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     

Multistream heat exchangers: Equation‐oriented modeling and flowsheet optimization

Multistream heat exchangers (MHEXs), typically of the plate‐fin or spiral‐wound type, are a key enabler of heat integration in cryogenic processes. Equation‐oriented modeling of MHEXs for flowsheet optimization purposes is challenging, especially when streams undergo phase transformations. Boolean variables are typically used to capture the effect of phase changes, adding considerable difficulty to solving the flowsheet optimization problem. A novel optimization‐oriented MHEX modeling approach that uses a pseudo‐transient approach to rapidly compute stream temperatures without requiring Boolean variables is presented. The model also computes an approximate required heat exchange area to determine the optimal tradeoff between operating and capital expenses. Subsequently, this model is seamlessly integrated in a previously‐introduced pseudo‐transient process modeling and flowsheet optimization framework. Our developments are illustrated with two optimal design case studies, an MHEX representative of air separation operation and a natural gas liquefaction process. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1856–1866, 2015     

Optimum heat storage design for solar‐driven absorption refrigerators integrated with heat exchanger networks

A methodology is presented for optimizing hybrid renewable energy‐fossil fuel systems with short‐term heat storage. The considered system is an absorption‐refrigeration (AR) cycle integrated with a heat exchanger network (HEN) requiring cooling below ambient temperature. The AR cycle can be driven by multiple energy sources including excess energy from hot process streams, renewable energy sources (solar and biofuels), and fossil fuels. A two‐step approach based on mixed integer nonlinear programming methods is used for the optimization. First, the problem of optimal energy integration in the hybrid energy system without heat storage is solved on a monthly basis by minimizing simultaneously the total annual cost and the overall greenhouse gas emissions. In the second step, the multi‐tank thermal energy storage (TES) design problem is solved. The design involves the identification of the optimal number of storage tanks, their sizes, configuration and operation policies. The TES optimization is carried out on an hourly basis while incorporating the design targets determined by the first step. © 2013 American Institute of Chemical Engineers AIChE J, 60: 909–930, 2014     

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     

A pseudo‐transient optimization framework for periodic processes: Pressure swing adsorption and simulated moving bed chromatography

Periodic systems are widely used in separation processes and in reaction engineering. They are designed for and operated at a cyclic steady state (CSS). Identifying and optimizing the CSS has proven to be computationally challenging. A novel framework for equation‐oriented simulation and optimization of cyclic processes is introduced. A two‐step reformulation of the process model is proposed, comprising, (1) a full discretization of the time and spatial domains and (2) recasting the discretized model as a differential‐algebraic equation system, for which theoretical stability guarantees are provided. Additionally, a mathematical, structural connection between the CSS constraints and material recycling is established, which allows us to deal with these conditions via a “tearing” procedure. These developments are integrated in a pseudo‐transient design optimization framework and two extensive case studies are presented: a simulated moving bed chromatography system and a pressure swing adsorption process. © 2017 American Institute of Chemical Engineers AIChE J, 64: 2982–2996, 2018     

Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis

The batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T² and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.     

Optimization of kinetic data for two‐stage batch adsorption of Pb(II) ions onto tripolyphosphate‐modified kaolinite clay

BACKGROUND: Most adsorption studies consider only the adsorption of pollutants onto low cost adsorbents without considering how equilibrium and kinetic data can be optimized for the proper design of adsorption systems. This study considers the optimization of kinetic data obtained for the removal of Pb(II) from aqueous solution by a tripolyphosphate modified kaolinite clay adsorbent. RESULTS: Modification of kaolinite clay with pentasodium tripolyphosphate increases its cation adsorption capacity (CEC) and specific surface area (SSA) from 7.81 to 78.9 meq (100 g)^?1 and 10.56 to 13.2 m² g^?1 respectively. X‐ray diffraction patterns for both unmodified and tripolyphosphate‐modified kaolinite clay suggest the modification is effective on the surface of the clay mineral. Kinetic data from the batch adsorption of Pb(II) onto the tripolyphosphate‐modified kaolinite clay adsorbent were optimized to a two‐stage batch adsorption of Pb(II) using the pseudo‐second‐order kinetic model. Mathematical model equations were developed to predict the minimum operating time for the adsorption of Pb(II). Results obtained suggest that increasing temperature and decreasing percentage Pb(II) removal by the adsorbent enhanced operating time of the adsorption process. The use of two‐stage batch adsorption reduces contact time to 6.7 min from 300 min in the single‐stage batch adsorption process for the adsorption of 2.5 m³ of 500 mg L^?1 Pb(II) under the same operating conditions. CONCLUSION: Results show the potential of a tripolyphosphate‐modified kaolinite clay for the adsorption of Pb(II) from aqueous solution and the improved efficiency of a two‐stage batch adsorption process for the adsorption of Pb(II) even at increased temperature. Copyright © 2009 Society of Chemical Industry     

Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

A novel data‐driven adaptive robust optimization framework that leverages big data in process industries is proposed. A Bayesian nonparametric model—the Dirichlet process mixture model—is adopted and combined with a variational inference algorithm to extract the information embedded within uncertainty data. Further a data‐driven approach for defining uncertainty set is proposed. This machine‐learning model is seamlessly integrated with adaptive robust optimization approach through a novel four‐level optimization framework. This framework explicitly accounts for the correlation, asymmetry and multimode of uncertainty data, so it generates less conservative solutions. Additionally, the proposed framework is robust not only to parameter variations, but also to anomalous measurements. Because the resulting multilevel optimization problem cannot be solved directly by any off‐the‐shelf solvers, an efficient column‐and‐constraint generation algorithm is proposed to address the computational challenge. Two industrial applications on batch process scheduling and on process network planning are presented to demonstrate the advantages of the proposed modeling framework and effectiveness of the solution algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3790–3817, 2017     

Optimal design of renewable energy systems with flexible inputs and outputs using the P‐graph framework

The P‐graph framework introduced by Friedler et al. (Chem Eng Sci. 1992;47:1973–1988) is a general mathematical methodology based on Graph Theory which is applicable to many process design problems. We propose an extension of the P‐graph framework and the associated MILP model to account for operating units and systems where the inputs and outputs are variable. This is important because the P‐graph framework in its current form would otherwise apply only to systems where the ratios of inputs to outputs are fixed. Consequently, it is difficult to apply the method to many emerging systems without the new mathematical model presented here. We discuss and develop the model in detail, and we then illustrate its application with the case study of an energy system. We establish a structure with optimal cost for a baseline heat demand, and we further explore how the energy system structure and the feedstocks change as the heat demand increases. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1143–1153, 2016     

Framework for work‐heat exchange network synthesis (WHENS)

Work and heat are the two predominant forms of energy in the process industry. Considerable savings can be achieved by synergizing the work and heat requirements of process streams. A generalized framework for integrating heat and work simultaneously is proposed based on a mixed‐integer nonlinear programing model for work‐heat exchange network synthesis. Starting with a set of streams with known flows, temperatures, and pressures, a network of single‐shaft‐turbine‐compressors with motors/generators, valves, heat exchangers, and utility heaters/coolers is synthesized for minimized total annualized cost. In contrast to existing works, (1) streams are not preclassified as hot/cold or high/low pressure, (2) pressure changes are allowed for streams with no net pressure change, (3) liquid‐vapor phase changes are allowed, and (4) phase‐based property correlations are used. Successful application of our approach to C3 splitting yields a nonintuitive configuration. Another application of an offshore natural gas liquefaction process is also studied. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2472–2485, 2018     

Toward more cost‐effective and greener chemicals production from shale gas by integrating with bioethanol dehydration: Novel process design and simulation‐based optimization

A novel process design for a more cost‐effective, greener process for making chemicals from shale gas and bioethanol is presented. The oxidative coupling of methane and cocracking technologies are considered for converting methane and light natural gas liquids, into value‐added chemicals. Overall, the process includes four process areas: gas treatment, gas to chemicals, methane‐to‐ethylene, and bioethanol‐to‐ethylene. A simulation‐optimization method based on the NSGA‐II algorithm for the life cycle optimization of the process modeled in the Aspen HYSYS is developed. An energy integration model is also fluidly nested using the mixed‐integer linear programming. The results show that for a “good choice” optimal design, the minimum ethylene selling price is $655.1/ton and the unit global‐warming potential of ethylene is 0.030 kg CO₂‐eq/kg in the low carbon shale gas scenario, and $877.2/ton and 0.360 kg CO₂‐eq/kg in the high carbon shale gas scenario. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1209–1232, 2015     

