Venting a sink pump
Okay, let me start off by explaining the situation..
The configuration of my house:
The sewer pipes connect to a city sewer system under the street, the main 4" pipe is under my driveway and connects to a 4" main stack which directly serves fixtures in a first floor bathroom and a second floor water closet directly above.
Under the dirt, a clay pipe branch rises out of the ground to connect to the kitchen sink drain, the kitchen sink being on the opposite side of the house. This branch also serves a utility sink into which the laundry drains, this piping is underground. The laundry room is on a slab, the remainder of the house is on crawlspace with dirt floor.
No venting was installed for the kitchen or utility sink, not even air admitance valve.
The clay pipe between the main stack and kitchen drain has collapsed. Not fully confirmed, but a blockage definitely exists and the problem was detected when water seeping up through the dirt was observed around the pipe coming out of the ground for the kitchen.
I am replacing it with a PVC system over the dirt. For the kitchen sink, achieving proper slope is no problem. The utility sink trap is too low and in order to tie in to the drain system near the kitchen, a sink pump is required.
Direct venting the sink pump is no problem, in fact due to windows obstructing direct venting of the kitchen, I plan to tie the kitchen vent into the utility sink vent. I'm just confused about where venting needs to tie in for the sink pump.
The pump itself provides an inlet, an outlet and a vent fitting. I bought a kit that includes a 7 gallon tank into which a sump pump goes, which is included in the kit, so the tank is vented. From the pump outlet, I'll be going up 2 feet then across to the kitchen sink.
My question is, does the outlet from the pump require to be tied to the vent where it begins going across horizontally? Or does this risk pushing water up into the vent, defeating the venting and maybe that makes it something I shouldn't do, just providing venting for the tank and where the drain ties in at the kitchen sink?
I tried reading through IPC, but honestly I can't tell if it has anything to say about this or not.. As an engineer, all I can think is that since this is a pressurized system rather than a gravity system, I can't feel certain that the rules for gravity systems with which I'm familiar necessarily apply.
I appreciate anyone taking time over Christmas to answer this, and as this all came up right before the holiday, consulting my AHJ is out until Monday, and with laundry and dishes accumulating, the wife has no interest in waiting that long.