WAFRA, Kuwait—The Arabian Peninsula has fueled the global economy with oil for five decades. How long it can continue to do so hinges on projects like one unfolding here in the desert sands along the Saudi Arabia-Kuwait border.

Saudi Arabia became the world's top oil producer by tapping its vast reserves of easy-to-drill, high-quality light oil. But as demand for energy grows and fields of "easy oil" around the world start to dry up, the Saudis are turning to a much tougher...