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22. March 2004 Department of Chemical Engineering, NTNU

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1 22. March 2004 Department of Chemical Engineering, NTNU
Process Integration Applied to the Design and Operation of Distillation Columns Hilde K. Engelien 22. March 2004 Department of Chemical Engineering, NTNU

2 Introduction & Overview
Process integration - definition Motivation Background Overview of talk: Introduction to multi-effect arrangements Minimum vapour flowrate considerations Vmin as a target Vmin-diagrams Multi-effect in practice selecting controlled variables industrial example Main contributions Concluding remarks I’d like to start by a definition of process integration and to give some motivation and background for my work. Then I’ll present some of the results from my thesis work, starting with an introduction to multi-effect distillation.. These arrangements are distillation column where pressure is used to integrated different column. This type of arrangement is highly energy savings. As the title of my thesis implies my work has focused both on design and control of such arrangements. I will start by talking about the design issues, which I have looked at in terms of minimum energy, then talk about the control aspects of selecting controlled variables. I will also briefly discuss an industrial case study before summarising the main contributions of my thesis and give some concluding remarks.

3 Introduction Process Integration - definition
“Systematic and general methods for design (and operation) of integrated process plants, focusing on efficient energy use and reduced environmental consequences”. International Energy Agency (IEA), 1993 The most known method of process integration is probably the method of pich technology for designing heat excahgner networks. However, the term process integration can be applied to many different industries and in many different ways, from water pinch, process synthesis, modelling and optimisation (even of operation of fishing boats on Iceland), to hydrogen pinch tecnology. A general definition of process integration is given by the International Energy Agency In this work systematic and general methods are used to look at design and operation of distillation column

4 Introduction Process Integration - definition
Motivation - energy savings, environment, innovation,... Distillation is a very common separation process: performs about 95% of fluid separations in the chemical industries. Distillation is a very energy consuming process: uses about 3% of the world total energy consumption. accounts for around % of energy usage in chemical and petroleum industry. Process integration saves energy and reduces the environmental impact of a process reduce site utility costs (e.g. steam, cooling water) may reduce capital costs Just to give some motivation for work on heat integrated distillation columns. Distillation is a very common process that is widely used in the chemical industries. For liquids it is the most common separation process used. Distillation is also very energy consuming and in the chemical and petroleum industry it accounts for around % of the energy usage. On a world basis this is about 3 % of the world total energy consumption (in 19??) Any savings in energy will therefore be beneficial from both an economic and environmental point of view.

5 Introduction Process Integration - definition
Motivation - energy savings, environment, innovation,… Background to heat-integrated distillation columns Multi-effect prefractionator arrangements have high energy savings - is therefore an interesting arrangement to study. Operation of energy-integrated systems can be more difficult - want to operate so that the energy savings are achieved. Not many publications on the control of the integrated prefractionator/sidestream columns [Cheng & Luyben, 1985, Ding & Luyben, 1990, Bildea & Dimian, 1999, Emtir et al., 2003] The use of different heat integrated distillation arrangements have been studied by many different people and many differetn options are available. The multi-effect arrangement studied in this work has potentially very high energy savings for certain applications and is therefore interesting to study. An important issued when studying energy integrated arrangements is that the operation can be more difficult. It is therefore important to ensure that the promised energy savings are achieved. The topic of control and operation is therefore very important. There has not been much published work on the control of the multi-effect arrangement studied here.

6 Multi-Effect Distillation
= where pressure is used to adjust the temperature levels in two (or more) columns so that the condensing duty of one column can be used to provide heat in the reboiler of another column. Multi-effect distillation can be defined as a distillation process where the pressure is used to adjust the temperature levels in two (or more) columns so that the condensing duty of one column can be used to provide heat in the reboiler of another column.

