If you really want to achieve the same as a long exposure you need to:
1. Make the delay times between shots negligible compared to the duration of each shot (if there are bright moving objects such as lights, some gaps can still be visible in the resulting image such as those seen on mutiexposure star trails).
2. Average the images with the following weights (upper to lower layer):
For 2 shots: 50%, 100%
For 3 shots: 33%, 50%, 100%
For 4 shots: 25%, 33%, 50%, 100%
and so forth
3. Use a linear (gamma=1) setting in Photoshop. No one has mentioned this, but as long as you use any gamma profile the result will not be a reliable simulation of a single exposure (remember a sensor is a linear photon counter).
If you accomplish with those 3 rules you'll achieve the same visual effect as a single longer exposure, but it will have a much higher noise quality since averaging will improve SNR.
Another drawback is that sharpness can be reduced because of minimal misalignment if you cannot lock the mirror up during all shooting time.
Regards