Multiobjective dynamic optimization of semibatch copolymerization reactors

Polymerization reactor optimal design and control problems are inevitably multiobjective in nature. Copolymerization problems encompass an even larger set of objective functions than homopolymerization. This work describes in some detail a set of typical components of the vector of objective functionals for copolymerization reactor problems. A subset of these is selected for detailed examination employing multiobjective function optimization techniques. Noninferior, or Pareto, sets of optimal solutions have been determined for the dual objectives of narrowing both copolymer composition and molecular weight distributions in the styrene-acrylonitrile system. Noninferior solutions occur when the two objectives are in conflict and no objective can be improved without sacrifice of the other. We show for several sets of control variables that, in the S-AN system, one should seldom, if ever, control with respect to one objective functional exclusively. Compromise policies can be found which are close to utopian for both objectives. A better quantitative understanding of the trade-offs between objectives in copolymerization engineering has been achieved.     

Steady state behavior of moving bed reactors

A relatively simple model for a moving bed reactor in which ignition takes place is presented and the steady state problem is solved analytically and numerically. The dependence of multiplicity and the nature of the solution on the parameters of the system are investigated. Some similarities in the analyses between fixed bed reactor theory and moving bed reactor theory are shown.     

Emulsion copolymerization of vinyl esters in continuous reactors: Comparison between loop and continuous stirred tank reactors

The high solids emulsion copolymerization of vinyl acetate and veova 10 was studied in a continuous loop reactor and in a continuous stirred tank reactor (CSTR) in an attempt to elucidate the similarities and differences between these reactors. Reactions were carried out under comparable conditions, namely, similar macromixing and the same feed composition and space time. The behavior of both reactors was almost the same when the heat generation rate was low; otherwise, thermal runaway occurred in the CSTR whereas the loop reactor temperature was easily controlled. © 1995 John Wiley & Sons, Inc.     

An experimental study of multiobjective dynamic optimization of a semibatch copolymerization process

Optimal open loop control strategies are developed for a semibatch free radical copolymerization of methyl methacrylate and vinyl acetate using the multiobjective dynamic optimization method. A detailed kinetic model is validated through experimentation and used for the design of optimal controls. Both monomer feed rate and reactor temperature are varied to produce the copolymer of desired composition and molecular weight. The open loop control policies are implemented in a process control computer and tested on an experimental stirred tank polymerization system. Excellent agreement between the model predictions and the experimental data have been obtained.     

Steady state simulation of continuous-flow stirred-tank slurry propylene polymerization reactors

Methodologies are developed for studying the steady-state operation of propylene polymerization in continuous-flow stirred tank reactors (CFSTRs). The effect of several reactor operating variables and reaction variables (e.g., mean residence time, catalyst deactivation rate, multisite catalyst activity, etc.) on polymer properties is obtained. It is found that a compromise has to be made between the yield of the polymer and its polydispersity index, since they usually show opposing trends with the mean residence time.     

Steady state multiplicity of fluidized bed reactors. The solid-circulation model

A solid circulation model is used to investigate the steady-state multiplicity features of a fluidized bed reactor in which a single, first-order, exothermic reaction occurs. The model predicts that up to five steady-state solutions may exist. Numerical examples seem to indicate that at most two of the states are stable. The temperature profiles computed by the solid-circulation model are similar to those computed by the axial conductivity model. A regular perturbation expansion is used to prove that the axial-conductivity model and the corresponding Danckwerts boundary conditions are a special limiting form of the solid-circulation model attained when the rate of solid exchange between the bubbles and the dense phase is high.     

Steady state multiplicity depending on coalescence in liquid—liquid continuous stirred reactors with reaction in the dispersed phase

The influence of drop coalescence and breakup on the existence of multiple steady states is studied for a two-phase stirred isothermal reactor where the chemical reaction in the d?ispersed phase obeys the rate expression ? r = kC/(1 + KC)². The random coalescence model developed by Curl was simulated using a modified Spielman and Levenspiel Monte Carlo technique.For certain range of the coalescence rate, Damköhler number, and dimensionless feed concentration, multiple steady states have been investigated.A special case has also been considered wherein the existence of multiple steady states for finite values of the coalescence rate is contrasted to the unique steady state solution for an infinite coalescence rate.     

Multiplicity of the steady state in fluidised bed reactors — I.: Steady state considerations

Multiple steady states are known to be possible in many types of chemical reactor due to the non-linear dependence of reaction rate on either temperature or reactant concentration. It is reasoned in this study that multiple steady states can also exist in a gas-solid fluidised bed reactor. The calculations are based on the two-phase theory of fluidisation and on the important assumption that the interstitial phase gas in completely mixed. Both thermal and concentration multiplicites are shown to be possible.     

Composition control of batch copolymerization reactors

Composition control of free-radically initiated batch copolymerization reactor by temperature manipulation is investigated through a program of calcula and experiment. The work of Ray and Gall is extended to explicit calculation of temperature vs time policies which eliminate or minimize composition dr Both continuous and discrete, piecewise-constant policies have been computed. The former are disjoint policies which can be found simply by manipulatin monomer mass balances; the latter are found through application of the discrete version of the maximum principle. Calculations are compared to experime done on the system styrene-acrylonitrile. It is demonstrated that implementation of some of the computed policies is feasible and quite beneficial. The discrete policies with small numbers of stages (less than ～six) perform much more poorly than the continuous policies indicating that the copolymeriz reactor is much more sensitive to deviations from optimality than batch reactors operating with other reaction schemes. Thus, effective implementatio tracking a continuous trajectory.     

