Empirical Rate Equation Research Articles

Kinetic investigation on palladium‐catalyzed carbonylation of allyl alcohol

AbstractPalladium‐catalyzed carbonylation of allyl alcohol to 3‐butenoic acid has been investigated. A significant effect of halide promoters, p‐tolylsulfonic acid (TsOH), water, solvents, and PPh3 concentration activity and selectivity has been studied. Detailed kinetics of this reaction was investigated in a temperature range of 363–383 K. The influence of parameters such as stirring speed, allyl alcohol, catalyst, benzyltriethylammonium chloride (BTEAC), TsOH concentrations, and CO partial pressures on the activity and selectivity has been studied. An empirical rate equation was suggested and found to be fairly consistent with observed rate data. In addition, the activation energy and kinetic parameters were evaluated.

Independent Control of the Width and Length of Semiconducting 2D Nanorectangles via Accelerated Living Crystallization-Driven Self-Assembly.

Self-assembly of conjugated polymers offers a powerful method to prepare semiconducting two-dimensional (2D) nanosheets for optoelectronic applications. However, due to the typical biaxial growth behavior of the polymer self-assembly, independent control of the width and length of 2D sheets has been challenging. Herein, we present a greatly accelerated crystallization-driven self-assembly (CDSA) system of polyacetylene-based conjugated polymer to produce 2D semiconducting nanorectangles with precisely controllable dimensions. In detail, rectangular 2D seeds with tunable widths of 0.2-1.3 μm were produced by changing the cosolvent% and grown in the length direction by uniaxial living CDSA up to 11.8 μm. The growth rate was effectively enhanced by tuning the cosolvent%, seed concentration, and temperature, achieving up to 27-fold increase. Additionally, systematic kinetic investigation yielded empirical rate equations, elucidating the relationship between growth rate constant, cosolvent%, seed concentration, and seed width. Finally, the living CDSA allowed us to prepare penta-block comicelles with tunable width, length, and height.

Deactivation kinetic study on vapor phase Beckmann rearrangement of cyclohexanone oxime and design of the multi-layer inclined channel bionic reactor

The optimal design of the reaction system of a large-scale industrial vapor phase Beckmann rearrangement of cyclohexanone oxime to caprolactam process requires both deactivation kinetics and reactor optimization. The deactivation kinetics was study in a micro fluidized bed reactor with online catalyst particle sampling system. An empirical coke formation rate equation was obtained based on time evolution of coke amounts. A Langmuir-Hinshelwood kinetics with deactivation factor based on coke amount was developed. Based on the obtained deactivation kinetics, a Multi-layer Inclined Channel Bionic Reactor was designed as a substitute of the conventional fixed-bed reactor. The hierarchical structure has four levels with inclined channel implementation in the third and fourth level to reduce the pressure drop and improve the flow distribution uniformity. The optimized massive structure of the Multi-layer Inclined Channel Bionic Reactor designed for 200 thousand tons of CPL productivity has a total pressure drop lower than 2kPa, and the maximal relative difference of the bed infiltration velocity is about 11 %.

Simulation of Cathode Catalyst Durability Under Fuel Cell Vehicle Operation - the Effect of Fuel Cell Stack Size

