Lumped Kinetic Model Research Articles

Discontinuous-Galerkin finite-element method for approximating a model of non-equilibrium liquid chromatography considering Bi-Langmuir isotherm

In this paper, a discontinuous-Galerkin finite-element method (DG-FEM) is applied for the numerical solution of multi-component, non-equilibrium, lump kinetic model of liquid chromatography under nonlinear conditions. The model is analyzed for standard Bi-Langmuir type adsorption isotherms using Danckwert boundary conditions. Packed bed processes of liquid chromatography are modeled as convection-diffusion partial differential equations (PDE). In these models, the diffusion term is strongly dominated by the convection term. Therefore simulation of packed bed chromatographic processes requires specialized numerical techniques. In this study, the (DG-FEM) is utilized for the space discretization and the resulting semi-discrete system of ordinary differential equations is solved numerically by using a total variation bounded (TVB) Runge–Kutta method. This technique resolves sharp discontinuities and achieves a high order accuracy. To inspect the impact of different parameters, the results of the proposed method are authenticated against the high-resolution finite-volume scheme (HR-FVS). These numerical results include a single-solute flow, two-component mixture flow, and three-component mixture flow. The developed numerical results could be helpful in optimal predictive control, systematic monitoring and efficient operation of chromatographic processes.

Hydroliquefaction kinetics of coal-derived preasphaltenes catalyzed by FeS and S

Hydroliquefaction behavior of preasphaltenes, derived from direct coal liquefaction, was carried out in a 30 mL autoclave with FeS + S catalyst and tetralin at initial hydrogen of 5.0 MPa, residence time of 0–60 min and reaction temperature of 380–440°C in order to optimize the conditions of direct coal liquefaction and improve oil yield. The products distribution and kinetic parameters of preasphaltenes catalytic hydroliquefaction were investigated. A new kinetic model was established to simulate the preasphalteneshydroliquefaction catalyzed by FeS + S catalyst using lump kinetic model. It was found that preasphaltenes were hydroliquefaction into asphaltenes and char directly, and then asphaltenes were hydrocracked into oil + gas products. Regressive reactions of preasphaltenes to char and asphaltenes to preasphaltenes occurred at higher temperatures. Higher temperature and longer time were favorable for increasing the conversion of preasphaltenes and the oil + gas yield. The hydroliquefaction of preasphaltenes under 440°C and 60 min reached 79.45% with 34.7% of oil + gas yield. The hydroliquefaction conversions calculated from the model agreed well with the experimental data, and the activation energies ranged within 50–245 kJ/mol.

Kinetics toward mechanism and real operation for ultra‐deep hydrodesulfurization and hydrodenitrogenation of diesel

AbstractAs the hydrodesulfurization (HDS) of diesel achieves ultra‐deepness, our understanding of its kinetics is still far from in‐depth. Therefore, herein, two lumped kinetic models for the ultra‐deep hydrodesulfurization (UHDS) and hydrodenitrogenation (HDN) are established based on experiments under a wide range of operating conditions. Meanwhile, a four‐lump kinetic model of the aromatic hydrosaturation (AHS) is erected. Our kinetic models disclose thermodynamic decisiveness in UHDS, which is unreachable beyond a temperature upper limit or a pressure lower limit. We also reveals the unexpected temperature dependence of organonitrogen inhibition to HDS, for less than 300°C this inhibition becomes even more potent despite nitrogen removal by HDN reactions. Subsequently, the HDS kinetics of total sulfur are deciphered as multi stages existed in the whole reaction coordinate. Accordingly, a four‐stage conceptual model involving mechanism and rate laws is proposed to better understand organonitrogen inhibition, thermodynamics, and kinetics in UHDS.

Kinetics of the direct DME synthesis from CO2 rich syngas under variation of the CZA-to-γ-Al2O3 ratio of a mixed catalyst bed.

The one-step synthesis of dimethyl ether over mechanical mixtures of Cu/ZnO/Al2O3 (CZA) and γ-Al2O3 was studied in a wide range of process conditions. Experiments were performed at an industrially relevant pressure of 50 bar varying the carbon oxide ratio in the feed (CO2 in COx from 20 to 80%), temperature (503–533 K), space-time (240–400 kgcat s mgas−3), and the CZA-to-γ-Al2O3 weight ratio (from 1 to 5). Factors favoring the DME production in the investigated range of conditions are an elevated temperature, a low CO2 content in the feed, and a CZA-to-γ-Al2O3 weight ratio of 2. A lumped kinetic model was parameterized to fit the experimental data, resulting in one of the predictive models with the broadest range of validity in the open literature for the CZA/γ-Al2O3 system.

