  Reprocessed X-ray radiation from active galactic nuclei (AGN) carries
important information about the properties of the circumnuclear material around
the black hole. The X-ray photons travel from the very center of the system and
interact with that material often producing strong emission lines. The
FeK$\alpha$ Compton shoulder is formed by fluorescent FeK$\alpha$ photons that
perform Compton scatterings with the intercepting material and lose energy to
form the distinct shoulder shape. In this work we use the ray-tracing code
RefleX to explore how the physical properties of the medium, as well as its
geometry, affect the shape of the Compton shoulder (CS). We start by running
simulations using a simple toroidal reflector, to test the effect of the metal
composition, metallicity, column density, dust presence and velocity on the
FeK$\alpha$ line and its Compton shoulder. We confirm that the shape of the
Compton shoulder is sensitive to the optical depth of the intercepting medium,
which can be regulated by either changing the metal composition or the line of
sight column density of the circumnuclear material. Next, we create a series of
models, which feature different geometrical configurations of dust and gas, and
explore how the Compton shoulder is affected by such configurations finding
that components that can regulate the line-of-sight column density affect the
FeK$\alpha$ and its CS. Finally, we test whether observatories such as the
recently launched XRISM and future Athena will make the Compton shoulder a
useful spectral feature of nearby AGN, by applying specific models on simulated
spectra of the Circinus galaxy. The CS has the potential to be used to help
constrain properties of the circumnuclear material yet with some limitations.
