First, you should be aware that Microsoft has announced the termination of Access Web Apps. If you have an Office 365 account, you will not be able to create new AWAs after June of this year. All existing AWAs will be removed
from Office 365 in April of 2018.
You have one year to identify an alternative and to begin migrating your existing AWAs to a different technology.
If you have an on-premises SharePoint site, support will continue for AWAs for approximately 5 years.
That said, for this current situation, you will have to create an internal table of users and departments. When someone logs in, you can use a Data Macro to lookup their username in that table to identify which department they are in. Then, set a localvar to that department and include it as a criteria in all queries that populate views which need to be filtered by department.