Dynamic model-based batch process monitoring

An integrated framework consisting of a multivariate autoregressive (AR) model and multi-way principal component analysis (MPCA) is described for the monitoring of the performance of a batch process. After pre-processing the data, i.e., batch data unfolding, mean-centring and scaling, the data are then filtered using an AR model to remove the auto- and cross-correlation inherent within the pre-processed batch data. Model order is determined using Akaike information criterion and the model parameters are estimated through the application of partial least squares to attain a stable solution. MPCA is then applied to the residuals from the AR model. Three monitoring statistics are considered for the detection of the onset of process abnormalities in the batch process. The main advantage of the proposed approach is that it can monitor batch dynamics along the mean trajectory without the requirement to estimate future observed values. The proposed AR model-based approach is illustrated through its application to two polymerization processes. The case studies indicate that it gives better monitoring results in terms of sensitivity and time to fault detection than the approaches proposed by Nomikos and MacGregor [1994. Monitoring batch processes using multi-way principal components. A.I.Ch.E. Journal 40(8), 1361-1375] and Wold et al. [1998. Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemometrics and Intelligent Laboratory Systems 44, 331-340].     

Evaluation of optimisation techniques and control variable formulations for a batch cooling crystallization process

The mathematical optimisation of a batch cooling crystallization process is considered in this work. The objective is to minimize the standard deviation of the final crystal size distribution (CSD), which is an important feature in many industrial processes. The results with the problem written as a nonlinear programming and solved with the successive quadratic programming (SQP) coupled with the discretization of the control variable are compared with those obtained when SQP coupled with the parameterisation of the control variable is applied. Also it is proposed the implementation of the genetic algorithm (GA) coupled with parameterisation of the control variable. Extensive evaluations show that the SQP method is sensitive both to the parameterisation formulation and to the initial estimate. The solution with GA provided the control variable profile that leads to the minimum standard deviation of the final CSD. Nevertheless, it is a very time-consuming technique, which hampers its utilization in real time applications. However, its feature of global searching suggests its suitability in solving offline problems, in order to provide initial setup profiles. Bearing this in mind, it is proposed an algorithm which allows for the implementation of GA solution in a real time fashion, taking advantage of its robustness to find out the optimal solution.     

Optimal operation of a batch cooling crystallizer

A theory of programmed cooling crystallization is presented based on the moment transformation of the population balance. Numerical predictions for the behaviour of a batch crystallizer agree closely with those from an alternative theory based on the discrete-supersaturation balance. A potential advantage of the present approach is shown to lie in the application of the Continuous Maximum Principle in optimal control theory to facilitate the numerical computation of optimal cooling curves.The transient behavior of a computed “size-optimal” operating policy which maximises the terminal size of the largest crystals is shown to be significantly different from either natural of linear cooling or from crontrolled cooling at a constant nucleation rate. A peak in the nucleation rate towards the end of the operation and an increased terminal crystal size is predicted for the conditions considered and this is supported by preliminary experimental work with potassium sulphate solutions in a laboratory-scale crystallizer.     

Dynamic modeling of a batch crystallization process: A stochastic approach for agglomeration and attrition process

This paper deals with the dynamic modeling of a batch crystallizer. A complete model taking into account primary and secondary nucleations, crystal growth, agglomeration and attrition mechanisms is established. The proposed model is not restricted to binary agglomeration and breakage phenomena. From markovian considerations, continuous kernel functions are built and the basic balance equations are then presented. The complete model is solved using a finite difference method for the discretization of the size variable. As to distinguish agglomeration and breakage parameters from the others, on line measurement of the Crystal Size Distribution is necessary, a new on line measurement strategy is proposed. Finally, simulations of the crystal size distribution are compared with experimental results at different times. It appears that simulated curves are in good agreement with the experimental data.     

Optimization of batch cooling crystallization

A novel framework has been proposed for optimizing batch cooling crystallization operation. The optimization strategy is effective for highly non-linear and dynamic mathematical systems such as batch cooling crystallization systems. The proposed framework can implement constrained multivariable optimization without the tendency of being trapped into local optima. Variables that can be optimized simultaneously include the cooling profile, seed size, mass of seeds, batch time, initial and final temperatures. Optimizations have been implemented on both seeded and unseeded processes of the citric acid-water system. The optimized operation leads to improvements that otherwise cannot be attained by using conventional approaches. Optimization results also suggest that seeding can increase the flexibility of the operation.     

Programmed cooling of batch crystallizers

An analysis of the programmed cooling of batch crystallizers, starting with the solution of the momentum equations of the population balance, is presented. Based on a general solution, conditions are discussed leading to limiting equations which had been published earlier. The model described in this paper determines the optimum cooling curve for a batch crystallizer with an arbitrary seeding and nucleation ratio, hence a more detailed analysis of the physical conditions of the process and a better comparison of the theory with experiment are possible. Kinetic data of crystallization can also be obtained from batch experiments.     

