Particle flow is the way to go, super simple setup, I can give you a quick rundown of how I would set it up.
OPen the particle view
Create a new empty pflow.
add a new event>birth, set the duration and amount of spent shells you want to emit.
add a postion icon, tick inheret emitter movement and set it to pivot. Move it to where you are ejecting shells from on the gun, match the size.
add a rotation (this is to rotate the shell casing to match the spent shell slot on the gun)
add a speed op (along arrow icon) and set it to something like 70 and add some divergence maybe 12
Add a shape instance, and select your spent shell casing. You can now use the rotate operator to align it correctly to the discharge slot.
Create a Gravity spacewarp and Add a force operator yto your pflow. Set the influence to 100%
add a spin operator and set the spin rate to something like 50 and Random3D
Create a standard deflector for your floor and add a collision test to your flow, then add the deflector.
create a new event and add Particle flow freebies stop gradually operator
Add a display operator to the flow and switch it to geometry.
Not perfect but without physics it close to as good as you are going to get.