Kinetic Expression Research Articles

Combined mathematical and artificial intelligence modeling of catalytic bio-methanol conversion to dimethyl ether

This study is devoted to developing a combined mathematical and artificial intelligence modeling for simulating the conversion of bio-methanol into dimethyl ether. This methodology couples a precise mathematical model with single-layer perceptron artificial neural networks formulated by several combinations of training and transfer functions, to constitute a machine learning that overcomes the computational tools with the capability of learning without being explicitly programmed, so that it may be used to teach these tools to handle the data with high efficiency in order to predict the upcoming unseen ones precisely. Hence, the novelty of this study deals with the development of a machine learning modeling combined with artificial neural networks, benefitting from an extended mathematical-model-driven dataset, applied for the first time in the conversion of bio-methanol into dimethyl ether in large-scale catalytic dehydration reactors, assessing two process schemes, namely adiabatic and water-cooled operations. To this scope, datasets have been generated by an accurate mathematical model validated experimentally by reference pilot data, adopting the best equilibrium and kinetic expressions, and the simulated numerical data have been then employed as the source of the machine learning models. Extended databanks for the sensitivity analyses of the two process schemes have been then generated by the model (2688 data points in each case), 70% of which has been employed for the artificial neural networks training with mean squared error as the performance function. A single-layer perceptron network yielded the best performances in the adiabatic and water-cooled process schemes, revealing less than 0.5% deviations for the input variables (feed temperature, pressure, flow rate, and concentration) and outputs (temperature, pressure, and flow rates of methanol, dimethyl ether, and water). The simulations revealed that, as the best result of this work, methanol may be converted into dimethyl ether up to ∼80% at 498 K, depending on the validated equilibrium constant adopted, with a maximum error of 0.11%. As a further relevant result, this study demonstrated that analyzing the methanol conversion into dimethyl ether reaction as a function of several variables such as feed flow rate, feed methanol concentration, and input temperature, the accuracy of the neural network with a small number of neurons (5) did not provide accurate output results, whereas 15 neurons in the hidden layer intensify their precision, with the interesting feature that a single-layer perceptron network may detect even small changes to the operating variables.

Experiments and modeling to evaluate global reaction kinetics of three-way catalyst light off for net-zero carbon fuels and selected fuel blends

Internal combustion engine exhaust composition can have a significant impact on the light-off characteristics of CO, NO, and organics in the three-way-catalyst during cold-start. The U.S. Department of Energy’s Co-Optimization of Fuels and Engines initiative was aimed at developing new high-performance fuels, which raises the question of how current three-way-catalysts will perform if the exhaust composition is significantly changed. This work is aimed at quantifying the performance of the catalyst under a variety of different fuel components and mixtures. To this end, a reduced-order model is developed wherein the set of organics examined are placed into molecular groups based on their reactivities and to model each organic within that group with a common kinetic expression. This strategy allows for a first approximation to the light-off characteristics of all organics that fall within that group and to make predictions for fuel blends.

Modeling biofilm and development of rate law expressions for biofilm kinetics

Biofilm processes are gaining significance in the field of wastewater treatment. Biofilm modeling has undergone immense development in the last few decades. The modeling involves developing a mass balance equation for nutrient transport across the biofilm matrix composed of microbes distributed within. The diffusion of nutrients within the biofilm matrix and their consumption by microbes govern the biofilm kinetics. For steady-state, the model becomes independent of time. The solution of steady-state Biofilm is used to calculate the mass flux entering the biofilm surface. This flux can be referred to as the biofilm reaction rate. A dimensionless number named 'Biofilm Number'(B) is formulated, which is used to develop the rate law expressions for the flux in terms of a function Ψ(S*), which measures the quality of transport across the biofilm matrix. The Biofilm reaction rate at Monod's half-saturation concentration is calculated, which is superior to the microbial reaction rate in suspended cultures. The Biofilm's effectiveness factor has been developed based on Ψ(S*) and B. The biofilm number gives the knowledge about the nutrient-consuming capacity of the Biofilm. The model presented in this work can be a fundamental tool for designing a typical biofilm-based reactor. The Biofilm model has been validated using the experimental data from the studies by Shukla 2021.

