Kapur's 69-66 saw him get to nine-under at the event hosted by Al Badia Golf Club.
Andrea Pavan is leading the field with identical 66s in first two rounds. He is 12-under and three shots clear of Kapur.
Kapur, who finished second on his last start on the European Challenge event in Foshan City, China, is lying 19th on the Money List and needs to get into the top-15 to confirm his full status on European Tour for 2014.
Winner of the first European Challenge Tour event this year in Ahmedabad, Kapur lost his European Tour card for the first after playing on it for seven year. Yesterday, he opened with a round of 69 and was placed seventh.
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He improved that to second place with a superb 66. His started birdie-birdie then gave away both shots with bogeys on next two holes. A birdie on seventh saw him fight back. On the back nine, Kapur was in z zone of his own. He birdied 10th, 11th and 12th in a row and then closed the day with a stunning eagle on the 18th. Two of the top four eagled the closing hole.
Pavan is the leader on European Challenge Tour Money List. He has already had two wins on the Challenge Tour this year.