Is it possible to get list of stored procs which only read data?

Is it possible to get list of stored procs which only read data?

Using SQL Server 2012. You can get a list of stored procs using TSQL like
this :
select * from information_schema.routines r where r.ROUTINE_TYPE =
'PROCEDURE'
Is there a way to only get a subset of the stored procs which only read
data (i.e. don't attempt INSERT or UPDATE statements within them, or any
stored procs that they invoke).
I'm thinking the answer to this question is no, but just throwing it in
here just in case.
The end goal is to try to create a database role which can only READ data
in the database, and not modify it. The db_datareader role helps, but
would also like to be able to call stored procs which only read data. The
last resort is to grant execute permission on each stored proc.