Conceptual design and optimization of chemical processes under uncertainty by two-stage programming

This contribution presents a method and a tool for modelling and optimizing process superstructures in the early phase of process design where the models of the processing units and other data are inaccurate. To adequately deal with this uncertainty, we employ a two-stage formulation where the operational parameters can be adapted to the realization of the uncertainty while the design parameters are the first-stage decisions. The uncertainty is represented by a set of discrete scenarios and the optimization problem is solved by stage decomposition. The approach is implemented in the computer tool FSOpt (Flow sheet Superstructure Optimization) FSOpt provides a flexible environment for the modelling of the unit operations and the generation of superstructures and algorithms for the translation of the superstructure into non-linear programming models.The approach is applied to two case studies, the hydroformylation of dodec-1-ene and the separation of an azeotropic mixture of water and formic acid.     

Optimizing inventory policies in process networks under uncertainty

We address the inventory planning problem in process networks under uncertainty through stochastic programming models. Inventory planning requires the formulation of multiperiod models to represent the time-varying conditions of industrial process, but multistage stochastic programming formulations are often too large to solve. We propose a policy-based approximation of the multistage stochastic model that avoids anticipativity by enforcing the same decision rule for all scenarios. The proposed formulation includes the logic that models inventory policies, and it is used to find the parameters that offer the best expected performance. We propose policies for inventory planning in process networks with arrangements of inventories in parallel and in series. We compare the inventory planning strategies obtained from the policy-based formulation and the analogous two-stage approximation of the multistage stochastic program. Sequential implementation of the planning strategies in receding horizon simulations shows the advantages of the policy-based model, despite the increase in computational complexity.     

Two-stage optimization problem with chance constraints

In general, chemical processes (CP) are designed with the use of inaccurate mathematical models. Therefore, it is important to create a chemical process that guarantees satisfaction of all design specifications either exactly or with some probability. The paper considers the issue of chemical process optimization when at the operation stage the design specification should be met with some probability and the control variables can be changed. We developed a new formulation of the two-stage optimization problem (TSOP) with chance constraints. On the basis of this formulation and approximate transformation of chance constraints into deterministic ones the iteration method of solving the TSOP with chance constraints is devised.     

Optimal experimental design for optimal process design: A trilevel optimization formulation

Typical optimal experimental design (OED) methods aim at minimizing the covariance matrix of the estimated parameters regardless of the intended application of the model that is being estimated. This can unnecessarily increase the experimental costs. Herein, we propose a new OED method, which tailors the designed experiments to the model application. The method is demonstrated for model-based process design and aims at mitigating a worst-case realization of the process design. The proposed formulation results in a min–max–min problem and is based on bounded-error OED. The method is illustrated via an ad hoc solution method using two examples, a simple illustrative example and the van de Vusse reaction, that show the differences between typical and the new tailored OED method: experimental designs can be considered good using the latter method, while the same design would be considered bad with the former methods.     

Adaptive two-stage optimal designs for phase II clinical studies that allow early futility stopping

Abstract

Adaptive designs play an important role in contemporary clinical trials to make designs flexible and efficient. In cancer clinical trials, given a relatively small sample size, it is important to obtain as much information as possible during this phase. We propose a new adaptive optimal design that stops for futility only in the first stage as Simon’s two-stage design. The existing adaptive two-stage designs are often allowed to be stopped for futility or efficacy due to computational advantage. It is difficult to search for an optimal design with futility stopping only in the first stage by using efficient search algorithms; for example, the branch-and-bound algorithm. We have to use multiple computational techniques to search for the optimal design. The proposed adaptive design meets the important property of the monotonic property that the second stage sample size is a nonincreasing function of the number of responses from the first stage. In this article, we show that the proposed adaptive design always has a smaller expected sample size than Simon’s optimal design. We recommend it for use in practice as an alternative to the commonly used Simon’s design.     

Fortschritte bei der Modellierung von Festbettreaktoren

Progress in the modeling of fixed bed reactors. Recent work on the modeling of catalytic fixed bed reactors have led to more realistic mathematical models and to a better understanding of problems connected with modeling. Nowadays standard routine computer programs are available for use in the design (and analysis) of catalytic fixed bed reactors for very complex reaction systems. The influence of bed structure on transport parameters was illustrated by experimental determination of axial and radial concentration and temperature distribution. Moreover the problem of multicomponent diffusion coupled with complex reactions in porous catalysts has been solved and can be included in the reactor model. However, the practical application of possible reactor models is limited by the availability of transport parameters for fixed beds.     

