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Special Issue: model-based experimental analysis
Chemical Engineering Science 63 (2008) 4637 -- 4639
Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / c e s
Editorial
Special Issue: model-based experimental analysis From Experimental Data to Mechanistic Models of Kinetic Phenomena in Reactive Systems Kinetic phenomena drive the macroscopic behaviour of process systems. Most notably, the kinetics of chemical reactions plays a decisive role in the manufacturing of bulk and specialty chemicals, pharmaceuticals or advanced materials. In single-phase systems, macro- and micro-mixing interferes with chemical conversion if the timescales of transport and reaction overlap. The correlation between chemical kinetics and transport phenomena is even more pronounced in multi-phase reactive systems because the location and extent of reaction depends on the kinetics of transport and reaction close to the interface. Interfacial area and morphology determine the kinetics of heat and mass transfer across the interface and hence the selectivity and conversion in a multi-phase reaction system. The situation is getting even more complicated if complex fluids comprising small and large molecules (such as proteins, oligomers or polymers) have to be considered. Then, reaction and transport kinetics strongly depend on the details of the molecular structure. Kinetic modelling of reactive process systems is still a challenge despite the progress we have seen in the last two decades. There is still no systematic means to derive and validate models, which capture the underlying physico-chemical mechanisms of an observed behaviour in particular if a number of phenomena are interacting as it is the case in multi-phase reactive systems. Any successful kinetic modelling strategy requires • a carefully designed experiment equipped with appropriate measurement techniques, • modelling and simulation on multiple scales including the integration between adjacent scales, • the formulation and solution of inverse problems to fit a model to the data, • methods for selecting the most suitable model structure from a set of possible candidates, and • model-based methods for the determination of experimental conditions which result in high information content for the type of identification problem considered. Experimentation should directly address interacting kinetic phenomena. Since interaction cannot be avoided completely, often largely unquantifiable levels of error result. Measurement techniques have to be developed to provide information on the major state variables in an experiment—ideally at high resolution rather than at a few points in time or spatial location. Consequently, large amounts of data have to be processed during model identification. Modelling has to address kinetic phenomena on multiple scales. Inevitably, modelling
0009-2509/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/S0009-2509(08)00459-4
will move from differential–algebraic equation systems and relatively few parameters to partial differential–algebraic models and many parameters to properly capture the kinetic mechanisms on a high level of resolution. The resulting inverse problems are becoming much more demanding for these types of equations. Intelligent problem formulations and adaptive solution algorithms are a key to successfully solve such estimation problems. The generation of candidate model structures and the subsequent selection of the best model structure for a given purpose is a key to the discovery of mechanistic models. Besides further developments within each of these individual areas, a systematic work process supported by computational tools to guide the modelling team in applying and efficiently combining the various techniques would be highly desirable. These problems have been at the heart of the collaborative research centre CRC 540, “Model-based experimental analysis of multiphase reaction systems”, which has been funded by the German Science Foundation DFG (Deutsche Forschungsgemeinschaft) since 1999. The centre has been formed by 13 research groups from various disciplinary fields including numerical mathematics, scientific computing, macromolecular chemistry, technical chemistry, laser technology, biochemical reaction engineering, thermal unit operations, multi-phase flow, engineering thermodynamics, heat and mass transfer and process systems engineering. The application-oriented research objectives have been focussing on the identification of mechanistic models for kinetic phenomena in reactive process systems largely on the meso-scale. Research projects have been targeting multi-component diffusion in liquid systems, rheology and dynamics of liquid–liquid and liquid–gas interfaces as well as liquid-phase chemical reactions which constitute important kinetic phenomena in multi-phase reactive systems. A falling film, a single levitated drop immersed in a continuous liquid, a hydrogel particle with immobilized enzymes immersed in a liquid and both, single-phase and segregated two-phase liquid stirred tank reactors have been used as model systems to roughly cover the enormous variety of configurations in industrial processes. Besides these application-oriented research topics, methods, technologies and tools in high resolution, in-situ measurements with an emphasis on field data, in multi-scale modelling and simulation as well as in the formulation and solution of inverse problems are further developed to address the particular needs of the selected application problems. Rather than merely developing novel or improved techniques in each of these three areas, the methodological focus of CRC 540 has been on the development and the assessment of an integrated and systematic work process which
4638
W. Marquardt / Chemical Engineering Science 63 (2008) 4637 -- 4639
experimental conditions
measurements model structure,
experimental design
experiment
inputs, parameters, initial conditions
measurement techniques
numerical simulation
formulation and solution parameters, of inverse problems sensor calibration
model selection inputs, states,
confidence regions
computed states and measurements
mathematical models
a-priori knowledge and intuition
extended understanding
Fig. 1. Model-based experimental analysis—a rough work flow.
