Nonlinear model of pneumatic conveying dryer for economic process control

Abstract

This paper presents a nonlinear dynamic model, suitable for economic process control of pneumatic conveying dryer for drying of food grains. The dynamic model is developed by reshaping the process equations derived for the batch drying, dilute phase, and a negative-pressure conveying system. The dynamic model parameters are identified by numerically solving a nonlinear least squares optimization problem, subject to a set of differential and algebraic equality constraints that describe the system dynamics and bounds in the parameters. A detailed parametric uncertainty and sensitivity analysis are performed providing valuable insight into the influence of critical model parameters on observables, the interplay among various parameter-state-measured disturbances, and quantifying uncertainties in the model. Further, different process economic performance and product quality indicator of uncertain dryer model are studied. The model validation study as performed with the underlying process shows a very good agreement in understanding necessary dynamic characteristics and interplay between the various parameter of interest.     

Axial Dispersion Model for Estimation of Ozone Self-Decomposition

A new method using the axial dispersion model for estimation of ozone self-decomposition kinetics in a semibatch bubble column reactor was developed. The reaction rate coefficients for literature equations of ozone decomposition and the gas phase dispersion coefficient were estimated and compared with literature data. The reaction order in the pH range 7–10 with respect to ozone 1.12 and 0.51 the hydroxyl ion were obtained, which is in good agreement with literature. The model parameters were determined by parameter estimation using a nonlinear optimization method. A sensitivity analysis was conducted to obtain information on reliability and identifiability of the estimated parameters.     

High Throughput Screening for the Design and Optimization of Chromatographic Processes: Assessment of Model Parameter Determination from High Throughput Compatible Data

Chromatographic processes can be optimized in various ways, and the two most prominent approaches are based either on statistical data analysis or on experimentally validated simulation models. Both strategies rely heavily on experimental data, the generation of which usually imposes a significant bottleneck on rational process design. The latter approach is followed in this work, and the utilizability of high throughput compatible experiments for the determination of model parameters which are required for in silico process optimization, is assessed. The unknown parameter values are estimated from batch uptake experiments on a robotic platform and from dynamic breakthrough experiments with miniaturized chromatographic columns. The identified model is then validated with respect to process optimization by comparison of model predictions with experimental data from a preparative scale column. In this study, a strong cation exchanger Toyopearl SP‐650M and lysozyme solved in phosphate buffer (pH 7), is used as the test system. The utilization of data from miniaturized and high throughput compatible experiments is shown to yield sufficiently accurate results, and minimizes efforts and costs for both parameter estimation and model validation.     

Determination of biogeochemical parameters in eutrophication models with simultaneous dynamic optimization approaches

This work addresses a parameter estimation problem in an ecological water quality model through a simultaneous dynamic optimization approach. The model is based on first principles and has a large number of parameters, which must be estimated based on data collected in the water body under study. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem, with a weighted least squares objective function. Main biogeochemical parameters have been obtained, which allow a close representation of the lake dynamics, as it is shown in the numerical results.     

Determination of the Henry's Coefficient and Mass Transfer for Ozone in a Bubble Column at Different pH Values of Water

In this study, the ozone gas-liquid mass transfer into water in a bubble column was investigated for different pH values. The ozone volumetric mass transfer coefficient and the Henry's coefficient were determined simultaneously by parameter estimation using a nonlinear optimization method. A sensitivity analysis was conducted to obtain information on the reliability and identifiability of the estimated parameters. A minor dependence of the Henry's law constant on pH was detected at the pH range 4 to 9.     

Modeling, simulation and experimental validation of a PEM fuel cell system

The aim of this work is the development and experimental validation of a detailed dynamic fuel cell model using the gPROMS modeling environment. The model is oriented towards optimization and control and it relies on material and energy balances as well as electrochemical equations including semi-empirical equations. For the experimental validation of the model a fully automated and integrated hydrogen fuel cell testing unit was used. The predictive power of the model has been compared with the data obtained during load change experiments. A sensitivity analysis has been employed to reveal the most critical empirical model parameters that should be estimated using a systematic estimation procedure. Model predictions are in good agreement with experimental data under a wide range of operating conditions.     

