Integrated ionic liquid and rate-based absorption process design for gas separation: Global optimization using hybrid models

A new method for integrated ionic liquid (IL) and absorption process design is proposed where a rigorous rate-based process model is used to incorporate absorption thermodynamics and kinetics. Different types of models including group contribution models and thermodynamic models are employed to predict the process-relevant physical, kinetic, and thermodynamic (gas solubility) properties of ILs. Combining the property models with process models, the integrated IL and process design problem is formulated as an MINLP optimization problem. Unfortunately, due to the model complexity, the problem is prone to convergence failure. To lower the computational difficulty, tractable surrogate models are used to replace the complex thermodynamic models while maintaining the prediction accuracy. This provides an opportunity to find the global optimum for the integrated design problem. A pre-combustion carbon capture case study is provided to demonstrate the applicability of the method. The obtained global optimum saves 14.8% cost compared with the Selexol process.     

Data-Driven Process Simulation Using Connected Surrogate Unit Models Exemplified on a Steam Methane Reforming Process

Process simulation based on physical models often faces computational problems with respect to convergence, especially if the underlying flowsheets are complex. The use of data-driven surrogate models connected to flowsheets promises to overcome these challenges. Using the steam methane reforming process, this paper presents the development of surrogate models – artificial neural networks – for the key units of the process that are subsequently connected to form the entire flowsheet. The accuracy of the individual surrogate models is analyzed based on the test error; the accuracy of the flowsheet is evaluated by a benchmark process simulation performed in Aspen Plus®. Therefore, the predicted key variables, here outlet temperatures and compositions, are compared to the benchmark. It is shown that their maximum error is below the typical measurement error. The comparison of the accuracy of the surrogate-based flowsheet simulation with the Aspen Plus® simulation proves to match very well, as long as the training ranges of the underlying surrogate models are not violated. The promising results of this paper pave the way for future work, such as the optimization of process parameters or superstructure optimization.     

A Simple Way for Implementing Extraction Columns of Infinite Height in Flowsheet Simulators

A surrogate model to implement an extraction column of infinite height in process simulation software is presented. The model consists of three decanters and a few specifications which are easy to implement in commercial process simulators. Using the model, the minimum solvent flow rate and the limiting product compositions are determined. In an example, the surrogate model for the extraction column is combined with standard unit operation models for describing an extraction process with a distillative solvent recycle.     

An algorithm to determine sample sizes for optimization with artificial neural networks

This article presents an algorithm developed to determine the appropriate sample size for constructing accurate artificial neural networks as surrogate models in optimization problems. In the algorithm, two model evaluation methods—cross‐validation and/or bootstrapping—are used to estimate the performance of various networks constructed with different sample sizes. The optimization of a CO₂ capture process with aqueous amines is used as the case study to illustrate the application of the algorithm. The output of the algorithm—the network constructed using the appropriate sample size—is used in a process synthesis optimization problem to test its accuracy. The results show that the model evaluation methods are successful in identifying the general trends of the underlying model and that objective function value of the optimum solution calculated using the surrogate model is within 1% of the actual value. © 2012 American Institute of Chemical Engineers AIChE J, 59: 805–812, 2013     

A Modular Approach for Surrogate Modeling of Flowsheets

Flowsheet simulation, an important building block in chemical process development and design, generally requires the solution of a nonlinear system of equations. Such a simulation can fail if either no solution exists for the chosen specifications or if the initial values for the solver are chosen unfavorably. In this work, to overcome such convergence failures, AI-based surrogate models are trained for unit operations of a flowsheet and then interconnected. For a pressure swing distillation with recycle, it is shown that such an interconnection of surrogate models yields more accurate results compared to a surrogate model for the whole flowsheet at once, and that adequate starting points for the flowsheet simulation can be obtained from the interconnected surrogates.     

Linear relationships for modeling CO2 absorption in aqueous alkanolamine solutions in a thermodynamically consistent way

A thermodynamically consistent model for the carbon dioxide (CO₂) absorption in aqueous alkanolamine system is of great importance in the research and development of a CO₂ capture process. To facilitate the development of thermodynamic models, linear Gibbs free energy, enthalpy, and heat capacity relationships using well-known amines as reference are used to correlate the standard reference state properties of ionic species with those of molecular species in the electrolyte system, which has been approved to provide a reliable and consistent way to estimate required parameters when there is minimal or no appropriate experimental data available. The proposed relationships have been applied to the development of an electrolyte nonrandom two liquid (NRTL) activity coefficient model for CO₂ absorption in aqueous 1-amino-2-propanol (A2P) solution, as an example to demonstration the methodology. With limited vapor–liquid equilibrium data and other thermodynamic properties, the parameters in the electrolyte NRTL model are identified with good accuracy.     

