Evaluation of half‐life of immobilized enzyme during continuous reaction in bioreactors: A theoretical study

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Abstract
A theoretical study has been carried out on the evaluation of the apparent half‐life of immobilized enzyme activity during continuous reaction both in a plug‐flow reactor (PFR) and in a continuous‐flow stirred‐tank reactor (CSTR). Two apparent half‐lives have been defined: the elapsed time at which the feedrate becomes half of the initial one when the feedrate of the substrate solution is lowered to keep the conversion fixed (constant‐conversion policy), and the elapsed time at which the conversion becomes half of the initial one when the feedrate (or space velocity) is kept constant (constant‐feedrate policy or constant‐space‐velocity policy). Under no intraparticle diffusional limitation, the constant‐conversion policy of operation in the PFR and CSTR gives the same half‐life as that of the enzyme inactivation regardless of the formula of the reaction rate, and the constant‐feedrate policy of operation in the PFR and CSTR offers the same half‐life as that of the enzyme inactivation only when the reaction is zero‐order. Under intra‐particle diffusional limitation, apparent half‐lives are always greater than that of enzyme denaturation, depending on many factors such as order of reaction, feeding policy (constant‐conversion and constant‐feedrate policies), initial conversion, and bioreactor configuration. It is suggested to perform the continuous operation with changing feedrate to keep the conversion (or outlet substrate concentration) fixed under the domain of zero‐order kinetics so as to obtain an apparent half‐life as close to the real one in industrial operation.