Non-isothermal Reaction Research Articles

CONSERVATION LAWS OF CHEMICAL REACTIONS IN A CLOSED NONISOTHRUM INCOMPLETE MIXING REACTOR

In chemical reactions occurring stationary or non-stationary in closed isothermal ideal mixing reactors (CSTR), the classical linear stoichiometric laws of conservation are always satisfied, reflecting the constancy of atoms of one type or another during the entire reaction. In real conditions, taking into account possible deviations from ideal mixing conditions or violations of the constancy of temperature conditions, various macroscopic factors (mass transfer, heat transfer) can have a noticeable influence on the course of the reaction. To study the kinetics of such processes, a more general mathematical model of an incomplete mixing reactor (IMR) is used. It is of interest to study the influence of diffusion and convection on the patterns of stationary modes of non-isothermal chemical reactions associated with the existence of more general (non-stoichiometric) conservation laws (kinetic invariants). It is more difficult to detect such invariants (especially temperature ones) in IMRs than in CSTR, and at present they are practically not studied. In this work, for chemical reactions occurring in a closed non-isothermal IMR according to the kinetic law of mass action, linear concentration and temperature conservation laws are established, which take into account the complicating processes of diffusion and convection. These conservation laws relate the stoichiometry of the reaction mechanism to the concentrations of reagents, the temperature of the reaction medium and the intensity of macrokinetic processes, which allows them to be used for a more reasonable identification of linear and nonlinear mechanisms of chemical reactions when solving the inverse problem of chemical kinetics. The new kinetic conservation laws presented in the work can be discovered a priori and verified experimentally. For citation: Kol'tsov N.I. Conservation laws of chemical reactions in a closed nonisothrum incomplete mixing reactor. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2024. V. 67. N 7. P. 111-118. DOI: 10.6060/ivkkt.20246707.6976.

Effect of ultrasound geometry on the production efficiency of damaged starch: Determining rheology parameters, and non-isothermal reaction kinetics

Present study investigates the effects of probe size geometry on thermodynamic kinetics, rheology, and microstructure of wheat and tapioca starch. Ultrasound treatment using different probe diameters (20 mm and 100 mm) significantly influenced the gelatinization process. Results showed reduced enthalpy (ΔH) and Gibbs energy (ΔG), indicating enhanced gelatinization efficiency. According to the results, using a 20 mm and 100 mm probe leads to a reduction of 52.7 % and 68.6 % in reaction enthalpy for wheat starch compared to native starch, respectively. Microstructure analysis revealed structural changes, with ultrasound treatment leading to granular fractures and a sheet-like structure with air bubbles. The rheological behavior of the starches is found to exhibit shear thinning behavior, with the Casson model providing the best fit for the experimental data. Moreover, rheology modeling using Herschel-Bulkley and power law models showed increased viscosity and shear stress in larger probes. Numerical simulation data demonstrated that probe size influenced ultrasonic pressure, sound pressure level, and thermal power dissipation density, affecting fluid motion and velocity field components. Moreover, the maximum dissipated power decreases from 8.43 to 0.655 mW/m3 with an increase in probe diameter from 20 to 100 mm. The average yield shear stress values are calculated as 3.36 and 3.14 for wheat and tapioca starches, respectively. The larger probe diameter leads to greater entropy increases, with tapioca starch showing a 4.72 % increase and wheat starch a 4.97 % increase, compared to 2.56 % and 3.11 %, respectively, with the smaller probe. Additionally, the Keller-Miksis model provided insights into bubble dynamics, revealing increased pressure and temperature with higher pressure amplitudes.

