Without knowing what shape your BVH nodes are, it's hard to tell how to compute something about them.
Guessing what's special about refracted rays and what's difficult about intersecting them with an AABB, if that's what you are trying to do, is even harder.
Maybe you can post some formulas or code to show where you are stuck. Are you writing some kind of ray tracer?
I want to write a real time gpgpu ray tracer with ideal soft shadows for simple objects like cubes, spheres and e.t.c. I want to project shadow figure (as analytic function) to light source plane and compute visibled from the point square of the light source .
BVH nodes consists from aabb volumes (cuboids) . compute intersection for refracted ray interests for cube and cuboid.