“I’ve been driving the ball really well, and this course there's a big premium on hitting a lot of fairways,” said Kapur, who is still searching for a maiden European Tour title.
“The driver has been behaving and I gave myself quite a few chances. Overall I just played quite solid.”
World Number Two Lee Westwood is also in the hunt and would have matched his Ryder Cup teammate's two rounds but for a late three-putt bogey.
McIlroy's first priority after he finished was to make sure there were no more ants on him.
His final drive finished close to an ant-hill and, although he was able to move his ball away and had a much easier shot as a result, he said: "I still feel there are some going up my legs.
"I don't feel I drove the ball particularly well. There were a couple of loose shots and I got some lucky breaks."
Like McIlroy, Westwood had four birdies in seven holes on the back nine, but his only gain on the outward half was a two on the short fifth and his dropped shot came two holes later.
Kapur's 67 put him one ahead of Scot Gary Orr and South African James Kingston before twice-winner Dyson and Siem made it a four-way tie for second with an early birdie each.
They were unlikely to finish their second rounds before nightfall, but a tournament held up first by vandalism to four greens and then by flooding should be back on track by Saturday night.
Welshman Stephen Dodd took over at the top with a dazzling run. After an opening birdie on the ninth he reduced the back nine to a mere 30 strokes with an eagle and three more birdies.
At eight under, Dodd led by one from Kapur and by two from Orr, Kingston and Siem, while Dyson was one further back after seven holes along with McIlroy and Swede Oscar Floren.