Agreed. Plant safety is a core subject, and a dissertation on one's experience in the subject forms an unavoidable item in the assessment process during the application to upgrade one's membership status in the IChemE.
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"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
From a course point of view, I would say the subject that best summed up chemical engineering for me was Transport Phenomena. You have to understand all the principles of heat and energy transfer, volume analysis and fluid mechanics and then tie them all together.
If you look at most process industries: oil and gas, pulp and paper, chemicals, etc they can be simplified down to heating/cooling stuff and moving it someplace to be either separated or mixed together to make something new. Repeat and refine as needed.
Of course, if you learn nothing else, learn to be safe. Heat, pressure and not being careful are what get people hurt.
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Eric Murphy - OPC Exchange - http://blog.matrikonopc.com
Unit Operations is probably the most important. The concept of unit operations is basically what defines chemical engineering and this concept is what differentiated ChE from Mechanical Engineering when contrived back in the very early part of the 20th century ultimately resulting in an entirely new branch of Engineering.