Move to Riyadh

hello
I'm a saudi citizen .
welcome to your second country in advance. ^^

as a person who is employed in one of the major companies in saudi. Your situation needs a little explanation.

First. The big companies have a scheme for nationalities for their expected salaries. so they can attract experts. that is the tricky part . lets say you are from a country in the middle of africa. you will not get as much as a Sweden guy. they lowest salary that they give the Swedish guy. for example lets consider 10k$/m the lowest price in their nationality salary scheme. while this is the maximum they can give if you are a from poor country. I hope you got the idea.

Due to that employees from western countries are sometimes their cost is not justified by their Experience/skills .While they can not give lower price salary for that country . This means the guy from india has a better luck than a Swedish since he costs less . But don't stop looking

Good?

The best way to get job in these big companies is by professional connections. and via the regular channels. Their job section in their website or LinkedIn .
Aramco is a good selection but there are a plenty of great companies out there . For example aramco has more than 15 international-saudi based contractor whom have a really good working environment. if I would suggest look for companies in eastern saudi arabia (damam-khubar-dahran,,etc)

recap.
Open your eyes a little . Don't focus on 2-3 companies. just look for a company that operate within your field of expert