7 Different Distillation Arrangements
Direct split (DS) Indirect split (IS) backward-integration (B) forward-integration (F) B HP LP LP HP I’ll start by introducing the most conventional non-integrated and integrated arrangements. Normally distillation of a multi-component mixture is carried out in a series of columns. Here I have shown two such arrangements for a ternary separation of components A, B and C. The first arrangement is called a direct split system, as the lightest component (the one with the lowest boiling point) is split off in the first column. The second column splits the middle boiling component and the heaviest boiling component. The second arrangement is called indirect split. Here the heaviest component is separated off in the first column and the second column splits the light and middle components. The columns can be heat integrated by running them at different pressures. For the direct split arrangement, if the first column is at a high pressure and the second column is at a low pressure this will raise the boiling point of the overhead stream which can then be used to boil the second low pressure column. The condenser in the top column and the reboiler in the second column can be integrated. This arrangement is called a forward integrated arrangement as the integration of heat is in the direction of the mass flow. Columns can also be integrated in a reverse fashion, here called backward integration, where the first column is at low pressure and the second column is at high pressure. The integration here is in the reverse direction of the mass flow. Both the direct and indirect systems can be integrated with forward or backward integration.

8 Different Distillation Arrangements
Prefractionator columns 30 % less energy prevents re-mixing effect of middle component Further energy savings can be made with multi-effect integration. Thermally coupled columns: Single column shell (divided wall column) 30 % reduction in capital cost Another method of separating a ternary feed is to use a prefractionator column. Instead of the direct or indirect split in the first column the prefractionator separates the lightest component (A) from the heaviest component (B). The main column then separates A and B in the top section and B and C in the bottom section. This prefractionator arrangement uses typically 30% less energy than the direct or indirect split arrangements. This arrangement is the basis fot the multi-effect arrangements that I have studied. Another version of this arrangement is the thermally coupled columns, where the reboiler here is replaced by a vapour stream from the main column and the condenser is replaced by a liquid stream. The same energy savings are achieved here. It is also possible to implement this arrangement in a single column shell where there many also be capital cost savings.

9 Multi-Effect Prefractionator
Forward integrated prefractionator (PF) If the first column is run at a higher pressure than the main column then the condenser at the top of the prefractionator can be integrated with the reboiler of the main column. The heat from the first column is used to drive the second column and the only heat input needed is to the HP column. This is the forward integrated prefractionator column (which is abbreviated PF). Heat input Integrated reboiler/condenser

10 Multi-Effect Prefractionator
Backward integrated prefractionator (PB) In the backward integrated prefractionator arrangement the second column is at the higher pressure so that the main column drives the prefractionator. The heat input is to the main column. Integrated reboiler/condenser Heat input

11 The integrated prefractionator arrangement is the best
Energy Consumption Percentage Savings of Different Energy Integrated Arrangements You can here see the different energy consumption’s of the different distillation arrangements just described. The numbers are expressed in % savings compared with the best of the direct or indirect split arrangement. For example in the first column the indirect split arrangement is the best so there is no savings (0 %). The direct split arrangement uses more energy (-1 %). The other arrangements have different savings, ranging from 33 to 62 %. These data have been calculated based on simple shortcut equations where the feed composition and difficulty of separation has been varied. From the results we can see that (in terms of energy) the integrated prefractionator arrangement (forward and backward integrated) is the best. You can also see that the savings are highest when there is a large amount of B in feed. Here the savings are near 72 % The integrated prefractionator arrangement is the best

12 Minimum Vapour Flowrate, Vmin
Vmin as a target - use to compare different designs Minimum vapour flow at infinite number of stages Can get within 10 % of Vmin target by using reasonable number of stages Assumptions: ideal mixtures, constant relative volatility, constant molar flows, sharp splits Can get within 10 % of Vmin-target using reasonable number of stages Energy (V) vs. number of stages (N) trade-off between number of stages and energy actual V approaches Vmin for N approximately 2 x Nmin or larger, typically: 2Nmin  + 20% Vmin 3Nmin  + 2 % Vmin 4Nmin  % Vmin The previous table showed data based on simple shortcut equations that calculate the minimum vapour flowrate required for each different arrangement. In this work the minimum vapour flowrate has been used as a target for comparing different integrated designs. Minimum vapour flowrate is calculated base on the assumption of infinite number of stages in the distillation column. Now, infinite number of stages can of course not be achieved in practice, but this is not in itself an important limitation since the actual vapour flow is usually close to the minimum. The trade-off between number of stages and energy is shown here in this graph. If the number of stages goes up then the energy required for a specific separation goes down and finally reaches a minimum. If the number of stages goes down then the energy required goes up. There is also a minimum number of stages. If the column has fewer number of stages then the separation will not be achieved even if more energy is added. The assumption of minimum vapour flowrate is not an unrealistic target since the actual vapour flowrate is close if we are allowed to add stages. Therefore minimum vapour flow is a good target for comparing energy usage for alternative arrangements. As you can see the price for reducing the energy is the cost of adding more stages. But, usually when energy consumption is an issue the energy prices are high. It is then reasonable to add more stages as the capital costs are justified.

