Powder mixing is a key step in many industrial processes. However, it remains difficult to control and predict due to the complexity of granular flows. Several numerical methods, notably DEM, have been developed to simulate particulate mixing. This approach provides access to individual particles positions and velocities, at each time step, at grain scale. Subsequently, DEM is computationally expensive[1] and non-applicable to process scale. Markov chain models, a stochastical approach, offer a macroscopic view of the mixing describing the overall dynamics of particulate systems, with significantly lower computational cost. Markov chain operators constructed based on DEM data were used to study particulate systems in horizontal rotating drums [2], [3], [4]. Mixing behaviors predicted by Markov chain models closely align with DEM results. From a process engineer point of view, investigating mixing at full scale own to limit the computational cost, even if this means losing some of the precision of the final result. This work proposes an approach to predict the dynamics of particle-based systems in a rotating drum using a homogeneous Markov Chain model determined from DEM data. The dense region of the mixture is identified and divided into cells with cylindrical coordinates. At each time step, particle transition probabilities between cells are computed. Several tests were conducted to determine the relevant parameters which are required to compute the average homogeneous transition matrix. The objective was to find a balance between mixing time simulated by DEM required to calculate the transition matrix and results accuracy with DEM reference simulation results. The mixture's homogeneity is assessed over time using well-chosen mixing indexes. The methodology was applied to various initial configurations and three observation scales. The impact of these parameters was investigated, revealing a significant influence on the mixing homogeneity. As a perspective, this methodology could be extended to segregating particulate.