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The projects could cost $50 million to $100 million in total.
The deepwater drilling programme, in 1100m of water, is likely to polarise opinion from local businesses, within the ranks of the Dunedin City Council and environmentalists.
The programme is not a major economic major windfall for Dunedin, but is nevertheless being welcomed as the first phase of what could develop into major opportunities during the next decade.
Anadarko only five weeks ago deferred a drilling programme for this year, but corporate affairs manager Alan Seay said yesterday drill ship Noble Bob Douglas, which is still under construction, would visit New Zealand for its maiden voyage and first work programme of up to three holes.
He expected one hole to be drilled in November or December next year off Oamaru, then another off Taranaki, and "ideally, depending on [earlier] results", a second either exploratory or appraisal hole well off Oamaru, at the Caravel prospect.
"A contract is signed. We are very committed to coming here," Mr Seay said yesterday.
Exploration off Oamaru in 1985 and 2006 found no commercial quantities of oil or gas.
The Dunedin City Council plays no regulatory role in offshore oil and gas exploration.
That is covered by recent exclusive economic zone legislation, for areas beyond 12 nautical miles offshore.
Consents for the EEZ are issued by the Environmental Protection Agency.
Senior Anadarko management from Houston are in New Zealand next week for a petroleum conference and will later visit Dunedin to again talk to local government and businesses.
While Port Chalmers would be used for crew changes and "resupplies", over a few weeks, Mr Seay said the modern drill ship was otherwise "very self-contained".
Otago Chamber of Commerce chief executive John Christie welcomed Anadarko's decision, but said a one-hole drilling programme was "just the first step".
"This is tremendous news for the region. [But] we have to look at the long term to see what ancillary roles or business services would be needed for the future," he said.
The first single-hole programme is expected to take four to six weeks, at an estimated cost of $US1 million a day.
Anadarko will probably be paying more to get the vessel to and from New Zealand.
Mr Seay was aware of mounting criticism in New Zealand of deepwater drilling. He said while there were "opinions across the spectrum", he "could not rule out the possibility" of the drill ship being met at sea by environmental protesters, as happened to a hydrographic survey ship off the North Island's East Coast last year.
Anadarko's three-year contract for the vessel is worth $US677 million ($NZ824 million).
Shell has a separate prospect to drill in the Great South Basin, but Mr Seay said the Noble Bob Douglas was contracted solely to Anadarko.
New Zealand Oil & Gas relinquished its permits off Oamaru a month ago, after it could not find a drilling partner.
• Separately, tenders close next week for 23 onshore and offshore oil and gas blocks around the country, including blocks in the Great South Basin, and onshore in Southland.