On a rig, the people who request, check and approve permits are almost never sitting at a desk, which is why permits that need a computer end up waiting until someone walks back to the office. Designing for mobile means the whole workflow, from raising the permit to gas testing to approval and closeout, can be done on a phone or tablet wherever the person is.
That also means short screens, simple inputs, offline support for areas with poor signal and notifications that reach the next approver as soon as it is their turn. Permit to Work in Interface sits in the mobile app for this reason, since the permit should move at the same pace as the people working on it.