Continuous Reactor Network Design for Rigid Polyol Productions

This thesis focuses on the development of continuous reactor networks that consist of continuous stirred tank reactors (CSTR) and plug flow reactors (PFR) with multiple injection points for the rigid polyol productions. To meet the product specifications of this polymerization process and to minimize the capital cost of the reactor configuration, four major topics are studied: 1. model development for rigid polyol production, 2. optimization formulations and solution strategies, 3. kinetic parameter estimation, 4. reactor network design under uncertainties in kinetic parameters.

First, a detailed mathematical model is developed to capture the dynamic behavior of the polymerization process. This model includes mass balance, and energy balance. Then, this model is utilized to estimate the values of kinetic parameters involved in this process. Next, production and safety specifications are incorporated into the model to find the optimal continuous reactor network design and corresponding operation recipes that would lead to a minimum capital cost. The results show that a single PFR with multiple monomer injection points is the best design. However, the performance can deteriorate in the presence of parameter uncertainties. Compact problem formulations with modifications on the constraint (back-off constraints) and multi-scenario formulation with each scenario corresponding to one discretized uncertainty level are adopted to develop the reactor network and operation recipe. Back off terms that are obtained from Monte Carlo simulations tighten the constraint and shrink the feasible region of the optimization problem to such a level that variations of the constraints in the worst case can still be handled and thus feasibility is ensured. The multi-scenario formulation is also tolerant to the uncertainties and has better performance than the back off method, since it allows different operation recipes (recourse variables) for different scenarios. On the other hand, multi-scenario approach increases the problem size dramatically.

In this work, we demonstrate the effectiveness of both uncertainty approaches and compare the results on the multi-product reactor network. For dynamic optimization, simultaneous collocation strategy is applied to discretize the continuous time/volume horizon into finite element mesh and to covert the differential-algebraic equation (DAE) optimization problems into nonlinear programming problems (NLP). These NLPs are further solved by NLP solvers IPOPTH or CONOPT.