One thing you might want to do is read some actual job descriptions since you don’t seem to understand what chemEs actually do. Many are far removed with anything to do with the petroleum industry. (My dh has never been involved in that sort of process.)
Here is a link that has a variety of job descriptions from process engineers to operation managers to plant managers (and yes, the plant maanager job I skimmed required a chemE degree, not some "manufacturing management degree…though in a different process that might be the case. But for chemical processes, plant managers are going to have a background in operations.)
http://www.engineerjobs.com/jobs/chemical-engineering/
(Here are three links off that site that I selected based on job titles. I have no idea what they actually are, so if they are petroleum related…oops. Plenty of others to go and read!)
Typical process engineer job description:
https://careers-anoplate.icims.com/jobs/1098/process-engineer/job
Typical operations manager description:
https://wrgrace-hr.silkroad.com/epostings/index.cfm?fuseaction=app.jobinfo&jobid=2699&company_id=16266&version=1&source=Indeed%20Sponsored%20
Plant manager:
http://www.indeed.com/viewjob?jk=d8bb80c31c4c037e&q