Macrokinetic Model Research Articles

A Python tool for parameter estimation of “black box” macro- and micro-kinetic models with Bayesian optimization – petBOA

We develop an open-source Python-based Parameter Estimation Tool utilizing Bayesian Optimization (petBOA) with a unique wrapper interface for gradient-free parameter estimation of expensive black-box kinetic models. We provide examples for Python macrokinetic and microkinetic modeling (MKM) tools, such as Cantera and OpenMKM. petBOA leverages surrogate Gaussian processes to approximate and minimize the objective function designed for parameter estimation. Bayesian Optimization (BO) is implemented using the open-source BoTorch toolkit. petBOA employs local and global sensitivity analyses to identify important parameters optimized against experimental data, and leverages pMuTT for consistent kinetic and thermodynamic parameters while perturbing species binding energies within the typical error of conventional DFT exchange-correlation functionals (20-30 kJ/mol). The source code and documentation are hosted on GitHub. Program summaryProgram title: petBOACPC Library link to program files:https://doi.org/10.17632/hwwvksbb75.1Developer's repository link: https://github.com/VlachosGroup/petBOALicensing provisions: MIT licenseProgramming language: PythonExternal routines: NEXTorch, PyTorch, GPyTorch, BoTorch, Matplotlib, PyDOE2, NumPy, SciPy, pandas, pMuTT, SALib, docker.Nature of the problem: An open-source, gradient-free parameter estimation of black-box microkinetic modeling tools, such as OpenMKM is lacking.Solution method: petBOA is a Python-based tool that utilizes Bayesian Optimization and offers a unique wrapper interface for expensive black-box kinetic models. It leverages the pMuTT library for consistent kinetic and thermodynamic parameter estimation and employs both local and global sensitivity analyses to identify crucial parameters.

Effect of isosymmetric phase transition in MIEC perovskite on the kinetic parameters of its interaction with oxygen

Oxygen partial pressure relaxation technique was used to study transient kinetics of re-equilibration in the reaction of nonstoichiometric oxide Ba0.5Sr0.5Co0.75Fe0.2Mo0.05O3-δ with oxygen within a region of 3-δ stoichiometry close to the nominal oxidation state 3+ for cobalt where an isosymmetric phase transition cubic perovskite P1 – cubic perovskite P2 is observed. The relaxation data were analyzed using a macrokinetic model that explicitly takes into account the power-law dependence of the surface reaction rate on the oxygen partial pressure. A twofold decrease in the power-law exponent (n = 0.7 to n = 0.3) was found at the point of the P1-P2 phase transition, which indicates a change in the mechanism of the rate-determining step of the reaction caused by the transition. At the same time, the functional dependence of the diffusion mobility of oxygen vacancies on the equilibrium oxygen pressure does not change at the transition point, which means that the transition does not affect the mechanism of bulk vacancy mobility.

Synthesis in Nb + 2Si Mixtures Produced in Different Modes of Discrete Mechanical Activation

An experimental study is performed of the two-stage mechanochemical synthesis of niobium silicide. Theoretical estimates are made on the basis of the resulting macrokinetic model. The initial Nb + 2Si mixture is mechanically activated in the first stage, and the NbSi2 product is synthesized in the second. The effect the period of mechanical treatment has on the activated mixture’s morphology, temperature, and rate of burning is studied, along with the phase composition of the final reaction product. Kinetic constants are calculated that describe the dynamics of the two-stage mechanochemical synthesis of niobium silicide.

Cross-Linking Mechanisms of a Rigid Plant Oil-Based Thermoset from Furfural-Derived Cyclobutane

cis-Cyclobutane-1,2-dicarbocylic acid (CBDA-2) was synthesized and used as a biobased hardener to cross-link epoxidized linseed oil to produce a fully biobased thermoset. The polymerization mechanism was studied by means of real-time attenuated total reflection-Fourier transform infrared (ATR-FTIR), differential scanning calorimetry (DSC), stochastically modulated temperature DSC, and rheometry. The study highlights the importance of hydrogen bonding of CBDA-2 and catalytic effect of hydroxyl groups created during the reaction. Evolution of reactive functions with temperature and time, variation of activation energy, and pre-exponential factor was correlated to macroscopic changes, such as heat capacity variations and chemorheology. A macrokinetic model was proposed to describe the complete polymerization mechanism. It is shown that the obtained parameters accurately describe the polymerization using parameters with a real physical meaning.

