D10 Controller experienced a loss of separation event involving two Air Carrier aircraft when utilizing minimally lateral spacing techniques and a less than expected departure speed.

Narrative

The two Air Carrier aircraft were on parallel RNAV departures Westbound. Aircraft X was on the Northern Westbound departure RNAV. I turned Aircraft X Southwest bound so I could climb him otherwise he would have had to level at 10;000 for 15 miles while he waited to pass the inbound arrival at 11;000. Aircraft Y was direct to a fix that had him on about a 240 track or so and I turned Aircraft X to a 220 heading. I knew this was a slightly converging heading but they were both right around 10;000 and I expected them both to increase speed so; although the space would close up slightly; it would happen slowly. The space closed up quicker than expected and I could not turn Aircraft X back to the right because I was still waiting for him to get above the arrival that was to the Northeast of Aircraft X and heading Southeast bound at 11000. I turned Aircraft Y to a 220 heading to parallel Aircraft X. As soon Aircraft X was separated from the arrival; I turned Aircraft X to the right but he didn't acknowledge. He answered when I turned him the second time. Aircraft X and Aircraft Y were on parallel headings but I don't think there was 3 miles laterally and I'm not sure how much altitude space was between them as I planned on keeping them laterally separated and was focused on increasing the lateral separation between them. I noticed Aircraft Y was showing a very slow speed and asked him what his speed was. He said 200. He was at 11;000' or so doing 200 kts. There is a speed on the RNAV that says 230 kts until 5000' so he either didn't comply or slowed after passing 5000' when I was expecting him to increase his speed which would have helped him stay more parallel with Aircraft X. I have seen Aircraft Y climb out at 200 kts before but because of the speed on the RNAV departure procedure; I didn't expect him to slow down after passing 5000'. I'd estimate that separation got to about 2-2.5 miles lateral but I'm not sure on altitude. I don't think Aircraft Y's speed caused the possible loss of separation; but it definitely was not expected and between that and the delay of having to turn Aircraft X twice because he didn't acknowledge the first time; it was enough to lose lateral separation. I've worked the same situation many times but it just didn't work today because of all the factors involved. I pride myself on not messing up and even though Aircraft Y's speed and Aircraft X not taking the first turn; it was my plan and I take responsibility for it not working. I could've just let Aircraft X sit at 10;000 instead for 15 nm instead of trying to get him up and out of the airspace so quickly but I was trying to help him out by getting him around and above the arrival and on his way. I probably could have turned Aircraft Y parallel immediately instead of waiting until it was getting close and then his speed wouldn't have come into play.