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.