Page 132 - Chemical process engineering design and economics

116 Chapters

K 2li YU
Z Y2v,i = I ————————————— = 1 (3.3.37)

When Equation 3.3.36 is subtracted from Equation 3.3.37, the final flash
equation is

(K 2 ; i -l)yu
Z ————————————— = 0 (3.3.38)
(Ky-l)(mzv/mi) +1
According to King [22], Equation 3.3.38 is mathematically well behaved.
The equation has no spurious roots and maximum or minimum. Also, the fraction
of liquid vaporized, m 2jv/nii, varies between 0 to 1 and is linear.
Similarly, we can also reduce the energy equation for Q = 0, Equation 3.3.5,
to a more usable form. First, divide Equation 3.3.5 by ni| to obtain Equation
3.3.39.

m 2V m 2L
h 2V —— + h 2L ——— h, = 0 (3.3.39)

The enthaply of the vapor phase,

h 2V = Z y2v,i h 2V, i (3.3.40)
and the enthalpy of the liquid phase,

ih 2Lji (3.3.41)
After subsituting Equation 3.3.35 into Equation 3.3.40 and Equation 3.3.34
into 3.3.41,

= Z ————————————— h 2V,i (3.3.42)
h 2v
(Ky-lMmzv/mO+l
and
yi,i
= Z ————————————— (3.3.43)
h 2L h 2Lji

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