SAN JOSE MINE, Chile — The first of 33 trapped miners is expected to be lifted to the surface late Tuesday after miraculously surviving more than two months about half a mile below ground, Chile’s Mining Minister Laurence Golborne announced.

The minister told a news conference that officials “hope to have at least one of our miners on the surface” before the end of the day – apparently the longest period anyone has ever been trapped underground.

President Sebastian Pinera was expected to arrive shortly before the first miner is pulled out in a carefully choreographed operation meant to minimize any risk.

After a series of successful tests with the escape capsule, his remarks suggested there was no reason to wait any longer. Rescue workers on Monday had suggested the men might not be pulled out until after dawn Wednesday.

Asked about the biggest technical problem that could hit the rescue operation, coordinator Andre Sougarett said: “A rock could fall.”

“There is no need to try to start guessing what could go wrong. We have done that job,” a confident Golborne said. “We have hundreds of different contingencies.”

Rescuers were keeping the miners busy on final preparations they were to climb into a custom-made capsule for what tests indicated should be a smooth ride to the outside world.

“The miners are very busy – that’s also to keep their spirits up,” Health Minister Jaime Manalich said. “It remains a paradox – they’re actually much more relaxed than we are.”

As the miners emerge, they will be sheltered from the glare of TV cameras. They will get an immediate medical check and gather with a few family members in an area closed to the news media. Officials say a siren will sound as each miner emerges.

Then, they will ride in helicopters – two at a time if they are in beds, or four at a time if they can sit up – to the regional hospital in Copiapo for a battery of physical and psychological exams.

“Our job is to provide benefit and not harm,” Manalich said, urging the media – more than 1,000 journalists are working on the story – to respect their privacy. “We have to protect them until the last minute, until they can return to normal lives with their families.”

Nearby, the miners’ families have been holding vigil at a place called “Camp Hope.”

“Here the tension is higher than down below. Down there they are calm,” said Veronica Ticona, sister of 29-year-old Ariel Ticona, a trapped rubble-removal machine operator.

After 68 days of shared fears and jitters – all of it under the close scrutiny of dozens of reporters that have now grown to a battalion – the early fellowship has frayed. Some relationships, once at least cordial, are as hostile as the desolate sands of the surrounding Acatama desert.

Relatives privately shared stories of the divisiveness with an Associated Press reporter who spent the past month at the camp, frequently bedding down in a tent beside theirs, sharing coffee and gossip.

The feuds and jealousies within families centered on such matters as who got to take part in weekend videoconferences with the miners, who received letters and why – or even who should speak to the media and how much they should be revealing about a family’s interior life.

Some relatives complained about distant kin seeking the international media limelight, giving interviews about trapped miners they barely know.

Then there are those who, despite only distant blood ties to miners, lined up for donated gifts including sexy lingerie, bottles of wine and electronic toys and Halloween costumes for children.

There were even fights over who constitutes a close relative – or even a miner’s preferred conjugal companion.

So Alberto Iturra, the chief of the psychology team advising the trapped men, decided that after each miner rides an escape capsule to daylight, the rescued man will meet with between one and three people whom the miner has personally designated.

Then there is the question of money.

It has already strained relations between families as some seem to be getting more than others, including from some news media, who outnumber the miners’ relations several fold.

Cognizant of the emotional toll, Iturra recommended Monday that the relatives leave the mine, go home and get some rest.

“I explained to the families that the only way one can receive someone is to first be home to open the door,” Iturra said.

The dramatic endgame was hastening as the rescuers finished reinforcing the escape shaft early Monday and the 13-foot (four-meter)-tall rescue chamber descended flawlessly nearly all the way to the trapped men in a series of test runs.

On Monday, the Phoenix I capsule – the biggest of three built by Chilean navy engineers, named for the mythic bird that rose from ashes – made its first test runs after the top 180 feet (55 meters) of the shaft were lined with steel pipe, the rescue leader said.

Then the empty capsule was winched down 2,000 feet (610 meters), just 40 feet (12 meters) short of the shaft system that has been the miners’ refuge since an Aug. 5 collapse.

“We didn’t send it (all the way) down because we could risk that someone will jump in,” a grinning Golborne told reporters on Monday.

Engineers had planned to extend the piping nearly twice as far, but they decided to stop after the sleeve – the hole is angled 11 degrees off vertical at its top before plunging down, like a waterfall – became jammed during a probe.

Officials have drawn up a secret list of which miners should come out first, but the order could change after paramedics and a mining expert first descend in the capsule to evaluate the men and oversee the journey upward.

First out will be the four miners fittest of frame and mind, health minister Jaime Manalich said. Should glitches occur, these men will be best prepared to ride them out and tell their comrades what to expect.

Next will be 10 who are weakest or ill. One miner suffers from hypertension. Another is a diabetic, and others have dental and respiratory infections or skin lesions from the mine’s oppressive humidity.

The last out is expected to be Luiz Urzua, who was shift chief when the men became entombed, several family members of miners told the AP, speaking on condition of anonymity because they did not want to upset government officials.

The men will take a 20-minute ride to the surface in the capsule, which will rotate as it passes through gentle bends in the bore hole. It should take about an hour for the rescue capsule to make a round trip, Aguilar told the AP.

Plans called for the media to be blocked by a screen from viewing the miners when they reach the surface. A media platform has been set up more than 300 feet (90 meters) away from the mouth of the hole.

After being extracted, the miners will be ushered through inflatable tunnels, like the ones used in sports stadiums, to ambulances that will take them to a triage station.

Once cleared by doctors there, they are to be taken to another area where they’ll be reunited with the chosen family members. Next stop: a heliport and the flight to Copiapo.

At the hospital, all the miners will be kept for 48 hours of observation that will begin when the last one exits the escape shaft.

Associated Press Writer Frank Bajak contributed to this report.