Kinetic modelling of Pt/γ-Al2O3–Cl catalysts formulation changes in n-heptane reforming

A common n-heptane reforming lumped kinetic model based on linear free energy relationships was developed on experimental data acquired over 19 Pt/γ-Al2O3–Cl catalysts presenting different formulations and support crystallite morphologies.

Effect of temperature variations on non-equilibrium and non-isothermal two-component liquid chromatography in cylindrical columns

The effect of temperature variations in liquid chromatographic columns of cylindrical geometry are studied by formulating a non-isothermal and non-equilibrium two-dimensional (2D) lumped kinetic model (LKM) simulating the flows of two-component mixtures. The developed models contain systems of coupled convection-dominated partial differential, differential, and algebraic equations for mass and energy balances in the mobile and stationary phases. For linearized isotherms, semi-analytical solutions are obtained by utilizing a sequential application of finite Hankel and Laplace transformations along with Tschirnhaus-Vieta and eigen-decomposition techniques. Temporal moments are also generated numerically from the derived semi-analytical solutions for a deeper understanding of the process execution. For nonlinear isotherms, a high-resolution finite volume scheme (HR-FVS) is employed to numerically simulate the model equations and also utilized to benchmark the precision scopes of derived semi-analytical solutions. A few case studies of linear and nonlinear chromatography are conducted. The connectivity of thermal waves with the concentration peaks is examined via numerical simulations and essential model parameters that affect the chromatographic column performance are identified. The results of this study will be very useful for optimizing and improving the non-isothermal and non-equilibrium liquid chromatography involving two-component mixtures and cylindrical-shaped columns.

In silico Determination of Some Conditions Leading to Glycolytic Oscillations and Their Interference With Some Other Processes in E. coli Cells.

Autonomous oscillations of species levels in the glycolysis express the self-control of this essential cellular pathway belonging to the central carbon metabolism (CCM), and this phenomenon takes place in a large number of bacteria. Oscillations of glycolytic intermediates in living cells occur according to the environmental conditions and to the cell characteristics, especially the adenosine triphosphate (ATP) recovery system. Determining the conditions that lead to the occurrence and maintenance of the glycolytic oscillations can present immediate practical applications. Such a model-based analysis allows in silico (model-based) design of genetically modified microorganisms (GMO) with certain characteristics of interest for the biosynthesis industry, medicine, etc. Based on our kinetic model validated in previous works, this paper aims to in silico identify operating parameters and cell factors leading to the occurrence of stable glycolytic oscillations in the Escherichia coli cells. As long as most of the glycolytic intermediates are involved in various cellular metabolic pathways belonging to the CCM, evaluation of the dynamics and average level of its intermediates is of high importance for further applicative analyses. As an example, by using a lumped kinetic model for tryptophan (TRP) synthesis from literature, and its own kinetic model for the oscillatory glycolysis, this paper highlights the influence of glycolytic oscillations on the oscillatory TRP synthesis through the PEP (phosphoenolpyruvate) glycolytic node shared by the two oscillatory processes. The numerical analysis allows further TRP production maximization in a fed-batch bioreactor (FBR).

A lumped kinetic model for high-temperature pyrolysis and combustion of 50 surrogate fuel components and their mixtures

Wide distillation fuels (WDF) and gasoline/diesel blends have been proposed as new fuel formulations for advanced combustion engines. Recent studies have shown that multi-component gasoline and diesel surrogate mixtures can accurately mimic the distillation curve, functional group or hydrocarbon class distribution, average molecular weight, and other combustion properties of real fuels. This work presents an updated decoupling methodology to construct a 50-component fuel model, which consists of a skeletal sub-mechanism for large hydrocarbon components present in gasoline, jet and diesel fuels, a reduced C5-Cn mechanism, and a detailed C0-C4 mechanism. The entire model contains 156 species and 1132 reactions. The chemical classes covered include n-alkanes, iso-alkanes, cyclo-alkanes and alkylbenzenes. Compared with the comprehensive detailed kinetic modeling approach, the present methodology largely reduces the model size due to the use of skeletal fuel mechanisms. Compared with the traditional decoupling methodology, our approach increases the model accuracy since it contains a detailed C0-C4 mechanism instead of a reduced C2-C3 mechanism. The present model was validated against experimental targets at high temperatures, including the pyrolysis and oxidation speciation data and global parameters such as ignition delay times and laminar flame speeds from 30 pure fuel components and 12 fuel mixtures. In general, the present model performs well against these experimental data, suggesting this methodology is a suitable approach for developing accurate kinetic models for multi-component fuels. Future work will extend the present framework to predict low-temperature combustion chemistry of multi-component fuels.