Ultrasonic-enhanced sulfuric acid leaching kinetics of high-grade germanium-containing materials

The study is based on the application of sulfuric acid in germanium leaching process, the leaching kinetic of high grade germanium-containing materials with sulfuric acid as solvent under ultrasonic assistance was studied. The influences of reaction temperature, sulfuric acid concentration and ultrasonic power on germanium leaching process were investigated.The results showed that when the sulfuric acid concentration was 110 g/L, the leaching temperature was 90 °C the leaching time was 30 min, the liquid-solid ratio was 10, and the ultrasonic power was 700 W, the germanium leaching effect was the best, and the leaching efficiency reached 92%.The leaching reaction process of germanium conforms to the unreacted shrinking core model. In the reaction process, loose product layer will be formed on the surface of the mineral, which hinders the diffusion of the leaching agent into the mineral. The leaching reaction control step of germanium in high-grade germanium-containing materials is internal diffusion control. According to the experimental data, the macro-kinetic model of the reaction was established, and the macro-kinetic equation was obtained with Ea (apparent activation energy) of 8.76 kJ/mol, A (pre-exponential factor) of 0.102.

Macrokinetic mechanosynthesis model comprising multidirectional factors characterizing the effect of mechanical treatment on the combustion of activated mixtures

A mathematical model was built using a new macrokinetic theory to investigate the mechanical treatment and two-step mechanochemical synthesis of inorganic substances in the mode of layer-by-layer combustion. Powders (SnO2, NiCrAl, Cu) and powder mixtures (SnO2 + Al, SnO2 + Si, Ti + Ni, Nb + Si) were used. The proposed macroscopic mathematical model expands the understanding of the macrokinetics of mechanochemical synthesis and identifies and classifies its mechanisms. The effect of mechanochemical pre-treatment on the mechanosynthesis of final products was taken into account by introducing the multidirectional parameters, such as structural (formation of the interfacial surface), kinetic (defect formation) and temperature factors, initial mechanochemical transformations, and formation of inert material due to the abrasion of milling tools. The inverse problem methods were proposed to determine the kinetic constants describing initial mechanochemical transformations and abrasion during mechanical activation.

Macrokinetic Models of Thermal Decomposition of Dolomite for Engineering Calculations

Macrokinetic Models of Thermal Decomposition of Dolomite for Engineering Calculations

ANALYSIS OF THE PARAMETERS OF DYNAMIC SUPERPLASTICITY THE INDUSTRIAL ALUMINUM ALLOYS

The problem of determining the features of the development of blurred phase transitions observed under conditions of dynamic superplasticity of aluminum alloys is solved using the specific heat capacity function. Within the framework of the developed model representations, the deformation mechanisms characteristic of superplasticity and boundary metastable states are analyzed using the Fokker-Planck equation. Using a macrokinetic model, an explicit expression is obtained for the function that characterizes the mechanism of grain boundary slippage (the “drift " coefficient) that prevails in superplasticity. By integrating the differential equations resulting from the model, the solution of which establishes the type of functions responsible for the implementation of the mechanisms of grain boundary slippage and diffusion processes. It is proposed that the diffusion coefficient is responsible for the accumulation of irreversible deformations outside the velocity range of superplasticity. The function responsible for the effects of grain boundary slippage (the "drift" coefficient) is particularly active towards the middle of the superplasticity velocity interval. It is confirmed that outside the velocity range of superplasticity, there is a redistribution of mass transfer forms, the responsibility for which is assigned to the diffusion coefficient. It is shown that the diffusion function shows a tendency to decrease when approaching the range of superplasticity rates. Metastable states are characterized by the competition of diffusion mechanisms and grain boundary slippage.

