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Finding the Minimum Reflux Ratio Using the Underwood Equations
Finding the Minimum Reflux Ratio Using the Underwood Equations
Consider a distillation column with a partial reboiler and a total condenser. This column is used to separate three hypothetical components , , and with relative volatilities and (i.e., the reference component is ) to be determined by the user. The calculation assumes that the reference component is the intermediate-boiling component, , and that the lightest and heaviest components are and , respectively. The feed to the column has a thermal quality, , also determined by the user. The feed composition is 40 mole% , 30 mole% , and 30 mole% . The fractional recoveries in the distillate of components and are 98% and 95%, respectively. The fractional recovery in the bottom of component is 95%. The distillate rate, , can be computed from the equations and for , where stands for fractional recovery. One can use as a basis a feed flow rate equal to 100 kmol/hr. In such a case, the distillate rate kmol/hr. The Demonstration applies the Underwood equations [1] in order to determine the minimum reflux ratio, .
A
1
A
2
A
3
α
12
α
32
A
2
A
2
A
1
A
3
q
A
1
A
2
A
3
A
1
A
2
A
3
D
D=D
N
c
∑
i=1
x
i,dist
D=F
x
i,dist
dist
FR
i
z
i
i=1,2,3
FR
D=69.92
R
min
The first and second Underwood equations are:
F(1-q)=F-ϕ
N
c
∑
i=1
α
i
z
i
α
i
V
min
N
c
∑
i=1
α
i
x
i,dist
α
i
The relevant root (between and 1) of the first Underwood equation is shown by the blue dot in the figure. The red curve is a plot of the function
α
32
f(ϕ)=-ϕ-(1-q)
N
c
∑
i=1
α
i
z
i
α
i
Finally, the green region indicates where the appropriate root, , of the first Underwood equation is expected.
ϕ