13 Minimum Vapour Flowrate Diagrams A Visual Tool for Process Integration
 = DC1/F VT/F PA/B PB/C PA/C Vmin(C22) Vmin (PF/PB) C21 C1 Vmin(C1) C21 Vmin(C21) The minimum vapour flowrate for distillation columns can be visualised in a Vmin diagram. I will first illustrate the diagram then show how it is drawn. The vapour flowrate required in the prefractionator column can be expressed in terms of the distillate flowrate. For sharp splits, that is pure products, the minimum vapour flow in the prefractionator column follows the blue line. The minimum for this column is given here in point PA/C We can do the same thing for the main column . In the upper part of the main column the minimum vapour flow is given by this green line and in the lower part it is given by the red line. For the integrated prefractionator arrangement the vapour flowrate for the whole arrangement is given where these two lines cross.

14 Drawing the Vmin-diagram
Prefractionator column (C1): Reference: Halvorsen (2003)  = DC1/F VT/F PA/B PB/C PA/C The Vmin diagram is easy to draw. The Vmin diagram has been presented extensively earlier by Ivar Halvorsen in his thesis looking at thermally coupled Petlyuk arrangements. The first part of the diagram, which is for the prefractionator column can be plotted from 3 points, using the feed composition, and roots from the Underwood equation. The first two points indicate a sharp A/B split and a sharp B/C split in the prefractionator column. Between these two points is where the amount of middle component B in the distillate from the prefractionator varies. The variation of the vapour flowrate with the distillate flowrate is linear so we can plot point PA/C, which is the minimum for the prefractionator arrangement. zA zA + zB Ref.: Halvorsen, Skogestad, 20003

15 Extending the Vmin-diagram
Upper section main column (C21):  = DC1/F VT/F PA/B PB/C PA/C PM3 PM2 Lower section main column (C22): PM4 PM1 Now, the diagram can be extended to include the relationships for the separation of component A and B and B and C. This is the vapour flow requirements for the upper section of the main column and the lower part of the main column. zA zA + zB

16 Using the Vmin-diagram Vapour Flowrate for Different Distillation Arrangements
Vmin for different arrangements. Visualise how columns are (un)balanced. 5 cases identified - different operating options available. Vmin (DSF/DSB) PB/C Vmin (Petlyuk + ISF/ISB) PA/B VT/F Vmin (PF/PB) PA/C Vmin(C1) This extended version of the Vmin diagram can be used to find the minimum vapour flowrate of the different distillation arrangements that I showed earlier. The integrated prefractionator arrangements have the lowest vapour flow. The minimum vapour flow for the thermally coupled Petlyuk arrangement is the highest peak in the Vmin diagram, here at PB/C. The multi-effect indirect arrangements is the highest of these two points and the multi-effect direct split arrangement is the highest of these two. It’s also possible to find the vapour flow required for the non-integrated DS and IS arrangements. DS is the sum of these two points and IS is the sum of these. The Vmin diagram can also be used to visualise how the columns are unbalanced. Here, for example, the upper part of the main column requires less vapour flow than the other two sections. The crossing of the lines will be different from each separation case. For example the two lines for the main column can cross above the prefractionator line. In the thesis it has been shown how there are five possible cases and some of the options available.  = DC1/F

17 Benefits of the Vmin-diagram
Easy visualisation of minimum vapour flow. Different distillation arrangements are presented in same diagram. Tool for further design - balanced/unbalanced columns gives different design options. Starting point for further rigorous simulations - Vmin target, optimum recovery  = (D/F) Just to summaries some of the benefits of the Vmin diagram…. Move on to the control and operation part.

