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The Perth-based company said it has drilled the well, located on the southern-most limb of the 3.1 square kilometre Na Sanun structure, to a total depth of 1060m.
A 77m interval with oil shows was intersected at a depth of 961m in the target volcanic reservoir, Carnarvon said.
But subsequent testing resulted in water production at a rate of 75 barrels per day, with minor traces of oil and gas.
Carnarvon plans to continue testing Na Sanun-3, which may involve setting a bridge plug to try and isolate the water that is suspected to be coming from the deepest set of perforations.
Elsewhere on the structure, operator Pan Orient was yesterday drilling the Na Sanun-4 appraisal well ahead at a depth of 800m.
Five potential volcanic reservoir intervals are targeted, all of which are interpreted to be at the shallowest depth on the Na Sanun structure at this location.
A total depth of 1400m is expected to be reached in about eight days time.