Very lengthy and extensive interview process. At my school, only a few students received an on-campus interview. This was a 1:1 behavioral interview. About 7 weeks later, I got a call to schedule a 2nd round phone interview. A week after the 2nd round, I was invited to the 3rd round on-site interview at the refinery. The company flew me out, and the first night was an informal dinner with exxonmobil engineers. This is a time for you to get to know the people you'll possibly be working with. And it's also a time to show them that you'd be a great person to be around. The next day was the real deal - I was onsite at the refinery for about 6 hours, where I went through 3 interviews, a refinery tour, and a lunch with a few other engineers. Of the 3 interviews, 1 was technical, 1 was on soft skills, and the last was behavioral. Although the on-site interview was lengthy, it's important to keep your interview hat on the entire time. A week after my onsite, I was offered a position.
Some tips for the application process, know EXACTLY whether you want to work downstream or upstream. And know EXACTLY whether you want to pursue the managerial or technical track. The Exxonmobil reps want to be sure you know exactly what you are interested in, and be sure to stick with it throughout the entire interview process. They don't want someone who's unsure of what they want to do.
Also, be personable. Everyone I met throughout my interviews was very smart but also personable. It helps to be very articulate as well, because they like good communicators.
And be sure to ask as many questions as you can because it'll show a genuine interest. Ask questions that are intelligent and job specific.