The concerns regarding climate change have made the researchers seek a clean alternative for the fossil fuel vehicles. Fuel cell vehicles (FCVs) are considered to be promising candidates owing to their efficient energy conversion and zero-carbon emission. However, a number of obstacles such as high cost and limited hydrogen infrastructure have made the FCVs commercialization process challenging. Polymer electrolyte membrane fuel cells (PEMFCs) have been proven promising for transportation applications. For heavy duty transportation applications, the PEMFC durability is also not yet proven, and extrapolating from lab data to real-world field operating conditions remains a significant challenge [1].In this work, the cathode catalyst degradation in PEMFC is studied to estimate the effect of stack size on fuel cell durability in the FCV application. Platinum dissolution and redeposition, platinum oxidation and platinum ion formation during the fuel cell operation are modeled using the Butler-Volmer approach presented in [2]. A drive cycle recorded based on a real-life transit bus operation in the city of Victoria is utilized to calculate the input fuel cell voltage profile based on the methodology presented by Ahmadi and Kjeang [3]. According to this methodology, the required cell power density is calculated using Newton’s second law considering the air flow drag force as a counteracting force against the vehicle movement. Then, the required voltage cycle is obtained by employing a polarization curve characterizing the fuel cell performance. Finally, the change of remaining electrochemically active surface area (ECSA) with time is calculated as the output of the model. The fuel cell is assumed to operate at 80 ℃ and the cell active area is considered to be 500 cm2. Simple Tafel kinetics is then used to determine the fuel cell voltage loss. A 10% voltage drop at 0.6 A/cm2 is considered as the failure criterion for the cathode lifetime. Moreover, the effect of the fuel cell stack size is studied. By increasing fuel cell stack size, the required cell power density drops, leading to a decrease in the voltage cycle amplitude while the voltage cycle period remains the same. According to the empirical kinetic rate equation, the catalyst degradation exponentially increases with increasing the voltage. Therefore, a higher degradation rate is observed for a catalyst operating on a voltage cycle with a lower amplitude while the period and the upper potential limit (UPL) are maintained the same, causing a significant platinum ion generation. Fig. 1 shows the change of remaining ECSA over time and resulting fuel cell lifetime for three stack sizes which are represented by the stack nominal powers. The results show that the fuel cell lifetime will be roughly doubled when the stack size is reduced by half. Stack sizing is thus an important consideration for fuel cell durability in the FCV application.In this regard, predicting fuel cell lifetime is a crucial step in commercializing FCVs. The present modeling framework could be utilized by FCV developers to predict lifetime for new products instead of carrying out time-consuming lifetime experiments. The factors influencing fuel cell durability can also be investigated using the present model framework to develop durables cells and stacks for a targeted FCV application. Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada, Canada Research Chairs, and Simon Fraser University Community Trust Endowment Fund.

Thermodynamic Analysis of the Landolt-Type Autocatalytic System

A recent work demonstrated the example of the Landolt-type reaction system and how the simplest autocatalytic loop is described by the kinetic mass action law and proper parametrization of direct and autocatalytic pathways. Using a methodology of non-equilibrium thermodynamics, the thermodynamic consistency of that kinetic model is analyzed and the mass action description is generalized, including an alternative description by the empirical rate equation. Relationships between independent and dependent reactions and their rates are given. The mathematical modeling shows that following the time evolution of reaction rates provides additional insight into autocatalytic behavior. A brief note on thermodynamic driving forces and coupling with diffusion is added. In summary, this work extends and generalizes the kinetic description of the Landolt-type system, placing it within the framework of non-equilibrium thermodynamics and demonstrating its thermodynamic consistency.

An intelligent equation for methane hydrate growth kinetics

We explore the use of deep artificial neural networks (DNNs) to impute data to the experimental data reported by the methane hydrate crystal growth at a bubble surface reported in the literature (Ma, et al., 2002; Sun et al., 2007). We use a genetic programming symbolic regressor to propose a novel empirical rate equation as a function of the temperature and the pressure from the new data set.

Kinetics of 1‐decene hydroformylation in an aqueous biphasic medium using a water‐soluble Rh‐sulfoxantphos catalyst in the presence of a cosolvent

AbstractThe kinetics of hydroformylation of 1‐decene has been studied in an aqueous biphasic medium using a water‐soluble Rh‐sulfoxantphos catalyst in the presence of N‐methyl pyrrolidone as a cosolvent at 383‐403 K. The rate was found to be first order, with concentrations of catalyst and olefin and partial order, with concentrations of hydrogen in the liquid phase. The plot of rate versus excess ligand and CO concentrations passed through maxima, indicating negative order dependence at higher concentrations. These trends have been interpreted based on the established hydroformylation mechanism. High selectivity towards the linear aldehyde was maintained (n: iso ratio > 30). An empirical rate equation has been proposed which was found to be in good agreement with the observed rate data within the experimental error. The activation energy was evaluated to be 74.76 kJ/mol.

