•In-silico generated random packings are used to successfully represent packed beds.•New constitutive equations for particle deposition are obtained.•Classical theory inadequate for 3D packings and for all mechanisms of deposition.•Polydisperse particles are considered: results very different from theoretical predictions. In this work we have performed an extensive CFD simulation campaign with the purpose of studying particle transport and deposition in different catalytic systems and under different conditions. Two types of geometric models representing different porous media were created. The first is a number of random packings of spheres created via rigid body simulations: this approach was tested in previous studies and was proved to result in realistic packings, validated in their geometric features and fluid dynamic behaviour. The second is a regular arrangement of spheres, which was also successfully employed in previous works to study fine particles dispersion. Using these random packings, simulations of particle deposition have been performed at different operating conditions. In the first part we calculated values of particle deposition efficiency and compared our results with the classical filtration theory, highlighting the criticalities in the use of the simplified models upon which the theory is based. In the second part we have studied the effect of polydisperse particle populations: this is also missing in the classical filtration theory, which always considers the transport of particles with uniform diameter. Thus, we have performed population balance modelling simulations for particle deposition, employing the quadrature method of moments (QMOM): as an accompanying technical addition, a study on the accuracy of the application of EQMOM in these systems is offered. Even more clearly in this case, the results show that the description of polydisperse populations has a very noticeable effect on the macro-scale description, which would dramatically improve the understanding of particle transport and deposition in filtration and catalytic processes.