Page 317 - Chemical Process Equipment - Selection and Design

9.12. COOLING TOWERS

EXAMPLE 9.11 or
Sizing of :a Cooliing Tower: Number of Transfer Units and
Height of ]Packing HTU = 5.51(L/G)0.s9.
Water is to be cooled from 110 to 75°F by contact with air that
enters countercurrently at 90°F with a dewpoint of 60°F. The data of Tower height:
London et al. i(1940) of Figure 9.16 for height of transfer unit are
applicable. Calculations will be made for two values of the Z = (HTU)(NTU).
coefficient ratio k,/k,, namely, 25 and ~0 Btu/("F) (lb dry air), of
Eq. (9.31). Tkx effect of the ratio of liquid to gas rates, L/G, will For several values of L/G:
be explored.
Ll G 0.6 I 1.4 1.7
HTU (ft) 4.08 5.51 6.72 7.54

Evaluation of interfacial temp and the WTU for L/G = 1 with
kJk, = 25:
T h T, l/&-b)
78.5 30.5 78.099 0.0864
89 41 88.517 0.0709
96 48 95.400 0.0575
106.5 58.5 105.581 0.0385
-
0.2533
Ts2 = 90 T, = 75 .'. NTU (110 - 75(0.2533)/4 = 2.217.
H = o.ola
h =27 For other values of L/G:
The maximum allowable L/G corresponds to equilibrium 1/(k - h)
between exit air and entering water at 110. The saturation enthalpy
at 110°F is 92, so that Eq. (9.30) becomes T h L/G=0.6 1 1.
78.5 30.5 0.0751 0.0864 0.0943 0.1043
'92 - 27 = 1.857. 89 41 0.0518 0.0709 0.1167 0.2200
max 110-75 96 48 0.0398 0.0575 0.1089 0.3120
106.5 58.5 0.0265 0.0385 0.0724 0.1987
--____
The several trials will be made at L/G = (0.6, 1.0, 1.4, 1.7). 0.1933 0.2533 0.3923 0.8350
The applicable equations with numerical substitutions are listed NTU + 1.691 2.217 3.433 7.306
here and incorporated in the computer program for solution of this
problem [Eqs. 1(9.30)-(9.33)] : With km/kh + m:
h = 27 + (L/G)(T - 75),
h3 = h + zqa - 75), ~ ~~
h, = 0.24T + (18/29)(0.45T + 1100)P,/(l- PSI, T h L/G=O.6 1 1.4 a .7
P, = exp[1:1.9176 - 7173.9/(q + 389.5)]. 78.5 30.5 0.0725 0.0807 0.90 0.1006
89 41 0.0494 0.0683 0.1107 0.2070
When km/kh+ 30, T, in Eq. (9.33) is replaced by T. 96 48 0.0376 0.0549 0.1020 0.2854
The four temperatures at which the integrands are evaluated 106.5 106.5 0.0248 0.0361 0.0663 0.1778
-___--
for the Chebyshev integration are found with Eq. (9.34) and 0.1844 0.2400 0.3700 0.7708
tabulated in the calculation summary following. NTU + 1.613 2.100 3.238 6.745
Equations (9.30) and (9.31) are solved simultaneously for h and 2- 6.58 11.57 21.76 50.86
h, with the aid of the Newton-Raphson method as used in the
computer program; the integrands are evaluated and the integration
are completed with Eq. (9.35).
The number of transfer units is sensitive to the value of L/G,
but the effect of kJk, is more modest, at least over the high range
used; data for this ratio do not appear to be prominently recorded.
Figure 9.16 shows a wide range of heights of transfer units for the
different kinds of packings, here characterized by the surface ad
(sqft/cuft) and substantial variation with L/G. The last line of the
cdculation summary shows variation of the tower height with L/G.
Data of Lmdon et al. (1940) of Figure 9.16:
(G/L)(HTU) = 5.51(G/L)0.41