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The most important characteristic of a PBR is that material flows through the reactor as a plug; they are also called plug flow reactors (PFR). Ideally, all of the substrate stream flows at the same velocity, parallel to the reactor axis with no back -mixing. All material present at any given reactor cross -section has had an identical residence time. The longitudinal position within the PBR is, therefore, proportional to the time spent within the reactor; all product emerging with the same residence time and all substrate molecule having an equal opportunity for reaction. The conversion efficiency of a PBR, with respect to its length, behaves in a manner similar to that of a well -stirred batch reactor with respect to its reaction time (Figure 5.2(b)) Each volume element behaves as a batch reactor as it passes through the PBR. Any required degree of reaction may be achieved by use of an idea PBR of suitable length.

The flow rate (F) is equivalent to Vol_S/t for a batch reactor. Therefore equation (5.5) may be converted to represent an ideal PBR, given the assumption, not often realised in practice, that there are no diffusion limitations:

(5.6)

In order to produce ideal plug -flow within PBRs, a turbulent flow regime is preferred to laminar flow, as this causes improved mixing and heat transfer normal to the flow and reduced axial back-mixing. Achievement of high enough Re may, however, be difficult due to unacceptably high feed rates. Consequent upon the plug -flow characteristic of the PBR is that the substrate concentration is maximised, and the product concentration minimised, relative to the final conversion at every point within the reactor; the effectiveness factor being high on entry to the reactor and low close to the exit. This means that PBRs are the preferred reactors, all other factors being equal, for processes involving product inhibition, substrate activation and reaction reversibility. At low Re the flow rate is proportional to the pressure drop across the PBR. This pressure drop is, in turn, generally found to be proportional to the bed height, the linear flow rate and dynamic viscosity of the substrate stream and (1 – e)²/e³ (where e is the porosity of the reactor; i.e. the fraction of the PBR volume taken up by the liquid phase), but inversely proportional to the cross-sectional area of the immobilised enzyme pellets. In general PBRs are used with fairly rigid immobilised-enzyme catalysts (1 -3 mm diameter), because excessive increases in this flow rate may distort compressible or physically weak particles. Particle deformation results in reduced catalytic surface area of particles contacting the substrate-containing solution, poor external mass transfer characteristics and a restriction to the flow, causing increased pressure drop. A vicious circle of increased back-pressure, particle deformation and restricted flow may eventually result in no flow at all through the PBR.

PBRs behave as deep-bed filters with respect to the substrate stream. It is necessary to use a guard bed if plugging of the reactor by small particles is more rapid than the biocatalysts’ deactivation. They are also easily fouled by colloidal or precipitating material. The design of PBRs does not allow for control of pH, by addition of acids or bases, or for easy temperature control where there is excessive heat output, a problem that may be particularly noticeable in wide reactors (> 15 cm diameter). Deviations from ideal plug-flow are due to back-mixing within the reactors, the resulting product streams having a distribution of residence times. In an extreme case, back-mixing may result in the kinetic behaviour of the reactor approximating to that of the CSTR (see below), and the consequent difficulty in achieving a high degree of conversion. These deviations are caused by channelling, where some substrate passes through the reactor more rapidly, and hold-up, which involves stagnant areas with negligible flow rate. Channels may form in the reactor bed due to excessive pressure drop, irregular packing or uneven application of the substrate stream, causing flow rate differences across the bed. The use of a uniformly sized catalyst in a reactor with an upwardly flowing substrate stream reduces the chance and severity of non-ideal behaviour.