Disc Space Requirements
If you're processing your entire database, you'll need twice as much space as what the database currently requires as an entire shadow copy of your database will be created and if processing is successful, the shadow copy will then replace your entire database.
There's several articles on SSAS best practices, much of them posted by the SQLCAT team. Even if the article is related to SSAS 2005, the practices mentioned should be applicable to SSAS 2008 also. Here's one of the articles. http://technet.microsoft.com/en-us/library/cc966525.aspx
Disk space requirements for Object Processing
During processing, Analysis Services stores copies of the objects it is processing in the processing transaction on disk until the processing is finished. When the processing is finished, the processed copies of the objects replace the original objects. Therefore, you must provide sufficient additional disk space for a second copy of each object to be processed. For example, if you plan to process a whole cube in a single transaction, you need sufficient hard disk space to store a second copy of the whole cube.