Modeling the selective oxidation of n-butane to maleic anhydride: From active site to industrial reactor

In this contribution to the Special Issue honoring 100 very successful years of Casale S.A., we review and critically discuss the current status of modeling the most demanding selective partial oxidation reaction industrially applied: the partial oxidation of n-butane to maleic anhydride. We examine theoretical model descriptions of this partial oxidation reaction covering all relevant length scales: from modeling the active site and elementary steps, microkinetic and macrokinetic models, to reactor models on all length scales from laboratory reactors up to industrial-size production reactors. We also include in our manuscript the latest CFD developments aiming at a better understanding of heat and mass transfer in industrial catalyst beds as well as effects of the local bed structure. The contribution also covers relevant experimental findings with respect to the catalytically active species or sites on the catalyst surface, the reaction mechanism as well as microkinetic considerations. 60 years of research have greatly improved our understanding of the selective partial oxidation reaction. However, a critical review of the different aspects of the n-butane oxidation and its industrially used catalyst reveals on all length scales that there still remain unanswered questions, and that there are still some inconsistencies in our fundamental understanding. This situation arises from the fact that the catalyst for n-butane partial oxidation is a highly complex and dynamic system and its performance depends on all details of its generation and its operational history.

Efficient Synthesis of α-FeOOH from Pickling Wastewater in Falling Film Tower and Its Kinetics.

An efficient way to synthesize α-FeOOH from pickling wastewater in a falling film tower was proposed for the first time. This method overcomes the shortcomings of the traditional air oxidation method, and its production efficiency is increased by 16 times. The purity of α-FeOOH synthesized from pickling wastewater can reach 96.3%, and the iron recovery rate is greater than 90%. At the same time, we have systematically studied its kinetics in the falling film tower. The reaction rate constant k at different temperatures was also determined with the activation energy Ea = 32.2497 kJ/mol and the pre-exponential A = 47.4132 s–1. In addition, based on the double-film theory, a corresponding macrokinetic model was established. Also, the Hatta number in the reaction system was obtained, which proved the excellent gas–liquid mass transfer performance in the falling film tower. This work provides a promising method for the efficient production of α-FeOOH and the recycling of pickling wastewater.

Macro-kinetic model for CuO–ZnO–ZrO2@SAPO-11 core-shell catalyst in the direct synthesis of DME from CO/CO2

An original kinetic model has been used to describe the performance of an original CuO–ZnO–ZrO2@SAPO-11 bifunctional catalyst on the one-stage synthesis of dimethyl ether (DME) from CO/CO2 hydrogenation. The model considers that certain individual reactions (the synthesis of methanol and the reverse water gas shift) occur in the metallic function (core) of the catalyst particle, whereas others (methanol dehydration) take place in the shell (acid function), and that the progress of these reactions is conditioned by the diffusion of the components. The kinetic parameters of the individual reactions and the deactivation kinetics have been calculated from experimental data obtained in a wide conditions range (H2/COx ratio, 2.5–4; CO2/COx ratio, 0–1; 10–50 bar; 250–325 °C; 1.25–20 g h molC−1). The use of the model for simulating the packed bed reactor has allowed evaluating the influence of the reaction conditions, as well as assessing the effect of the catalysts particle size. The model predicts DME yields of 64% for syngas (H2+CO) feeds, 38% for CO2/COx ratio of 0.50 and 17% for H2/CO2, respectively, at 70 bar and 290 °C. The maximum conversion of CO2 predicted by the model for the same space time value and temperature surpasses 30% for H2+CO2 feedstocks at 70 bar, greater than the experimental value obtained at 50 bar at the same temperature (∼25%).

Automated Conditional Screening of Multiple Escherichia coli Strains in Parallel Adaptive Fed-Batch Cultivations.

In bioprocess development, the host and the genetic construct for a new biomanufacturing process are selected in the early developmental stages. This decision, made at the screening scale with very limited information about the performance in larger reactors, has a major influence on the efficiency of the final process. To overcome this, scale-down approaches during screenings that show the real cell factory performance at industrial-like conditions are essential. We present a fully automated robotic facility with 24 parallel mini-bioreactors that is operated by a model-based adaptive input design framework for the characterization of clone libraries under scale-down conditions. The cultivation operation strategies are computed and continuously refined based on a macro-kinetic growth model that is continuously re-fitted to the available experimental data. The added value of the approach is demonstrated with 24 parallel fed-batch cultivations in a mini-bioreactor system with eight different Escherichia coli strains in triplicate. The 24 fed-batch cultivations were run under the desired conditions, generating sufficient information to define the fastest-growing strain in an environment with oscillating glucose concentrations similar to industrial-scale bioreactors.

A General Process-Based Model for Describing the Metabolic Shift in Microbial Cell Cultures.

