Abstract: A process simulator and modeling methodology employs instantaneous property measures. The instantaneous measures of various polymer properties are tracked throughout the subject polymer manufacturing system and used to calculate respective property distribution functions. For example, property distributions of composition, molecular weight, stereoregularity and long chain branching are calculated, tracked in time and location throughout the manufacturing system, and used to model the polymer manufacturing system and polymerization process performed by the system. More specifically, the present invention calculates full distribution of polymer properties from the instantaneous property measures and tracked instantaneous property distributions. This enables accurate and computationally efficient modeling of the polymerization process and manufacturing system for carrying out the same.

Abstract: A total impurity concentration which is a result of the solution of a diffusion equation at the immediately preceding point of time is used to solve, for each mesh point, an equation for determining an electrically active impurity concentration to approximately determine an electrically active impurity concentration. A ratio between the approximate value of the electrically active impurity concentration and the total concentration of the impurities at the preceding point of time is determined for each mesh point. A value of the ratio is determined by interpolating values at mesh points at the opposite ends of each mesh branch. A diffusion equation which includes the total concentration of the impurities as a variable and employs an effective diffusion constant is solved to determine a total impurity concentration at the present point of time of analysis.

Abstract: A model predictive controller for a process control system which includes a real-time executive sequencer and an interactive modeler. The interactive modeler includes both a process model and an independent disturbance model. The process model represents the dynamic behavior of the physical process, while the disturbance model represents current and future deviations from the process model. The interactive modeler estimates current process states from the process model and input data received from the executive sequencer. The executive sequencer then projects a set of future process parameter values, which are sought to be controlled, over a predetermined control horizon. The interactive modeler then solves a set of equations as to how the physical process will react to control changes in order to determine an optimized set of control changes. As a result, the process control system will be able to accurately track a predetermined set-point profile in the most effective and cost efficient manner.