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4.7 A single equilibrium stage in a distillation column isshown in Fig. E4.7. The model that describes this stage isdtdHx1RA+44 +44 +a,Assume that the molar holdup H in the stage is constantand that constant molal overflow occurs. Thus, Li-L andV. =リ.(a) Linearize the resulting model and introduce deviationvariables.(b) For constant liquid and vapor flow rates, derive the fourtransfer functions relating outputs x and y, to inputs x andy2. Place it in standard form.0xoV1V.1Figure E4.7

Question
4.7 A single equilibrium stage in a distillation column is
shown in Fig. E4.7. The model that describes this stage is
dt
dHx1
RA
+44 +44 +a,
Assume that the molar holdup H in the stage is constant
and that constant molal overflow occurs. Thus, Li-L and
V. =リ.
(a) Linearize the resulting model and introduce deviation
variables.
(b) For constant liquid and vapor flow rates, derive the four
transfer functions relating outputs x and y, to inputs x and
y2. Place it in standard form.
0
xo
V1
V.
1
Figure E4.7
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4.7 A single equilibrium stage in a distillation column is shown in Fig. E4.7. The model that describes this stage is dt dHx1 RA +44 +44 +a, Assume that the molar holdup H in the stage is constant and that constant molal overflow occurs. Thus, Li-L and V. =リ. (a) Linearize the resulting model and introduce deviation variables. (b) For constant liquid and vapor flow rates, derive the four transfer functions relating outputs x and y, to inputs x and y2. Place it in standard form. 0 xo V1 V. 1 Figure E4.7

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Step 1

Part (a)

Assume that the molar holdup (H) of the given stage is constant and the molar overflow which occurs is also constant. Therefore, Lo = L1 and V2 = V1. Thus, from the given first equation,

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Step 2

Now, apply this in the second given equation as shown below.

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Step 3

Apply Tylor series expansion on the given equation of y1 ...

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