The metabolic shift between respiration and fermentation at high glucose concentration is a widespread phenomenon in microbial world, and it is relevant for the biotechnological exploitation of microbial cell factories, affecting the achievement of high-cell-densities in bioreactors. Starting from a model already developed for the yeast Saccharomyces cerevisiae, based on the System Dynamics approach, a general process-based model for two prokaryotic species of biotechnological interest, such as Escherichia coli and Bacillus subtilis, is proposed. The model is based on the main assumption that glycolytic intermediates act as central catabolic hub regulating the shift between respiratory and fermentative pathways. Furthermore, the description of a mixed fermentation with secondary by-products, characteristic of bacterial metabolism, is explicitly considered. The model also represents the inhibitory effect on growth and metabolism of self-produced toxic compounds relevant in assessing the late phases of high-cell density culture. Model simulations reproduced data from experiments reported in the literature with different strains of non-recombinant and recombinant E. coli and B. subtilis cultured in both batch and fed-batch reactors. The proposed model, based on simple biological assumptions, is able to describe the main dynamics of two microbial species of relevant biotechnological interest. It demonstrates that a reductionist System Dynamics approach to formulate simplified macro-kinetic models can provide a robust representation of cell growth and accumulation in the medium of fermentation by-products.

4-Scale model for macromolecule conversion over mesoporous and hierarchical alumina catalysts

Mathematical model for macromolecule catalytic conversion in a flow reactor includes four interconnected numerical calculations of different scales for the following phenomena: effect of increasing the concentration of coke grains and their size (nanometers, scale of coke particles) on porosity, tortuosity, and specific area of the catalyst computing percolation graphs of the mesoporous and hierarchically porous catalysts (dozens of nanometers, scale of percolation graph); kinetic patterns for asphaltene conversion and catalyst deactivation in the mesoporous and hierarchically porous pellets (millimeters, catalyst pellet scale); macrokinetic model for reactor operation filled with mesoporous and hierarchically porous pellets (centimeters, reactor scale). Mathematical instruments involves both discrete (Lubachevsky-Stillinger, Dijkstra algorithm) and continuous (Fick’s law, kinetic equations) methods. Rate constants for kinetic modeling of the reactor operation were extracted by approximating the experimental points for the conversion of asphaltenes at the conditions close to industrial ones by numerically obtained curves. Striking difference in the texture evolution of mesoporous and hierarchical catalysts, observed by both catalytic experiments and theory, during asphaltene conversion (HDAs) resulted in fast deactivation of the first catalyst while the second one showed a long-term stability. The model is an excellent tool for the targeted design of high-performance hierarchical catalysts and catalytic layers and gives new possibilities in selection of the catalyst preparation ways.

Kinetic Model of Structural Relaxation in Diblock Copolymer Film

A relaxation model for the structure ripening under annealing of a microphase-separated polymer film has been developed. Equations have been derived that describe the appearance and annihilation of defects in the kinetically controlled mode based on the experimental data on the hexagonal structure evolution. Using that equations, the time dependences of the defect-free area size have been analyzed. It has been found that the predominance of the defect annihilation upon their triple contact leads to the power-law dependence of the orientation correlation length ξor ~ t1/4, which is observed experimentally at high annealing temperatures. A more detailed analysis of the evolution of two types of defects (dislocations and disclinations) shows that this dependence can also be realized in a model that takes into account the annihilation of disclination pairs and quadruples providing that dislocations influence this process. The results demonstrate that macrokinetic models can describe structural rearrangements in block copolymer films.

Elementary reaction pathway study and a deduced macrokinetic model for the unified understanding of Ni-catalyzed steam methane reforming

DFT based microkinetics and macrokinetics that give quantitative explanations of the Ni-catalyzed steam methane reforming reactions.

Investigation of a He micro plasma-jet utilized for treatment of prostate cancer cells

Present study investigated the applicability of the macro-kinetic description for RONS production by an atmospheric pressure micro-plasma jet operated in He gas flow. The concentrations of H2O2, NO2− and NO3− in the deionized water were measured using UV absorption spectroscopy. The contact and non-contact modes were identified and the concentrations of H2O2, NO2− and NO3− were higher in the contact mode. In the contact mode the concentrations of H2O2 and NO3− increased with the applied voltage and treatment duration while He flow rate also influenced the concentrations. The production rates of H2O2 and NO3− correlated with the amount of transferred charge of ionization waves during positive half period. The dependence of the production rates of RONS on the He flow rate suggests that the gas flow influences the gas composition in active discharge zone and limits the applicability of macro-kinetic model with the used plasma jet setup. As a potential application the plasma treated water was applied to prostate cancer cells. The viability of prostate cancer cell decreased linearly with the increase of H2O2 and NO3− concentrations while the NO2− concentration had no clear correlation with cell viability. The H2O2 was found to be the main agent responsible for the decreased cell viability. The amount of dissolved NO3− on the other hand determined the pH of the plasma treated water.