Composition estimation of multicomponent reactive batch distillation with optimal sensor configuration

An inferential state estimation scheme based on extended Kalman filter (EKF) with optimal selection of sensor locations using principal component analysis (PCA) is presented for composition estimation in multicomponent reactive batch distillation. The properties of PCA are exploited to provide the most sensitive dynamic temperature measurement information of the process to the estimator for accurate estimation of compositions. The state estimator is supported by a simplified dynamic model of reactive batch distillation that includes component balance equations together with thermodynamic relations and reaction kinetics. The performance of the proposed scheme is evaluated by applying it for composition estimation on all trays, reboiler, reflux drum and products of a reactive batch distillation column, in which ethyl acetate is produced through an esterification reaction between acetic acid and ethanol. This quaternary system with azeotropism is highly nonlinear and typically suited for implementation of the proposed scheme. The results demonstrate that the proposed EKF estimation scheme with optimal temperature sensor configuration is effective for inferential estimation of compositions in multicomponent reactive batch distillation.     

The influence of random packed column parameters on the liquid holdup and interfacial area

Carbon dioxide capture via solvent absorption in packed columns has emerged as a potential technology to mitigate coal-fired power plant CO₂ emissions. Parameters, including packing types, solvent properties, and operating conditions, could potentially affect the packed column CO₂ capture efficiency. To understand the importance of those parameters and help packed column optimization, a design of experiments (DoEs) method was proposed to generate input parameter matrix. Combined with multiphase computational fluid dynamics (CFD), the random packed column parameter influence on the liquid holdup and interfacial area can be efficiently investigated. Surrogate-based sensitivity analysis shows that the solvent flow rate and contact angle are key factors dictating liquid holdup and interfacial area. On the other hand, solvent viscosity has a marginal impact on the interfacial area. The sensitivity scores were calculated for each input parameter to guide the selection of dimensionless numbers for the liquid holdup and interfacial area correlation development.     

A systematic approach to SMB processes model identification from batch experiments

The optimization, monitoring and control of simulated moving bed (SMB) units require the use of a process model and the estimation of the model parameters. A systematic numerical procedure for determining parameters of SMB models from batch experiments is presented and evaluated. The unknown parameters are estimated by minimizing a cost function measuring the difference between experimental and simulated concentration profiles. In contrast with previous studies, parameter identifiability is studied and errors on the estimated parameters are calculated. A sensitivity analysis is used to design the experiments and to compare the identifiability of different chromatographic models. Then, the influence of local minima is evaluated by applying the numerical procedure on fictitious measurements generated from a model with known parameters.     

SBR恒曝气量好氧硝化过程动态DO模拟:模型辨识与KLa确定

通过简化活性污泥法1号模型(activated sludge model No.1,ASM1)建立两步硝化反应的数学模型,实现了对序批式反应器(sequencing batch reactor,SBR)恒曝气量好氧过程中溶解氧(dissolved oxygen,DO)动态变化过程的数学模拟,模型辨识科学地区分了可以直接取值的参数包括产率系数、DO饱和常数(或底物饱和常数)和需要重新估计的参数。采用文献推荐参数值模拟了过程中主要状态变量的动力学过程,模拟结果呈现出了多个DO平台,这与实际反应结果数据相符,验证了所建模型的正确性。优化实验设计,获取了典型SBR恒曝气好氧硝化过程动态DO数据,通过理论分析和对数据进行二阶微分处理提出了确定总氧传递系数K_La和相对饱和溶解氧S_O^eq的简单方法,为后续参数估计奠定了基础。     

Influence of model parameter estimation methods and regression algorithms on curing kinetics and rheological modelling

The accuracy of the phenomenological curing and rheological models are strongly related to the estimated start parameters and selected regression algorithms. Considering the versatile methods for model start parameter estimation (model‐free vs. model‐fitting, dynamic vs. isothermal) and regression analysis algorithm (linear vs. nonlinear, single‐target vs. multi‐target), this paper investigates the theoretical basis and influence of these aspects on the model development process and model quality. The curing kinetics is modelled by model‐free and model‐fitting start parameters and different regression algorithms, followed by cross model validation at the final. The results showed that the different parameter estimation methods and evaluation algorithms have a remarkable influence on the final model parameters and its quality. The study shows the correlation between the different aspects and provides a basis for better selection of model parameter evaluation methods and regression algorithms for model development with improved quality and accuracy. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45137.     