On-line optimal control of a seeded batch cooling crystallizer

In this paper, an on-line optimal control methodology is developed for the optimal quality control of a seeded batch cooling crystallizer process. An extended Kalman filter is successfully implemented to predict seven unmeasured state variables based on three measurements in the batch process. A PI controller is used in a feedback control system to implement the optimal path. It is found that the PI controller can ensure tracking of the optimal path. The simulation results show that on-line optimal control strategy leads to a substantial improvement of the end product quality expressed in terms of the mean size and the width of the distribution. The effects of the plant/model mismatch and disturbances are also tested and discussed.     

Application of parametric sensitivity to batch process safety: Theoretical and experimental studies

The generalised thermal parametric sensitivity criterion is applied to the thermal behaviour of the esterification of 2-butanol with propionic anhydride in a batch reactor under isoperibolic conditions. The reaction is catalysed by sulphuric acid, and the study covered the effects of both catalyst concentration and, in the absence of catalyst, jacket temperature. The experimental location of regions of parametric sensitivity agreed well with theoretical predictions. However, the process conditions that meet conventional standards for safe process design fall into the supercritical sensitivity region of the parametric model. This apparently contradictory result is discussed. The usefulness of the parametric sensitivity approach is illustrated by practical examples of scale-up and heat transfer in reactions prone to thermal runaway.     

A study on crystallization kinetics of pentaerythritol in a batch cooling crystallizer

The crystallization kinetics of pentaerythritol (PeE) in aqueous solution in the presence of impurity or not in a batch cooling crystallizer was explored. Also, the solubility and the nucleation and crystal growth kinetics of PeE in aqueous solution were investigated. A second-order dependence of PeE growth rate on supersaturation is observed in pure PeE-water system. The crystal growth rate of PeE-water system in the presence of impurity is proportional to the supersaturation to the 3.5 power. The nucleation and crystal growth behaviors for PeE-water system in a batch cooling crystallizer were grasped according to Mersmann's criteria. The nucleation in this crystallizer was found to act with heterogeneous nucleation. In this system, it suggests that the crystal growth is controlled by a complex mechanism behavior of surface integrated and diffusion limited. Simplified relation was derived for calculation of mean crystal size of product crystals from the batch cooling crystallizer. The obtained relation was verified by a set of experiments.     

一种基于聚类方法的多阶段间歇过程监控方法

针对阶段不等长的多阶段间歇过程,提出了一种基于k-均值聚类方法的阶段分段策略,可以将不等长的阶段准确分类。首先,将间歇过程的三维训练数据按变量方向展开成二维矩阵,再通过k-均值聚类的方法按照相关性将数据聚成多类并运用主元分析（PCA）方法分别对每一类建立模型。在线监控时,通过计算样本与模型之间的相似系数以选择最合适的模型进行在线监控。此方法可以将不同批次在同一采样时刻的过程数据按照相关性分到多个阶段,更符合生产过程中常见的过程数据阶段不等长的情况。最后利用青霉素仿真验证了该方法的有效性。     

Material response of a semicrystalline thermoplastic polymer and composite in relation to process cooling history

A model capable of predicting the process-induced macroscopic in-plane material response of semicrystalline thermoplastic matrices and their composites was developed. Thi sinvestigation focused on the material response of a single layer or ply of neat PEEK matrix and its carbon fiber composite (APC-2) when subjected to various processing histories. Specifically, the response of the material moduli and processing strains as a function of temperature and the degree of crystallinity were studied. The kinetic-viscoelastic response of the matrix was determined from a modified form of the Standard Linear Solid model. A constitutive relation was proposed to quantify resign shrinkage as a function of thermal history, which incorporated crystallization. For a specific process history, the effective composite mechanical properties were determined from micromechanics models. Both neat and composite processing strains were evaluated to show the effect of fibers on the matrix dominated response (90° direction). In addition, comparisons of model moduli predictions with experimental measurements were performed. This study demonstrated that an increase in the degree of crystallinity results in an asymmetric shift of the modulus in the glass transition region to higher temperatures. Also, strains due to crystallization were predicted to be much smaller in comparison to the strains resulting from thermal contraction of the PEEK matrix.     

Optimization and nonlinear control of a batch crystallization process

Crystallization process has been widely used for separation in many chemical industries due to its capability to provide high purity product. To obtain the desired quality of crystal product, an optimal cooling control strategy is studied in the present work. Within the proposed control strategy, a dynamic optimization is first preformed with the objective to obtain the optimal cooling temperature policy of a batch crystallizer, maximizing the total volume of seeded crystals. Two different optimization problems are formulated and solved by using a sequential optimization approach. Owing to the complex and nonlinear behavior of the batch crystallizer, the nonlinear control strategy which is based on a generic model control (GMC) algorithm is implemented to track the resulting optimal temperature profile. The optimization integrated with nonlinear control strategy is demonstrated on a seeded batch crystallizer for the production of potassium sulfate.     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

Application of controlled cooling and seeding in batch crystallization

Some aspects of batch cooling crystallization in the industrial practice are analysed by computer simulations. The results indicate that without appropriate kinetics and very accurate process control, even the qualitative effects of applying controlled cooling and seeding are highly unpredictable. An increase in product size by applying controlled cooling is likely to be successful only rather randomly and the size distribution becomes broader. A linear or weakly non-linear cooling curve usually produces larger crystals than a natural cooling curve, and a better reproducibility than a controlled cooling curve. Seeding increases both size and reproducibility, but is also likely to increase significantly the coefficient of variation of the product distribution. The product weight mean size and coefficient of variation may increase or decrease at increasing amount of seeds, depending on governing kinetics.     

