Determination of biogeochemical parameters in eutrophication models with simultaneous dynamic optimization approaches

This work addresses a parameter estimation problem in an ecological water quality model through a simultaneous dynamic optimization approach. The model is based on first principles and has a large number of parameters, which must be estimated based on data collected in the water body under study. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem, with a weighted least squares objective function. Main biogeochemical parameters have been obtained, which allow a close representation of the lake dynamics, as it is shown in the numerical results.     

基于RAGA的PPE模型评价油页岩矿坑积水水质的研究

通过构造投影指标函数进行优化设计,建立基于实数编码的加速遗传算法的投影寻踪综合评价模型对油页岩露天矿坑积水水质进行评价.结果表明,该水质评价模型的相关系数为0.9999,对于油页岩矿坑积水水质评价精度较高,分析可知,评价水样多数为V类水,水质情况较差.进一步研究发现,RAGA-PPE模型对水质的评价是有一定的局限性的,评价水质指标超过最大指标标准过多,会导致评价模型精度下降.     

Water sustainability: A systems engineering approach to restoration of eutrophic Lakes

We address restoration of eutrophic lakes and reservoirs through the formulation of dynamic optimization problems subject to complex PDAE systems representing biogeochemical processes in the water bodies. The model includes phytoplankton, zooplankton, fish, nutrients, DO, particulate and dissolved carbon dynamics. The PDAE has been transformed into an ordinary differential algebraic equation system by spatial discretization into two water layers. An optimal control problem for the implementation of three different restoration techniques and their combinations has been formulated within a control vector parameterization approach. Numerical results for the different problems provide optimal profiles for tributary deviation flowrate through a nearby wetland, aeration rates and fish removal rates, as restoration strategies.     

Dynamic modelling of a gas phase catalytic fixed-bed reactor—I: Experimental apparatus and determination of reaction kinetics

A large scale fixed bed pilot reactor for performing dynamic experiments is described. The reactor system is especially designed to suppress secondary dispersion effects not characteristic for the packed bed itself.As a model reaction the reaction between oxygen (<1%) and hydrogen on a platinum catalyst supported by alumina has been used.Differential reactor experiments disclosed a hysteresis phenomenon in the catalyst activity. The catalyst is generally more active when going from high to low temperatures than vice versa.A global first order reaction rate expression with Arrhenius temperature dependency fits the fixed-bed reactor profiles well but the static gains badly. However by simultaneous estimation of frequency factor and activation energy in several axial segments a much better approximation to the static gains was obtained. This result indicates that the reaction kinetics is more complicated than first assumed. However for dynamic modelling the exact reaction mechanism is not needed.     

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     

Reactor modeling and recipe optimization of polyether polyol processes: Polypropylene glycol

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     

聚丙烯环形反应器模拟与分析：（Ⅱ）动态特性和操作稳定性

建立了聚丙烯环形反应器动态数学模型,通过模拟计算,研究了工艺参数扰动时聚丙烯环形反应器的动态响应规律、反应器结构参数对动态特性的影响,并对冷却水流量和冷却水入口温度进行了动态操作稳定性分析。     

Studies on melt spinning. II. Analysis of the deformation and heat transfer processes

A generalized, empirical equation is proposed which takes into account the dependence of elongational viscosity on both elongation rate and temperature. From this, a mathematical model for simulating the melt spinning process has been developed. The model has been tested against experimentally observed velocity profiles in fibers of polystyrene and high-density polyethylene spun into an isothermal chamber. It has been found that predicted velocity profiles agree well with experimentally observed ones. The mathematical model has been used to predict velocity and temperature profiles in fibers spun into a cooling medium. The simultaneous solution of momentum and energy balance equations by means of a numerical integration scheme has generated important information such as distributions of force components involved in spinning and distributions of the total rate of heat transfer along the spinning way.     

