Last week, the Perth-based company was forced to stop drilling at the well, after what it described as large volumes of pure oil started flowing to surface from the top of the Stones River Formation.
Now the well has been fitted with a beam pump and flow-lines connected to storage tanks at the Riddle-11 site.
Initial indications are that the Riddle-13 well was likely to be a good producer, Westralian said.
The company is applying to drill more wells on the Riddle lease, with approval expected in the next three weeks.