We study mass transfer through random assemblies of fixed spherical catalyst particles experiencing an external convective-diffusive fluid stream. Chemical species are transported through the array and are diffused from fluid to solid phase through particles surface. An internal first order irreversible chemical reaction takes place within the porous catalyst particles. We address the determination of mass transfer coefficient by performing direct numerical simulations with fully internal-external coupling using concentration and flux continuity boundary conditions at the solid-fluid interface. We derive a theoretical prediction of the profiles of cup-mixing concentration, average of mean surface and average of mean volume concentration of the particles along the height of the domain. The model for the dimensionless mass transfer coefficient (‘reactive’ Sherwood number) is accounting for the five dimensionless parameters that control the physics of the system: the Reynolds number , the Schmidt number, the Damköhler  number, the internal-to-external diffusion coefficient ratio and the solid volume fraction . We use a coupled Sharp Interface/ Discrete Lagrange Multiplier-Fictitious Domain Method (SIM-DLM/FD), thoroughly validated in our previous study (Sulaiman et al., 2019) to test the accuracy of the model over a wide range of dimensionless parameters and solid volume faction (from dilute to dense regime). We show and discuss the limitations of the proposed model.