Global Rate Equation Research Articles

Uso didáctico de reactores agitados continuos para la determinación de cinéticas de reacción heterogénea

<p class="p1">Se describen la modelación, la construcción y el uso de un reactor continuo de tanque agitado para la obtención de datos experimentales de rapidez de reacción heterogénea. En primer lugar, mediante análisis de balances de materia se enfatiza cómo la capacidad de este tipo de reactor de operar en estado estacionario es ventajosa para el estudio de sistemas catalíticos heterogéneos. Consecuentemente, se propone una práctica experimental para determinar ecuaciones de rapidez globales a partir de ecuaciones intrínsecas obtenidas por el método de la etapa limitante. Se emplea un reactor continuo de tanque agitado cuya fabricación y operación son sencillos y se describen a detalle. La hidrólisis de sacarosa se implementa como reacción modelo a 60 °C y 1 atm, siendo de fácil monitoreo. La reacción se cataliza con una resina ácida (Amberlite 120 H, capacidad total de intercambio ≥ 1.80 eq/L). El experimento ilustra una aplicación del método de la etapa limitante para la obtención de ecuaciones de rapidez de reacción global y es una herramienta didáctica para reforzar el aprendizaje práctico en cursos de ingeniería de reacciones heterogéneas.</p>

Multiphysics simulation of moisture-graphite oxidation in MHTGR

A small amount of moisture on the ppm level could present in the primary helium coolant under normal operations of High-Temperature Gas-cooled Reactors (HTGRs). One potential safety issue related to HTGRs is the chronic moisture-graphite oxidation, which could affect the integrity of the fuel blocks and reflectors in the reactor core, and the support columns in the hot plenum. However, it is infeasible to perform chronic moisture-graphite oxidation tests under the prototypic high-pressure, high-temperature conditions over a long period of time that is comparable to the full service time, i.e., 36 months for Modular High Temperature Gas-cooled Reactor (MHTGR). As an alternate, accelerated moisture-graphite oxidation tests at the atmospheric pressure and high moisture concentrations have been performed in the literature. Through these accelerated tests, global reaction rate equations have been proposed, which makes it possible to study the moisture-graphite oxidation numerically. This paper is aimed to establish a multiphysics model that can evaluate the moisture-graphite oxidation under MHTGR normal operation condition. COMSOL Multiphysics was applied to couple the modeling of the fluid flow, heat and mass transfer, chemical reaction and material structural changes. To reduce the calculation time, the prototypic three-dimensional structures were simplified into a two-dimensional simulation domain. The performance of four nuclear grades of graphite (IG-110, 2114, PCEA, and NBG-17) over a 36-month service period was then investigated under the most likely prototypic condition of MHTGR. The simulation results indicate that most oxidation occurs in the three or four bottom fuel blocks due to their higher temperatures. In general, however, only a thin layer of about 1.5 mm into the graphite will be considerably oxidized even for those three or four bottom fuel blocks.

A fast regression model for the interpretation of electrochemical impedance spectra of Intermediate Temperature Solid Oxide Fuel Cells

A frequency domain transformation method is applied to a physically consistent model of an IT-SOFC with MIEC electrolyte. Fast computation of the impedance spectra is achieved, which allows to apply the model to kinetic studies using traditional regressive techniques. The model includes conservation equations of mass and charge, gas diffusive transport effects and leakage current effects due to the semiconductor electrolyte. Global rate equations for the electrocatalytic semi-reactions guarantee economy of calibrated parameters. Two sets of impedance experiments collected on electrolyte-supported Cu-Pd-CZ80-SDC/SDC/LSCF-GDC cells are analyzed. The description of the H2 oxidation process is improved based on experiments with H2/N2 mixtures at fixed temperature and increasing H2 molar fraction (700 °C, 30–100% H2). The introduction of constant phase elements proves essential to closely predict Nyquist and Bode plots: strong inhomogeneity of the anode structure emerges, while the cathodic determining process is better identified via refinement of the double layer capacitance. Novel impedance experiments, performed with a CO-rich mixture (97% CO, 3% CO2) between 600 °C and 700 °C, allow to estimate the kinetic constant for CO electro-oxidation. The variation of the CPE parameters suggests that carbon deposition during exposure to CO simultaneously reduces the anodic active area and double layer capacitance.

