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     

A superstructure‐based model for multistream heat exchanger design within flow sheet optimization

Multistream heat exchangers (MHEXs) are often used in energy‐intensive cryogenic processes. Modeling them within a process optimization formulation has been a challenge due to the needs to accommodate phase changes and ensure temperature approach. In this work, we present a nonlinear model for MHEXs based on a novel single‐stage superstructure of two‐stream exchangers. Our formulation guarantees a minimum temperature approach for all heat exchanges, estimates heat exchange areas for individual stream matches, requires no prior knowledge of phase changes, uses no Boolean variables, and enables seamless optimization of a process with multiple MHEXs. Furthermore, it facilitates dedicated constant‐phase intervals that allow accurate estimation of heat‐transfer parameters for various stream matches. We optimize two natural gas liquefaction processes involving MHEXs, and report better solutions than the existing literature. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3764–3777, 2017     

基于状态空间超级结构的多流股换热网络最优设计

多流股换热器以其结构紧凑、高效低耗等特点,成为过程强化研究的热门领域,但对于多流股换热的过程与设备优势所在仍然值得商榷。基于多流股换热匹配改进状态空间超级结构,将多流股换热网络综合转化为超级换热器设计。首先,构造级联多流股换热器匹配过程操作算子,通过相邻换热流股匹配,传递温位效应,实现多流股间传热严格计算;借助热容流率混合分配机制,实现各流股间任意分混操作。然后,考虑散热因素,改进目标函数,引入冷热损失和保温材料费用项,清晰体现多流股换热器因换热面互相覆盖而带来的外表面封包优势。进而,建立相应非线性数学规划模型,实现公用工程、设备投资、冷热损耗同步优化。最终,通过文献示例对所提方法可行性与优越性进行验证。     

Modeling multistream heat exchangers with and without phase changes for simultaneous optimization and heat integration

A new equation‐oriented process model for multistream heat exchangers (MHEX) is presented with a special emphasis on handling phase changes. The model internally uses the pinch concept to ensure the minimum driving force criteria. Streams capable of phase change are split into substreams corresponding to each of the phases. A novel disjunctive representation is proposed that identifies the phases traversed by a stream during heat exchange and assigns appropriate heat loads and temperatures for heat integration. The disjunctive model can be reformulated to avoid Boolean (or integer) variables using inner minimization and complementarity constraints. The model is suitable for optimization studies, particularly when the phases of the streams at the entry and exit of the MHEX are not known a priori. The capability of the model is illustrated using two case studies based on cryogenic applications. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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     

Multistream heat exchanger modeling and design

A new model formulation and solution strategy for the design and simulation of processes involving multistream heat exchangers (MHEXs) is presented. The approach combines an extension of pinch analysis with an explicit dependence on the heat exchange area in a nonsmooth equation system to create a model which solves for up to three unknown variables in an MHEX. Recent advances in automatic generation of derivative‐like information for nonsmooth equations make the method tractable, and the use of nonsmooth equation solving methods make the method very precise. Several illustrative examples and a case study featuring an offshore liquefied natural gas production concept are presented which highlight the flexibility and strengths of the formulation. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3390–3403, 2015     

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     

Optimization of sub-ambient separation systems with embedded cubic equation of state thermodynamic models and complementarity constraints

A previously developed equation-based flowsheet optimization framework is extended and applied to design sub-ambient separation systems for oxy-fired coal power systems with carbon capture. Unlike most commercial flowsheet design and optimization tools, the proposed methods use exact derivatives and large-scale nonlinear programming algorithms to solve large flowsheet design problems with many degrees of freedom, including the simultaneous design of air separation units (ASUs) and their accompanying multistream heat exchangers. Emphasis is placed on additional model improvements regarding thermodynamic calculations. In order to maintain differentiability, complementarity constraints are used to model switches, including vanishing and reappearing phases. Nevertheless, these complementarity constraints may construct trivial phase equilibrium solutions, and a procedure based on embedded bubble and dew points calculations is proposed to avoid them. Furthermore, additional complementarity constraints for the cubic equation of state model are proposed to ensure correct phase identification in the supercritical region. Finally, the efficacy of these new models are demonstrated by optimization of the CO₂ processing unit and compression train for an oxy-fired power plant.     

