Started 2003 Xc90, it was running for about 20mins and it shut off. Battery is now dead. Any ideas as to what's going on?

 

My best guess would be that the alternator gave up and your car was just running on the battery. Now that said it could be that your battery is bad, the alternator needs to have a good battery to regulate it's output.
Most auto parts stores can test both for free but you'll have to get your battery charged and tested first. Most batteries only last about 4yrs.