On the E-H transition in inductively coupled radio frequency oxygen plasmas: II. Electronegativity and the impact on particle kinetics

In this series of two papers we present results about the E-H transition of an inductively coupled oxygen discharge driven at radio frequency (13.56 MHz) for different total gas pressures. The mode transition from the low density E-mode to the high density H-mode is studied using comprehensive plasma diagnostics. The measured electron density can be used to distinguish between the different operation modes. This paper focuses on the determination of the negative atomic ion density and the electronegativity by two experimental methods and global rate equation calculation. As a result, the electronegativity significantly decreases over two orders of magnitude from about 25 in the E-mode to about 0.1 in the H-mode. The temporal behavior of the electronegativity in pulsed ICP shows that the negative atomic ion density reaches a steady state after 10 ms. Negative atomic ions are mainly produced by the dissociative attachment with the molecular ground state. The ion–ion recombination with the positive molecular ions and the collisional detachment with the singlet molecular metastables contribute significantly to the loss of the negative atomic ions.

On the E-H transition in inductively coupled radio frequency oxygen plasmas: I. Density and temperature of electrons, ground state and singlet metastable molecular oxygen

In this series of two papers, the E-H transition in a planar inductively coupled radio frequency discharge (13.56 MHz) in pure oxygen is studied using comprehensive plasma diagnostic methods. The electron density serves as the main plasma parameter to distinguish between the operation modes. The (effective) electron temperature, which is calculated from the electron energy distribution function and the difference between the floating and plasma potential, halves during the E-H transition. Furthermore, the pressure dependency of the RF sheath extension in the E-mode implies a collisional RF sheath for the considered total gas pressures. The gas temperature increases with the electron density during the E-H transition and doubles in the H-mode compared to the E-mode, whereas the molecular ground state density halves at the given total gas pressure. Moreover, the singlet molecular metastable density reaches 2% in the E-mode and 4% in the H-mode of the molecular ground state density. These measured plasma parameters can be used as input parameters for global rate equation calculations to analyze several elementary processes. Here, the ionization rate for the molecular oxygen ions is exemplarily determined and reveals, together with the optical excitation rate patterns, a change in electronegativity during the mode transition.

Thermogravimetry study of Gd2O3 chlorination

The reaction between Gd2O3(s) and Cl2(g) was studied in a high-resolution thermogravimetric system. The reaction product was GdOCl, which was the unique solid phase produced in all the temperature range studied. The GdOCl is subsequently chlorinated producing GdCl3 for temperatures above 1123 K. The system is under chemical control for temperatures below 723 K. It was found that the reaction order with respect to the chorine partial pressure is 0.77 and the activation energy is 132 kJ mol−1 for the temperature range of 623–723 K. The global rate equation was developed. The GdOCl obtained was characterized by X-ray diffraction, scanning electron microscopy and magnetic measurements. The structure of GdOCl was refined with the Rietveld method, and it crystallized in a tetragonal form of REOX possessing the Matlockite-type (PbFCl) structure. The magnetic measurements indicated that the sample is paramagnetic at all the measurement ranges. The parameters of the Curie–Weiss law obtained were as follows: θ = −12.0 K, C = 7.9592 emu K mol−1 and µ eff = 7.98µ B.

CO2 gasification rate analysis of coal in molten blast furnace slag—For heat recovery from molten slag by using a chemical reaction

The coal gasification rate of Datong coal in molten blast furnace slag using carbon dioxide as gasifying agent was studied at the temperature ranging from 1473 to 1723 K. The kinetic model was developed. The influence of reaction temperature and coal/slag mass ratio in the reaction rate was analyzed. The reaction rate has a strong dependence on reaction temperature and coal/slag ratio. The peak value of reaction rate increases firstly, and then levels off, or even decreases a little as temperature increases. Within the same reaction time, the carbon conversion and peak value of reaction rate increase with increasing coal/slag ratio. Molten BF slag is active catalyst for carbon gasification. The volume reaction model A1 has the best fit on coal gasification in molten BF slag. The kinetic parameters applicable to volume reaction model at high temperature with different coal/slag ratios were obtained. The value of intrinsic activation energy is between 50 kJ/mol and 90 kJ/mol. The global rate equation that includes these parameters was developed.Rate=ⅆxⅆt=k0iexp(−EaiRT)(1−x)

