A systematic framework for design of process monitoring and control (PAT) systems for crystallization processes

A generic computer-aided framework for systematic design of a process monitoring and control system for crystallization processes has been developed to study various aspects of crystallization operations. The systematic design framework contains a generic crystallizer modelling toolbox, a tool for generation of the supersaturation set-point for supersaturation control, as well as a tool for design of a process monitoring and control system (also called Process Analytical Technology (PAT) system). This systematic design allows one to generate the necessary problem-chemical system specific model, the necessary supersaturation set-point as well as a PAT system design including implementation of monitoring tools and control strategies in order to produce the desired target product properties notably crystal size distribution (CSD) and shape for a wide range of crystallization processes. Application of the framework is highlighted through a case study involving the design of a monitoring and control system for a potassium dihydrogen phosphate (KDP) crystallization process, where also the one-dimensional CSD and two-dimensional CSD modelling features are highlighted.     

Product quality improvement of batch crystallizers by a batch-to-batch optimization and nonlinear control approach

Batch crystallization is one of the widely used processes for separation and purification in many chemical industries. Dynamic optimization of such a process has recently shown the improvement of final product quality in term of a crystal size distribution (CSD) by determining an optimal operating policy. However, under the presence of unknown or uncertain model parameters, the desired product quality may not be achieved when the calculated optimal control profile is implemented. In this study, a batch-to-batch optimization strategy is proposed for the estimation of uncertain kinetic parameters in the batch crystallization process, choosing the seeded batch crystallizer of potassium sulfate as a case study. The information of the CSD obtained at the end of batch run is employed in such an optimization-based estimation. The updated kinetic parameters are used to modify an optimal operating temperature policy of a crystallizer for a subsequent operation. This optimal temperature policy is then employed as new reference for a temperature controller which is based on a generic model control algorithm to control the crystallizer in a new batch run.     

A model-based systems approach to pharmaceutical product-process design and analysis

This is a perspective paper highlighting the need for systematic model-based design and analysis in pharmaceutical product-process development. A model-based framework is presented and the role, development and use of models of various types are discussed together with the structure of the models for the product and the process. The need for a systematic modelling framework is highlighted together with modelling issues related to model identification, adaptation and extension. In the area of product design and analysis, predictive models are needed with a wide application range. In the area of process synthesis and design, the use of generic process models from which specific process models can be generated, is highlighted. The use of a multi-scale modelling approach to extend the application range of the property models is highlighted as well. Examples of different types of process models, model analysis and model generation are presented.     

Modular dynamic simulation for integrated particulate processes by means of tool integration

In this contribution a sequential modular strategy for the dynamic simulation of particulate process flowsheets is presented and the efficiency of the approach is demonstrated by means of an example process for the crystallization of pentaerythritol. The flowsheet of the process consists of a number of different unit operations, e.g. evaporator, crystallizer, hydrocyclone, and mixer, which are described by mathematical models of largely varying complexity and structure. A key advantage of the presented sequential modular strategy is that specialized tools can be selected for the modelling and solution of each unit operation in the flowsheet. The tools are then coupled together by means of the tool integration framework CHEOPS in order to capture the overall structure of the flowsheet. In a case study, a startup of a crystallization flowsheet is carried out. As a result, detailed information about the dynamic plantwide process behavior is obtained. The practical relevance of the approach is demonstrated by means of a scenario where potential blocking of the filters following the crystallizer has been analyzed.     

Crystallization and pressure filtration of anhydrous milk fat: Mixing effects

Melt crystallization of anhydrous milk fat and subsequent filtration of the slurry is a common process for obtaining milk fat fractions with different physical and chemical properties. The crystallization mechanism is very complex and little is known about how the crystallizer conditions and the crystal size distribution (CSD) affect the filtration process. The objective of this study was to characterize the fractionation process and determine which geometric parameters of the crystallizer affect the filtration step. Two scales of fractionation were studied, 0.6 L and 3.6 L, with crystallization at 28°C. The slurry was pressure-filtered after 24 h at 500 kPa in a 1-L chamber. Impeller diameters and speeds were varied for both scales. Photomicroscopy and spectrophotometry were used to characterize the crystallization process, and filtration rates were measured by weighing the amount of filtrate passing through the filter. Filtration resistance values, calculated using the constant pressure filtration equation, as well as photomicroscopy results indicated that the agglomerates and crystals that formed had different morphological characteristics for the different mixing and flow regimes in the crystallizer. Crystallization conditions that provide an optimal filtration time, a solid fraction with minimal liquid entrainment, and a CSD with an intermediate range of sizes (80–500 μm) having good packing properties for filtration were found.     

