A conceptual model for chemical product design

The fundamental principles of chemical product design and associated systematic tools, within a broad domain of chemical products including molecules, formulations, and devices, are still under development. In this article, we propose a simple and fundamental conceptual model that defines the chemical product design problem as the inversion of three central design functions: quality, property, and process functions. The classic iterative cycles of product design problems may be envisioned as alternating between inversion and evaluation of these three functions, or in other words alternating between synthesis and analysis of solutions. On top of the proposed basic structure of the overall design problem, we then discuss the formulation of some subproblems as optimization problems and describe some useful solution tools. Three application examples are provided, including a more detailed case of formulation of a pharmaceutical ointment. © 2014 American Institute of Chemical Engineers AIChE J, 61: 802–815, 2015     

Optimization issues of the broke management system in papermaking

This paper presents an optimization strategy for the design and operation of a broke management system in a papermaking process. A stochastic model based on a two-state Markov process is presented for the broke system and a multiobjective and bi-level stochastic optimization model is developed featuring (i) a multiobjective operational subproblem for the optimization of the broke dosage and (ii) a multiobjective design problem formulation. An efficient optimization strategy is proposed for the operational subproblem along with a simulation based Pareto optimal solution for the design problem, and illustrated with a detailed case study.     

A reactive optimization strategy for the simultaneous planning,scheduling and control of short-period continuous reactors

The efficient and economic operation of processing systems ideally requires a simultaneous planning, scheduling and control framework. Even when the optimal simultaneous solution of this problem can result in large scale optimization problems, such a solution can represent economic advantages making feasible its computation using optimization decomposition and/or few operating scenarios. After reducing the complexity of the optimal simultaneous deterministic solution, it becomes feasible to take into account the effect of model and process uncertainties on the quality of the solution. In this work we consider those changes in product demands that take place once the process is already under continuous operation. Therefore, a reactive strategy is proposed to meet the new product demands. Based on an optimization formulation for handling the simultaneous planning, scheduling, and control problem of continuous reactors, we propose a heuristic strategy for dealing with unexpected events that may appear during operation of a plant. Such a strategy consists of the rescheduling of the products that remain to be manufactured after the given disturbance hits the process. Such reactive strategy for dealing with planning, scheduling and control problems under unforeseen events is tested using two continuous chemical reaction systems.     

通过模型为基础的溶液选择来调控药品化合物的形貌

In this paper we present a strategy for tuning the crystal morphology of pharmaceutical compounds by the appropriate choice of solvent via an optimization model. A three-stage approach involving a pre-design stage, a product design stage and a post-design experimental verification stage is presented. The pre-design stage addresses the tormulation of the property constraint tor crystal morphology. This involves crystallization experiments aria development of property models and constraints for morphology. In the design stage various property requirements for the solvent along with crystal morphology are considered and the product design problem is formulated as a mixed integer nonlinear programming model.The design stage provides an optimal solvent/list of candidate solvents. Similar to the pre-design stage, in the post design experimental verification stage, the morphology of the crystals （precipitated from the designed solvent） is verified through crystallization experiments followed by product characterization via scanni＇ng electron microscopy, powder X-ray diffraction imaging and Fourier transform spectra analysis.     

A formulation methodology for multicomponent distillation sequences based on stochastic optimization

Based on stochastic optimization strategy, a formulation methodology is proposed for synthesizing distillation column sequences, allowing more than one middle component as the distributing components between a pair of key components in the non-sharp split. In order to represent and manipulate the distillation configuration structures, a new coding procedure is proposed in the form of one-dimensional array. Theoretically, an array can represent any kind of split (non-sharp and sharp).With the application of a binary sort tree approach, a robust flow sheet encoding and decoding procedure is developed so that the problem formulation and solution becomes tractable. In this paper, the synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem and an improved simulated annealing approach is adopted to solve the optimization problem. Besides, a shortcut method is applied to the evaluation of all required design parameters as well as the total function.     

An integrated production planning model with load-dependent lead-times and safety stocks

The divergence over the years of research paradigms addressing the production planning problem has led to the development of an extensive set of techniques, each of which can address a particular aspect of the practical problem and none of which provides a complete solution. In particular, most approaches fail to address the circular, non-linear dependency between resource utilization, lead-times and safety stocks. We present a non-linear programming formulation of the integrated problem using clearing functions that determines a work release schedule guaranteeing a specified service level in the face of stochastic demand. We introduce an iterative heuristic solution procedure that solves a relaxed LP approximation of the original NLP at each iteration to determine the lead-time profile to set safety-stock levels. Computational experiments suggest that our proposed iterative procedure performs well relative to conventional LP models that assume fixed, workload-independent lead-times.     

Closed-loop dynamic real-time optimization with stabilizing model predictive control

Dynamic real-time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set-point trajectories that are in turn passed on to the lower-level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed-loop DRTO (CL-DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper-level DRTO. The resulting CL-DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single-input single-output and multi-input multi-output continuous stirred tank reactor case studies.     

