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rate of conduction (a temperature 'gradient)

rate of conduction (a temperature 'gradient)

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Fig. 5.1. The temperature in the local environment of the organism depends on the balance between heat generation and heat removal. This example is given in the context of a fermentation carried out within a tray, where the main heat removal mechanism in the bed is conduction. The "local environment" of interest is at mid-height in the bed. (a) Whether the temperature in the local environment remains constant, increases or decreases depends on the balance between the rate of metabolic heat production (which is proportional to the growth rate) and the rate of heat removal by conduction to the bed surface (which is proportional to the temperature gradient across the substrate bed). (b) Due to the change in the rate of production of waste metabolic heat as the growth rate changes, the temperature in the local environment changes over time. During early growth the rate of waste heat production increases. This causes the temperature to increase until the rate of heat removal once again equals the rate of heat production. However, since growth continues to accelerate, the rate of heat production continues to rise, so the local temperature must continue to rise in order to continue to increase heat removal. Later during growth, as the growth rate and therefore the rate of heat production decreases, the local temperature decreases o c time middle height top

Fig. 5.1. The temperature in the local environment of the organism depends on the balance between heat generation and heat removal. This example is given in the context of a fermentation carried out within a tray, where the main heat removal mechanism in the bed is conduction. The "local environment" of interest is at mid-height in the bed. (a) Whether the temperature in the local environment remains constant, increases or decreases depends on the balance between the rate of metabolic heat production (which is proportional to the growth rate) and the rate of heat removal by conduction to the bed surface (which is proportional to the temperature gradient across the substrate bed). (b) Due to the change in the rate of production of waste metabolic heat as the growth rate changes, the temperature in the local environment changes over time. During early growth the rate of waste heat production increases. This causes the temperature to increase until the rate of heat removal once again equals the rate of heat production. However, since growth continues to accelerate, the rate of heat production continues to rise, so the local temperature must continue to rise in order to continue to increase heat removal. Later during growth, as the growth rate and therefore the rate of heat production decreases, the local temperature decreases

So the basic question that we need to answer in order to understand the scale-up problem has become: "What is the effect of scale on the ability of the transport processes to remove heat at a rate that is sufficient to prevent local temperatures from reaching values that limit growth?" The effect of scale on the effectiveness of transport phenomena will be discussed here in relation to convective and conductive heat removal in static beds. With respect to solids mixing phenomena, suffice to say that the effectiveness of mixing tends to decrease as scale increases.

Figure 5.2 illustrates the problem, using a packed-bed bioreactor as an example. As explained in Fig. 4.3, the convective flow of air through a static bed in which an exothermic reaction is occurring leads to an increase in the bed temperature between the air inlet and the air outlet. For a given organism, one of the major factors affecting the slope of the temperature gradient in the bed is the air flow rate. A laboratory-scale bioreactor may operate with the temperature exceeding the optimum temperature for growth by only a few degrees. However, as scale increases, the deviations from the optimum temperature will be much greater, especially if the same volumetric flow rate is used. It is possible to try to combat these deviations by changing key operating variables as scale increases. For example, it might appear reasonable to maintain the superficial air velocity constant (the superficial air velocity being the volumetric air flow rate divided by the overall cross-section of the bioreactor). In the simplest case, this will maintain the same temperature gradient in the bioreactor. However, due to the greater height, the temperature in the upper region of the bioreactor will reach much higher values than those that were reached at laboratory scale (Fig. 5.2). One strategy might be to increase the superficial velocity of the air (VZ, m s-1) in direct proportion to the height (H, m) of the bioreactor (that is, to maintain VZ/H constant). This might in fact prevent the bed from ever exceeding the maximum temperature observed in the laboratory bioreactor, however, it might also lead to unacceptably high pressure drops, or the required air velocity might fluidize the bed.

