Like many other white-collar criminal cases, the one against a former BP executive accused of lying to the FBI amid a federal investigation of the Deepwater Horizon oil spill is shaping up to hinge on what he knew and when he knew it.

In opening arguments before a federal jury on Tuesday, government lawyers pressed their case that David Rainey, BP’s former vice president of exploration in the Gulf of Mexico, manipulated his calculations about how much oil was flowing from the damaged rig in order to arrive at a figure near the 5,000-barrels-per-day estimate already offered by government scientists. Prosecutors argued that Rainey knew the flow was much worse.

Justice Department lawyer Leo Tsao told jurors that witness testimony, phone records and Rainey’s own calculations would prove that Rainey knew about the government’s lowball estimate when he made his calculation. And that, in turn, would help prove that he lied to FBI agents a year later when he said he had not been aware of the previous estimate when he reported his own best guess to a U.S. House subcommittee in the weeks after the explosion.

“That question was critical because how big of a problem BP had on its hands depended on how much oil was flowing out of that well,” Tsao told jurors.

Tsao said one text message that Rainey received from a BP colleague actually discussed the government’s 5,000-barrels number specifically.

Rainey’s lawyer, Brian Heberlig, told jurors that Rainey had probably forgotten about the text by the time he sat down with investigators in 2011.

And he said prosecutors have offered no convincing reason why Rainey would have wanted to lie to investigators in the first place. He called Rainey “a fundamentally honest man” who was put at the middle of “an extremely demanding situation” and worked “in good faith” despite having no experience calculating oil-flow estimates.

As oil flowed from BP’s runaway well, Rainey and others at the Unified Command center were focused more on plugging the well than calculating the flow of oil, Heberlig told the jury. “This was truly a fool’s errand: a request to calculate the unknown,” he said.

Rainey faces a single charge of making false statements during the FBI interview. U.S. District Judge Kurt Engelhardt on Monday dismissed a separate charge that he obstructed a congressional inquiry. The judge cited questions about whether Rainey would be able to present a full defense after several high-ranking government witnesses — including a sitting U.S. senator — refused to testify, citing a constitutional privilege.

Days after the Deepwater Horizon rig caught fire and exploded 50 miles off Louisiana’s coast, BP estimated that 1,000 barrels of oil per day were flowing into the Gulf. A week later, a National Oceanic and Atmospheric Administration scientist put the number at closer to 5,000 barrels but qualified the estimate as “highly unreliable.”

Rainey developed BP’s next best-guess estimate, which was close to the government’s number. Prosecutors allege that Rainey manipulated his calculations to arrive near NOAA’s “preliminary and heavily qualified” estimate.

In court on Tuesday, Tsao described NOAA’s estimate as “designed to be just enough to raise the level of urgency,” almost like a wake-up call to BP’s Unified Command center, where the oil spill cleanup and response efforts were coordinated.

In his interview with investigators, Rainey allegedly said he wasn’t aware of NOAA’s estimate when he made his own calculations.

After opening arguments, the government called its first witness, Avi Gesser, a former deputy director of the U.S. Justice Department’s Deepwater Horizon Task Force, which was responsible for investigating and prosecuting BP and its partners.

Gesser testified that he and his fellow investigators wanted to interview Rainey because they “had a hard time understanding how he had come to his estimate.”

Defense attorney Reid Weingarten walked Gesser through the 33-page FBI interview. He took time to highlight a few mistakes contained in the report, hoping to raise questions about how accurately Rainey’s remarks were taken down.

The interview was not recorded, Gesser acknowledged.

Sounding incredulous, Weingarten said the transcript contained “relevant, critical, inaccurate information,” and asked, “This is your only record of the interview?”

The 12-member jury is expected to continue hearing testimony through the end of the week or early next week.

Rainey is only the second former BP worker to stand trial in connection with alleged misdeeds after the deadly accident, which killed 11 men and led to the largest oil spill in U.S. history.

Follow Richard Thompson on Twitter, @rthompsonMSY.