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.     

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.     

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.     

Steady state modeling and simulation of an industrial sugar continuous crystallizer

The profile of supersaturation along a continuous crystallizer of sugar factories, is the decisive factor that determines the performance of this apparatus. In order to control this profile, a mathematical model was developed taking into account the main physicochemical phenomena involved in crystallization process. The model is based on flow pattern, which was assumed and validated against plant measurements using a tracer test. The steady state mathematical model developed describes the most important aspects of the crystallizer behavior in each compartment: supersaturation, crystal size distribution and flow rate of the product crystals. The model can also describe the undesirable behavior such as dissolution and nucleation. Validation of the developed model was performed using industrial data. A parametric sensitivity study confirmed that the syrup supply distribution is the main variable that should be manipulated to achieve good performance for the crystallizer.     

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.     

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。     

Modeling and optimization of the cyclic steady state operation of adsorptive reactors

Adsorptive reactors(AR),in which an adsorptive functionality is incorporated into the catalytic reactors,offer enhanced performance over their conventional counterparts due to the effective manipulation of concentration and temperature profiles.The operation of these attractive reactors is,however,inherently unsteady state,complicating the design and operation of such sorption-enhanced processes.In order to capture,comprehend and capitalize upon the rich dynamic texture of adsorptive reactors,it is necessary to employ cyclic steady state algorithms describing the entire reaction-adsorption/desorption cycle.The stability of this cyclic steady state is of great importance for the design and operation of adsorptive reactors.In this paper,the cyclic steady state of previously proposed novel adsorptive reactor designs has been calculated and then optimized to give maximum space–time yields.The results obtained revealed unambiguously that an improvement potential of up to multifold level could be attained under the optimized cyclic steady state conditions.This additional improvement resulted from the reduction of the regeneration time well below the reaction-adsorption time,which means,in turn,more space–time yield.     

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.     

Optimization of styrene acrylonitrile random bulk copolymerization reactors

Bulk polymerization of random styrene‐acrylonitrile (SAN) copolymer using AIBN initiator, in nonisothermal batch reactors is optimized using single and multiple objective functions. The objectives are selected from among: minimization of the reaction time, maximization of the overall monomer conversion, and maximization of the number average molecular weight of the product. Constraints are used for the mole fraction of styrene in the copolymer produced (so as to produce copolymer having desired properties), and on the permissible range of temperature in the reactor. Pareto optimal solutions are obtained for some sample 2‐ and 3‐objective optimization problems. The optimization toolbox of MATLAB with genetic algorithm as the solver is used. Different points in the Pareto set are associated with different optimal temperature histories, a few of which are provided. POLYM. ENG. SCI., 55:2377–2387, 2015. © 2015 Society of Plastics Engineers     

Design strategy and process optimization for reactors with continuous transport of an immobilized enzyme

In order to operate a process which uses immobilized enzymes at constant conversion and constant capacity, the refreshment of the enzyme must be continuous. In this paper, two reactor types with continuous refreshment of the biocatalyst are discussed: the stirred tank and the multistage fluidized bed. A method is presented for dimensioning a reactor in such a way that the costs for the conversion of substrate to product are minimized. These costs are calculated as the sum of the biocatalyst consumption and overall reactor costs.In contrast with the stirred-tank reactor, the multistage fluidized bed can be operated at a non-uniform temperature. For the glucose isomerase process, an optimal temperature gradient results in a small reduction in the biocatalyst consumption (±5%). It is concluded that, in general, a temperature gradient will only favour the economy of processes with relatively expensive biocatalysts.Compared with conventional reactor types, such as the continuous stirred-tank reactor and the fixed-bed reactor, the multistage fluidized-bed reactor can improve the economy of an enzyme-catalysed reaction significantly.