Dynamic optimization for grade transition processes using orthogonal collocation on molecular weight distribution

To meet the demands of a competitive market, an industrial plant often produces several grades of polymer product through the same process in an economical way. As molecular weight distribution (MWD) is a crucial quality index of polymers, dynamic optimization for grade transition based on MWD is highly important, but challenging. This study considers the development of optimization models for MWD-based grade transition. An MWD reconstruction method using orthogonal collocation in two dimensions is developed to capture the dynamic feature of MWD in time and the distributive feature in chain length. The simultaneous collocation approach is adopted to discretize the model. Two optimization formulations are proposed to describe minimizing the transition time as well as off-spec production. Both formulations inherit the advantages of the simultaneous collocation approach. The numerical results show that the proposed methods can efficiently solve the grade transition problem with MWD specification, and obtain high performance control profiles to reduce the production cost. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1198–1210, 2019     

A novel strategy for dynamic optimization of grade transition processes based on molecular weight distribution

To achieve different end‐use properties of polymers, an industrial plant must produce several grades of the product through the same process under different operating conditions. As molecular weight distribution (MWD) is a crucial quality index of polymers, grade transition based on MWD is of great importance. Dynamic optimization of the grade transition process using MWD is a challenging task because of its large‐scale nature. After analyzing the relationships among state variables during polymerization, a novel method is proposed to conduct the optimal grade transition using dynamic optimization with a small‐scale moment model, combined with a steady‐state calculation of the MWD. By avoiding expensive computation in dealing with dynamic MWD optimization, this technique greatly reduces the computational complexity of the process optimization. The theoretical equivalence of this simplification is also proved. Finally, an industrial high‐density polyethylene slurry process is presented to demonstrate the efficiency and accuracy of the proposed strategy. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2498–2512, 2014     

Simulation of transient gas flow using the orthogonal collocation method

Proper evaluation of the dynamics of the transmission system is the key element in the design and operation of natural gas pipelines. Basic equations describing the transient flow of gas in pipes are derived from the Euler equations. The orthogonal collocation technique is employed as the mathematical method for the numerical solution of the governing equations. This method leads to a set of non-linear ordinary differential equations which can be solved by the Runge–Kutta–Fehlberg method. The performance of the proposed method is tested using two practical examples. The predicted results clearly demonstrate that the proposed method can successfully simulate the isothermal and non-isothermal unsteady flow in gas transmission systems.     

Integrated scheduling and dynamic optimization of batch processes using state equipment networks

A systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Monte-Carlo simulation of the collapse transition of a two-dimensional polymer

Two-dimensional self-avoiding lattice chains with the attraction of monomers are studied by the Monte-Carlo method. A new version of the simulation technique is described. The dependence of the chain sizes, number of contacts and specific heat on the temperature and number of links are obtained and the existence of the collapse transition is proved. The precise determination of the ?-point, tricritical exponent v_t and crossover exponent Φ based on the scaling treatment yielded: ? = 1.54, v_t = 0.59, Φ = 0.6. This is in good agreement with recent theoretical predictions and experimental data. The relation with early works is also discussed.     

Modeling of semibatch styrene suspension polymerization processes

We developed a mathematical model to describe the behavior of semibatch styrene suspension polymerization processes, where the constituents of a typical emulsion polymerization process are added into the reaction vessel during the course of a typical suspension reaction. This technique was recently described for the production of core–shell polymer particles. The model assumes that the nucleated emulsion particles can agglomerate with the sticky and much bigger suspension particles and that the agglomeration rate constant is a function of the internal states of the suspended droplets. The proposed model presented good agreement with experimental conversion, average molecular weight, and molecular weight distribution data. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1950–1967, 2005     

Modeling of poly(L‐lactide) thermal degradation: Theoretical prediction of molecular weight and polydispersity index