18 Control Problems with Heat-Integrated Distillation Columns
Integrated columns have added complexity. Integrated columns may be difficult to control as : dynamic upsets can propagate back & forth between columns. the system is non-linear, multivariable and interacting. Energy savings may not be achieved (or may be worse) if the columns are not operated correctly. The heat and mass integration of distillation columns causes additional control problems compared to single columns. Integrating two distillation columns can cause additional control problems. Integrated columns are more complex than non-integrated columns and they may be more difficult to control. If they are not operated correctly then, apart from the more serious consequences, the energy savings may not be achieved. It is therefore essential to develop good control systems to ensure satisfactory operation

19 Implementing Optimal Operation of Multi-effect Prefractionators
Objective: to implement a simple “optimal” control scheme for integrated distillation systems. Want to find the controlled variables that will directly ensure optimal economic operation. “Optimal” - means near-optimal operation. It is economically acceptable to be a certain distance from optimum (but not too far…). The objective of this work has been to, in a simple, easy way, implement an “optimal” control scheme for integrated distillation systems. We want to find what variables to control in order to ensure optimal economic operation. So, when there are disturbances in the system we do not have to re-optimise. By “optimal” we mean near optimal operation - it is economically acceptable to be at some distance away from the actual optimum. What we we want to achieve is to operate the columns so that they are close to the optimum and not more than a certain acceptable distance away from the optimum.

20 Steady State Optimisation
Objective : Selection of controlled variables Method: Self-optimizing control (Skogestad, 2000) The method of self-optimizing control involves a search for the variables that, when kept constant, indirectly lead to near-optimal operation with acceptable loss. Loss imposed by keeping constant setpoint for the controlled variable Slide 6 - Steady State Opimization The objective of this work was to study a multi-effect distillation system to find what variables should be controlled, by using the method of self-optimizing control. This is going one step back from the usual control studies which normally looks at the pairing of controlled and manipulated variables. The method involves a search for the variables that, when kept constant, indirectly lead to near-optimal operation with acceptable loss. The basis of this can be explained from this graph. We have here a process that at its nominal operating point, d*, has an optimum J. When the process moves away from its nominal operating point we have to re-optimize to find the new optimal value - this gives us the red curve. If, instead of re-optimizing we keep a constant set-point in a variable c we get a loss as we move away from the nominal operating point. Now, we will get different losses by keeping different variables constant. The blue lines represent the cost when keeping two different variables constant. You can see from the figure that in this case keeping variable c1 constant gives a smaller loss than keeping c2 constant. This is the basis of the method of self-optimizing control - to find the variable or variables that gives us the lowest acceptable loss when we move away from the nominal operating point. I will now give you a summary of how this method is carried out.

21 Steady State Optimisation
The method of self-optimizing control consists of six steps: 1) Finding the DOF for optimisation. 2) Formulation of a of cost function, J, to be maximised for optimal operations & constraints. 3) Identification of the most important disturbances. 4) Solving the nominal optimisation problem. 5) Identification of candidate controlled variables. 6) Evaluation of loss (at constant setpoints): L = J - Jopt Ref.: Sigurd Skogestad, "Plantwide control: the search for the self- optimizing control structure”, Journal of Process Control, 10, 2000. Slide 7 - Steady State Optimization The method of self-optimizing control has six main steps: First you have to determine the number of degrees of freedom available for the optimization. Then a cost function is defined and you have to specify the constraints that have to be satisfied during operation. Step 3 is identifying the most important disturbances and step 4 is solving the optimization problem. In the optimization it is necessary to evaluate the optimum for the nominal operating point and also find the optimum for the disturbances. The optimum for the disturbances is needed so that the loss can be calculated. From the optimization we also find the active constraints. Candidates for the controlled variables are then defined and finally we evaluate the loss when each of the candidate variables are kept constant while subjecting the system to the chosen disturbances.

22 Steady State Optimisation
DOF analysis for multi-effect columns : DOF = = 7 Objective function: Operational constraints: the LP column pressure must be  1 bar the HP column pressure must be  15 bar the purity of the products must be  99 mol% there is a maximum area in the integrated reboiler/condenser the duty of the HP condenser must equal the duty of the LP reboiler (equality constraint) non-negative flows Process constraints - the mass, energy and component balances J = pDD + pSS + pBB - pFF - pVV When assuming a fixed feedrate the number of degrees of freedom for the multi-effect prefractionator arrangement is eleven. We have four levels that needs to be stabilised and that has no steady state effects. There are therefore 7 degrees of freedom in this system. The objective is to produce as much valuable product as possible, while using as little energy as possible. The cost function is defined as the value of the products, minus the cost of feedstock and cost of boilup. If we assume that the products have the same value then with a given feedrate the first four terms are fixed. Minimising J is then equivalent to minimising the vapour boilup. The operational constraints are the pressure restrictions in both columns, the product purity of the product streams and a maximum available area in the integrated reboiler/condenser. The process constraints are the mass, energy and component balances.

