Lumped Kinetic Model Research Articles

Theoretical Analysis of a Nonequilibrium Transport Model of Two-Dimensional Nonisothermal Reactive Chromatography Accounting for Bi-Langmuir Isotherm.

The current study investigates a nonequilibrium and nonlinear two-dimensional lumped kinetic transport model of nonisothermal reactive liquid chromatography, considering the Bi-Langmuir adsorption isotherm, heterogeneous reaction rates, radial and axial concentration variations, and the adsorption and reaction enthalpies. The mathematical models of packed bed chromatographic processes are expressed by a highly nonlinear system of coupled partial differential algebraic equations connecting the phenomena of convection, diffusion, and reaction, for mass and energy balance, the differential algebraic equations for mass balance in the solid phase, and the algebraical expressions for the adsorption isotherms and for the reaction rates. The nonlinearity of the reaction term and the adsorption isotherm preclude the derivation of an analytical solution for the model equations. For this reason, a semidiscrete, high-resolution, finite-volume technique is extended and employed in this study to obtain the numerical solution. Several consistency checks are performed to evaluate the model predictions and analyze the precision of the proposed numerical scheme. A number of heterogeneously catalyzed stoichiometric reactions are numerically simulated to examine reactor performance under the influence of temperature and Bi-Langmuir adsorption dynamics, the level of coupling between mass and energy fronts, and to study the effects of various critical parameters. The numerical results obtained are beneficial for optimal predictive control and process optimization during production and the development of methods for systematic design and fault detection of nonisothermal liquid chromatographic reactors, and hence constitute the first step to provide deeper insight into the overall evaluation of integrated reaction and separation processes.

Study on the Preparation of Clean Liquid Fuel by Wide Fraction High-Temperature Coal Tar Deep Hydro-Upgrading on a Pilot Plant Trickle Bed Reactor.

High-temperature coal tar contains a high content of heavy components, and the mechanism of its hydrogenation to fuel oil has not been completely revealed at present. In this work, clean environmental friendly fuel oil was obtained from wide fraction high-temperature coal tar (WHTCT) hydrotreated in a three-stage continuous pilot-scale trickle bed reactor filled with commercial catalysts. The effect of reaction temperature (345-405 °C), reaction pressure (10-18 MPa), and LHSV (0.2-0.4 h-1) on the product properties was investigated while the hydrogen/oil ratio remained constant (2000:1). Simultaneously, four lumped kinetic models were established to study the effects of reaction conditions on each component and interconversion between them. The results showed that the increase in temperature and pressure and the decrease in LHSV can effectively improve the quality of products. Under the reaction conditions of a temperature of 390 °C, a pressure of 16 MPa, an LHSV of 0.25 h-1, and a hydrogen/oil ratio of 2000:1, the S and N in the feedstocks can be reduced from 4600 and 6800 μg/g to 24.06 and 14.32 μg/g in the products, respectively. So WHTCT can be used as a suitable feed to obtain gasoline and low-freezing point diesel blending components through hydrogenation. Tail oil (TO) can easily be converted into diesel fraction (DF) and gasoline fraction (GF) with high selectivity. DF can be converted into GF only at higher temperatures, and GF hardly undergoes cracking to gas. The established kinetic model can accurately predict the content of TO, DF, GF, and gas of the products. Therefore, the results can provide a certain valuable reference for further development of industrial applications.

Mathematical Modeling and Experiments on Pyrolysis of Walnut Shells Using a Fixed-Bed Reactor

Pyrolysis is a low-emission and sustainable thermochemical technique used in the production of biofuels, which can be used as an alternative to fossil fuels. Understanding the kinetic characterization of biomass pyrolysis is essential for process upscaling and optimization. There is no accepted model that can predict pyrolysis kinetics over a wide range of pyrolysis conditions and biomass types. This study investigates whether or not the classical lumped kinetic model with a three-competitive reaction scheme can accurately predict the walnut shell pyrolysis product yields. The experimental data were obtained from walnut shell pyrolysis experiments at different temperatures (300–600 °C) using a fixed-bed reactor. The chosen reaction scheme was in good agreement with our experimental data for low temperatures, where the primary degradation of biomass occurred (300 and 400 °C). However, at higher temperatures, there was less agreement with the model, indicating that some other reactions may occur at such temperatures. Hence, further studies are needed to investigate the use of detailed reaction schemes to accurately predict the char, tar, and gas yields for all types of biomass pyrolysis.

