Improving Convergence Behavior of Nonlinear Equation Systems in Intensified Process Models by Decomposition Methods

The two decomposition methods Dulmage-Mendelsohn (DM) decomposition and bordered block transformation (BBTF) have been examined on their capabilities to eliminate convergence problems during the iteration of large, nonlinear equation systems as they occur frequently in process modeling. They both divide the overall system into lower dimensional subsystems, which can be solved separately in sequence. Exemplarily these methods were applied on the model of a reactive distillation column, where the decomposed systems show a higher robustness with respect to systematically selected initial points compared to the original system. Nevertheless, the improvement in DM seems small since a large subsystem with 576 of the 664 model equations remains. The convergence result from the iteration of the BBTF decomposed system depends a lot on the initial values for certain strongly coupled variables called tearing variables. In future, methods will be investigated and may also be developed to further reduce the dimension of the subsystems in DM and provide accurate initial values for the tearing variables in BBTF

Development of a Fusion Fuel Cycle Systems Code

The tritium inventory in a D-T fusion experiment, like ITER, may be the major hazard onsite. This tritium is distributed throughout various systems and components. A major thrust of safety work has been aimed at reducing these tritium inventories, or at least at minimizing the amount of tritium that could be mobilized. I have developed models for a time-dependent fuel cycle systems code, which will aid in directing designers towards safer, lower inventory designs. The code will provide a self-consistent picture of system interactions and system interdependencies, and provide a better understanding of how tritium inventories are influenced. A ``systems`` approach is valuable in that a wide range of parameters can be studied, and more promising regions of parameter space can be identified. Ultimately, designers can use this information to specify a machine with minimum tritium inventory, given various constraints. Here, I discuss the models that describe tritium inventory in various components as a function of system parameters, and the unique capabilities of a code that will implement them. The models are time dependent and reflect a level of detail consistent with a systems type of analysis. The models support both a stand-alone Tritium Systems Code, and a module for the SUPERCODE, a time-dependent tokamak systems code. Through both versions, we should gain a better understanding of the interactions among the various components of the fuel cycle systems