Development of mathematic model for coffee decaffeination with leaching method

A simple mathematic model for caffeine kinetic description during the extraction process (leaching) of coffee bean was developed. A non­steady diffusion equation coupled with a macroscopic mass transfer equation for solvent was developed and them solved analytically. The kinetic of caffeine extraction from coffee bean is depend on initial caffeine content, final caffeine content, caffeine content at certain time, mass­transfer coefficient, solvent volume, surface area of coffee beans, process time, radius of coffee bean, leaching rate of caffeine, caffeine diffusivity and a are constan, solvent concentration, activation energy, temperature absolute and gas constant. Caffeine internal mass diffusivity was estimated by fitting the model to an experiment using acetic acid and liquid waste of cocoa beans fermentation. The prediction equation for leaching rate of caffeine in coffee beans has been found. It was found that Dk (m2/sec)=1.345x10­7—4.1638x10­7, and kL (m/sec)=2.445x10­5—5.551x10­5 by acetic acid as solvent depended on temperature and solvent concentration. The prediction equation for length of time to reduce initial caffeine content to certain concentration in coffee beans has been developed, Caffeine diffusivity (Dk) and mass­transfer coefficient (kL) was found respectively 1.591x 10­7—2.122x10­7 m2/sec and 4.897x10­5—6.529x10­5 m/sec using liquid waste of cocoa bean fermentation as solvent which depend on temperature and solvent concentration. Key words: Coffee, caffeine, decaffeination, leaching, mathematic model.