Numerical simulation of the general rate model of chromatography using orthogonal collocation

Process chromatography is a critical manufacturing step in the purification of biopharmaceutical therapeutics and monoclonal Antibody (mAb) capture using Protein A-chromatography is the most expensive step in the entire production chain. Protein A-chromatography performance is hard to predict due to variations in chromatography column characteristics causing wastage and reduced efficiency. Additionally, it is not yet established how to use Protein A-chromatography optimally in continuous manufacturing. Mechanistic modeling of the chromatography process enables simulation-based optimization of operations to both reduce waste and increase productivity in continuous manufacturing. We present an easy-to-use, yet computationally efficient Python package called Simulation Testbed for Liquid Chromatography (STLC). STLC is a chromatography simulator implementing a solver for the General rate model, a comprehensive mathematical model in the field, and the simplified Lumped kinetic model. STLC uses orthogonal collocation to discretize the spatial domain turning the equations into an algebraic system of ordinary differential equations. The equations are integrated in time with a fixed step length backward Euler method. We evaluate STLC in numerical trials and benchmark against high-resolution references showing high-order convergence. This allows for reduced computation system size making the package a good choice for use in the rapid prototyping of simulated chromatography processes.

A Review on Lumped-Kinetic Modelling Methodologies for an industrial FCCU - riser reactor for catalytic cracking

A comprehensive review of scientific literature on various lumped kinetic models used in modelling FluidisedCatalytic Cracking Units (FCCU) used in the petrochemical industry has been done, along with a brief introductionto the working of FCCU. The most popular four lumped kinetic model has been discussed in detail along with themathematical model and then solved using MATLAB. The modified form of the model that considers axialdispersion has also been discussed. The results of the simulation have been plotted and analysed. A brief overviewof three, five, six, seven, nine, and twelve lumped kinetic models has also been discussed.

Magnetic CoFe2O4@carbon yolk-shell nanoparticles as catalysts for the catalytic wet peroxide oxidation of paracetamol: kinetic insights

<p>This work focuses on the use of carbon-coated magnetic cobalt ferrite nanoparticles as catalysts for catalytic wet peroxide oxidation (CWPO) of the emerging concern pollutant paracetamol (PCM). The magnetic core of the catalyst is composed of CoFe2O4 developed by a sol-gel method. The core is subsequently coated with a formaldehyde-resorcinol resin and TEOS, further carbonized at 600 ºC, and etched with NaOH to create a yolk-shell structure denoted as CoFe2O4@void@C. X-ray diffraction (XRD), transmission electron microscopy (TEM), and Fourier transformed infra-red (FTIR) analysis revealed that the uncoated core is composed of a CoFe2O4 cubic spinel structure with a crystallite size of 53 nm calculated using the Williamson-Hall (W-H) method, matching very well the average size observed by TEM (53.51  4.2 nm). Comparing the performances of CoFe2O4@void@C and the bare CoFe2O4 in the CWPO of paracetamol, total organic carbon (TOC) removals of 58% and 46% are obtained respectively after 24 h of reaction. An empirical kinetic model based on second-order and autocatalytic expressions was developed to suitably describe the decomposition of H2O2 and the removal of paracetamol using CoFe2O4@void@C as catalyst. The disappearance of TOC was well-described (r2 = 0.98) by a lumped kinetic model as the sum of TOCA, TOCB and TOCC, where TOCA is the TOC of the PCM, TOCB refers the intermediate products and TOCC is the TOC of the final products obtained during the CWPO of PCM.</p>

Numerical Approximation of the Nonequilibrium Model of Gradient Elution Chromatography Considering Linear and Nonlinear Solvent Strength Models.