Multiobjective design of interplant trigeneration systems

A systematic approach for heat integration into an eco‐industrial park through an integrated trigeneration system is presented. The approach is based on a new superstructure formulated as a multiobjective mixed‐integer nonlinear programming model, where intraplant and interplant heat exchange for the process streams is allowed, in addition to the energy integration into the utility system that is constituted by a steam Rankine cycle (to produce electric power and hot utility), an organic Rankine cycle (to recover waste heat and produce electric power), and an absorption refrigeration cycle (to recover waste heat and provide refrigeration). To run the utility system, several external heat sources (solar, fossil fuels, and biofuels) are considered, which impact the economic, environmental, and social objectives considered in the model. A systematic approach to tradeoff the objectives considered is presented. Two examples are presented, where the advantages of the integrated eco‐industrial park are shown. © 2013 American Institute of Chemical Engineers AIChE J, 60: 213–236, 2014     

Preparation and characterization of higher degree‐deacetylated chitosan‐coated magnetic adsorbent for the removal of chromium(VI) from its aqueous mixture

Chitosan (90% deacetylated) coated magnetic adsorbent prepared by coprecipitation method to remove Cr(VI) from its aqueous solution. The experimental studies depicts that the predominant option for removal of Chromium by adsorption from its aqueous phase using Magnetic‐Chitosan (MC). The subsequent physical, chemical, and magnetic properties of MC were characterized by X‐ray powder diffraction, scanning electron microscopy, Fourier transform infrared spectrometer, vibrating sample magnetometer. The influence of batch process parameters such as contact time, initial concentration, pH, and coexisting anions were investigated. The Box‐Behnken experimental design in response surface methodology was performed to design the experiment optimal operating conditions. The maximum percentage reduction of Cr(VI) is 96.3 that was obtained by magnetic chitosan with the optimal operating conditions of 149.53 mg/L at pH of 5.32 at the contact time of 80 min and at the temperature of 303 K. The average diameter of the magnetic chitosan was calculated from X‐ray diffractometer analysis as 24.5 nm. The equilibrium adsorption isotherm models such as Langmuir and Freundlich and the adsorption kinetics such as pseudo first order, pseudo second order and intra‐particle diffusion kinetic model were analyzed. The experimental data's suited for the best fit with the Langmuir isotherm model and pseudo first order kinetic model. It also revealed that Cr(VI) adsorption on MC is intrinsically exothermic and spontaneous. The magnetic chitosan was also used to investigate for the removal of Cr(VI) from the real water sources such as surface, underground, and tannery wastewater. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45878.     

A preliminary evaluation of a continuous‐flow reactor for liquid–liquid–solid phase‐transfer catalyzed synthesis of n‐butyl phenyl ether

This study evaluates the feasibility of using a continuous‐flow stirred vessel reactor (CFSVR) to synthesize n‐butyl phenyl ether (ROPh) from n‐butyl bromide (RBr) and sodium phenolate (NaOPh) by liquid–liquid–solid phase‐transfer catalysis (triphase catalysis). The factors affecting the preparation of triphase catalysts, the etherification reaction in a batch reactor, and the performance in a CFSVR were investigated. The kinetic study with a batch reactor indicated that when the initial concentration of NaOPh or RBr was high, the conversion of RBr would depend on the initial concentration of both RBr and NaOPh. The reaction can be represented by a pseudo‐first‐order kinetic model when the concentration of NaOPh is in proper excess to that of RBr, and the apparent activation energy is 87.8 kJ mol^?1. When the etherification reaction was carried out in the CFSVR, the catalyst particles did not flow out of the reactor, even at a high agitation speed. The conversion of RBr in the CFSVR was, as predicted, lower than that in the batch reactor, but was higher than the theoretical value because the dispersed phase is not completely mixed. Copyright © 2004 Society of Chemical Industry     

Synthesis of C‐H‐O Symbiosis Networks

The concept of synthesizing carbon, hydrogen, and oxygen (C‐H‐O) SYmbiosis Networks (CHOSYNs) for the design of eco‐industrial parks is introduced. Within a CHOSYN, compounds containing C‐H‐O are exchanged, converted, separated, mixed, and allocated. The use of C‐H‐O as the basis for integration creates numerous opportunities for synergism because C, H, and O are the primary building blocks for many industrial compounds that can be exchanged and integrated. A particularly attractive feature of the CHOSYN framework is its ability to use atomic‐based targets to establish benchmarks for the design of macroscopic systems involving multiple processes. Several structural representations, benchmarking, and optimization formulations are developed to embed potential CHOSYN configurations of interest and to synthesize cost‐effective networks. A case study with several scenarios is solved to demonstrate the new concept and tools. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1242–1262, 2015     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

