Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
Question
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Chapter 6, Problem 6.18E
Interpretation Introduction

(a)

Interpretation:

The response of the tank temperature for the given process is to be simulated for a step change in the heat input of the heater from 3×107 cal/h to 5×107 cal/h.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

The difference in the actual variable (y) and the original variable (ˉy) is known as deviation variable (y). It is generally used while modelling a process. Mathematically it is defined as:

y=yˉy

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(b)

Interpretation:

The overall transfer function for the given heating system including tank and the heater is to be determined.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

The difference in the actual variable (y) and the original variable (ˉy) is known as deviation variable (y). It is generally used while modelling a process. Mathematically it is defined as:

y=yˉy

In steady-state process, the accumulation in the process is taken as zero.

Interpretation Introduction

(c)

Interpretation:

The response of the tank temperature for the given process is to be simulated for a step change in the heat input for the transfer function derived in part (b).

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

The difference in the actual variable (y) and the original variable (ˉy) is known as deviation variable (y). It is generally used while modelling a process. Mathematically it is defined as:

y=yˉy

In steady-state process, the accumulation in the process is taken as zero.

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Sulphur dioxide is absorbed in a packed bed absorption tower with 25 mm ceramic Intalox saddles (packing factor of 300 m) using water solvent in a countercurrent arrangement. The feed gas contains 0.05 kmol SO-/kmol air, and it is desired to reduce the SO, content of exit gas to 3% of its inlet concentration. The gas flow rate is 0.067 kmol's of air, and the water rate is 3,08 kmol/s. The equilibrium relation is given by: Y= 30 X. Calculate: (a) number of transfer units; (b) column diameter, (c) the height of the packing. Assuming the entire process is gas-film controlled. Design for a pressure drop of 21 mm H-O/m packing. P = 1.21 kg/m: p = 1000 kg/m³: д, = 0.018×10-3 N.s/m² = 10³ N./m²; D₁ =1.45x10 m³/s; D₁ = 1.7x10m²/s. H=0.011, (Sc)( 0.305 111 De 2 3.05) 035 H₁ = 0.305 (Sc) K (305)
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