(370f) Reactor Modeling and Recipe Optimization of Polyether Polyol Processes: Polyoxyalkylene Block
This paper addresses reactor modeling and recipe optimization of semi-batch polyether polyol processes, extending our previous results on homopolymerization to polyoxyalkylene copolymers. We first develop a rigorous first-principles reactor model based on the population balance, heat balance, reaction kinetics, and vapor-liquid equilibria (VLE) etc. For VLE, we use the Flory-Huggins theory and Antoine equation to calculate reactor pressure predictions. The resulting model is a large set of stiff differential algebraic equation (DAE) system. A reformulation procedure based on nullspace projection methods is applied to separate the fast dynamic modes from the differential equations and model their quasi-steady states in the algebraic form. The reformulated model has lower stiffness and fewer differential equations but still remains large scale. Therefore, we develop an aggregated model by using the method of moments. The moment model is able to track average polymer qualities and its size is independent of the polyol chain length.
Based on the developed models, a recipe optimization problem is formulated to design the reactor operating policy to minimize polymerization time and incorporate additional process constraints in accordance with final product properties and process safety requirements. The decision variables are the reactor temperature and monomer feed rates over time. The obtained dynamic optimization problem is translated to a nonlinear program by using the simultaneous collocation method, and further solved by the interior point method.
In the case study example of a PO-EO block diol, both the population balance and moment models show satisfactory matches between their reactor pressure predictions and the historical plant data. The recipe optimization results with both models suggest process improvement that 40% polymerization time reductions may be possible. It should be noted that the base case recipe and set of process constraints are chosen to illustrate the use of dynamic optimization and do not necessarily reflect the true capability or restrictions of the plant. The actual potential reaction time saving may vary, but it is still significant. Moreover, the moment model shows superiority over the population balance model in terms of computational efficiency.