In both linear and nonlinear chromatography, the lumped kinetic model is a suitable model for predicting elution bands when appropriate equilibrium functions and mass transfer coefficients are accessible. This model also works well in the case of gradient elution chromatography if variations in the equilibrium functions due to changes in the mobile phase composition are known. The rational selection of an optimum gradient is explored in this study from three different perspectives using the lumped kinetic model. Elution profiles generated by using (a) linear solvent strength, (b) quadratic solvent strength, and (c) power law are investigated. The effectiveness and reliability of the suggested numerical approach, utilizing the flux-limiting finite volume method, are demonstrated through numerical simulations. The impacts of axial dispersion, nonlinearity coefficient, Henry’s constant, mass transfer coefficient, and gradient parameters are studied on single and two-component elution profiles.

Analysis of reaction path and different lumped kinetic models for asphaltene hydrocracking

The product distribution of asphaltenes hydrocracking was studied in an autoclave with decalin as the liquid-phase system at different reaction temperatures and times to elucidate the relevant reaction mechanism. The results showed that the reaction products might be reversely condensed to generate secondary asphaltenes, resulting in a trend of first increasing and then decreasing the yields of some products at 420 °C. The significant yield increase of gas and gasoline at 420 °C might be due to the cracking of saturated and aromatic fractions to form light fractions. The conclusion was drawn the reaction behavior of asphaltenes hydrocracking under the research conditions followed the first-order reversible reaction kinetics by the reaction kinetic analysis, which further supported the inference that some products could recondense to form secondary asphaltenes. The four-lumped, five-lumped, and six-lumped models were constructed to study in depth the reaction behavior of asphaltene hydrocracking in the current system, and the results showed that the more similar the structure and composition of the reaction products to asphaltenes, the faster the reaction rate of their condensation to asphaltenes. Furthermore, the higher the temperature was more favorable to improve the selectivity and yield of transportation fuel diesel under the temperature of 380 °C-420 °C by the analysis of the ratio of rate constant. Although the applicability of lumped model was not positively correlated with the number of lumps, it is concluded that the six lumped model was the best model among the three models from the combined analysis of the applicability and the richness of the reaction information of the model.

A Novel Numerical Treatment of Nonlinear and Nonequilibrium Model of Gradient Elution Chromatography considering Core-Shell Particles in the Column

An extended method of semidiscrete high-resolution finite volume is used in this paper to obtain numerical solutions for a formulated nonlinear lumped kinetic model of liquid chromatographic process to examine the effect of chromatographic column overloading gradient elution considering core-shell particles. The model constitutes linear solvent strength (LSS), Henry’s constant, coefficient of nonlinearity, and coefficient of axial dispersion. The effects of modulator concentration changes for the elution of single and two components are analyzed. The advantages of introducing gradient elution against isocratic elution in terms of core radius fraction are investigated intensively. Numerical temporal moments are generated from the solutions obtained for a more in-depth examination of the considered model. Moreover, multiple forms of a single- and two-component mixture are generated to analyze the influences of core radius fractions on gradient elution. For example, the obtained results are utilized to investigate the effects of the slope of gradient, concentration of modulator, solvent strength parameter, coefficient of nonlinearity, coefficient of mass transfer, and coefficient of axial dispersion on the profiles of concentration in order to improve the process performance using optimal core radius fraction parameter values.

Lumped kinetic modelling of polyolefin pyrolysis: A non-isothermal method to estimate rate constants

The measurement of kinetic parameters in the pyrolysis of polyolefins requires the use of a lumped kinetic model for predicting the product distribution of wax, oil and gas yields. A non-isothermal method was established, in which a sample is heated in a tube reactor to a desired temperature at a constant rate of temperature rise. This method avoided the error present in the heating up stage which is inherent in any practical isothermal method in which reaction proceeds to a significant extent before the operating temperatures of polyolefin pyrolysis are reached, which results in challenges when defining the reaction time. The non-isothermal measurements were conducted between 450 and 550 °C for polypropylene (PP) and polyethylene (HDPE and LDPE) and the temperature and lump yields are non-linearly regressed to achieve the kinetic parameters. The measured kinetic rate constants have the same trend as those reported in the literature using the isothermal method, but are lower than the values reported at similar conditions. The kinetic parameters derived are then validated by using isothermal experimental data. The calculated data using the measured kinetic parameters are generally in agreement with the experimental data. The non-isothermal method established in this work proves to be a much faster method for the measurement of intrinsic rate constants at high temperatures.

