(663b) An Observer-Based Methodology for Estimating Effective Diffusion Coefficients during Osmodehydration of Apple Cubes

Fruits osmodehydration is a mass transfer (MT) process wherein the product is immersed in a hypertonic solution. During this process, simultaneous mass fluxes such as water loss (WL) and solid gain (SG) occur within the product, which can be described by means of Fick´s second law of diffusion. An alternative approach to evaluate the dynamic behavior of effective diffusion (ED) coefficients based on state estimators have been recently explored for describing more accurately those fluxes, as well as the time required to achieve the equilibrium (steady state). The aim of this work was to develop an observer-based methodology to estimate the dynamic behavior of ED coefficients during apple osmodehydration. Apple cv. Granny Smith cubes (1.2×1.2×1.2 cm) were osmodehydrated with grape cv. Victoria juice concentrate (50 and 60°Brix, at 40°C and 10 g solution/ g product) during different immersion times (t = 0-5760 min). After the immersion time, water activity (a_w) of dehydrated product and the osmotic media were analyzed and WL and SG of the cubes was determined through mass balances. All measurements were carried out by triplicate. The experimental data were modeled through a Luenberger observer, which estimate the dynamic behavior of water and solute ED. The observer methodology consists of a set of ordinary differential equations: i) describing the dynamic of measureable states for WL and SG, and ii) describing the dynamic of model parameter (ED). Dynamic model also includes the tuning parameters with a term dependent on estimation errors (convergence and noise), which are minimized to ensure that the observer converges locally to zero. The numerical integration of observer methodology was performer with Matlab R2020b. Average volumetric of estimations were compared with ED calculated using Crank’s analytical simplified solution of Fick´s second law for a cubic geometry. The obtained results showed that equilibrium conditions were reached at t > 1080 min when osmotic solution and product a_w did not present significant differences (p > 0.05). The equilibrium parameters of WL and SG were 0.54-0.66 g water/ g fresh product and 0.095-0.107 g solutes/ g fresh product, respectively. The estimation of experimental data indicates that the observer adequately describes the dynamic behavior of water and solute ED during the osmodehydration process with an eigenvalue λ = -80, of multiplicity two. Estimated water and solute ED through observer-based methodology were in ranges of 2.31-2.44×10^-10 and 2.12-2.34×10^-10 m²/s, respectively, with a correlation coefficient > 0.90. Overall, the observer solution presented a better fitness than that obtained by Crank’s analytical simplified solution.