EXTENDED KALMAN FILTER CONTROLLER: FIRST PRINCIPLES MODELS TO NEURAL NETWORKS

Extended Kalman filters (EKF) have been widely employed for state and parameter estimation in chemical engineering systems. Gao et al. [Gao, F., Wang, F. and Li, M. (1999). Ind. Eng. Chem. Res., 38, 2345-2349] have proposed the use of EKF for control computation using a neural network representation of the system in a discrete-time framework. In the present study, an EKF controller is proposed in a continuous time framework with models incorporating different levels of process knowledge. The problem of process-model mismatch is handled by incorporating EKF-based state and/or parameter estimation along with control computation. A batch reactor temperature control problem for a highly exothermic reaction between maleic anhydride and hexanol to form hexyl monoester of maleic acid is considered as a test bed to evaluate the performance of the proposed control schemes. Three different models are considered, namely the first principles model, a reduced-order process model, and an artificial neural network (ANN) model for formulation of the control schemes. The performance of the proposed control scheme using first principles model is compared to that of generic model control, and a similar performance is achieved. The present study illustrates the usefulness of the proposed control schemes and can be easily extended to general chemical engineering systems.     

Computer-aided modelling template: Concept and application

Modelling is an important enabling technology in modern chemical engineering applications. A template-based approach is presented in this work to facilitate the construction and documentation of the models and enable their maintenance for reuse in a wider application range. Based on a model decomposition technique which identifies generic steps and workflow involved, the computer-aided template concept has been developed. This concept is implemented as a software tool, which provides a user-friendly interface for following the workflow steps and guidance through the steps providing additional information and comments on model construction, storage and future use/reuse. The application of the tool is highlighted with a multi-scale modelling case study involving a catalytic membrane fixed bed reactor and a two-phase system for oxidation of unsaturated acid with hydrogen peroxide. Both case studies reflect different aspects of template creation and use with respect to model development.     

A Hybrid Method for Stochastic Performance Modeling and Optimization of Chemical Engineering Processes

As chemical engineers seek to improve plant safety, reliability, and financial performance, a wide range of uncertaintyladen decisions need to be made. It is widely agreed that probabilistic approaches provide a rational framework to quantify such uncertainties and can result in improved decision making and performance when compared with deterministic approaches. This article proposes a novel method for design and performance analysis of chemical engineering processes under uncertainty. The framework combines process simulation tools, response surface techniques, and numerical integration schemes applied in structural reliability problems to determine the probability of a process achieving a performance function of interest. The approach can be used to model processes in the presence or absence of performance function(s), with or without parameter interactions, at both design and operational phases. With this, process behavior can be quantified in terms of stochastic performance measures such as reliability indices and the associated most probable process design/operating conditions, providing a simple way to analyze a wide range of decisions. To validate the applicability of the proposed framework, three case study systems are considered: a plug flow reactor, a heat exchanger, and finally a pump system. In each case, performance criteria based on the original physical model and the surrogate model are set up. Reliability analysis is then carried out based on these two models and the results are assessed. The results show that the proposed framework can be successfully applied in chemical engineering analysis with additional benefits over the traditional deterministic methods.     

Kinetic modelling: Regression and validation stages,a compulsory tandem for kinetic model assessment

The development of robust and reliable kinetic models is vital to build safe, eco-friendly, and cost-competitive chemical processes. Establishing kinetic models for complex chemical systems such as biomass valorization is cumbersome because the kinetic modeller must test different models and fit several experimental observables (or concentrations). Usually, in chemical reaction engineering, kinetic model assessment is based solely on the regression stage outputs. The implementation of a validation stage can aid in choosing the most reliable kinetic models, essentially in the case of complex chemical systems. We studied the solvolysis of 5-hydroxymethylfurfural (5-HMF) to butyl levulinate (BL) as a model reaction constituting several consecutive and parallel reaction steps. From an existing kinetic model, we created 60 synthetic runs in batch conditions. In the first part, we tested four different models with 5 degrees of noise, and we carried out the modelling on the 60 synthetic runs. In the second part, two types of holdout methods were evaluated. In the last part, cross-validation, namely the k-fold method, was used. We found that the 10-fold method allowed more efficient selection results even when the noise level was high. Besides, k-fold allows for not scarifying experimental runs and selecting the most reliable model.     

Reactive crystallization of calcium carbonate by gas-liquid and liquid-liquid reactions

Crystallization of calcium carbonate by gas-liquid and liquid-liquid reactions in a continuous MSMPR crystallizer was conducted over a wide range of suspension densities. The effects of operating factors and reaction mechanism on the cyrstallization kinetics were investigated. The crystallization kinetics for both reaction systems are correlated by the power law model and these correlations depend on the suspension density regions. The kinetic orders in the power law model are correlated with carbonate alkalinity irrespective of the reaction mechanism and the suspension density.     