Chemorheological Kinetic Modeling of Uncatalyzed Hydroxyl‐Terminated Polybutadiene and Isophorone Diisocyanate

AbstractCatalysts are often employed to enable nonisothermal reaction kinetic studies when tracking cure progression of polyurethane reactions. However, when quickly reacting, catalyzed materials are prepared through mixing followed by the addition of fillers or additives, subsequent processing of the partially reacted material becomes difficult. Here, chemorheology is used to track changes in viscoelastic properties of uncatalyzed polybutadiene‐diisocyanate reactions for multiple days, which quantifies the degree of cure during polymerization. Viscosity profiles are accurately captured by the two‐stage Arrhenius model (r2>0.95), and conversion progress is adequately represented by the Kamal–Sourour model (r2>0.76). Transition state analysis via Wynne–Jones–Eyring–Evans theory (WJEE) reveals the presence of an associative mechanism according to entropic and enthalpic activation energies ΔS# = −96.9 J K−1 and ΔH# = 36.4 kJ, respectively. These rheokinetic modeling results align with Fourier transform infrared spectroscopy findings. To the knowledge, no rheokinetic studies have tracked cure progress of this uncatalyzed system for the extended timeframe presented here. The cure profile also presents unique viscosity growth, representative of molecular weight buildup, compared to catalyzed systems. This finding emphasizes the novelty of applying previously developed chemorheological models to multiday thermosetting reactions within a flow field in a manner that is generalizable to many long‐term curing systems.

Investigation of ultrasound-assisted starch acetylation by single- and dual- frequency ultrasound based on rheology modelling, non-isothermal reaction kinetics, and flow/acoustic simulation

To achieve wheat starch acetylation (AC) with a high degree of substitution (DS), the acetylation process was carried out using various ultrasonication frequencies, including 25 kHz, 40 kHz, and 25 + 40 kHz. In the second step, wheat starch's ultrasound-assisted acetylation (UAA) is simulated using various approaches including the rheology models, non-isothermal reaction kinetics, and flow/acoustic modelling. The computational fluid dynamics (CFD) simulation solves the non-linear acoustic governing equation to determine the flow field and the amount of delivered ultrasound energy. The acetylated starch increased peak and final viscosity, with the highest values observed for the 25 + 40 kHz frequency than other single frequencies (25 kHz and 40 kHz). The viscosity of the starch is specified based on the experimental data using Herschel–Bulkley, power law, and Casson rheology models. According to differential scanning calorimetry (DSC) analysis, the gelatinization parameters and enthalpy of gelatinization (ΔHgel), were found to be lower in acetylated starches at the frequency of 25 + 40 kHz compared to those at frequencies of 25 kHz and 40 kHz, as well as native starches (NS). Moreover, the gelatinization process is examined by implementing the non-isothermal reaction kinetics to obtain the activation energy and reaction order. Based on the results obtained, implementing sonication at 25 kHz reduces the activation energy by 70.3 % compared to native starch. However, the same parameter is obtained to be 69.9 % and 67.1 % for the application of 40 and 25 + 40 kHz transducers, respectively. Additionally, during the sonication treatment, the yield shear stress increases between 24.1 and 31.8 %, based on the applied frequency. Morphology analysis determined by scanning electron microscopy (SEM) revealed that the surfaces and small granules underwent more damage in acetylated starches at frequencies of 25 kHz and 40 kHz. However, in acetylated starches at 25 + 40 kHz, the larger granules were more affected than the smaller ones.

Kinetic Study of Non-Isothermal Reactions on the Pyrolysis of Various Biomass Waste by using Thermogravimetric Data

Population growth causes an increase in the need for petroleum. However, petroleum as primary energy is currently increasingly limited in availability. Required alternative energy sources that can be renewed to overcome these problems, one of which is bio-oil. Bio-oil is produced by a pyrolysis process using biomass such as sugarcane bagasse, rice husk, and empty oil palm fruit bunches (EFB), by heating in the absence of oxygen. Kinetic studies on pyrolysis of this type of biomass (sugar cane bagasse, rice husk, and empty oil palm fruit bunches) were carried out using the thermogravimetric method. The Coats-Redfern method was used in this study. The purpose of this study is to obtain the most appropriate reaction kinetics model to represent the pyrolysis process for each type of biomass. In addition, to determine the optimal temperature used in forming bio-oil. Approximately 5 g of each biomass is used with a heating rate of 10°C/minute. Pyrolysis was carried out until the temperature reached 750°C. The results of the research on the selected kinetic model for each biomass is a geometric model with a correlation coefficient (R2) close to 1 and the optimum temperature for producing bio-oil is around 550 - 600°C.

