By Sharq Khan and Arati Somasikar

NEW YORK/HOUSTON, June 5 (Reuters) - In a city that bills itself as the world's pipeline hub, nearly 400 oil storage tanks around Cushing, Oklahoma, are nearly empty as refiners around the world turn to them to fill a massive global supply gap caused by the war in the Middle East.

Cushing is one of the world's largest oil storage hubs. Oil levels there have fallen rapidly since the start of the war and Iran's effective disruption of oil tanker traffic through the Strait of Hormuz.

Refineries around the world sought to purchase crude oil from wherever it was available to compensate for the 20 million barrels that passed through the strait daily before the war. The world has lost more than a billion barrels of oil supply since the conflict began.

Cushing is of paramount importance in the global market as the delivery point for West Texas Intermediate (WTI) crude oil, the benchmark for one of the world's leading oil contracts. Storage levels there significantly impact the prices of oil futures contracts, which are traded daily in billions of dollars.

Two sources said that Phillips 66, an oil refiner, believes that storage levels in Cushing may reach the minimum required for operation. Cushing is a major source of crude oil for Phillips 66 and many other U.S. refiners.

The two sources requested anonymity because they were not authorized to discuss internal market forecasts. Philips 66 declined to comment.

Data released by the US government on Wednesday showed that Cushing inventories fell to 22.4 million barrels as of May 29, a decrease of about four million barrels compared to levels on February 27, the day before the start of the US-Israeli war on Iran.

Oil storage data provider Alpha PPL said inventories fell by 500,000 barrels between May 29 and June 2. The company uses drones, manned aircraft, and satellites to measure and estimate oil inventories.

Jeremy Irwin, head of global crude oil at Energy Aspects, said operational challenges could arise when oil levels in Cushing fall below 20 million barrels. Government data shows this level has not been seen since the United States lifted restrictions on oil exports in 2015.

The Energy Information Administration stated that Cushing's storage capacity is approximately 78.4 million barrels.

Irwin said, "When operations reach their lowest level, there isn't enough oil in the reservoir to pump and transfer between tanks, and blending the oil becomes a challenge, which could delay or stop the flow of oil out of Cushing."

Inventories at other U.S. storage centers have also declined in the past few weeks as the country has increased exports to an unprecedented level.

U.S. crude oil exports jumped to an all-time high of 5.6 million barrels per day in May as the Middle East crisis led to increased demand from Asian and European refineries for U.S. oil.

Overall, U.S. crude oil inventories have fallen to 43.4 million barrels after six weeks of consecutive drawdowns, down about 63.9 million barrels, or 7.5 percent, since the start of the war due to large drawdowns from commercial stockpiles and the Strategic Petroleum Reserve.