| The mathematical modeling of the transient behavior of a complex chemical process naturally leads to the formulation of large sets of Differential and Algebraic equations (DAEs). The very flexible and effective equation-based (EB) approach in dynamic process flowsheeting calls for the simultaneous solution of the DAE set. However the numerical solution of DAEs is not trivial. The convergence properties of the numerical methods used for solving DAE systems depend upon a very important and peculiar property of a DAE, its index. Problems of index higher than two cannot be adequately handled by existing DAE codes and are practically unsolvable. It was shown that the index is affected by, among other factors, the choice of design variables and equations. Since these choices are often made rather arbitrarily, an important conclusion is that the index should be a criterion in making this choice. An algorithm was presented for selecting design equations and variables to ensure the formation of an index-one DAE. Furthermore alternative index-reducing formulations for incorporating design variables in the DAE model were shown to be possible.; Strategies were presented for predicting the overall flowsheet index given the indices of single units, or groups of units, and the topology of the flowsheet. As a result, the formidable task of estimating the entire flowsheet index becomes more manageable since it can be dealt with on a smaller scale. The strategy proposed first partitions the flowsheet into groups of units to be considered together for their index identification. The information obtained from the application of the partitioning algorithm is subsequently combined with the results of the index analysis on integrated two-unit systems to obtain the particular flowsheet index. The proposed strategy was evaluated by applying it to a number of test problems representing relatively complex flowsheets.; The insight that was gained from the index analysis was applied toward the development of a new EB dynamic process flowsheeting package, DSEQUEL-II. This package was successfully used for the simulation of flowsheeting problems, some involving process control schemes, of size up to several hundred variables. A number of computational issues was also studied toward the development of a truly robust and efficient dynamic simulator. |