A mathematical model to describe the molecular weight and polydispersity index (Q) in poly(L ‐lactide) (PLLA) thermal degradation has been developed. Based on the random chain scission mechanism, effects of temperature and time on the molecular weight and polydispersity index are included in this model. It incorporates the degradation and recombination reaction of PLLA thermal degradation, while taking into account the equal probability assumption. The developments of molecular weight and polydispersity index of PLLA polymer in the thermal degradation process were investigated at temperature ranging from 180–220°C, the experimental data show PLLA reaches its thermal degradation equilibrium in 2 h. The simulated results of this model are compared with the measured molecular weight and polydispersity index of the PLLA polymer. The changes of the molecular weight and polydispersity index in the PLLA thermal degradation can be predicted by this model. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2557–2562, 2003     

Mathematical model for the bulk polymerization of styrene using the symmetrical cyclic trifunctional initiator diethyl ketone triperoxide. I. Chemical initiation by sequential decomposition

In this study, we experimentally and theoretically investigated the use of the symmetrical cyclic trifunctional initiator diethyl ketone triperoxide (DEKTP) in the bulk polymerization of styrene. The experimental study consisted of a series of isothermal batch polymerizations at different temperatures (120 and 130°C) with different initiator concentrations (0.005, 0.01, and 0.02 mol/L). A mathematical model was developed to predict the evolution of the reacting chemical species and the produced molecular weight distributions. The kinetic model included chemical and thermal initiation, propagation, transfer to the monomer, termination by combination, and reinitiation reactions. The simulation results predict the concentration of diradicals, monoradicals, and polymeric chains, characterized by the number of undecomposed peroxide groups. The experimental results showed that at reaction temperatures of 120–130°C, initiation by DEKTP produced an increase in the polymerization rates (R_p's) and average molecular weights, depending on the initiator concentration, due to sequential decomposition. The mathematical model was adjusted and validated with the experimental data. The theoretical predictions were in very good agreement with the experimental results. Also, an optimum initiator concentration was observed that achieved high R_p's and high molecular weights simultaneously. For polymerization temperatures of 120–130°C, the optimum concentration was 0.01 mol/L. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

丁二烯气相聚合产物分子量分布和粒径分布模型研究

对非均相催化的丁二烯气相聚合,基于聚合物多层模型,考虑催化剂颗粒间活性位初始浓度和粒径分布对聚合物分子量分布和粒径分布的影响,建立了聚合物分子量分布和粒径分布的数学模型。模拟了反应温度、催化剂颗粒间活性位初始浓度和粒径分布等因素的影响,结果表明。随着温度升高,聚合物颗粒平均粒径变小,粒径分布变窄,聚合物分子量变小,分子量分布变宽;催化剂颗粒间的活性组分负载越均匀,聚合物分子量越大,分子量分布和粒径分布越窄;随着催化剂平均粒径变大,聚合物分子量变小,分子量分布变宽,不存在催化剂颗粒粒径分布和聚合物颗粒粒径分布间的复制现象。模型模拟结果与实验结果吻合较好,可用于预测丁二烯气相聚合产物的分子量、分子量分布和粒径分布。     

Heterogeneous bulk polymerization of styrene in the presence of polybutadiene: Calculation of the macromolecular structure

A mathematical model is presented that simulates the polymerization of styrene in the presence of polybutadiene (PB) for producing high‐impact polystyrene (HIPS) via the heterogeneous bulk process. The model follows the polymerization in two phases; and calculates in each phase the main reaction variables and the molecular structure of the three polymeric components: free polystyrene (PS), unreacted PB, and graft copolymer. Two polymerizations (at 90 and 120°C) were carried out and simulated. The model was validated with measurements of the monomer conversion, the grafting efficiencies, and the average molecular weights. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 99: 3023–3039, 2006     

分子量及其分布的测量方法在生物高分子领域中的应用

分子量是生物高分子性质的一项重要参数,决定了生物高分子的许多理化特性和生物效应.准确测定生物高分子的分子量有利于了解其性质,是其有效应用的前提.文章主要简述了近年来常用的测定生物高分子分子量的方法,如黏度测量法、凝胶渗透色谱法、基质辅助激光解暖-飞行时间质谱法、电喷雾电离质谱法,并对其进行分析和比较,为微生物合成生物高...     

