Granular media are ubiquitous in industrial processes, as is the need to simulate their behavior. Despite increasing computational power, the Discrete Element Method (DEM) still faces two major limitations: first, physical constraints restrict the simulation timestep to around 10-6 seconds; second, computational resources rarely allow simulations involving more than 107 particles. As a result, accurately simulating industrial-scale processes—often involving billions of particles over several hours—remains out of reach. To overcome the limitation on particle numbers, several approaches have been proposed. Among Lagrangian methods, the coarse-graining technique is the most common [1]. It consists of simulating "grains" with particular contact laws so they represent clusters of real particles. While this method significantly accelerates simulations, it remains approximate and does not fully capture the underlying physics—for instance, the inertial number [2], which governs the flow regime of granular materials, depends on the particle diameter. As a result, altering the diameter through coarse-graining inevitably modifies the flow behavior. In this study, an alternative approach is explored. Rather than modifying grain size and contact laws, the system size is scaled homothetically, while maintaining both a constant grain size and filling rate. The goal is to observe how key quantities of interest evolve with increasing scale, and to infer their behavior at large scales. Although this method requires multiple simulations, it has the potential to yield more accurate results and provide deeper insights into the underlying physics—especially considering the limited availability of scaling laws in the current literature. As a practical application, the method is applied to the DEM simulation of a screw conveyor. The primary quantity of interest is the residence time distribution (RTD), along with information related to mixing, such as active layer renewal. The evolution of the model parameters with respect to system scale is analyzed, with particular attention given to the issue of the clearance gap between the screw and the casing.