First you have to find the right hook...And second your code is not correct. Your $order_id is undefined...
You have to check the action hook's argument list to see what is being passed on the callback and include that in your custom function.
And why are you using that hook? I think you should use the first available checkout hook that processes the cart whether complete or not because you need to know if a purchase was made/attempted and what that was for...etc.