分子水平动力学模型在催化裂化反应中的应用

催化裂化反应作为一个重要的原油二次加工过程,反应中存在成百上千的物质和化学反应,是一个典型的复杂反应体系,建立这些复杂反应的分子水平动力学模型是动力学研究的重点之一。开发分子水平动力学模型对认识催化裂化反应和工艺开发具有重要的理论和现实意义。本文详细地介绍了近年来国内外催化裂化反应分子水平动力学模型具有代表性的研究成果,对比了单事件模型、结构导向型集总、KMT、熵近似因子模型以及结构化模型等动力学模型的特点、使用范围及优缺点。指出建立更为细致的分子水平动力学模型来预测关键组分的收率、产物的组成和性质将是催化裂化动力学模型研究领域以后发展的主要方向。     

Automatic data-driven stoichiometry identification and kinetic modeling framework for homogeneous organic reactions

Data-driven and knowledge-driven methods are two approaches used in studying reaction kinetics. This article proposes a hybrid-modeling framework for homogeneous synthesis reactions, which combines the advantages of high level of automation in the data-driven approach and improved accuracy in the knowledge-driven approach. A constrained enumeration method is proposed to generate possible candidate stoichiometries, and dynamic response surface methodology, target factor analysis, and mass balance are used together for identifying stoichiometries one-by-one, without the necessity of an expert-generated candidate list. Then, the previously screened stoichiometries are formed into different groups that represent candidate reaction systems, and the group (or groups) with the greatest likelihood will be identified, based on kinetic fitting and reaction dynamic criteria. This framework has been demonstrated by several examples of different reaction systems. The true reaction stoichiometries are all correctly identified, and the accurate kinetic models are obtained, showing satisfactory performance of the proposed method.     

Effects of radiation absorption and catalyst concentration on the photocatalytic degradation of pollutants

This study is dealing with the reaction rate dependence on catalyst concentration and light absorption in photocatalytic processes. Models relating the reaction rate to the absorbed radiation by the catalyst (titania in suspension) are proposed. To apply these models, the system is divided into layers and each layer is divided into cells, assuming that there is only one particle (agglomerate) of catalyst in each cell. The extensive reaction rate can be calculated as the sum of the reaction rate in each cell, being this proportional to the light absorbed by each particle. Two different models are proposed for light propagation through the reaction medium (exponential and probabilistic model). The extinction coefficients have been estimated by using transmittance measurements related to sedimentation rates changing according to catalyst concentration and pH. The integration of these models, taking into account the expression of the reaction rate, allows to obtain equations that can explain the trends observed in the photocatalytic treatment of Cr(VI) and phenol, by using TiO₂ (Degussa-P25) in suspension.     

Mathematical Analysis of Chemical Reaction Systems

The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially distributed. Here we focus on mathematical models based on deterministic mass-action kinetics. These models are systems of coupled nonlinear differential equations on the positive orthant. We explain how mathematical properties of the solutions of mass-action systems are strongly related to key properties of the networks of chemical reactions that generate them, such as specific versions of reversibility and feedback interactions.     

Parameter estimation in simultaneous phase and reaction equilibria

The estimation of parameters of models describing simultaneous phase and reaction equilibria is generally difficult to accomplish, due to strong correlation between the parameters. We show in this paper that these models possess intermediate properties between reduced and implicit models. This makes it convenient to develop ad-hoc algorithms for this class of problems which are of considerable importance in process design. We present a method for parameter estimation based on implicit differentiation, which makes it possible to use a gradient algorithm with respect to a reduced number of parameters, which greatly enhances global convergence.     

INVITED REVIEW ON THE USE OF CHEMICALLY STRUCTURED MODELS FOR BIOREACTORS

An individual cell is an immensely complicated self-regulated chemical reactor that can alter its biosynthetic machinery to meet the demands of a changing environment. The biochemical engineer must build a large macroscopic reactor to harness the cells for desirable chemical conversions. The design and control of such bioreactors would be facilitated with effective mathematical models of the response of the culture to changes in nutrients or other environmental variables. Because of the inherent internal plasticity of the cell, models must reflect the changing structure of the biomass. This paper reviews some examples of models which contain components representing various chemical fractions within the cell. The advantage of these models is their potential ability to predict the dynamic behavior of a cellular population. In addition such models are potential tools for testing hypotheses concerning cellular control mechanisms and consequently the development of more effective cell strains. Models of populations based on a finite-representation technique using an ensemble of chemically structured single-cell models are emphasized. These latter models are capable of accurate a priori prediction of bioreactors to perturbations in flow rates or feed concentrations. Models which aspire to the a priori quantitative prediction of cell population behavior must be sufficiently complex that shifts in growth-rate limiting processes can be taken into account; consequently a high-level of chemical structure will characterize the best models.     

