You say you believe the 12GB partition/drive should not appear in Disk Management, yet it's clearly labeled Recovery Partition. So, the 12GB partition is the Recovery Partition put there by Acer and it's there in case you need to restore your system to it's original configuration. This, i.e., a Recovery Partition, is standard on practically all computers on the market in recent years.
And, if you use the Recovery Partition to restore the system, the Recovery Partition will continue to exist after you've done a restore.
So, based on your post, I really don't see a problem. Can you re-state or clarify what you feel is the problem?