Dynamic optimization of the methylmethacrylate cell‐cast process for plastic sheet production

Traditionally, the methylmethacrylate (MMA) polymerization reaction process for plastic sheet production has been carried out using warming baths. However, it has been observed that the manufactured polymer tends to feature poor homogeneity characteristics measured in terms of properties like molecular weight distribution. Nonhomogeneous polymer properties should be avoided because they give rise to a product with undesired wide quality characteristics. To improve homogeneity properties force‐circulated warm air reactors have been proposed, such reactors are normally operated under isothermal air temperature conditions. However, we demonstrate that dynamic optimal warming temperature profiles lead to a polymer sheet with better homogeneity characteristics, especially when compared against simple isothermal operating policies. In this work, the dynamic optimization of a heating and polymerization reaction process for plastic sheet production in a force‐circulated warm air reactor is addressed. The optimization formulation is based on the dynamic representation of the two‐directional heating and reaction process taking place within the system, and includes kinetic equations for the bulk free radical polymerization reactions of MMA. The mathematical model is cast as a time dependent partial differential equation (PDE) system, the optimal heating profile calculation turns out to be a dynamic optimization problem embedded in a distributed parameter system. A simultaneous optimization approach is selected to solve the dynamic optimization problem. Trough full discretization of all decision variables, a nonlinear programming (NLP) model is obtained and solved by using the IPOPT optimization solver. The results are presented about the dynamic optimization for two plastic sheets of different thickness and compared them against simple operating policies. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A-A-O法处理焦化废水的技术改进及工艺控制

对原有A-A-O废水处理系统进行改进:预处理部分在2个事故水池间搭建虹吸桥管,以提高其利用率;污泥回流系统改液下泵为液上泵,并将其与二沉池回流管连接,确保污泥回流系统正常运行;缺氧池加装压缩空气吹扫及充氧管,保证好氧池进水并通过对进水水质和工艺控制,使A-A-O处理系统的出水达国家二类一级排放标准,全部回用于熄焦用水。改进后的A-A-O处理工艺经济效益、社会效益良好。     

Advances in simultaneous strategies for dynamic process optimization

Following on the popularity of dynamic simulation for process systems, dynamic optimization has been identified as an important task for key process applications. In this study, we present an improved algorithm for simultaneous strategies for dynamic optimization. This approach addresses two important issues for dynamic optimization. First, an improved nonlinear programming strategy is developed based on interior point methods. This approach incorporates a novel filter-based line search method as well as preconditioned conjugate gradient method for computing search directions for control variables. This leads to a significant gain in algorithmic performance. On a dynamic optimization case study, we show that nonlinear programs (NLPs) with over 800,000 variables can be solved in less than 67 CPU minutes. Second, we address the problem of moving finite elements through an extension of the interior point strategy. With this strategy we develop a reliable and efficient algorithm to adjust elements to track optimal control profile breakpoints and to ensure accurate state and control profiles. This is demonstrated on a dynamic optimization for two distillation columns. Finally, these algorithmic improvements allow us to consider a broader set of problem formulations that require dynamic optimization methods. These topics and future trends are outlined in the last section.     

OPTIMAL CONTROL OF THE PRIMARY AND SECONDARY DRYING STAGES OF BULK SOLUTION FREEZE DRYING IN TRAYS

The problem of operating a tray freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem with the use of the rigorous unsteady state mathematical model of Sadikoglu and Liapis [9] that has been found to describe satisfactorily the experimental dynamic behavior of the primary and secondary drying stages of bulk solution freeze drying of pharmaceuticals in trays. The heat input to the material being dried and the drying chamber pressure are considered to be control variables. Constraints are placed on the system state variables by the melting and scorch temperatures during primary drying, and by the scorch temperature during secondary drying. Necessary conditions of optimality for both the primary and secondary drying stages are derived and presented, and an approach for constructing the optimal control policies that would minimize the drying times for both the primary and secondary drying stages, is presented. The theoretical approach presented in this work was applied in the freeze drying of skim milk, and significant reductions in the drying times of primary and secondary drying were obtained, when compared with the drying times obtained using the operational policies reported in the literature, by using the optimal control policies constructed from the theory presented in this work. Furthermore, it is shown that the optimal control policy leads to the desired in practice result of having at the end of secondary drying temperature and bound water concentration profiles (in the dried layer) whose gradients are very small. It is also shown that by using the optimal control policy and an excipient capable of increasing the melting temperature without affecting product quality, one can significantly reduce the drying time of the primary drying stage.     