Integration of machine learning and first principles models

Model building and parameter estimation are traditional concepts widely used in chemical, biological, metallurgical, and manufacturing industries. Early modeling methodologies focused on mathematically capturing the process knowledge and domain expertise of the modeler. The models thus developed are termed first principles models (or white-box models). Over time, computational power became cheaper, and massive amounts of data became available for modeling. This led to the development of cutting edge machine learning models (black-box models) and artificial intelligence (AI) techniques. Hybrid models (gray-box models) are a combination of first principles and machine learning models. The development of hybrid models has captured the attention of researchers as this combines the best of both modeling paradigms. Recent attention to this field stems from the interest in explainable AI (XAI), a critical requirement as AI systems become more pervasive. This work aims at identifying and categorizing various hybrid models available in the literature that integrate machine-learning models with different forms of domain knowledge. Benefits such as enhanced predictive power, extrapolation capabilities, and other advantages of combining the two approaches are summarized. The goal of this article is to consolidate the published corpus in the area of hybrid modeling and develop a comprehensive framework to understand the various techniques presented. This framework can further be used as the foundation to explore rational associations between several models.     

Identification of uncertain MIMO Wiener and Hammerstein models

Several approaches can be found in the literature to perform the identification of block oriented models (BOMs). In this sense, an important improvement is to achieve robust identification to cope with the presence of uncertainty.In this work, two special and widely used BOMs are considered: Hammerstein and Wiener models. The models herein treated are assumed to be described by parametric representations. The approach introduced in this work for the identification of the multiple input-multiple output (MIMO) uncertain model is performed in a single step. The uncertainty is described as a set of parameters which is found through the solution of an optimization problem.A distillation column simulation model is presented to illustrate the robust identification approach. This process is an interesting benchmark due to its well-known nonlinear dynamics. Both Hammerstein and Wiener models are used to represent this plant in the presence of uncertainty. A comparative study between these models is established.     

A comprehensive phenomenological model for erosion of materials in jet flow

A phenomenological erosion model, which captures the effects of impingement velocity, angle, particle size, properties of target, has been developed. The model incorporates removal of material due to both deformation damage and cutting. For the cutting removal, the volume loss has a power-law relation with particle's impingement velocity, angle, mass and size and the exponents depend on the particle's shape (cutting ways). Two critical cases, line cutting and area cutting, indicate that the range of the exponent of impingement velocity is 2∼2.75 which is consistent with the experimental findings. For deformation damage removal, the model indicates that the exponent of the particle's mass is independent on the target material, while the exponents of particle's impingement angle, velocity and density depend on the properties of target material. To validate the model, the simplified version of the model was applied to predict erosion rates, impingement angle where the maximum weight loss occurs and particle size effect. The predictions are in good agreement with the experiments conducted by Finnie. Such models could be used locally together with CFD models to predict erosion and wear patterns under varying flow scenarios.     

Heat of sorption: A comparison between isotherm models and calorimeter measurements of wood pulp

This article introduces a method to validate heat of sorption measurements from isotherms by comparing them to direct measurements using reaction calorimetry. We have evaluated some frequently used single-temperature isotherm models (BET, GAB) as well as two multi-temperature isotherm equations (Anderson, Heikkilä). It turned out that the isotherm models with better isotherm curve fitting characteristics did not deliver the best results for the heat of sorption. Multi-temperature isotherm models such as the Heikkilä equation are able to deliver good results in terms of modelling the isotherm data and determining the heat of sorption. Single-temperature models fit the isotherm data better than multi-temperature models, but failed to deliver correct values for the heat of sorption. We specifically investigated the heat of sorption at very low moisture content, which is most relevant for paper drying. The resulting heat of sorption curves were analyzed with respect to their saturation behavior, which is expected to occur below BET monolayer moisture. The heat of sorption from the Heikkilä’s model was the only one to show the expected saturation at very low moisture content.     

