Simulation of chemical reactors is often considered as a routine task, tacklable with standard models and standard simulators. However, the analysis, design, and optimization of novel integrated reactor concepts require specialized approaches. A countercurrent wall reactor concept for the autothermal coupling of high-temperature endothermic and exothermic reactions is discussed as a case study in order to demonstrate the importance of individual solutions. The custom of insisting on a given model formulation regardless of its numerical implications is addressed in particular. It is demonstrated how simple modifications and heuristics improve the solvability of a problem. The role of model reduction in capturing the multiplicity of solutions is discussed. The comprehensive picture obtained in this way provides a safe basis for deciding on the practical feasibility of the investigated process. It finally generates guidelines for a specific process optimization.