Global superstructure optimization for the design of integrated process water networks

We propose a general superstructure and a model for the global optimization for integrated process water networks. The superstructure consists of multiple sources of water, water‐using processes, wastewater treatment, and pre‐treatment operations. Unique features are that all feasible interconnections are considered between them and multiple sources of water can be used. The proposed model is formulated as a nonlinear programing (NLP) and as a mixed integer nonlinear programing (MINLP) problem for the case when 0–1 variables are included for the cost of piping and to establish optimal trade‐offs between cost and network complexity. To effectively solve the NLP and MINLP models to global optimality we propose tight bounds on the variables, which are expressed as general equations. We also incorporate the cut proposed by Karuppiah and Grossmann to significantly improve the strength of the lower bound for the global optimum. The proposed model is tested on several examples. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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     

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 ammonia production through process synthesis and global optimization

Current ammonia production technologies have a significant carbon footprint. In this study, we present a process synthesis and global optimization framework to discover the efficient utilization of renewable resources in ammonia production. Competing technologies are incorporated in a process superstructure where biomass, wind, and solar routes are compared with the natural gas-based reference case. A deterministic global optimization-based branch-and-bound algorithm is used to solve the resulting large-scale nonconvex mixed-integer nonlinear programming problem (MINLP). Case studies for Texas, California, and Iowa are conducted to examine the effects of different feedstock prices and availabilities. Results indicate that profitability of ammonia production is highly sensitive to feedstock and electricity prices, as well as greenhouse gas (GHG) restrictions. Under strict 75% GHG reductions, biomass to ammonia route is found to be competitive with natural gas route, whereas wind and solar to ammonia routes require further improvement to compete with those two routes. © 2018 American Institute of Chemical Engineers AIChE J, 65: e16498 2019     

A hierarchical method to integrated solvent and process design of physical CO2 absorption using the SAFT‐γ Mie approach

Molecular‐level decisions are increasingly recognized as an integral part of process design. Finding the optimal process performance requires the integrated optimization of process and solvent chemical structure, leading to a challenging mixed‐integer nonlinear programming (MINLP) problem. The formulation of such problems when using a group contribution version of the statistical associating fluid theory, SAFT‐γ Mie, to predict the physical properties of the relevant mixtures reliably over process conditions is presented. To solve the challenging MINLP, a novel hierarchical methodology for integrated process and solvent design (hierarchical optimization) is presented. Reduced models of the process units are developed and used to generate a set of initial guesses for the MINLP solution. The methodology is applied to the design of a physical absorption process to separate carbon dioxide from methane, using a broad selection of ethers as the molecular design space. The solvents with best process performance are found to be poly(oxymethylene)dimethylethers. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3249–3269, 2015     

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.     

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     

Synergistic optimization framework for the process synthesis and design of biorefineries

The conceptual process design of novel bioprocesses in biorefinery setups is an important task,which remains yet challenging due to several limitations.We propose a novel framework incorporating superstructure optimization and simulation-based optimization synergistically.In this context,several approaches for superstructure optimization based on different surrogate models can be deployed.By means of a case study,the framework is introduced and validated,and the different superstructure optimization approaches are benchmarked.The results indicate that even though surrogate-based optimization approaches alleviate the underlying computational issues,there remains a potential issue regarding their validation.The development of appropriate surrogate models,comprising the selection of surrogate type,sampling type,and size for training and cross-validation sets,are essential factors.Regarding this aspect,satisfactory validation metrics do not ensure a successful outcome from its embedded use in an optimization problem.Furthermore,the framework’s synergistic effects by sequentially performing superstructure optimization to determine candidate process topologies and simulationbased optimization to consolidate the process design under uncertainty offer an alternative and promising approach.These findings invite for a critical assessment of surrogatebased optimization approaches and point out the necessity of benchmarking to ensure consistency and quality of optimized solutions.     