Three‐step macrokinetic model of butane and propane steam conversion to methane‐rich gas

AbstractLow‐temperature steam conversion (LTSC) of a methane‐butane mixture (95% methane and 5% butane) into a methane‐rich gas over an industrial Ni‐based catalyst has been studied with the following reaction conditions: temperature 200–320°C, pressure 1 bar, gas hour space velocity 1200–3600 h–1, and steam to carbon ratio 0.64. A three‐step macrokinetic model has been suggested based on the kinetic parameters found. The model includes the following reactions: (1) irreversible steam reforming; (2) CO2 methanation, which occurs in a quasi‐equilibrium mode at temperatures above 260°C; (3) hydrogenolysis of propane and butane, which is essential at temperatures below 260°C. Steam reforming was shown to limit the overall reaction rate, whereas hydrogenolysis and CO2 methanation determined the product distribution in low‐ and high‐temperature regions, respectively. Temperature dependencies of the product distribution for the LTSC of a model ternary methane‐propane‐butane mixture (85% methane, 10% propane, and 5% butane) have been successfully simulated using the three‐step model suggested.

Output uncertainty of dynamic growth models: Effect of uncertain parameter estimates on model reliability

Mechanistic models are simplifications of bio-physical systems, for which the true values of the model parameters are sometimes unknown. Therefore, before using model-based predictions to study or improve a process, it is essential to ensure that the outputs of the model are reliable.This paper covers the development and application of a framework for practical identifiability and uncertainty analyses of dynamic growth models for bioprocesses. By exploring the numerical properties of the sensitivity matrix, a simple algorithm to determine the presence of non-identifiable parameters in models with high output uncertainty is presented. The framework detects the existence of non-identifiable parameters within the model and proposes a regularisation technique, in conjunction with Monte Carlo Analysis. As an example, the framework was used to analyse a macro-kinetic growth model of Escherichia coli describing a fed-batch process. The results show a reduction in the uncertainty of model outputs from a maximum coefficient of variation of 748% to 5% after regularization, and a 15-fold improvement in the accuracy of model predictions for two independent validation datasets. The presented framework aims to improve the reliability of model predictions and promote a more thorough handling of dynamical models to extend their use in biotechnology.

Model for UV induced growth of semiconductor nanoparticles in polymer films

A theoretical macrokinetic model for photoinduced growth of semiconductor nanoparticles was developed with allowance for specific features of their optical properties in the near ultraviolet region. In [A. A. Smirnov et al., Optical Materials Express, 8 (2018) 1603–1612] the Polymethylmethacrylate (PMMA) film containing good soluble CdS precursors [Cd(N(SCNEt2)2)2] (TEDBCd) was irradiated by an ultraviolet light emitting diode (UV LED) with a central wavelength of 365 nm at different fixed temperatures and at different fixed intensities. The authors in situ followed the evolution of absorbance at a wavelength of 405 nm where the film is initially transparent. The corresponding photon energy is larger than the bandgap of the bulk CdS crystals. The increase in absorbance of the irradiated film at this wavelength was associated with the CdS nanoparticle growth. The main result is that at a given temperature, the effect of UV radiation on the sample is determined by the exposure (dose) rather than the light intensity and the irradiation time separately. The presented paper aims at constructing a model of the semiconductor particle growth initiated by the light-induced destruction of good soluble precursor molecules and fitting this model to the experimental data, making it possible to estimate the most important parameters of the process. The photoinduced formation of CdS nanoparticles is a complicated process that includes photo-mediated destruction of the precursor molecules followed by diffusion-assisted growth of nanoclusters. The feature of the growing semiconductor nanoparticles is that rather small particles do not absorb radiation at a particular wavelength because of the quantum confinement. The theory also takes into account the finite thickness of the sample and the nonlinear effects of radiation shielding.