Power law models as descriptors of the kinetics of complex systems: Temperature effects

The effects of temperature on power law models for the kinetics of parallel first order systems are studied. The variation of the empirical power law parameters with temperature provides information on the relationship between the rate constant and activation energy distributions; in particular. if the power law exponent increases with temperature, there is a positive correlation between the rate constants and the activation energies; if the power law exponent decreases with temperature, there is a negative correlation between the rate constants and the activation energies; Arrhenius plots will always be concave unless the activation energies for all the reactions are equal. Application of the techniques described here to data from the catalytic cracking of gas oil over LaY zeolite reveals a compensation effect among the reacting hydrocarbon species.     

IDENTIFICATION OF UNOBSERVED COMPONENTS MODELS

Abstract. Unobserved components ARIMA models are common in time series applications. However, fitting models of this type leads to problems of model identification. In this paper we derive a methodology to check whether a proposed model is identifiable. We show that this kind of identification can be checked using the autocovariance generating function and/or the (pseudo-)spectral generating function.     

A STUDY OF THE APPLICATION OF STATE-DEPENDENT MODELS IN NON-LINEAR TIME SERIES ANALYSIS

Abstract. The theory of state-dependent models was developed by Priestley (1980), and a few simple applications were given in Priestley (1981). In this paper, an extensive study of the application of state-dependent models to a wide variety of non-linear time series data is carried out. Both real and simulated data are used in the study, and the problems encountered are highlighted. The method is demonstrated to be successful in practice in many cases, and suggestions for the further development of the algorithm are also given.     

A k-Factor GARMA Long-memory Model

Long-memory models have been used by several authors to model data with persistent autocorrelations. The fractional and fractional autoregressive moving-average (FARMA) models describe long-memory behavior associated with an infinite peak in the spectrum at f = 0. The Gegenbauer and Gegenbauer ARMA (GARMA) processes of Gray, Zhang and Woodward (On generalized fractional processes. J. Time Ser. Anal. 10 (1989), 233–57) can model long-term periodic behavior for any frequency 0 ≤ f ≤ 0.5. In this paper we introduce a k -factor extension of the Gegenbauer and GARMA models that allows for long-memory behavior to be associated with each of k frequencies in [0, 0.5]. We prove stationarity conditions for the k -factor model and discuss issues such as parameter estimation, model iden- tification, realization generation and forecasting. A two-factor GARMA model is then applied to the Mauna Loa atmospheric CO₂ data. It is shown that this model provides a reasonable fit to the CO₂ data and produces excellent forecasts.     

EQUILIBRIUM,KINETICS, AND BREAKTHROUGH STUDIES FOR ADSORPTION OF Cr(VI) ON CHITOSAN

Wastewater containing low levels of pollutants can be effectively treated by the adsorption technique. In the present work, an adsorption study was carried out using chitosan as adsorbent in a fixed-bed column for the removal of Cr(VI) from wastewater solutions. The column performance of Cr(VI) adsorption onto chitosan was studied at different bed heights (3–9 cm), flow rates (50–200 mL/min), initial metal concentrations (2–10 mg/L), pH values (2–7), and temperatures (30°–60°C). The equilibrium data for the batch adsorption of Cr(VI) on chitosan were tested using the Langmuir, Freundlich, and BET isotherm models. The Langmuir model was found to be the most suitable, with a maximum adsorption capacity of 35.7 mg/g and a correlation coefficient (R ²) = 0.952. The experimental data were found to fit well with the pseudo-second-order kinetic model, with R ² = 0.999. The dynamics of the adsorption process was modeled using the Adams-Bohart, Thomas, and mass transfer models. The models were used to predict the breakthrough curves of adsorption systems and to determine the characteristic design parameters of the column. The adsorption data were observed to fit well with all three models. The model parameters were derived using MATLAB software. In order to compare quantitatively the applicability of adsorption dynamic models in fitting to experimental data, the percentage relative deviation (P) was calculated and found to be less than 5, confirming that the fit is good for all three models.     