Simulations of liquid chromatography using two-dimensional non-equilibrium lumped kinetic model with bi-Langmuir isotherm

A two-dimensional non-equilibrium and non-linear lumped kinetic model of liquid chromatography is formulated and numerically approximated to simulate the separation of multi-component mixtures in a packed fixed bed cylindrical column operating under isothermal conditions. The model equations incorporate the bi-Langmuir adsorption thermo-dynamics as well as the radial and axial variations of concentration. By introducing distinct regions of injection at the column inlet, radial concentration gradients are generated to intensify the effect of mass transfer rate in the radial-direction, inside the column. The mathematical model is developed by a system of non-linear convection-diffusion partial differential equations for mass balance in the mobile phase, coupled with differential equation for mass balance in the stationary phase and algebraic equations for adsorption isotherm. In this study, a high-resolution, semi-discrete, finite-volume technique is formulated and applied to gain the numerical solution of the governing non-linear-model equations. A few numerical case studies are performed to investigate the effects of the various critical parameters on the process performance. The developed numerical algorithm provide an efficacious mechanism for investigating the retention behavior, systematic monitoring and efficient operation of non-equilibrium, liquid chromatographic processes.

Optimisation of the degradation of 4-nitrophenol by Fenton's process

Processes optimisation is one of the main issues to take into account for the design of new chemical processes applied to wastewater treatment plants (WWTPs). Particularly, it can be achieved using design of experiments (DoE) tools, and can represent progress in the process performance and cost reduction. In this work, an advanced oxidation process (AOP), namely Fenton's process, is applied to degrade a nitrophenol model compound, i.e., 4-nitrophenol (4NP), in a lab-scale batch reactor. To optimise the process parameters (such as the temperature of the reaction - T, and the initial concentrations of hydrogen peroxide – [H2O2] – and ferrous ion – [Fe2+]), DoE was applied, namely central composite design (CCD) and response surface methodology (RSM). The 4NP degradation and mineralisation were evaluated as process outputs. The maximum 4NP and TOC removals (100 and 49.2%, respectively) and a non-toxic effluent (determined by the inhibition of Vibrio fischeri bacteria) were achieved after 60 min of reaction using the optimum conditions provided by the model (T = 70.2 °C, [H2O2] = 2.945 g/L and [Fe2+] = 5.9 mg/L). Some strategies, i.e. gradual addition of H2O2 and UV/visible radiation application, were still adopted to increase the mineralisation. However, the complete removal of 4NP and 80% of mineralisation was achieved when the Fenton process was assisted with UV/visible radiation. The lumped kinetic model (LKM) proposed, and used for the first time to describe the mineralisation of 4NP by Fenton's reaction, described well the profile of the residual carbon (i.e., the fraction of carbon not mineralised) during the treatment time for these experiments.

Size-Controlled Nanoparticles Embedded in a Mesoporous Architecture Leading to Efficient and Selective Hydrogenolysis of Polyolefins.

A catalytic architecture, comprising a mesoporous silica shell surrounding platinum nanoparticles (NPs) supported on a solid silica sphere (mSiO2/Pt-X/SiO2; X is the mean NP diameter), catalyzes hydrogenolysis of melt-phase polyethylene (PE) into a narrow C23-centered distribution of hydrocarbons in high yield using very low Pt loadings (∼10-5 g Pt/g PE). During catalysis, a polymer chain enters a pore and contacts a Pt NP where the C-C bond cleavage occurs and then the smaller fragment exits the pore. mSiO2/Pt/SiO2 resists sintering or leaching of Pt and provides high yields of liquids; however, many structural and chemical effects on catalysis are not yet resolved. Here, we report the effects of Pt NP size on activity and selectivity in PE hydrogenolysis. Time-dependent conversion and yields and a lumped kinetics model based on the competitive adsorption of long vs short chains reveal that the activity of catalytic material is highest with the smallest NPs, consistent with a structure-sensitive reaction. Remarkably, the three mSiO2/Pt-X/SiO2 catalysts give equivalent selectivity. We propose that mesoscale pores in the catalytic architecture template the C23-centered distribution, whereas the active Pt sites influence the carbon-carbon bond cleavage rate. This conclusion provides a framework for catalyst design by separating the C-C bond cleavage activity at catalytic sites from selectivity for chain lengths of the products influenced by the structure of the catalytic architecture. The increased activity, selectivity, efficiency, and lifetime obtained using this architecture highlight the benefits of localized and confined environments for isolated catalytic particles under condensed-phase reaction conditions.

