Kinetic Intersections as a Source of Information on Rate Coefficients

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Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach

A coupled solver for population balance systems is presented, where the flow, temperature, and concentration equations are solved with finite element methods, and the particle size distribution is simulated with a stochastic simulation algorithm, a so-called kinetic Monte-Carlo method. This novel approach is applied for the simulation of an axisymmetric model of a tubular flow crystallizer. The numerical results are compared with experimental data

Simulations of an ASA flow crystallizer with a coupled stochastic-deterministic approach

A coupled solver for population balance systems is presented, where the flow, temperature, and concentration equations are solved with finite element methods, and the particle size distribution is simulated with a stochastic simulation algorithm, a so-called kinetic Monte-Carlo method. This novel approach is applied for the simulation of an axisymmetric model of a tubular flow crystallizer. The numerical results are compared with experimental data

Operator Splitting Monte Carlo Method for Aerosol Dynamics

Aerosol dynamics are described by the population balance equation (PBE). In principle, three typical methods (i.e., direct discretization, method of moments, and stochastic method) have been widely used to solve the PBE. Stochastic method is the most flexible among the three methods. However, stochastic method is computationally expensive. Recently, an operator splitting Monte Carlo (OSMC) method has been developed so as to improve the numerical efficiency while preserving the flexibility of the stochastic method. Within the OSMC, nucleation and surface growth are handled with deterministic means, while coagulation is simulated with a stochastic method (the Marcus‐Lushnikov stochastic process). The stochastic and deterministic treatments of various aerosol dynamic processes are synthesized under the framework of operator splitting. Here, the operator splitting errors of various schemes are analyzed rigorously, combined with concrete numerical examples. The analyses not only provide sound theoretical bases for selecting the most efficient operator splitting scheme for the usage of the OSMC, but also shed lights on how to adopt operator splitting in other PBE solving methods, i.e., direct discretization, method of moments, etc

On the role of pre and post-processing in environmental data mining

The quality of discovered knowledge is highly depending on data quality. Unfortunately real data use to contain noise, uncertainty, errors, redundancies or even irrelevant information. The more complex is the reality to be analyzed, the higher the risk of getting low quality data. Knowledge Discovery from Databases (KDD) offers a global framework to prepare data in the right form to perform correct analyses. On the other hand, the quality of decisions taken upon KDD results, depend not only on the quality of the results themselves, but on the capacity of the system to communicate those results in an understandable form. Environmental systems are particularly complex and environmental users particularly require clarity in their results. In this paper some details about how this can be achieved are provided. The role of the pre and post processing in the whole process of Knowledge Discovery in environmental systems is discussed

Population balance model-based optimal control of batch crystallisation processes for systematic crystal size distribution design

