Depends. If you want an office job, then you won't travel much at all. If you want a on-site job, you will be doing a LOT of traveling, often oversea. My grandfather was a petroleum engineer for a major oil company, traveled almost everywhere before becoming management in his company. He's been to Europe, South America, Asia, Middle East... as well as various oil rigs in the Gulf and other places.
Usually, if you get an on-site job, you are away for 2-3 weeks, and then get a week or 2 break to come home.
Also, office jobs for starting petroleum engineers usually pays a lot less than on-site jobs.