Predictive Models in Espresso Coffee Percolation

The trade of coffee market is comparable in size to that of oil and steel. This leads to a high level of competitiveness among the players operating in the sector, and the need to ensure the environmental sustainability of the sector. These aspects can be supported by the scientific research to improve the quality and the efficiency of the extraction process and to reduce the negative impact of coffee market on the environment. In this thesis we consider two different mathematical models for the espresso coffee extraction process to face the two main goals of coffee industry: the beverage customisation and the sustainability of the sector. The reduced model is used to predict the extraction efficiency. Two different numerical schemes are proposed: the finite difference approximation scheme and a radial basis functions (RBFs) approximation scheme; both the schemes are based on the Crank-Nicolson method for the integration with respect to time. The reliability of the model together with the proposed solving strategies is assessed experimentally, by comparing the efficiency of real and simulated extractions conducted under different physico-chemical conditions. Also a complete 3D model for the espresso coffee extraction is considered and a wide campaign of chemical laboratory analyses of espresso extracted samples is used for its calibration and validation. Finally, the equation governing the dynamics of the water during the espresso extraction to predict the flux behaviour is considered. The corresponding initial-boundary value problem is solved by using the Crank-Nicolson scheme with respect to the time, whereas the spatial derivatives are approximated via RBFs. The preliminary reliability of the proposed solving strategy is experimentally assessed by comparing the hydraulic head behaviour with different initial pressures of the incoming water.