I am a plumber, I have installed black water/ grey water systems...maybe i can help
grey water is the discharge water from...lavitory sinks, bathtubs, laundry tubs, clothes washer
the kitchen sink >>>IF<<< ther is NO garbage disposal
black water is the discharge from toilets, kitchen sinks with disposals..any fixture that has fecal or biological mater [poo poo/ food]
i generally install a septic tank with a bypass pipe around the tank for grey water
or..in simpler nterms, a tee tied into theoutlet side of tank
another methoid, is to pipe the grey water into a "lift station"
a plastic barrell, with a float pump installed inside it,,,you can pump out of this tank to water plants or pump it to?
usefull info on greywater
needed to add to this..if you do install a pump....you must install a check valve on the outlet side of the pump...if not...your pump will kick on and off
till it burns up...we call this jacking off...nasty, but thats what its called...there are 2 types of ck valves..and it maters which you use..if installed in a horizontal pipe..use a swing check...must be level
if installing in a vert. line install a spring ck... i perfer a swing...no/little obstruction. a spring is obstructed...by code..these need to be installed with a ball valve and a union
if no bal valve..when you go to replace it....all kinda "stuff" is going to spray on to you...install upstream of ck with union