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The Optimizer

© 2000 AEA Technology plc - All Rights Reserved.Chem 8_5.pdf

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WorkshopIn this example, a simple distillation column to separate Tetrahydrofuran (THF) from Toluene is simulated. The object of the exercise is to select the product specifications such that profit is maximized. A special tool in HYSYS, the Optimizer, will be used to find the optimum operating conditions.

Learning ObjectivesOnce you have completed this section, you will be able to:

• Use the Optimizer tool in HYSYS to optimize flowsheets• Use the Spreadsheet to perform calculations

PrerequisitesBefore beginning this section you need to be able to:

• Add Streams and Operations• Model columns in HYSYS

Fast track to page 9.

Process Overview

Column Overview

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Building the Simulation

Defining the Simulation BasisFor this case, you will be using the Wilson Activity Model. The components are: Tetrahydrofuran and Toluene.

1. On the Binary Coeffs tab, check that the UNIFAC VLE estimation method is chosen, and press the Unknowns Only button to estimate the missing Interaction Parameters.

2. Enter the Simulation Environment.

Adding the Feed Stream

Add a material stream with the following values:

Binary interaction parameters are used to correlate lab data with a thermodynamic model. When lab data is not available, you can estimate the parameters with HYSYS UNIFAC estimation method.

In This Cell... Enter...

Conditions

Name Feed

Temperature 10°C (50°F)

Pressure 140 kPa (20 psia)

Mass Flow 3700 kg/h (8160 lb/hr)

Composition - Mass Fraction

THF 0.44

Toluene 0.56

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Add the Distillation Column

Add a Distillation Column with the following values:

Make the following specifications:

In This Cell... Enter...

Connections

Column Name T-100

No. of Stages 10

Feed Feed, Stage 5

Condenser Type Total

Bottoms Liquid Toluene

Ovhd Liquid THF

Condenser Energy Stream Cond Q

Reboiler Energy Stream Reb Q

Pressure

Delta P, Condenser and Reboiler 0 kPa

Condenser 103 kPa (15 psia)

Reboiler 107 kPa (15.5 psia)

In This Cell... Enter...

Specs

Reflux Ratio 2 (Estimate)

Distillate Rate 1500 kg/h (3305 lb/hr) (Estimate)

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Create two new Column Component Fraction specifications as shown below:

These two specifications should be Active. The DOF for the column should now be 0.

The column should now solve automatically. If it does not, press the Run button to start the solver.

Save your case!

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Changing the Column Tolerances

In order for the optimizer to work properly, we have to tighten the tolerances of the column solver. There are two tolerances that the column must meet before it can be considered as solved.

• The Equilibrium Error Tolerance• The Heat/Spec Error Tolerance

We want to set the value for both of these tolerances at 1e-6. Note that this will increase the solving time of the column, but this column solves very fast anyway, so the tighter tolerances are acceptable in this case.

To change the tolerances, follow these steps:

1. Access the Solver page of the Parameters tab.

2. Enter 1e-6 for both the tolerance values. These cells are located in the Solving Options group box.

This completes the changing of the tolerances. We are now ready to begin to optimize the column.

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Adding the OptimizerIn today’s highly competitive market place, with stringent plant emissions controls and increased competition, a plant’s survivability is often determined by its ability to remain competitive. Optimization methods are now available that give the process engineer the necessary tools to perform on-going process improvement studies. Optimization studies lead directly to improved plant performance, efficient plant operation and finally to increased profitability. Typically, optimization studies involve an ‘economic model’ composed of a Profit Function and operating constraints.

HYSYS contains a multi-variable Steady State Optimizer. Once your Flowsheet has been built and a converged solution has been obtained, you can use the Optimizer to find the operating conditions which minimize or maximize an Objective Function. The Optimizer owns its own Spreadsheet for defining the Objective Functions as well as any constraint expressions to be used. This allows you to construct Objective Functions which maximize profit, minimize utilities or minimize exchanger UA.

