Go to the Properties Module > List View.
Leave the Title box blank but select the Department you want to clean up the properties for (1). Click the Apply and Refresh button (2).
Sort the results by the “Sub. In” column. (Sort it so the black triangle indicator is pointing up. this puts the older projects at the top of the list)
Select then R-Click (Control Click) on a property. (You can select multiple Properties at one time to archive; However the more properties you have selected the longer the archiving process will take. 10 properties at a time is a good amount.) Select Archive from the Pop-up menu.