Synthesis and optimization of membrane cascade for gas separation via mixed‐integer nonlinear programming

Currently, membrane gas separation systems enjoy widespread acceptance in industry as multistage systems are needed to achieve high recovery and high product purity simultaneously, many such configurations are possible. These designs rely on the process engineer's experience and therefore suboptimal configurations are often the result. This article proposes a systematic methodology for obtaining the optimal multistage membrane flow sheet and corresponding operating conditions. The new approach is applied to cross‐flow membrane modules that separate CO₂ from CH₄, for which the optimization of the proposed superstructure has been achieved via a mixed‐integer nonlinear programming model, with the gas processing cost as objective function. The novelty of this work resides in the large number of possible interconnections between each membrane module, the energy recovery from the high pressure outlet stream and allowing for nonisothermal conditions. The results presented in this work comprise the optimal flow sheet and operating conditions of two case studies. © 2017 American Institute of Chemical Engineers AIChE J, 63: 1989–2006, 2017     

Reference Trajectory Optimization Under Constrained Predictive Control

Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed‐loop dynamics of the MPC‐controlled process in the reference trajectory optimization results in a multi‐level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush‐Kuhn‐Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process.     

A framework for ammonia supply chain optimization incorporating conventional and renewable generation

Ammonia is an essential nutrient for global food production brought to farmers by a well‐established supply chain. This article introduces a supply chain optimization framework which incorporates new renewable ammonia plants into the conventional ammonia supply chain. Both economic and environmental objectives are considered. The framework is then applied to two separate case studies analyzing the supply chains of Minnesota and Iowa, respectively. The base case results present an expected trade‐off between cost, which favors purchasing ammonia from conventional plants, and emissions, which favor building distributed renewable ammonia plants. Further analysis of this trade‐off shows that a carbon tax above $25/t will reduce emissions in the optimal supply chain through building large renewable plants. The importance of scale is emphasized through a Monte Carlo sensitivity analysis, as the largest scale renewable plants are selected most often in the optimal supply chain. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4390–4402, 2017     

Optimization‐based design of polymer sheeting dies using generalized Newtonian fluid models

A polymer sheeting die design methodology is presented, which integrates finite element flow simulations, numerical optimization, and design sensitivity analyses to compute die cavity geometries capable of giving a near‐uniform exit velocity. This work extends earlier die design methods to include generalized Newtonian fluid (GNF) models that represent the shear‐thinning behavior of polymer melt. Melt flow computations and design sensitivity analyses are provided using the generalized Hele‐Shaw flow approximation with isothermal power‐law, Carreau‐Yasuda, Cross, Ellis, and Bingham fluid models. The nonlinear equations for die cavity pressure are solved using the Newton‐Raphson iteration method and design sensitivities are derived with the adjoint variable method. The die design method is applied to an industrial coat hanger die, in which a design parameterization is defined that allows for an arbitrary gap height distribution in the manifold of the die. In addition, die performance is assessed and compared for power‐law and Carreau‐Yasuda fluid flow over a range of die operating conditions. Pareto optimal die designs are also considered in this study. POLYM. ENG. SCI., 45:953–965, 2005. © 2005 Society of Plastics Engineers     

Automatic design of conventional distillation column sequence by genetic algorithm

Synthesis of the optimum conventional (with non‐sharp separations) distillation column sequence (DCS) is a challenging problem, in the field of chemical process design and optimization, due to its huge search space and combinatorial nature. In this paper, a novel procedure for the synthesis of optimum Conventional Distillation Column Sequence is proposed. The proposed method is based on evolutionary algorithms. The main criterion used to screen alternative DCS's is the Total Annual Cost (TAC). In order to estimate the TAC of each DCS alternative all columns that exist in the DCS are designed using short‐cut methods. The performance of the proposed method and other alternatives are compared based on the results obtained for four standard benchmark problems used by researchers working in this area. Based on the results of the comparison, the proposed method outperforms the other methods and is also more flexible than other existing methods.     

Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

Optimal synthesis of p‐xylene separation processes based on crystallization technology

This article addresses the synthesis and optimization of crystallization processes for p‐xylene recovery for systems with feed streams of high concentration, a case that arises in hybrid designs where the first step is commonly performed by adsorption. A novel superstructure and its corresponding mixed‐integer nonlinear programming (MINLP) model are proposed. The distinct feature of this superstructure is the capability to generate optimum or near optimum flow sheets for a wide range of specifications of p‐xylene compositions in the feed stream of the process. To cope with the complexity of the MINLP model, a two‐level decomposition approach, consisting of the solution of an aggregated model and a detailed model, is proposed. The results obtained show good performance of the decomposition strategy, and the optimal flow sheets and p‐xylene recoveries are in agreement with the results reported in patents. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Simultaneous process synthesis and control design under uncertainty: A worst‐case performance approach