Thin liquid films on a slippery vertical cylinder in presence of chemical reaction

In industrial settings, chemical reactions often affect thin liquid films that flow down vertical cylinders. However, the effect of non-isothermal reactions on the dynamics of these films is not fully comprehended. To address this issue, this study investigates the behavior and stability of thin film flows on uniformly heated vertical cylinders that exhibit wall slippage when subjected to a pseudo-zero-order exothermic or endothermic chemical reaction. A reduced model is developed for thin liquid films flowing down vertical cylinders in the presence of exothermic or endothermic chemical reactions, assuming the film thickness is much smaller than the cylinder radius. The heat from the reaction and/or wall heating initiates a thermocapillary Marangoni effect, which is further enhanced by wall slippage, directly affecting the dynamics of the free surface. Linear and weakly nonlinear stability analyses show that wall slip amplifies the instability, while exothermic reactions stabilize the system and endothermic reactions destabilize it. It is also found that chemical reactions significantly influence the supercritical stable, subcritical unstable, unconditional stable, and explosive zones of the thin film. A direct numerical simulation confirms the results of linear and weakly nonlinear analyses.

Effects of different atmosphere on reaction behaviors of metallised burden

ABSTRACT The utilisation of metallised burden in blast furnace (BF) as a way of CO2 emission reduction has been widely considered. One of the major concerns is its reoxidation by CO2 in the upper part of BFs. In this study, the non-isothermal reaction behaviours of metallised burden with a metallisation ratio of 70% in different CO2 + CO gas mixtures were analysed. The results showed that the metallised burden can be oxidised by CO2 under sufficiently large CO2 partial pressure. In a 50%CO2 + 50%CO gas mixture, Fe was oxidised to FeO. And the reaction started at 718°C, which is much higher than the temperature in the upper shaft of BFs. The metallised burden cannot be oxidised by CO2 in the low temperature zone of BFs. During the descent of the burden, temperature increases and the reduction atmosphere strengthens in an actual BF. The CO2 partial pressure is insufficient to oxidise the metallised burden.

Hydrogen storage thermodynamics and kinetics of the as-cast and milled Ce-Mg-Ni-based alloy

Aiming at investigating the improvement of hydrogen storage performance of the ternary Ce5Mg85Ni10 alloy after mechanical ball milling, the phase transformation and microstructure evolution of the milled alloys are observed by XRD, SEM and TEM. After ball milling, the alloys mainly exhibit nanocrystalline and amorphous structures and consist of Mg, Mg2Ni and CeMg12 phases. After hydrogen absorption, the milled alloys consist of MgH2, Mg2NiH4 and CeH2.73 phases. Isothermal and non-isothermal reaction curves of hydrogen absorption and desorption of the milled alloys are characterized by an Sievert apparatus, DSC and TGA. The Arrhenius and Kissinger equations are used to calculate the hydrogen desorption activation energy. For the Ce5Mg85Ni10 alloy, its structure and thermodynamics and kinetics performance of hydrogen storage strongly depend on the ball milling time. The results shows that ball milling for 5 h can achieve the optimal activation and kinetics performances but further prolonging the ball milling time lead to the impairment of hydrogen storage performance. Besides, ball milling time has little effect on thermodynamic property. Experiments results show that the 5 h-milled alloy after activation can absorb 4 wt% H2 in 18 s at 473 K and 3 MPa, and can desorb 3 wt% H2 in 906 s at 533 K and 1 × 10−4 MPa. In addition, the hydrogen desorption enthalpy change of the 5 h-milled alloy is 75.28 kJ/mol and the hydrogen desorption apparent activation energy of this alloy is 62.69 kJ/mol.