尿素流程高压洗涤器的模拟计算及分析

基于严格的热力学机理模型 ,对尿素工艺流程中高压洗涤器中下两段分别建立了平衡级模型 ,通过迭代求解两个模块 ,使连接两模块的中间流股收敛 ,完成了对整个洗涤器的模拟计算 ,计算结果同设计值吻合较好。针对该体系的强非理想性及数学模型的强非线性 ,提出可行的求解策略 ,算法稳定且收敛性较好。该研究为改造、优化工艺操作及单元设备结构提供了理论依据     

Using surrogate models for efficient optimization of simulated moving bed chromatography

A new approach of using computationally cheap surrogate models for efficient optimization of simulated moving bed (SMB) chromatography is presented. Two different types of surrogate models are developed to replace the detailed but expensive full-order SMB model for optimization purposes. The first type of surrogate is built through a coarse spatial discretization of the first-principles process model. The second one falls into the category of reduced-order modeling. The proper orthogonal decomposition (POD) method is employed to derive cost-efficient reduced-order models (ROMs) for the SMB process. The trust-region optimization framework is proposed to implement an efficient and reliable management of both types of surrogates. The framework restricts the amount of optimization performed with one surrogate and provides an adaptive model update mechanism during the course of optimization. The convergence to an optimum of the original optimization problem can be guaranteed with the help of this model management method. The potential of the new surrogate-based solution algorithm is evaluated by examining a separation problem characterized by nonlinear bi-Langmuir adsorption isotherms. By addressing the feed throughput maximization problem, the performance of each surrogate is compared to that of the standard full-order model based approach in terms of solution accuracy, CPU time and number of iterations. The quantitative results prove that the proposed scheme not only converges to the optimum obtained with the full-order system, but also provides significant computational advantages.     

Uncertainty quantification and global sensitivity analysis of complex chemical process using a generalized polynomial chaos approach

Uncertainties are ubiquitous and unavoidable in process design and modeling. Because they can significantly affect the safety, reliability and economic decisions, it is important to quantify these uncertainties and reflect their propagation effect to process design. This paper proposes the application of generalized polynomial chaos (gPC)-based approach for uncertainty quantification and sensitivity analysis of complex chemical processes. The gPC approach approximates the dependence of a process state or output on the process inputs and parameters through expansion on an orthogonal polynomial basis. All statistical information of the interested quantity (output) can be obtained from the surrogate gPC model. The proposed methodology was compared with the traditional Monte-Carlo and Quasi Monte-Carlo sampling-based approaches to illustrate its advantages in terms of the computational efficiency. The result showed that the gPC method reduces computational effort for uncertainty quantification of complex chemical processes with an acceptable accuracy. Furthermore, Sobol’s sensitivity indices to identify influential random inputs can be obtained directly from the surrogated gPC model, which in turn further reduces the required simulations remarkably. The framework developed in this study can be usefully applied to the robust design of complex processes under uncertainties.     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

Product tri-section based crude distillation unit model for refinery production planning and refinery optimization

Accuracy of a crude distillation unit (CDU) model has a significant impact on refinery production planning. High accuracy is typically accomplished via nonlinear models which causes convergence difficulties when the entire refinery model is optimized. CDU model presented in this work is a mixed-integer linear model with a modest number of binary variables; its accuracy is on par with rigorous tray to tray CDU models. The model relies on the observation¹² that a line through the middle of the product true boiling point (TBP) curve depends on the crude feed properties and the yields of the adjacent products. Novelty of the product tri-section CDU model is that it does not require models of individual distillation towers comprising the CDU, thereby leading to a much simpler model structure. Significant reduction in the computational effort required for the optimization of nonlinear refinery models is illustrated by comparison with previous work.     

A comparative study of n-heptane, methyl decanoate, and dimethyl ether combustion characteristics under homogeneous-charge compression-ignition engine conditions

Combustion characteristics of n-heptane, a surrogate for hydrocarbon diesel, methyl decanoate, a surrogate for biodiesel, and dimethyl ether, a fuel that can be derived from bio-feedstocks, are investigated with a homogeneous constant-pressure reactor model and a homogeneous-charge compression-ignition engine thermodynamic simulation model, with focus on two variables: ignition delay and NO formation, under conditions of varying oxygen concentration. Negative temperature coefficient (NTC) behavior is observed for the three fuels. Reducing oxygen concentration increases ignition delay for all fuels. The results and conclusions with the two models differ because it is necessary to vary initial conditions in the engine model to optimize combustion phasing and maximize indicated efficiency.     

