Criteria for a unique steady state for enzymatic depectinization of bael (Aegle marmelos) juice in a continuous stirred tank reactor

Abstract

The depectinization kinetics of bael (Aegle marmelos) juice using the enzyme pectinase was evaluated and it was observed to follow the Michaelis–Menten model. The suitable reaction time and enzyme concentration were estimated to be 60 min and 0.25% w/w, respectively. The conditions to obtain a unique steady state for such a reaction in a continuous stirred tank reactor were determined using the fixed point theorem and contraction mapping. The phase space plot was generated using parameters and , involving the operating conditions and kinetic constants (V is the reactor volume, v_max and K_M are the kinetic parameters of the Michaelis–Menten model, v₀ is the volumetric flow rate and C_A0 is the feed concentration of the substrate), and the envelope of a unique steady state was developed. From the iso-conversion curves, the values of α and β were identified so that the reactor can operate at a unique steady state. It was found that β > 4 results in a feasible steady state. The range of α was reduced at a higher β in order to get a unique steady state. The critical residence time of the reactor decreased with the enzyme concentration and became invariant beyond 0.20% w/w. Deviation of the CSTR from ideal behavior led to an increase in the critical residence time. The present analysis is extendable to other reaction kinetic models as well, for appropriate design and scale up of commercial reactors so as to prevent the occurrence of multiple steady states leading to inaccurate product specifications.