Study of solubility and swelling ratio in polymer‐CO2 systems using the PC‐SAFT equation of state

We use the PC‐SAFT equation of state to model the solubility of CO₂ in various homopolymers. We also model the swelling ratio of the PP (polypropylene)‐CO₂ mixture using PC‐SAFT and then compare the results with Sanchez‐Lacombe (S‐L) and Simha‐Somcynsky (S‐S) equations. The results show that PC‐SAFT can describe the solubility of CO₂ in polymers very well. We compare two sets of parameters in the PC‐SAFT equation, Gross et al.'s and Chen et al.'s. As for the swelling ratio, PC‐SAFT using Chen et al. parameters is better than S‐L equation, which is commonly used by early researchers in studying the solubility of CO₂ in polymers. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44804.     

Modeling the phase behavior in binary mixtures involving blowing agents and thermoplastic resins

The thermophysical properties of mixtures of thermoplastic resins and blowing agents, together with the knowledge of the solubilities of these components, are the basis for the manufacturing of plastic foams. In this work, the solubilities of blowing agents trichlorofluoromethane, dichlorodifluoromethane, chlorodifluoromehane, and 1,2‐dichloro‐1,1,2,2‐tetrafluoroethane in thermoplastic resins poly(styrene), high density poly(ethylene), low density poly(ethylene), poly(propylene), poly(vinyl chloride), poly(carbonate) and poly(propylene oxide) were modeled by using the Perturbed Chain‐Statistical Associating Fluid Theory (PC‐SAFT) and the Sánchez‐Lacombe equations of state (EoS), fitting a single temperature‐dependent binary interaction parameter. PC‐SAFT is a theoretically based equation of state with three pure component parameters that describe efficiently the thermodynamics of complex systems. Earlier works with this EoS have already predicted the phase coexistence properties of various refrigerants and higher order alkane series compounds, along with their mixtures. The pure component parameters for the blowing agents were obtained by regression of vapor pressure and liquid density data, while the pure component parameters for the thermoplastic resins were obtained by regression of pure liquid PVT data. The parameter estimation was performed by using a modified maximum likelihood method. The solubility results obtained with both EoS have been compared; the results from PC‐SAFT showed a higher accuracy in terms of solubility pressure deviations. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Fluid phase behavior modeling of CO2 + molten polymer systems using cubic and theoretically based equations of state

Phase equilibrium data of CO₂ + molten polymer systems are of great relevance for chemical engineers because these are necessary for the optimal design of polymer final‐treatment processes. This kind of processes needs information about gas solubilities in polymers at several temperatures and pressures. In this work, CO₂ solubilities in molten polymers were modeled by the perturbed chain‐statistical associating fluid theory (PC‐SAFT) equation of state (EoS). For comparison, the solubilities were also calculated by the lattice gas theory (LGT) EoS, and by the well‐known Peng‐Robinson (PR) cubic EoS. To adjust the interactions between segments of mixtures, there were used classical mixing rules, with one adjustable temperature‐dependent binary parameter for the PC‐SAFT and PR EoS, and two adjustable binary parameters for the LGT EoS. The results were compared with experimental data obtained from literature. The results in terms of solubility pressure deviations indicate that the vapor–liquid behavior for CO₂ + polymer systems is better predicted by the PC‐SAFT model than by LGT and PR models. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Multi‐Objective Optimization of Pseudo‐Dynamic Operation of Naphtha Pyrolysis by a Surrogate Model

A simple pseudo‐dynamic surrogate model is developed in the framework of the state space model with the feed‐forward neural network to replace the complex free radical pyrolysis model. The surrogate model is then applied to investigate the multi‐objective optimization of two key performance objectives with distinct contradiction: the mean yields of key products and the day mean profits. The ?‐constraint method is employed to solve the multi‐objective optimization problem, which provides a broad range of operation conditions depicting tradeoffs of both key objectives. The Pareto‐optimal frontier is successfully obtained and five selected cases on the frontier are discussed, suggesting that flexible operations can be performed based on industrial demands.     