Outer approximation algorithm with physical domain reduction for computer‐aided molecular and separation process design

Integrated approaches to the design of separation systems based on computer‐aided molecular and process design (CAMPD) can yield an optimal solvent structure and process conditions. The underlying design problem, however, is a challenging mixed integer nonlinear problem, prone to convergence failure as a result of the strong and nonlinear interactions between solvent and process. To facilitate the solution of this problem, a modified outer‐approximation (OA) algorithm is proposed. Tests that remove infeasible regions from both the process and molecular domains are embedded within the OA framework. Four tests are developed to remove subdomains where constraints on phase behavior that are implicit in process models or explicit process (design) constraints are violated. The algorithm is applied to three case studies relating to the separation of methane and carbon dioxide at high pressure. The process model is highly nonlinear, and includes mass and energy balances as well as phase equilibrium relations and physical property models based on a group‐contribution version of the statistical associating fluid theory (SAFT‐γ Mie) and on the GC⁺ group contribution method for some pure component properties. A fully automated implementation of the proposed approach is found to converge successfully to a local solution in 30 problem instances. The results highlight the extent to which optimal solvent and process conditions are interrelated and dependent on process specifications and constraints. The robustness of the CAMPD algorithm makes it possible to adopt higher‐fidelity nonlinear models in molecular and process design. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3484–3504, 2016     

Electrolytic removal of ammonia from brine wastewater: scale‐up,operation and pilot‐scale evaluation

Brine wastewater with a high ammonia content from an iodine processing plant (commonly called kansui in Japan) was treated by electrolysis. The system, which can be considered as an indirect electrolytic treatment process, generates chlorine at the anodes and initiates the formation of mixed oxidants like hypochlorous acid. The oxidants then act as agents for ammonia destruction. Laboratory‐scale experiments showed that high ammonia concentrations (as much as 200 mg dm^?3) could be completely removed within a few minutes, and could be considered a good alternative for efficient ammonia removal from saline wastewaters. From laboratory‐scale experiments in the batch and continuous modes, the charge dose was analyzed and used as the operating and scale‐up factor. The value of the charge dose was not severely affected by changes in operating conditions such as electrode spacing and temperature. The charge dose from batch and continuous runs was found to be in the range of 23 C (mg NH₄‐N removed)^?1 to 29 C (mg NH₄‐N removed)^?1. Using the charge dose obtained from laboratory‐scale continuous electrolysis experiments as the scale‐up factor, a pilot‐scale reactor was designed, and the operating conditions were calculated. In the pilot‐scale reactor tests at different flow rates, the effluent ammonia concentrations were reasonably close to the calculated values predicted from the charge dose equation. Copyright © 2004 Society of Chemical Industry     

Fault detection and isolation in hybrid process systems using a combined data‐driven and observer‐design methodology

A combined data‐driven and observer‐design methodology for fault detection and isolation (FDI) in hybrid process systems with switching operating modes is proposed. The main contribution is to construct a unified framework for FDI by integrating Gaussian mixture models (GMM), subspace model identification (SMI), and results from unknown input observer (UIO) theory. Initially, a GMM is built to identify and describe the multimodality of hybrid systems using the recorded input/output process data. A state‐space model is then obtained for each specific operating mode based on SMI if the system matrices are unknown. An UIO is designed to estimate the system states robustly, based on which the fault detection is laid out through a multivariate analysis of the residuals. Finally, by designing a set of unknown input matrices for specific fault scenarios, fault isolation is performed through the disturbance‐decoupling principle from the UIO theory. A significant benefit of the developed framework is to overcome some of the limitations associated with individual model‐based and data‐based approaches in dealing with the problem of FDI in hybrid systems. Finally, the validity and effectiveness of the proposed monitoring framework are demonstrated using a numerical example, a simulated continuous stirred tank heater process, and the Tennessee Eastman benchmark process. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2805–2814, 2014