A periodic boundary value problem with switchings under nonlinear perturbations

We investigate the existence of solutions of weakly nonlinear periodic boundary value problems for systems of ordinary differential equations with switchings and the construction of these solutions. We consider the critical case where the equation for the generating constants of a weakly nonlinear periodic boundary-value problem with switchings does not turn into an identity. We improve the classification of critical and noncritical cases and construct an iterative algorithm for finding solutions of weakly nonlinear periodic boundary value problems with switchings in the critical case. As examples of application of the constructed iterative scheme, we obtain approximations to the solutions of a periodic boundary value problem for the mathematical model of nonisothermal chemical reactions. To check the accuracy of the proposed approximations, we evaluate discrepancies in the original equation.

Polypropylene pyrolysis kinetics under isothermal and non-isothermal conditions: a comparative analysis

Abstract The kinetics of polypropylene pyrolysis has been studied under isothermal and non-isothermal conditions using Arrhenius and Kissinger–Akahira–Sunose (KAS) equations. Under isothermal conditions, applying first order kinetic model, activation energy (Ea) and pre-exponential factor (A) were investigated and observed as 119.7 kJ mol−1 and 1.2 × 1010 min−1, while in case of non-isothermal kinetics using Kissinger–Akahira–Sunose method, the average Ea and A were found to be 91.23 kJ mol−1 and 2.3 × 107 min−1, respectively. A comparison among the isothermal and non-isothermal reactions was made on the basis of kinetics parameters. The results from both the methods showed trivial variation in kinetic parameters of the pyrolysis reaction which may be due to two major reasons. Firstly, the selection of the kinetic model applied and secondly the inconsistency due to various experimental conditions used which can be reduced at optimized conditions. As the disposal of plastic materials need reliable kinetics information to model their decomposition reactions, therefore, the kinetics data thus obtained from pyrolysis reaction of model polypropylene will help in the utilization of polypropylene waste as energy source on industrial scale.

Well-posedness for the reaction-diffusion equation with temperature in a critical Besov space

We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical reaction with general mass kinetics. From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.

Polysaccharides Release in a Laboratory-Scale Batch Hydrothermal Pretreatment of Wheat Straw under Rigorous Isothermal Operation.

Hydrothermal pretreatment (HP) is an eco-friendly process for deconstructing lignocellulosic biomass (LCB) that plays a key role in ensuring the profitability of producing biofuels or bioproducts in a biorefinery. At the laboratory scale, HP is usually carried out under non-isothermal regimes with poor temperature control. In contrast, HP is usually carried out under isothermal conditions at the commercial scale. Consequently, significant discrepancies in the values of polysaccharide releases are found in the literature. Therefore, laboratory-scale HP data are not trustworthy if scale-up or retrofitting of HP at larger scales is required. This contribution presents the results of laboratory-scale batch HP for wheat straw in terms of xylan and glucan release that were obtained with rigorous temperature control under isothermal conditions during the reaction stage. The heating and cooling stages were carried out with fast rates (43 and −40 °C/min, respectively), minimizing non-isothermal reaction periods. Therefore, the polysaccharide release results can be associated exclusively with the isothermic reaction stage and can be considered as a reliable source of information for HP at commercial scales. The highest amount of xylan release was 4.8 g/L or 43% obtained at 180 °C and 20 min, while the glucan release exhibited a maximum of 1.2 g/L or 5.5%. at 160 °C/180 °C and 30 min.

Mathematical Analysis of Non-Isothermal Reaction–Diffusion Models Arising in Spherical Catalyst and Spherical Biocatalyst

The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- and boundary-value problems with singularity at the time t=0. The main objective of this paper is to make use of some mathematical analytic tools and techniques in order to numerically solve some reaction–diffusion equations, which arise in spherical catalysts and spherical biocatalysts, by applying the Chebyshev spectral collocation method. The proposed scheme has good accuracy. The results are demonstrated by means of illustrative graphs and numerical tables. The accuracy of the proposed method is verified by a comparison with the results which are derived by using analytical methods.

