The startup of two huge oil refineries earlier this year in the Middle East is set to shake up fuel markets from Asia to Europe as the oil-producing region expands its influence beyond just exporting vast amounts of unprocessed crude. The projects, together with a third large refinery that began operating in Saudi Arabia last year, are expected to process 1.2 million barrels of oil a day at full capacity in the next few months, equivalent to slightly more than 1% of the world’s total oil-refining capacity. They will produce a variety of oil products from diesel fuel to gasoline and jet fuel, with diesel making up for more than half the output. Once up and running, the refineries should have considerable competitive advantages, thanks to new technology, cheap crude-oil feedstock and proximity to markets in Europe and Africa, where they could displace traditional suppliers from Asia and the U.S. “It’s going to be battleground Europe as far as diesel exports are concerned,” said Johannes Benigni, founder of energy consulting firm JBC Energy. The firm expects diesel-fuel exports from the Middle East to Europe to increase to 173,000 barrels a day by 2018, nearly eight times the level in 2012. Over the same period, exports of refined diesel products from Asia to Europe could drop by one-fourth to 96,000 barrels a day. The refineries started in the past few weeks include a joint venture between state-run Saudi Arabian Oil Co., or Saudi Aramco, and China’s Sinopec0386, -0.33% SNP, -2.44% , called the Yanbu Aramco Sinopec Refining. Ltd. Abu Dhabi National Oil Co., meanwhile, has started operations at an expanded wing of the Ruwais refinery in the United Arab Emirates. Mari Iwata in Tokyo contributed to this article. An expanded version of this report appears on WSJ.com.