Developing global reaction rate model for CO oxidation over Au catalysts from past data in literature using artificial neural networks

In this work, the literature for CO oxidation kinetics over Au based catalysts was analyzed using artificial neural networks to test the possibility of developing global reaction rate models representing the entire literature. A database was constructed using the data obtained from nineteen papers published between the years 1997 and 2011; then, the reaction rate was modeled as a function of catalyst preparation and operational variables by using neural networks. Next, global reaction rate equations in the form of power law were developed for each support type by the help of the neural network model, and the order of reaction with respect to each reactant and the parameters of Arrhenius relation were estimated. These power law models were successfully validated by using the information reported in the literature; hence, it was concluded that they can be used for the initial estimation of the reaction rates in the absence of more specific rate equations.

Kinetic Study of Europium Oxide Chlorination

The kinetics of europium oxide (Eu2O3) chlorination using gaseous chlorine as a chlorination agent was studied between 523 K and 1223 K (250 °C and 950 °C). The relative mass change during the chlorination reaction was continuously monitored using a high resolution thermogravimetric system. The starting temperature for the reaction of Eu2O3(s) with chlorine was determined at about 523 K (250 °C) with the formation of solid europium oxychloride (EuOCl). For temperatures above 1123 K (850 °C), the EuOCl(s) is chlorinated producing EuCl3(l). The influence of gaseous flow rate, sample mass, chlorine partial pressure, and temperature on the reaction rate was analyzed. The results showed that for 673 K (400 °C) and temperatures below, the system is under chemical control. Concerning the influence of chlorine partial pressure, it was determined that pressures greater than 50 kPa do not modify the kinetic regime. For the experiment at 673 K (400 °C), it was found that the chlorination rate was proportional to a potential function of the partial pressure of chlorine whose exponent is 0.54. The conversion curves were analyzed with the Johnson–Mehl–Avrami description. Intrinsic activation energy of 115 kJ mol−1 was obtained for the temperature range of 573 K to 673 K (300 °C to 400 °C). Finally, a global rate equation that includes these parameters was developed.

Multivacuum initial conditions and the arrow of time

Depending on the type and arrangement of metastable vacua in the theory, initial conditions in a de Sitter vacuum with arbitrarily large entropy can be compatible with the observed arrow of time, if the causal patch or related measures are used to regulate divergences. An important condition, however, is that the initial vacuum cannot produce observers from rare fluctuations (Boltzmann brains). Here we consider more general initial conditions where multiple vacua have nonzero initial probability. We examine whether the prediction of an arrow of time is destroyed by a small initial admixture of vacua that can produce Boltzmann brains. We identify general criteria and apply them to two nontrivial examples of such initial probability distributions. The Hartle-Hawking state is superexponentially dominated by the vacuum with smallest positive cosmological constant, so one might expect that other initial vacua can be neglected; but in fact, their inclusion drastically narrows the range of theory parameters for which an arrow of time is predicted. The dominant eigenvector of the global rate equation of eternal inflation is dominated by the longest-lived metastable vacuum. If an arrow of time emerges in the single-initial-vacuum approximation, then we find that this conclusion survives the admixture of other initial vacua. By global-local measure duality, this result amounts to a successful consistency test of certain global cutoffs, including light-cone time and scale-factor time.

