* Flows still scheduled to be reversed June 1 * Lack of pipelines south has depressed WTI prices * Reversal is historic move to ease Midwest glut By Bruce Nichols HOUSTON, Feb 21 (Reuters) - Enterprise Products has begun purging the Seaway pipeline ahead of a reversal that will move crude out of the glutted Midwest and into the U.S. Gulf Coast refining hub and likely bring U.S. oil futures closer in line with world prices. "We just started that this weekend. We're not really giving information out as to when it will be completed. But we will still expect to be able to reverse flow by June 1. We're on schedule," Enterprise spokesman Randy Burkhalter said. "We expect to be able to flow up to 150,000 barrels per day (bpd) south," Burkhalter said. To empty the line for reversal, Genscape estimates 90,000 bpd are being pushed into Cushing, the only direction in which purging could occur prior to reversal, Genscape spokesman Abudi Zein said. With 2.3 million barrels in the line, which historically has run from the Gulf Coast to Cushing, it will take weeks to accomplish emptying, Genscape said. Burkhalter could not confirm the details. The decision to reverse the line followed sale of Conoco Phillips' 50-percent interest in the line to Enbridge last fall. Enbridge then agreed with the other owner, Enterprise, to reverse the line to ease the oil glut at Cushing. It appears that initially, purging Seaway will add to oil inventories at Cushing. Oil markets did not appear to react to the news, with WTI up more than $1.50 and North Sea benchmark Brent up 45 cents at 10:13 a.m. CST (1613 GMT). Reversal is planned to take place in stages, with an initial 150,000 bpd flowing from Cushing to refineries in the Houston area by June 1, according to the schedule most recently disclosed by Enterprise. Since announcement of the reversal plan, the companies have begun talk about expanding it to 800,000 bpd. The U.S. Midwest has been inundated with rising flows of crude from Canada and North Dakota over the past year and a shortage of pipeline outlets to the Gulf Coast. Historically, oil flowed from the Gulf Coast to the Midwest. That has driven up inventories of crude in the region, which includes the Cushing, Oklahoma, delivery point for the New York Mercantile Exchange's U.S. oil futures contract. The regional glut has weakened prices for U.S. oil futures, also called West Texas Intermediate, relative to international benchmark Brent as well as other regional U.S. crudes. Producers have been scrambling to find ways to send crude out of the Midwest and into the giant U.S. refining complex along the Gulf Coast, where it fetches a healthy premium. The build up of inventories has pushed Brent to record premiums to West Texas Intermediate, hitting $28 a barrel in October of 2011 before receding on news of the Seaway reversal plan in November. The spread widened out again in February, topping $21 on Feb. 7 as inventories in the region began to grow again. Genscape monitors key pipelines by measuring the amount of power being used at pump stations.