• Primary Variables - these are flowsheet variables whose values are manipulated in order to minimize (or maximize) the objective function. You set the upper and lower bounds for the primary variables, which are used to set the search range.

• Objective Function - this is the function which is to be minimized or maximized. The function has to be defined within the Spreadsheet. This allows the user a great deal of flexibility in defining the function.

• Constraint Functions - inequality and equality functions are defined in the Spreadsheet. In solving the Objective Function, the Optimizer must also meet any constraints that are defined by the user.

Open the case OptOptimizer.hsc

Only user-specified process variables can be used as Primary Variables

Restrictions on the Optimizer

• only available for Steady-State calculations

• it cannot be used in Templates.

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In our column example, the Profit Function/Cost Function (sometimes referred to as the Objective Function, Performance Criterion or Performance Index) requires calculating a net profit for the column. The Profit Function is a function of the revenue generated from desired products THF and Toluene, within the limit of product purity constraints. While increased profits is directly linked to increased production of the desired product, plant profitability is generally offset by operating costs. In our column, operating costs are associated with the column utility requirements for the reboiler and condenser. In general a profit function is given by:

where:

PF = Profit Function/time

= Product Flows * Product Values

= Feedstock Flows * Feedstock Costs

OC = Operating Costs

Profit = (THF Product + Toluene Product) – Heating Cost – Cooling Cost – Feed Cost

Typically, the economic model includes operating constraints (equality or inequality constraints or equations). The operating constraints comprise the model of the process or equipment. In this case, we have no process constraints.

To invoke the Optimizer, select Optimizer under Simulation in the Menu Bar, or press <F5>.

Which variable can we change to affect the Revenue?________

PF F

p∑ pMp FfMf

f∑– OC–=

FpMp∑FfMf∑

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Variables tab

When you invoke the Optimizer for the first time, you are placed on the Variables tab. On the Variables tab you define the Adjusted (Primary) Variables to be used in the optimization.

In this case, our Primary Variables are the purity of our products, THF and Toluene.

1. Press the Add button to add the first variable, T-100, Spec Value, THF Purity Spec.

2. Set the Upper Bound at 0.9, and the Lower Bound at 0.90.

3. Add the second variable, T-100, Spec Value, Toluene Purity Spec, with the same bounds as above.

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Defining the SpreadsheetThe Optimizer has its own Spreadsheet for defining the Objective and Constraint functions. Primary Variables may be imported and functions defined within the Optimizer Spreadsheet, which possesses the same capabilities as the Main Flowsheet Spreadsheet

1. Press the Spreadsheet button on the Optimizer view to open the Spreadsheet.

2. Move to the Spreadsheet tab.

Importing and Exporting Variables

You may import virtually any variable in the simulation into the Spreadsheet and you can export a cell’s value to any specific field in your simulation.

• Object Inspection - object inspect (secondary mouse button) the cell which you want to Import into, or Export from. From the Menu that appears, select Import Variable or Export Formula Result. Then, using the Variable Navigator, select the variable you wish to import or export.

• Connections page tab - select the Add Import or Add Export button. Then, using the Variable Navigator, select the variable you wish to import or export.

• Drag ‘n’ Drop - using the secondary mouse button, click the variable value (from the WorkBook or Property View) you wish to import, and drag it to the desired location in the Spreadsheet. If you are exporting the variable, drag it from the Spreadsheet to the exported location.

The Spreadsheet is an operation and thus the Spreadsheet cells get updated when Flowsheet variables change

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Adding Formulas

Complex mathematical formulas can be created, using syntax that is similar to conventional Spreadsheets. Arithmetic, logarithmic and trigonometric functions can be performed in the Spreadsheet.

All common functions must be preceded by a + symbol. Special Functions must be preceded by the @ symbol.

