This work proposes a scale-up approach for the numerical simulation of blood flow, which is a challenging topic due to the multi-phase nature of this biological fluid. The choice of a specific method among the ones available in literature is often motivated by the physical scale of interest. Single-phase approximation of blood with non-Newtonian assumption allows for lower computational time, but does not consider this multi-phase nature. Cell-level simulation, on the other hand, requires high computational resources and is limited to small scales. In this context, unresolved CFD-DEM method offers the possibility to simulate hundreds of thousands of particles with limited computational effort, but requires specific models for fluid-particle interactions. In this study, a previously developed reduced-order model for red blood cells (RBCs) is employed to obtain data from cell-level simulations. Afterward, these data are used to derive corresponding model equations for the unresolved CFD-DEM method, namely drag and lift force correlations for RBCs. These forces are responsible for several bio-physical phenomena happening at the macro-scale, such as Fahræus-Lindqvist effect, which leads to an increase in blood apparent viscosity and discharge hematocrit. Furthermore, they are particularly important in the design of bio-microfluidics devices aimed at separation of blood plasma and RBCs. The process of verification and validation of the model is presented together with some applications, to highlight potential and limitations of the model. Up to half a million RBCs could be simulated with reasonable computational resources, returning satisfying results when compared to experiments in large microfluidics channels. Future perspectives include further improvement of the model, such as a deeper understanding of cell-cell interactions.