We report the theoretical derivation of a kinetic model for the prediction of average block structures such as number-average blocks, average block length, and average number of linkage points per chain, etc., in chain shuttling polymerization in the presence of dual catalysts based on the proposed mechanism. We further investigate how the chain shuttling rate constant and virgin chain shuttling agent (CSA) feed rate affect the average block structures predicted by this theoretical model for polymers produced in a continuous stirred tank reactor (CSTR). The simulations demonstrate that the coordination of dual catalysts and CSA is the key to enabling a successful chain shuttling polymerization system.
The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles including the mass and population balances, reaction kinetics, and vapor‐liquid equilibria. Next, the obtained differential algebraic model is reformulated by applying a nullspace projection method that results in an equivalent dynamic system with better computational performance. The reactor model is validated against plant data by adjusting model parameters. A dynamic optimization problem is then formulated to optimize the process recipe, where the batch processing time is minimized, given a target product molecular weight as well as other requirements on product quality and process safety. The dynamic optimization problem is translated into a nonlinear program using the simultaneous collocation strategy and further solved with the interior point method to obtain the optimal control profiles. The case study result shows a good match between the model prediction and real plant data, and the optimization approach is able to significantly reduce the batch time by 47%, which indicates great potential for industrial applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2515–2529, 2013
We propose a model-based optimization approach for the integration of production scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. The process is described by the resource task network (RTN) representation coupled with detailed first-principles process dynamic models. General complications in scheduling and control can be fully represented in this modeling framework, such as customer orders, transfer policies, and requirements on product quality and process safety. The scheduling and operation layers are linked with the task history state variables in the state space RTN model. A tailored generalized Benders decomposition (GBD) algorithm is applied to efficiently solve the resulting large nonconvex mixed-integer nonlinear program by exploring the particular model structure. We apply the integrated optimization approach to a polymerization process with two parallel semibatch reactors and continuous storage and purification units. The two polymerization reactors share cooling utility from the same source, and the utility price is dependent on the consumption rate. The optimization objective is to design the process schedule and reactor control policies simultaneously to maximize the overall process profit. The case study results suggest improvements in plant profitability for the integrated approach, in contrast to the typical sequential approach, where recipes of the polymerization tasks are individually optimized but the interactions among process units are overlooked.
This paper addresses reactor modeling and recipe optimization of semibatch ring-opening polymerization processes for making block copolymers. Two rigorous reactor models are developed on the basis of the population balance and method of moments, respectively. The complete polymerization process model also includes vapor−liquid equilibrium equations from applying Flory−Huggins theory. The accuracies of both reactor models are validated against historical plant data by adjusting model parameters such as kinetic rate constants. The recipe optimization problem is formulated to design the optimal reactor operating policy to minimize polymerization time and incorporate additional process constraints in accordance with final product properties and process safety requirements. The resulting 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, both reactor models show satisfactory matches between their predictions and the historical plant data. The recipe optimization with both models demonstrates significant process improvement and reductions in batch operating time. Moreover, the moment model shows superiority over the population balance model in terms of computational efficiency.
A mixed integer linear programming (MILP) model is developed for the optimal reactive scheduling of a mixed batch/continuous process, based on the discrete time resource task network (RTN) representation and extensions. The scheduling task is complicated with the mixed process units and network structure, as well as operation rules such as product changeovers. The extended RTN model introduces modifications to the conventional RTN models such as multiextent resource balances and, also, adds more features such as resource limit balances and resource slacks. These extensions allow for efficient modeling of the mixed plant in great detail. The extended RTN model is further reformulated to the state space form by incorporating lif ted state variables that represent task histories. The state space RTN model facilitates reactive schedule design, particularly when used with the rolling horizon scheme. In the case study, we show the advantages of the state space RTN model in periodic rescheduling under process disruptions.
In this work, we review the theory behind solution viscosity and show how it inspires the mathematical formulation of semi-empirical models. We then demonstrate parameter estimation and model discrimination using experimental data for established product designs and, finally, validate the model by applying it to developmental products.
There has been rapid growth in the application of in situ optical spectroscopy techniques for reaction and process monitoring recently in both academia and industry. Vibrational spectroscopies such as mid-infrared, near-infrared spectroscopy, and Raman spectroscopy have proven to be versatile and informative. Accurate determination of concentrations, based on highly overlapped spectra, remains a challenge. As an example, 1,2-butylene oxide (BO) polymerization, an important industrial reaction, initiated by propylene glycol (PG) and catalyzed by KOH, is studied in this work in a semi-batch fashion by using in situ attenuated total reflectance Fourier transform infrared spectroscopy (ATR FT-IR) monitoring. The weak BO absorbance, the constantly changing interference from the product oligomers throughout the course of the reaction, and the change in BO spectral features with system polarity posed challenges for quantitative spectral analysis based on conventional methods. An iterative concentration-guided classical least-squares (ICG-CLS) method was developed to overcome these challenges. Taking advantage of the concentration-domain information, ICG-CLS enabled the estimation of the pure oligomer product spectra at different stages of the semi-batch process, which in turn was used to construct valid CLS models. The ICG-CLS algorithm provides an in situ calibration method that can be broadly applied to reactions of known order. Caveats in its applications are also discussed.
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