Drying–toasting kinetics of presoaked soybean. A mathematical model considering variable diffusivity, shrinkage and coupled heat transfer

• Fluidised bed drying–toasting of soaked soybean at 100–160 °C was modeled and simulated.
• Two stage shrinkage model was used to describe volume reduction.
• Effective diffusion coefficient depends on temperature and moisture content.
• Heat transfer coefficient and Arrhenius parameters were estimated solving inverse problems.
• Solving a coupled heat and mass transfer problem provides better insight on diffusion coefficient estimation.

In this work, the kinetics of drying–toasting of presoaked soybean in fludised thin layer at air temperatures between 100 and 160 °C was mathematically modeled. A two-stage shrinkage model was developed, which relates soybean radius with the average moisture content. Spherical geometry was assumed with radial diffusion, and a local mass balance coupled with an overall heat balance in the soybeans was solved by finite difference and the Euler method, respectively. The heat transfer coefficient was estimated from the energy balance using experimental drying rates. Values varied from 176 to 312 W/(m2 °C). The effective diffusion coefficient was proposed to be a function of temperature and moisture content. The temperature dependence was described by an Arrhenius relationship, while the moisture content dependence, found by extending the shrinkage behavior to a local level. The Arrhenius parameters were estimated by solving an inverse problem for the whole dataset. The activation energy was 51.9 kJ/(mol K), with a pre-exponential factor of 0.0237 m2/s. Predicted temperatures and average moisture content agreed well with experimental measurements.