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The purpose if this paper is to present a fixed point result constructed by finite sequences. Using iterated function systems and related fractal operators, a mixed patterns generated by the a finite sequence patterns construct the sets of patterns built by black and white squares. A complete metric space related to a mixed pattern sequence is defined using the distance based on difference of the black squares' area. The main result of the paper highlights that these fractal operators has unique fixed points for the sets generated by the mixed patterns. Moreover, the main theorem is also applied for Vicsek fractals such that results also hold for mixed Vicsek patterns. Motivated by various studies on growing graph sequences and related large structures, this paper underlines a new connection between fixed point theory and network science. Using circle patterns, the paper also interprets the main result on sets mixed patterns based on touching circles. Thus, the paper focuses a fixed point theorem on the sets mixed patterns built by iterated function systems and the distances calculated between the areas of these geometric shapes. [ABSTRACT FROM AUTHOR]

In-silico amine screening is a fast, low-cost and promising way of efficiently evaluating new amine molecules which are proposed for carbon-dioxide capture purposes. In order to implement the screening environment, reliable and robust absorber models are required. This contribution presents the modeling and validation results of a CO2 capture pilot absorber operated with monoethanolamine (MEA), as the first step of the in-silico solvent screening framework. The simulation results have shown that the outlet amine loading can be predicted with a 10% deviation from the experimental values for one column, with larger deviations for the second. In addition the model was extended to include the calculation of the overall mass transfer coefficient from laboratory based wetted-wall experiments completed at CSIRO Newcastle, Australia. This further improved the overall model prediction and significantly reduced the amine loading prediction error for the column 1. Note that no parameter fitting was performed on the pilot plant experimental data, other than to include a heat loss to the atmosphere term, and the model relies entirely on engineering and property correlations available in the scientific literature. [ABSTRACT FROM AUTHOR]

Abstract: This article investigates monitoring technologies, which provide systematic solutions for nucleation detection based on external bulk video imaging (BVI). The methods under investigation rely on multivariate image analysis, image feature descriptors and statistical control charts (SPCs). For the design of SPCs the video information is transformed into time series. The application of SPCs may be hindered by autocorrelated time series, which show oscillatory patterns due to light reflections from the stirrer blades; however, the autocorrelation can be reduced by performing operations with the first principal component (PC1) of the captured color image or by stacking the frames based on the dominating frequency. Another option is to design digital signal filters in the frequency domain to decrease the autocorrelation of the time series. It was found that the fastest methods for nucleation onset detection were the monitoring in the principal score space and control chart based monitoring of the mean gray intensity of the PC1 images sampled at 25Hz. Furthermore, it was observed that performing principal component analysis (PCA) calculations on multidimensional or multispectral information not only provides the combination of variables that explain most of the variance at a certain time instance but also decreases the autocorrelation of the resulting time series. For acoustic signal based monitoring the gray scale images were converted into a 2 channel stereo sound. It was found that this method has less performant nucleation onset detection capabilities compared to the methods which rely directly on the images. [Copyright &y& Elsevier]

Abstract: This contribution describes the pattern recognition based data analysis of an existing industrial batch dryer, and the comparison of three artificial intelligence techniques suited to perform classification tasks: neural networks trained using the Levenberg–Marquardt and the Levenberg–Marquardt method with Bayesian regularization, the neuro-fuzzy model based on clustering and grid partition, and the Takagi–Sugeno fuzzy models. The classifiers are used to quantify the dryer batch time and its variation during a certain production period, thus the motivation behind the work is genuine. The presented pattern recognition method implements a supervised learning approach and is based on pressure measurement profiles recorded by the plant data management software—the PI System from OSIsoft. It is found that the neural networks trained with the Bayesian regularization have shown the most robust classification performance with respect to separation threshold selection. Furthermore, it is concluded that the application of artificial intelligence techniques in real chemical manufacturing facilities is feasible and provides useful information for process performance monitoring purposes. The pattern recognition findings presented in this paper are not case specific and can be directly used for the monitoring of a large variety of drying processes since the pressure profile features – vacuum check, pressure decrease, vacuum break – do not depend on the chemicals which are dried. Since the development of the artificial intelligent classifiers is presented in detail and step by step, this work may be interesting as a pattern recognition tutorial for chemical engineers. [Copyright &y& Elsevier]