The problem is more severe in the cases where significant amounts of heat are removed from the bed at small scale by conduction, such as in a tray bioreactor, or within a packed-bed bioreactor with a cooled surface. If geometric similarity is maintained, then the distance between the center of the bed and the surroundings or heat transfer surface increases with increase in scale. The effectiveness of conduction in removing heat decreases in proportion to the square of the distance over which conduction must occur. Therefore, maintaining geometric similarity will decrease the relative contribution of conductive heat removal. In fact, it is desirable to maintain the "conduction distances" constant as scale increases. For this reason tray bioreactors are scaled-up by increasing the number of trays, and not the thickness of the substrate layer within the tray. Likewise, as will be seen in Chaps. 7 and 23, it may be interesting for large-scale packed beds to have internal heat transfer plates arranged such that the large-scale version has the same "conduction distances" as a laboratory-scale bioreactor.

In general, as a bioreactor is scaled-up from the laboratory to production scale, it is not a simple matter to keep constant either VZ/H or the distance over which conduction must occur. As a consequence, the local conditions, at least in some

scale-up to a geometrically similar larger version

Fig. 5.2. Scale up on the principle of geometric similarity is not a simple matter. (a) Scale-up on the basis of geometric similarity. Both the radius and length have increased 10-fold. (b) Temperature profiles along the central axis that might be expected at the time of peak heat production. Key (—) Temperature profile in the small-scale bioreactor; (—) Temperature profiles that might be expected in the large-scale bioreactor for different strategies regarding the aeration rate, if the results with the small-scale bioreactor had been obtained under a condition where the side walls were insulated (i.e., with no heat removal by conduction though the side walls); (• • •) Temperature profiles that might be expected in the large-scale bioreactor for different strategies regarding the aeration rate, if the results with the small-scale bioreactor had been obtained under a condition where the side walls were not insulated and heat was removed by cooling water in a jacket or waterbath. The different strategies regarding the aeration rate are indicated directly on the figure

Fig. 5.2. Scale up on the principle of geometric similarity is not a simple matter. (a) Scale-up on the basis of geometric similarity. Both the radius and length have increased 10-fold. (b) Temperature profiles along the central axis that might be expected at the time of peak heat production. Key (—) Temperature profile in the small-scale bioreactor; (—) Temperature profiles that might be expected in the large-scale bioreactor for different strategies regarding the aeration rate, if the results with the small-scale bioreactor had been obtained under a condition where the side walls were insulated (i.e., with no heat removal by conduction though the side walls); (• • •) Temperature profiles that might be expected in the large-scale bioreactor for different strategies regarding the aeration rate, if the results with the small-scale bioreactor had been obtained under a condition where the side walls were not insulated and heat was removed by cooling water in a jacket or waterbath. The different strategies regarding the aeration rate are indicated directly on the figure regions of the bioreactor, will be less favorable for growth than those that the organism experienced at laboratory scale. The average volumetric productivity of the large-scale bioreactor (kg of product produced per cubic meter of bioreactor volume per hour) will then be smaller than the volumetric productivity achieved with the laboratory-scale bioreactor. The scale-up problem becomes more difficult when we realize that this discussion has not explored all the potential problems and complications. Some further considerations are:

• in mixed beds, the efficiency of mixing is likely to decrease with scale;

• in some beds both convection and conduction play important roles in heat removal. The optimum combination of these two mechanisms may change with scale. For example, in some cases conduction plays an important role in removal at small scale, but its contribution decreases as scale increases as the surface area to volume ratio of the bioreactor decreases;

• bioreactor design will affect the ease of substrate handling, and ease of substrate handling may be an important consideration in the economics of the process, especially in relation to the need for manual labor;

• pressure drop and fluidization considerations may put a limit on possible air flow rates;

• the sensitivity of the microorganism to damage by mixing may put a limit on the frequency with which the bed can be mixed;

• increases in bed heights may have side effects, such as the deformation of particles at the bottom of the bed, affecting inter-particle void fractions, or even crushing the particles.

Given this complexity, we are only likely to achieve the maximum possible efficiency in large-scale bioreactors if we understand the phenomena that combine to control bioreactor performance and if we use quantitative approaches to the scale-up problem.

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