Mathematical modelling of water sorption isotherms and thermodynamic properties of wastewater sewage sludge

Abstract

Abstract This study was aimed at determining wastewater sewage sludge moisture sorption characteristics using a static gravimetric method at 303 K, 313 K and 323 K. Eleven mathematical models were adopted to simulate the experimental data, and the optimal model was analysed. The indexes included the net isosteric heat of adsorption (qst), differential entropy (△S), spreading pressure (π), net integral enthalpy (qin) and net integral entropy (△Sin) to evaluate the thermodynamic properties of the sludge. The isotherm curves exhibited type II behaviour according to the Brunauer--Emmett--Teller classification. The sorption isotherm fitting showed that the Gugghenheim--Anderson--de Boer model was able to reproduce the equilibrium moisture content evolution with water activity for a moisture range varying from 6% to 89% (0.991 < R2 < 0.999). The net isosteric heat of sorption and differential entropy were evaluated through direct use of moisture isotherms via the Clausius–Clapeyron equation and used to investigate the enthalpy–entropy compensation theory. The net isosteric heat and differential entropy obviously decreased as the equilibrium moisture content increased, which satisfied the compensation theory. The spreading pressure of the sludge sorption process decreased as the temperature increased at a given water activity and increased as the water activity increased at a given temperature. When the spreading pressure was at a fixed level, the net integral enthalpy decreased as the equilibrium moisture content increased, whereas the net integral entropy decreased as the equilibrium moisture content increased to a minimum value of −93.17, −98.34 and −93.28 J/(mol.K) at 303 K, 313 K and 323 K, respectively, and then tended to increase.