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.     

Robustness analysis of chemical process systems based on complex network non-linear load capacity model

In the complex network of chemical process systems, if a node fails, it may trigger cascading failures and affect normal operation. To enhance the ability of chemical process systems to maintain normal operation after the cascading failure, this paper presents cascading failure modelling and robustness analysis of chemical process systems based on the complex network non-linear load capacity model. First, based on complex network theory, a complex network model of the chemical process is constructed; then, three cascading failure models are constructed using a combination of linear and non-linear load capacity models and initial load and initial residual capacity redistribution strategies; and finally, the nodes with the maximum node degree are deliberately attacked to analyze the robustness of the chemical process system in response to cascading failure. The case study shows that the proposed models are valid and feasible, and the robustness of the chemical process system is enhanced as the load and capacity parameters are increased. By reasonably setting the initial load and adjusting the model parameters, the robustness can be effectively improved, providing a theoretical reference for improving the robustness of the actual chemical process system in response to cascading failure.     

Predictive control of particlesize distribution of crystallization process using deep learning based image analysis

The challenges to regulate the particle-size distribution (PSD) stem from on-line measurement of the full distribution and the distributed nature of crystallization process. In this article, a novel nonlinear model predictive control method of PSD for crystallization process is proposed. Radial basis function neural network is adopted to approximate the PSD such that the population balance model with distributed nature can be transformed into the ordinary differential equation (ODE) models. Data driven nonlinear prediction model of the crystallization process is then constructed from the input and output data and further be used in the proposed nonlinear model predictive control algorithm. A deep learning based image analysis technology is developed for online measurement of the PSD. The proposed PSD control method is experimentally implemented on a jacketed batch crystallizer. The results of crystallization experiments demonstrate the effectiveness of the proposed control method.     

Mathematical Model of the Dissolution Stage in Cooling Batch Crystallization

Abstract

Experiments were performed in a cooling batch crystallizer to develop a phenomenological model that represents the dissolution stage in crystallization. Two models were used: a theoretical and a black box, comparing their results with the experimental ones through the simulation of these models (use the mean and the standard deviation of crystal size like comparative means). The theoretical model was obtained by population's balance, mass and energy balances, and constitutive relations (decrease speed and production‐reduction speed). The black box model consisted of a set of equations, which are functions of the mean, standard deviation, agitation speed and time.     

Handling sensor malfunctions in control of particulate processes

This work focuses on feedback control of particulate processes in the presence of sensor data losses. Two typical particulate process examples, a continuous crystallizer and a batch protein crystallizer, modeled by population balance models (PBMs), are considered. In the case of the continuous crystallizer, a Lyapunov-based nonlinear output feedback controller is first designed on the basis of an approximate moment model and is shown to stabilize an open-loop unstable steady-state of the PBM in the presence of input constraints. Then, the problem of modeling sensor data losses is investigated and the robustness of the nonlinear controller with respect to data losses is extensively investigated through simulations. In the case of the batch crystallizer, a predictive controller is first designed to obtain a desired crystal size distribution at the end of the batch while satisfying state and input constraints. Subsequently, we point out how the constraints in the predictive controller can be modified as a means of achieving constraint satisfaction in the closed-loop system in the presence of sensor data losses.     

A state-space model for chemical production scheduling

We express a general mixed-integer programming (MIP) scheduling model in state-space form, and show how common scheduling disruptions, which lead to rescheduling, can be modeled as disturbances in the state-space model. We also discuss how a wide range of scheduling models, with different types of decisions and processing constraints, can be expressed in state-space form. The proposed framework offers a natural representation of dynamic systems, thereby enabling researchers in the chemical process control area to study scheduling problems. It also facilitates the application of known results for hybrid systems, as well as the development of new tools necessary to address scheduling applications. We hope that it will lead to the development of scheduling solution methods with desired closed-loop properties, a topic that has received no attention in the process operations literature.     

Crystallisation of ferrous sulphate heptahydrate: Experiments and modelling

Crystallisation is an industrially important unit operation for purifying and separating chemical mixtures. A generic crystallisation modelling framework has been implemented in the general process modelling system (gPROMS) software (of PSE, UK). This framework can be used to model the batch cooling crystallisation of ferrous sulphate heptahydrate (FSH). The parameter estimation and sensitivity of the predicted results with various numerical parameters was studied for batch crystalliser. An Excel “front‐end” to the gPROMS model was developed to facilitate the interactive use of the model. © 2011 Canadian Society for Chemical Engineering     

AGGLOMERATION, BREAKAGE, POPULATION BALANCE, AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.     

AGGLOMERATION,BREAKAGE, POPULATION BALANCE,AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.