Sustainable design of geothermal energy systems for electric power generation using life cycle optimization

This article addresses the sustainable design of organic Rankine cycle-based geothermal binary power systems under economic and environmental criteria. A novel superstructure with multiple heat source temperatures, working fluids, and heat rejection systems is proposed. Based on the superstructure, a life cycle optimization model is formulated as a mixed-integer nonlinear fractional program (MINFP) to determine the optimal design. The nonconvex MINFP is efficiently solved by a tailored global optimization algorithm. Two case studies are considered to demonstrate the proposed modeling framework and solution algorithm. One case is based on a geothermal energy system located in California, and the other one is in New York (NY) State. The results show that the geothermal energy system in California is much more economically competitive than that in NY State. The difference in life cycle environmental impacts is less pronounced because the environmental impacts are less sensitive to geological conditions than the capital investments.     

Refrigeration system synthesis based on de-redundant model by particle swarm optimization algorithm

Simultaneous optimization of refrigeration system (RS) and its heat exchanger network (HEN) leads to a large-scale non-convex mixed-integer non-linear programming (MINLP) problem. Conventionally, researchers usually adopted simplifications to confine problem scale from being too large at the cost of reducing solution space. This study established an optimization framework for the simultaneous optimization of RS and HEN. Firstly, A more comprehensive and compact model was developed to guarantee a relatively complete solution space while reducing model scale as well as its solving difficulty. In this model, a tandem arrangement of connecting sub-coolers and expansion valves was considered in the superstructure; and the pressure/temperature levels were optimized as continuous variables. On this basis, we proposed a “two-step transformation method” to equivalently transform the cross-level structure into a non-cross-level structure, and the de-redundant superstructure was established with ensuring comprehensiveness and rigor. Furthermore, the MINLP model was developed and solved by Particle Swarm Optimization algorithm. Finally, our methodology was validated to get better optimal results with less CPU time in two case studies, an ethylene RS in an existing plant and a reported propylene RS.     

Equation‐oriented flowsheet simulation and optimization using pseudo‐transient models

Tight integration through material and energy recycling is essential to the energy efficiency and economic viability of process and energy systems. Equation‐oriented (EO) steady‐state process simulation and optimization are key enablers in the optimal design of integrated processes. A new process modeling and simulation concept based on pseudo‐transient continuation is introduced. An algorithm for reformulating the steady‐state models of process unit operations as differential‐algebraic equation systems that are statically equivalent with the original model is presented. These pseudo‐transient models improve the convergence of EO process flowsheet simulations by expanding the convergence basin. This concept is used to build a library of pseudo‐transient models for common process unit operations, and this modeling concept seamlessly integrates with a previously developed time‐relaxation optimization algorithm. Two design case studies are presented to validate the proposed framework. © 2014 American Institute of Chemical Engineers AIChE J 60: 4104–4123, 2014     

Equation‐oriented optimization of process flowsheets with dividing‐wall columns

We present a new modeling approach for dividing‐wall columns (DWCs) that is amenable to equation‐oriented flowsheet simulation and optimization. The material, equilibrium, summation, and heat (MESH) equations describing a DWC are highly coupled and nonlinear, making DWC‐based process flowsheets challenging to simulate. Design optimization poses further challenges, typically requiring integer variables to select the number of column stages. To address these difficulties, we represent DWCs as networks of pseudo‐transient (differential‐algebraic) subunit models. We show that these networks have the same steady‐state solution as the original (algebraic) MESH equations, but present significant numerical benefits. We then embed these models in a previously developed pseudo‐transient flowsheet modeling and optimization framework. We further reformulate the models to require only continuous decision variables when selecting the optimal number of stages during design optimization. To illustrate these concepts, we discuss the DWC‐based intensification of the dimethyl ether process. © 2015 American Institute of Chemical Engineers AIChE J, 62: 704–716, 2016     

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non‐convex mixed‐integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on–off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non‐convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4277–4296, 2016     

Optimal design and planning of heap leaching process. Application to copper oxide leaching

Although the process of heap leaching is an established technology for treating minerals, such as copper, gold, silver, uranium and saltpeter, as well as remediating soil, no studies to date have investigated process optimization. This work presents a methodology for the design and planning of heap leaching systems to optimize the process. This methodology consists of the creation of a superstructure that represents a set of alternatives to search for the optimal solution; from this superstructure, a mixed integer nonlinear programming (MINLP) model was generated, and a BARON-GAMS solver was used to find the optimal solution. This method was applied to the extraction of copper from systems with one, two and three heaps, and the effects of copper price, ore grade and other variables were analyzed for each system. From the results, it can be concluded that this methodology can be used to optimize heap leaching processes, including planning and design issues.     

