The above applies for a differential section. Integrating over a packed bed H feet tall
which gives where
at rqq at c
A more detailed derivation which spells out the assumptions is gives elsewhere (87,112,113).
Number of transfer units (NTU). NTU is defined by Eq. (9.8). This is a measure of the difficulty of separation. Figure 9.16 illustrates thai concept. The NTU relates the change in bulk phase composition to tfc* average driving force.
Height of transfer unit (HTU). The height of a transfer unit is best defined from Eq. (9.7) as the height of packing which gives a change composition equivalent to one transfer unit. It is therefore a dirad measure of column efficiency.
Analogy to tray columns. In concept, the NTU is analogous to the number of theoretical stages in a trayed column. It only depends on the equilibrium and component balance curves (Fig. 9.16) and is unaffected by the mode of contact. The main difference between NTU and number of theoretical stages is that NTU is a measure of the separation difficulty best related to a continuous contactor, while the number of theoretical stages is a measure of separation difficulty more useful for a stage-by-stage contactor. In a similar manner, the HTU is analogous to the inverse of tray efficiency.
The concept of HETP (height equivalent of a theoretical plate) was introduced to enable comparison of efficiency between packed and plate columns. HETP is defined as
A similar HETP value can be obtained for a plate column if the tray spacing is known
Relationship between HTU and HETP. The relationship between HETP and HTU has been shown to be (111,113,114)
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