Some of the functions available are:

• Addition (+): +A1+A2• Subtraction (-): +A1-A2• Multiplication (*): +A1*A2• Division (/): +A1/A2• Power (^): +A1^3• Absolute Value (@ABS):@ABS(A1)• Square Root (@SQRT):@SQRT(A1)• Natural Log (@ln):@ln(A1)• Exponential (@exp):@exp(A1)

The following variables need to be imported into the Spreadsheet. Text entries are added to the spreadsheet by typing them in the appropriate cell.

The quickest way of importing variables is to right-click on the desired cell. Select Import Variable, and use the variable navigator to locate the desired variable.

Use this method to import the variables above now.

Press the Function Help button to view the Available Spreadsheet Functions and Expressions.

Cell... Object... Variable...

B1 Cond Q Heat Flow

B2 Reb Q Heat Flow

B3 THF Mass Flow

B4 THF Comp Mass Frac THF

B5 Toluene Mass Flow

B6 Toluene Comp Mass Frac Toluene

B7 Feed Mass Flow

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Enter the following constants on the spreadsheet. The comments can be added, if desired.

Enter the following product prices:

Note: the prices of the products decrease as the impurities increase.

The Objective Function is placed in Cell D8. The equation is:

+(b3*d4+b5*d6)-b7*d7-(b1*d1+b2*d2)/3600

Pay special attention to the units in this equation. If using field units, you may have to add an additional term to this equation to convert between hours and days.

Cell Value (SI Units) Value (Field) Comment

D1 0.471 ($/kWh) 138 ($/MMBtu) Cooling Cost

D2 0.737 ($/kWh) 216 ($/MMBtu) Heating Cost

D7 0.05 ($/kg) 0.024 ($/lb) Feed Cost

CellEquation(SI Units)

Equation (Field) Description

D4 +0.333*b4^3 ($/kg) +0.151*b4^3 ($/lb) THF Price (corrected for purity)

D6 +0.163*b6^3 ($/kg) +0.074*b6^3 ($/lb) Toluene Price (corrected for purity)

What is the value of cell D8, the Profit? __________

You can change the Variable Type to Unitless for dollar value variables.

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Functions tab

The Functions tab contains two groups, the Objective Function and the Constraint Functions. However, in this example we do not have constraint functions.

1. In the Cell area of the Objective Function group, specify the Spreadsheet cell that defines the Objective Function. Use the drop down menu in the Edit Bar to select the appropriate cell. The Current Value of the Objective Function will be provided.

2. Select the Maximize radio button.

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Parameters tab

The Parameters tab is used for selecting the Optimization Scheme.

• Box - Handles inequality constraints but not equality constraints. It generally requires a large number of iterations to converge on the solution.

• SQP - Sequential Quadratic Programming, handles inequality and equality constraints. Considered by many to be the most efficient method for minimization.

• Mixed - Handles inequality constraints only. It is a combination of the Box and SQP methods. It starts the minimization with the Box method using a very loose convergence tolerance. After convergence, the SQP method is used to locate the final solution.

• Fletcher Reeves - Does not handle constraints. Efficient method for general minimization.

• Quasi-Newton - Does not handle constraints. Similar method to Fletcher Reeves.

1. Select the Mixed method as the Scheme.

2. Use the defaults for Tolerance and Number of Iterations.

Monitor tab

The Monitor tab displays the values of the Objective Function and Primary Variables during the Optimizer calculations.

1. Move to the Monitor tab and press the Start button to begin the optimization.

For more information on the Optimization Schemes, refer to the manual section 17.2 or the on-line Help.

Save your case!

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Analysing the ResultsOnce the Optimization is complete, examine the results and fill in the following table:

Base Case Optimized Case

THF mass flow 1650.8 kg/h (3639.4 lb/hr)

THF purity 0.95

Toluene mass flow 2049.2 kg/h (4517.7 lb/hr)

Toluene purity 0.95

Cond duty 9.926e5 kJ/h (9.408e5 Btu/hr)

Reb duty 1.5980e6 kJ/h (1.5146e6 Btu/hr)

Profit 106.3 $/hr

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Exercise 1

We are going to introduce a constraint on the liquid volume flow of the stream THF and examine how it affects the results, profit and products purities.

