Info

Headspace

Bed

sl al vr position of the front at equal time intervals^

Headspace

Bed plug-flow with axial dispersion m well-mixed plug-flow with axial dispersion m well-mixed

time after pulse introduced at the air inlet

Ideal plug flow: equal to the shape of the signal at the air inlet (same number of seconds width on the x-axis)

time after pulse introduced at the air inlet

Fig 4.6. Gas flow patterns in bioreactors. (a) Ideal plug-flow (b) Plug-flow with axial dispersion. In both cases the movement of a front through the bioreactor is indicated (i.e., if it were possible at the air inlet to add a thin "plug" of tracer molecules across the whole cross-section). Examples are shown where air is forced through a static bed (Group II bioreactors) and through a headspace (Group III bioreactors). (c) Residence time distribution patterns for (—) ideal plug-flow, (■ ■ ■) plug-flow with axial dispersion, and (---) a well-mixed system. Note that the inlet pulse is the same for all cases (the areas under the curves are equal)

across the bed due to the tortuous flow path

Fig. 4.7. The phenomenon of pressure drop. (a) Flow of air through an empty column. (b) Flow of air through a substrate bed constituted by small particles. In each case the diagram on the left is a schematic representation of the system and indicates the velocity profile (normal to the direction of air flow); the diagram in the middle shows a magnification of the microscale, highlighting the energy loss due to viscous interactions between successive air layers; the diagram on the right shows the pressure as a function of axial position within the bed (the diagram is reproduced in the same orientation as the bioreactor/column in the diagram on the left)

across the bed due to the tortuous flow path

Fig. 4.7. The phenomenon of pressure drop. (a) Flow of air through an empty column. (b) Flow of air through a substrate bed constituted by small particles. In each case the diagram on the left is a schematic representation of the system and indicates the velocity profile (normal to the direction of air flow); the diagram in the middle shows a magnification of the microscale, highlighting the energy loss due to viscous interactions between successive air layers; the diagram on the right shows the pressure as a function of axial position within the bed (the diagram is reproduced in the same orientation as the bioreactor/column in the diagram on the left)

If for some reason the resistance is not uniform, then air can follow preferential paths: a majority of the air may flow through low resistance regions while air may hardly flow through high resistance regions, meaning that in these areas O2 supply is limited to diffusion and heat removal is limited to conduction, the same situation as occurs in trays. This problem, called channeling, will be discussed in relation to packed-bed bioreactors in Chap. 7.

Due to these phenomena, one would expect laminar flow in a column without any filling, at least at the air flow rates typically used in packed beds, with each layer of air flowing at a different speed (Fig. 4.7(a)). There would be a parabolic velocity profile, with the flow rate being fastest at the center of the column and slowest near the wall. In fact the velocity is zero right at the wall, since a static boundary layer of gas molecules is absorbed to the wall. The situation is quite different when the column is packed with substrate particles. The air must pass through torturous pathways, with almost equal resistance across the whole column, which tends to even out the velocity profile across the bioreactor, such that the flow regime approaches plug flow.

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