tightly links experimentation, modelling and simulation as well as model identification from a systems engineering perspective. Such an integrated work process is different from nowadays practice in research and industrial application. Rather than analyzing coupled kinetic phenomena by detailed models in simulation studies and comparing the predictions obtained with experimental data, the research approach of CRC 540 aims at the balanced development of the mathematical model and the refinement of the experimental conditions. Model refinement should only be pursued if supported by experimental evidence. Detailing the model beyond the constraints of experimental observations should be avoided because validation is impossible in principle. Unavoidable measurement error has to be systematically considered in model fitting and validation to assess the predictive quality of the model. Model structure identification and model-based optimal experimental design are considered crucial for the success of mechanistic modelling. The systematic work process towards mechanistic models of kinetic phenomena in reactive systems is called model-based experimental analysis. In the tradition of process systems engineering, the model identification problem is addressed by model-based techniques as sketched in Fig. 1. Any a-priori knowledge on the experiment to be conducted can be cast into a first, typically very crude mathematical model of the experiment. Virtual experiments by means of numerical simulations with this model shed light into its characteristics and help to improve the experimental set-up and the choice of informative measurement techniques. Based on this additional insight, the experiment together with the measurement devices is designed and built in the laboratory. Though the experiments provide information on the kinetic phenomena of interest, they rarely have access to the physical quantities of interest. Model-based techniques are necessary to identify the causes of the observed effects. These inverse problems come in a variety of flavours ranging from simple measurement calibration to state, parameter and input estimation or even to model selection including structure identification and discrimination. The models can also be used in experimental design to decide on the design or operational degrees of freedom of an experiment to obtain the best possible information at minimum experimental effort to successfully solve the modelling task at hand.
More information on the research approach and the research projects can be found on the home page of CRC 540 at http://www. sfb540.rwth-aachen.de/ as well as in two survey papers (Marquardt, 2005; Bardow and Marquardt, 2008). This special issue includes a selection of papers relevant to the research topics of CRC 540. The papers are of different origin. They have been either presented during international workshops of CRC 540 or they have been submitted for publication in reaction to the call for this special issue. The papers can be largely grouped into three different areas, including high-resolution measurement techniques, modelling and simulation on multiple scales and methods and tools for the formulation and solution of inverse problems. The first four papers deal with different types of high-resolution measurements which allow to access field information rather than point information of selected quantities. Information-rich measurements are mandatory for model identification and for the discrimination of competing model structures. Rather than providing qualitative information, mechanistic modelling is only possible if quantitative measurement data and estimates of unavoidable measurement errors are available. Such quantification often calls for a model of the measurement device itself to relate the primary measurement data to the physical state variables of interest. The first two papers present experimental techniques for high-resolution monitoring of two-phase flows. While the paper of Gladden and co-workers shows the merits of three-dimensional MRI in comparison to classical pressure drop and conductance measurements to study the transition between flow regimes in trickle beds, Faes and Glasmacher study the mixing of two liquids with high spatial resolution by means of laser-induced fluorescence. The following paper by Kempkes, Eggers and Mazzotti presents an experimental study of the particle size distribution by means of a combination of focused beam reflectance measurements and in-situ microscopy. A model of the measurement device is presented to successfully convert chord length into particles size distributions. Scharfer, Schabel and Kind present a diffusion model to correlate the data obtained from confocal Raman microscopy concentration measurements during mass transport in a polymer membrane.
