Emulsion copolymerization of styrene and butyl acrylate in the presence of a chain transfer agent. Part 2: parameters estimability and confidence regions

Accurate estimation of the model parameters is required to obtain reliable predictions of the products end-use properties. However, due to the mathematical model structure and/or to a possible lack of measurements, the estimation of some parameters may be impossible. This paper will focus on the case where the main limitations to the parameters estimability are their weak effect on the measured outputs or the correlation between the effects of two or more parameters. The objective of the method developed in this paper is to determine the subset of the most influencing parameters that can be estimated from the available experimental data, when the complete set of model parameters cannot be estimated. This approach has been applied to the mathematical model of the emulsion copolymerization of styrene and butyl acrylate, in the presence of n-dodecyl mercaptan as a chain transfer agent. In addition, a new approach is used to better assess the true confidence regions and evaluate the accuracy of the parameters estimates in more reliable way

A geometric observer-assisted approach to tailor state estimation in a bioreactor for ethanol production

In this work, a systematic approach based on the geometric observer is proposed to design a model-based soft sensor, which allows the estimation of quality indexes in a bioreactor. The study is focused on the structure design problem where the set of innovated states has to be chosen. On the basis of robust exponential estimability arguments, it is found that it is possible to distinguish all the unmeasured states if temperature and dissolved oxygen concentration measurements are combined with substrate concentrations. The proposed estimator structure is then validated through numerical simulation considering two different measurement processor algorithms: the geometric observer and the extended Kalman filter

Modelling of biological systems using multidimensional population balances

Biological systems are intrinsically heterogeneous and, consequently, their mathematical descriptions should account for this heterogeneity as it often influences the dynamic behaviour of the individual cells. For example, in the cell cycle dependent production ofproteins, it is necessary to account for the distribution of the individual cells with respect to their position in the cell cycle as this has a strong influence on protein production. A second notable example is the formation of cancerous cells. In this case, the failure of regulatory mechanisms results in the transition of somatic cells to their cancerous state. Therefore, in developing the corresponding mathematical model, it is necessary to consider both the different states of the cells as well as their regulation. In this regard, the population balance equation is the ideal mathematical framework to capture cell population heterogeneity as it elegantly takes into account the distribution of cell populations with respect to their intracellular state together with the phenomena of cell birth, division, differentiation and recombination. Recent developments in solution algorithms together with the exponential increase in computational abilities now permit the efficient solution of one-dimensional population balance models which attribute the heterogeneity of cell populations to differences in the age or mass of individual cells. The inherent complexity of biological systems implies that the differentiation of cells based on a single characteristic alone may not be sufficient to capture the underlying biological phenomena. Therefore, current research is focussing on the development of multi-dimensional population balances that consider the differentiation of cells based on multiple characteristics, most notably, the state of cells with respect to key intracellular metabolites. However, conventional numerical techniques are inefficient for the solution of the formulated population balance models and this warrants the development of novel, tailor-made algorithms. This thesis presents one such solution algorithm and demonstrates its application to the study of several biological systems. The algorithm developed herein employs a finite-volume technique to convert the partial-differential equation comprising the population balance model into a set of ordinary differential equations. A two-tier technique based on the solution technique for inhomogeneous differential equations is then developed to solve the system of ordinary differential equations. This approach has two main advantages: (a) the decomposition technique considerably reduces the stiffness of the system of equations enabling more efficient solution, and (b) semianalytical solutions for the integrals employed in the modelling of cell division and differentiation can be obtained further reducing computation times. Further improvements in solution efficiency are obtained by the formulation of a two-level discretisation algorithm. In this approach, processes such as cell growth which are more sensitive to the discretisation are solved using a fine grid whereas less sensitive processes such as cell' division - which are usually more computationally expensive - are solved using a coarse grid at a higher level. Thus, further improvements are obtained in the efficiency of the technique. The solution algorithm is applied to various multi-dimensional population balance models of biological systems. The technique is first demonstrated on models of oscillatory dynamics in yeast glycolysis, cell-cycle related oscillations in eukaryotes, and circadian oscillations in crayfish. A model of cell division and proliferation control in eukaryotes is an example of a second class of problems where extracellular phenomena influence the behaviour of cells. As a third case for demonstration, a hybrid model of biopolymer accumulation in bacteria is formulated. In this case, cybernetic modelling principles are used to account for intracellular competitions while the population balance framework takes into consideration the heterogeneity of the cell population. Another important aspect in the formulation ofmulti-dimensional population balances is the development of the intracellular models themselves. While research in the biological sciences is permitting the formulation of detailed dynamic models of various bioprocesses, the accurate estimation of the kinetic parameters in these models can be difficult due to the unavailability of sufficient experimental data. This can result in considerable parametric uncertainty as is demonstrated on a simple cybernetic' model of biopolymer accumulation in bacteria. However, it is shown that, via the use of systems engineering tools, experiments can be designed that permit the accurate estimation of all model parameters even when measurements pertaining to all modelled quantities are unavailable.Imperial Users onl