Abstract: This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe. [Copyright &y& Elsevier]

Abstract: The purpose of the paper is twofold: it describes the proof of concept of the newly introduced bulk video imaging (BVI) method and it presents the comparison with existing process analytical technologies (PAT) such as focused beam reflectance measurement (FBRM) and ultra-violet visible (UV/vis) spectroscopy. While the latter two sample the system in small volumes closely to the probe, the BVI approach monitors the entire or large parts of the crystallizer volume. The BVI method is proposed as a complementary noninvasive PAT tool and it is shown that it is able to detect the boundaries of the metastable zone with comparable or better performance than the FBRM and UV/vis probes. [Copyright &y& Elsevier]

Abstract: In this article the optimal selection of the reboiler vessels, rectification columns and connection pipes with regard to reboiler swelling, and tray and pipe flooding is investigated. Since the reboilers are constrained by liquid swelling, while pipes and columns are constrained by flooding it is important to pair the equipment so that the vapor rate limitations are as close as possible, thus ensuring maximal equipment capacity usage. Calculations at 1 and 0.25bar pressure are performed for the standardized 1.6, 2.5, 4 and 6.3m3 reboiler vessels [Rührbehälter Basler Norm, N 253, 1977] and sieve tray rectification columns with nominal diameters ranging from 0.2 up to 0.6m. The dynamic operation of the batch distillation process having the vapor load and reflux ratio as input profiles is evaluated by formulating and solving an optimal control problem constrained by the hydraulic limitations. The open-loop optimization problem is solved using a dedicated Matlab tool – OptCon – which implements the multiple shooting strategy and the large-scale non-linear programming problem is handled by the HQP engine. [Copyright &y& Elsevier]

Abstract: This article presents the modeling and optimization of an industrial batch reactor operation with regard to production safety constraint which is represented by the reactor content swelling. Swelling occurs due to the evacuation of a coupled product which passes through the liquid in order to reach the reaction mass surface. In order to model the reaction system a chemical model linked to a hydrodynamic model is developed. The goal of the optimization is to calculate the temperature and pressure profiles which maximize conversion rates, without exceeding the maximum reactor level. The optimal temperature profile is calculated using the optimal control optimization method and the results show that a productivity increase of up to 36% can be achieved as compared to the industrial process. [Copyright &y& Elsevier]

Abstract: A novel method is presented for the rigorous propagation of uncertainties in initial concentrations and in dosing rates into the errors in the rate constants fitted by multivariate kinetic hard-modelling of spectroscopic data using the Newton–Gauss–Levenberg/Marquardt optimisation algorithm. The method was successfully validated by Monte-Carlo sampling. The impact of the uncertainties in initial concentrations and in the dosing rate was quantified for simulated spectroscopic data based on a second and a formal third order rate law under batch and semi-batch conditions respectively. An important consequence of this study regarding optimum experimental design is the fact that the propagated error in a second order rate constant is minimal under exact stoichiometric conditions or when the reactant with the lowest associated uncertainty in its initial concentration is in a reasonable excess (pseudo first order conditions). As an experimental example, the reaction of benzophenone with phenylhydrazine in THF was investigated repeatedly (17 individual experiments) by UV–vis and mid-IR spectroscopy under the same semi-batch conditions, dosing the catalyst acetic acid. For all experiments and spectroscopic signals, reproducible formal third order rate constants were determined. Applying the proposed method of error propagation to any single experiment, it was possible to predict 80% (UV–vis) and 40% (mid-IR) of the observed standard deviation in the rate constants obtained from all experiments. The largest contribution to this predicted error in the rate constant could be assigned to the dosing rate. The proposed method of error propagation is flexible and can straightforwardly be extended to propagate other possible sources of error. [Copyright &y& Elsevier]

Crystallization is one of the most important unit operations used for the separation and purification of crystalline solid products. Appropriate design and control of the crystallization process is paramount to produce crystalline products with tailor-made-properties. This paper provides an overview of selected recent developments in the modelling, monitoring and control of crystallization processes. We consider the topics discussed in this review to be enabling technologies for the development of the next generation of crystallization processes with significantly improved predictability, robustness and controllability. [ABSTRACT FROM AUTHOR]