Mathematical modeling of emulsion copolymerization reactors

This article presents the physical mechanism and the mathematical structure of a comprehensive dynamic emulsion polymerization model (EPM). EPM combines the theory of coagulative nucleation of homogeneously nucleated precursors with detailed species material and energy balances to calculate the time evolution of the concentration, size, and colloidal characteristics of latex particles; the monomer conversions; the copolymer composition; and molecular weight in an emulsion system. The capabilities of EPM are demonstrated by comparisons of its predictions with experimental data from the literature covering styrene and styrene/methyl methacrylate polymerizations. EPM can successfully simulate continuous and batch reactors over a wide range of initiator and added surfactant concentrations.     

Low-density polyethylene vessel reactors: Part I: Steady state and dynamic modelling

By the use of a perfectly mixed model and an imperfectly mixed one for lowdensity polyethylene vessel reactors, we show that increases in the initiator consumption with polymerization temperature are due to mixing limitations at the initiator feed. With all its parameters independently estimated, the imperfectly mixed model provides an excellent agreement with experimental data for several initiators, feed flow rates and polymerization pressures. In the temperature region of industrial interest for each type of initiator, the open-loop reactor dynamics drastically change from open-loop unstable, at low temperatures, to open-loop stable at high polymerization temperatures.     

Steady state optimization with guaranteed stability of a tryptophan biosynthesis model

In this article we address the steady state design of a nonlinear tryptophan biosynthesis model with guaranteed stability of the optimal solution in the presence of parametric uncertainty. The optimization based approach – denoted constructive nonlinear dynamics (CNLD) – is based on constraints that enforce a minimal distance in the space of the uncertain parameters between a stability boundary and the optimal solution. The results obtained with CNLD are compared to results recently presented by Chang and Sahinidis [Chang, Y. J., & Sahinidis, N. V. (2005). Optimization of metabolic pathways under stability considerations. Computers and Chemical Engineering, 29 (3), 467–479], where the optimization of the tryptophan biosynthesis model was addressed by a global optimization algorithm. CNLD takes the nonlinearities of the process exactly into account and satisfies the specified robustness criteria without being overly conservative.     

正丁醇-水混合物双塔精馏流程的稳态模拟及优化

本文采用UNIFAC模型计算正丁醇-水混合物的汽液平衡数据,应用SRK状态方程计算气、液相的焓值,对正丁醇-水混合物双塔精馏流程进行了稳态模拟和优化,得到了各物料流的温度、压强、流量和组成以及精馏塔理论板上的温度分布、汽(液)相流量分布和组成分布及再沸器的热负荷,该计算对正丁醇-水系统双塔精馏工艺的设计和操作具有实际意义。     

The dynamic behavior of continuous polymerization reactors—II Nonisothermal solution homopolymerization and copolymerization in a CSTR

The possible types of dynamic behavior have been determined for a CSTR in which bulk or solution free radical polymerization is carried out. To illustrate the methodology, the expected behavior of reactors for vinyl acetate or methylmethacrylate homopolymerization and vinyl acetate-methylmethacrylate copolymerization has been explicitly determined. The monomer feed ratios, solvent concentrations, and reactor cooling capacity which allow multiple steady states and limit cycles have been carefully mapped.     

Method of multiobjective optimization for imprecise objectives

A method of multiobjective optimization for imprecise objectives is presented. The problem consisted in a minimization of the distance between the set of admissible solutions and an ideal point. Applicability of the method is illustrated by the choice of best impeller from a group of seven different types tested. The optimum process conditions were selected, taking as optimization objective the maximization of k_La and minimization of P_G.     

Stability of continuous emulsion polymer reactors

The stability of continuous emulsion polymer reactors having steady feed streams was studied. Analysis of a population balance model supported the notion of micelle deprivation as the chief cause of reactor instabilities. Analysis of the moments of the distribution indicated that the system may be uniquely stable in one case. Only one steady-state operating point was predicted for the case where the decrease in the termination rate constant due to the gel effect was neglected.     

Stability of continuous emulsion polymer reactors

The stability of continuous emulsion polymer reactors having steady feed streams was studied. Analysis of a population balance model supported the notion of micelle deprivation as the chief cause of reactor instabilities. Analysis of the moments of the distribution indicated that the system may be uniquely stable in one case. Only one steady-state operating point was predicted for the case where the decrease in the termination rate constant due to the gel effect was neglected.     

Sustainable biopolymer synthesis via superstructure and multiobjective optimization

Sustainable polymers derived from biomass have great potential to replace petrochemical based polymers and fulfill the ever‐increasing market demand. To facilitate their industrialization, in this research, a comprehensive superstructure reaction network comprising a large number of reaction pathways from biomass to both commercialized and newly proposed polymers is constructed. To consider economic performance and environmental impact simultaneously, both process profit and green chemistry metrics are embedded into the multiobjective optimization framework, and MINLP is used to enable the effective selection of promising biopolymer candidates. Through this proposed approach, this study identifies the best biopolymer candidates and their most profitable and environmentally friendly synthesis routes under different scenarios. Moreover, the stability of optimization results regarding the price of raw materials and polymers and the effect of process scale on the investment cost are discussed in detail. These results, therefore, pave the way for future research on the production of sustainable biopolymers. © 2017 American Institute of Chemical Engineers AIChE J, 63: 91–103, 2018