During recent years crystallisation has found applications in many chemical industries, such as pharmaceutical, petrochemical, micro-electronics and food industries. Crystallisation is a basic step for purification or separation for a large variety of organic, inorganic and pharmaceutical compounds. Most of the product qualities are directly related to the shape of the crystal size distribution (CSD). The main difficulty in batch crystallisation processes is to accomplish a uniform and reproducible CSD. On-line control during the process allows for improved crystalline product quality, shorter process times and reduction or elimination of compromised batches. The actual prediction and estimation of the shape of the distribution at the end of the batch can provide useful information for monitoring or designing the operating curve for the supersaturation controller. Model-based approaches provide consistency of the CSD, can be used for better control and also for product design by reverse engineering the process to achieve the desired CSD and shape. This research presents a novel methodology for solving the population balance equation (PBE) for the estimation of the shape of the crystal size distribution for batch crystallisation processes. The approach combines the quadrature method of moments (QMOM) and the method of characteristics (MOCH), and provides a computationally efficient technique for the reconstruction of the whole crystal size distribution. The technique was used to estimate the kinetic parameters for the size-dependent growth and secondary nucleation, for potash alum-water system using industrial pilot plant data provided by BASF, Chemical Company. The combined technique was also used to estimate the size-dependent dissolution parameters for potash alum-water system, using laboratory scale data. The QMOM-MOCH solution approach is evaluated in a model-based dynamic optimization study, with the aim to obtain the optimal temperature profiles, which drive the system in both the supersaturated and under-saturated region, to achieve desired target CSD. Using growth, dissolution and nucleation parameters the technique was used to optimise the temperature trajectories to obtain bimodal and mono-modal distributions. The technique can serve as a soft sensor for predicting the CSD, or as a computationally efficient algorithm for off-line design or on-line adaptation of operating policies based on knowledge of the full CSD data. Additionally, the PBE model was solved using the method of characteristics under the assumption of constant supersaturation. At constant supersaturation growth is the dominating phenomenon, yielding a simplified analytical expression for the prediction of the CSD. The research presents the new methodology for the systematic design of the setpoint operating curves for supersaturation controlled crystallisation processes, which produces a desired target crystal size distribution (CSD) at the end of the batch. A design parameter, was introduced as a function of the supersaturation and time, and is evaluated for supersaturation controlled processes. Based on the design parameter and the simplified analytical model, the supersaturation setpoint and batch time are determined using an optimisation approach to obtain a target distribution with a desired shape. Two additional methods are also proposed that use the seed in conjunction with the supersaturation setpoint design, and analytical CSD estimator for shaping the product CSD. The first approach designs a seed recipe as a mixture of crystals resulting for example from standard sieve analysis. In this approach the seed was introduced at the beginning of the batch. The second approach introduces the dynamic seeding concept, which allows an easily implementable methodology to achieve complex target CSDs using seed with mono-modal distribution as a process actuator. These methodologies were validated for potassium dichromate-water system. Size-dependent growth kinetic parameters for the potassium dichromate-water system were identified using as experimental setup developed at Loughborough University. The experiments presented in the thesis also illustrates the simultaneous application of in situ Process Analytical Technology (PAT) tools, such as focused beam reflectance measurement (FBRM) for nucleation detection, attenuated total reflection (ATR) UV/Vis spectroscopy for concentration monitoring, as well as the in-line use of a Mastersizer for real-time CSD measurement in the case of the potassium dichromate in water system. The approaches provide a comprehensive framework for model-based dynamic optimisation of crystallisation processes, which combines efficient numerical solution approaches of the PBE with the formulation of novel optimisation problems. The techniques presented include controlled dissolution, simultaneous optimisation of operating policies and seed recipes and dynamic seeding. Simulation and experimental evaluations of the proposed approaches demonstrate the potential of the techniques to provide significant improvement in the current state-of-the-art in crystallisation control

Robustness properties of estimators in generalized Pareto Models

We study global and local robustness properties of several estimators for shape and scale in a generalized Pareto model. The estimators considered in this paper cover maximum likelihood estimators, skipped maximum likelihood estimators, moment-based estimators, Cramér-von-Mises Minimum Distance estimators, and, as a special case of quantile-based estimators, Pickands Estimator as well as variants of the latter tuned for higher finite sample breakdown point (FSBP), and lower variance. We further consider an estimator matching population median and median of absolute deviations to the empirical ones (MedMad); again, in order to improve its FSBP, we propose a variant using a suitable asymmetric Mad as constituent, and which may be tuned to achieve an expected FSBP of 34%. These estimators are compared to one-step estimators distinguished as optimal in the shrinking neighborhood setting, i.e., the most bias-robust estimator minimizing the maximal (asymptotic) bias and the estimator minimizing the maximal (asymptotic) MSE. For each of these estimators, we determine the FSBP, the influence function, as well as statistical accuracy measured by asymptotic bias, variance, and mean squared error—all evaluated uniformly on shrinking convex contamination neighborhoods. Finally, we check these asymptotic theoretical findings against finite sample behavior by an extensive simulation study