23 Steady State Optimisation
Results from optimisation: Active constraints: Pressure in LP column Product purity of sidestream Product purity of bottom stream Area in integrated exchanger Non-active constraints: pressure in HP column product purity in distillate Implement active constraint control + control distillate composition DOF Accounts: 11 DOF total - 4 active constraints - 4 levels with no steady state effect - 1 fixed feedrate - 1 controlling distillate composition = 1 DOF left for self-optimising control From the optimisation it was found that four constraints were active, meaning that they were at the constraint value. For the optimised solution the pressure in the LP column has to be at 1 bar, the product purity in the sidestream and bottom stream should be at 99%. Also the area in the integrated exchanger should be maximised. The pressure in the HP column and the distillate purity were not active constraints. It is optimal to keep the active constraints at their limit so we therefore implement active constrain control. We also found that to there were very small losses when controlling the distillate composition at 99 %. This leaves one degree of freedom for which a self-optimising variable can be found. One DOF left for control - find a self-optimising control variable

24 Steady State Optimisation
Calculate loss L = (J - Jopt) for the selected disturbances (zF, F). Identify the best variable(s) for control, where the loss is small. To find the self-optimising variable we test a number of candidate variables. The loss is calculated for each candidate variable while subject to the disturbance, while keeping the candidate variable at its optimum value found from the nominal optimisation. From the results you can see that different variables have different losses. We have identified the best variable, amongst the ones tested, as the distillate to feed rate ratio. Result: Control DHP/F

25 Implementing Optimal Operation of Multi-Effect Prefractionators
Based on the analysis the following control structure was selected: To control the holdups: The reflux flow is used for level control in the HP condenser. The distillate flows is used for level control in the LP condenser. The bottom flowrate from the HP column is used to control the level in the HP column. The bottom flowrate from the LP column is used to control the level in the LP column. Active constraint control loops: The pressure in the LP column is controlled using the condensation rate in the LP condenser. The bottom product purity is controlled using the sidestream flowrate (SLP). The sidestream product purity is controlled using the boilup in the HP column. This has been implemented in a cascade scheme to allow for local disturbance rejection. The boilup is used to control the composition of A in the bottom of the HP column, and the setpoint for this bottom composition is used as an independent variable to control the sidestream purity in the LP column. The maximum area in the integrated reboiler/condenser is used (not actual control loop, bypass valve is fully closed). Self-optimising" loops (2): The distillate product purity is controlled using the reflux flowrate The flow ratio DHP/F is controlled at a constant setpoint (self-optimising loop).

26 5 % increase in feedrate F 0.5 increase in middle component feed (zF)
Dynamic Simulations System is controllable. System is sensitive to disturbances. The control of bottom composition (main column) is poor. Use of feed tank to reduce the feed disturbances (zF, F) Other control configurations possible. 5 % increase in feedrate F The dynamic simulations of the proposed control structure shows that the multi-effect prefractionator arrangement is controllable but that it is sensitive to disturbances. Here you can see the response of the three product compositions when there are disturbances in the feedrate and the feed composition. The control of the top composition is very good and that the control of the bottom composition is especially poor. If implementing a multi-effect prefractionator arrangement the use of a feed tank to reduce the feed disturbances is recommended. 0.5 increase in middle component feed (zF)

27 An Industrial Separation Example
3 cases for integration: Column I and II Column II and III Column III and IV Minimum vapour flowrates: Case 3 has highest savings of 55 % PF/PB is the best ISF/ISB is 2. best Finally I’ll just briefly present an industrial example. Four existing columns for the separation of a hydrocarbon mixture has been studied to see if any could be integrated using the multi-effect prefractionator arrangement. There are three possible cases for integration, column I and II, column II and III and column III and IV. Minimum vapour flowrate calculations showed that Case 3 has the highest energy savings for the PF arrangement.

28 Possible Integration for Case III
Indirect Split (IS) PF ISF (existing arrangement) Energy savings from rigorous simulations: Rigorous simulations were carried for Case 3 out to find the actual energy savings. Three column configurations were compared. The existing indirect split arrangement, the integrated prefractionator arrangement and the integrated indirect split arrangement. The energy savings of the two integrated arrangements were compared using the existing number of stages in the column and infinite number of stages.

