No, it will not be vulnerable. Using prepared statements is the suggested way to protect against SQLi.
If you are sure department_type
parameter is not affected from any user input, then it is safe to place it directly into the query.
A variable's being affected from user input is a bit complicated though. This effect can be indirect as well. For example if department_type
is retrieved from database, which was saved on another page being affected by user then it is indirectly affected from user input and should be considered as "not trusted".