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Fig. 19.1. Some important considerations about particle size and shape. (a) The effect of particle shape on nutrient accessibility. For two substrate particles of the same overall volume, the more spherical the shape then the greater the average depth from the surface and the lower the surface area to volume ratio. (b) Effect of particle size on porosity and pressure drop, illustrated with regularly-packed spherical particles. For the two different particle sizes, the percentage of the total volume occupied by the void spaces is identical. However, for forced aeration at the same superficial velocity, the pressure drop across the bed will be greater for the bed on the right, that is, with the smaller particles. (c) The overall particle size can increase early during the fermentation and then decrease during the latter stages. This is a result of two phenomena, the consumption of residual substrate and the expansion of the biofilm that in models of SSF bioreactors the particle size does not appear within the kinetic equation, which is usually simply an empirical description of observed growth curves. Experiments should be done in the laboratory with different particle sizes in order to determine the optimum particle size from the point of view of growth kinetics.

The particle size will also influence the packing within the bed and therefore the aeration of the bed. Comparing two beds of different particle sizes but the same porosity (void fraction), it will be more difficult to force air through the bed of smaller particles (the phenomenon of pressure drop) (Fig. 19.1(b)). However, on the other hand, the air may tend to follow preferential routes in a bed of larger particles (the phenomenon of channeling). Therefore studies to determine the optimal particle size for the process should also be done in the production-scale bio-reactor, if possible.

The particle diameter may appear within various correlations that are used in modeling, for example, in correlations for heat and mass transfer coefficients that appear in the model. Therefore it may be necessary to determine the particle diameter experimentally. This may not be simple for irregularly-shaped particles. For non-spherical but regular particles, it is possible to use the equivalent radius, defined as the volume of the particle divided by its surface area.

Determination of the particle size will be further complicated if not all particles are identical. The homogeneity of particle size and shape will depend on the source of the particles and the manner in which they were prepared. For example, grains might be expected to be more homogeneous than substrates like chopped straw or rasped tubers. For heterogeneous substrates, it will be necessary to determine the particle size distribution. For particles with a shape that is reasonably close to spherical, this can be done by passing a sample through a number of graded sieves. Of course, sieves can also be used to select a particular range of particle sizes for use in the fermentation.

As mentioned in Chap. 2, the particle size can change during the process. The overall particle size, that is, the overall diameter of the biomass layer and the residual substrate, can first increase and then later decrease (Fig. 19.1(c)). However, as yet there is little quantitative data available and, although some models have been proposed to describe particle size reduction during the fermentation (Ra-jagopalan et al. 1997), such models are typically not incorporated into bioreactor models.

19.2.2 Particle Density

It may be useful to know the density of the prepared substrate particles since, as described in Sect. 19.2.4, this parameter can be used in an estimation of the bed porosity. However, substrate particle density is not necessarily an easy parameter to determine. If the prepared particles do not absorb water and therefore do not swell quickly when put into contact with excess water, one method may be to flood a sample of particles with water within a container such as a measuring cylinder. The substrate particle density can then be calculated as:

Vtotal - mw 1 Pw Vs where mtatui is the mass of the system after flooding (g), mcontaiiner is the mass of the empty container (g), mw is the mass of the water added to flood the bed (g), Vtotai is the total volume of the flooded bed (L), pw is the density of water (g L-1), and ms is the mass of the substrate particles (g). The advantage of using this system of units is that it will give the correct numerical value of the substrate density in SI (since g L-1 is equivalent to kg m-3).

19.2.3 Bed Packing Density

It is often necessary to know the apparent density of the bed, that is, the bed packing density (pb) (Fig. 19.2). This relates the bed mass with the volume that the bed will occupy. It can be determined experimentally by packing the substrate, prepared in a manner identical to preparation for the fermentation, to fill a container of known volume (V, liters) and mass, and reweighing. The difference between the masses of the container when it is packed with substrate and when it is empty is the packed mass of the bed (mp, g). Of course, the packing process must also be identical to that which is used in the fermentation. The packing density is then calculated as:

volume of voids ,. , total bed mass porosity = - bed packing density =-

total bed volume total bed volume

Fig. 19.2. Physical meaning of two important bed properties: the porosity (void fraction) and bed packing density m p

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