A new methodology that includes process synthesis and control structure decisions for the optimal process and control design of dynamic systems under uncertainty is presented. The method integrates dynamic flexibility and dynamic feasibility in a single optimization formulation, thus, reducing the costs to assess the optimal design. A robust stability test is also included in the proposed method to ensure that the optimal design is stable in the presence of magnitude‐bounded perturbations. Since disturbances are treated as stochastic time‐discrete unmeasured inputs, the optimal process synthesis and control design specified by this method remains feasible and stable in the presence of the most critical realizations in the disturbances. The proposed methodology has been applied to simultaneously design and control a system of CSTRs and a ternary distillation column. A study on the computational costs associated with this method is presented and compared to that required by a dynamic optimization‐based scheme. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2497–2514, 2013     

An optimization‐based approach for structural design of self‐assembled DNA tiles

DNA tiles are self‐assembled nanostructures, which offer exciting opportunities for synthesis of novel materials. A challenge for structural design of DNA tiles is to identify optimal locations for so‐called crossovers, which are bridges between DNA double helices formed by pairs of single‐stranded DNA. An optimization‐based approach is presented to identify optimal locations for such crossovers. Minimization of a potential‐energy model for a given structural design demonstrates the importance of local minima. Both deterministic global optimization of a reduced model and multistart optimization of the full model are applied successfully to identify the global minimum. MINLP optimization using a branch‐and‐bound algorithm (GAMS/SBB) identifies an optimal structural design of a DNA tile successfully with significant reduction in computational load compared to exhaustive enumeration, which demonstrates the potential of the proposed method to reduce trial‐and‐error efforts for structural design of DNA tiles. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1804–1817, 2017     

Decreasing the cycle time for in‐mold coating (IMC) of sheet molding compound (SMC) compression molding

In‐mold coating (IMC) is a thermosetting liquid applied to compression molded sheet molding compound (SMC) exterior automotive or truck body panels as an environmentally friendly primer to improve surface quality and make the part conductive for subsequent electrostatic painting. The IMC is injected onto the surface of the SMC then cures and bonds to provide a smooth conductive and protective surface. In IMC as in many other reactive polymer processes, to have short cycle time while maintaining adequate flow time and pot life is required. This allows enough time to fill the mold before solidification. In this study, the effect of inhibitor (p‐benzoquinone), initiator (t‐butyl peroxybenzoate), and mold temperature on the flow and cure time of IMC materials has been experimentally investigated using differential scanning calorimeter. A cure model is developed based on experiments to predict inhibition and cure time. A multiple criteria optimization method was employed to identify the setting parameters of the controllable process variables that provide the best compromise (Pareto frontier [PF]) between flow and cure time. The analysis shows that simultaneous addition of initiator and inhibitor allows the molding to be performed at a higher temperature, which moves the PF toward the ideal location. Hence, minimizes the cure time and maximizes the flow time simultaneously. POLYM. ENG. SCI., 59:1158–1166 2019. © 2019 Society of Plastics Engineers     

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     

Advanced trust region optimization strategies for glass box/black box models

We present an improved trust region filter (TRF) method for optimization of combined glass box/black box systems. Glass box systems refer to models that are easily expressed in an algebraic modeling language, providing cheap and accurate derivative information. By contrast, black box systems may be computationally expensive and derivatives are unavailable. The TRF method, as first introduced in our previous work (Eason and Biegler, AIChE J. 2016; 62:3124–3136), is able to handle hybrid systems containing both glass and black box components, which can frequently arise in chemical engineering, for example, when a multiphase reactor model is included in a flow sheet optimization problem. We discuss several recent modifications in the algorithm such as the sampling region, which maintains the algorithm's global convergence properties without requiring the trust region to shrink to zero in the limit. To benchmark the development of this optimization method, a test set of problems is generated based on modified problems from the CUTEr and COPS sets. The modified algorithm demonstrates improved performance using the test problem set. Finally, the algorithm is implemented within the Pyomo environment and demonstrated on a rigorous process optimization case study for carbon capture. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3934–3943, 2018     

Optimization by lumped control of reactors with langmuir-hinshelwood catalyst deactivation

A method is proposed for solving the problem of temperature optimal control in tubular fixed-bed reactors with reaction systems described by Langmuir-Hinshelwood-Hougen-Watson kinetic equations. The optimization problem is formulated by N state differential equations corresponding to the N differential fixed-bed reactors in which the integral reactor is divided. It is solved using the control vector parameterization computational technique. The proposed method when applied to a simple reaction system reported previously in the literature gives analogous results, and thus validates the theory. This theory is applied to the dehydrogenation of benzyl alcohol to benzaldehyde. An analysis of optimality problem shows a strong influence of the temperature dependence of the ratio of reaction rate to deactivation reaction rate on the optimal policy.     