Renewable fuels production from the hydrotreating over NiMo/γ-Al2O3 catalyst of castor oil methyl esters obtained by reactive extraction

In recent years, many studies have been published on the hydrotreating of non-edible vegetable oils, however, a limited number of them deal with the hydroprocessing of their corresponding fatty acid methyl esters for the productions of renewable fuels. In this study is outlined the production of renewable fuels from castor bean seeds (Ricinus communis L.) in two stages, the first one is to obtain the respective castor oil methyl esters by reactive extraction and the second one is to apply the hydrotreating process to these methyl esters by using a commercial NiMo/γ-Al2O3 catalyst in an isothermal batch reactor. A method was used to characterize the feedstock and the hydrotreating products from their TGA data by applying a proposed correlation equation for converting thermogravimetric measurements into simulated distillation results. Then, these estimated simulated distillation curves were used to obtain finally their characterization by composition based on real components.A chemical reaction network of four lumps along with its lumped kinetic model representing the hydrotreating of castor oil methyl esters was obtained from experiments conducted in a batch reactor operating under isothermal conditions at 395, 410, and 425 °C, 50 barg, and with reaction times from 2 to 4 h, and it was found that at severe operating conditions the yield and product selectivity of kerosene fraction increases, therefore, in order to obtain a higher production of renewable diesel fraction in this reaction system, the hydrotreating reaction time and temperature must be moderate.

Numerical approximation of a two-dimensional non-equilibrium model of non-isothermal liquid chromatography considering core-shell particles

A nonlinear and non-isothermal two-dimensional lumped kinetic model (2D LKM) is solved numerically to simulate the transport of multi-component mixtures in fixed-bed liquid chromatographic columns of cylindrical geometry packed with core-shell particles. The model considers axial and radial dispersions, interfacial mass, and heat transfers, nonlinear adsorption, and rectangular pulse injections. It is formed by a nonlinear system of partial differential equations coupled with differential and algebraic equations. A semi-discrete high-resolution finite volume scheme (HR-FVS) is extended and applied to approximate the model equations. A few case studies related to single and multi-component elution are considered to illustrate the effects of important parameters, such as core radius fraction, enthalpy of adsorption, radial and axial-dispersion coefficients, equilibrium constant, as well as film mass and heat transfer coefficients. A typical performance criterion is adopted to quantify the influence of thermal effects on the process performance and to evaluate the optimum value of inert core radius. The results obtained in various case studies are useful for understanding and upgrading liquid chromatographic processes considering non-isothermal conditions and core-shell particles.

Non-catalytic supercritical water partial oxidation mechanism of coal

Supercritical water partial oxidation (SCWPO) is a clean and efficient coal conversion method to produce H2. However, the detailed SCWPO mechanism of coal is still unknown at present. In this paper, a lumped kinetic model is used to propose a non-catalytic SCWPO mechanism of coal. The results show that oxidation reaction of intermediate carbon is under diffusion control. Bituminous coal is harder to be gasified than lignite, due to the denser structure of bituminous coal. CH4 is produced only from coal pyrolysis, and it is negligible for steam reforming of CH4 without catalyst. The ash in coal plays a certain catalysis on water-gas shift reaction. The proposed mechanism provides important insights in SCWPO process of coal.