Rovibrational internal energy transfer and dissociation of $\mathbf { \rm N_2(^1\Sigma _g^+)-\rm N(^4S_u)}$N2(1Σg+)−N(4Su) system in hypersonic flows

A rovibrational collisional model is developed to study energy transfer and dissociation of N(2)((1)Σ(g)(+)) molecules interacting with N((4)S(u)) atoms in an ideal isochoric and isothermal chemical reactor. The system examined is a mixture of molecular nitrogen and a small amount of atomic nitrogen. This mixture, initially at room temperature, is heated by several thousands of degrees Kelvin, driving the system toward a strong non-equilibrium condition. The evolution of the population densities of each individual rovibrational level is explicitly determined via the numerical solution of the master equation for temperatures ranging from 5000 to 50,000 K. The reaction rate coefficients are taken from an ab initio database developed at NASA Ames Research Center. The macroscopic relaxation times, energy transfer rates, and dissociation rate coefficients are extracted from the solution of the master equation. The computed rotational-translational (RT) and vibrational-translational (VT) relaxation times are different at low heat bath temperatures (e.g., RT is about two orders of magnitude faster than VT at T = 5000 K), but they converge to a common limiting value at high temperature. This is contrary to the conventional interpretation of thermal relaxation in which translational and rotational relaxation timescales are assumed comparable with vibrational relaxation being considerable slower. Thus, this assumption is questionable under high temperature non-equilibrium conditions. The exchange reaction plays a very significant role in determining the dynamics of the population densities. The macroscopic energy transfer and dissociation rates are found to be slower when exchange processes are neglected. A macroscopic dissociation rate coefficient based on the quasi-stationary distribution, exhibits excellent agreement with experimental data of Appleton et al. [J. Chem. Phys. 48, 599-608 (1968)]. However, at higher temperatures, only about 50% of dissociation is found to take place under quasi-stationary state conditions. This suggest the necessity of explicitly including some rovibrational levels, when solving a global kinetic rate equation.

High pressure kinetics of CH4, CO and H2 combustion over LaMnO3 catalyst

A high pressure kinetic study was carried out in a wide range of operating conditions to study the effects of pressure, temperature, fuel concentration and equivalence ratio on the catalytic combustion of methane, hydrogen and carbon monoxide over a perovskite-based catalyst. A plate type reactor configuration was chosen. This geometry allowed working in a kinetic control avoiding mass transfer limitations if appropriate experimental conditions are chosen. Since especially for GT application it is important to study the ignition phenomenon, which results to be ruled by kinetics, the study of the kinetics of CH4, H2 and CO catalytic combustion was carried out in a range of temperature consistent with the ignition temperatures and global reaction rate equations were derived.

Kinetic study of Hubnerite (MnWO4) chlorination

The kinetics of Argentinean Hubnerite (MnWO4) chlorination using gaseous chlorine as chlorination agent was studied between 750 and 950°C. The relative mass change during the chlorination reaction was continuously monitored using a high resolution thermogravimetric system. The starting temperature for the reaction of the manganese tungstate with chlorine was determined at about 650°C. The influence of gaseous flow rate, sample mass, chlorine partial pressure, and temperature on the reaction rate was analyzed. The dependence of the reaction rate with sample mass clearly indicates that the reaction is not occurring under chemical control, so the reaction proceeds under mixed control for sample masses greater than 0.5mg. In those conditions, an apparent activation energy of 198±9kJmol−1 was obtained with an isoconversional method. Concerning the influence of chlorine partial pressure, it was determined that pressures greater than 35kPa do not modify the kinetic regime. For the experiment at 850°C, it was found that the chlorination rate was proportional to a potential function of the partial pressure of chlorine whose exponent is around 0.85. Finally, a global rate equation that includes these parameters was developed.

Destruction of methylphosphonic acid in a supercritical water oxidation bench-scale double wall reactor

The destruction of methylphosphonic acid (MPA), a final product by hydrolysis/neutralization of organophosphorus agents such as sarin and VX (O-ethyl S-[2-(diisopropylamino)ethyl] methylphosphonothionate), was investigated in a a bench-scale, continuous concentric vertical double wall reactor under supercritical water oxidation condition. The experiments were conducted at a temperature range of 450-600°C and a fixed pressure of 25 MPa. Hydrogen peroxide was used as an oxidant. The destruction efficiency (DE) was monitored by analyzing total organic carbon (TOC) and MPA concentrations using ion chromatography on the liquid effluent samples. The results showed that the DE of MPA up to 99.999% was achieved at a reaction temperature of 600°C, oxygen concentration of 113% storichiometric requirement, and reactor residence time of 8 sec. On the basis of the data derived from experiments, a global kinetic rate equation for the DE of MPA and DE of TOC were developed by nonlinear regression analysis. The model predictions agreed well with the experimental data.

