The lifespan of refractory results from a complex interaction between chemistry, thermal heat science and mechanics. The development of numerical models able to predict the results of such complex multi-physics couplings require an intensive use of the thermodynamic 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. This talk will summarize the theoretical framework illustrated on refractory lining application following by a description of the case of the reactive impregnation of refractory by slag. Ensuring numerical convergence and results accuracy require small time step and fine space discretization craftily coupled that results which lead to a very long computational time. To overcome the numerical difficulties and to speed up the computation time, a new numerical method based on percolation theory is proposed. The basics of this method and the first numerical results in one dimension will be presented.