Front Matter

v¼

VmaxS

KmþS

¼

VmaxKS

m

1 þKS

m

¼

Vmaxb

1 þb

ð 21 Þ

At low levels ofS/Kmorbwhere a high degree of conversion can be obtained, or a

low substrate concentration is used, the reaction rate is essentially first order. Here

the reaction time required to give a particular degree of conversion is directly pro-

portional toS/Kmorb. However, at high values ofS/Kmorbwhere the reaction is

essentially zero order, the time needed to reach a given degree of conversion is

independent ofS/Kmorb. In industrially practicable processes, high degrees of con-

version of substrate to product are usually required and, therefore, the time required

for a comparatively small increase in conversion is critically dependent on the pre-

vailing value ofS/Kmorb. For the production of SSL in packed-bed reactors and

using solvent-free systems, the termS/Kmis related directly to the substrate molar

ratio. It was found that the reaction time needed for a half-maximum incorporation of

acyl donors increased rapidly with the increase of substrate molar ratio (Xu et al.,

1998b).

In PBR, there is an important relationship between the flow rate through the re-

actor (mF) and the degree of conversion (X). The increase ofmFwill lead to the de-

crease of X [Equation (20)]. It was observed previously that the incorporation of

caprylic acid was decreased with the increase of flow rate in the reaction between

canola oil and caprylic acid (Xu et al., 2000). However, the activity of immobilized

enzymes is increased by the increase of flow rate. The phenomenon can be reflected

by the increase of incorporation per unit time, which leads to the higher productivity

of the reactor.

One of the special features of PBR is the pressure drop through the bed. This can

be described by theoretical equations or statistical models. Excessive pressure drop

often leads to the compression of biocatalyst particles due to friction between the

fluids and the support particles, or due to partial blockage of the column bed by

particulate materials. Compaction of the packed bed is especially likely when small

or irregularly shaped or packed particles are used in long columns over a long period.

The pressures generated cause deformation or fracture of the enzyme particles, and

result in the gradual decrease in the void volume. Compaction can be minimized by

using relatively large, incompressible, smooth, spherical, and evenly packed parti-

cles, or sectionalized columns, or by reducing the length-to-diameter ratio of the

column. The set-up of two flexible layers in the ends of the packed bed, with glass

wool for example, was also shown to be effective for the reduction of pressure drop

(Xu et al., 1998b).

Nonideal flow of PBR is caused by back-mixing, convection, or the creation of

stagnant regions in the reactor, for instance by channeling. Back-mixing of reactants

in packed-bed reactors arises because the presence of solid particles in the column,

causes elements of the flowing fluid to mix, and because the different fluid elements

take different routes through the reactor. Thus, different fluid elements have different

residence times in the reactor, giving an opportunity for different extents of reaction

to take place. Nonideal flow can be minimized by the use of even-sized, smooth,

spherical, evenly packed support particles and by the absence of accumulated solids

or gases in the column. Back-mixing certainly affects the yield of the reaction and the

11.6 Bioreactors for the lipase-catalyzed interesterification 205