2.6.1 Space Time

The space time tau, τ, is obtained by dividing the reactor volume by the volumetric flow rate entering the reactor:

2-26

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τ is an important quantity!

The space time is the time necessary to process one reactor volume of fluid based on entrance conditions. For example, consider the tubular reactor shown in Figure 2-12, which is 20 m long and 0.2 m3 in volume. The dashed line in Figure 2-12 represents 0.2 m3 of fluid directly upstream of the reactor. The time it takes for this fluid to enter the reactor completely is called the space time tau. It is also called the holding time or mean residence time.

Space time or mean residence time τ = V/υ0

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Figure 2-12. Tubular reactor showing identical volume upstream.

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For example, if the reactor volume is 0.2 m3 and the inlet volumetric flow rate is 0.01 m3/s, it would take the upstream equivalent reactor volume (V = 0.2 m3) shown by the dashed lines a time τ equal to

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to enter the reactor (V = 0.2 m3). In other words, it would take 20 s for the fluid molecules at point a to move to point b, which corresponds to a space time of 20 s.

In the absence of plug flow, the space time is equal to the mean residence time in the reactor, tm (see Chapter 13 from the fourth edition of Elements of Chemical Reaction Engineering now on the DVD-ROM). This time is the average time the molecules spend in the reactor. A range of typical processing times in terms of the space time (residence time) for industrial reactors is shown in Table 2-4.

Table 2-4. Typical Space Time for Industrial Reactors*

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* Trambouze, Landeghem, and Wauquier, Chemical Reactors (Paris: Editions Technip, 1988; Houston: Gulf Publishing Company, 1988), p. 154.

Practical Guidelines

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The space times for a number of industrial reactions are given on the Professional Reference Shelf R2.2 on the DVD-ROM/Web.

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