A superstructure representation,generation, and modeling framework for chemical process synthesis

We present a framework for the efficient representation, generation, and modeling of superstructures for process synthesis. First, we develop a new representation based on three basic elements: units, ports, and conditioning streams. Second, we present four rules based on “minimal” and “feasible” component sets for the generation of simple superstructures containing all feasible embedded processes. Third, in terms of modeling, we develop a modular approach, and formulate models for each basic element. We also present a canonical form of element models using input/output variables and constrained/free variables. The proposed methods provide a coherent framework for superstructure‐based process synthesis, allowing efficient model generation and modification. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3199–3214, 2016     

Production of benzene,toluene, and xylenes from natural gas via methanol: Process synthesis and global optimization

A systematic global optimization‐based process synthesis framework is presented to determine the most profitable processes to produce aromatics from natural gas. Several novel, commercial, and/or competing technologies are modeled within the framework, including methanol‐to‐aromatics, toluene alkylation with methanol, selective toluene disproportionation, and toluene disproportionation and transalkylation with heavy aromatics, among others. We propose a stand‐alone chemicals facility: the main products are aromatics with allowable by‐products of gasoline, liquefied petroleum gas, and electricity. Several case studies are discussed that produce varying ratios of para‐, ortho‐, and meta‐xylene across multiple refinery capacities. The results indicate that utilizing natural gas for the production of aromatics is profitable with net present values as high as $3800 MM dollars and payback periods as low as 6 years. The required investment for these refineries represents as much as a 65% decrease compared to published estimates of similar coal‐based capacity plants. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1531–1556, 2016     

Global optimization for sustainable design and synthesis of algae processing network for CO2 mitigation and biofuel production using life cycle optimization

Global optimization for sustainable design and synthesis of a large‐scale algae processing network under economic and environmental criteria is addressed. An algae processing network superstructure including 7800 processing routes is proposed. Based on the superstructure, a multiobjective mixed‐integer nonlinear programming (MINLP) model is developed to simultaneously optimize the unit cost and the unit global warming potential (GWP). To efficiently solve the nonconvex MINLP model with separable concave terms and mixed‐integer fractional terms in the objective functions, a global optimization strategy that integrates a branch‐and‐refine algorithm based on successive piecewise linear approximations is proposed and an exact parametric algorithm based on Newton's method. Two Pareto‐optimal curves are obtained for biofuel production and biological carbon sequestration, respectively. The unit annual biofuel production cost ranges from $7.02/gasoline gallon equivalent (GGE) to $9.71/GGE, corresponding to unit GWP's of 26.491 to 16.52 kg CO₂‐eq/GGE, respectively. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3195–3210, 2014     

Sustainable design and synthesis of algae‐based biorefinery for simultaneous hydrocarbon biofuel production and carbon sequestration

The superstructure optimization of algae‐based hydrocarbon biorefinery with sequestration of CO₂ from power plant flue gas is proposed. The major processing steps include carbon capture, algae growth, dewatering, lipid extraction and power generation, and algal biorefinery. We propose a multiobjective mixed‐integer nonlinear programming (MINLP) model that simultaneously maximizes the net present value (NPV) and minimizes the global warming potential (GWP) subject to technology selection constraints, mass balance constraints, energy balance constraints, technoeconomic analysis constraints, and environmental impact constraints. The model simultaneously determines the optimal decisions that include production capacity, size of each processing unit, mass flow rates at each stage of the process, utility consumption, economic, and environmental performances. We propose a two‐stage heuristic solution algorithm to solve the nonconvex MINLP model. Finally, the bicriteria optimization problem is solved with ε‐constraint method, and the resulting Pareto‐optimal curve reveals the trade‐off between the economic and environmental criteria. The results show that for maximum NPV, the optimal process design uses direct flue gas, a tubular photobioreactor for algae growth, a filtration dewatering unit, and a hydroprocessing pathway leading to 47.1 MM gallons of green diesel production per year at $6.33/gal corresponding to GWP of 108.7 kg CO₂‐eq per gallon. © 2013 American Institute of Chemical Engineers AIChE J, 59: 1599–1621, 2013     

Operational strategy and planning for raw natural gas refining complexes: Process modeling and global optimization

Optimal operational strategy and planning of a raw natural gas refining complex (RNGRC) is very challenging since it involves highly nonlinear processes, complex thermodynamics, blending, and utility systems. In this article, we first propose a superstructure integrating a utility system for the RNGRC, involving multiple gas feedstocks, and different product specifications. Then, we develop a large‐scale nonconvex mixed‐integer nonlinear programming (MINLP) optimization model. The model incorporates rigorous process models for input and output relations based on fundamentals of thermodynamics and unit operations and accurate models for utility systems. To reduce the noncovex items in the proposed MINLP model, equivalent reformulation techniques are introduced. Finally, the reformulated nonconvex MINLP model is solved to global optimality using state of the art deterministic global optimization approaches. The computational results demonstrate that a significant profit increase is achieved using the proposed approach compared to that from the real operation. © 2016 American Institute of Chemical Engineers AIChE J, 63: 652–668, 2017     

