As of 8am this morning, Sydney time, the Indigo Minerals 29-1well was at 200m.
The well will target the Frio formation and is planned to reach target depth of 1400m over the weekend, according to Pryme.
"The well will test a high-priority seismic anomaly which was identified in the Turner Bayou 3D seismic shoot," the company said.
Indigo Minerals 29-1 follows the previous well, Trifolia 9-1, which was temporarily shut-in as a future gas producer on June 23.
However, the two wells drilled in last year's Turner Bayou program had mixed results.
The first well (Bordelon 25-1) found gas and was completed for production, but the second (Dupuy 11-1) failed to produce hydrocarbons.
At the time, Pryme chief operating officer Ryan Messer said the dry well had given critical information that helped define what the seismic signatures meant.
"This type of analysis greatly increases our future success," he said. "We will learn from this and continue to advance the project as planned."
Pryme has a 52% working interest (39% net revenue interest) in the Turner Bayou project, which is contained within about 205 square kilometres of proprietary 3D seismic.
Primary targets consist of six prospective formations ranging from the shallowest Frio, at a depth of 910m, to the Tuscaloosa at 4880m.
"Executing the Turner Bayou Project has been an important objective since Pryme's ASX listing," the company said.
"It has the potential to produce substantial value for shareholders."