Optimal control of particle size distribution in semi-batch emulsion polymerisation

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Development of monitoring and control systems for biotechnological processes

The field of biotechnology represents an important research area that has gained increasing success in recent times. Characterized by the involvement of biological organisms in manufacturing processes, its areas of application are broad and include the pharmaceuticals, agri-food, energy, and even waste treatment. The implication of living microorganisms represents the common element in all bioprocesses. Cell cultivations is undoubtedly the key step that requires maintaining environmental conditions in precise and defined ranges, having a significant impact on the process yield and thus on the desired product quality. The apparatus in which this process occurs is the bioreactor. Unfortunately, monitoring and controlling these processes can be a challenging task because of the complexity of the cell growth phenomenon and the limited number of variables can be monitored in real-time. The thesis presented here focuses on the monitoring and control of biotechnological processes, more specifically in the production of bioethanol by fermentation of sugars using yeasts. The study conducted addresses several issues related to the monitoring and control of the bioreactor, in which the fermentation takes place. First, the topic concerning the lack of proper sensors capable of providing online measurements of key variables (biomass, substrate, product) is investigated. For this purpose, nonlinear estimation techniques are analyzed to reconstruct unmeasurable states. In particular, the geometric observer approach is applied to select the best estimation structure and then a comparison with the extended Kalman filter is reported. Both estimators proposed demonstrate good estimation capabilities as input model parameters vary. Guaranteeing the achievement of the desired ethanol composition is the main goal of bioreactor control. To this end, different control strategies, evaluated for three different scenarios, are analzyed. The results show that the MIMO system, together with an estimator for ethanol composition, ensure the compliance with product quality. After analyzing these difficulties through numeric simulations, this research work shifts to testing a specific biotechnological process such as manufacturing bioethanol from brewery’s spent grain (BSG) as renewable waste biomass. Both acid pre-treatment, which is necessary to release sugars, and fermentation are optimized. Results show that a glucose yield of 18.12 per 100 g of dried biomass is obtained when the pre-treatment step is performed under optimized conditions (0.37 M H2SO4, 10% S-L ratio). Regarding the fermentation, T=25°C, pH=4.5, and inoculum volume equal to 12.25% v/v are selected as the best condition, at which an ethanol yield of 82.67% evaluated with respect to theoretical one is obtained. As a final step, the use of Raman spectroscopy combined with chemometric techniques such as Partial Least Square (PLS) analysis is evaluated to develop an online sensor for fermentation process monitoring. The results show that the biomass type involved significantly affects the acquired spectra, making them noisy and difficult to interpret. This represents a nontrivial limitation of the applied methodology, for which more experimental data and more robust statistical techniques could be helpful

Development of a computationally efficient model for the control of Ziegler-Natta catalysed industrial production of high density polyethylene