MULTI-REGION MODELS FOR DESCRIBING OXYGEN TENSION PROFILES IN HUMAN TUMORS

Multi-region simultaneous diffusion-reaction models are presented for describing oxygen tension profiles in human tumors. The models characterize the spherical tumor mass as either two regions, a central core of necrosis surrounded by a viable layer, or three regions where the viable layer is divided into a hypoxic region surrounded by a well-oxygenated rim. Estimates for the model parameters are based on steady-state clinical measurements obtained in-vivo in humans via a microelectrode—CT scanning technique developed and performed at the Fox Chase Cancer Center. Models employing linear kinetic rate forms for oxygen consumption via cell respiration accurately reproduce the oxygen tension profiles in the ten different carcinoma and sarcoma investigated. Large tumors (7.0 cm in diameter or larger) which typically outgrow their blood supply have sharp profiles that are accurately represented by a two-region model. Conversely, small tumors (4.8 cm in diameter or less)which have a relatively high degree of vascularity require a three-region model to accurately reproduce their oxygen tension profiles.     

株洲神农城湖水水质保护及净化处理技术提炼

介绍了株洲神农城核心景观区之神农湖的概况;分析了人工湖水质污染的主要原因及其处理措施;提出了神农湖水质保护与净化处理的工程方案。为维护神农湖的景观水质,本工程主要采取以下两个处理措施:一是增加水体的溶解氧量,保持水体的鲜活力;二是采用循环过滤的方式去除浊度污染。     

DYNAMIC BEHAVIOR OF REACTIVE DISTILLATION COLUMNS. EQUILIBRIUM SYSTEMS

This paper deals with the dynamic behavior of simultaneous reaction-separation systems which operate at or near the chemical equilibrium in the liquid phase. The process under study comprises a whole set of “instantaneous”, and very fast reversible reactions where the difference in volatilities favors both the progress of reaction and product separation. The main aim of our study is to gain a deeper understanding of the dynamic behavior of distillation columns by using a model that is simple and efficient, yet informative. This kind of model is outstanding for synthesis and design of control schemes which require a careful modelling and understanding of process response to different changes in the environment. We use a suitable transformation of variables (after Barbosa and Doherty, 1988b) in order to define a new set of state variables; as a result, the balance equations become identical to those for conventional distillation. Also, an efficient physicochemical algorithm that can handle both the original and new state variables is used. Thus, a composition-holdup dynamic model is simulated in the “transformed field” using a stage-by-stage approach. To further reduce computational time, the transformed problem has also been solved by means of a reduction procedure based on approximating by orthogonal polynomials the transformed composition and flow profiles in the column. The performance of the two proposed methods are compared by using the top section of a quaternary reactive column. The results obtained shown that reactive distillation dynamics has certain peculiarities derived from superimposing reaction and separation phenomena.     

BATCH AND SEMIBATCH REACTORS MODELLING AND VALIDATION BASED ON ON-LINE pH MEASUREMENT

Based on on-line pH measurement, a comparative study between batch and semibalch reactors performance has been carried out in a glass-jacketed reactor of 51 provided with the measuring, data acquiring and controlling system. The reaction system chosen was an acid-base reaction, the concentrations of the species in the reactor were obtained simply by measuring the pH of reaction solution. Based on the conductivity profiles of the solution at different temperatures, the kinetic equation of this acid-base reaction was established. The thermal behaviors of batch reactor were investigated by heating and cooling water in the reactor. The dynamic behavior of batch reaction could be described by a set of differential equations resulting from the mass and energy balance of the reaction mixture, the energy balance of the jacket wall and the circulating fluid inside the jacket. This model has been validated with experimental results, and could be applied to the complex control situations.     

Optimal Control of Saccharomyces cerevisiae. Fermentation Process

This article demonstrates the existence of multiple optimal control profiles for the fermentation process involving Saccharomyces cerevisiae. The Jones–Kompala model is used to model the dynamics of the fermentation process. Both dilution rate and the oxygen mass transfer coefficient are used as the control variables individually and together. While it was demonstrated recently that the steady-state optimization for the Jones–Kompala model would reveal multiple optimum solutions, this work demonstrates the existence of multiple optimum control profiles when dynamic optimization is performed. To perform the dynamic optimization, the differential equations were converted to a nonlinear program (NLP) using Radau collocation with finite elements and the state-of-the-art optimization program CONOPT (constrained optimizer) was used to obtain the local optimum profiles. The global solution was confirmed using the deterministic global optimization program branch-and-reduce optimization navigator. Both the programs were accessed through the network enabled optimization system (NEOS) server.     

A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements

Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014     

采用同步策略的化工动态优化求解(英文)

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control variables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at element knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refinement more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting elements to track optimal control profile breakpoints and ensure accurate state and control profiles. Four classic benchmarks of dynamic optimization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferable in improving the solution accuracy of chemical dynamic optimization problem.