A phenomenological–mathematical approach in simulating the loss in weight of chlorine during sodalite synthesis

In a previous paper we described the results of a sodalite synthesis, performed by the mixing of metakaolinite and NaCl within an alumina crucible, heated in an oven at a temperature of 850 °C and ambient pressure. During the synthesis process, a loss of weight of the open crucible, attributed to chlorine (Cl) diffusion through the granular material contained inside the crucible, was observed. A very simple model was proposed, aimed at reproducing mathematically the experimental data behavior. Nevertheless, experimental and numerical result comparisons suggested the need for some modeling improvements. Thus, in this paper the already proposed analytical solution, based on the usual “first principles” approach, was modified through a backfitting phenomenological–analytical approach. We explored the assumptions that at the beginning of the experiment, the inventory of chlorine was completely or partially bound in the matrix, and that it was transformed into a gas free to diffuse only gradually over the transient. In addition, we explored the effect of full or partial variability in time of the diffusion coefficient. The apparent delay in the release of chlorine gas through the matrix mixture could be justified by an incomplete heating of the crucible at 850 °C and/or by some structure change of the mixture during the synthesis processes, eventually resulting in changes of diffusion coefficient values. The influences of the actual measurement process on the mathematical modeling setting, in particular the removal of some quantity of substance for diffractometer analysis, are also discussed. The final numerical results show an excellent agreement with the experimental data. Finally, it is worth noting that, notwithstanding the proposed methodology is addressed to the specific problem, it could have application in different fields.