The shaft furnace process is highly complex to analyse, due to the high temperatures, harsh operating conditions and the multiphase flow. To increase the process understanding a Computational Fluid Dynamics (CFD) model has been developed. It includes a full-way coupling between gaseous phase and a Discrete Element Model (DEM) used for the description of the particle phase. The model implemented into OpenFOAM enables prediction of heat, combustion and species transport phenomena in the furnace. To reduce the simulation time different techniques such as a Time Scale Splitting Model (TSSM) and a specific chemical reaction modelling are developed. To allow an accurate description of the void fraction in highly mesh-resolved regions the Volume Fraction Smoother (VFS) is developed. It enables a much more representative mapping of the porosity from the particle to the gas phase using a newly developed approach. Particle-particle heat radiation as well as conduction are implemented into the DEM code. A detailed comparison between simulation and measurement results shows that the model precisely predicts the transport effects inside packed beds. For the calculation of nitrogen oxide formation, a model based on flamelet data has been developed for further postprocessing. In the first step, the fast flamelet model is used to calculate the flow, temperature, pressure, turbulence and species fields. However, the flamelet model is not able to predict nitrogen oxides precisely. This is because of the non-applicability of the flamelet model for slow chemical reactions such as the nitrogen oxide formation. Therefore, subsequently the chemical reactions are implemented using a detailed reaction mechanism. The highly accurate and computationally effective model predicts the formation of nitrogen oxide. For the model verification a detailed comparison with the measurements is provided. One of the main focuses in this doctoral thesis is to find strategies to reduce the simulation time. Only through these computational improvements, it is possible to apply the complex multi-physical model to large-scale geometries. Two different types of real-scale shaft furnaces are simulated. The first type is the directly fired furnace with the pre-mixed gas-air mixture injected into the particle bed, so that combustion takes place between the particles. And the second one is a shaft furnace with an external combustion chamber. For both units, the particle behaviour and nitrogen oxide formation are studied. The application of the model has shown that only by using the speed up strategies the model becomes applicable for industrial scale geometries. The model provides a three-dimensional representation of the process and offers a much more detailed insight into the furnace than any measurement could do. The next step is to study the transport behaviour of the shaft furnace more in detail and to find further strategies to reduce the calculation time.