Non‐Newtonian Heat Transfer on a Plate Heat Exchanger with Generalized Configurations

For the configuration optimization of plate heat exchangers (PHEs), the mathematical models for heat transfer and pressure drop must be valid for a wide range of operational conditions of all configurations of the exchanger or the design results may be compromised. In this investigation, the thermal model of a PHE is adjusted to fit experimental data obtained from non‐Newtonian heat transfer for eight different configurations, using carboxymethylcellulose solutions (CMC) as test fluid. Although it is possible to successfully adjust the model parameters, Newtonian and non‐Newtonian heat transfer cannot be represented by a single generalized correlation. In addition, the specific heat, thermal conductivity and power‐law rheological parameters of CMC solutions were correlated with temperature, over a range compatible with a continuous pasteurization process.     

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     

Stady‐state and Dynamical Simulation of an Autothermal Gasoline Reformer

Detailed numerical simulation is an important tool for the analysis, development and optimization of new reactor systems. In this contribution results of steady‐state and dynamic simulations of a hydrogen production system for mobile applications based on gasoline are presented. The system consists of an autothermal reformer, a high temperature shift reactor and a countercurrent heat exchanger for heat integration. The simulations are based on 1‐D, multiphase, dynamic models, which are solved with the simulation tool PDEX‐Pack. Firstly steady‐state and dynamic simulations of the autothermal reformer alone are presented. Concentration and temperature profiles in the reformer under different operation conditions are discussed and possibilities to improve the performance are assessed. Dynamic simulations of load change and cold start show the fast dynamic response of the reformer due to its low thermal mass. Simulations of the coupled system underline the impact of the heat exchanger design for the system performance, especially under dynamic conditions. Finally dynamic simulations of a possible cold start strategy for the system are discussed.     

Shell and tube heat exchanger design using mixed‐integer linear programming

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017     

Heat exchanger network synthesis with detailed exchanger designs—2. Hybrid optimization strategy for synthesis of heat exchanger networks

We propose a new strategy to synthesize heat exchanger networks with detailed designs of individual heat exchangers. The proposed strategy uses a multistep approach by first obtaining a heat exchanger network topology through solving a modified version of the mixed integer nonlinear programming (MINLP) stage-wise superstructure of Yee and Grossmann, which includes a smoothed LMTD approximation and pressure drops. In a second nonlinear programming (NLP) suboptimization step, we allow for nonisothermal mixing to solve problems with or without exchanger bypasses. The selected heat exchangers along with the mass and energy balances obtained are then used to design the network with detailed exchanger designs through solving a sequence of NLPs for individual heat exchanger designs. The NLPs are based on the detailed discretized optimization models of Kazi et al., which solve quickly and reliably to obtain heat exchangers based on rigorous, first-principles derived coupled differential equations. These models solve a differential algebraic equation system and do not rely on usual assumptions associated with other heuristic-based exchanger design methods, such as log mean temperature difference and F_T correction factors. These detailed exchanger designs are then used to update the network optimization model through sets of correction factors on heat exchanger area, number of shells, heat transfer coefficients, and pressure drops of each exchanger design, in a method based on that of Short et al. The method solves reliably, guaranteeing feasible exchangers for every potential network generated by the shortcut models, through validation with rigorous heat exchanger models at every iteration. In addition, the method does not increase the nonlinearity of the MINLP model, nor does it require any manual intervention or initialization from the user. Three examples are solved and the results are compared to those obtained in the literature.     

