A numerically verified analytical framework for immobilised-enzyme packed-bed reactor design in the kinetically controlled regime applied to dihydroxyacetone production
- 1Hitachi Cambridge Laboratory, J. J. Thomson Ave., Cambridge, United Kingdom, CB3 0US
- 2Department of Biochemistry, University of Cambridge, Sanger Building, 80 Tennis Court Road, Cambridge, United Kingdom, CB2 1GA
- 3Department of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Dr., Cambridge, United Kingdom, CB3 0AS
Abstract
Continuous-flow biocatalysis can decouple enzymatic productivity from the cellular growth constraints inherent to fermentation, but exploiting this advantage requires a reactor design framework that links enzyme kinetics, immobilisation penalties, and catalyst deactivation to industrially relevant performance metrics. We develop an analytical quasi-steady-state (QSS) plug-flow reactor model for immobilised-enzyme packed-bed reactors (PBRs) operating under first-order catalyst deactivation, and verify its transport assumptions against a two-dimensional axisymmetric COMSOL™ finiteelement model. The close agreement between the analytical and numerical solutions confirms that reactor performance is kinetically controlled across the investigated operating window, and yields a closed-form expression for the time-averaged space–time yield (𝑆𝑇𝑌 ) that factorises into five independently controllable design levers. We apply this framework to a feasibility study on the continuous enzymatic conversion of formaldehyde to dihydroxyacetone (dha) using immobilised formolase (FLS), a reaction of interest for C1 biomanufacturing. Parametric mapping across substrate concentration, enzyme loading, and immobilisation-induced activity penalties, combined with sensitivity analysis incorporating enzyme deactivation, identifies substrate concentration, enzyme loading, substrate affinity (𝐾M), and catalyst stability as the principal parameters governing productivity, and shows that continuous immobilised FLS operation can sustain greater than 8-fold higher timeaveraged productivity than fermentation across the full range of product yields and operating scenarios considered. Beyond the specific case study, the verified QSS framework and its design-lever decomposition are directly transferable to other immobilised-enzyme PBR systems, offering a general route from laboratory kinetic data to quantitative reactor and catalyst design targets for continuous biomanufacturing.
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BibTeX
@misc{roy2026numerically,
title = {{A numerically verified analytical framework for immobilised-enzyme packed-bed reactor design in the kinetically controlled regime applied to dihydroxyacetone production}},
author = {P. E. Roy and W. Rostain and F. Brossard and C. Smith and J. Molloy and L. Fruk and N. Mertig and Pierre Roy},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15009721/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009721/v1},
note = {CC BY-NC},
}
RIS
TY - UNPB
TI - A numerically verified analytical framework for immobilised-enzyme packed-bed reactor design in the kinetically controlled regime applied to dihydroxyacetone production
AU - P. E. Roy
AU - W. Rostain
AU - F. Brossard
AU - C. Smith
AU - J. Molloy
AU - L. Fruk
AU - N. Mertig
AU - Pierre Roy
PY - 2026
DA - 2026/10/01
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009721/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009721/v1
AB - Continuous-flow biocatalysis can decouple enzymatic productivity from the cellular growth constraints inherent to fermentation, but exploiting this advantage requires a reactor design framework that links enzyme kinetics, immobilisation penalties, and catalyst deactivation to industrially relevant performance metrics. We develop an analytical quasi-steady-state (QSS) plug-flow reactor model for immobilised-enzyme packed-bed reactors (PBRs) operating under first-order catalyst deactivation, and verify its transport assumptions against a two-dimensional axisymmetric COMSOL™ finiteelement model. The close agreement between the analytical and numerical solutions confirms that reactor performance is kinetically controlled across the investigated operating window, and yields a closed-form expression for the time-averaged space–time yield (𝑆𝑇𝑌 ) that factorises into five independently controllable design levers. We apply this framework to a feasibility study on the continuous enzymatic conversion of formaldehyde to dihydroxyacetone (dha) using immobilised formolase (FLS), a reaction of interest for C1 biomanufacturing. Parametric mapping across substrate concentration, enzyme loading, and immobilisation-induced activity penalties, combined with sensitivity analysis incorporating enzyme deactivation, identifies substrate concentration, enzyme loading, substrate affinity (𝐾M), and catalyst stability as the principal parameters governing productivity, and shows that continuous immobilised FLS operation can sustain greater than 8-fold higher timeaveraged productivity than fermentation across the full range of product yields and operating scenarios considered. Beyond the specific case study, the verified QSS framework and its design-lever decomposition are directly transferable to other immobilised-enzyme PBR systems, offering a general route from laboratory kinetic data to quantitative reactor and catalyst design targets for continuous biomanufacturing.
ER -