Page 120 - Chemical process engineering design and economics

104 Chapters

tl2,2 = f(t2) (3.2.17)
h, = f(t 3') (3.2.18)

h 4 = f(t 4) (3.2.19)
Economic Relations

t 4 - t wl' = 9.0 °F (3.2.20)

m 3' / m, = 2.09 Ibmol water/lbmol air (3.2.21)
Variables

Vi,i - Yi,2 - Y2,i - Yz,2 - Yiw- in] - m 2 - rat - p lw - p 2>is - Ah vw - hj - h 2 - h 3 - h 4 - h (il - h 1]2 -
h 2,i - h 2, 2 - t 2 - t 4
Degrees of Freedom

F = 21-21=0

tions 3.2.15 and 3.2.17). Equations 3.2.18 and 3.2.19 give the enthalpies for pure
water.
Finally, Table 3.2.1 contains two economic relations or rules-of-thumb.
Equation 3.2.20 states that the approach temperature differences for the water,
which is the difference between the exit water temperature and the wet-bulb tem-
perature of the inlet air, is 5.0 °C (9 °F). The wet-bulb temperature of the surround-
ing air is the lowest water temperature achievable by evaporation. Usually, the
approach temperature difference is between 4.0 and 8.0 °C. The smaller the ap-
proach temperature difference, the larger the cooling tower, and hence the more it
will cost. This increased tower cost must be balanced against the economic bene-
fits of colder water. These are: a reduction in the water flow rate for process cool-
ing and in the size of heat exchangers for the plant because of an increase in the
log-mean-temperature driving force. The other rule-of-thumb, Equation 3.2.21,
states that the optimum mass ratio of the water-to-air flow rates is usually between
0.75 to 1.5 for mechanical-draft towers [14].
As before, prime all the known variables in the equations listed in Table
3.2.1. The table shows that there are twenty-one unknowns and equations, result-
ing in zero degrees of freedom. Thus, we have completely defined the problem.
Before obtaining numerical answers, we must derive equations for the func-
tional relationships expressed in Table 3.2.1, which are given in Table 3.2.2. Equa-
tion 3.2.27 is the psychrometric relation, derived by Bird et al. (3.15). This relation

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