Using NSGA‐II and TOPSIS Methods for Interior Ballistic Optimization Based on One‐Dimensional Two‐Phase Flow Model

In order to meet the design demands of new gun systems or new types of projectiles, the interior ballistic charge design seems especially important. In this paper, a one‐dimensional two‐phase flow model is presented. The model describes the transient combustion of granular propellants in a gun, and pressure waves are considered as an objective. This study adopts a hybrid method to solve the problem. In the first stage, the non‐dominated sorting genetic algorithm (NSGA‐II) with “a “filter” is employed to approximate a set of Pareto‐optimal solutions. In the subsequent stage, a multi‐attribute decision‐making (MADM) approach is adopted to rank these solutions from the best to the worst. The ranking of Pareto‐optimal solutions is based on the technique ordered preference by similarity to ideal solution (TOPSIS) method. In TOPSIS method each objective needs a corresponding weight coefficient, and a practical problem is introduced. Both the entropy method and linear analysis method are adopted to get two sets of weights for the objectives, respectively. The two pairs of final, best compromise solutions are compared for satisfying the designer’s aim. For the analysis of the results, a two‐phase flow interior ballistic model for design optimization is established, and the hybrid approach could get a reasonable design scenario.     

Predicting phase behavior in aqueous systems without fitting binary parameters II: Gases and non‐aromatic hydrocarbons

This investigation continues a series of studies evaluating the capability of the recently proposed CP‐PC‐SAFT and sPC‐SAFT of Liang et al. to estimate the thermodynamic properties of aqueous systems in the entirely predictive manner. Similarly to the previously considered systems, CP‐PC‐SAFT remains a realistic estimator of the available data on critical loci, high pressure‐high temperature phase equilibria and volumetric properties also in the cases of non‐polar gases and non‐aromatic hydrocarbons from argon and nitrogen till n‐eicosane and squalene while keeping zero values of binary parameters. Nevertheless, such application of the model poses certain unavoidable compromises on its accuracy. Inter alia, CP‐PC‐SAFT is a particularly inaccurate estimator of the water‐rich liquid phases away from the critical points. sPC‐SAFT predicts these data in a more reliable manner. Moreover, its predictive capability goes beyond the liquid phases and it exhibits a remarkable accuracy in forecasting various phase equilibria below the critical point of water. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Multi‐Objective Optimization of Interior Ballistic Performance Using NSGA‐II

This paper investigates an interior ballistic design with equal and unequal web thicknesses of seven‐perforation propellant grains using optimization methods. In order to reveal the influence of the web thickness of the propellant grains on the overall interior ballistic performance, burning seven‐perforation propellant grains with both equal and unequal web thickness is modeled. A currently popular evolution algorithm (EA) is used to compare two charge shapes, and to seek which one could achieve the optimal ballistic performance. Complete optimization of the interior ballistic performance is a complex process in view of the conflicting objectives to be achieved and a solution to such problems is sought by converting them into a single composite objective and using many tedious measurements. In this paper, a true multi‐objective optimization of the interior ballistic charging design is carried out by considering three objectives simultaneously. The non‐dominated sorting genetic algorithm version II (NSGA‐II) is used to solve this multi‐objective optimization problem (MOP). In order to check its implementation, both the conventional optimization algorithm‐hill climbing method (HCM) and NSGA‐II are used to solve the same single objective problem. The NSGA‐II used to capture the full Pareto‐optimal front is capable of identifying the trade‐off among the conflicting objectives thereby providing alternative useful designs for a designer. Furthermore, for seven‐perforation propellant grains, the results of using equal web thickness are compared with those of unequal web thickness, and it is shown that the two charge shapes produce no distinct difference in the interior ballistic performance.     

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     

Solving Multi‐objective MILP Problems in Process Synthesis using the Multi‐Criteria Branch and Bound Algorithm

The paper briefly describes the problem of process synthesis in the area of chemical engineering, and suggests its formulation as a Multi‐Objective Programming problem. Process synthesis optimization is usually modeled as Mixed Integer Linear Programming (MILP) or Mixed Integer Non‐Linear Programming (MINLP) with an economic objective function. We claim that incorporating more criteria (e.g., environmental criteria) in this kind of combinatorial optimization problem offers the decision makers the opportunity to refine their final decision by examining more than one solution (a set of efficient or Pareto optimal solutions instead of one optimal solution). For solving the multi‐objective process synthesis problem, an improved version of the Multi‐Criteria Branch and Bound (MCBB) algorithm, which has been developed by the same authors, is used. MCBB is a vector maximization algorithm capable of deriving all efficient points (supported and unsupported), for small and medium sized Multi‐Objective MILP problems. The application of MCBB in two examples from process synthesis is also presented.     

