Applied online through company website (October 2016) , Online tests, Skype interview and then assessment centre in Southampton (March 2017).
Took a while to get back to me between stages but this was because they were changing their process.
Skype interview was general competency questions (Tell us about a time you...), I didn't have a webcam available but this was not an issue.
No feedback for months, emailed occasionally showing my interest and asking for feedback, eventually invited to an assessment centre. Over night stay at a hotel, dinner and drinks with employees and around 20 other candidates the night before. This wasn't assessed but was good to talk to graduates and get a feel for the job.
Assessment centre was split into four sections:
Individual task - Read information and do some basic calculations to decided between two options (Retrofit or New plant). There is no right answer, just want to see your thought process. Don't just do the required calculations, try to use all the relevant information your given.
Task Based Interview - Talking to a senior engineer about why you made your decision. They might disagree and tell you the other is correct. Neither is correct, they just want to see how your react and respond.
Task Based Group Presentation - Each given different information about the previous task, must decide whether yours is relevant and then come to a decision as a group about which option you are going to present. Present to around 8 senior engineers and then take questions. Make sure you speak up and make yourself noticed while not interrupting others.
Interview - 2 senior engineers asking competency questions for around 45 minutes. Prepare examples from uni projects, previous work experience and extra-curricular activities which show leadership and disagreements, use the STAR answer system.
Afew tips:
ExxonMobil's main focus is ALWAYS saftey.
ExxonMobil don't invest in things which MIGHT help at some point in the future, everything needs to have a justification.