High density polyethylene is commonly produced by the slurry phase co-polymerisation of ethylene and other alkenes, using heterogeneous titanium-based Ziegler-Natta catalysts. During grade transitions, when reactor conditions are manipulated to change polymer properties, significant quantities of off-specification product result. Implementing a model-predictive controller based on a dynamic reactor model may allow for minimising losses during unsteady-state operation. Such a model must be developed from a fundamental understanding of polymerisation reaction kinetics and the interaction of effects at various scales, including those of catalyst sites, catalyst/polymer particles and reactor hydrodynamics. The model must also be computationally efficient enough for application to real-time control. The recently-developed pseudo-sites model was used as a fundamental kinetic explanation of polymer property distributions and catalyst activity profiles, in contrast to empirical multi-site models. Laboratory polymerisation experiments were performed at industrially-relevant conditions. Kinetic parameters were fitted to the data, using a novel proposed regression procedure to extract meaningful kinetic parameters. A dynamic reactor model was developed, based on the Segregation Approach. Whereas the more common Population Balance Model must consider multivariate distributions of population members within a chosen volume and requires partial differential equation solution, the Segregation Approach can generate the moments of a distribution by evaluating the evolution of properties without requiring solution over the whole volume. The Segregation Approach and PBM were rigorously compared in the context of Particle Size Distributions, and the Segregation Approach shown to be an order of magnitude more computationally efficient. Steady-state industrial data was used to reconcile model predictions for laboratory and industrial polymerisation. This was the first application of the pseudo-sites model to laboratory data, and first extension to industrial scale. Unsteady-state data from three industrial grade transitions was used to validate the reactor model, which closely matched industrial reactor performance. The model simulated 30-40 hours of real time in 15-25 seconds of calculation time. The reactor model was used to propose improved grade transition strategies; transition duration and waste production were improved by 20-40%. The reactor model has been shown to accurately reproduce real-world results, and is computationally efficient enough to be applied to model-based control applications

Dynamic modeling and parameter estimation for an ethlyene-propylene-diene polymerization process

New Page 1 A general dynamic model for continuous EPDM polymerization in which crosslinking and gel formation are attributable to reactions between pendant double bonds has been developed. A pseudo-kinetic rate constant method is introduced to construct a moment model for a pseudo-homopolymer that approximates the behavior of the actual terpolymer under long chain and quasi-steady state assumptions. The pseudo-homopolymer model is then used as the basis for application of the numerical fractionation method. The proposed dynamic model is capable of predicting polydispersities and molecular weight distributions near the gel point with as few as eleven generations, and in the post-gel region with as few as five. The overall molecular weight distribution (MWD) of the sol was constructed by assuming a Schulz two parameter distribution for each generation. A parameter selection procedure is proposed to determine the kinetic parameters that can be estimated from the limited plant data. The procedure is based on the steady-state parameter output sensitivity matrix. The overall effect of each parameter on the measured outputs is determined using Principal Component Analysis (PCA). The angles between the sensitivity vectors are used as a measure of collinearity between parameters. A simple algorithm which provides a tradeoff between overall parameter effect on key outputs and collinearity yields a ranking of parameters by ease of estimation, independent of the available data. Its nonlinear and dynamic extensions are also developed and tested to address the nonlinearity and dynamics of the parameters\u27 effects on the outputs. The key kinetic parameters determined by the parameter selection procedure were estimated from steady-state data extracted from dynamic plant data, using a newly developed steady state detection tool. A hierarchical extended Kalman filter (EKF) design is proposed to estimate unmeasured state variables and key kinetic parameters of the EPDM kinetic model. The estimator design is based on decomposing the dynamic model into two subsystems, by exploiting the triangular model structure and the different sampling frequencies of the on-line and laboratory measurements directly related to the state variables of each subsystem. Simulation tests show that the hierarchical EKF generates satisfactory predictions even in the presence of measurement noise and plant/model mismatch