The model described here is based on that developed for the Zymotis bioreactor of Roussos et al. (1993) by Mitchell and von Meien (2000). The version used here has been modified by the inclusion of a water balance.
The model of the Zymotis packed-bed must account for heat transfer in two directions in the substrate bed: (1) the direction that is co-linear with the air flow, which causes convective and evaporative heat removal; and (2) the horizontal conduction to the cooling plates, which is normal to the direction of the air flow. Typically front-to-back gradients will be negligible (Fig. 24.9).
In this model the same growth kinetic equations are used as described by Eqs. (22.1), (22.2), and (22.3) (see Sect. 22.2). The solids and gas phases are assumed to remain in thermal and moisture equilibrium with one another. In other words, the gas phase remains saturated at the temperature of the bed. The differential term dHsJdT in the energy balance is given by Eq. (19.20) (see Sect. 19.4.1).
The parameter values used in the base-case simulation are the same as those given in Table 24.1 for the traditional packed-bed. There are several extra parameters that do not appear in that model, all of which are associated with the heat transfer plates. The spacing between plates (L) was varied, the overall heat transfer coefficient for heat transfer from the edge of the substrate bed across the plate wall to the cooling water (h) was taken as 95 W m-2 °C-1 a value that is typical of heat exchangers and, finally, the cooling water temperature (Tw) was set at 38°C in various simulations and varied according to a control scheme in others.
24.3.2 Insights into Optimal Design and Operation of Zymotis Packed-Beds
The model can be used to explore the effect of operating conditions on bioreactor performance. Simulations will not be shown for the effects of superficial air velocity, inlet air temperature, or bioreactor height. The general principles are the same as for the traditional packed-bed discussed in Sect. 24.2, although the effects are not exactly the same, because of the extra heat removal by the heat transfer plates. These parameters are therefore discussed generally, without new simulations being done. Readers with greater interest are encouraged to consult Mitchell and von Meien (2000) and also to use the simulation program provided to explore the performance of Zymotis packed-bed bioreactors in more detail.
After this, the effects of the new design and operating variables introduced by the internal heat transfer plates, namely the spacing between the plates and the temperature of the cooling water, are explored.
General principles (overall trends). The model predictions in Fig. 24.10(a)). show clearly the temperature gradients vertically through the bed (i.e., parallel to the direction of air flow) and horizontally (i.e., normal to the direction of air flow). Figure 24.10(b) compares the central axis temperatures for the Zymotis bioreactor and a traditional packed-bed that is wide enough for heat removal through the side walls to be negligible. The comparison is done for the same microorganism, that is, in both cases novt is set at 0.236 h-1, and for the same operating conditions. Along the central axis of the bioreactor, due to the greater heat removal rate in the Zymotis bioreactor, the temperature does not reach such high values in the top half of the bioreactor, although the performance is reasonably similar in the bottom half. Note, however, that for the Zymotis bioreactor the curve represents only the central axis temperature, while for the traditional packed-bed it represents the temperature at all radial positions for that height. In the Zymotis packed-bed the remainder of the bed is cooler than the central axis at the corresponding height, and therefore growth is correspondingly better.
gradients in this direction assumed negligible
surface in contact with cooling plate x = 0
(b) energy storage, due to temperature change in the bed dx
axial convection and evaporation x =l dT"-
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