Nickel leaching kinetics of high-grade nickel matte with sulfuric acid under atmospheric pressure

The nickel leaching kinetics of high-grade nickel matte with sulfuric acid under atmospheric pressure were studied. The effects of stirring speed, high-grade nickel matte particle size, reaction temperature and sulfuric acid concentration on the percentage of nickel dissolved were investigated. In the leaching process, the Ni3S2 in the dense high-grade nickel matte is decomposed which conforms to the shrinking core model. The results show that the unreacted Cu2S solid film has little effect on the reaction product diffusion, while the reaction temperature and particle size of the high-grade nickel matte have significant effects on the leaching process. The activation energy of the decomposition reaction is 39 kJ mol−1 according to the Arrhenius equation and the reaction order is 0.24 with respect to acid concentration. The corresponding kinetic expression for the leaching process is 1 − (1 − x)1/3 = 1.32 × 103c0.235r0−1exp(−39,034/RT)·t which indicates that the process is controlled by the interfacial chemical reaction.

Investigation of zero-valent iron (ZVI)/H2O continuous processes using multivariate analysis and artificial neural networks

Multivariate statistical techniques and artificial neural networks (ANNs) were used for the analysis, interpretation, and modeling of the results obtained in the study of zero-valent iron (ZVI) reactive beds designed for contaminant removal. A wide range of operating conditions was evaluated through more than 120 rapid small-scale column tests (RSSCT). The production of Fe(II) and Fe(III) species, dissolved oxygen consumption, and pH variation along the reactive bed were used as response variables for evaluating the process performance. Due to the complexity of the system, and the difficulty in defining and fitting kinetic parameters, ANN models were used to simulate the system without the need for kinetic expressions. Therefore the latter were used for assessing the system behavior within the investigated experimental domain and for evaluating the relative importance of the operating factors. In addition, the application of the multivariate techniques cluster analysis (CA) and principal component analysis (PCA) revealed underlying relationships among the response variables. Moreover, although multiple physicochemical processes are involved, the results obtained through PCA indicate that the main trends can be rationalized by considering a few key reactions only. The strategy of analyzing RSSCT results with different numerical techniques provides valuable knowledge for designing real-scale ZVI-based treatments aimed at the efficient elimination of a wide range of contaminants in the aqueous phase.

Kinetic modelling of a dark fermentation process using tequila vinasses as substrate for hydrogen production

In this work, a search methods strategy based on optimization algorithms is proposed for the kinetic modelling of a dark fermentation process using tequila stillage substrate for hydrogen production. Kinetic model based on the ADM1 approach is fitted to the experimental data to evaluate the dynamic behaviour of the metabolites produced and consumed during the mixed-culture fermentation. This batch fermentative process is based on mass balance analysis and correlated kinetic expressions following a Monod type dependence. In previous works, batch experiments were performed using different substrates to characterize the metabolic transformations involved in hydrogen production. Where, a kinetic model was developed and fitted to the obtained temporal profiles using Matlab and Excel solvers, allowing a satisfactory description of the metabolic pathways leading to hydrogen production. The aim of this research is to show the efficacy of the proposed optimization strategy to find the kinetic parameters of the model that will allow predictions on the behaviour of hydrogen production.

Traversable wormholes solutions in f(ℛ,φ,χ) gravity under conformal symmetry

The present analysis deals with the wormhole (WH) solutions in [Formula: see text] gravity, where [Formula: see text], [Formula: see text] and [Formula: see text] represent the Ricci scalar, kinetic expression and potential field, respectively. To complete this analysis, we use the WH geometry via spherical spacetime with the anisotropic matter distribution. Further, we consider the Gaussian distribution as non-commutative geometry to complete the analysis under conformal symmetry. We calculate the exact WH shape function by plugging the possible conformal Killing vectors. Further, we have discussed the embedded surface to understand the WH geometry. Furthermore, the Tolman–Oppenheimer–Volkoff equation is considered to discuss the stability of WH configuration with the Gaussian energy density source.

