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14Optimization Examples

For more information see Aspen Plus User Guide Chapter 22, Optimization.

Use optimization to maximize or minimize a user-specified objective function by

manipulating decision variables (feed stream, block input, or other input variables).

The objective function can be any valid Fortran expression involving one or more flowsheet

quantities. The tolerance of the objective function is the tolerance of the convergence block

associated with the optimization problem.

You have the option of imposing equality or inequality constraints on the optimization.

Equality constraints within an optimization are similar to design specifications. The

constraints can be any function of flowsheet variables computed using Fortran expressions

or in-line Fortran statements. You must specify the tolerance of the constraint.

Tear streams and the optimization problem can be converged simultaneously or separately.

If they are converged simultaneously, the tear stream is treated as an additional constraint.

Aspen Plus solves optimization problems iteratively. By default Aspen Plus generates and

sequences a convergence block for the optimization problem. You can override the

convergence defaults, by entering convergence specifications on Convergence forms. Use the

SQP and Complex methods to converge optimization problems. See Chapter 17,

Convergence for a complete discussion of optimization convergence.

The value of the manipulated variable that is provided in the Stream or Block input is used

as the initial estimate. Providing a good estimate for the manipulated variable helps the

optimization problem converge in fewer iterations. This is especially important for

optimization problems with a large number of varied variables and constraints.

There are no results associated directly with an optimization problem, except the objective

function. You can view the final value of the manipulated an/or sampled variables directly,

on the appropriate Stream or Block results sheets. To find the summary and iteration

history of the convergence block, select the Results sheet of the appropriate block, located in

the Convergence Convergence sheet.

Optimization problems can be difficult to formulate and converge. It is important to have a

good understanding of the simulation problem before adding the complexity of optimization.

The recommended procedure for creating an optimization problem is:

1. Start with a simulation (instead of starting with optimization). There are a number of

reasons for this approach:

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It is easier to detect flowsheet errors in a simulation.

You can get a good feel for what reasonable specifications are.

You can get a good feel for a reasonable range of decision variables.

You can get a good estimate for the tear streams.

2. Perform sensitivity analysis before optimization, to find appropriate decision variables

and their ranges.

3. Evaluate the solution using sensitivity analysis, to find out if the optimum is broad or

narrow.

Example for Maximizing Operating Margin

See file - Optimiz2.bkp

Optimiz2.bkp

The value of a process is calculated as the value of the product and the byproduct, minus

the cost of the raw material, and minus the cost of steam for the reactor. The Fortran sheet

is used to calculate the cost function:

C

C CPROD = PRICE OF PRODUCT, $/LB

CPROD = 1.30

C

C CBYPR = PRINCE OF BYPRODUCT, $/LB

CBYPR = 0.11

C

C CFEED = PRICE OF FEED, $/LB

CFEED = .20

C

C CSTEAM = COST OF STEAM, $/MMBTU

CSTEAM = 4.00

C

C COST FUNCTION

CFUNC = CPROD * P + CBYPR * G - CFEED * A - CSTEAM * Q /1D6

There are two constraints: one specifying the maximum duty for the reactor and the other

specifying the minimum product purity.

Optimization is used to find the reaction temperature and the feed flow rate thatmaximizes the cost function.

The molar flow rate of P and of G in stream PROD, the molar flow rate of A in stream

FEED and the reactor duty are the sample variables for the optimization. These

variables are called P, G, A, and Q, respectively.

The optimization problem is converged when CFUNC is at a maximum.

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There are two manipulated variables; the reactor temperature and the flow rate for the

reactant A in the feed. The optimization convergence block finds the combination of

values that makes CFUNC a maximum subject to the constraints.

The Fortran sheet is used to calculate the cost function CFUNC.

The manipulated variables are specified in the blocks just as if there were no

optimization. The specified value is the initial estimate used by the optimizationconvergence block.

You do not have to specify convergence of the design specification. ASPEN PLUS

automatically generates a convergence block to converge the specification.

There are two constraints associated with the optimization problem. They are called

DUTY and PURITY.

The constraint DUTY is satisfied when the reactor duty is less than or equal to 3

MMbtu/hr.

The constraint PURITY is satisfied when mole fraction of P in the stream PROD is

greater or equal to than 0.9.