Combining multivariate curve resolution and lumped kinetic modelling for the analysis of lignin degradation by copper-catalyzed Fenton-like systems

Efficient lignin degradation was achieved by dark cupro-Fenton treatment. Optimal conditions were assessed by using OED and SRM. Kinetic profiles obtained by MCR-ALS decomposition of UV-vis spectra allowed the development of a lumped kinetic model.

Gasification of horse dung in supercritical water

Horse dung naturally contains phosphorus and nitrogen which affect the environment negatively, if the nutrients are not recovered and utilized. In this paper, the influence of alkali on the gasification of horse dung at 560 °C, 25 MPa was investigated. The results show that LiOH addition increased H2 fraction and the gas yield. The precipitated alkali in the reactor still showed high catalytic effect on the subsequent gasification of horse dung without further adding the alkali. A novel 4-lump kinetic model for horse dung in SCWG including feedstock, CH4, CO, and CO2 lumps is proposed.

High-Temperature Pyrolysis and Combustion of C5–C19 Fatty Acid Methyl Esters (FAMEs): A Lumped Kinetic Modeling Study

In the effort to mitigate the depletion of fossil fuels and climate change, biodiesels are considered to be one of the most suitable substitutes for petro-diesel in compression ignition engine applications. As a follow up to prior modeling studies for gasoline and jet surrogate fuel components (Zhang, X.; Mani Sarathy, S. Fuel, 2021, 286, 119361), this work proposes a lumped kinetic model for both saturated and unsaturated C5–C19 fatty acid methyl esters (FAMEs) based on the same methodology. The present lumped model includes 52 FAME fuel components, covering a wide range of biodiesel surrogate fuel components, as well as components typically found in biodiesels. This methodology decouples the combustion of FAME fuels into two stages: the pyrolysis of fuel molecules and the oxidation of pyrolysis intermediates. Lumped reaction steps are used to describe the (oxidative) pyrolysis of each fuel molecule, while a detailed model (Aramcomech 2.0) is adopted as the base mechanism to describe the subsequent conversion of these key intermediates. Rate rules adopted for all the FAME fuels are consistent. The present lumped model is validated against experimental data from 20 pure FAMEs and six diesel/biodiesel surrogates, including around 130 sets of validation data. In general, the present lumped model satisfactorily captures most of these validation targets. This lumped model performs comparably with the detailed models developed in the literature under combustion conditions. Combined with the lumped model for 50 hydrocarbon fuels developed in previous work by this group, the lumped kinetic model for FAME fuels developed here can be used to predict the pyrolysis and combustion chemistry of diesel/biodiesel surrogates in CFD simulations after necessary model reduction for the base model. Also, the stoichiometric parameters of the lumped reactions for various pure FAMEs can be used as the database for data science study in FGMech development for real biodiesels.