Kinetics of yttrium oxide carbochlorination

The chlorination kinetics of the Y 2O 3–sucrose carbon system was studied by thermogravimetry. This work is a continuation of a previous one in which the reaction stages and the stoichiometry of each reaction have been determined. The influence of carbon content, total flow rate, sample initial mass and chlorine partial pressure was evaluated. The effect of carbon content on the reactive mixture was studied between 6.7 and 70% (carbon mass/total mass). The results showed that the reaction rate of each stage is strongly increased as the carbon content increases and the range of occurrence of the stages depends on the amount of carbon in the solid reactive mixture. The formation reaction of YOCl ( STAGE I) is chemically controlled for temperatures lower than 700 °C with average effective activation energies of 165 ± 6 and 152 ± 7 kJ/mol for 8.7 and 16.7%C, respectively. The formation of the YOCl follows a nucleation and growth mechanism, with a combination of continuous nucleation and site saturation, and anisotropic growth controlled by diffusion. The kinetics of STAGE I can be expressed by the following global rate equation that includes the variables analyzed: d α d t = k 0 B exp − E a R g T p C l 2 { n ( 1 − α ) [ − ln ( 1 − α ) ] } ( n − 1 ) / n where k 0 B = 1.9 × 10 4, n = 1.20 for 8.7%C, and k 0 B = 8.4 × 10 3, n = 1.14 for 16.7%C. STAGES II and III correspond to the YOCl carbochlorination to form YCl 3, being these stages kinetically different. It was not possible to obtain kinetic parameters for these stages. The reaction rate of STAGE II is affected by diffusion of Cl 2 through the gas film surrounding the sample and mass changes in STAGE III have two opposite components: formation and evaporation of liquid YCl 3.

Kinetic study of Argentinean asphaltite gasification using carbon dioxide as gasifying agent

The kinetics of Argentinean asphaltite char gasification using carbon dioxide as gasifying agent was studied between 1048 and 1223 K. The chars were obtained by pyrolysis of an asphaltite in a fixed bed reactor. The relative mass change during the gasification reaction was continuously monitored using a high resolution thermogravimetric system. The starting temperature for the reaction of the char with carbon dioxide was determined at about 800 K. The influence of gaseous flow rate, sample mass, carbon dioxide partial pressure and temperature in the reaction rate was analyzed. The experimental condition under which the progress of gasification reaction is chemically controlled was established. In those conditions, an activation energy of 185 kJ mol −1 was obtained with an isoconversional method. Concerning the influence of carbon dioxide partial pressure, it was determined that pressures greater than 50 kPa do not alter the kinetics regime. Finally a reaction order of 0.5 for carbon dioxide partial pressure was determined and a global rate equation that includes these parameters was developed. Rate = d α dt = ( 1 - α ) 2 / 3 · 1.1 × 10 5 exp - 185 kJ mol - 1 R · T · P CO 2 0.5

Kinetics of Char Gasification with CO2 under Regime II Conditions: Effects of Temperature, Reactant, and Total Pressure

There are relatively few studies reported in the literature characterizing the kinetics of high-pressure, high-temperature char gasification reactions. Of particular interest to the application of kinetic data to gasification models are studies that provide links between reaction rate data relevant to high-temperature conditions, where some extent of pore diffusion limitation may apply, and lower-temperature, intrinsic gasification reactivity data. This work describes the effects of temperature, reactant partial pressure, and total pressure on the kinetics of the char−CO2 reaction under conditions where reactant diffusion through the pores of the reacting char has been shown to impact the overall conversion rate. A global nth-order rate equation was used to describe these kinetics, in particular, the effect of temperature (via the activation energy) and reactant pressure (via the reaction order). As expected, activation energies at high temperatures (≥∼1300 K) were consistently less than those obtained un...

