THE stricken Fukushima Dai-ichi nuclear plant is the world’s most complex and costly industrial clean-up. The first three of Fukushima Dai-ichi’s six reactors melted down in March 2011 and the fourth was damaged. TEPCO’s early guess was that decommissioning would take 30-40 years. That is certainly optimistic.

Engineers are grappling with problems with little precedent. Akira Ono, the plant manager, says cameras have begun peeking into the first reactor to check the state of 100 tonnes of molten fuel. A robot needs to be developed to extract the fuel. Last October the utility pushed back the start of this removal work by five years, to 2025. Dale Klein, a former chairman of America’s Nuclear Regulatory Commission, says that the schedule for decommissioning the plant is pure supposition until engineers figure out how to remove all the fuel.

One victory for engineers is with reactor four. Late last year the last of 1,535 highly toxic fuel rods was plucked from the spent-fuel pool a year ahead of schedule. The fear was that the complex could not withstand another strong earthquake.

Solutions create new problems. Water is pumped in to keep melted uranium at the bottom of reactors one, two and three from overheating. A purification system, known on-site as the “seven samurai”, is struggling to keep up with the flow of contaminated water being produced—370,000 tonnes and rising is stored in vast tanks. Even when the worst nuclides are filtered out, TEPCO will face huge opposition with plans to dump the water into the Pacific.

Then there is the ice wall. TEPCO is attempting to freeze the ground in a huge ring around the four damaged reactors to prevent toxins from reaching the groundwater and flowing into the sea. Workers have dug vast holes and filled them with coolant. In May they will begin refrigerating the coolant to up to -40ºC. Whether the wall can take another big earthquake or work in the baking summer is not proven. The cost for this so far: ¥32 billion ($272m).

Meanwhile, a lower-tech clean-up is taking place beyond the Dai-ichi site over a big swathe of Fukushima’s rolling countryside. Armed with Geiger counters, men in mechanical diggers or with shovels are skimming off contaminated soil. Once the land is clean, at least some residents have a hope of returning home—71,000 nuclear refugees remain in temporary housing. But it could take years.

The price tag for the whole clean-up is as uncertain as its duration. For one, decontamination costs depend on lowering annual radiation to 1 millisievert, a goal now widely seen as unrealistic, says Tatsujiro Suzuki, a former vice-chairman of the Japan Atomic Energy Commission.

TEPCO says decommissioning Dai-ichi’s four damaged reactors will cost ¥980 billion, but that does not include the clean-up, fuel storage or compensation. On a broader reckoning, the Japan Centre for Economic Research, a private research institute, puts the bill over the next decade at ¥5.7 trillion-¥20 trillion, but that still excludes compensation to the fisheries and farming industries. A still broader calculation by the same institute puts the entire cost of the disaster at ¥40 trillion-¥50 trillion. Thanks to government bail-outs, the company that so mismanaged Fukushima Dai-ichi carries on. It even says it will make a profit this year.