Numerical modelling of a high temperature silicification process in the carbon-carbon porous medium

Abstract

A mathematical model has been developed to describe the process of a high-temperature silicification process in a carbon-carbon porous material. The statement of the problem is based on general equations describing the clogging of tubules in a porous medium with various kinds of impurities. In the problem under consideration, the cause of blockage is the condensation of gaseous silicon on the inner walls of the pores. Temperature dependences for the coefficients of condensation and evaporation are proposed, which characterize the intensity of this process. It is assumed that the diffusion of gas is the main mechanism of initial filling pores of the material. Numerical modeling was carried out by the finite difference method using an explicit scheme in the case of a constant value of the mobile concentration at the input and for imposed linear temperature distribution on the vertical boundaries of the sample. Such temperature distribution made it possible to describe a partially silicified region and to delimit from it the sample part that remains “dry” during this process. The dynamics of the main physical characteristics, i.e. porosity of the composite material and concentration of the immobile component in the volume, is analyzed. The external factors influencing the intensity of the condensation process are considered quantitatively, namely, the concentration of the mobile component in the volume is calculated as a function of time. For the characteristic time interval, the maximum change in the porosity of the medium is calculated, on the basis of which the time of complete saturation of the material is estimated, which, as it turned out, is equal about 2 hours. The results of numerical simulation for silicification time and weight gain of the product are in qualitative and quantitative agreement with the known experimental data.