The trick is not so much the design of the catcher as it is estimating the volume it should contain and how often it can be disposed of.

Several ref here.
https://duckduckgo.com/?q=slug+catcher+design&...

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

It seems like this post is referenced to petroleum engineering. You should move it to a relevant forum.

There are some guidelines written by companies like Shell and ExxonMobil, but no generic guide that I know of.

A finger type slug catcher is really a series of first stage separators so the art is to first equally distribute the incoming three phase fluid, often by dividing equally one to two to four or a header.

Then allow the gas to go off the top. Hence gas velocity at that point should be <5m/sec to avoid taking all the liquid with the gas...

Storage volume is an estimate. Basing it on worst case (usually the pigging case) would lead to a massive set of pipes so it's usually a compromise, but always leave room and flanges so that you can add pipes. Fluid composition changes over a field life so you can have more liquid later on so might need more fingers. Also if you have some surge capacity for dealing with the liquid that would help a lot.

The bottom will end up with water so have a water line and a HC line to your process plant. The interface between the two can be corrosive so make sure you internally coat the fingers and also allow flanges on the bottom header to clear out all the dirt and dead rates etc which somehow end up there.

Angle is up to you but 10 degrees rings a bell. too steep and the inlet ends up miles in the air.

These type of slug catchers are interesting to design as there is no one answer and in reality the input data is usually a bit conservative from the analysis software so don't sweat the last degree of accuracy. In the end if its too small they just add a few more fingers or have to slow the start ramp rate or flow down a bit.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Refer to Taylor Forge for design of the Slug Catcher...
https://www.tfes.com/products/slug-catchers/

That's quite a neat design alright - A lot depends on how much space you have and the particular gas and liquid flows.

Slug catchers are never intended to be super effective at gas liquid separation, the intent is just to stop the first stage separators from getting overwhelmed with liquid flow from either start up, ramp up or pigging. Given that the flow of liquid can vary hugely for the same gas rate, sometimes up to 100 times the instantaneous flow over a 5 second period, then it is just a bit of judgement as to how to design these things, but always leave room to add another couple of fingers in case reality doesn't turn out the same as the theoretical calculation.

At the end of the day, if the slug catcher doesn't work as well as you want then the first stage separator just trips on HH level and the plant stops for a little while. The designer then just says that the composition and flowrate of the fluid coming in is different to what the design basis said....

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.