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Fig. 24.3. Predicted growth profiles at different heights within the bed. The lines at the top of the graph represent the bottom of the bed. The lines at the bottom represent the top of the bed, which is much hotter and therefore causes growth to be slower. The dashed line at the left represents logistic growth with n=^(ptt throughout the growth phase. The darker solid line in the middle of the lighter lines represents the average biomass concentration in the bed t-1-r

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Fig. 24.3. Predicted growth profiles at different heights within the bed. The lines at the top of the graph represent the bottom of the bed. The lines at the bottom represent the top of the bed, which is much hotter and therefore causes growth to be slower. The dashed line at the left represents logistic growth with n=^(ptt throughout the growth phase. The darker solid line in the middle of the lighter lines represents the average biomass concentration in the bed

Note the similarity of the general appearance of Fig. 24.2(a) to the experimental results obtained by Weber et al. (2002) in Fig. 7.6(a). Of course, the temperatures and times are different because the organism simulated by the model is quite different from that which they used. One feature that is common to the two graphs is the lack of symmetry around the peak, that is, the decrease in temperature takes slightly longer than the initial rise in temperature.

As a result of the spatial temperature profiles, growth will occur at different rates in the different regions of the bed (Fig. 24.3).

24.2.3 Insights that Modeling Has Given into Optimal Design and Operation of Traditional Packed-Beds

Section 7.2 showed that the design and operational variables that can be manipulated for traditional packed-bed bioreactors are the inlet air temperature and flow rate, the presence of a water jacket and the temperature of the water in this jacket, and the height and width of the bioreactor. The model can be used to investigate the effect of some of these design and operating variables on bioreactor performance. It cannot describe the effect of the bioreactor width or of a water jacket since it does not describe heat removal by conduction normal to the direction of air flow.

In the simulations presented in this section, in which only the effect of temperature on growth is considered, the aim is to minimize temperature gradients in order to maintain the average temperature as close as possible to the optimum temperature for growth and product formation. The effects of bed height, aeration rate, and air temperature are interrelated, but, in the subsections that follow, one-at-a-time changes will be made in order to make the contribution of each individual variable clear.

Effect of inlet air temperature. The inlet air temperature can be reduced below the optimum for growth in order to combat the temperature rise that occurs within the bed. However, it is important not to maintain the air temperature at a constant low value during the fermentation. During the initial stages of the fermentation the air temperature must remain near the optimum in order not to retard the initial growth. Therefore, in the simulations shown in Fig. 24.4, a simple temperature control scheme was included in the model:

where K is a factor that determines by how much the temperature of the inlet air (Tin) is decreased for a given rise in the outlet air temperature (Tout) above the optimum temperature for growth (Topt).

This strategy causes the temperature in the bed to vary around the optimum for growth (Fig. 24.4(a)). At the time of maximum heat production, the axial temperature profile is actually steeper than for aeration with the inlet air at Topt: Fig. 24.4(a) shows a difference of almost 15°C between the air inlet and outlet, com pared to 10°C in Fig. 24.2(a). However, the maximum deviation from the optimum temperature for growth (38°C) is only 7.5°C, and the average deviation from Topt is also smaller, because the axial gradient straddles the optimum temperature. This leads to corresponding predictions of better growth (Fig. 24.4(b)).

Effect of inlet airflow rate. Doubling the airflow rate (i.e., increasing the superficial velocity of the air from 0.05 to 0.1 m s-1) in the absence of any control of the air temperature, the performance of the bioreactor is predicted to improve significantly. Increasing the air flow rate decreases the gradient of the axial temperature profile: the highest temperature reached decreases from 48°C (Fig. 24.2(a)) to 45°C (Fig. 24.5(a)) and, as a result, the growth profiles in the different regions of the bed are closer to the optimum profile (Fig. 24.5(b)).

No work has been done to investigate the upper limits on the superficial velocities that can be used in packed-bed bioreactors, and this model does not take pressure drops into account. Obviously, the higher the airflow rate, the greater the operating cost, not only because more air must be supplied, but also because the pressure drop is greater. Therefore an economic optimum will need to be found between improved packed-bed performance and increasing operating costs. The best strategy might be to increase the air flow rate only during the period of peak heat production. In this case fluidization of the particles in the bed will not be a problem, because the microorganism will bind the particles together before high air flow rates are used. However, it is possible for the pressure drop to be sufficiently high that the whole knitted bed is ejected from the bioreactor!

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