Mathematical modeling and simulation of gel drying with supercritical carbon dioxide

Abstract

Mathematical models of alumina/silica gel supercritical drying with carbon dioxide were studied using supercritical drying experimental data. An alumina/silica gel with zinc chloride was synthesized and dried with superciritical carbon dioxide, and its weight change was monitored as a function of drying time. The pore size distribution of the obtained aerogel was determined using the BET method and nitrogen adsorption/ desorption. The mathematical model of the supercritical drying of the wet gel was represented as unsteady and one-dimensional diffusion of solvent through the aerogel pores filled with supercitical carbon dioxide. Parallel pore model and pores in series model were developed on the basis of the measured porous structure of the aerogel. It was found that these models which use different effective diffusivity value for each pore size were in much better agreement with the experimental data than models which use an overall effective diffusivity. The local effective diffusivity coefficients were calculated using different tortuosity values for each pore size, and they were distributed according to the pore size distribution data. Model simulations of the superciritical drying with carbon dioxide confirmed that the drying temperature and gel particle diameter have a significant influence on the drying time.

U ovom radu su ispitani matematički modeli sušenja alumosilikatnog gela sa natkritičnim ugljen-dioksidom na osnovu eksperimentalnih podataka natkritičnog sušenja. Sintetizovani alumosilikatni gel sa cink-hloridom je sušen sa natkritičnim ugljen dioksidom, pri čemu je praćena njegova promena mase sa vremenom. Raspodela veličina pora aerogela je određena BET metodom i adsorpcijom/desorpcijom azota. Matematički model natkritičnog sušenja je prikazan kao nestacionarna jednodimenziona difuzija rastvarača kroz pore aerogela ispunjene natkritičnim ugljen- dioksidom. Model paralelnih pora i model redno vezanih pora su razvijeni na osnovu izmerene porozne strukture dobijenog aerogela. Rezultati ukazuju da je slaganje modela paralelnih pora i modela redno vezanih pora sa različitim vrednostima efektivne difuzivnosti za pore različitih veličina i eksperimentalnih podataka, znatno bolje nego u slučaju modela koji koriste jednu vrednost efektivne difuzivnosti. Koeficiejenti efektivne difuzivnosti su dobijeni korišćenjem različitih vrednosti lokalnih izuvijanosti pora za svaku dimenziju pora, pri čemu su ovi koeficijenti efektivne difuzivnosti distribuirani na osnovu podataka o raspodeli veličina pora. Simulacijom natkritičnog sušenja je potvrđeno da temperatura sušenja i dimenzije gela imaju značajan uticaj na vreme sušenja.