EJB 3.1 has (finally) standarized the global JNDI entries and your EJB code looks fine, what is failing , I think, is the config on your application.xml. Your env entry should look like this:
<env-entry>
<env-entry-name>logDirName</env-entry-name>
<env-entry-type>java.lang.String</env-entry-type>
<env-entry-value>/app/Project_Data/logs/</env-entry-value>
</env-entry>
i.e. the container will set you entry under java:app/env/ by you.
Cheers