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14-88 EQUIPMENT FOR DISTILLATION, GAS ABSORPTION, PHASE DISPERSION, AND PHASE SEPARATION
FIG. 14-84 Cost of towers including installation and auxiliaries. To convert
inches to millimeters, multiply by 25.4; to convert feet to meters, multiply by
0.305; and to convert dollars per foot to dollars per meter, multiply by 3.28.
(Peters and Timmerhaus, Plant Design and Economics for Chemical Engineers,
4th ed., McGraw-Hill, New York, 1991.)
However, droplet systems can enable much higher energy input
(via gas phase pressure drop in cocurrent systems) and, as a result,
dominate applications where a quick quench is needed. See Examples
21 and 22. Conversely, droplet systems can also be designed for very
low pressure drop which is advantageous in applications such as vacuum
condensers.
Unstable Systems: Froths and Hollow Cone Atomizing
Nozzles We usually think of interfacial contact as a steady-state
system of raining droplets or rising bubbles, but some of the most efficient
interfacial contactors take advantage of unstable interfacial
geometry. The most common is the distillation tray which operates
with a wild mix of bubbles, jets, films, and droplets. The mix is often
described as froth. Gas pressure drop provides the energy to create
the froth.
A variant on the froth contact is the reverse jet contactor (Example
22), which can be considered as an upside-down distillation tray, operated
above the flooding velocity in cocurrent flow of gas and liquid. It
is limited to one stage.
An entirely different unstable contactor involves the thin expanding
liquid film produced by a hollow cone spray nozzle. Because of fresh surface
and the thinness of the film, this can give very high transfer for liquid-limited
systems. Two applications are direct contact condensation
and removal of volatile components from a high-boiling residual liquid.
Surface Tension Makes Liquid Sheets and Liquid Columns
Unstable Surface tension is the energy required to make an increment
of interfacial surface. A sheet or column of liquid has more surface
than a sphere, hence surface tension converts sheets and columns
to droplets. See Fig. 14-86.
There are many different atomizers, but the underlying principle of
all is the same—to first generate a flat sheet or a liquid column. Liquid
sheets and columns are unstable, a small surface disturbance on either
will propagate, and the liquid will reshape itself into droplets. The key
property in controlling this process is surface tension. Surface tension
gets a high exponent in all the atomization correlations.
Little Droplets and Bubbles vs. Big Droplets and Bubbles—
Coalescence vs. Breakup When big drops are subjected to shear
forces, as in falling rain, the droplets are distorted; and if the distor-
tions are great enough, the big droplets break into little ones. This is
why raindrops never exceed a certain size. A variant on this is breakup
in highly turbulent systems such as in high-velocity quench systems or
pneumatic nozzles. Here the droplets are distorted by the energy of
the turbulent eddies.
But little droplets and bubbles have more surface per unit of liquid
than big ones. Hence little droplets tend to coalesce into big ones, and
will grow in size if given enough quiet time.
While the primary difficulty is estimating the interfacial area due to
the unstable interface, a secondary problem is that freshly made,
unstable surface gives higher transfer than older, more stable surface.
Empirical Design Tempered by Operating Data The net of
these is that interfacial area is difficult to predict and interfacial contactors
are difficult to design.
Prediction methods are given below but should always be tempered
by operating experience.
INTERFACIAL AREA—IMPACT OF DROPLET
OR BUBBLE SIZE
Transfer is aided by increased interfacial area. Interfacial area per unit
volume aD of a single droplet or bubble is inversely proportional to the
diameter of the droplet or bubble D.
aD = 6/D (14-177)
To estimate the total interfacial area in a given volume, the ad value is
multiplied by the fractional holdup of dispersed phase in the total
volume.
a = aD(ΦD) (14-178)
where a = interfacial area/volume and ΦD = fraction of volume in dispersed
phase = holdup. Fractional holdup in a continuous process
depends on the velocities of the two phases, as if they were flowing by
themselves.
ΦD = (dispersed phase volume)/(volume of dispersed and
continuous phases)
Example 14: Interfacial Area for Droplets/Gas in Cocurrent
Flow For equal mass flow of gas and liquid and with gas density 0.001 of liquid
density, the gas velocity in cocurrent flow will be 1000 times the liquid velocity.
This sets Φ D.
ΦD = 1/(1 + 1000) = 0.00099
If the droplets are 500 µm in diameter, Eqs. (14-177) and (14-178) give
a = (6/0.0005)(0.00099) = 12 m2 /m3 If the droplets are 100 µm in diameter, Eqs. (14-177) and (14-178) give
a = (6/0.0001)(0.00099) = 60 m2 /m3 Example 15: Interfacial Area for Droplets Falling in a Vessel
Droplet systems rarely exceed a ΦD value of 0.01. At this low level, ΦD in a lowvelocity
countercurrent contactor can be approximated by Eq. (14-179).
ΦD = UL/(Ut − UG) (14-179)
where UL = liquid superficial velocity
Ut = terminal velocity of droplet
UG = gas superficial velocity
With a gas superficial velocity of 1.5 m/s, for equal mass flow of gas and liquid,
with gas density 0.001 of liquid density, and with 500-µm-diameter droplets
falling at a terminal settling of 2.5 m/s, Eq. (14-179) gives a fractional holdup of
liquid of
ΦD = (0.001)1.5/(2.5 − 1.5) = 0.0015
Equations (14-177) and (14-178) then give
a = (6/0.0005)(0.0015) = 18 m 2 /m 3
Example 16: Interfacial Area for Bubbles Rising in a Vessel
For bubble systems (gases dispersed in liquids) fractional holdup can approach
0.5 as shown by Fig. 14-104. However, before reaching this holdup, the bubble
systems shift to an unstable mix of bubbles and vapor jets. Hence an exact