How rigourous is the background check for petrochemical engineering?

It will be quite difficult given your history, although not impossible. As you probably know, the petrochemical industry is very selective when it comes to its employees. After all, its not just their product at stake, but other lives. You will have the mandatory drug test and for most places, a background check second to a government type position. I will tell you this, after working for a period in the refining business, I found that the larger companies (BP, Shell, Chevron, etc) will be more likely to hire those with questionable backgrounds, as they need personnel more than the smaller ones.  more