基于线性时变扰动模型的间歇过程最优迭代学习控制

A batch-to-batch optimal iterative learning control (ILC) strategy for the tracking control of product quality in batch processes is presented. The linear time-varying perturbation (LTVP) model is built for product quality around the nominal trajectories. To address problems of model-plant mismatches, model prediction errors in the previous batch run are added to the model predictions for the current batch run. Then tracking error transition models can be built, and the ILC law with direct error feedback is explicitly obtained. A rigorous theorem is proposed, to prove the convergence of tracking error under ILC. The proposed methodology is illustrated on a typical batch reactor and the results show that the performance of trajectory tracking is gradually improved by the ILC.     

Integrated process design,scheduling, and model predictive control of batch processes with closed-loop implementation

Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed-integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed-loop implementation. We use multi-parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base-2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.     

Freeze drying process: real time model and optimization

Freeze drying is a separation process based on the sublimation phenomenon. This process has the following advantages compared to the conventional drying process: the material structure is maintained, moisture is removed at low temperature (reduced transport rates), product stability during the storage is increased, the fast transition of the moisturized product to be dehydrated minimizes several degradation reactions. Freeze drying process has not been studied well enough. In order to put it to practice, a mathematical model based on fundamental mass and energy balance equations has been developed, based on a deterministic mathematical model proposed by Liapis and Sadikoglu [Drying Technol. 15 (3–4) (1997) 791], and used to calculate the amount of removed water and amount of residual water. The proposed model contains the freeze drying equations, which are solved by the orthogonal collocation and polynomial approximation—Jacobi method. The results show that the dynamic mathematical model represents well the process and is especially well suited for real time optimization. As a case study to illustrate the model utilization in a real time optimization procedure, the freeze drying process was optimized by the method of Successive Quadratic Programming (SQP) used for solution of non-linear equations, for skimmed milk and soluble coffee. The optimization procedure showed to be an important tool to improve the process performance since lower energy consumption and hence lower cost has been achieved to obtain the product with the same quality.     

Generalized initialization for the dynamic simulation and optimization of grade transition processes using two-dimensional collocation

Optimization modeling tools are essential to determine optimal design specifications and operation conditions of polymerization processes, especially when quality indices based on molecular weight distributions (MWDs) must be enforced. This study proposes a generalized MWD-based optimization strategy using orthogonal collocation in two dimensions, which can capture the dynamic features of MWDs accurately. To enable the strategy, this study considers generalized initialization methods for large-scale simulation and optimization. Here, a homotopy method based on intermediate solutions is adopted to generate initial values for general steady-state simulation models, starting from an arbitrary known solution for any steady-state simulation model. For dynamic simulation models, the response of a first-order linear system is adopted to initialize the state variables. Case studies show the effectiveness of this procedure to enable systematic, reliable, and efficient solution of the optimization problem.     

Simultaneous solution approach to model‐based experimental design

A model‐based experimental design is formulated and solved as a large‐scale NLP problem. The key idea of the proposed approach is the extension of model equations with sensitivity equations forming an extended sensitivities‐state equation system. The resulting system is then totally discretized and simultaneously solved as constraints of the NLP problem. Thereby, higher derivatives of the parameter sensitivities with respect to the control variables are directly calculated and exact. This is an advantage in comparison with proposed sequential approaches to model‐based experimental design so far, where these derivatives have to be additionally integrated throughout the optimization steps. This can end up in a high‐computational load especially for systems with many control variables. Furthermore, an advanced sampling strategy is proposed which combines the strength of the optimal sampling design and the variation of the collocation element lengths while fully using the entire optimization space of the simultaneous formulation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4169–4183, 2013     

A multi-priority hierarchical optimization method for double-layer model predictive control

Considering the demand for the sequential regulation of manipulated variables in actual industrial process control, the conventional solution of double-layer model predictive control faces the problem that the weight coefficients are difficult to tune. This paper proposes an improved hierarchical optimization method for manipulated variables in the steady-state optimization layer of double-layer model predictive control. The proposed method can adjust the manipulated variables sequentially without an accurate weight coefficient to avoid difficulty in tuning the weight coefficients. The relation between the optimal solution and the feasible region of the steady-state optimization layer is analysed to describe the reoptimization of the key manipulated variables. The impact of the economic cost coefficient on the optimal solution with the sensitivity analysis method is studied, and the complexity of using the weight coefficient to solve the priority optimization problem of the manipulated variables is assessed. The steady-state optimization solution procedure is improved based on the theory of the multiobjective complete hierarchical method. The hierarchical and sequential optimization of the manipulated variables results in expanding the space and freedom of the key manipulated variables, increasing efficiency, reducing consumption, and improving economic performance. The improved hierarchical optimization method is direct and simple in achieving optimization sequentially and satisfies the need for adjusting the manipulated variables according to human intentions.     