Design of shell and tube heat exchangers considering the interaction of fouling and hydraulics

We extend a formulation of the heat exchanger design optimization with fouling modeling to consider the effect of fouling on hydraulics. A shell-side fouling model was added so the optimization can consider cases with fouling in the tube and shell sides. The focus is the design of heat exchangers with fouling behavior associated with a threshold model, like in crude preheat trains. We solve the optimization problem by using a newly proposed Set Trimming technique. We compare our results with the traditional approach of using fixed fouling factors and the previous approach of not considering the hydraulic impact of fouling. We conclude that considering the deposit thickness leads to more realistic results that are different than the ones obtained using the previous approaches. Moreover, we show that previous approaches can render designs with larger pressure drops than the maximum imposed by the constraints, as well as exchangers with higher areas.     

UASB+高负荷生物滤池法/固体接触法工艺在生活污水处理中的应用

广东省某城市污水处理厂根据当地情况,采用了复合UASB＋高负荷生物滤池法／固体接触法（TF／SC）工艺,该工艺是近年来最新的生物处理技术之一,并且在广东地区首次使用。本文主要介绍了该污水处理厂的工艺流程、技术参数及工程设计情况。同其他二级处理工艺相比,该工艺流程简单,建设及运行成本低,出水水质好,而且特别适用于年均温度较高的南方地区的城市污水处理厂建设。     

Integrated control and process design during optimal polymer grade transition operations

In this work we address the simultaneous process control and design problem of polymerization reactors during dynamic grade transition operation. The problem is cast as a Mixed-Integer Dynamic Optimization (MIDO) formulation and, by using the full discretization approach for solving dynamic optimization problems [Kameswaran, S., & Biegler, L. T. (2006). Simultaneous dynamic optimization strategies: Recent advances and challenges. Computers & Chemical Engineering, 30 (10–12), 1560–1575], is transformed into a Mixed-Integer Nonlinear Program (MINLP). The resulting MINLP is solved using a full space nonconvex optimization formulation [Flores-Tlacuahuac, A., & Biegler, L. T. (2007). Simultaneous Mixed-Integer Dynamic Optimization for integrated design and control. Computers & Chemical Engineering, 31, 588–600]. The control and design formulation has been applied to two polymerization reactors featuring highly nonlinear behavior. In both cases, the proposed MIDO formulation was capable of finding optimal solutions. This amounts to finding optimal steady states, reactor designs, as well as open-loop and closed-loop dynamic optimal trajectories, control structures and controller parameters by specifying either the polymer molecular weight distribution or monomer conversion. Because CPU solution time tends to increase with system complexity, some strategies for lowering CPU time are discussed.     

Comparison of various modeling methods for analysis of powder compaction in roller press

Recently used models relating basic properties of the feed material, roller press design and its operating parameters are reviewed. In particular, we discuss the rolling theory for granular solids proposed by J.R. Johanson in the 1960s, later trials utilizing slab method and newly developed final element models. These methods are compared in terms of efficiency and accuracy of predicting the course of basic process variables like nip angle, pressure distribution in roll nip region, neutral angle, roll torque and roll force.

The finite element method offers the most versatile approach because it incorporates adequate information about powder behavior, geometry and frictional conditions. This enables to perform realistic computer experiments minimizing costs, time and resources needed for process and equipment optimization.     

Optimization‐based support for process design under uncertainty: A case study

The use of two‐stage stochastic optimization for the support of the solution of process design problems in the early phase of process development where the different potential elements of the production process can only be described with significant uncertainty is discussed. The first stage variables are the design decisions which are fixed after the process has been built, while the second stage variables are the operational parameters which can be adapted to the realization of the uncertainties. The application of the approach to the design of a hydroformylation process in a thermomorphic solvent system is demonstrated. The proposed designs which are computed using the software framework FSOpt are analyzed and compared using different graphic representations which provide insight into what the most important design decisions are. Finally, the experience with the proposed formulation and solution techniques and point out where further advances are needed is reviewed. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3404–3419, 2016     

Optimal design of chemical processes with chance constraints

Generally, chemical processes (CP) are designed with the use of inaccurate mathematical models. Therefore, it is important to create a chemical process that guarantees satisfaction of all design specifications either exactly or with some probability. The paper considers the issue of chemical process optimization when at the operation stage the design specification should be met with some probability and the control variables can be changed. We have developed a common approach for solving the broad class of optimization problems with normally distributed uncertain parameters. This class includes the one-stage and two-stage optimization problems with chance constraints. This approach is based on approximate transformation of chance constraints into deterministic ones.     

Design and operation of an enhanced pervaporation device with static mixers

Pervaporation has a high potential for separating miscible solutions, particularly azeotropic mixtures. However, mass transfer limitations have long been a common concern in pervaporation device design. Therefore, in this work, we design a static mixer-based pervaporation device using water–ethanol separation as a model system and further develop computational fluid dynamics tools to investigate systematically all the influencing parameters. In the experiments, we use three-dimensional printed helical static mixers in the feed liquid channel to enhance mass transfer and implement a Sulzer pervaporation membrane for fast removal of water from ethanol. Using flow and mass-transfer simulations, we fit the membrane mass transfer coefficient and provide predictive models for optimal process design. Our pervaporation assembly exhibits promising performance and potential toward pervaporation processes for the removal of water from organics and is preferably scaled out by using stackable designs.     