Kinetics and Mechanism of Catalytic Oxidation Desulfurization of Gasoline Liquefied Petroleum Gas in MeroxTM Process with Microfluidics

AbstractCatalytic oxidation desulfurization of gasoline liquefied petroleum gas (LPG) is a key process for the utilization of petroleum hydrocarbons. However, the inherent mechanism remains unclear and the kinetic investigation is usually performed in processes with limited mass transfer rates. Herein, the kinetics and mechanism of catalytic oxidation of sodium ethyl mercaptide were investigated with microfluidics. The effects of temperature, pressure, residence time, and gas‐liquid flow ratio on the oxidation were assessed on the basis of eliminating mass transfer resistance. According to the results of UV‐vis spectra and binding constant, it was confirmed that the catalytic center was in the form of the dimer. A heterogeneous reaction kinetic model was proposed as such. The kinetic parameters close to intrinsic kinetics and corresponding kinetic rate expression were obtained.

Characterisation of a 10-Layer SOC Stack Under Pressurised CO2 Electrolysis Operation

One promising way of facing recent challenges to slow down the climate crisis or to reduce dependencies on fossil energy sources, e.g. natural gas, is using renewable methane and other e-fuels for storage and distribution via existing infrastructure. Solid oxide cell (SOC) reactors play an important role in the conversion of sustainable electric power into chemicals as they can be obtained from combined steam and CO2 co-electrolysis for syngas production. The pressurised electrolysis operation is a key factor for increasing the system efficiency of PtX-processes, including balance-of-plant (BoP) components, electrochemical reactors and high pressure downstream processes.In general, the yield of CO2 electrochemical reduction at atmospheric and pressurised conditions in high temperature co-electrolysis is still controversially discussed. Previously, several SOC short stacks were thoroughly analysed in pressurised steam- and co-electrolysis operation in a test-rig environment. These experimental results indicate marginal influence of pressure on the performance of electrolyte supported cells (ESC). In contrast, electrochemical impedance spectroscopy (EIS) suggests that pressurisation of pure CO2 electrolysis significantly reduces the fuel electrode impedance contribution, especially at lower temperatures around 700 °C [1,2].This work aims to experimentally determine the kinetic behaviour of pure CO2 electrolysis by varying operating conditions like pressure, temperature, reactant conversion and feed gas composition. The investigation of kinetic parameters during these experiments could complement the formerly described research. Furthermore, the kinetic expressions can be used when studying co-electrolysis operation to identify the shares of: (i) the reverse water-gas-shift (rWGS) and (ii) the CO2 electrochemical reduction. Polarisation curves were dynamically recorded and different current densities were evaluated in steady-state operation. Additionally, EIS measurements were performed at open circuit voltage (OCV), as well as under different current densities. The kinetic parameters were estimated by curve-fitting analysis of the experimental results. The resulting expressions will be implemented in the in-house modelling framework, TEMPEST, based on [3,4] with the aim to increase the accuracy of modelling high-temperature CO2 electrolysis and co-electrolysis systems. [1]Riedel, M., Heddrich, M. P., & Friedrich, K. A. (2020). Experimental Analysis of the Co-Electrolysis Operation under Pressurized Conditions with a 10 Layer SOC Stack. Journal of The Electrochemical Society, 167(2), 024504, DOI: 10.1149/1945-7111/ab6820.[2]Riedel, M. (2020, October 20–23). Experimental analysis of SOE stacks under pressurized co- and CO2 electrolysis operation [Paper presentation]. 14th European SOFC & SOE Forum, Lucerne, Switzerland.[3] Tomberg, M., Santhanam, S., Heddrich, M. P., Ansar, A., & Friedrich, K. A. (2019). Transient Modelling of Solid Oxide Cell Modules and 50 kW Experimental Validation. ECS Transactions, 91(1), 2089, DOI: 10.1149/09101.2089ecst.[4] Srikanth, S., Heddrich, M. P., Gupta, S., & Friedrich, K. A. (2018). Transient reversiblesolid oxide cell reactor operation–Experimentally validated modeling and analysis. Applied Energy, 232, 473-488, DOI: 10.1016/j.apenergy.2018.09.186.

