The main meltdowns of the past at civilian plants were Three Mile Island in 1979, the St.-Laurent reactor in France in 1980, and Chernobyl in Ukraine in 1986.
One of the first safety codes to emerge after Three Mile Island was the Modular Accident Analysis Program. Running on a modest computer, it simulates reactor crises based on such information as the duration of a power blackout and the presence of invisible wisps of radioactive materials.
Robert E. Henry, a developer of the code at Fauske & Associates, an engineering company near Chicago, said that a first sign of major trouble at any reactor was the release of hydrogen — a highly flammable gas that has fueled several large explosions at Fukushima Daiichi. The gas, he said in an interview, indicated that cooling water had fallen low, exposing the hot fuel rods.
The next alarms, Dr. Henry said, centered on various types of radioactivity that signal increasingly high core temperatures and melting.
First, he said, “as the core gets hotter and hotter,” easily evaporated products of atomic fission — like iodine 131 and cesium 137 — fly out. If temperatures rise higher, threatening to melt the core entirely, he added, less volatile products such as strontium 90 and plutonium 239 join the rising plume.
The lofting of the latter particles in large quantities points to “substantial fuel melting,” Dr. Henry said.
He added that he and his colleagues modeled the Japanese accident in its first days and discerned partial — not full — core melting.
Micro-Simulation Technology, a software company in Montville, N.J., used its own computer code to model the Japanese accident. It found core temperatures in the reactors soaring as high as 2,250 degrees Celsius, or more than 4,000 degrees Fahrenheit — hot enough to liquefy many reactor metals.
“Some portion of the core melted,” said Li-chi Cliff Po, the company’s president. He called his methods simpler than most industry simulations, adding that the Japanese disaster was relatively easy to model because the observable facts of the first hours and days were so unremittingly bleak — “no water in, no injection” to cool the hot cores.
“I don’t think there’s any mystery or foul play,” Dr. Po said of the disaster’s scale. “It’s just so bad.”
The big players in reactor modeling are federal laboratories and large nuclear companies such as General Electric, Westinghouse and Areva, a French group that supplied reactor fuel to the Japanese complex.
The Sandia National Laboratories in Albuquerque wrote one of the most respected codes. It models whole plants and serves as a main tool of the Nuclear Regulatory Commission, the Washington agency that oversees the nation’s reactors.
Areva and French agencies use a reactor code-named Cathare, a complicated acronym that also refers to a kind of goat’s milk cheese.
On March 21, Stanford University presented an invitation-only panel discussion on the Japanese crisis that featured Alan Hansen, an executive vice president of Areva NC, a unit of the company focused on the nuclear fuel cycle.
“Clearly,” he told the audience, “we’re witnessing one of the greatest disasters in modern time.”
Dr. Hansen, a nuclear engineer, presented a slide show that he said the company’s German unit had prepared. That division, he added, “has been analyzing this accident in great detail.”
The presentation gave a blow-by-blow of the accident’s early hours and days. It said drops in cooling water exposed up to three-quarters of the reactor cores, and that peak temperatures hit 2,700 degrees Celsius, or more than 4,800 degrees Fahrenheit. That’s hot enough to melt steel and zirconium — the main ingredient in the metallic outer shell of a fuel rod, known as the cladding.
“Zirconium in the cladding starts to burn,” said the slide presentation. At the peak temperature, it continued, the core experienced “melting of uranium-zirconium eutectics,” a reactor alloy.
A slide with a cutaway illustration of a reactor featured a glowing hot mass of melted fuel rods in the middle of the core and noted “release of fission products” during meltdown. The products are radioactive fragments of split atoms that can result in cancer and other serious illnesses.
Stanford, where Dr. Hansen is a visiting scholar, posted the slides online after the March presentation. At that time, each of the roughly 30 slides was marked with the Areva symbol or name, and each also gave the name of their author, Matthias Braun.
The posted document was later changed to remove all references to Areva, and Dr. Braun and Areva did not reply to questions about what simulation code or codes the company may have used to arrive at its analysis of the Fukushima disaster.
“We cannot comment on that,” Jarret Adams, a spokesman for Areva, said of the slide presentation. The reason, he added, was “because it was not an officially released document.”
A European atomic official monitoring the Fukushima crisis expressed sympathy for Japan’s need to rely on forensics to grasp the full dimensions of the unfolding disaster.
“Clearly, there’s no access to the core,” the official said. “The Japanese are honestly blind.”