It's likely weatherproof paper and a grease pencil. We deal with EMS agencies and modern technology is often useless for them in harsh weather. Screens can be difficult to read outdoors and any touch devices are unresponsive in a downpour or very cold weather. Not to mention they often have blood on their hands so contamination is also an issue with any tech. I'm sure the greasy filth of an oil rig doesn't play well with most tech either.

Big pieces of paper are much easier to work collaboratively with than diagrams on than tiny screens, unfortunately. Lots of people still get paper maps and charts for this reason.

The company that makes a cheap roll-up non-backlit e-paper display will make billions if they figure this market out.

Besides the reasons already explained why (moisture-resistant) paper still works better for the location than electronic pads, I'm guessing refinement would still be welcome in more cheaply/quickly printing new paper diagrams on demand.

You would have to have special spark resistant kit though oil rigs are a major fire hazard

Software for reading blueprints and technical specs is beyond abysmal.