Page 314 - Chemical Process Equipment - Selection and Design

278 DRYERS AND COOLING TOWERS

TABLE 9.19. Product Numbers and Performance of a 30 X Both forms of the integral are employed in the literature to define
29 in. Pilot Plant Spray Dryer the number of transfer units. The relation between them is
(a) Product Numbers of Selected Materials k,,,Z/G = (L/G)(NTU). (9.27)
Material Product number The height of a transfer unit is
HTU = Z/(NTU) = L/km = (L/G)(G/k,). (9.28)
1. COLOURS
Reactive dyes 5- 6 The quantity G/km sometimes is called the height of a transfer unit
Pigments 5-11 expressed in terms of enthalpy driving force, as in Figure 9.16, for
Dispersed dyes 16-26 example:
2. FOODSTUFFS G/k, = (G/L)(HTU). (9.29)
Carbohydrates 14-20
Milk 17 Integration of Eq. (9.21) provides the enthalpy balance around
Proteins 16-28 one end of the tower,

3. PHARh4ACEUTICALS L(T - TI) + G(h - hl). (9.30)
Blood insoluble/soluble 11-22
Hydroxide gels 6-10 Combining Eqs. (9.22) and (9.23) relates the saturation enthalpy
Riboflavin 15 and temperature,
Tannin 16-20
h, = h + (k,/kh)(T - T,). (9.31)
4. RESINS
Acrylics 10-11
Formaldehyde resin 18-28 In Figure 9.15(c), Eq. (9.31) is represented by the line sloping
Polystyrene 12-15 upwards to the left. The few data that apparently exist suggest that
the coefficient ratio is a comparatively large number. In the absence
5. CERAMICS of information to the contrary, the ratio commonly is taken infinite,
Alumina 11-15 which leads to the conclusion that the liquid film resistance is
Ceramic colours 10 negligible and that the interface is at the bulk temperature of the
water. For a given value of T, therefore, the value of h, in Eq.
(Bowen Engineering Inc.). (9.25) is found from the equilibrium relation (hs, T,) of water and
the corresponding value of h from the balance Eq. (9.30). When the
coefficient ratio is finite, a more involved approach is needed to find
the integrand which will be described.
The equilibrium relation between T, and h, is represented on
(b) Performance of the Pilot Unit as a Function of Product the psychrometric charts Figures 9.1 and 9.2, but an analytical
Numbera representation also is convenient. From Section 9.1,

h, = 0.24T, + (18/29)(0.45T, + 11OO)[p,/(l -ps)], (9.32)
3200
3000 where the vapor pressure is represented by
2800
ps = exp[11.9176 - 7173.9/(T, + 389.5)]. (9.33)
2600
2400 Over the limited ranges of temperature that normally prevail in
cooling towers a quadratic fit to the data,
2200
BTU, LB.
EVAPN h, = a + bT, + CT?
2000
1900 may be adequate. Then an analytical integration becomes possible
1800 for the case of infinite k,,,/kh. This is done by Foust et al. (1980) for
example.
1700
The Cooling Tower Institute (1967) standardized their work in
terms of a Chebyshev numerical integration of Eq. (9.25). In this
100 method, integrands are evaluated at four temperatures in the
80 interval, namely,
60
LBIHR T, + 0. l(Tz - Tl), corresponding integrand ZI,
EVAPN
40 T, + 0.4(T, - TI), corresponding integrand Z,,
30 (9.34)
TI - 0.4(Tz - TI), corresponding integrand Z3,
20
T, - O.l(T, - T,), corresponding integrand Z4.
PRODUCT NUMBER (DRYING EFFECTIVENESS)
Then the integral is
"Example: For a material with product number=lO and air inlet
temperature of 500°F. the evaporation rate is 53Ib/hr, input Btu/lb
evaporated = 1930, and the air outlet temperature is 180°F. = 0.25( T, - TI)(Zl + Z, + Z3 + Z4). (9.35)
(Bowen Engineering). q hs-h