Accuracy of approximations for CIELAB chroma and hue difference computation

The transformation in CIELAB from differences in the L^*, a^*, b^* coordinates to those in lightness, chroma, and hue, ΔL^*, ΔC_ab^*, ΔH_ab^*, can be approximated by a rotation in 3-space. Expressions for the error in the approximation of chroma and hue differences are developed. Significant errors are introduced if either the hue angle or chroma difference between reference and sample colors are large. A computed example illustrates the use of the analysis. © 1997 John Wiley & Sons, Inc. Col Res Appl, 22, 61–64, 1997.     

Detailed kinetic analysis of oil shale pyrolysis TGA data

There are significant resources of oil shale in the western United States, which if exploited in an environmentally responsible manner would provide secure access to transportation fuels. Understanding the kinetics of kerogen decomposition to oil is critical to designing a viable process. A dataset of thermogravimetric analysis (TGA) of the Green River oil shale is provided and two distinct data analysis approaches—advanced isoconversional method and parameter fitting are used to analyze the data. Activation energy distributions with conversion calculated using the isoconversional method (along with uncertainties) ranged between 93 and 245 kJ/mol. Root mean square errors between the model and experimental data were the lowest for the isoconversional method, but the distributed reactivity models also produced reasonable results. When using parameter fitting approaches, a number of models produce similar results making model choice difficult. Advanced isoconversional method is better in this regard, but maybe applicable to a limited number of reaction pathways. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Second-order statistical regression and conditioning of replicate transient kinetic data

A new method has been developed to estimate physico-chemical parameters from transient kinetic data: second-order statistical regression (SOSR). It allows to account for heteroskedasticity and nonwhiteness of the noise in the time series measured. SOSR makes use of replicates to estimate the second-order statistics, i.e. the autocovariance pattern of the noise. A sample principal noise component analysis of the experimental time series allows nonlinear least-squares (NLSQ) regression of the latter. The method has been validated by regression of artificially generated experimental data and the results have been compared with those obtained with direct NLSQ regression. The SOSR has also been applied to the irreversible adsorption of oxygen on a reduced vanadia/silica catalyst and the interaction of propane with a copper/ceria catalyst, as studied with a temporal analysis of products (TAP) setup. In general, compared with those obtained with direct NLSQ regression, the parameter estimates and their confidence intervals are more accurate.     

The use of neural networks for fitting complex kinetic data

In this paper the use of neural networks for fitting complex kinetic data is discussed. To assess the validity of the approach two different neural network architectures are compared with the traditional kinetic identification methods for two cases: the homogeneous esterification reaction between propionic anhydride and 2-butanol, catalysed by sulphuric acid, and the heterogeneous liquid-liquid toluene mononitration by mixed acid. A large set of experimental data obtained by adiabatic and heat flux calorimetry and by gas chromatography is used for the training of the neural networks. The results indicate that the neural network approach can be used to deal with the fitting of complex kinetic data to obtain an approximate reaction rate function in a limited amount of time, which can be used for design improvement or optimisation when, owing to small production levels or time constraints, it is not possible to develop a detailed kinetic analysis.     

Reliability of kinetic data used for estimating multifront detonation parameters

A faster increase in the cell size and other important parameters of multifront detonation than that predicted by kinetic calculations is obtained for fuel-oxygen mixtures of hydrogen and typical hydrocarbons diluted by nitrogen. In a stoichiometric hydrogen-oxygen mixture diluted by an additional amount of oxygen or hydrogen, experimental and calculated data are also found to diverge with increasing concentration of the added species. This effect, however, is not observed if these mixtures are diluted by helium or argon. An assumption about the reason for this difference in data is put forward. A conclusion is made that kinetic data should be corrected as applied to detonation conditions. __________ Translated from Fizika Goreniya i Vzryva, Vol. 45, No. 3, pp. 89–94, May–June, 2009.     

Applying Tikhonov regularization to process the kinetic data of polymerization

Most experimental polymerization kinetic data are in the form of degree of polymerization versus time plots. However, to explore kinetic models it is more useful to have the data as polymerization rate versus degree of polymerization plots. Converting degree of polymerization into rate is an ill‐posed problem in that if inappropriate methods are used the noise in the data will be amplified, leading to unreliable results. This paper describes a procedure, based on Tikhonov regularization, to perform this conversion. The procedure is independent of kinetic models and keeps noise amplification under control. Its performance is demonstrated using several sets of published polymerization kinetic data. In each case the computed rates are used to determine the parameters in the rate expression proposed in the original papers. Modified rate expressions will also be explored. The ease with which such investigations can be performed highlights the advantages of this new procedure. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1625–1633, 2004     

Non-uniqueness of penultimate model reactivity ratios and treatment of kinetic data

Non-linear curve-fitting regression method using parametric equation as ‘user model’ has been utilized to determine reactivity ratios signifying effects of terminal and penultimate groups in copolymerization. Residuals, standard errors and correlation coefficients have been compared with those of terminal model using Fukuda's data on styrene-methyl methacrylate copolymerization. Non-uniqueness and occurrence of two sets of values for the penultimate model reactivity ratios have been explained on the basis of specified feed composition calculations. The two sets of reactivity ratios corresponding to explicit penultimate model have been used for treatment of kinetic data and consistent and acceptable values of various kinetic constants have been obtained with only one set. The value of ? obtained corresponds very closely to theoretically predicted value.     

Comparison of transverse mixing kinetic data obtained from a rolling drum

Cursory correlations between data obtained in different rotating drums are not valid without detailed modelling and a complete understanding of all experimental variables.     