A New Insight Into Seawater-Basalt Exchange Reactions Based on Combined δ18O—Δ′17O—87Sr/86Sr Values of Hydrothermal Fluids From the Axial Seamount Volcano, Pacific Ocean

The δ18O values of submarine vent fluids are controlled by seawater-basalt exchange reactions, temperature of exchange, and to a lesser extent, by phase separation. These variations are translated into the δ18O values of submarine hydrothermal fluids between ca. 0 and + 4‰, a range defined by pristine seawater and equilibrium with basalt. Triple oxygen isotope systematics of submarine fluids remains underexplored. Knowing how δ17O and δ18O change simultaneously during seawater-basalt reaction has a potential to improve i) our understanding of sub-seafloor processes and ii) the rock-based reconstructions of ancient seawater. In this paper, we introduce the first combined δ17O-δ18O-87Sr/86Sr dataset measured in fluids collected from several high-temperature smoker- and anhydrite-type vent sites at the Axial Seamount volcano in the eastern Pacific Ocean. This dataset is supplemented by measurements of major, trace element concentrations and pH indicating that the fluids have reacted extensively with basalt. The salinities of these fluids range between 30 and 110% of seawater indicating that phase separation is an important process, potentially affecting their δ18O. The 87Sr/86Sr endmember values range between 0.7033 and 0.7039. The zero-Mg endmember δ18O values span from -0.9 to + 0.8‰, accompanied by the Δ′17O0.528 values ranging from around 0 to −0.04‰. However, the trajectory at individual site varies. The endmember values of fluids from focused vents exhibit moderate isotope shifts in δ′18O up to +0.8‰, and the shifts in Δ′17O are small, about −0.01‰. The diffuse anhydrite-type vent sites produce fluids that are significantly more scattered in δ′18O—Δ′17O space and cannot be explained by simple isothermal seawater-basalt reactions. To explain the observed variations and to provide constraints on more evolved fluids, we compute triple O isotope compositions of fluids using equilibrium calculations of seawater-basalt reaction, including a non-isothermal reaction that exemplifies complex alteration of oceanic crust. Using a Monte-Carlo simulation of the dual-porosity model, we show a range of possible simultaneous triple O and Sr isotope shifts experienced by seawater upon reaction with basalt. We show the possible variability of fluid values, and the causal effects that would normally be undetected with conventional δ18O measurements.

Dissipation-Driven Selection under Finite Diffusion: Hints from Equilibrium and Separation of Time Scales.

When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available energy, might be dominant in dictating the stationary populations of all chemical states out of equilibrium. This phenomenology has been theoretically explored mainly in the infinite diffusion limit. Here, we show that the regime in which the diffusion rate is finite, and also slower than some chemical reactions, might bring about interesting features, such as the maximisation of selection or the switch of the selected state at stationarity. We introduce a framework, rooted in a time-scale separation analysis, which is able to capture leading non-equilibrium features using only equilibrium arguments under well-defined conditions. In particular, it is possible to identify fast-dissipation sub-networks of reactions whose Boltzmann equilibrium dominates the steady-state of the entire system as a whole. Finally, we also show that the dissipated heat (and so the entropy production) can be estimated, under some approximations, through the heat capacity of fast-dissipation sub-networks. This work provides a tool to develop an intuitive equilibrium-based grasp on complex non-isothermal reaction networks, which are important paradigms to understand the emergence of complex structures from basic building blocks.

Determining the kinetic constants leading to mineralization of dilute carbamazepine and estradiol-containing solutions under continuous supercritical water oxidation conditions

Continuous subcritical and supercritical water oxidation experiments were conducted on dilute carbamazepine- and estradiol-containing synthetic solutions used to simulate the removal of model emerging pollutants from secondary municipal effluents. The operating conditions comprised 340–500 °C, retention time of 24–453 s and a stoichiometric oxidant ratio (O.C.) between 4 and 64. The transformation of the various species was determined at the outlet and by modeling a segmented non-isothermal reaction system. Four empirical power law kinetic models were established to represent both the pollutants' degradation and TOC removal efficiencies, using nonlinear multiple regression coupled with bootstrapping and K-fold cross-validation. The mineralization and degradation models for both pollutants yielded a R2 of 67–80.5% vs. the experimental results. Discussion on the various model assumptions revealed that attributing full model deviations to the constant oxygen concentration or to the laminar reactor flow, yielded a deviation of 6% and 15% in the removal efficiencies, respectively. However, the expected deviation of the models was lower than 0.32% at conditions leading to (almost) full mineralization (45–60 s, 480–500 °C and O.C.s of 5–10). The methodologies developed in the study are useful for interpreting future results obtained from SCWO of actual secondary effluent solutions.