Sustainable biopolymer synthesis via superstructure and multiobjective optimization

Sustainable polymers derived from biomass have great potential to replace petrochemical based polymers and fulfill the ever‐increasing market demand. To facilitate their industrialization, in this research, a comprehensive superstructure reaction network comprising a large number of reaction pathways from biomass to both commercialized and newly proposed polymers is constructed. To consider economic performance and environmental impact simultaneously, both process profit and green chemistry metrics are embedded into the multiobjective optimization framework, and MINLP is used to enable the effective selection of promising biopolymer candidates. Through this proposed approach, this study identifies the best biopolymer candidates and their most profitable and environmentally friendly synthesis routes under different scenarios. Moreover, the stability of optimization results regarding the price of raw materials and polymers and the effect of process scale on the investment cost are discussed in detail. These results, therefore, pave the way for future research on the production of sustainable biopolymers. © 2017 American Institute of Chemical Engineers AIChE J, 63: 91–103, 2018     

Interval based MINLP superstructure synthesis of combined heat and mass exchanger networks

An interval based superstructure approach for combining the synthesis of heat and mass exchanger networks is presented in this paper. The technique involves combining the interval based MINLP superstructure (IBMS) for the synthesis of heat exchanger networks (HENs) with that of mass exchanger networks (MENs). The two networks are made to interact through the lean stream in the mass exchange network. The new approach involves the use of the lean substream concept to explore potential mass exchange temperatures. An example which involves a one-lean stream mass exchange problem alongside regeneration and hot and cold utilities is presented.     

Efficient generalized shortcut distillation model with improved accuracy for superstructure-based process synthesis

We propose a general shortcut distillation column model that can address a wide range of types of separations including nonsharp/sloppy splits. The model can automatically identify key components and estimate the energy requirement of a desired separation in the presence, potentially, of components with zero flow rates. To obtain more practical column height and vapor flow rates, we augment the model with constraints inspired by the Fenske equation. We also propose valid constraints to enhance the computational performance of the proposed model. Due to its flexibility and computational efficiency, the proposed model can be readily used for superstructure-based process synthesis.     

A multi‐objective optimization approach to polygeneration energy systems design

Polygeneration, typically involving co‐production of methanol and electricity, is a promising energy conversion technology which provides opportunities for high energy utilization efficiency and low/zero emissions. The optimal design of such a complex, large‐scale and highly nonlinear process system poses significant challenges. In this article, we present a multiobjective optimization model for the optimal design of a methanol/electricity polygeneration plant. Economic and environmental criteria are simultaneously optimized over a superstructure capturing a number of possible combinations of technologies and types of equipment. Aggregated models are considered, including a detailed methanol synthesis step with chemical kinetics and phase equilibrium considerations. The resulting model is formulated as a non‐convex mixed‐integer nonlinear programming problem. Global optimization and parallel computation techniques are employed to generate an optimal Pareto frontier. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Superstructure optimization of integrated fast pyrolysis‐gasification for production of liquid fuels and propylene

Motivated by the apparent advantages of fast pyrolysis and gasification, a novel integrated biorefinery plant is systematically synthesized for coproducing premium quality liquid fuels and propylene. The required heat and fluidization promotion of the fast pyrolyzer are provided by hot syngas from the gasifier. Light gas and syngas from the fast pyrolyzer are finally converted to hydrocarbons via Fischer‐Tropsch synthesis. Multiple syngas production technologies, hydrocarbon production and downstream upgrading routes are incorporated within a superstructure optimization based process synthesis framework. This is the first article to investigate the benefits associated with the introduction of conventional catalytic cracking and dewaxing from a systems engineering perspective. Surrogate models describing the gasifiers and rigorous equations for Fischer‐Tropsch effluents validated by our experimental collaborator are introduced. Through investigation of five scenarios the primary parameters affecting overall economic performance are identified through ranking of the relevant candidates. Comparisons of the hybrid conversion route and stand‐alone routes are made. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3155–3176, 2016     

Systematic modeling of discrete‐continuous optimization models through generalized disjunctive programming

Discrete‐continuous optimization problems are commonly modeled in algebraic form as mixed‐integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed‐integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3276–3295, 2013     

Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach

We address short‐term batch process scheduling problems contaminated with uncertainty in the data. The mixed integer linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998; 37(11):4341–4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp‐MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4184–4211, 2013     

Global optimization of large‐scale mixed‐integer linear fractional programming problems: A reformulation‐linearization method and process scheduling applications

Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation–linearization method, which integrates Charnes–Cooper transformation and Glover's linearization scheme, to transform general MILFPs into their equivalent mixed‐integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous‐time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general‐purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large‐scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4255–4272, 2013     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013     

Surrogate‐based superstructure optimization framework

In principle, optimization‐based “superstructure” methods for process synthesis can be more powerful than sequential‐conceptual methods as they account for all complex interactions between design decisions. However, these methods have not been widely adopted because they lead to mixed‐integer nonlinear programs that are hard to solve, especially when realistic unit operation models are used. To address this challenge, we develop a superstructure‐based strategy where complex unit models are replaced with surrogate models built from data generated via commercial process simulators. In developing this strategy, we study aspects such as the systematic design of process unit surrogate models, the generation of simulation data, the selection of the surrogate's structure, and the required model fitting. We also present how these models can be reformulated and incorporated into mathematical programming superstructure formulations. Finally, we discuss the application of the proposed strategy to a number of applications. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Scheduling of crude oil operations under demand uncertainty: A robust optimization framework coupled with global optimization

Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed‐integer nonlinear programming (MINLP) optimization model. In practice, uncertainties are unavoidable and include demand fluctuations, ship arrival delays, equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this article, the robust optimization framework proposed by Lin et al. and Janak et al. is extended to develop a deterministic robust counterpart optimization model for demand uncertainty. The recently proposed branch and bound global optimization algorithm with piecewise‐linear underestimation of bilinear terms by Li et al. is also extended to solve the nonconvex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach, and the extended branch and bound global optimization algorithm for demand uncertainty. The computational results demonstrate that the obtained schedules are robust in the presence of demand uncertainty. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2373–2396, 2012     

Sustainable process design and synthesis of hydrocarbon biorefinery through fast pyrolysis and hydroprocessing

The process design and synthesis of hydrocarbon biorefinery, which is composed of fast pyrolysis, biocrude collection, hydroprocessing and hydrogen production sections, under economic and environmental considerations are concerned. A superstructure is developed that includes multiple process alternatives in each stage of the process flow diagram. A bi‐criteria mixed integer nonlinear programming model is proposed to maximize the economic performance measured by the net present value and minimize the global warming potential according to life cycle assessment procedures. The bi‐criteria mixed integer nonlinear programming model is solved with the ε‐constraint method, and the resulting Pareto curve reveals the trade‐off between the economic and environmental performance of the process. The two selected “good choice” optimal designs indicate net present values of 573 and 93.6 $MM (unit costs of $3.43 and $5.26 per gallon of gasoline equivalent), corresponding to global warming potentials of 100 and 53 kton CO₂ equivalent per year (unit greenhouse emissions of 1.95 and 2.04 kg CO₂ per gallon of gasoline equivalent), respectively. © 2014 American Institute of Chemical Engineers AIChE J, 60: 980–994, 2014     

Targeting climate-neutral hydrogen production: Integrating brown and blue pathways with green hydrogen infrastructure via a novel superstructure and simulation-based life cycle optimization

This article addresses the sustainable design of hydrogen (H₂) production systems that integrate brown and blue pathways with green hydrogen infrastructure. We develop a systematic framework to simultaneously optimize the process superstructure and operating conditions of steam methane reforming (SMR)-based hydrogen production systems. A comprehensive superstructure that integrates SMR with multiple carbon dioxide capture technologies, electrolyzers, fuel cells, and working fluids in the organic rankine cycle is proposed under varying operating conditions. A life cycle optimization model is then developed by integrating superstructure optimization, life cycle assessment approach, techno-economic assessment, and process optimization using extensive process simulation models and formulated as a mixed-integer nonlinear program. We find that the optimal unit-levelized cost of hydrogen ranges from $1.49 to $3.18 per kg H₂. Moreover, the most environmentally friendly process attains net-zero life cycle greenhouse gas emissions compared to 10.55 kg CO₂-eq per kg H₂ for the most economically competitive process design.     

化工过程综合问题MINLP算法中整型变量的连续化

化工过程系统综合问题需要同时考虑设备结构参数和工艺操作参数,一般用整型变量表示设备的取舍,用连续变量表示操作参数,这就构成一个流程的超结构,在数学形式表现为一个混合整型非线性规划（MINLP）问题。混合整型非线性规划问题的求解成为化工过程综合优化的关键。今根据超结构中整型变量的特征,提出整型变量连续化处理的思路,将MINLP问题简化为NLP问题,然后采用罚函数法求解。最后将该算法运用于加氢脱烷基化（HDA）过程综合的实例研究,结果表明该算法克服了传统方法在处理整型变量时出现的麻烦,为有效快速地进行化工过程综合优化问题提供了一种新的途径。