatures.
Now if we use the Arrhenius equation at two temperatures 10 C apart and solve for activation energy, here is what we learn: starting at room temperature (20 C), the activation energy would need to be ~50 kJ/mol for the rate of reaction to double with a 10 C increase, but starting at 70 C, it needs to be nearly 70 kJ/mol. Just for reference later, the activation energy required, starting at 160 C (320 F), is just over 110 kJ/mol.
Therefore, to state that a reaction rate would double with a 10 C increase is highly dependent on the activation energy of that reaction and the starting temperature. The typical activation energy required to oxidize a mineral oil falls around 100 ± 30 kJ/mol, and for a PAO, it is 140 ± 30 kJ/mol; so, the rule of thumb only becomes valid for both types of oils at a temperature of 160 C or higher.
For a more reasonable temperature range of 70 C to 160 C, the rate of reaction for every 10 C increase is closer to one-and-a-half than double—but that does not quite have the same ring to it. An important takeaway is that the rate of reaction is not linear across a wide temperature range. However, the other issue is that the rate of reaction does not remain constant, even at a stable temperature.
Oxidation is an autocatalytic type of chemical reaction, meaning the product of the reaction acts as a catalyst for the same, or even a coupled, reaction—the snowball effect. What this means is that as an oil oxidizes, it will form acids and deplete the antioxidant additive, and these reactions will accelerate the rate of further oxidation (notwithstanding any increase in wear metals, particles contaminants or moisture).
So, this rule of thumb is really not that effective for an expected oil life calculation, but it does get the point across that lubricants fare better the cooler they are maintained.
Evan Zabawski, CLS, is the senior technical advisor for TestOil in Calgary, Alberta, Canada. You can reach him at ezabawski@testoil.com.