W. Marquardt / Chemical Engineering Science 63 (2008) 4637 -- 4639
A set of modelling papers is started off by Kerkhof and his coauthors who study their new theory of multicomponent molecular mass transport in a Stefan tube in simulation employing a mixture of water-vapor and nitrogen. Papadopoulos et al. present a twodimensional model of an intradiffusion NMR experiment to study the interplay between magnetic field distortion and diffusion in order to prepare for a future quantitative interpretation of diffusive transport observed by NMR imaging. Meza and Balakotaiah present an excellent review on modelling and simulation of falling film flows together with validating experiments. A multi-scale modelling case study of the particle segregation in a complex polyolefines reactor is presented by Kiparissidis and co-workers showing the necessity to consider a large number of kinetic phenomena on a variety of scales to properly explain the macroscopic observed behaviour of the reactor. The following 11 papers deal with various methodological aspects of inverse problems. The first two papers of Davidescu and Jorgensen and of Bardow et al. address model identifiability. While Davidescu and Jorgensen study structural identifiability of biochemical reaction kinetics by means of a generating series expansion method, Bardow et al. present an enlightening study of local identifiability of the parameters in the established k– turbulence model in a channel flow experiment using classical sensitivity analysis. The following three papers address concrete examples for estimating parameters of reaction kinetic models in complex situations. Heidebrecht et al. present a novel identification method for gasphase reaction kinetics employing temperature programmed reduction and illustrate it exemplarily with measurements of iron oxide in a hydrogen gas. Drews and Arellano-Garcia present a case study in reaction kinetic modelling of high cell density fermentations where the model parameters have to be switched at a certain cell density to obtain a reasonable model fit. Puxty and a team of co-authors from different laboratories around the world demonstrate the merits of multivariate hard modelling of spectroscopic data to obtain reliable reaction kinetic models. Two chemical systems and different experimental set-ups are used to derive general conclusions. Hulhoven, Vandewouwer and Bogaerts present a novel approach to the identification of (bio-)reaction kinetic models which combines asymptotic observers for model-free estimation of reaction rates and a movinghorizon estimator for joint state and parameter estimation. Novel parameter estimation algorithms are presented in two papers by Lo, Haslam and Adjiman and by Zavala, Laird and Biegler. The first of the two papers introduces and assesses algorithms for parameter estimation in stochastic differential equations with application to a polymer rheology model. The second paper presents a powerful numerical algorithm based on the interior-point method to
4639
efficiently and robustly solve parameter estimation problems in an error-in-variables setting. The last group of papers addresses various issues of model-based design of experiments. Franceschini and Machietto present a comprehensive, excellent review of the state of the art of model-based methods for experimental design for parameter precision which will be very useful to all those researchers who want to either make use of these methods or to improve on them. Heine, Kawohl and King present a novel method for the derivative-free computation of the information content in an optimal experimental design which is based on the Unscented Transformation and yields the same results as the Fisher Information Matrix for models linear in the parameters. Finally, Bertakis, Kalem and Pfennig show the benefit of optimal experimental design of a Nitsch cell to study reactive extraction kinetics in two-phase liquid systems. A tremendous gain in information content is possible with the model-based design compared to heuristic designs taken from literature. The papers of this special issue show the full breadth of research in model-based experimental analysis and its application to the mechanistic modelling of reactive systems. An educated application of existing statistical and systems engineering methods to assist the model building process not only reduces the experimental effort tremendously but result in models of much higher quality and versatility. Though most of the papers deal with lumped parameter systems, the most challenging problems in future research are related to distributed parameter systems. In the field of reaction engineering these are often multi-phase transport problems with chemical reaction. High-resolution measurement techniques, modelling and simulation methods for the solution of the direct (or forward) problem as well as methods for the solution of inverse problems for parameter or model structure identification and optimal experimental design constitute great challenges and rewarding research areas which can only be solved by interdisciplinary research approaches such as the one pursued in CRC 540. References Marquardt, W., 2005. Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems. Transactions of the IChemE 83 (A6), 561–573. Bardow, A., Marquardt, W., 2008. Incremental identification methods for reaction and transport kinetics. In: Floudas, C.A., Pardalos, P.M. (Eds.), Encyclopedia of Optimization, second ed., Springer, New York, In press.
