How much free space do I need for mongoDB? and how to reclaim lost space?
There are two operations here 
1. Compact - This is an in place compact of data inside the data files. This will however not release any of the data files. Even thought it does not return the free space to the file system mongo should be able to use the space for growth. 
2. Repair - This will release any unused space back to the filesystem. This is what you need. However repair requires the same amount of space as your database. So if you want to repair you will 800GB + few extra GB for repair to complete.