You cannot store the file itself in the session.
Instead,
generate a random name[
^] for the file.
Save the file[
^] in a folder on your server which is not exposed to the public, using that random name. Store the random name in the session, and use it to read the file each time you want to process it.
You'll probably want to add some code to clean up old files after they haven't been used for a while. Otherwise you risk having your server's disk fill up with old files.