Class 29 - Modeling Of A Distillation Column
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System Modeling Coursework
Class 29: Modeling of a Distillation Column
P.R. VENKATESWARAN Faculty, Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Karnataka 576 104 INDIA Ph: 0820 2925154, 2925152 Fax: 0820 2571071 Email: [email protected], [email protected] Web address: http://www.esnips.com/web/SystemModelingClassNotes
WARNING! • I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation. • For best results, it is always suggested you read the source material. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
2
Difficulties in Control of Distillation Column 1. Towers with many trays are slow in responding to control action. 2. Separation is affected by many variables, requiring many control loops, which interact with one another. 3. On-line analysis is not always available. 4. Distillation units are the last in the chain of processing operations, hence are subject to changes in throughput from all upstream units. 5. The factors affecting separation are not readily interpreted in terms of control system requirements. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
3
Distillation Control problem
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
4
Factors affecting Control • Although the figure indicates only a binary separation, the concept will be advanced later to multicomponent and multi stream towers. • The block diagram reveals two extremely important facts: – Energy is necessary for separation. In fact, it may be assumed that no separation will take place if no energy is introduced. – The relative composition of the two product streams is intimately bound up with their relative flow rates. More of a given component cannot be withdrawn than is being fed to the tower: the material balance must be satisfied. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
5
Material Balance equation • To be sure, tray efficiency, loading etc., also colour the picture, but the two factors above are so outstanding in their effects that they must be the prime consideration in any system design. • In the steady state, material balance is given by as much material must be withdrawn as enters the tower: F = D+B Where F = molar feed rate, D= Distillate flow, B = bottoms flow
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
6
Material Balance equation • A material balance on each component also be closed using z,y and x to represent the mole fraction of the light component in F, D and B: Fz=Dy+Bx • From the overall material balance it is evident that the flow of only one of the product streams can be set independently. The flow of the other is determined by the feed rate and is therefore a dependent variable. • But one flow must be set by some criterion, since they cannot both be allowed to drift. For the moment, distillate flow will be chosen to be manipulated by the control system, either directly or indirectly. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
7
Material Balance equation •
•
•
Bottoms flow must then be manipulated by a controller which senses liquid level at the bottom of the tower in order to close the material balance by maintaining constant liquid inventory. Bottoms flow is thus dependent on current values of feed and distillate: B= F- D Substituting for B in the material balance of the light component permits expressing the relationship between the quality of both products in terms of distillate flow: Fz=Dy+(F-D)x The ratio D/F determines the relative composition of each D z−x product: = F y−x
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
8
Graph of the Material Balance equation
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
9
Solution to Material Balance equation • Unfortunately, however, the material-balance equation alone is insoluble. It is a single equation with two unknowns, x and y. To provide a solution, another equation of x and y must be found. • The Fenske equation was derived for the purpose of estimating the number of theoretical trays n required to effect a given separation between components whose relative volatility is a, at total reflux:
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
10
Solution to Material Balance equation • Equation needs to be modified to allow extension to situations other than total reflux:
• The term S is defined as the separation and is a function of o, n, and the energy to feed ratio. Solving the equation for y in terms of x and for x in terms of y, • A direct solution of these equations with the material balance cannot be readily obtained. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
11
Solution to Material Balance equation • Should any other value of x or y be desired at the prevailing conditions of feed composition and separation, it can be obtained by appropriate adjustment of D/F. • A value for y, for example, is first selected, and a corresponding value of x is then calculated from the modified Fenske equation. With these values of x, y, and x, the required D/F can be found from the material balance. • The next figure illustrates how distillate and bottoms compositions would vary with D/F for this example. The slope of each curve at D/F = 0.5 represents the process gain at that point. It happens that the two curves have identical slopes at that time
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
12
D/F curve
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
13
Conclusions • A 1 percent change in D/F will change distillate and bottoms composition by 0.9 percent. • Three conclusions may be drawn from the foregoing discussion: – Composition of both product streams is profoundly affected by distillate to feed ratio. – Changes in feed composition can be offset by appropriate adjustment of D/F. – If separation is constant, control of composition of either product will also result in control of composition of the other product. (The relationship between x and y is fixed for a given separation.) July – December 2008
prv/System Modeling Coursework/MIT-Manipal
14
References 1. Process Control Systems – Shinskey.
