State-space thermodynamic modeling of vanilla ethanolic extract spray drying with heat pump and N2

State-space thermodynamic modeling of vanilla ethanolic extracts spray drying with heat pump and N-2 was developed. Thermodynamic modeling considers activity coefficients for Raoult law deviations of ethanol vapor pressure, water vapor pressure, ethanol evaporation latent heat and water evaporation latent heat in a N-2-ethanol-water-vanilla solids system. State space considers 12 ordinary differential equations (ODEs) for ethanol and water concentrations in solid, N-2 and condensed liquid; temperatures and condensed liquid rate. The model was validated with 32 treatments of vanilla ethanolic extract experimentally spray dried with heat pump and N-2. The mathematical model reproduced the experimental gas outlet temperature with 4% of averaged error. An additional two parameters fit reached 11.4% of averaged error with respect to product outlet moisture and gas outlet temperature simultaneously. Proposed model demonstrated that heat pump spray drying can reach a 58% of thermal efficiency and a conventional spray drying can reach only 30%.