The strike, involving 42 Unite members at Grangemouth, near Falkirk, will run until Monday morning, with striking workers taking turns to man the picket lines.
They warned there could be more strikes if the dispute over cuts to pay and pensions is not resolved.
The drivers, employed by BP, will observe an overtime ban when they return to work.
Describing the mood on the picket line, a Unite spokesman said: "They've been on since 4am. They don't want to be here but they're buoyant."
The industrial action comes after 90% of drivers balloted voted for strike action to defend their pensions and protest at the loss of a company share scheme as a result of the imminent aviation contract transfer from BP to another firm, DHL.
Unite industrial officer Tony Trench said: "We've had a tremendously solid start to this strike action and our members are resolute in our pursuit of pay and pensions justice. We're in this for the long haul.
"On a normal day up to 10 million litres of fuel will pass through the refinery gates and out to airports and forecourts across the country, but not today.
"Our message to BP is simple: Do the right thing. Pay up on the cuts our members will suffer – it's a drop in the tank for a company worth nearly £8 billion."
Unite claims some drivers could be up to £1500 a year worse off over the loss of the share-match scheme and that some stand to lose up to £13,000 a year from their pension on retirement when the changes happen.
The union plans further strike action next week if no resolution to the dispute emerges.
"We've notified the employer that there will be further strikes from next Thursday," the union spokesman said.
"At the same time, we're perfectly happy to get back round the negotiating table with BP, but they're going to need to come up with something that's going to see our members adequately compensated.
"On Monday morning a ban on overtime begins. For an industry that has its backbone built on overtime, we'll see how that transpires."
Unite has previously said the action will hit aviation supplies and deliveries to BP forecourts across Scotland and the north-east of England.
Asked about the potential impact on the public, the spokesman said: "We're not going out of our way to inconvenience anybody, but I think that anybody who was going to be undergoing the scale of cuts that our members are would take the same course of action."
A spokesman for BP said its priority was the safe supply of fuel products to its customers.
He added: "Since we became aware of the prospect of a strike, we have been working, and continue to work, on contingency plans to minimise any potential disruption to our customers."
Scottish Finance Secretary John Swinney called for an urgent resolution to the dispute. He said: "I have spoken with Unite and BP to encourage them to resolve this issue before any strike action was called. I am therefore disappointed a resolution has not been found to date.
"It is now essential that additional efforts are made to resolve the dispute and I have asked both parties to meet with Acas [the Advisory, Conciliation and Arbitration Service] as a matter of urgency to seek a resolution.
"I am confident that the necessary contingency arrangements are in place to minimise disruption to the public."