Dynamic surface-coverage alteration based on microkinetic analysis for enhanced ammonia synthesis over ruthenium catalysts at low temperatures

The ammonia (NH3) synthesis reaction has been well established via Harbor-Bosch process, but recent demands of NH3 as a hydrogen carrier necessitates the synthesis operations at much milder conditions for renewable energy utilization. Catalytic ammonia synthesis is among the most investigated heterogeneous catalytic reactions but the detailed kinetic studies especially at low temperatures are still missing. This study investigated thorough microkinetic analysis at a wide range of reaction temperatures from 200 to 400 °C for NH3 synthesis. Although the united kinetic expression for the NH3 synthesis was established at all temperature range, the rate at low temperatures was found to be strongly reduced not only by hydrogen but also NH3 (NHx) surface intermediates that become more significant as the conversion increases. Knowing these strong inhibitions by both the reactant (H2) and product (NH3), transient perturbation of the surface intermediates by alternating between pure H2 and N2 gas flow was tested, which may lead to rate jumps by controlling the most abundant surface intermediates. The results show dramatic enhancement of the overall NH3 synthesis rate of as high as > 1 mmol g−1 h−1 over 5 wt% Ru/CeO2 catalysts at 200 °C and 0.1 MPa. The results not only give insight into improving existing catalysts and catalytic reaction operations, but also cast doubts on the consistency of how to report the rates of ammonia synthesis due to the strong dependence of the catalysts on ammonia yield, especially at low temperatures.

Experimental and population balance model interpretation of foam physics in porous media

Foam has been used as an effective displacing fluid for gas mobility control in enhanced oil recovery (EOR) and subsurface remediation. In this study, a series of core flooding experiments are performed on cores with a wide permeability ranging from 3.3 to 2749 mD to evaluate the impact of foam quality and permeability on foam performance. It is found that the steady-state foam mobility control factor is related to permeability in a non-linear, non-monotonic manner. A full physics, mechanistic foam model is proposed by incorporating a novel flowing foam fraction relation grounded-up from pore-level observations, and a new kinetic expression of foam coalescence rate by oil based on pinch-off foam rupture mechanism into the population-balance framework of Almajid et al. (Advances in Water Resources, 2021, 150: 103877). The proposed model is applied to match foam flow experimental results in the absence and in the presence of oil. Results show that our model captures the high-quality and low-quality foam regimes observed in previous oil-free foam flow experiments. Within the medium permeability range, in the absence of oil, lower gas mobility is observed in the lower permeability core due to faster foam film thinning at higher capillary pressure, while in the presence of residual oil, the difference in foam mobility fades away due to the insignificant impact of capillary pressure on the stability of pseudoemulsion films.

Modelling fast pyrolysis of biomass in a fluidized bed reactor

AbstractA compartmental one‐dimensional model of a fluidized bed pyrolytic converter of biomass is presented. Reference conditions are those of non‐catalytic fast pyrolysis of biomass in a shallow fluidized bed with external regeneration of the bed material. The fate of biomass and of the resulting char has been modelled by considering elutriation of biomass and char particles, char attrition as well as bed drain/regeneration. The course of primary and secondary pyrolitic reactions is modelled according to a semi‐lumped reaction network using well‐established kinetic parameters taken from the literature. A specific focus of the present study is the role of the heterogeneous volatile–char secondary reactions, whose rate has been modelled by borrowing a kinetic expression from the neighbouring area of tar adsorption/decomposition over char. The results of computations highlight the relevance of heterogeneous volatile–char secondary reactions and of the closely associated control of char loading in the bed. The sensitivity of the reactor performance to char elutriation and attrition, to proper management of bed drain/regeneration, and to control of gas phase backmixing is demonstrated. Model results provide useful guidelines for optimal design and control of fluidized bed pyrolyzers and pinpoint future research priorities.

On the estimation of effectiveness factor in metallic monoliths presenting non-uniform coatings

The one dimensional two-zone model (1D-2Z) to estimate effectiveness factor in non-uniform coatings of metallic monolith channels with sinusoidal cross-section is thoroughly tested in this contribution. The model relies on the idea of splitting the cross-section of the coating in two zones that can be modelled independently taking into account the diffusion and simultaneous reaction in a single direction (1D). One of the zones is considered as a slab, while the previously developed variable diffusivity model (1D-VD) is applied to the other. The predictive capabilities of the 1D-2Z model is assessed for three kinetic expressions: a first order reaction and two more challenging cases defined by Langmuir-Hinshelwood-Hougen-Watson expressions: one of them with a moderate self-inhibition effect and the other with a strong self-inhibition effect, close to the onset of the multiple steady states behaviour. Simultaneously, different degrees of non-uniform coatings are considered. The 1D-2Z model allows obtaining a remarkable precision in the estimation of the effectiveness factors for the complete range of Thiele modulus with maximum errors below 5.6%.

