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190 Applied Process Design for Chemical and Petrochemical Plants

This represents the fraction of the total available head R volume fraction of phase, dimensionless
between points A and B, which represents the sensible x weight fraction of vapor or gas (quality),
heating zone. This neglects liquid friction in the sensi- dimensionless
ble zone and assumes the liquid level in the distillation X tt correlating parameter, dimensionless, for Figure
column is maintained even with the top of the 10-113
tubesheet. Equation 10-170 then gives the fractional Z vertical height, ft
Z vertical distance in which two-phase flow occurs, ft
tube length devoted to sensible heating. Refer to Figure

parameter for two-phase flow, dimensionless
10-110 and note that:
( t/ p) s slope of vapor pressure curve
CD tube length for vaporization (Figure 10-110)
2
p B total pressure at point B in flow loop, lb/in (abs);
D point D in flow loop (Figure 10-110)
(point at entrance to vertical reboiler) f Force
2
p A total pressure at point A in flow loop, lb/in (abs)
fh heating medium fouling
(liquid level in distillation column bottoms) s saturated
2
p total pressure, lb/in (abs)
tp two-phase mixture
Z vertical height, ft T total flow
g gravitational constant, 32.2 ft/sec 2 v vaporization
2
g c conversion factor, 32.2 (lb) m (ft)/(lb) f (sec )
w tube wall
3.1416 2
a cross-sectional area, ft
D i I.D. of tube, ft 2
A total (inside) surface for heat transfer, ft
N t number of tubes
c specific heat, Btu/(lb) (°F)
t w temperature of tube wall, °F
d differential operator
t l temperature of liquid phase, °F
f fanning friction factor, dimensionless
W T mass rate, total flow, lb m /sec
F friction loss, (ft) (lb f )/lb m
c l specific-heat, liquid phase, Btu/lb (°F) g c conversion factor, 32.2 (lb m ) (ft)/(lb f ) (sec )
2
2
h l heat transfer coefficient, liquid phase, Btu/hr-ft -°F
L equivalent length of pipe, ft
x E weight fraction of vapor or gas (quality), dimension-
q heat transfer rate, Btu/hr
less at reboiler exit 2
r resistance to heat transfer, (hr) (ft ) (°F)/Btu
( t/ p) s slope of vapor pressure curve. This may be calculated
r composite resistance to heat transfer,
from Antoine type vapor pressure equation or obtain 2
(hr) (ft ) (°F)/Btu
from a plot. t temperature, °F
tp two-phase density lb m /ft 3
T absolute temperature, °R
2
U overall heat transfer coefficient, Btu/(hr) (ft ) (°F)
4. Obtain average values: V linear velocity, ft/sec
a. two-phase density, tp , at x E /3. x weight fraction of vapor or gas (quality),
b. pressure drop factor,
, at 2 x E /3. dimensionless
X tt correlating parameter, dimensionless
where
tp two-phase density, lb m /ft 3 Greek letters
R g volume fraction of phase, dimensionless, gas phase correction factor for nucleate boiling, dimensionless
R L 1 R g ; volume fraction of phase, dimensionless, correction factor for convective transfer,
liquid phase dimensionless
tp g R g L R L acceleration loss group (Equation 10-169),
t overall temperature difference, °F dimensionless
p pressure loss, lb/in 2 P pressure loss, lb f /ft 2
P pressure loss, lb/ft 2 t overall temperature difference, °F
2
p total pressure, lb/in abs.
latent heat of vaporization, Btu/lb m
2
P total pressure, lb/ft abs. viscosity, lb m /(ft) (hr)
L equivalent length of pipe, ft constant, 3.1416 . . .
BC tube length for sensible heating, Figure 10-110, ft density, lb m /ft 3
CD tube length for vaporization, ft, Figure 10-110 _ 3
average density, lb m /ft
2
G mass velocity, lb/(sec) (ft ) surface tension, lb f /ft
_
D i I.D. of tube, ft
average value of
2
G t mass velocity in tube, lb/(sec) (ft of cross-section) parameter for two-phase physical properties,
F B-C Friction loss from part B to part C in tubes, feet dimensionless
liquid
g gravitational constant, 32.2 ft/(sec) (sec) Subscripts
2
k thermal conductivity, Btu/(hr) (ft ) (°F/ft) BC tube length for sensible heating (Figure 10-110)
viscosity, lb/(ft)(hr) C point C in flow loop (Figure 10-110)