Graduate Thesis Or Dissertation
 

Optimal convergence of complex recycle process systems

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  • The asymptotic convergence acceleration method used in steady state process simulation is examined in detail, and a criterion is developed to decide when it should be applied. The criterion is related to the rate of convergence of each variable and does not require any prejudgment of its tolerance level by the user. A method of developing model systems of equations with any desired characteristics is presented and used to study the behavior of iterative systems. The new asymptotic technique is compared to previous variations of the asymptotic method and the direct substitution method using 11 equation sets and process systems. The new method resulted in more successful convergence promotion than the other methods and reduced the number of iterations to converge the example systems by an average of 50% when compared to direct substitution. Many of the alternative cut sets for a given problem are shown to be nearly equivalent and will ultimately converge at the same rate by the method of successive substitutions. Cut sets in the equivalent group calculate the units of each individual recycle loop in the order in which the units appear in the loop. This is equivalent to the requirement that no single loop should be cut more than once. Mathematical analysis of a single variable, multiple loop problem showed that any cut set not in the equivalent group will converge at a slower rate than those in the equivalent group. Several process examples are used to demonstrate that cut sets in the non-equivalent group will also converge slower in the more general multiple variable, multiple loop case. These process examples also demonstrate that the equivalent cut sets will be more amenable to convergence promotion by the asymptotic method.
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