If you want to move particles up a certain distance over time, just set the Spread operator value to a fraction of that distance, and then set the timing of the Spread operator (in its Timing rollout) to your distance divided by that fraction.
So if you want to move up 50 units over 100 frames, set Spread timing to frame 0-99 (or 1-100 or whatever your 100 frame range needs to be), and the z-axis spread value to 0.5.
So if you want to move up 50 units over 100 frames, set Spread timing to frame 0-99 (or 1-100 or whatever your 100 frame range needs to be), and the z-axis spread value to 0.5.