A simple but sound approach for processing crystal growth kinetic data

The effects of common data smoothing techniques, on the estimating of the kinetic and thermodynamic parameters of the crystal growth process, were discussed in the light of birth and spread model. Adoption of the moving average, and filtration caused a noticeable misunderstanding of the real ruling growth mechanism, especially, during the early period of the crystal growth.In this work, a MATLAB routine was developed with standard, and reliable method to treat the prolonged concentration-time data sets, as obtained from continuous recording of refractometric °Brix readings of pure sucrose solutions in laboratory batch crystallization process. The method consists of finding the median of the residence time for every °Brix concentration, with and without interference of previous and post readings. In addition to 30% reduction in the evaluated interfacial free energies, up to 5-folds of increase in the estimates of the overall kinetic coefficients were reported using the common smoothing techniques instead of the proposed routine.     

Latent variable projections of sensitivity data for experimental screening and kinetic modeling

In microkinetic modeling the number of kinetic parameters is large and the precision of the “known” parameters is often very low. The standard approach is then to fit only the most uncertain parameters while regarding the fixed parameter as “true”. This assumption will have consequences also on the fitted parameters since the correlation structure often is quite significant. In this study we have taken the approach to fit many parameters and then try to use more efficient experimental designs to break the correlation structure and thus obtain more precise parameter estimation despite the large number of fitted parameters. After performing sensitivity analysis of many candidate experiments, a latent variable model (PCA) is made from the resulting sensitivity matrix and the score matrix is used as a candidate set prior to experiment selection. Due to the correlation structure in the sensitivity matrix, the number of components from the PCA model is fewer than the number of parameters. The columns in the score matrix are furthermore orthogonal whereas the columns in the original sensitivity matrix are not. Different designs were generated using the original sensitivity matrix, the score matrix as well as using a space-filling design and performing a sequential approach. Both steady state and transient experiments were evaluated. These different designs were used to fit kinetic parameters to a simulated dataset made using published parameter values. The results show no significant difference when using the original sensitivity matrix or the score matrix. However, since the score matrix has fewer columns than the full sensitivity matrix, the use of designs based on the score matrix enables more efficient designs when few experiments are required. The number of components in the PCA model also gives the rank of the parameter space induced by the candidate experiments. This is useful information when fitting many parameters in a microkinetic model and provides an assessment of the value of every candidate experiment before it is even performed.     

The accuracy of kinetic parameters estimated from batch and integral reactor data

The accuracy of rate constant estimates obtained by minimizing the sum of squares of differences between observed and calculated concentrations is considered. Closed solutions are obtained for some basic types of first order reaction schemes. The results are presented in the form of plots of the dimensionless variance of parameter estimates. The kineticist can use the plots both in analyzing experiments and in planning them for maximum economy. Such advance studies are capable of providing valuable insight into questions of experimental design even when the reaction scheme is unknown.     

基于热重法的准东煤等转化率热解动力学模型

准东煤热解脱挥发分特性对其热加工利用过程具有重要影响,建立准东煤热解通用动力学模型对预测挥发分产率及反应性能具有重要意义。采用热重测量了不同升温速率条件下的准东煤脱挥发分失重特性,使用Friedman、Flynn-Wall-Ozawa（FWO）和Kissinger-Akahira-Sunose（KAS）3种等转化率模型来处理热重实验数据,仔细分析了不同模型参数的获得方法及不同模型中活化能及指前因子的差异。研究结果表明,准东煤活化能分布函数呈现单峰分布;相比其他模型,FWO模型能够较好地描述准东煤的热解过程。     

Evaluation of kinetic parameters from TVA data. A computer simulation approach

A simple computer simulation of linear temperature-programmed thermal volatilization analysis (TVA) provides useful insights into the effects of the order of reaction n, the Arrhenius preexponential factor A, the overall activation energy δE, and the linear rate of heating β on the position and shape of TVA thermograms. Analysis of the numerical results of simulation experiments leads to a method for evaluating ΔE, A, and n from TVA data. The computer-simulation approach can easily incorporte mechanistic complexity. The latter possibility is applied to cases where n and ΔE are changing during the course of reaction, and it is shown that the proposed method gives good recovery of ΔE for such reactions.     

New methods of determination of kinetic parameters of theoretical models from experimental data

Integral and integro-differential methods have been developed for determining unknown characteristics of a kinetic experiment, including the rates of chemical reactions, the initial concentrations of substances, and Michaelis constants. These methods are applicable to a wide class of reactions and are most efficient when the system of differential equations considered is linear with respect to all, or a group of, unknown parameters. For an open multienzyme system obeying the Michaelis-Menten system of equations that is nonlinear in unknown parameters, it is demonstrated how the initial system of equations can be transformed into a new system that is linear with respect to new variables functionally depending on the initial parameters. A method has been developed for reformulating the initial nonlinear problem of determining the unknown parameters into a linear one. In this method, the initial problem is immersed into the more general problem of identifying the coefficients of a differential equation such that the initial formula is one of the solutions of this equation. This method can also be used to determine kinetic parameters of theoretical models that are formulated in terms of both concentrations and activities. A method of complete identification of chemical kinetic problems has been analyzed for the case of the incomplete observability of some components of the reaction, and it has been concluded that the kinetics of the substrate and intermediates in a multistep consecutive reaction can be qualitatively and quantitatively reconstructed by monitoring its product provided that the product concentration is precisely determined.