Adding standpipe to existing sink

[njsteam]

In my basement, there is an existing wash sink that drains directly into the main drain line via a 1.5" pipe. The washing machine currently drains into the sink but I would like to add a standpipe for it to drain into.

First off, is my current setup fine the way it is installed without a vent?
Secondly, how can I add a standpipe to this system? Can I tie both the sink and a standpipe into the main at the existing wye if I increase the drain pipe to 2"? Or will I need a vent as well?
Thanks

 

[Terry]

I would have vented the floor sink between the trap and stack.
A washer standpipe and trap I would have taken off the stack, and vented between the stack and the p-trap. A santee could be added to the stack on the vertical.

 

[Sponsor]

 

[njsteam]

Is a vent required on the current setup (with just the sink piped)?

Also, is there a drawback to having the drain connect at the horizontal main versus attaching to the stack? I'd prefer to keep the modifications to a minimum if possible.

 

[Terry]

The washer if installed on the horizontal, would need to be 2" at that point, and wye in between the 4" line and the vent for the mop sink.
The washer would get it's own p-trap, standpipe and vent for that.
A vent for the mop sink and a vent for the washer.