Large scale optimization of a sour water stripping plant using surrogate models

In this work, we propose a new methodology for the large scale optimization and process integration of complex chemical processes that have been simulated using modular chemical process simulators. Units with significant numerical noise or large CPU times are substituted by surrogate models based on Kriging interpolation. Using a degree of freedom analysis, some of those units can be aggregated into a single unit to reduce the complexity of the resulting model. As a result, we solve a hybrid simulation-optimization model formed by units in the original flowsheet, Kriging models, and explicit equations.We present a case study of the optimization of a sour water stripping plant in which we simultaneously consider economics, heat integration and environmental impact using the ReCiPe indicator, which incorporates the recent advances made in Life Cycle Assessment (LCA).The optimization strategy guarantees the convergence to a local optimum inside the tolerance of the numerical noise.     

Machine learning-based distributed model predictive control of nonlinear processes

This work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed-loop stability and performance properties. Extensive open-loop data within a desired operating region are used to develop long short-term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov-based DMPC to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed-loop performance is very close to the one of a centralized MPC system.     

Applying a Thermodynamic Model to the Non‐Stoichiometric Precipitation of Barium Sulfate

Thermodynamic models for aqueous Ba²⁺‐SO₄^2–‐Na⁺‐Cl^–‐solutions are compared in their accuracy to predict ion activities in saturated and supersaturated solutions. The Pitzer and the Bromley model are employed, taking into account ion pair formation of barium sulfate. Such models are then used to describe particle nucleation and growth, and finally they are imbedded in a mechanistic mixing‐precipitation model for a single feed semibatch process. The effect of the key operating parameters on the mean particle size is analyzed through simulations. The results are compared with previous experimental data, thus highlighting the significance of a proper choice of the thermodynamic model.     

水合物法分离CH4/CO2研究现状及展望

介绍了国内外水合物法CH₄/CO₂分离技术的研究现状。首先综述了针对该工艺的促进强化措施,主要包括热力学促进、动力学促进与综合促进。其中,热力学促进能改变反应条件,但会降低分离效率;动力学促进能提高反应速率,但不能改变反应条件;综合促进集合了前两者的优点,但技术还不成熟,是未来的研究重点。接着,讨论了针对该过程的数学模型,主要为热力学模型和动力学模型。目前,所建立的热力学模型多是针对无促进作用体系,且不能同时用于准确地计算相平衡条件和各项组成;动力学模型主要针对水合物生长过程。然后分析了针对该工艺的流程分析现状,即主要停留在实验阶段和平衡条件下的模型计算。最后,基于现状分析,认为提高反应效率,强化热力学、动力学促进和完善热力学、动力学模型等是今后主要的研究方向。     

Kinetic studies of the autothermal reforming of tetradecane over Pt/Al2O3 catalyst in a fixed-bed reactor

Kinetics of autothermal reforming (ATR) of tetradecane on Pt-Al₂O₃ catalyst over the temperature range 750-900 °C is investigated. Experimental results obtained from NETL (US-DOE) are used for model parameter estimation and validation. Two Langmuir-Hinshelwood-Hougen-Watson (LHHW) type rate models are developed and subjected to parameter estimation and model discrimination. LHHW model in which hydrocarbon is adsorbed on the catalyst surface as alkyl intermediate species by scission of C-H bond gave physically meaningful parameters. Parameters are estimated by using generalized reduced gradient method in spreadsheet and sequential quadratic programming in Matlab. The estimated parameters for the selected model are thermodynamically consistent. The developed kinetic model could capture the experimental behavior of the process and could predict the outlet composition within 25% error.     

基于EGO算法的常压塔能量优化

常减压装置能量消耗约占炼厂总用能的25%～30%,在保证产品产量与质量的条件下,优化常减压蒸馏塔操作条件,可有效降低能耗.为了避免随机优化算法对常压塔机理模型进行操作优化时,存在计算资源消耗大、效率低的问题,文中采用基于代理模型的全局优化方法优化常压塔的余热回收过程,在优化迭代过程中用Kriging代理模型来代替耗时的精确模型评估.实验表明模型调用次数相较于粒子群优化算法减少了90%,优化时间减少了85%,实现了能量优化并且保证了侧线产品之间的分离精度.