In this paper we introduce the clus model, which has been newly implemented in the X-ray spectral fitting software package SPEX. Based on 3D radial profiles of the gas density, temperature, and metal abundance as well as the turbulent, inflow, and outflow velocities, the clus model creates spectra for a chosen projected region on the sky. Additionally, it can also take into account the resonant scattering. We show a few applications of the clus model on simulated spectra of the massive elliptical galaxy NGC 4636; galaxy clusters A383, A2029, A1795, and A262; and the Perseus cluster. We quantify the effect of projection as well as the resonant scattering on inferred profiles of the iron abundance and temperature, assuming a resolution similar to Chandra ACIS-S and XRISM Resolve. Our results show that depending on the mass of the object as well as the projected distance from its core, neither a single-temperature or double-temperature model nor the Gaussian-shaped differential emission measure model can accurately describe the input emission measure distribution of these massive objects. The largest effect of projection as well as resonant scattering was observed for projected profiles of iron abundance of NGC 4636, which is where we could reproduce the observed iron abundance drop in its innermost few kiloparsecs. Furthermore, we find that projection effects also influence the best-fit temperature, and the magnitude of this effect varies depending on the underlying hydrodynamical profiles of individual objects. In the core, the projection effects are the largest for A1795 and NGC 4636, while in the outskirts, the largest difference between 2D and 3D temperature profiles is for Perseus and A1795, regardless of the instrumental resolution. These findings might potentially have an impact on cross-calibration studies between different instruments as well as on the precision cosmology.