Stannous Chloride Reductive Treatment and Kinetics Using Hexavalent Chromium in Water Supplies

Hexavalent chromium [Cr(VI)] occurs in groundwater and poses potential health concern when present above 10 μg/L in drinking water. Cr(VI) redox conversion to Cr(III), a less toxic and soluble chromium species at groundwater pH, is potentially an effective strategy to control Cr(VI). Stannous chloride (SnCl2), which is already approved for use in drinking water treatment, was investigated in model and real Arizona groundwater for Cr(VI) reduction to Cr(III) by using a jar testing apparatus. With <1 min of mixing, SnCl2 chemically reduced Cr(VI), producing both soluble and particulate forms of tin and chromium. The rate and extent of this reaction varied as a function of Sn(II):Cr(VI) dosing ratios and pH. An empirical rate equation was parameterized using experimental data: d[Cr(VI)]/dt = −k[H+]−0.25[Sn2+]0.85[CrO42−]3 with k = 0.033 μM−2.6s−1. Experimental results and equilibrium modeling showed that apparent competition occurs in real groundwater where coexisting oxyanions (e.g., arsenate) likely react with SnCl2. While freshly prepared commercial-grade and reagent-grade SnCl2 solutions behaved similarly, exposure to the air for 1 to 2 weeks resulted in >50% reduction in Cr(VI) removal capability and raised concern over on-site storage or intermittent use as a wellhead treatment strategy. Results suggest that SnCl2 reductive treatment is a simple, rapid, and highly effective method to treat Cr(VI) in groundwater.

Kinetic characterization of hexavalent chromium stabilization in contaminated soils amended with cocopeat

Cocopeat is a cheap and easily available organic product. In this study, kinetics of hexavalent chromium [Cr(VI)] stabilization by cocopeat in three soils with different pH and organic carbon content, and the effects of influencing factors including ionic strength (0.03, 0.1 and 0.3 M KCl), temperature (10, 25 and 35 °C) and pH (5.2, 6.2 and 7.2) were investigated in a set of batch experiments by varying Cr(VI) and cocopeat concentrations. In this research, there was no possibility of spiking the soils with the same range of initial Cr(VI) concentration. Addition of Cr(VI) in higher levels masked the effect of soil on Cr(VI) reduction in a calcareous soil, while lower levels resulted in complete stabilization of Cr(VI) in a slightly acid soil. Cocopeat efficiently stabilized Cr(VI) in the soil suspensions within a few days. The time trend of Cr(VI) reduction was different in the three soil samples. The rate of Cr(VI) stabilization strongly increased with decreasing pH and increasing temperature, while remained unchanged with changes in ionic strength. Finally, the overall empirical pseudo-first order rate equation was determined to describe the reduction rate of Cr(VI) by cocopeat in soils.

Deactivation Kinetics of the Catalytic Alkylation Reaction

A kinetics theory of catalyst deactivation is presented of the solid acid-catalyzed alkylation reaction of isobutane with propylene or butene that gives alkylate, a high octane fuel, as product. The intimate relation between the kinetics network of the reaction, catalyst deactivation kinetics, and residence time distribution is analyzed. The question is addressed why the deactivation of the alkylation reaction in a continuously stirred tank reactor (CSTR) is slow compared to that in a tubular plug flow reactor (PFR). Conditions are derived where such differences will be minimum and maximum. In the reaction regime of high alkylate selectivity, linear and quadratic power law kinetics equations in propylene concentration can be deduced from microkinetics. They are used to derive analytical expressions of deactivation times for CSTR and PFR. The theoretical power law kinetics equations can be related to previously established empirical rate equations of catalyst deactivation. We show that, in the CSTR, the self-alkylation reaction path contributes substantially to the deactivation time. In the self-alkylation reaction, alkylate is formed by reaction of the isobutene reaction intermediate and isobutane. Catalysts of high proton strength can benefit catalyst deactivation times by suppressing the carbenium ion deprotonation reaction that produces alkenes as isobutene. In the PFR, selective alkylate formation occurs only when the reaction occurs in a reaction zone of the catalyst bed. Deactivation is faster than in CSTR because of the reactant profile in the reaction zone. This reaction zone has restricted mobility due to the fast deactivation of reactive protons located behind the reaction zone by alkenes formed by nonselective reactions in the reaction zone. In PFR, as long as the reaction is limited to an immobile reaction zone, deactivation time is independent of reaction site density and contact time. Contact time dependence arises when the reaction zone is mobile. Overall deactivation time then depends strongly on the degree of deactivation of the protons behind the reaction zone.

