Convergence parameters are used to tune the solution algorithm and enhance convergence. Only those parameters applicable to the Column Algorithm selected in the Column Main Window are available.
Enter the desired parameter in the appropriate data entry field, replacing the default value.
Damping Factor (Not available with SURE algorithm)
A damping factor of less than one may be used to improve convergence when the outer loop is oscillating. Refinery complex fractionators are given a default damping factor of 0.8. Chemicals columns may require more severe damping.
Damping Cutoff (CHEM and LLEX algorithms only)
The damping factor is only applied when the sum of the errors is greater than this value. The default is 10-8.
Error Increase Factor (Not available with SURE algorithm)
This factor limits the increase in the sum of the errors from iteration to iteration. PRO/II supplies a default value of 1.0 for the Inside-Out and Enhanced I/O algorithm and 100 for the other algorithms. See PRO/II Technical Bulletin One for further information.
Composition Variable Option (CHEM algorithm only)
This option specifies the mathematical basis for composition calculations. Different options may enhance convergence in certain circumstances. In particular, the ADAPTIVE option is useful in simulations having trace components in the feeds or on trays at final solution.
Note: Use of CVAR is not allowed for VLLE systems, or columns with tray efficiencies. CVAR is compatible with reactive distillation.
LOG ChemDist solves all components using the natural logarithms of their mole fractions as iteration variables. This enhances convergence of highly non-linear VLE equations because the log form significantly reduces the non-linearity of the equation forms. It is the default, and usually should be used. A draw-back of using the logarithm form for compositions is that it may reduce the accuracy of the matrix inversion. This is due to scaling issues introduced by the presence of trace components in the Jacobian matrix.
LINEAR When using this option, ChemDist solves all component compositions using the mole fractions (not their logarithms) as iteration variables. The LINEAR option is recommended when using ideal thermodynamic methods. Experience shows that the LOG option usually converges better than the LINEAR option for non-ideal thermodynamic systems.
ADAPTIVE This is a hybrid of the LOG and LINEAR options. Calculations begin using the natural logarithms of the mole fractions as iteration variables. At the beginning of each iteration, trace components are identified on each tray, and their logarithmic compositions are converted back to (linear) mole fractions. Once on the LINEAR basis, components are not switched back to the LOG basis. When trace components are present on multiple trays at the final solution, the ADAPTIVE option usually works well to speed convergence (sometimes greatly) by requiring fewer iterations.
Example: A non-ideal distillation with 25 trays is to use the CHEMDIST
algorithm with a maximum of 12 iterations. The default
CVAR=LOG declared explicitly for demonstration purposes.
PARA CHEMDIST=12, TRAYS=25, CVAR = LOG
Component Averaging Factor (SURE algorithm only)
Factor for computing the next set of trial compositions. A value of unity gives equal weight to the current and last set of compositions when they are averaged. A value of 2.0 gives double weight to the last set of compositions. Values higher than 3.0 are not recommended.
Key Component (SURE algorithm only)
The key component is normally determined by PRO/II. In rare circumstances, specifying a key component can enhance the convergence.
Stop if no improvement (SURE algorithm only)
The limit on consecutive trial solutions without convergence improvement, even if the Number of Iterations in the Column Main Window has not been reached.
The damping factor is the most useful tuning factor. For Inside-Out and Enhanced I/O columns, it will usually aid in the convergence of columns in which the inner loop is converging and the outer loop is oscillating with an error that is close to the convergence tolerance. For highly non-ideal thermodynamic systems a value of 0.25 - 0.50 may aid convergence. Use of a damping factor increases the number of outer loop iterations needed for column solution.
The component averaging factor for Sure columns is analogous to the damping factor for Inside-Out columns and may aid convergence of columns in which the overall error is oscillating close to a converged solution. The component averaging feature increases the number of iterations needed for column convergence.
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