Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
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Chapter 4, Problem 4.6E

A stirred-tank blending system can be described by a first-order transfer function between the exitcomposition x and the inlet composition X 1 (both are mass fractions of solute):
   X ( s ) X i ( s ) = K τ s + 1
where K = 0.6 (dimensionless) and T = 10 min . When the blending system is at steady state ( x ¯ = 0.3 ) , thedynamic behavior is tested by quickly adding a large amount of a radioactive tracer, thus approximating animpulse function with magnitude 1.5.
a. Calculate the exit composition response x ( t ) using Laplace transforms and sketch x ( t ) . Based on thisanalytical expression, what is the value of x ( 0 ) ?
b. Using the Initial Value Theorem of Section 3.4, determine the value of x ( 0 ) .
c. If the process is initially at a steady state with x ¯ = 0.3 , what is the value of x ( 0 ) ?
d. Compare your answer for parts (a)-(c) and briefly discuss any differences.

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Hydrogen, important for numerous processes, can be produced by the shift reaction: CO+H2O-CO2 +H2 In the reactor system shown in the Figure, the conditions of conversion have been adjusted so that the H2 content of the effluent from the reactor is 3 mol %. Based on the data in following figure: a. Calculate the composition of the fresh feed. b. Calculate the moles of recycle per mole of hydrogen produced. Recycle CO, H2O Feed CO H₂O Reactor % 3 mol % H₂ Separator % CO₂ 48 H₂ 48 CO 4

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