Wolfgang Marquardt AVT—Process Systems Engineering RWTH Aachen University 52056 Aachen, Germany
Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / c e s
Editorial
Special Issue: model-based experimental analysis From Experimental Data to Mechanistic Models of Kinetic Phenomena in Reactive Systems Kinetic phenomena drive the macroscopic behaviour of process systems. Most notably, the kinetics of chemical reactions plays a decisive role in the manufacturing of bulk and specialty chemicals, pharmaceuticals or advanced materials. In single-phase systems, macro- and micro-mixing interferes with chemical conversion if the timescales of transport and reaction overlap. The correlation between chemical kinetics and transport phenomena is even more pronounced in multi-phase reactive systems because the location and extent of reaction depends on the kinetics of transport and reaction close to the interface. Interfacial area and morphology determine the kinetics of heat and mass transfer across the interface and hence the selectivity and conversion in a multi-phase reaction system. The situation is getting even more complicated if complex fluids comprising small and large molecules (such as proteins, oligomers or polymers) have to be considered. Then, reaction and transport kinetics strongly depend on the details of the molecular structure. Kinetic modelling of reactive process systems is still a challenge despite the progress we have seen in the last two decades. There is still no systematic means to derive and validate models, which capture the underlying physico-chemical mechanisms of an observed behaviour in particular if a number of phenomena are interacting as it is the case in multi-phase reactive systems. Any successful kinetic modelling strategy requires • a carefully designed experiment equipped with appropriate measurement techniques, • modelling and simulation on multiple scales including the integration between adjacent scales, • the formulation and solution of inverse problems to fit a model to the data, • methods for selecting the most suitable model structure from a set of possible candidates, and • model-based methods for the determination of experimental conditions which result in high information content for the type of identification problem considered. Experimentation should directly address interacting kinetic phenomena. Since interaction cannot be avoided completely, often largely unquantifiable levels of error result. Measurement techniques have to be developed to provide information on the major state variables in an experiment—ideally at high resolution rather than at a few points in time or spatial location. Consequently, large amounts of data have to be processed during model identification. Modelling has to address kinetic phenomena on multiple scales. Inevitably, modelling
0009-2509/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/S0009-2509(08)00459-4
will move from differential–algebraic equation systems and relatively few parameters to partial differential–algebraic models and many parameters to properly capture the kinetic mechanisms on a high level of resolution. The resulting inverse problems are becoming much more demanding for these types of equations. Intelligent problem formulations and adaptive solution algorithms are a key to successfully solve such estimation problems. The generation of candidate model structures and the subsequent selection of the best model structure for a given purpose is a key to the discovery of mechanistic models. Besides further developments within each of these individual areas, a systematic work process supported by computational tools to guide the modelling team in applying and efficiently combining the various techniques would be highly desirable. These problems have been at the heart of the collaborative research centre CRC 540, “Model-based experimental analysis of multiphase reaction systems”, which has been funded by the German Science Foundation DFG (Deutsche Forschungsgemeinschaft) since 1999. The centre has been formed by 13 research groups from various disciplinary fields including numerical mathematics, scientific computing, macromolecular chemistry, technical chemistry, laser technology, biochemical reaction engineering, thermal unit operations, multi-phase flow, engineering thermodynamics, heat and mass transfer and process systems engineering. The application-oriented research objectives have been focussing on the identification of mechanistic models for kinetic phenomena in reactive process systems largely on the meso-scale. Research projects have been targeting multi-component diffusion in liquid systems, rheology and dynamics of liquid–liquid and liquid–gas interfaces as well as liquid-phase chemical reactions which constitute important kinetic phenomena in multi-phase reactive systems. A falling film, a single levitated drop immersed in a continuous liquid, a hydrogel particle with immobilized enzymes immersed in a liquid and both, single-phase and segregated two-phase liquid stirred tank reactors have been used as model systems to roughly cover the enormous variety of configurations in industrial processes. Besides these application-oriented research topics, methods, technologies and tools in high resolution, in-situ measurements with an emphasis on field data, in multi-scale modelling and simulation as well as in the formulation and solution of inverse problems are further developed to address the particular needs of the selected application problems. Rather than merely developing novel or improved techniques in each of these three areas, the methodological focus of CRC 540 has been on the development and the assessment of an integrated and systematic work process which
4638
W. Marquardt / Chemical Engineering Science 63 (2008) 4637 -- 4639
experimental conditions
measurements model structure,
experimental design
experiment
inputs, parameters, initial conditions
measurement techniques
numerical simulation
formulation and solution parameters, of inverse problems sensor calibration
model selection inputs, states,
confidence regions
computed states and measurements
mathematical models
a-priori knowledge and intuition
extended understanding
Fig. 1. Model-based experimental analysis—a rough work flow.