A DIAGNOSTIC TEST FOR NONLINEAR SERIAL DEPENDENCE IN TIME SERIES FITTING ERRORS

Abstract. Time series analysts have begun to consider the applicability of nonlinear models. In order for nonlinear models to be accepted by practitioners, practicai tests must be avilable to test for the presence of nonlinearity in both raw time series and in the residuals from fitted models. A diagnostic test, based on the bispectrum, for the presence of nonlinear serial dependence in these time series is investigated here using artificial data. Detection of such nonlinear dependence is taken to indicate that nonlinear modelling methods are necessary. The theory behind the test is reviewed and simulations driven by pseudorandom numbers are presented for a variety of models and sample sizes. The simulations indicate that the test has substantial power for many models. In addition, theoretical and empirical results are presented which show that the bispectral diagnostic test is equally powerful for both the source series and for the fitting errors from a line& model. Thus, while the test is suitable for use as a diagnostic test on the fitting errors of linear time series models, prior linear modeling of the time series is not required.     

The Mathematical Models of the Initial Stage of the Thermal Degradation of Poly(Vinyl Chloride)

Abstract

The mathematical models of the initial stage of the thermal dehydrochlorination of PVC are proposed. It is shown that abnormal unstable fragments having constants of rates of degradation equal to 10^?3–10^?4sec^?1 have the greatest influence on the thermal degradation of PVC at 180–200°C. The groups having chlorine near tertiary carbon and chloroallylic groups may be such fragments.     

Effects of Particle Size Distribution on the Kinetics of Hydration of Tricalcium Silicate

An analysis of the validity of approximating selected particle size distributions by small numbers of size classes was carried out. It was determined that the selection of a small number of particle size classes is not adequate to describe a particle size distribution. One consequence of this is that the particle size distribution, if not properly accounted for, can mask the kinetics of a hydration process. The hydration rates of two finnesses of tricalcium silicate, each with known particle size distributions, were measured by isothermal calorimetry for a period of 28 d. These data were integrated, normalized, and represented as α-time curves as a basis for comparison with kinetic models of hydration. Agreement with kinetic models was found to be strongly influenced by the effect of particle size distribution. However, the rate-limiting mechanisms appear to be independent of particle size distribution No single kinetic model was adequate to describe C₃S hydration over the first 28 d. A kinetic model that assumes initial surface-area control with diffusion control dominating subsequently provided an excellent fit to the experimental data.     

KINETIC MODELS FOR LIQUID-PHASE CATALYTIC OXIDATION OF TOLUENE TO BENZOIC ACID WITH PURE OXYGEN

The liquid phase oxidation of toluene to benzoic acid by pure oxygen has been performed in a bubble reactor by using cobalt acetate tetrahydrate as catalyst. The influence of the oxygen partial pressures on the reaction kinetics were first investigated, and the results showed that the influence was neglectable in the high oxygen pressure range (>0.5 MPa) under 155°C. Thereby, the reaction rates in the oxidation using pure oxygen are independent of the oxygen partial pressure and expressed as the first order to liquid reactants. Based on a kinetic scheme that involves both benzyl alcohol and benzaldehyde, the kinetic models can well describe the reaction process. Furthermore, the results indicated that the production of benzyl alcohol is much slower than its consumption to form benzaldehyde and the scheme can be further simplified to a kinetic equation, which involves only benzaldehyde as intermediate. The simplified reaction scheme also well describes the reaction, and, thus, the derived kinetic models agree well with the experimental data. The reaction constants follow the Arrhenius law. The estimated activation energies are in the range from 92.63 kJ·mol^?1 to 67.81 kJ·mol^?1.     

Studies on fermentation with recombinant yeast cells: plasmid stability and kinetics of biomass and protein production

Plasmid stability of the recombinant Saccharomyces cerevisiae YPB‐G strain harbouring a YEp plasmid with α‐amylase and glucoamylase genes as a fusion has been investigated in shake flasks and in a bioreactor using various compositions of media containing glucose or starch as the main carbon source. The medium composition affected both the growth characteristics and the stability of the plasmid. Superior plasmid stability was obtained in yeast minimal medium and in complex medium with glucose. Plasmid stability was substantially increased at high growth rates. Additional data were collected in the same system to investigate the kinetic characteristics of biomass and protein production, and unstructured kinetic models were used to interpret the results. At high initial glucose concentrations, where the biomass and protein production rates were similar, the kinetic models displayed good fits associated with high degrees of correlation. © 2000 Society of Chemical Industry