PE-UHMW分子量及其分布表征技术进展

针对常规分子量表征手段很难用于超高分子量聚乙烯(PE–UHMW)的分子量测试现状,综述了PE–UHMW分子量分布及其大小测试方法。PE–UHMW分子量分布可以通过以下方式实现:利用不同温度时溶解性不同实现分离,利用凝胶色谱柱实现分离,利用运动速度与分子量之间的关系实现分离。PE–UHMW分子量测试目前主要有黏度法、凝胶色谱连用技术、流变仪法等,其中黏度法在实际生产中得到了广泛应用,但这种方法重复性差,其可靠性和准确性还不稳定。     

Modeling and simulation of photofabrication processes using unsaturated polyester resins

Several kinetic models have been proposed to simulate thermosetting cure reactions. The most complex models, based on a mechanistic approach of cure reactions, are developed based on the concepts of free radical polymerization and the mechanism of reactions with diffusion. However, mechanistic models are usually quite impractical for engineering purposes because of the difficulty in obtaining the model parameters. An alternative to these mechanistic models are the phenomenological models, formulated in terms of the degree of cure and much easier to apply. Phenomenological models have been largely used to study thermal‐initiated cure reactions, although only few works used them to model the kinetics of ultraviolet‐initiated cure reaction. This work proposes a photo‐thermal‐kinetic model to study the behavior of unsaturated polyester resins during ultraviolet‐initiated cure reactions. The model considers samples with different amounts of initiator concentration and cure reactions performed under different ultraviolet light intensities. The model has been numerically solved using the finite element technique. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

A generalized framework for solving dynamic optimization problems using the artificial chemical process paradigm: Applications to particulate processes and discrete dynamic systems

The solution of optimal control problems (OCPs) becomes a challenging task when the analyzed system includes non-convex, non-differentiable, or equation-free models in the set of constraints. To solve OCPs under such conditions, a new procedure, LARES-PR, is proposed. The procedure is based on integrating the LARES algorithm with a generalized representation of the control function. LARES is a global stochastic optimization algorithm based on the artificial chemical process paradigm. The generalized representation of the control function consists of variable-length segments, which permits the use of a combination of different types of finite elements (linear, quadratic, etc.) and/or specialized functions. The functional form and corresponding parameters are determined element-wise by solving a combinatorial optimization problem. The element size is also determined as part of the solution of the optimization problem, using a novel two-step encoding strategy. These building blocks result in an algorithm that is flexible and robust in solving optimal control problems. Furthermore, implementation is very simple.The algorithm's performance is studied with a challenging set of benchmark problems. Then LARES-PR is utilized to solve optimal control problems of systems described by population balance equations, including crystallization, nano-particle formation by nucleation/coalescence mechanism, and competitive reactions in a disperse system modeled by the Monte Carlo method. The algorithm is also applied to solving the DICE model of global warming, a complex discrete-time model.     

A multistep method for steady-state Monte Carlo simulations of polymerization processes

Identifying the microscopic information of polymers is of great significance for polymerization processes. Monte Carlo (MC) simulation is a powerful tool to predict the microscopic structure of polymers. Currently, most MC methods are designed for dynamic polymerization processes based on time evolution. The study on MC simulation for steady-state processes is scarce and current approaches face challenges in addressing complex mechanisms. In this work, a multistep method is proposed for the steady-state MC simulation. By introducing the “buffer pool” concept, the proposed method is computationally efficient and flexible to derive accurate predictions for processes with various polymerization mechanisms. Three applications with increasing complexity in the kinetic mechanisms, including both linear and branching polymerizations, are presented to demonstrate the applicability of the proposed method.     