29 Lessons from the Industrial Example
PF requires more stages to achieve potential energy savings. Revamp should therefore be accompanied by an increase in number of stages. If sufficient number of stages are allowed the rigorous simulations show that the PF arrangement has high energy savings (57 %). The challenge is to implement the arrangement and achieve the savings in practice ! As you could see from the rigorous simulations the ISF arrangement was better than the PF arrangement when using the existing number of stages. In this case more stages should be allowed to avchieve the required energy savings. Additional stages can be added by replacing the column trays with more efficient trays, or structured packing.

30 Main Contributions Comparison of multi-effect prefractionator with other multi-effect arrangements and non-integrated arrangements. Graphical visualisation of minimum energy for the multi-effect arrangements in a Vmin-diagram. Systematic method applied in the selection of controlled variables for the forward integrated prefractionator arrangement. Control variables are identified that will give low energy losses during operation. Analysis of the integrated prefractionator arrangement in an industrial setting . The main contributions of the thesis are the comparisons of the multi-effect prefractionator with other integrated and non-integrated arrangements. Especially the graphical visualisation of the multi-effect arrangements in the Vmin diagram. In terms of control and operation systematic methods were used to identify controlled variables that will keep the system close to the optimum when there are disturbances. Finally the integrated prefractionator arrangement has been analysed in an industrial setting.

31 Concluding Remarks Focus of work is on the energy savings of multi-effect systems, especially the integrated prefractionator arrangement. Screening of multi-effect arrangements are based on minimum vapour flow at infinite number of stages (PF/PB can achieve up to 70 % savings). Minimum vapour flow (Vmin) is a good target, as by adding stages the actual value of vapour flow (V) is usually close to the minimum. The energy requirements for multi-effect arrangements are visualised in Vmin-diagrams. Selection of controlled variables using the systematic method of self-optimising control. Controlling the right variables can give low energy losses during operation. Industrial case study - high energy savings if sufficient number of stages are allowed. So, to conclude my talk. The work in the thesis is focused on the energy savings of the multi-effect systems, especially on the integrated prefractionator arrangement. Minimum vapour flow has been used as a target for screening different arrangements. This has showed that the multi-effect prefractionator arrangement is a very promising energy saving solutions that can reduce the energy requirements up to 70 %. The minimum vapour flowrate for different distillation arrangements have been visualised in the Vmin diagram, which is a tool for screening and design. The selection of controlled variables have been studied with the objective of finding the variables that ensure that the energy savings are still obtained during operation when there are disturbances in the system. Finally, an industrial case study was presented, which showed that high energy savings are possible as long as we allow sufficient number of stages in the columns.

32 References Bildea, C.S., Dimian, A.C., 'Interaction between design and control of a heat-integrated distillation system with prefractionator', Tans IChemE, 1999, Vol. 77, Part A, pp Cheng, H. C., Luyben, W., 'Heat-integrated distillation columns for ternary separations', Ind. Eng. Chem. Process Des. Dev., 1985, 24, Ding, S.S., Luyben, W., ‘Control of a heat-integrated complex distillation configuration’, Ind. Eng. Chem. Res.¸1990, 29, Emtir, M., Mizsey, P., Fonyó, Z., ' Economic and controllability investigation and comparison if energy integrated distillation schemes', Chem. Biochem. Eng. Q., 2003, 17(1), 31-42 Halvorsen, I.J, Skogestad, S., ‘Minimum energy consumption in multicomponent distillation. 1. Vmin diagram for a two product column’, Ind. Eng. Chem. Res., 2003, 42, Hewitt, G., Quarini, J., Morell, M., ‘More efficient distillation’, The Chemical Engineer, 21 Oct. 1999 Skogestad, S., 2000, Plantwide control: the search for the self-optimizing control structure, J. Proc. Control, Vol.10,

33 Study Trip…. … sampling at the Glenfiddich Distillery,
Scotland and Jameson Distillery, Ireland.

34 Practical Considerations for the Multi-Effect Prefractionator
When considering a multi-effect distillation system for a practical application it is important to look at: Operating costs (energy) Capital costs Total annual costs (operating + capital) Control Operability Flexibility Integration with overall process Usually these factors are not independent and a trade-off must be made to achieve an “optimal” design.

35 Possible Vmin Diagrams

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