Fluidized Bed Pyrolysis of Biomass: A Model-Based Assessment of the Relevance of Heterogeneous Secondary Reactions and Char Loading

A model of non-catalytic fast fluidized bed pyrolysis of biomass has been developed with the aim of investigating the relevance of secondary heterogeneous reactions between primary products of biomass decomposition and the char accumulated in the bed. The fate of biomass and the extent of biomass and char holdup in the pyrolyzer have been modeled by considering entrainment and elutriation of biomass and char particles, char attrition, as well as bed drain/regeneration. The kinetics of primary and secondary pyrolitic reactions is modeled according to a semi-lumped reaction network using kinetic parameters selected among published correlations. The rate of heterogeneous volatile–char secondary reactions has been modeled borrowing a kinetic expression from the neighboring area of tar adsorption/decomposition over char during biomass gasification. Model computations are helpful to assess the role of heterogeneous vapor–char secondary reactions. The sensitivity of the pyrolyzer performance on char loading in the bed as a result of combined char entrainment, elutriation, attrition, and bed drain/regeneration, the extent of gas-phase backmixing, the process temperature, the gas superficial velocity and residence time, and the particle size is demonstrated and discussed. Model results provide useful guidelines and pinpoint future research priorities for optimal design and control of fluidized bed pyrolyzers.

The role of Heisenberg spin exchange and the quantum Zeno effect in the spin-selective reaction between spin-1/2 and spin-1 particles.

The kinetics of spin-selective reactions involving triplet molecules, such as triplet-triplet annihilation or electron transfer to dioxygen molecules in the ground triplet spin state, are strongly dependent on the dipole-dipole interaction (DDI) of electron spins in spin-1 particles. The effect of this interaction on the intersystem crossing in the reaction encounter complex of the paramagnetic particles was previously considered for some particular cases using oversimplified approaches. In this study, we consider a rigorous kinetic model of the irreversible reaction between the spin-1/2 and spin-1 particles in an encounter complex with the reactive doublet state. This model explicitly includes both isotropic exchange coupling of the reactants and spin dependence of the reaction rate in the form of the Haberkorn reaction term. For the time-independent DDI, an analytical expression for the reaction kinetics was derived. The effect of DDI fluctuations was analyzed using numerical simulations. It was found that increasing both the exchange coupling and the reaction rate constants can significantly slow down the quartet-doublet spin transitions and, as a consequence, the observed spin-selective reaction rate. Additionally, the presence of the irreversible reaction in the doublet states affects a coherent evolution in the non-reactive quartet subsystem.

2D model of the transfer processes for CO2 methanation in a microchannel reactor

A dynamic two-dimensional model was developed for transfer processes in a microchannel reactor in an innovative plant concept for CO2 methanation. The model is based on balance equations together with deactivation and sulfidation submodels taking into account the chemisorption of impurity (H2S). The deactivation of the catalyst is described by Levenspiel’s deactivation kinetic model (LDKM). Sulfidation is defined by the shrinking core model (SCM) equation. Following the rate-determining step assumption, a simplified mechanism is derived for CO2 and CO methanation in a microchannel reactor with kinetic rate expressions. The developed 2D model adequately describes transient and steady-state behavior of the microchannel methanation reactor following the trend in experimental profiles available in the literature.

Investigation of photocatalytic activity of TiO2 nanotubes synthesized by hydrothermal method

