The lack correlation but having equaltions for relating is good answer. There is way too much scatter on crude sulfurs (your companies tech presentations on crudes often have the chart that shows crude “bubbles” of different size representing the volume or supply against the API & Sulfur axis and the relationship is scatter trend not correlation. Correlation means there is at least 80-90% relationship between the items beeing correlated and very few things in petcoke industry make it there.
But EIA has chart showing history of US Crude import volumes vs domestic supply one chart and another showing total Refining Crude Sulfur levels ……. they crossed in about 1989 where imports rose to +50% of volume and Sulfur levels started increasing parallel to import curve/line. If you plot average US refining crude sulfur levels (from EIA tables) against the estimated average US petcoke sulfur level (havent seen it newer EIA tables probably have buy someones (Jacobs/CRU/CERA) estimate of this now) they “TREND” fairly well but do not correlate.
You have to do some volumetric adjustments if your going to try calculate it because of big volume shrink on heavy portion of crude that keeps 75-80% of metals & sulfur all the way down into the petcoke …… thats how you upgrade to get the products by removing carbon and sulfur while increasing ratio of Hydrogen (hence increasing API). Heavy resid is often about 50% crude but carries ~75% sulfur (&metals), and then about 50% resid becomes petcoke which has 75% of resid sulfur (& metals). So you see that makes it start following a logrithmic or exponential function – which is why you would need look at multiple variables for your equation and then sort down to important ones. Except for vary stable crude slate on consistent coker cycle operation and same type petcoke make (fuel/shot) it isnt going to be worth the effort for just a 55-70% trend on the sulfur equations.