Reactor Modeling and Recipe Optimization of Ring-Opening Polymerization: Block Copolymers

Nie, Yisu; Biegler, Lorenz T.; Villa, Carlos; Wassick, John M.

doi:10.1021/ie402770k

Cited by 11 publications

(28 citation statements)

References 18 publications

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“…where T ad is the adiabatic end temperature, which is constrained below an upper bound for safety. Finally, because monomer B is potentially explosive in nitrogen; an upper limit to y B , the vapor phase concentration of B, is given as a linear function of temperature and pressure in [30]. For implementation of the optimization model, both population balance and moment models are implemented in the General Algebraic Modeling System (GAMS) [24] platform after discretization into NLP form.…”

Section: Process Recipe Optimizationmentioning

confidence: 99%

“…To develop the kinetic model, one begins with the balances for both monomers described in :

true \begin{matrix} right1 & left \frac{normald M^{normalA}}{normald t} = F^{normalA} - V^{- 1} \\ right1 & left [\begin{matrix} k_{i}^{A} (G_{0, 0} + Q_{0, 0}) + k_{p}^{AA} \sum_{n_{A} = 1}^{\infty} \sum_{n_{B} = 0}^{\infty} (G_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalA} + Q_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalA}) + \\ k_{p}^{BA} \sum_{n_{A} = 0}^{\infty} \sum_{n_{B} = 1}^{\infty} (G_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalB} + Q_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalB}) + \\ k_{t} \sum_{n_{A} = 0}^{\infty} \sum_{n_{B} = 0}^{\infty} (G_{{normaln}_{normalA}, {normaln}_{}} \end{matrix} \end{matrix}

…”

Section: Modeling Of Copolymerization Processmentioning

confidence: 99%

“…The liquid density is solely dependent on the reactor temperature since the effects of molecular weight on density are found to be minor. The liquid volume V is calculated in as a linear function of temperature and the total reactor pressure P is calculated as the sum of the partial pressures of volatile components, determined from the liquid phase activities and saturated vapor pressures:

true P = \sum_{normali} P_{normali}

true P_{normali} = a_{normali} P_{normali}^{normalsat}

…”

Section: Modeling Of Copolymerization Processmentioning

confidence: 99%

Section: Process Recipe Optimizationmentioning

confidence: 99%

“…Consequently, an optimization model with 191 408 variables and 185 147 constraints was solved by IPOPT in 5221 CPU s. The optimal batch time (at a normalized value of 0.588) is slightly worse than the one obtained with the moment model, and the end‐point values of the final time process constraints are similar to the moment model case. As described in detail in , the optimal control recipe generated with the population balance model is very similar to the optimal moment model solution. On the other hand, the population balance model is able to reveal the chain length distribution, with three‐dimensional plots shown in for the product and byproduct chains.…”

Section: Process Recipe Optimizationmentioning

confidence: 99%

See 4 more Smart Citations

Integrated Dynamic Optimization and Scheduling of Polymerization Processes with First Principle Models

Nie

Biegler

2017

Chemie Ingenieur Technik

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An integrated dynamic optimization strategy is presented for block copolymerization processes. First the reactor model, which has unstable modes and may lead to unbounded profiles under certain design and operating conditions, is derived. Second, optimal recipes for operating of the copolymerization process are determined. Finally, an optimization strategy for the integration of scheduling and dynamic process operation for general continuous/batch processes is considered. The resulting approach leads to significant improvements in productivity, while maintaining safe operation and satisfaction of product specifications.

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Section: Process Recipe Optimizationmentioning

confidence: 99%

“…To develop the kinetic model, one begins with the balances for both monomers described in :

true \begin{matrix} right1 & left \frac{normald M^{normalA}}{normald t} = F^{normalA} - V^{- 1} \\ right1 & left [\begin{matrix} k_{i}^{A} (G_{0, 0} + Q_{0, 0}) + k_{p}^{AA} \sum_{n_{A} = 1}^{\infty} \sum_{n_{B} = 0}^{\infty} (G_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalA} + Q_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalA}) + \\ k_{p}^{BA} \sum_{n_{A} = 0}^{\infty} \sum_{n_{B} = 1}^{\infty} (G_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalB} + Q_{{normaln}_{normalA}, {normaln}_{normalB}}^{normalB}) + \\ k_{t} \sum_{n_{A} = 0}^{\infty} \sum_{n_{B} = 0}^{\infty} (G_{{normaln}_{normalA}, {normaln}_{}} \end{matrix} \end{matrix}

…”

Section: Modeling Of Copolymerization Processmentioning

confidence: 99%

true P = \sum_{normali} P_{normali}

true P_{normali} = a_{normali} P_{normali}^{normalsat}

…”

Section: Modeling Of Copolymerization Processmentioning

confidence: 99%

Section: Process Recipe Optimizationmentioning

confidence: 99%

Section: Process Recipe Optimizationmentioning

confidence: 99%

See 3 more Smart Citations

Integrated Dynamic Optimization and Scheduling of Polymerization Processes with First Principle Models

Nie

Biegler

2017

Chemie Ingenieur Technik

Self Cite

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Continuous reactor network design for multiple rigid polyol productions

Wen

Biegler

Ochoa

et al. 2021

J Adv Manuf & Process

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This study focuses on developing continuous reactor network models able to produce multiple rigid polyol products under strict product and safety specifications. We first determine reactor networks and operating decisions for minimum capital cost, and then find reactor networks with optimal profit through multi‐criteria optimization, using a Pareto chart to analyze the relationship between capital cost and net sales. Based on our previous study, we narrow down the types of continuous reactors that can be part of the network to two: plug flow reactor (PFR) with multiple feed injection points and a network of continuous stirred tank reactors (CSTR). The CSTR model can be written as a mixed integer nonlinear programming (MINLP) problem. The PFR model is a differential algebraic equation (DAE) optimization problem. The simultaneous collocation method is applied to transform the resulting DAE model into an MINLP, which is solved as a NLP by fixing the binary terms. Both capital cost and multi‐criteria problems are formulated as multi‐scenario optimization problems to determine the best single network design to produce multiple polymer products.

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Modeling of Ring Opening Polymerization: A short review with insights on how to develop the method of moments

Rosa

Ferreira

Lona

2021

Chemical Engineering Science

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Reactor Modeling and Recipe Optimization of Ring-Opening Polymerization: Block Copolymers

Cited by 11 publications

References 18 publications

Integrated Dynamic Optimization and Scheduling of Polymerization Processes with First Principle Models

Integrated Dynamic Optimization and Scheduling of Polymerization Processes with First Principle Models

Continuous reactor network design for multiple rigid polyol productions

Modeling of Ring Opening Polymerization: A short review with insights on how to develop the method of moments

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