Optimization 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:

·  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.

  1. Perform sensitivity analysis before optimization, to find appropriate decision variables and their ranges.
  2. Evaluate the solution using sensitivity analysis, to find out if the optimum is broad or narrow.

Example for Minimizing Steam Use

See file - Opt.bkp

In a dichloro-methane solvent recovery system, two flashes, TOWER1 and TOWER2 are run adiabatically, with a 200 psi steam feed to each flash: STEAM1 and STEAM2, respectively.

There is a constraint specifying the maximum allowable concentration of Dicloro-methane in the effluent stream from TOWER2.

Optimization is used to find the steam flow rates. [See file opt.bkp.]

·  The mass flow rate of stream STEAM1 and STEAM2 are the sample variables for the optimization. These variables are called STEAM1 and STEAM2, respectively.

·  The optimization objective function is STEAM1 + STEAM2.

·  The optimization problem is converged when STEAM1 + STEAM2 is at a minimum.

·  Fortran expressions, such as STEAM1 + STEAM2, can be used in any part of the optimization problem.

·  The mass flow rates of the steam streams are also the manipulated variables. The optimization convergence block finds the flow rates that make STEAM1 + STEAM2 a minimum.

·  The manipulated variable is specified in the streams, just as if there were no optimization. The specified value is the initial estimate used by the optimization convergence block.

·  You do not have to specify convergence of the design specification. ASPENPLUS automatically generates a convergence block to converge the specification.

·  There is one constraint associated with the optimization problem, called EFFL.

·  The constraint EFFL is satisfied when the concentration of dichloro-methane is less than 150 ppm.

·  The constraint is expressed in logarithms.