A New Method for Measuring Kinetic Parameters of Nonisothermal Coke and Sinter Reaction under Different CO Concentrations

A New Method for Measuring Kinetic Parameters of Nonisothermal Coke and Sinter Reaction under Different CO Concentrations

Insight into CO 2 reforming of CH 4 via NiO /dolomite catalysts for production of H 2 rich syngas

Dry reforming of methane (DRM) over Ni-based catalyst has become very popular way used for the generation of hydrogen rich syngas. In this study, synergetic effect between NiO and high basicity support of dolomite was investigated to determine their activity and stability in DRM process. In this regard, series of monometallic catalyst samples (NiO/Dolomite) at different metal loadings of 5 to 15 wt% of NiO over dolomite support were prepared via wet impregnation method. The catalyst performance evaluation on the production of H2 rich syngas was performed and the obtained results showed that 10 wt% NiO/dolomite catalyst sample recorded the maximum conversion of CH4 and CO2 to H2 at 850°C temperature, 9000 hours−1 g·cat−1 gas hourly space velocity and 0.2 g catalyst loading without in-situ reduction of 5% H2 gas. 10% NiO/dolomite shows better performance on H2 selectivity recording up to 75% and H2/CO ratio of 1:1. The reaction maintained 98% of CH4 and CO2 conversion for up to 10 hours reaction time, with very low coke formation. Non-isothermal reaction of catalyst under CH4:N2 (1:9) proves self-reduced properties of catalyst on dry reforming environment (CH4:CO2) started at 300°C. The prepared catalyst samples were successfully characterized using X-ray photoelectron spectroscopy, temperature-programmed oxidation, field emission scanning electron microscopy, and thermogravimetric analysis to study their physiochemical properties, which could give clue on their activity toward DRM. Kinetic and mechanistic studies prove that DRM reaction of NiO/dolomite catalyst follow dual site associative adsorption of both CH4 and CO2 with bimolecular surface reaction.

Non-isothermal reaction mechanism and kinetic analysis for the synthesis of monoclinic lithium zirconate (m-Li2ZrO3) during solid-state reaction

Non-isothermal reaction mechanism and kinetic analysis for the synthesis of monoclinic lithium zirconate (m-Li2ZrO3) were investigated by processing of TG-DTA, along with XRD, DLS, and HRTEM. For this purpose, the solid-state reaction of Li2CO3 with ZrO2 was carried out by TG-DTA at different heating rates (10, 20, and 30 °C/min) from room temperature to 1100 °C. The thermal data was used to calculate the kinetic parameters by two types of isoconversional methods: Flynn-Wall-Ozawa (FWO) and Kissinger-Akahira-Sunose (KAS). The reaction mechanism was determined by the model-fitting method, applying the Coats-Redfern (CR) approximation to the different solid-state reaction models. The results confirmed the formation of pure m-Li2ZrO3, consists of semispherical particles of about 490 nm, using a very short reaction time. The average activation energy obtained by FWO and KAS methods were 274.73 and 272.50 kJ/mol, respectively. It was found that the formation of m-Li2ZrO3 from Li2CO3 with ZrO2 is governed by the three-dimensional diffusion mechanism. Based on these results, a microscopic reaction model of the formation of m-Li2ZrO3 was proposed.

On the p(x) approximation in the non-isothermal reaction kinetics by a generalized exponential integral the concept

A non-Arrhenius model based on the Mittag-Leffler function has been conceived as a basic concept. This approach allows modelling both sub-Arrhenius and super-Arrhenius behaviours and giving rise to modified temperature integrals.