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     

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     

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

We modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Solubility Calculation of Oil‐Conta‐minated Drill Cuttings in Supercritical Carbon Dioxide Using Statistical Associating Fluid Theory (PC‐SAFT)

Supercritical fluid extraction is a new technology that could be effectively used to treat oil‐contaminated drill cuttings generated during drilling for oil and gas. In this work, the solubility of oil‐contaminated drill cuttings in supercritical carbon dioxide is obtained by an experimental flow type apparatus. The solubility was measured at 200 bar pressure, over a temperature range of 55–79.5 °C. The measured solubility and experimental data for oil in drill cuttings were correlated using the PC‐SAFT, PR and SRK EOS models, without any adjustable parameters. Average absolute derivations of less than 15.1 %, 98.7 %, and 99.3 % are achieved between predicted and experimental values for the PC‐SAFT, PR and SRK EOS models, respectively, over a wide range of temperatures.     

Predicting phase behavior in aqueous systems without fitting binary parameters I: CP‐PC‐SAFT EOS,aromatic compounds

This study examines an accuracy of CP‐PC‐SAFT attached by the 4C cross‐association scheme and zero values of binary parameters in predicting the high temperature‐high pressure phase behavior in aqueous systems of aromatic compounds containing one and two benzoic rings, CO₂ and cis‐decalin. In spite of the noteworthy complexity of these systems and the entirely predictive nature of the current approach, it correctly predicts the topology of phase behavior and typically yields the quantitatively accurate estimations of critical loci and the hydrocarbon–rich liquid phases in wide range of conditions. The available single phase volumetric data are also predicted accurately. Unfortunately, it is not a case of the water–rich phases exhibiting very small hydrocarbon concentrations. Nevertheless, the model is still capable of capturing the solubility minima characteristic for these phases around the room temperature. Predictions of the recent version of Simplified PC‐SAFT proposed by Liang et al. (2014) are also discussed. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4124–4135, 2017     

Phase‐dependent binary interaction parameters in industrial low‐density polyethylene separators

In the production process of low‐density polyethylene (LDPE), an important step is the flash separation of monomers and other small molecules from the polymer produced. The process is carried out adiabatically in two stages. To improve the performance of thermodynamic models, it is very important to analyze the use of model binary interaction parameters (BIP) dependent on the phase characteristics for each phase (phase‐dependent BIP). In this work the PC‐SAFT (perturbed‐chain statistical associating fluid theory) equation of state (EOS) is applied to the flash simulation of LDPE industrial separators using eight different resins. The main numerical aspects are examined with emphasis on the optimization strategy for the EOS BIP that explicitly characterizes each phase involved separately. The results demonstrate good predictive behavior. As a result of improved and more consistent modeling, a new strategy for optimized operation can be envisaged for the sequence of separators. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2106–2117, 2013     

A practical equation of state for non‐spherical and asymmetric systems for application at high pressures. Part 1: Development of the pure component model

A practical, mathematically and computationally simple, equation of state (EOS) has been developed to accurately describe pure component phase behaviour of spherical and chain‐like molecules. The EOS consists of a newly developed hard sphere model and a perturbation term based on the Barker and Henderson approach using the Chen and Kreglewski intermolecular potential model and a double constrained summation as a mathematical expression thereof. The perturbed hard chain theory (PHCT) approach is used to extend the EOS to non‐spherical molecules. The EOS compares well with other more complex models such as the simplified perturbed hard chain theory (SPHCT) and statistically associating fluid theory (SAFT) models and will be extended to describe mixtures in Part 2 of this series. © 2011 Canadian Society for Chemical Engineering     

Some efficient approaches for multi-objective constrained optimization of computationally expensive black-box model problems

Multi-objective constrained optimization problems which arise in many engineering fields often involve computationally expensive black-box model simulators of industrial processes which have to be solved with limited computational time budget, and hence limited number of simulator calls. This paper proposes two heuristic approaches aiming to build proxy problem models, solvable by computationally efficient optimization methods, in order to quickly provide a sufficiently accurate approximation of the Pareto front. The first approach builds a multi-objective mixed-integer linear programming (MO-MILP) surrogate model of the optimization problem relying on piece-wise linear approximations of objectives and constraints obtained through brute-force sensitivity computation. The second approach builds a multi-objective nonlinear programming (MO-NLP) surrogate model using curve fitting of objectives and constraints. In both approaches the desired number of approximated solutions of the Pareto front are generated by applying the ɛ-constraint method to the multi-objective surrogate problems. The proposed approaches are tested for the cost vs. life cycle assessment (LCA)-based environmental optimization of drinking water production plants. The results obtained with both approaches show that a good quality approximation of Pareto front can be obtained with a significantly smaller computational time than with a state-of-the-art metaheuristic algorithm.