Spray Dryer Modeling in Theory and Practice

This article considers the modeling of spray dryers at various levels and the selection of the most appropriate level of detail for practical situations. The following model levels are described: (1) Heat and mass balances; (2) Equilibrium based models; (3) Rate based models; (4) Computational fluid dynamic (CFD) models. The value of each is discussed in relation to some typical problem scenarios. These include preliminary process design; process improvement; and troubleshooting operational and product quality problems. One particular focus of this article is finding realistic models of the performance characteristics of spray dryers which can be included in process flow sheet simulations while not imposing excessive run times and complexity.     

Strategies for formulating and solving two-stage problems for process design under uncertainty

This paper describes a systematic procedure for formulating process design under uncertainty as two-stage problems and proposes a computational scheme for solving such problems. This formulation procedure introduces extra variables and constraints arising from capacity requirements and fixed computational order and generates all possible allocations of variables and constraints. The proposed computational scheme combines experimental design with gradient-based NLP algorithms. With the Han-Powell algorithm adapted for this purpose, this scheme proves to be more efficient than the method by Malik and Hughes[1].     

Φ3.6m两段炉煤气站模拟设计

根据设计依据中原料煤和所需煤气参数,经过计算和对气化、净化以及脱硫工艺的分析,确定采用5台Φ3.6 m两段炉为气源,经除尘、除焦油、脱硫得到净化煤气后,送往用气点。核算分析表明,煤气站气化炉选型合理,工艺路线确定合适,净化煤气等参数满足用气点要求,模拟设计达到设计要求。     

State estimation for high-dimensional chemical processes

The application of conventional observer designs for high-dimensional systems may not always be practical due to high computational requirements or the resulting observers being too sensitive to measurement noise. In order to address these issues, this paper presents two observer design techniques for state estimation of high-dimensional chemical processes. One technique is used for systems with inputs, whereas the other one is specifically geared towards systems that are not excited from the outside. Both of these observers are applicable to linear and with a modification to non-linear systems.The main idea behind the presented observer designs is that a reduced-order observer is implemented instead of a conventional state estimator. The motivation is that subspaces, which are close to being unobservable, cannot be correctly reconstructed in a realistic setting due to measurement noise and inaccuracies in the model. The presented approaches make use of this observation and only reconstruct the parts of the system where accurate state estimation is possible. The observer designs are illustrated on a 30-tray distillation column model. Additionally, it has been shown that the location of process measurements has a major effect on the performance of the presented reduced-order observers.     

Multiobjective batch process design aiming at robust performances

The most common batch design approach in practice and literature is a deterministic one. However, given the uncertainties prevailing in early stages of process design, a deterministically calculated productivity is not sufficient to select one of the large number of optional designs. Therefore, we propose a Tabu Search multiobjective optimization framework, which allows to approximate the Pareto-optimal set of designs while considering uncertain variables in the initial recipe. As a novel technique, we include performance robustness as a separate objective function within the multiobjective optimization alongside with productivity of a design, thus obtaining not only designs with high productivity or solely robust designs, but both high productivity and robust designs in one set of solutions. We examined several robustness criteria as a possible quantification of performance deviations under uncertain recipe variables. The implementation of a Tabu Search framework in combination with Monte-Carlo simulation and Latin Hypercube sampling provides a huge flexibility in the problem specification, in particular in the definition of parameter uncertainties. As a result we successfully demonstrate that metaheuristic optimization techniques are capable to approximate the Pareto-optimal set under uncertainty and are able to capture potentially antagonistic solution qualities such as high productivity and robustness by multiobjective optimization. With the help of this approach, parameters can be identified that have to be put into the focus of process research and development efforts in order to obtain high performance batch process designs.     

Empirical colorant mixture models

The color behavior of unconventional colorant systems and certain other mixtures cannot be described adequately by available theory. In such cases alternative approaches to formulation and shading need to be developed. In this article we investigate empirical models using Scheffé polynomials to describe color response surfaces for three- and four-component olorant mixtures. We describe experimental designs that allow the efficient estimation of the coefficients of high-order polynomial models over the full mixture-design space and that also allow estimation of lower-order models over subspace mixture regions. The experimental designs are applied to real colorant systems, and the accuracy of color response prediction from linear, quadratic, cubic, and quartic polynomial models is compared to that of theoretical models. The color response surfaces are visualized by preparing contour plots that depict color variation over a compositional region. These maps allow one to observe the relationship between color and composition, to assess the color gamut available with a given colorant set, and to estimate the formula or adjustments required to match a given color position. The effective use of model predictions to perform a sensitivity analysis on the compositional variables is also demonstrated in the context of manufacturing process control.