Characterization of Biodiesel and Biodiesel Particulate Matter by TG, TG−MS, and FTIR

Biodiesel is a potential renewable and carbon-neutral alternative to fossil fuels, and it is environmentally and economically attractive. This paper studies the decomposition kinetics of biodiesel using thermal gravimetric analysis (TGA) in one-stage pyrolysis. Biodiesel can be decomposed at 119−237 °C. The kinetic parameters for biodiesel pyrolysis were obtained from the TGA experiments. The global rate equation for biodiesel pyrolysis can be expressed as dX/dt = 2.6 × 107 exp(−16.2/8.314 × 10−3T)(1 − X)0.52 (X denotes the reaction conversion). Characteristics of diesel and biodiesel and the associated diesel particulate matter (DPM) emitted from a nonroad diesel generator were also analyzed by Fourier transform infrared (FTIR) spectroscopic methods. The FTIR spectra of biodiesel showed a C═O stretching band of methyl ester at 1743 cm−1 and C−O bands at 1252, 1200, and 1175 cm−1. Furthermore, the FTIR spectra of DPM were similar to those of the fuels, an indication that the chemical structures of DPM are closely related to the fuel and engine oil properties, consistent with our previous study. The temperature series of 11 fragments have been analyzed in nitrogen, which include m/z 29, 31, 44, 74, 87, 105, 143, 263, 294, 296, and 298. The fragments at m/z 294, 296, and 298 represent the methyl ester components of biodiesel, and the fragment at m/z 44 is carbon dioxide, fragments at m/z 29 and 105 represent aldehyde compounds, and fragments at m/z 87 and 143 are shorter chain methyl esters, all of which can be byproducts from biodiesel combustion. The fragments at m/z 57, 67, 95, and 109 represent hydrocarbon components, which may be fragmented from the long carbon chains of methyl esters, and the fragment at m/z 31 is a methoxy group, which may be fragmented from methyl esters. The information of TG−MS as analyzed above can offer a better understanding of the byproduct formation mechanisms of biodiesel combustion.

Reduction of NO by activated carbon in the presence of vanadium

The NO reduction characteristics of a vanadium supported activated carbon catalyst have been examined without addition of reducing agent (i.e., ammonia, NH 3). The catalyst was prepared from commercial coconut activated carbon that was impregnated with 2.8 wt.% vanadium. The NO reduction reactions were conducted under conditions with 3% O 2 and without O 2 in a fixed bed reactor. In the condition with O 2, 84% NO conversion resulted at 360 °C, though the catalyst began to burnout at a temperature higher than 300 °C and with large quantities of CO and CO 2 being emitted. In the condition without O 2, the burnout of the catalyst was insignificant and resulted in small amounts of CO and CO 2. The NO conversion increased gradually with the reaction temperature reaching 78% at 450 °C. SEM photographs and BET measurements are useful tools for understanding the burnout phenomena with the catalyst. The burnout in the condition with O 2 resulted in the catalyst rapidly losing its activity. However, in the condition without O 2, the catalyst gradually lost its activity and finally approached a steady state. Moreover, the modified mechanism scheme of the NO reduction reactions without NH 3 and with the catalyst is described and the global rate equation for the reaction without O 2 is obtained.

Oxidation Kinetics of Spent Low-Level Radioactive Resins

Experimentally, two-stage oxidation of spent low-level radioactive resin was found by thermo-gravimetric analysis (TGA). About 24% of the spent resins was oxidized at 600 to 900 K. Online Fourier transform infrared spectra showed that the decomposition of the -SO3H species in the resin to SO2 occurred at 670 and 1020 K. The numerical calculation from TGA weight loss data at different heating rates showed that the global activation energies for oxidation of the spent resins were 108 to 138 kJ·mol–1. The reaction orders for resin and oxygen were about 1.0 and 3.5, respectively. The global rate equations for oxidation of the resin in the first and second stages can be expressed as dx1/dt (s–1) = 2.3 × 107 (s–1)exp[–117 900(J·mol–1)/T(K)][1 – x (%)]0.82 [O2 (vt%)]3.5 (x denotes the reaction conversion) and dx2/dt = 8.4 × 1017 exp(–239 500/RT) (1 – x)0.9[O2]4.5, respectively.