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Separator Design 281

From Newton's law for the gravitation force, Archimedes principle for the
buoyant force, and the definition of the drag force, the force balance on a drop
becomes

Pv PL v v
m Lg = m L — g + C D A L —— (6.10)
PL 2g
where: m^ is the mass of a drop, g the acceleration of gravity, p the density of ei-
ther liquid or vapor, C D the drag coefficient, A L the projected area of a drop, and
v v, the maximum vapor velocity.

Solving for the maximum vapor velocity, we find that

v v = l ————— I ————— (6.11)
I C D A L p L ) \. p v )

Equation 6.11 does not accurately describe the physical situation. In prac-
tice, what is done is to set the coefficient of Equation 6.11 equal to ky so that

I ————— I (6.12)
v v = k v
I Pv >/
where k is an empirical constant that depends on the properties of the fluids, the
v
design of the separator, the size of the drops, the vapor velocity, and the degree of
separation required.

Knock-Out Drums

Knock-out drums, used when the liquid content of the incoming stream is low, is a
special case of a gas-liquid separator. The drum is placed before a compressor
inlet to prevent liquid drops from entering and damaging the compressor. In this
case, allowing a sufficient residence time for the liquid is not a consideration.
To determine the length and diameter of knock-out drums, Younger [11]
recommends using a value of k v of 0.2 ft/s (0.01 m/s) without a mist eliminator or
35 ft/s (0.107 m/s) with a mist eliminator, and an L/D ratio of 2. A calculation
procedure for solving the equations listed in Table 6.7, is given in Table 6.8. The

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