tightly links experimentation, modelling and simulation as well as model identification from a systems engineering perspective. Such an integrated work process is different from nowadays practice in research and industrial application. Rather than analyzing coupled kinetic phenomena by detailed models in simulation studies and comparing the predictions obtained with experimental data, the research approach of CRC 540 aims at the balanced development of the mathematical model and the refinement of the experimental conditions. Model refinement should only be pursued if supported by experimental evidence. Detailing the model beyond the constraints of experimental observations should be avoided because validation is impossible in principle. Unavoidable measurement error has to be systematically considered in model fitting and validation to assess the predictive quality of the model. Model structure identification and model-based optimal experimental design are considered crucial for the success of mechanistic modelling. The systematic work process towards mechanistic models of kinetic phenomena in reactive systems is called model-based experimental analysis. In the tradition of process systems engineering, the model identification problem is addressed by model-based techniques as sketched in Fig. 1. Any a-priori knowledge on the experiment to be conducted can be cast into a first, typically very crude mathematical model of the experiment. Virtual experiments by means of numerical simulations with this model shed light into its characteristics and help to improve the experimental set-up and the choice of informative measurement techniques. Based on this additional insight, the experiment together with the measurement devices is designed and built in the laboratory. Though the experiments provide information on the kinetic phenomena of interest, they rarely have access to the physical quantities of interest. Model-based techniques are necessary to identify the causes of the observed effects. These inverse problems come in a variety of flavours ranging from simple measurement calibration to state, parameter and input estimation or even to model selection including structure identification and discrimination. The models can also be used in experimental design to decide on the design or operational degrees of freedom of an experiment to obtain the best possible information at minimum experimental effort to successfully solve the modelling task at hand.
More information on the research approach and the research projects can be found on the home page of CRC 540 at http://www. sfb540.rwth-aachen.de/ as well as in two survey papers (Marquardt, 2005; Bardow and Marquardt, 2008). This special issue includes a selection of papers relevant to the research topics of CRC 540. The papers are of different origin. They have been either presented during international workshops of CRC 540 or they have been submitted for publication in reaction to the call for this special issue. The papers can be largely grouped into three different areas, including high-resolution measurement techniques, modelling and simulation on multiple scales and methods and tools for the formulation and solution of inverse problems. The first four papers deal with different types of high-resolution measurements which allow to access field information rather than point information of selected quantities. Information-rich measurements are mandatory for model identification and for the discrimination of competing model structures. Rather than providing qualitative information, mechanistic modelling is only possible if quantitative measurement data and estimates of unavoidable measurement errors are available. Such quantification often calls for a model of the measurement device itself to relate the primary measurement data to the physical state variables of interest. The first two papers present experimental techniques for high-resolution monitoring of two-phase flows. While the paper of Gladden and co-workers shows the merits of three-dimensional MRI in comparison to classical pressure drop and conductance measurements to study the transition between flow regimes in trickle beds, Faes and Glasmacher study the mixing of two liquids with high spatial resolution by means of laser-induced fluorescence. The following paper by Kempkes, Eggers and Mazzotti presents an experimental study of the particle size distribution by means of a combination of focused beam reflectance measurements and in-situ microscopy. A model of the measurement device is presented to successfully convert chord length into particles size distributions. Scharfer, Schabel and Kind present a diffusion model to correlate the data obtained from confocal Raman microscopy concentration measurements during mass transport in a polymer membrane.