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
15
And, before we break… • Blessed are those who can give remembering and take without forgetting.
without
– Elizabeth Bibesco
Thanks for listening…
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
16
Class 29: Modeling of a Distillation Column
P.R. VENKATESWARAN Faculty, Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Karnataka 576 104 INDIA Ph: 0820 2925154, 2925152 Fax: 0820 2571071 Email: [email protected], [email protected] Web address: http://www.esnips.com/web/SystemModelingClassNotes
WARNING! • I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation. • For best results, it is always suggested you read the source material. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
2
Difficulties in Control of Distillation Column 1. Towers with many trays are slow in responding to control action. 2. Separation is affected by many variables, requiring many control loops, which interact with one another. 3. On-line analysis is not always available. 4. Distillation units are the last in the chain of processing operations, hence are subject to changes in throughput from all upstream units. 5. The factors affecting separation are not readily interpreted in terms of control system requirements. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
3
Distillation Control problem
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
4
Factors affecting Control • Although the figure indicates only a binary separation, the concept will be advanced later to multicomponent and multi stream towers. • The block diagram reveals two extremely important facts: – Energy is necessary for separation. In fact, it may be assumed that no separation will take place if no energy is introduced. – The relative composition of the two product streams is intimately bound up with their relative flow rates. More of a given component cannot be withdrawn than is being fed to the tower: the material balance must be satisfied. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
5
Material Balance equation • To be sure, tray efficiency, loading etc., also colour the picture, but the two factors above are so outstanding in their effects that they must be the prime consideration in any system design. • In the steady state, material balance is given by as much material must be withdrawn as enters the tower: F = D+B Where F = molar feed rate, D= Distillate flow, B = bottoms flow
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
6
Material Balance equation • A material balance on each component also be closed using z,y and x to represent the mole fraction of the light component in F, D and B: Fz=Dy+Bx • From the overall material balance it is evident that the flow of only one of the product streams can be set independently. The flow of the other is determined by the feed rate and is therefore a dependent variable. • But one flow must be set by some criterion, since they cannot both be allowed to drift. For the moment, distillate flow will be chosen to be manipulated by the control system, either directly or indirectly. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
7
Material Balance equation •
•
•
Bottoms flow must then be manipulated by a controller which senses liquid level at the bottom of the tower in order to close the material balance by maintaining constant liquid inventory. Bottoms flow is thus dependent on current values of feed and distillate: B= F- D Substituting for B in the material balance of the light component permits expressing the relationship between the quality of both products in terms of distillate flow: Fz=Dy+(F-D)x The ratio D/F determines the relative composition of each D z−x product: = F y−x
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
8
Graph of the Material Balance equation
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
9
Solution to Material Balance equation • Unfortunately, however, the material-balance equation alone is insoluble. It is a single equation with two unknowns, x and y. To provide a solution, another equation of x and y must be found. • The Fenske equation was derived for the purpose of estimating the number of theoretical trays n required to effect a given separation between components whose relative volatility is a, at total reflux:
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
10
Solution to Material Balance equation • Equation needs to be modified to allow extension to situations other than total reflux:
• The term S is defined as the separation and is a function of o, n, and the energy to feed ratio. Solving the equation for y in terms of x and for x in terms of y, • A direct solution of these equations with the material balance cannot be readily obtained. July – December 2008
prv/System Modeling Coursework/MIT-Manipal
11
Solution to Material Balance equation • Should any other value of x or y be desired at the prevailing conditions of feed composition and separation, it can be obtained by appropriate adjustment of D/F. • A value for y, for example, is first selected, and a corresponding value of x is then calculated from the modified Fenske equation. With these values of x, y, and x, the required D/F can be found from the material balance. • The next figure illustrates how distillate and bottoms compositions would vary with D/F for this example. The slope of each curve at D/F = 0.5 represents the process gain at that point. It happens that the two curves have identical slopes at that time
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
12
D/F curve
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
13
Conclusions • A 1 percent change in D/F will change distillate and bottoms composition by 0.9 percent. • Three conclusions may be drawn from the foregoing discussion: – Composition of both product streams is profoundly affected by distillate to feed ratio. – Changes in feed composition can be offset by appropriate adjustment of D/F. – If separation is constant, control of composition of either product will also result in control of composition of the other product. (The relationship between x and y is fixed for a given separation.) July – December 2008
prv/System Modeling Coursework/MIT-Manipal
14
References 1. Process Control Systems – Shinskey.
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
15
And, before we break… • Blessed are those who can give remembering and take without forgetting.
without
– Elizabeth Bibesco
Thanks for listening…
July – December 2008
prv/System Modeling Coursework/MIT-Manipal
16
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