Prediction of product distribution in the delayed coking of Iranian vacuum residue

The delayed Coker process as an upgrading process has main impact on the productivity of the Refinery Complexes. To determine the impact of different operating conditions on the product yield distribution of the delayed coking process, several experiments were designed and conducted in a prefabricated pilot plant. The experiments were conducted on different Iranian vacuum residues at temperatures ranging from 420°C to 480°C and at atmospheric pressure. Reaction times were within the range of 5-120 minutes. A four lumps kinetic model has been developed based on the experimental results. The lumps—which included Volatile products, coke, feed, and an intermediate phase between coke and feed—were defined to precisely monitor the yield distribution of products throughout the reaction time. The feedstocks utilized were three different vacuum residues and their blends. The mixtures were produced by using different mixing ratios of the three vacuum residues. The Statistical analysis shows that this model has R-squared, RMSE, SSE, and MRE equal to 0.99, 0.022, 0.08, and 3.537%, respectively. This shows that the developed model is sufficiently accurate. The experimental and modeling results in this research reveal that by increasing the temperature, the yield of coke and gas is abated. However, the yield of the distillate is escalated. This investigation illustrates that the production of an intermediate reaction has the highest amount of activation energy in comparison with the other reactions. Also, the results indicate that the production reaction rate of coke has the highest amount in comparison with other reactions.

Development and experimental validation of reactor kinetic model for catalytic cracking of eugenol, a potential bio additive fuel blend

Abstract An integrated kinetic model representing catalytic cracking of eugenol in a fixed bed reactor is developed. Eugenol, a major component of clove oil can act as the most potential bio additive fuel for improving the diesel quality thereby reducing the exhaust emission of the engine. The proposed integrated model includes four lump kinetic model which is plugged with catalyst deactivation model. The reactor design parameters are also included in the integrated model. The effectiveness of the proposed integrated model is compared with the conventional kinetic models and the results are presented. The proposed integrated model is validated against the real time data obtained by conducting an experiment in a real time setup with MoS2(Ni2P) Al-SBA-15(10) as the catalyst. The advantages of the proposed integrated model are highlighted.

Hybrid Models for the simulation and prediction of chromatographic processes for protein capture

The biopharmaceutical industries are continuously faced with the pressure to reduce the development costs and accelerate development time scales. The traditional approach of heuristic-based or platform process-based optimization is soon getting obsolete, and more generalized tools for process development and optimization are required to keep pace with the emerging trends. Thus, advanced model-based methods that can reduce the can ensure accelerated development of robust processes with minimal experiments are necessary. Though mechanistic models for chromatography are quite popular, their success is limited by the need to have accurate knowledge of adsorption isotherms and mass transfer kinetics. As an alternative, in this work, a hybrid modeling approach is proposed. Thereby, the chromatographic unit behavior is learned by a combination of neural network and mechanistic model while fitting suitable experimental breakthrough curves. Since this approach does not require identifying suitable mechanistic assumptions for all the phenomena, it can be developed with lower effort. Thus, allowing the scientists to concentrate their focus on process development. The performance of the hybrid model is compared with the mechanistic Lumped kinetic Model for in-silico data and experiments conducted on a system of industrial relevance. The flexibility of the hybrid modeling approach results in about three times higher accuracies compared to Lumped Kinetic Model. This is validated for five different isotherm models used to simulate data, with the hybrid model showing about two to three times lower prediction errors in all the cases. Not only in prediction, but we could also show that the hybrid model is more robust in extrapolating across process conditions with about three times lower error than the LKM. Additionally, it could be demonstrated that an appropriately tailored formulation of the hybrid model can be used to generate representations for the underlying principles such as adsorption equilibria and mass transfer kinetics.

Numerical approximation of nonlinear and non-equilibrium model of gradient elution chromatography

A nonlinear lumped kinetic model of liquid chromatography is formulated and solved numerically to theoretically investigate the effect of column overloading on gradient elution. Linear solvent strength (LSS) model is utilized for Henry’s constant, non linearity coefficient and axial dispersion coefficient. A semi-discrete high-resolution finite volume scheme is extended and applied to obtain the approximate solutions of the governing model equations. The effects of changing modulator concentration are examined on the single and two-component elution. The benefits of gradient elution over isocratic elution are thoroughly discussed. The influences of optimizing free-parameters available in gradient chromatography are analyzed on the efficiency of the column and on the production of targeted components. For instance, the results obtained are used to study the effects of gradient slope, modulator concentration, solvent strength, nonlinearity coefficient, mass transfer coefficient, and axial dispersion coefficient on the concentration profiles.