Arsenite removal from groundwater in a batch electrocoagulation process: Optimization through response surface methodology

In this study, influences of seven process variables such as initial pH (pH_i), applied current (i), operating time (t_EC), initial As(III) concentration (C_o), diameter of Fe ball anode (d_p), column height in the electrocoagulation (EC) reactor (h) and airflow rate (Q_air) for removal of As(III) from groundwater by a new air-fed fixed-bed EC reactor were evaluated with a response surface methodology (RSM). The proposed quadratic model fitted very well with the experimental data for the responses. The removal efficiencies and operating costs were determined to be 99% and 0.01 $/m³ at the optimum operating conditions (a pH_i of 8.5, 0.05 A, 4.94 min, d_p of 9.24 mm, h of 7.49 cm, Q_air of 9.98 L/min for 50 µg/L). This study clearly showed that the RSM in the EC process was a very suitable method to optimize the operating conditions at the target value of effluent As(III) concentration (10 µg/L) while keeping the operating cost to minimal and maximize the removal efficiency.     

Development of a batch manager for dynamic scheduling and process management in multiproduct batch processes

A batch manager is developed for the dynamic scheduling and on-line management of process operations. The developed system consists of a process monitoring module and a dynamic scheduling module. When a deviation from the initial schedule is detected in a process monitoring module, dynamic scheduling is performed in the dynamic scheduling module and the initial schedule is adjusted to the proper schedule by using rescheduling algorithms presented in this paper. The adjusted schedule is shown in the process monitoring module. The dynamic scheduler in the batch manager copes with several unexpected process events of batch process operations by adjusting the EST (Earliest Start Time) of equipment, redetermining the batch path and reassigning tasks to equipment. This study focuses on the implementation of a batch manager with on-line dynamic scheduling for batch process management. Examples of fodder production batch processes illustrate the efficiency of the algorithms. This paper was supported by nondirected research fund, Korea Research Foundation, 1997.     

Dynamic fracture behavior of piezoelectric ceramics under impact: Force-electric response and electrical breakdown

The brittle fracture may occur in the application of piezoelectric ceramics, but the traditional research is still limited to the static fracture of the materials. Based on the improved Hopkinson pressure bar loading system and high-speed photography technology, the experimental study on the fracture behavior of piezoelectric ceramics under impact loading was carried out. The dynamic mechanical and electrical response of lead zirconate titanate (PZT) and the possible electric breakdown phenomenon were analyzed. The experimental results show that the output voltage is stable and the maximum output voltage is 889 V when the impact load does not cause the material to fracture. When the material breaks, its macroscopic output voltage fluctuates due to electric breakdown. Combined with the finite element simulation of the impact fracture process, the distribution characteristics of the stress field and electric field near the crack during the fracture process were analyzed. The results show that the sliding between grains formed the crack cavity parallel to the electric field during the impact process. Furthermore, based on the theory of dielectric breakdown, the possibility of electric breakdown in the initial defect and the elliptical cavity formed by the impact is analyzed.     

Impeller geometry effect on crystallization kinetics of borax decahydrate in a batch cooling crystallizer

The effects of impeller type and diameter in a batch cooling crystallizer on the nucleation and crystal growth kinetics as well as on the shape and size distribution of borax decahydrate crystals were investigated. Two different types of impellers of various sizes were applied. Chosen impeller configurations generate completely different fluid flow patterns in the crystallizer what allows to investigate the influence of the axial and radial flow on the kinetic parameters as well. The nucleation in crystallizer was taking place by the heterogeneous nucleation mechanism at all mixing conditions. The number of crystals formed by this mechanism increases as ratio D/d_T decreases and it is higher when an axial flow pattern in crystallizer has been developed. The crystal growth rate increases with increasing the impeller size in observed supersaturation range. The radial impeller defined by ratio D₂/d_T = 0.58 could be considered as viable option for growth of borax crystal, since the further enlargement of this ratio does not increase growth rate and can only cause higher power consumption. The maxima in the coarser and finer fractions of CSD indicate a different influence of mixing conditions on the crystal grow and secondary nucleation. An axial flow pattern in crystallizer favors agglomeration of growing crystals increasing that way product mean crystal size, while radial flow results with more regular shape of borax crystals.