Model of an Immobilized Biocatalyst Tubular Reactor

Immobilized biocatalysts are used in the manufacture of many industrial products in the pharmaceutical, chemical and food industries. This Demonstration illustrates an immobilized biocatalyst reactor composed of two concentric cylinders: the inner cylinder contains a substrate and product solution flowing in laminar flow, and the annulus is filled with an enzyme (or cells) immobilized in a porous gel. The two cylinders are separated by a semipermeable ultrathin membrane that allows passage of the substrate and product but not the biocatalyst.

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The partial differential equation describing the steady-state substrate mass conservation in the reactor:
,
where
and
where
and stand for the inner and outer radii,
is the substrate,
and are the axial and radial coordinates,
and are the diffusivities of the fluids in the inner and outer cylinders,
is the laminar velocity in the inner tube,
is the maximum fluid velocity,
is a first-order catalyzed reaction, where is the reaction rate constant.
The properties of the fluids in the two cylinders are assumed to be constant, and axial diffusion is neglected.
The integration limits are:
, and ,
where is the length of the reactor, with boundary values
,
and
.
The average concentrations of the substrate in the lumen and in the biocatalyst are:
and
,
respectively.
The equations are solved with the built-in Wolfram Language function NDSolve. You can use the sliders to vary the values of the fluid velocity, the reaction rate constant and the ratio of the outer to the inner radius to observe their effect on the substrate concentration in the reactor.
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