Mathematical Modelling of Two Separate Phases Enzymatic Membrane Reactor
Advancing the chemical engineering fundamentals
Chemical Reaction Engineering: Practical Applications (T2-2c)
Keywords: Enzyme membrane reactor, kinetic resolution, mathematical modelling, enantiomer
Lipases are useful biocatalysts in kinetic resolutions for they specific interaction with one of the two enantiomers present in a racemic mixture. Their lifetime in terms of catalytic activity and stability is the major problem for their application in industry. The stability of lipase is increased by immobilization at the organic/aqueous interface within the porous structure of asymmetric membranes.
In this work, the modelling of a two-separate-phases enzymatic membrane reactor was developed considering the hydrolysis of S-naproxen methyl-ester. The modelled system consists in a catalytic membrane separating an organic phase containing the S-ester (reactant) and an inorganic phase for naproxen acid recovery (the reaction product); both the phases are continuously re-circulated. The S-naproxen ester diffuses from the organic bulk solution to the boundary layer and then into the enzyme layer inside the membrane, where it is catalytically converted into naproxen acid. The naproxen acid diffuses from the enzyme membrane layer towards the bulk inorganic solution in the other membrane side.
The slow reaction rate and the relative fast re-circulation allows the bulk phases to be considered as well-mixed batch systems. Therefore, the dimensionless mathematical model consists of:
• the 1-D transient mass balance (partial differential equations) for S-enantiomer naproxen methyl-ester (reactant) and naproxen acid (product) inside the catalytic membrane;
• the ordinary differential equations for the evolution of reactant and product concentration in the organic and inorganic phases, respectively.
The same equations can be written for the R-enantiomer; however, owing to the high selectivity of the catalyst for the S-ester the reaction rate of the R-ester is too low when compared to that of S-ester.
Naproxen methyl ester conversion and naproxen acid production as a function of reaction time for different values of dimensionless parameters were calculated. Moreover, reactant and product profiles inside the catalytic membrane were obtained. The results shown that the performance depends on many factors such as: mass transport, reaction rate, membrane area to organic phase volume ratio and membrane thickness. In particular, a key role is played by the maximum velocity parameter of Michaelis-Menten kinetics to the effective diffusivity ratio (vMAX/Deffective). The model validated with some literature data shows interesting results for studying the catalytic membrane performance of these systems.
Acknowledgement: The “Ministero dell’Università e della Ricerca” Progetto “FIRB-CAMERE RBNE03JCR5 – Nuove membrane catalitiche e reattori catalitici a membrana per reazioni selettive come sistemi avanzati per uno sviluppo sostenibile” is grateful acknowledged for the financial support.
Presented Tuesday 18, 16:40 to 17:00, in session Chemical Reaction Engineering: Practical Applications (T2-2c).
