The Deepwater Horizon oil disaster had some awful, undisputed consequences: 11 people died when the BP oil rig exploded on 20 April 2010, and oil poured unchecked into the Gulf of Mexico for 86 days.

After that, however, the picture gets murkier. Hundreds of thousands of people and businesses were affected by the disaster but, as every month goes by, 10,000 more claimants emerge. Tomorrow, lawyers for BP will appear in court in New Orleans to argue that its huge bill for compensation is out of sync with the facts and under attack from fraudsters.

BP will attempt once again to argue that the terms of last year's agreement to compensate victims of the spill are being abused by "fraudulent, excessive or improper claims".

The oil giant is not alone in fearing that its compensation scheme is being abused. Last week, the judge Carl Barbier, who is overseeing the multibillion-dollar civil damages case against BP, appointed Louis Freeh, a former judge and head of the FBI, to look into allegations of misconduct at the office that administers compensation claims.

So far, the company has had little luck arguing against the scheme that it set up last March. A panel of three judges will hear tomorrow's appeal, in which each side has 20 minutes to state its case. BP argues that the compensation committee is ignoring the accepted legal meaning of words such as "revenue" and "earnings" in the way that it assesses claims. BP is represented by Theodore Olsen, the lawyer from Gibson, Dunn & Crutcher who was solicitor general under George W Bush and has an impressive track record, but observers say the case is particularly difficult.

"They [BP] lost the first round because the judge said they had drafted the terms and now they didn't want to live with it," said Fadel Gheit, managing director and senior analyst at Wall Street bank Oppenheimer. "The idea was that in good faith they wanted to help the people of this region, a lot of people were very badly affected. What they did not expect was that the other side would take advantage."

"Anything can happen in Louisiana," said Daniel Jacobs, visiting scholar at UCLA institute of the environment and sustainability. Even so, Jacobs also argued that BP would struggle to overturn a scheme that the company itself had it set up.

The oil company set aside $8.2bn (£5.3bn) to settle claims but it is burning through that fund far faster than expected. Ken Feinberg, the original administrator, handed out $6.1bn to 221,000 claimants before he was replaced last March by Patrick Juneau, a Louisiana lawyer who has been seen as even more encouraging to claimants than his predecessor.

With new claims pouring in, Gheit, BP and others argue that many are fraudulent or, at least, stretch the terms of the legal basis of the claim agreement beyond anything that should be legally acceptable. If BP's appeal is successful, the oil company would have the right to reclaim money that has already been paid to some businesses and their lawyers.

In New Orleans, disaster can be a lucrative business for some. Hurricanes regularly wreak havoc along the gulf coast and insurance scams are common, said Gheit. One lawyer's letter touting for BP claims business states: "The craziest thing about the settlement is that you can be compensated for losses that are unrelated to the spill."

Freeh's appointment came after news reports that a lawyer working for Juneau had been accused of misconduct. According to the reports, the lawyer was referring claims to a local law firm in return for a share in future payouts. That lawyer has been suspended and has resigned from Juneau's staff. Barbier said independent external investigation was needed "to ensure the integrity of the programme for the benefit of the parties and the public".

It was never going to be easy to determine losses from the Deepwater Horizon disaster. In court, documents filed in March by BP cited Wall's Gator Farm, a seller of alligator skins around 40 miles from New Orleans, as an example of what is wrong with the compensation scheme. Wall's suffered as recession hit the luxury goods business and in 2008-09 it lost around $289,000 per year. In 2010, however, the company made a profit of $1.565m – yet it was awarded $1.2m in compensation.

For BP, this is an example of improper claims, while Wall's lawyers argue that the firm has been rightly compensated and that the return to profit did not mitigate the $2m in losses suffered after local authorities flooded alligator breeding grounds to hold back the encroaching oil.

According to Jacobs, such disagreements are inevitable given that the settlement agreement is more than 1,000 pages long and leaves plenty of room for legal manoeuvres.

He said: "Different claims administrators are going to [be interpreted] differently. It's hard enough to get four lawyers to agree on where to go for dinner." He said that it had been obvious from the start of the process that some of the claims were fraudulent.

"Ken Feinberg spoke to my students when he was the claims administrator and [he] was clear that there were some bogus cases. He mentioned that he had had one from Scandinavia – perhaps it was a restaurant that couldn't get gulf shrimp. The settlement agreement has geographic limitations and claims like that should be denied."

Jacobs said Freeh's appointment was further evidence of Barbier's determination to make sure that BP received a fair hearing. "If you really want something investigated, you hire Freeh. He is going to get to the bottom of it. I have a lot of faith in Barbier, he's doing an incredible job. These are serious allegations and they are being treated seriously," he said.

"BP has been whining for a while, maybe because they think Juneau is more lenient than Feinberg, but Barbier has the jurisdiction to reverse any of these awards and is overseeing the appeals process. I don't know what else BP wants to be done here."

Jacobs added that it was difficult to see BP as an innocent victim given its record in the US. The company has been fined and publicly censured for other accidents, including the Texas City refinery explosion in 2005 that killed 15 people and injured 170.

"BP writ large is a felon and a recidivist. They have a terrible record in the environmental arena and other areas. On the other hand, I credit them for not acting like Exxon did in Exxon Valdez [oil spill in Alaska]. They have been pretty straightforward."

But BP may have been too straightforward for some. Exxon spent decades fighting off claims arising from its 1989 tanker disaster. For Gheit, BP might have made a tactical error in the aftermath of the Deepwater disaster by agreeing to a compensation scheme too quickly. For a company that pays "tens of millions of dollars" a month in legal fees, said Gheit, BP shouldn't be in this position in the first place.

"Shame on BP and shame on their lawyers," he said.