The lifespan of refractory results from a complex interaction between chemistry, thermal conditions, and mechanics. The development of numerical models able to predict the results of such complex multi-physics couplings requires an intensive use of the thermodynamics of irreversible processes framework. Today, the main barriers to reach fully predictive simulations are: the access to relevant data at high temperature (chemical kinetics, chemical expansion coefficient, etc), the numerical complexity and the computational time. The theoretical framework is briefly illustrated on refractory lining applications with a focus on the impact of the swelling induced by corrosion. Then, the numerical difficulties to ensure the numerical convergence and the accuracy of the results when solving classical partial differential equations are examined. Finally, a new approach to model the capillary impregnation by slag, based on percolation theory, is proposed. The basics of this method and the first numerical results are presented.