Simultaneous design and operation optimization of renewable combined cooling heating and power systems

Combined cooling, heating, and power (CCHP) systems are promising solutions for conserving energy and reducing emissions. This article proposes a new mixed-integer linear programming (MILP) model for simultaneous design and operation optimization of a renewable CCHP system, considering component nonlinear operating characteristics and performance degradation with time. A bi-objective MILP problem is solved to achieve a trade-off between total annual cost (TAC) and greenhouse gas emissions (GHGe). A case study of a commercial region is employed to demonstrate our proposed methodology. The results shows, in comparison with conventional cost minimization, our solution features a tardy increase of 12.8% in TAC and a sharp reduction of 75.5% in GHGe. Moreover, we find that ignoring performance degradation leads to an over-estimation of 2.3–13.7% in system economic performance. The proposed methodology provides an effective and flexible framework for optimal design and operational analysis of renewable CCHP systems.     

Coproduction of acetic acid and hydrogen/power from natural gas with zero carbon dioxide emissions

A process plant flow sheet that coproduces acetic acid and hydrogen/power from natural gas with zero carbon dioxide emissions is developed. Two cases are explored: the production of acetic acid and hydrogen (Case 1) and the production of acetic acid and power (Case 2). This is realized by the selection of an appropriate reaction cluster whose sum results in the overall reaction that coproduces acetic acid and hydrogen/power. The concept of energetic self‐sufficiency is introduced and it imposes constraints on the system defined in terms of the ratio of oxygen feed to acetic acid produced. Heat and power integration of the converged flow sheet reveals an operating range for each case that guarantees energetic self‐sufficiency. Operating points are chosen to conduct a preliminary economic analysis and a carbon dioxide cost and performance metric calculation to quantify profitability and carbon capture potential of the overall process. © 2017 American Institute of Chemical Engineers AIChE J, 64: 860–876, 2018     

Optimum design of integrated liquid recovery plants by variable population size genetic algorithm

Increase in the price of energy sources as well as economic problems have caused cryogenic natural gas plants to become more complex and efficient. After selecting the process configuration, the flow rate, pressure, and temperature of the process fluid streams are determining factors which should be tuned in order to find the optimum condition. Products specification and operating costs of the plant are two significant parameters which should be considered in an optimal design. Moreover, process design limitations contribute to the problem being more difficult. This paper shows how the optimal operating point in an integrated NGL recovery plant can be found through solving a complex constrained optimization problem. A Variable Population size Genetic Algorithm (VPGA) was used for optimization. As well, the role of VPGA algorithm parameters in solving the process design problems is investigated in this study. The analysis showed that the VPGA method has better performance compared to the general GA methods. The plant‐wide net profit increases 12493360 $/year only by changing the selected operating conditions to its optimal value.     

Techno‐economic optimization model for “sustainable” insulation material developed for energy efficiency

Renewable insulation materials are produced within the scope of this study using clay, fly ash, expanded perlite, epoxidized hemp oil, and hemp fiber. Density, thermal conductivity, and compressive‐tensile strength of the produced materials are analyzed. Economic and environmental analysis of the best sample with the most appropriate characteristics for an insulation material is conducted using a hybrid mathematical model developed for this study. Mathematical formulas of an economic evaluation technique of P₁‐P₂ method is integrated into Simulated Annealing Algorithm as one of the metaheuristic optimization approaches. Applicability of the proposed material for externally insulated walls is tested. For this purpose, optimum insulation thickness, payback period, energy savings for 10 years of lifetime, and CO₂‐SO₂ emissions were calculated for 5 types of energy sources along with a sensitivity analysis. This method is developed and coded in a software platform and used for the first time for the optimization of insulation material thickness. The experimental results obtained from evaluation of the sample H36 indicate that using this material for insulation purposes in the buildings have the potential of making significant contribution for energy efficiency along with various environmental benefits.     

一种生态工业园区碳-氢-氧共生网络的多目标优化与决策方法

针对生态工业园区中碳-氢-氧共生网络,基于多尺度原子标定方法,同时考虑经济和环境因素及回用副产碳氢氧化合物,本工作提出了一种多目标优化及决策的方法,从备选方案中获得最优方案。该方法采用数学规划法,分别以最小总年度成本和二氧化碳年度排放量为目标函数进行全局优化,建立了混合整数非线性规划模型;采用ε-约束法,将二氧化碳年度排放量转化为约束条件,得到了总年度成本与二氧化碳年度排放量帕累托前沿,发现总年度成本与二氧化碳排放量成反比;采用多维偏好分析的线性规划和逼近于理想解的排序决策方法对帕累托前沿进行最优决策,发现两者选择同一点作为最优决策。基于所提出的方法对某工业园区进行优化,结果表明,合理利用现有副产碳氢氧化合物,可以减少原材料成本,从而使总年度成本和二氧化碳年度排放量分别减少了63.44%和76.99%。     

改进的全息搜索策略及其在化工优化中的应用

引言 基于样本数据估计反应动力学参数是常见的化工优化问题.参数估计的通用规则是偏差最小化,许多经典的序贯类寻优方法都可用于这一目的,例如Powell共轭梯度法、模式搜索法、变度量法等.