Process design and control optimization: A simultaneous approach by multi‐parametric programming

We present a framework for the application of design and control optimization via multi‐parametric programming through four case studies. We develop design dependent multi‐parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework (Pistikopoulos et al, Chem Eng Sci. 2015;136:115–138). The process and the design dependent explicit controllers undergo a mixed integer dynamic optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

A pinch‐like targeting framework for systematic thermal process intensification

The design of intensified systems remains an “Edisonian” effort, whereby new intensification schemes are the product of creativity rather than the result of applying systematic procedures. Under this motivation, this article presents a novel and systematic approach for identifying targets for thermal process intensification, defined as combining two or more heat sources and sinks present in a process flowsheet, possibly along with a thermal utility stream, in a single intensified device where heat exchange takes place. The targeting problem is formulated as a mixed‐integer linear program. An extensive case study illustrating its application is presented. © 2017 American Institute of Chemical Engineers AIChE J, 64: 877–885, 2018     

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     

浅谈炼化装置冷换框架的设计

从炼化装置中冷换框架的构架结构特点、换热器相关管道的工艺要求、配套管线设计和绘图软件应用等设计方面出发,结合现场安全操作生产、维护和检修方便等几个方面,对冷换框架的设计步骤和设计要点进行阐述。着重介绍了构架的各层层高的确定方法、换热器的配管和配套设施的规划设计等,并就设计过程中的绘图技巧进行了简单介绍。     

Heat exchanger network synthesis with detailed exchanger designs: Part 1. A discretized differential algebraic equation model for shell and tube heat exchanger design

A new method for the detailed design of shell and tube heat exchangers is presented through the formulation of coupled differential heat equations, along with algebraic equations for design variables. Heat exchanger design components (tube passes, baffles, and shells) are used to discretize the differential equations and are solved simultaneously with the algebraic design equations. The coupled differential algebraic equation (DAE) system is suitable for numerical optimization as it replaces the nonsmooth log mean temperature difference (LMTD) term. Discrete decisions regarding the number of shells, fluid allocation, tube sizes, and number of baffles are determined by solving an LMTD-based method iteratively. The resulting heat exchanger topology is then used to discretize the detailed DAE model, which is solved as a nonlinear programming model to obtain the detailed exchanger design by minimizing an economic objective function through varying the tube length. The DAE model also provides the stream temperature profiles inside the exchanger simultaneously with the detailed design. It is observed that the DAE model results are almost equal to the LMTD-based design model for one-shell heat exchangers with constant stream properties but shows significant differences when streams properties are allowed to vary with temperature or the number of shells are increased. The accuracy of the solutions and the required computational costs show that the model is well suited for solving heat exchanger network synthesis problems combined with detailed exchanger designs, which is demonstrated in Part 2 of the paper.     

Gray‐Box Modeling for the Optimization of Chemical Processes

The availability of predictive models for chemical processes is the basic prerequisite for offline process optimization. In cases where a predictive model is missing for a process unit within a larger process flowsheet, measured operating data of the process can be used to set up such models combining physical knowledge and process data. In this contribution, the creation and integration of such gray‐box models within the framework of a flowsheet simulator is presented. Results of optimization using different gray‐box models are shown for a virtual cumene process.     

Heat‐transfer characteristics of polymer hollow fiber heat exchanger for vaporization application

The heat‐transfer characteristics of polymer hollow fiber heat exchanger were investigated by analyzing the heat‐transfer coefficient (HTC) and the heat‐transfer resistance (HTR) distributions of both the lumen side and the shell side. The influences of the fiber wall thickness and the polymer thermal conductivity on the heat‐transfer performance were studied numerically based on the experimental validated simulation model. It is found that the original overall HTC value is below 1032 W/m²·K and the HTR is focus on the fiber wall. However, if enhancing the polymer thermal conductivity to be higher than 1.0 W/m·K and/or lowering the fiber wall thickness to be less than 0.1 mm, the overall HTC could be improved to over 2000 W/m²·K, which indicates that the fiber wall HTR is no longer the limiting factor of the polymer hollow fiber heat exchanger applications. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1783–1792, 2018