基于随机优化的热耦合复杂精馏系统的综合(Ⅰ)模型化方法

基于随机型最优化策略,针对包含简单塔、带有侧线蒸出及侧线汽提塔的复杂塔、全热耦合（或Petlyuk）塔的热耦合复杂精馏塔系统的综合问题,提出一种模型化方法.针对热耦合复杂精馏流程系统所需塔段数目以及冷凝器和再沸器数目的不确定性,提出了一种分解求解策略,将原问题分解成一系列具有不同塔段数的子问题分别求解;针对流程结构的优化提出一种流程结构的编码表达法,该方法将问题的分离序列结构和热耦合方式分别用两组编码表示,对分离序列的编码采用了数据结构理论中的二叉树排序方法,使流程结构的描述变得更加简便;最后以预分馏塔组分回收率及回流比为连续变量,建立了热耦合复杂精馏系统优化的[JP+1]混合整数非线性规划（MINLP）模型,该模型用改进的模拟退火算法求解,可同时得到优化的流程结构和操作参数.     

Design of multipurpose production facilities: A RTN decomposition-based algorithm

A general mathematical formulation for the design of multipurpose facilities has recently been presented by Barbosa-Póvoa and Pantelides (1997). The model proposed permits a detailed consideration of the design problem taking account of trade-offs between capital costs, revenues and operational flexibility. The optimal solution involves the selection of the required processing and storage equipment items and the required levels of provision of other production resources such as utilities, manpower, cleaning and transportation equipment.In order to guarantee solution optimality, the above design formulation has to consider a large number of equipment items, out of which it will select the ones that will actually be incorporated in the plant. This may result in large mixed-integer linear programming (MILP) problems that are expensive to solve.This paper presents a decomposition approach for the solution of large batch process design problems. The approach involves the iterative solution of a master problem (representing a relaxation of the original design problem) and a design sub-problem (in which several of the design decisions are already fixed).An example illustrating the effectiveness of the proposed decomposition approach is presented.     

基于实验设计与偏最小二乘逆模型的产品设计方法

现代市场中,同类产品规格多样、更新换代速度加快,快速经济地设定新产品操作条件成为生产过程的迫切需求。本文首先改进实验设计(DOE)优化方法中的响应曲面法(RSM),可随着新实验数据的累积在线更新搜索算法的外延步长;然后提出RSM与偏最小二乘(PLS)逆模型的结合方法,可保证模型具有良好的内插和外延性能,显著减少实验次数、快速找到满足新产品要求的操作条件;最后通过数值仿真以及某化工过程的应用仿真验证了方法的可行性和有效性。     

通过模型为基础的溶液选择来调控药品化合物的形貌

In this paper we present a strategy for tuning the crystal morphology of pharmaceutical compounds by the appropriate choice of solvent via an optimization model. A three-stage approach involving a pre-design stage, a product design stage and a post-design experimental verification stage is presented. The pre-design stage addresses the formulation of the property constraint for crystal morphology. This involves crystallization experiments and development of property models and constraints for morphology. In the design stage various property requirements for the solvent along with crystal morphology are considered and the product design problem is formulated as a mixed integer nonlinear programming model. The design stage provides an optimal solvent/list of candidate solvents. Similar to the pre-design stage, in the post design experimental verification stage, the morphology of the crystals (precipitated from the designed solvent) is verified through crystallization experiments followed by productcharacterization via scanning electron microscopy, powder X-ray diffraction imaging and Fourier transform spectra analysis.     

基于KPLS模型的间歇过程产品质量控制

针对间歇过程所具有的非线性特性,提出了一种基于核偏最小二乘(KPLS)模型的最终产品质量控制策略。利用初始条件、批次展开后的过程数据以及最终产品质量建立了间歇过程的KPLS模型;采用基于主成分分析(PCA)映射的预估方法对未知的过程数据进行补充,实现了最终产品质量的在线预测。为了解决最终产品质量的控制,利用T2统计量确定KPLS模型的适用范围,并作为约束引入产品质量控制问题,提高控制策略的可行性;采用粒子群优化(PSO)算法实现了优化问题的高效求解。仿真结果表明,与基于偏最小二乘(PLS)模型的控制策略相比,所提出的方法具有更高的预测精度,且能有效解决产品质量控制中出现的各种问题。     

A modified iterative IOM approach for optimization of biochemical systems

The presented previously indirect optimization method (IOM) developed within biochemical systems theory (BST) provides a versatile and mathematically tractable optimization strategy for biochemical systems. However, due to the local approximations nature of the BST formalism, the iterative version of this technique possibly does not yield the true optimum solution. In this work, an algorithm is proposed to obtain the correct and consistent optimum steady-state operating point of biochemical systems. The existing linear optimization problem of the direct IOM approach is modified by adding an equality constraint of describing the consistency of solutions between the S-system and the original model. Lagrangian analysis is employed to derive the first order necessary optimality conditions for the above modified optimization problem. This leads to a procedure that may be regarded as a modified iterative IOM approach in which the optimization objective function includes an extra linear term. The extra term contains a comparison of metabolite concentration derivatives with respect to the enzyme activities between the S-system and the original model and ensures that the new algorithm is still carried out within linear programming techniques. The presented framework is applied to several biochemical systems and shown to the tractability and effectiveness of the method. The simulation is also studied to investigate the convergence properties of the algorithm and to give a performance comparison of standard and modified iterative IOM approach.