AppleScript to tell Adobe Reader to close a certain document
"Adobe Reader" is not really scriptable, you can't access to the objects (window, document), but You can use the GUI Scripting.

This script works well here.

set theTitle to "this name.pdf"

tell application "System Events"
    tell process "Adobe Reader"
        tell window theTitle to if exists then perform action "AXPress" of (get value of attribute "AXCloseButton")
    end tell
end tell


This script requires that you enable access for assistive devices in the Universal Access System Preference pane.