It said that based fluid levels recorded in the well bore, the current rate is believed to be restricted by the slim hole casing design of POE-9A.
An earlier test of a deeper volcanic zone failed to produce hydrocarbons at commercial rates.
In permit L44/43, the NS3-D1ST sidetrack appraisal well is drilling ahead at a depth of 928m within a volcanic tuff above the main volcanic target zone.
Lost circulation of about 200bbl of oil per hour has been encountered in the volcanic tuffs, Carnarvon said.
Drilling is expected to be completed in about 12 days.
Carnarvon added the L44H-D2 well in the same permit has reached a total depth of 2357m and is currently running logging operations.
Oil shows were observed at 1080-1100m, 1505-1510m and 1845-1850m.
Five deeper previously untested volcanic intervals have also been encountered at 1079m, 1154m, 1483m, 1698m and 1824m.
Once logging is completed, testing on up to four zones will be carried out, Carnarvon said.
Testing of the new zones is expected to be completed within 21 days.
In other news, the joint venture partners have received approval for 32 drilling locations at the Na Sanun East and Wichian Buri Oil fields.
Construction is underway at NSE9-G, at the crest of the NSE central fault compartment where up to three horizontal wells would be drilled.
Drilling is anticipated to start in about five weeks.
Carnarvon has a 40% stake in the Thailand projects while Pan Orient is the operator holding the remaining 60%.