Anyways, recently did 10.1.3.5.2 upgrade and we saw that ESB connection pool (ESBPool) was growing 100 connections per hour. After deprived sleep multiple nights, we found that it was another ESB bug. There were constant error messages like "Unclosed connection detected : 'oracle.oc4j.sql.spi.ConnectionFinalizer@" in log.xml. Upon creating multiple different test cases, I found that it was with a very specific pattern:
AQ -> ESB Consumer -> ESB Async Routing Rule -> Asyn BPEL
The Async Routing Rule was the culprit and such flows were found in OOTB AIA code. Once we fixed it from Async to Sync, connections never went up more than 2, and life was back to normal again.