Did you watch Armageddon? Well the oil patch is not anything like that
The oil field separates into two distinct areas, Upstream (exploration and Production) and downstream (refining).
Both offer opportunities for oversea work (I am assuming the flat bit is somewhere in the US)
Downstream is typically civil and chemical engineering skill sets, basically building large process plants. Essentially really really expensive plumbing.
There is shipping, crude oil trading and refined product trading and marketing, but I am guessing this is not the area of the oil patch you are interested in.
Downstream is the side from seismic and other exploration, through drilling exploration wells, drilling appraisal and development wells and installing the appropriate completion equipment, through to the production, which is really primary separation and a bit of pumping (watching expensive plumbing work, dull dull dull)
So as an engineer (physicists and geoscientist are also around) you can find a lot of places to slot in. Plenty of opportunities in the production and upstream sides, this is the regular steady long term civil/chemical engineer project work. An upstream engineer may pop in to tell me I am full of it, and they would no doubt be correct.
Downstream on the drilling side the industry has 3 main branches, (I am ignoring the Geological and Geophysics side here)
The Oil company (shell, Exxon, bp, Total etc etc
The Service Providers (Schlumberger, Baker Hughes, Weatherford, Smith, Halliburton etc)
The Drilling Contractors (Transocean, Global, Pride, Precision et etc etc etc etc etc etc )
Joining the operators you Hill probably need a degree or masters in Drilling or Petroleum engineering. Head off to Colorado Scholl of Mines. This is just the way they recruit, although they do look at mech eng as well. The operator engineers are involved in well planning, completion design etc. They are the clients and call all the shots, although as an operator they are entirely dependent on the service and rig suppliers to actually do anything. This leads to a very uneasy relationship.
The service providers are probably the easiest and toughest way into the oil industry. This is to say, you could get a job easily, you just might quit it after 2 months of being treated somewhat worse than cattle. To make money the service providers need to be very efficient with people and equipment, which is to say you may find yourself in assendofnowhereistan with half the kit you need and two trainees as your crew. Service provides perform services such as fluid engineering, directional and measurement while drilling, Logging, data logging, cementing engineering. Good entry , make some money, have a party life (short periods of time off forget regular 4 on 4 off), learn , get the hell out. Do not expect to continue a relationship with your S.O. Most people I know (myself included) relationships did not last. Relationships started once within the industry seam to fare a lot better. YMMV terms and conditions apply
The drilling contractor is the people who met the drilling rig the oil co. They provide the rig, the driller, the roughnecks and roustabouts. This is essentially a construction crew, Rig engineering is mostly dealt with in the offices and rig manufacturing sites. Offshore rigs, particularly the deep water drillships and 54th and 5th generation semisubs do keep a rig engineer on board. Their task are mostly related to preventative maintenance and troubleshooting. These are very expensive pieces of kit with day rates touching 600k a day.
The 600k a day figure is one reason why people in the industry tend to have short fuses, people get very agitated when things go wrong.
Anyway that is some waffle on the industry.
But to answer your questions
What words? I Quit
What was the work like? I have had some very good time, I have had some very shitty times, I have had some excruciatingly tedious times, but on the whole it is entertaining.
Qualifications : Masters Physics
One thing you really need to put forward is why you want to go oversees.
There may be better ways to archive those goals than the O&G industry