Equation‐oriented simulation and optimization of process flowsheets incorporating detailed spiral‐wound multistream heat exchanger models

Multiple chemical processes rely on multistream heat exchangers (MHEXs) for heat integration, particularly at cryogenic temperatures. Owing to their geometric complexity, the detailed design of MHEXs is typically iterative: the exchanger geometric parameters are selected to match process specifications resulting from a flowsheet optimization step; then, the flowsheet is reoptimized with the predictions of the MHEX model, and these steps are repeated until a convergence criterion is met. This paper presents a novel framework that allows—for the first time, to our knowledge—for the simultaneous optimization of the process flowsheet and the detailed MHEX design. Focusing on spiral‐wound MHEXs, we develop an equation‐oriented exchanger model using industry‐accepted heat transfer and pressure drop correlations for single‐phase and multiphase streams. We embed this model in our previously developed pseudo‐transient equation‐oriented process simulation and optimization framework. We demonstrate our approach on an industrial case study, the PRICO^® natural gas liquefaction process. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3778–3789, 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     

Membrane system design for multicomponent gas mixtures via mixed-integer nonlinear programming

An optimal design strategy for membrane networks separating multicomponent gas mixtures based on an approximate permeator model and mixed-integer nonlinear programming (MINLP) is proposed. A permeator system superstructure is used to embed a very large number of possible network configurations and allows the permeator feed-side pressure to be fixed or a design variable. A MINLP design model is developed to minimize the total annual process cost by simultaneous optimization of the permeator configuration and operating conditions. Case studies for the separation of acid gases (CO₂ and H₂S) from crude natural gas mixtures with spiral-wound permeators are presented. Permeator configurations are derived for different number of separation stages for both continuous and discrete membrane areas. The method is sufficiently robust to handle product compositions that vary five orders of magnitude. The proposed approach provides an efficient methodology for preliminary screening of multi-stage membrane separation systems for multicomponent gas mixtures.     

A novel hybrid feedstock to liquids and electricity process: Process modeling and exergoeconomic life cycle optimization

This article proposes a novel hybrid low‐rank coal (LRC)/biomass/natural gas process for producing liquid fuels and electricity. The hybrid process highlights coexistence of indirect and direct liquefaction technologies, cogasification of char and biomass, and corefinery of LRC syncrude and Fischer–Tropsch syncrude. A process simulation based on detailed chemical kinetics is present to illustrate its feasibility. In addition, we propose an exergoeconomic life cycle optimization framework that seeks to maximize the primary exergy saving ratio, primary total overnight cost saving ratio, life cycle waste emissions avoidance ratio, and primary levelized cost saving ratio by comparing the proposed hybrid process to its reference stand‐alone subsystems. From the results, we can determine four optimal designs which yield competitive breakeven oil prices ranging from $1.87/GGE to $2.13/GGE. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3739–3753, 2014     

Waste high-density polyethylene recycling process systems for mitigating plastic pollution through a sustainable design and synthesis paradigm

This article addresses the sustainable design and synthesis of open-loop recycling process of waste high-density polyethylene (HDPE) under both environmental and economic criteria. We develop by far the most comprehensive superstructure for producing monomers, aromatic mixtures, and fuels from waste HDPE. The superstructure optimization problem is then formulated as a multi-objective mixed-integer nonlinear fractional programming (MINFP) problem to simultaneously optimize the unit net present value (NPV) and unit life cycle environmental impacts. A tailored global optimization algorithm integrating the inexact parametric algorithm with the branch-and-refine algorithm is applied to efficiently solve the resulting nonconvex MINFP problem. Results show that the optimal unit NPV ranges from $107.2 to $151.3 per ton of HDPE treated. Moreover, the unit life cycle greenhouse gas emissions of the most environmentally friendly HDPE recycling process are 0.40 ton CO₂-eq per ton of HDPE treated, which is 63% of that of the most economically competitive process design.     

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