Optimization of the synthesis of polyhydroxyurethanes using dynamic rheometry

Polyhydroxyurethanes (PHUs) produced by the reaction between dicyclocarbonate and diamine groups are often presented as possible candidates to substitute for classical polyurethanes based on isocyanate precursors. In the literature, the synthesis of this class of polymers is often performed according to arbitrary conditions of time and temperature without any scientific justification. As such, the real potential of PHUs is probably not fully known. Numerous contradictions in previously published results seem to support this hypothesis. Our paper proposes two methodologies based on dynamic rheometry to determine optimized conditions for the synthesis of PHUs. The case of a PHU formed by the reaction between 1,10‐diaminodecane and a dicyclocarbonate bearing a central aromatic group is described more precisely. The first approach consists of conducting various rheological experiments (kinetics, thermomechanical analyses) in situ on the reaction mixture. The second one retains the same technique to qualify the viscoelastic properties of PHUs synthesized according to various conditions. In this latter case, all samples show thermomechanical behaviour of amorphous thermoplastic polymers. But discrepancies are observed with regard to the value of the glass transition temperature and the existence or not of a rubbery zone. Comparison of these data with size exclusion chromatography results shows that these differences are direct consequences of the polymer molecular weight that can be predicted using macromolecular theory. The properties of the PHUs obtained after optimization of the polymerization reaction were compared with literature data in order to complete the evaluation of the efficiency of the rheological methodology. Copyright © 2012 Society of Chemical Industry     

Characterization of the molecular structure of masticated natural rubber using rheological techniques

Mastication can improve the plasticity and reduce the molar mass of natural rubber (NR). The end product properties greatly depend on the efficiency of mastication. For NR before and after mastication, the changes in molecular properties are mainly attributed to the effects of mechanical and thermo-oxidative degradation. We investigated the variations in molecular weight, molecular weight distribution, degree of branching, and thermal stability of NR after mastication at 35, 75, and 110 rpm for 20 min. The results show that NR has a smaller molecular weight, broader molecular weight distribution, and a lower degree of structural branching at higher rotor speeds. Additionally, the rheological measurements were compared with gel permeation chromatography results, and the comparative outcomes reflect a strong correlation between these data. Rheological analysis reveals considerable complex relationships, and this measurement is more efficient, simple, and convenient than the other technique.     

锂离子电池正极涂层孔隙结构优化的数值模拟

以磷酸铁锂(LFP)为正极材料的锂离子电池在电子产品、电动汽车等领域应用广泛,但其能量密度仍有待提升以进一步满足不同场景应用需求。锂离子在正极孔隙电解液中的扩散过程是LFP锂离子电池性能的控制因素之一,通过优化电极孔隙结构可以在一定程度上减小锂离子在电解质中的扩散阻力进而提升能量密度。采用准二维模型描述电池内部的传质电化学过程,考察了当锂离子电池正极孔隙存在梯度分布后对锂离子电池能量密度的影响及作用机理。通过对比孔隙率均匀分布和梯度分布的电池模拟结果,发现孔隙率的梯度分布能提高单位活性材料的利用率,提升电解质通量和电极活性材料的嵌锂量,从而增加电池能量密度。随着电极厚度的增加,孔隙率分布的梯度越大,对能量密度的提升效果越显著,研究结果对于厚电极涂层的制备工艺具有重要意义。     

Gas‐phase polymerization of butadiene. Data acquisition using minireactor technology and particle modeling

Minireactor technology has been used for kinetic studies on polymerization kinetics, phase equilibrium, and mass transfer on a very small scale. There is a nonlinear influence of temperature and pressure on the polymerization rate. The phase equilibrium can be described by a Flory–Huggins approach, with a temperature‐dependent interaction parameter. The diffusion coefficient seems to be slightly pressure dependent, and the temperature dependence can be described with an Arrhenius equation. A simple formal kinetic scheme with formation of active sites, chain propagation, chain transfer to cocatalyst, and deactivation of active sites has been applied. This kinetic scheme was implemented in two different models; they are, a particle model taking into account mass transfer and a simple chemical model with no mass transfer. In principle, both models describe the experimental results for rate and molecular weight distribution equally well, with rate constants of the same magnitude. Molecular weight distributions calculated by the chemical model are narrower. However, the chemical model gives no explanation for the experimental observed rate dependence on catalyst particle size. With increasing catalyst activity, the differences between both models become more significant and the particle model becomes more and more important. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 270–279, 2003     

聚合物生产分子量分布建模与控制研究

分子量分布是关系聚合物性质的重要性能指标 ,针对聚合过程分子量分布的建模和控制关键技术进行了分析和综述 ,指出各自的优缺点 ,给出了这一领域今后的研究方向