I have not been able to find any specific information reagarding dry wells since in many areas they are not allowed under current regulations. You should check with your locat authorities for information on this subject. 

If all you are going to run into this dry well is your water softener, you might consider just using your existing septic system. The current thought is that the volume and timing of water from water softeners does not have a detrimental effect on a drainfield or septic tank.