First, the case must be set back to its state before the optimization.

1. Go to the column subflowsheet.

2. On the Design tab, Monitor page, enter the initial value of 0.95 for the THF and Toluene purity specifications.

3. Re-run the column.

The constraint on the liquid flow is that it must not exceed 1.85 m3/h (65.5 ft3/hr).

The THF Liquid Flow must first be imported into the spreadsheet (use an empty cell), and the constraint value must be written in the spreadsheet. Remember to write the comments next to the values so that they can be understood.

1. On the Functions tab of the Optimizer press the Add button.

2. Type in the reference of the cell where the variable constraint is located.

3. In the Cond column, use the scroll down arrow to find the less than sign. Type in the reference of the cell where the value of the constraint is written.

4. Go to the Monitor tab and start the Optimizer.

The constraint values are positive if inequality constraints are satisfied and negative if inequality constraints are not satisfied.

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What differences, if any, does the constraint make to the first optimized solution? Fill in the following table:

Base CaseOptimized Case

Optimized Case 2

THF Mass Flow 1650.8 kg/h

THF Purity 0.95

Toluene Mass Flow

2049.2 kg/h

Toluene Purity 0.95

Cond Duty 9.926e5 kJ/h

Reb Duty 1.5980e6 kJ/h

Profit 106.3 $

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Exercise 2

Here, we are going to model the reboiler with a steam-heated shell and tube heat exchanger. The heat exchanger will be modelled with 115 psia steam and the maximum flow of steam available to the reboiler is limited to 840 kg/h (1850 lb/hr). (Note that there are a few approaches that can be taken with the heat exchanger modelling so two of the possibilities are listed). The cost of the 115 psia steam is 0.682 $/kWh ($200/MMBtu).

1. Add Water as a component. This must be done in the Basis Environment.

2. Open the Column’s Property viewer; on the Monitor page, reset the THF and Toluene purity specifications to 0.95.

3. Add a new internal stream (on the Flowsheet tab), ToReb with the following attributes:

4. Run the column.

5. Return to the Main Environment (notice that the "To Reb" stream is now shown on the PFD. Add a heat exchanger. The stream ToReb is the shell side feed and steam is on the tube side.

6. Set the Shell and Tube side pressure drops to 0.

7. Specify the Steam inlet conditions at Vf = 1.0; P = 790 kPa (115 psia); Flow = 770 kg/h (1700 lb/hr). The outlet steam is at its bubble point (Vf = 0.0).

8. Add a Duty Spec to the Heat Exchanger but do not specify a value (pass is Overall).

Use the Mixed optimization scheme for this exercise.

In This Cell... Enter...

Type Liquid

Net/Total Total

Stage 10

Export Yes

What is the Heat Exchanger Duty? __________

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9. Add an Adjust operation. The Adjusted Variable is the Steam flow rate and the Target Variable is the Spec Calc Value (Duty Spec).

10. Export the RebQ Heat Flow value (you will have to make this Exportable first) from the Optimizer spreadsheet into the Target value for the Adjust operation. A cell on the spreadsheet can not be simultaneously imported and exported. Copy the value of cell B2 to another empty cell by entering the formula "+B2". The value in this new cell can then be exported to the Target Value of the Adjust operation.

11. Change the Heating Cost value to 0.682 $/kWh ($200/MMBtu) (Cell D2 on the spreadsheet) and Start the Adjust.

12. Add the Steam Mass Flow (must be less than 840 kg/h (1850 lb/hr)) constraint to the Optimizer.

13. Start the Optimizer.

What is the Exchanger Duty and what is the Steam mass flow rate? __________ & __________

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