I applied for the msc pet. geophysics course last year, I was offered a place and attended interview for a scholarship, although I was not successful. I assume the process is the same for the other courses.
The interview was carried out by the course director and representatives from several oil companies who fund the scholarships. The set up was a bit intimidating, you're at a table on your own and they are in a kind of horse shoe arrangement around you. They were very friendly though, there were no trick questions or anything so don't worry.
The questions were pretty standard fare - the first was "Why this subject?", then there were a few competency based questions, things like "tell me about a time you had to resolve a conflict" etc. Read over your application since they have it in front of them - if you've mentioned a project or work experience you've done, they are likely to ask you something about it.
The final question was "you have 30 seconds to tell us why we should give the scholarship to you". If the format is the same this year, it would be a good idea to think about how you would answer this, imo it was the more important question - if you've been given an offer they are already happy with your academic performance, so motivation is a big part I think.
Show an interest in the industry - have a look at the Society of Petroleum engineers, membership is cheap or free for students, and you can mention that you are a member. They also offer separate funding that you can apply for in the event you don't get the Msc scholarship.