Excellent question Sergio:  ...

Excellent question Sergio:  The goal of treating any waste, whole, grey water, or black water, is to return it to nature in its elemental/nutritional form. (foot print of Zero).  Adding any kind of chemical or expensive infrastructure automatically negate their co habitat status with nature.  (imagine you are in a generational space craft to another star system). Reuse everything insitu. The technology is available here and now.  I am very amused at all of the 1950's technology being suggested.  All you really need is the correct microbe from nature to do the job and follow basic parameters in the microbial bioremediation world.