Identification of Reaction Pathways and Kinetic Modeling of Olefin Interconversion over an H-ZSM-5 Catalyst

Kinetic investigations with a commercial H-ZSM-5 catalyst were performed to enable the modeling of the interconversion reactions of olefins in a temperature range from 420 to 490 °C. Different olefin feedstocks ranging from C2 up to C7 were investigated using a Berty-type reactor. Additional mixed olefin feedstock experiments were performed to obtain improved information about the bimolecular reaction pathways. The experiments include a wide range of conversions to cover the full range of typical industrial process conditions. The reaction pathways and the rate law approach of olefin cracking were analyzed systematically to identify a suitable and comprehensive model structure. A lumped kinetic model with 11 interconversion reactions based on a Langmuir–Hinshelwood–Hougen–Watson approach is found to be the best trade-off between accuracy and model complexity. The comparison between the model and experiments demonstrates that the kinetic model can predict the olefin behavior with a high accuracy for mixed as well as single olefin feedstock. A detailed kinetic model for the formation of side products has also been derived but will be discussed separately in another publication on hydrogen transfer on H-ZSM-5. Compared to existing kinetic models, the kinetic model proposed in this work shows distinct advantages because of the use of mixed feedstock, the widest range of conversions investigated so far, the use of a gradient-free and isothermal Berty-type reactor, and high-performance online gas chromatography analytics.

Simulation of nonisothermal reactive liquid chromatography using two‐dimensional lumped kinetic model

AbstractA nonisothermal two‐dimensional lumped kinetic model of reactive liquid chromatography is formulated and applied to simulate the separation of multicomponent mixtures in a fixed‐bed cylindrical column operating under nonisothermal condition. The axial and radial variations of concentration and temperature as well as reversibility of the chemical reactions are incorporated in the model equations. The model comprises a system of convection‐diffusion‐reaction partial differential equations coupled with algebraic and differential equations. Due to the nonlinearity of adsorption and reaction kinetics, it is required to apply an accurate numerical scheme for solving the model equations. In this study, an efficient and accurate high‐resolution flux‐limiting finite‐volume scheme is proposed to solve the model equations. A number of stoichiometrical reactions are numerically simulated to determine the level of coupling between the temperature and concentration profiles. Moreover, the effects of various critical parameters on the process performance are examined. The results obtained are beneficial for understanding reaction and separation processes inside a liquid chromatographic reactor and to improve its performance.

Analysis of temperature variations in fixed-bed columns using non-isothermal and non-equilibrium transport model

A non-isothermal and non-equilibrium two-component lumped kinetic model of fixed-bed column liquid chromatography is formulated with the linearized isotherm and solved analytically to study the influence of temperature variations on the process. The model equations constitute a system of convection-diffusion PDE for mass and energy balances in the bulk phase coupled with differential equations for mass and energy balances in the stationary phase. The analytical solutions are derived for Dirichlet boundary conditions by implementing the Laplace transformation, Tschirnhaus-Vieta approach, the linear decomposition technique and an elementary solution technique of ODE. An efficient and accurate numerical Laplace inversion technique is applied to bring back the solution in the actual time domain. In order to validate the derived analytical solutions for concentration and temperature fronts, the high resolution upwind finite volume scheme is applied to approximate the model equations numerically. Various case studies are carried out assuming realistic model parameters. The results obtained will be beneficial for interpreting mass and energy profiles in non-equilibrium and non-isothermal liquid chromatographic columns and provide deeper insight into the sensitivity of the separation process without performing costly and time-consuming laboratory experiments.

A four kinetic model for delayed coking process of Qingdao vacuum residues

Batch coking reaction experiments of Qingdao vacuum residues were carried out in the temperature range of 420–480 °C and at reaction times in the range of 5–90 min. A four lump kinetic model was developed for delayed coking process of Qingdao vacuum residues. The feedstock and products were considered as a unique and three separated lumps, respectively, in the model. The product lumps were included gas (C1~C4), distillate (C5+~500 °C) and coke (toluene insoluble and 500+ °C). Reactions were assumed in first order and based on Arrhenius reaction rates. The kinetic model was developed to predict unconverted feed values and product yields. The results showed a very good agreement between the experimental yield and predicted yield of different pseudocuts was obtained.

Improved understanding of reaction kinetic identification problems using different nonlinear optimization algorithms

The correct answer regarding which nonlinear optimization algorithm should we use for a given problem is that “it depends.” In this paper, we would like to add that “it depends, but use multiple programs whenever possible.” Here we consider 23 algorithms, implemented in MATLAB, evaluating their performance both on a lumped kinetic model for vacuum gas oil hydrocracking and a few-step kinetic model for ethane pyrolysis; the former particularly raised our interest as the kinetic parameters have no reference values in such models. We can use the results of such a study to estimate model variance; moreover, the statistical analysis of the identified minimum values can also quantify the parameter uncertainty. We can also identify key operating conditions where the applied kinetic model shows the highest sensitivity to the identified parameters, opening up the possibility to further reduce the uncertainty by targeting additional experimental work or by refining the identification problem.

