His preflop range could be as wide as like:
http://www.pokerstrategy.com
Equity Win Tie
MP2 35.31% 34.54% 0.76% { 99+, ATs+, KQs, QJs, JTs, 87s, 76s, 65s, AJo+ }
MP3 64.69% 63.93% 0.76% { QdQc }
If he cbets everything, folds all no-pair/no-draw hands to the shove, and calls with everything else (because he is getting 2:1), then:
1. the above generous range is 112 combos
2. he folds half his hands: off suit big aces, and non-diamond suited stuff that didn't make a pair. It's nice that you have the Qd.
3. against what's left, you are a 2:1 dog:
http://www.pokerstrategy.com
Board: 8d7d9h
Equity Win Tie
MP2 64.29% 62.39% 1.91% { 99+, JTs, T9s, 98s, 87s, 76s, 65s, AdKd, AdJd, QdJd, AdTd }
MP3 35.71% 33.80% 1.91% { QdQc }
So EV(shove) = .5 * 15 + .5 * (.35 * 40 - .65 * 25) = 7.5 (he folds) + 7 (he calls and loses) - 8 (he calls and wins) = 6.5 pretty nice.
And I think it's even better for you if his range is not so wide but still not just '4betting superhands'.