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.     

过程系统变负荷下的数据校正与参数估计方法

过程系统的数据校正与参数估计是进行实时操作优化与过程控制的基础。过程系统变负荷下由于模型参数变化的非线性及显著误差的影响,导致数据校正与参数估计的结果不准确,从而影响实时操作优化与过程控制的效率。针对此问题,本文提出了一种用于变负荷下的数据校正与参数估计方法。此方法主要包括过程的稳态检测与数据采样,多工况下的数据聚类和基于多组测量的数据校正与参数估计。首先选择有效和可靠的过程测量数据,根据变负荷下工况的波动性与系统的非线性特征进行数据聚类,最后基于聚类结果调整模型参数使得模型输出与过程测量数据偏差最小。此方法可有效地减小模型参数变化的非线性及显著误差对数据校正与参数估计结果的影响。基于现场的测量数据,将此方法应用于空气分离流程系统中,结果显示了基于此方法的数据校正与参数估计结果更准确。     

Unstationary Film Model for the Determination of Absolute Gas-Liquid Kinetic Rate Constants: Ozonation of Acid Red 27, Acid Orange 7, and Acid Blue 129

A method for the determination of absolute kinetic rate constants is proposed using an unstationary film model. This methodology avoids the experimental determination of parameters like the enhancement factor or the Hatta number which are usually model-dependent. The mathematical model is general for gas-liquid systems with irreversible second order reactions. An optimization procedure based on artificial neural networks is used to estimate the initial guess of the parameters and the subsequent application of Gauss-Newton algorithm for the final nonlinear parameter estimation. The model is tested with the ozonation reaction of Acid Red 27, Acid Orange 7 and Acid Blue 129. The second-order kinetic rate constants for the direct reaction with O₃ are 1615 ± 93, 609 ± 83, and 49 ± 2 M^?1s^?1, respectively.     

基于有限测量信息的过程系统参数可估计性分析

实时优化与过程对象模型的精确程度有关。如果过程对象模型与实际模型偏差较大,则会引起优化结果与过程实际的最优结果不一致,并导致优化的效率降低。在实时优化中应采用参数估计,调整过程对象模型的参数,从而保证过程对象模型与实际模型相一致或偏差最小。基于系统可估计性定义,本文根据有限测量信息的参数估计问题特点,提出了系统的参数可估计性定义;通过分析线性系统与非线性系统,指出系统具有参数可估计性的充分条件;并分析了如果系统不具有参数可估计性时,则需要固定哪些参数才能使得整个系统具有参数可估计性。最后分析了当测量变量有多组测量时对系统参数可估计性的影响,通过线性与非线性实例验证了分析结果的有效性。     

非线性分布参数系统状态估计的最佳测量位置

研究了分布参数系统状态估计中特有的最佳测量位置问题．建立了基于后集中方法的分布参数系统的非线性状态估计器,包括状态估计偏微分方程和微分灵敏度矩阵偏微分方程,并用适当的数值计算方法实现状态估计器的求解;以一个最小化的空间域上积分函数表达最佳测量位置的目标函数,并相应地用非线性约束优化方法求解系统具有一个或多个测量时的最佳测量位置．还以壁冷式单管固定床反应器为例,讨论了各种因素对最佳测量位置的影响及其灵敏度,并得出了一些有普遍意义的结论．     

Nonlinear parameter estimation through particle swarm optimization

Parameter estimation procedures are very important in the chemical engineering field for development of mathematical models, since design, optimization and advanced control of chemical processes depend on model parameter values obtained from experimental data. Model nonlinearity makes the estimation of parameter and the statistical analysis of parameter estimates more difficult and more challenging. In this work, it is shown that many of these difficulties can be overcome with the use of heuristic optimization methods, such as the particle swarm optimization (PSO) method. Parameter estimation problems are solved here with PSO and it is shown that the PSO method is efficient for both minimization and construction of the confidence region of parameter estimates. Moreover, it is shown that the elliptical approximation of confidence regions of nonlinear model parameters can be very poor sometimes and that more accurate likelihood confidence regions can be constructed with PSO, allowing for more reliable statistical analysis of the significance of parameter estimates.     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.