Model based strategies towards protein A resin lifetime optimization and supervision

The high cost of protein A resins drives the biopharmaceutical industry to maximize its lifetime, which is limited by several processes, usually referred to as resin aging. In this work, two model based strategies are presented, aiming to control and improve the resin lifetime. The first approach, purely statistical, enables qualitative monitoring of the column state and prediction of column performance indicators (e.g. yield, purity and dynamic binding capacity) from chromatographic on-line data (e.g. UV signal). The second one, referred to as hybrid modeling, is based on a lumped kinetic model, which includes two aging parameters fitted on several resin cycling experimental campaigns with varying cleaning procedures (CP). The first aging parameter accounts for binding capacity deterioration (caused by ligand degradation, leaching, and pore occlusion), while the second accounts for a decreased mass transfer rate (mainly caused by fouling). The hybrid model provides important insights into the prevailing aging mechanism as a function of the different CPs. In addition, it can be applied to model based CP optimization and yield forecasting with the capability of state estimation corrections based on on-line process information. Both approaches show promising results, which could help to significantly extend the resin lifetime. This comes along with increased understanding, reduced experimental effort, decreased cost of goods, and improved process robustness.

A Detailed Finite Element Model of Internal Short Circuit and Venting During Thermal Runaway in a 32650 Lithium-Ion Battery

The frequent accidents of power lithium-ion battery have become the major reason to hinder the development of electric vehicles. In this paper, the thermal runaway process for a 32650 battery is analyzed based on 300°C oven heating experiment in adiabatic rate calorimeter, the rise of temperature, the drop of voltage and the leakage of electrolyte are observed before exploding, which could be used as predictor variables for thermal runaway warning. A large number of smoke releases and diffuses after explosion, which could be utilized as a criterion for determining the explosion. And a lumped chemical reaction kinetics model coupled with three-dimensional heat transfer model is constructed for further discussion. The thermal runaway process of the battery could be accurately calculated by the coupled model. Thermal radiation plays a more important role in heat transfer than heat convection in the process of thermal runaway. The explosion happens when the temperature achieves around 230°C, and the active material mainly starts to decompose at this moment.

Ebullated bed process for high conversion of heavy hydrocarbons with a low sediment yield

One of the commercial means to convert heavy oil residue is hydrocracking in an ebullated bed. The ebullated bed reactor includes a complex gas–liquid–solid backmixed system which attracts the attention of many scientists and research groups. This work is aimed at the calculation of the internal recycle flow rate and understanding its effect on other parameters of the ebullated bed. Measured data were collected from an industrial scale residual hydrocracking unit consisting of a cascade of three ebullated bed reactors. A simplified block model of the ebullated bed reactors was created in Aspen Plus and fed with measured data. For reaction yield calculation, a lumped kinetic model was used. The model was verified by comparing experimental and calculated distillation curves as well as the calculated and measured reactor inlet temperature. Influence of the feed rate on the recycle ratio (recycle to feed flow rate) was estimated. A relation between the recycle flow rate, pump pressure difference and catalyst inventory has been identified. The recycle ratio also affects the temperature gradient along the reactor cascade. Influence of the recycle ratio on the temperature gradient decreased with the cascade member order.

The wet oxidation of aqueous humic acids

Humic acids are highly distributed in aqueous environments. This article examines in depth the advanced oxidation of humic acid aqueous solutions, in order to understand more complex oxidation processes such as those of the sewage sludge or landfill leachate, or the matrix effects triggered by the humic acids of natural organic matter (NOM) in the oxidation of other aqueous compounds as herbicides.Humic acids were efficiently oxidized; higher temperatures (180−220 °C) involved higher mineralization, the formation of intermediates with lower colour and also led to a higher concentration of organic acids at the end of the treatment, particularly acetic and oxalic ones. Nevertheless, humic acid wet oxidation was not sensitive to changes in the pressure, at least in the range tested (65−95 bar), but the initial pH (4–13) was found to be a key factor. Thus, alkaline media accelerated the humic acid removal, but more refractory intermediates were generated, and the organic acids, excepting malic acid, were more stable than in neutral or acidic media. Eventually, a lumped kinetic model was proposed and successfully fitted to the experimental data, including the effect of all the operating variables studied.