W. Marquardt / Chemical Engineering Science 63 (2008) 4637 -- 4639
A set of modelling papers is started off by Kerkhof and his coauthors who study their new theory of multicomponent molecular mass transport in a Stefan tube in simulation employing a mixture of water-vapor and nitrogen. Papadopoulos et al. present a twodimensional model of an intradiffusion NMR experiment to study the interplay between magnetic field distortion and diffusion in order to prepare for a future quantitative interpretation of diffusive transport observed by NMR imaging. Meza and Balakotaiah present an excellent review on modelling and simulation of falling film flows together with validating experiments. A multi-scale modelling case study of the particle segregation in a complex polyolefines reactor is presented by Kiparissidis and co-workers showing the necessity to consider a large number of kinetic phenomena on a variety of scales to properly explain the macroscopic observed behaviour of the reactor. The following 11 papers deal with various methodological aspects of inverse problems. The first two papers of Davidescu and Jorgensen and of Bardow et al. address model identifiability. While Davidescu and Jorgensen study structural identifiability of biochemical reaction kinetics by means of a generating series expansion method, Bardow et al. present an enlightening study of local identifiability of the parameters in the established k– turbulence model in a channel flow experiment using classical sensitivity analysis. The following three papers address concrete examples for estimating parameters of reaction kinetic models in complex situations. Heidebrecht et al. present a novel identification method for gasphase reaction kinetics employing temperature programmed reduction and illustrate it exemplarily with measurements of iron oxide in a hydrogen gas. Drews and Arellano-Garcia present a case study in reaction kinetic modelling of high cell density fermentations where the model parameters have to be switched at a certain cell density to obtain a reasonable model fit. Puxty and a team of co-authors from different laboratories around the world demonstrate the merits of multivariate hard modelling of spectroscopic data to obtain reliable reaction kinetic models. Two chemical systems and different experimental set-ups are used to derive general conclusions. Hulhoven, Vandewouwer and Bogaerts present a novel approach to the identification of (bio-)reaction kinetic models which combines asymptotic observers for model-free estimation of reaction rates and a movinghorizon estimator for joint state and parameter estimation. Novel parameter estimation algorithms are presented in two papers by Lo, Haslam and Adjiman and by Zavala, Laird and Biegler. The first of the two papers introduces and assesses algorithms for parameter estimation in stochastic differential equations with application to a polymer rheology model. The second paper presents a powerful numerical algorithm based on the interior-point method to
4639
efficiently and robustly solve parameter estimation problems in an error-in-variables setting. The last group of papers addresses various issues of model-based design of experiments. Franceschini and Machietto present a comprehensive, excellent review of the state of the art of model-based methods for experimental design for parameter precision which will be very useful to all those researchers who want to either make use of these methods or to improve on them. Heine, Kawohl and King present a novel method for the derivative-free computation of the information content in an optimal experimental design which is based on the Unscented Transformation and yields the same results as the Fisher Information Matrix for models linear in the parameters. Finally, Bertakis, Kalem and Pfennig show the benefit of optimal experimental design of a Nitsch cell to study reactive extraction kinetics in two-phase liquid systems. A tremendous gain in information content is possible with the model-based design compared to heuristic designs taken from literature. The papers of this special issue show the full breadth of research in model-based experimental analysis and its application to the mechanistic modelling of reactive systems. An educated application of existing statistical and systems engineering methods to assist the model building process not only reduces the experimental effort tremendously but result in models of much higher quality and versatility. Though most of the papers deal with lumped parameter systems, the most challenging problems in future research are related to distributed parameter systems. In the field of reaction engineering these are often multi-phase transport problems with chemical reaction. High-resolution measurement techniques, modelling and simulation methods for the solution of the direct (or forward) problem as well as methods for the solution of inverse problems for parameter or model structure identification and optimal experimental design constitute great challenges and rewarding research areas which can only be solved by interdisciplinary research approaches such as the one pursued in CRC 540. References Marquardt, W., 2005. Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems. Transactions of the IChemE 83 (A6), 561–573. Bardow, A., Marquardt, W., 2008. Incremental identification methods for reaction and transport kinetics. In: Floudas, C.A., Pardalos, P.M. (Eds.), Encyclopedia of Optimization, second ed., Springer, New York, In press.
Wolfgang Marquardt AVT—Process Systems Engineering RWTH Aachen University 52056 Aachen, Germany