TiO2 nanotubes were synthesized by hydrothermal reaction using commercially available TiO2 powder at 150 °C for 24 h. The transmission electron microscopy, X-ray diffraction, nitrogen adsorption-desorption isotherms and Fourier Transform-Infrared spectroscopy were used to characterize the nanotubes. Anatase phase was not transformed into rutile phase in the range of calcination temperature studied. Increase in calcination temperature result in enhancement of crystallinity and reduction in BET surface area. Photocatalytic removal of Reactive Red 239 (RR239) was investigated using prepared TiO2 nanotubes. Effects of pH, TiO2 nanotube dosage, initial RR239 concentration and calcination temperature were studied. 99%, 97% and 55% of removal efficiency values were attained at pH = 3, 5 and 7, respectively within 60 min or reaction time. With an increase in dosage of TiO2 nanotube in the range of 0.25–0.75 g dm−3, removal rate increased by a steeper slope. Complete removal of RR239 was observed at 20 mg dm−3 RR239 concentrations within 30 min but longer time was required for complete removal at higher concentrations. Langmuir-Hinshelwood kinetic expression was proposed based on nonlinear regression analysis. The removal efficiency of nanotubes calcined at 300 − 450 °C significantly increased but further increase in calcination temperature caused to decrease the efficiency.100% and 85% removal efficiency values were observed using actual solar light within 120 min of reaction time in July and January, respectively. Experiments conducted with scavengers showed that holes and adsorbed hydroxyl radicals were the major species involved in removal of RR239. A pathway for degradation of RR239 was suggested according to detected intermediate compounds.

Modelling of an Anaerobic Digester: Identification of the Main Parameters Influencing the Production of Methane Using the Sobol Method

Anaerobic digestion is a promising method of organic waste valorisation, particularly for fish farm waste, which has experienced a high growth rate in recent years. The literature contains predictive mathematical models that have been developed by various authors, allowing the prediction of the composition of bio-gas production from organic waste. In general, Monod’s kinetic expression is the basis for describing the enzymatic reaction rates for anaerobic digestion. In this work, several parameters are taken into account, such as temperature, cell growth inhibition, and other operating parameters, and systems of differential equations coupling the kinetics and stoichiometry for bio-reactions are applied to better describe the dynamics. Because of the high number of initial parameters that need to be defined for the anaerobic digester, the use of this model requires significant resources and a long calculation time. For this reason, a global sensitivity analysis (GSA) is applied to this predictive model based on the Sobol index method, in order to identify the most influential key parameters and the interactions between them. For the digestion of fish waste, it is observed that the key parameters influencing methane production are the lipid concentration of the waste, temperature, and hydraulic retention time (HRT).

The Assessment of the Real-Time Radiative Properties and Productivity of Limnospira platensis in Tubular Photobioreactors.

The development of tools to predict the photobioreactors’ (PBRs) productivity is a significant concern in biotechnology. To this end, it is required to know the light availability inside the cultivation unit and combine this information with a suitable kinetic expression that links the distribution of radiant energy with the cell growth rate. In a previous study, we presented and validated a methodology for assessing the radiative properties necessary to address the light distribution inside a PBR for varying illuminating conditions through the cultivation process of a phototrophic microorganism. Here, we sought to utilise this information to construct a predictive tool to estimate the productivity of an autotrophic bioprocess carried out in a 100 [L] tubular photobioreactor (TPBR). Firstly, the time-dependent optical properties over ten batch cultures of L. platensis were calculated. Secondly, the local volumetric rate of photon absorption was assessed based on a physical model of the interaction of the radiant energy with the suspended biomass, together with a Monte Carlo simulation algorithm. Lastly, a kinetic expression valid for low illumination conditions has been utilised to reproduce all the cultures’ experimentally obtained dry weight biomass concentration values. Taken together, time-dependent radiative properties and the kinetic model produced a valuable tool for the study and scaling up of TPBRs.

Kinetic Changes in B7 Costimulatory Molecules and IRF4 Expression in Human Dendritic Cells during LPS Exposure.

A key aspect of the inflammatory phenomenon is the involvement of costimulatory molecules expressed by antigen-presenting cells (APCs) and their ability to secrete cytokines to set instructions for an adaptive immune response and to generate tolerance or inflammation. In a novel integrative approach, we aimed to evaluate the kinetic expression of the membrane and soluble B7 costimulatory molecules CD86, ICOS-L, PDL1, PDL2, the transcription factor Interferon Regulatory Factor 4 (IRF4), and the cytokines produced by monocyte-derived dendritic cells (Mo-DCs) after challenging them with different concentrations of stimulation with E. coli lipopolysaccharide (LPS) for different lengths of time. Our results showed that the stimuli concentration and time of exposure to an antigen are key factors in modulating the dynamic expression pattern of membrane and soluble B7 molecules and cytokines.