Axial and Radial Temperature Gradients in Static Beds

The gas flow pattern within the bed of a packed-bed bioreactor that does not suffer from channeling problems is probably closest to plug flow with axial dispersion (see Fig. 4.6). However, studies have neither been done to confirm this nor to quantify the degree of axial dispersion. This plug-flow of the gas phase has implications for the operation of packed-beds. Firstly, the inlet end tends towards the inlet air temperature but, due to the lack of mixing and the unidirectional air flow, the temperature of the air increases as it flows along the bed towards the outlet end (Fig. 4.3(b)). One of the major challenges in designing and operating large-scale packed-beds will be to avoid excessive axial temperature gradients.

The increase in the temperature of the air as it flows through the bed increases the water-carrying capacity of the air and therefore evaporation will occur. Note that evaporation will occur even if saturated air is used at the air inlet (Fig. 4.3(c)).

In general, conduction along the axis in the direction of the air flow will be negligible compared to the convective and evaporative heat removal (Gutierrez-Rojas et al. 1996). The contribution of conduction normal to the direction of the air flow will depend on the design of the packed-bed. In traditional packed-beds that have diameters of the order of a few centimeters and in the Zymotis design, it can make a significant contribution, and there can be significant temperature gradients normal to the air flow. In contrast, in large-scale packed-beds, which might typically have diameters of the order of 1 m or more, the amount of energy removed from the bed by transfer through the side walls is likely to be small, even if the bed is water-jacketed. Various studies have been done that show how the appearance of axial and radial temperature gradients depends on the design and operation of the bioreactor. These are described below.

Temperature gradients in thin bioreactors. Saucedo-Castaneda et al. (1990) used a bioreactor of 6 cm diameter, containing a bed 35 cm high. Further, the column was immersed in a constant temperature waterbath at 35°C. They noted a steep temperature gradient in the first 5 cm along the axis of the bed, where the temperature increased by up to 12°C (Fig. 7.6). In contrast, in the upper 30 cm of the bed, the maximum increase in temperature along the axis was approximately 3°C. Note that, at some times and in some regions, the temperature actually decreased with axial distance, which might be related to evaporative cooling. However, Saucedo-Castaneda et al. (1990) did not measure water contents in the bed, so it is not possible to confirm this. The axial temperature in the upper 30 cm of the column did not remain constant; rather it increased with time over the period of 15 to 26 h. In contrast to the axial temperature gradients, the radial gradients were quite steep: at the time of peak heat production, there was an 11°C difference between the central axis and the bioreactor wall, which represents a distance of only 3 cm. These results suggest that in the case of thin bioreactors a significant amount of heat is removed through the side walls.

radial position (cm)

Fig. 7.6. Radial and axial temperature gradients at various times within a thin packed-bed bioreactor when Aspergillus niger was cultivated on cassava chips (Saucedo-Castaneda et al. 1990). The radial temperature gradient was determined at approximately mid-height in the bed. The superficial velocity of the air was 1 cm s-1. Adapted from Saucedo-Castaneda et al. (1990) with kind permission from John Wiley & Sons, Inc.

radial position (cm)

Fig. 7.6. Radial and axial temperature gradients at various times within a thin packed-bed bioreactor when Aspergillus niger was cultivated on cassava chips (Saucedo-Castaneda et al. 1990). The radial temperature gradient was determined at approximately mid-height in the bed. The superficial velocity of the air was 1 cm s-1. Adapted from Saucedo-Castaneda et al. (1990) with kind permission from John Wiley & Sons, Inc.

Temperature gradients in wide or insulated bioreactors. The studies of Ghild-yal et al. (1994), Gowthaman et al. (1993a, 1993b), and Weber et al. (2002) allow insights into heat transfer in wider bioreactors. The bioreactor of Ghildyal et al. (1994) and Gowthaman et al. (1993a, 1993b) was 15 cm in diameter with a 34.5 cm bed height, while that of Weber et al. (2002) was 20 cm in diameter with a 50 cm bed height. Note that the bioreactor of Weber et al. (2002) was insulated on the sides, in order to mimic the situation at large scale where heat transfer through the walls makes a negligible contribution to heat removal. Note also that different organisms were used in the various studies, with quite different optimal temperatures for growth, so the actual temperatures involved are quite different.

Weber et al. (2002) measured the temperature as a function of time at various axial positions (Fig. 7.7(a)). At all heights, there was a temperature peak, whose maximum value occurred around day 4, with the height of the peak (that is, the maximum temperature reached) increasing with bed height.

Ghildyal et al. (1994) presented results that show the effect of the aeration rate on the axial temperature profile. Three different experiments were done, with air flow rates of 5 L min-1, 15 L min-1, and 25 L min-1. The temperature was monitored at the central axis at mid-height in the bed. The height of the temperature peak increased as the air flow rate was decreased (Fig. 7.7(c)). They interpolated their data points to obtain a three-dimensional graph of the peak temperature obtained as a function of both bed height and air velocity (Fig 7.7(d)). In general terms, the temperature appears to increase linearly with increase in bed height and also to increase linearly with decrease in the air flow rate, except at the lowest bed height, where the peak temperature first increased only slowly as the air flow rate was decreased, but then shot up steeply at low air flow rates.

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