Organic phase
The immobilized-lipase-filled fixed bed reactor for the esterification reaction is modeled as a cascade of σ CSTR reactors according to equation (11). For each CSTR j, a mole flow\(\dot{n}\)CSTR,j,i is defined which contains the concentrations of all cinnamyl derivatives for the subsequent CSTR j+1. A deactivation of Novozym®435 was not noted over time; therefore no time-dependent deactivation constant is implemented. Due to temperature variations between the extraction step and the fixed bed reactor, a temperature-dependent concentration change is implemented through a temperature-dependent change in density ρ of the organic phase. Since component precipitation in the organic-phase cycle was not noted due to the high saturation concentrations of the cinnamyl derivatives, no storage term is implemented in this sub-model. Based on kinetic measurements, the lipase reaction rate is described according to a bi-bi mechanism with substrate excess inhibition of cinnamic acid (CAC) for the present reaction system. Equation (12) shows the lipase reaction rate as implemented in the model, and the corresponding parameters are described in table 3.