Kinetics of hydroformylation of camphene using rhodium‐phosphite catalyst

AbstractKinetics of hydroformylation of camphene was investigated in the presence of [Rh(CO)2(acac)]/P(OPh)3 catalyst in a temperature range of 363–383 K. The influence of parameters such as stirring speed, camphene, catalyst, ligand concentrations, and partial pressures of H2 and CO on the activity and selectivity of the catalyst has been studied. The rate showed a first‐order dependence with respect to catalyst and camphene concentrations. The effect of partial pressure of hydrogen showed fractional order dependence. The plots of rate versus excess ligand, that is, (P(OPh)3) concentration and rate versus CO partial pressure passed through maxima and showed typical substrate/ligand inhibited kinetics. An empirical rate equation has been proposed and found to be in good agreement with the observed rate data. The kinetic parameters and activation energy were also evaluated.

A Unique Methodology for Tool Life Prediction in Machining

In this paper, a unique approach for estimating tool life using a hybrid finite element method coupled with empirical wear rate equation is presented. In the proposed approach, the computational time was significantly reduced when compared to nodal movement technique. However, to adopt such an approach, the angle between tool’s rake and flank faces must be constant through the process and at least two cutting experiments need to be performed for empirical model calibration. It is also important to predict the sliding velocity along the tool/flank face interface accurately when using Usui’s model to predict the tool wear rate. Model validations showed that when the sliding velocity was assumed to be equivalent to the cutting speed, poor agreement between the predicted and measured wear rate and tool life was observed, especially at low cutting speed. Furthermore, a new empirical model to predict tool wear rate in the initial or break-in period as a function of Von Mises stress field was developed. Experimental validation shows that the newly developed model substantially improved the initial tool wear rate in terms of trend and magnitude.

A highly efficient and stable Ni/SBA-15 catalyst for hydrogen production by ethanol steam reforming

The production of hydrogen by steam reforming of ethanol was carried out on SBA-15-supported nano NiO catalyst synthesized by the equivalent-volume impregnation method with two different Ni sources (nickel nitrate and nickel sulfamate). The catalyst was characterized by N2 adsorption–desorption, X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy to examine the physical and chemical properties. The activity tests were performed with the steam, with water/ethanol molar ratio ranging from 2:1 to 15:1, the N2 flow rate from 20 to 120 mL min−1 to determine the space-time, and the temperature range from 623 to 923 K on the two different Ni source catalysts. A favorable operating condition was established at 823 K using water/ethanol = 6 molar ratio and carrier gas (N2) flow of more than 50 mL min−1 for nickel nitrate source, but for nickel sulfamate source, the optimum temperature changed to 773 K and other conditions were the same as for the nickel nitrate source. After eliminating the influence of internal and external diffusion factors, an empirical power-law kinetic rate equation was derived from the experimental data. The non-linear regression method was used to estimate the kinetic parameter. The activation energy of the catalyst was then calculated, and the supported nickel nitrate and nickel sulfamate catalysts were 25.345 and 41.449 kJ mol−1, respectively, which was in agreement with the experimental and model-predicted results.

Adsorption kinetics at solid/aqueous solution interfaces: On the boundaries of the pseudo-second order rate equation

The empirical pseudo-second order rate equation has become the equation of choice to account for adsorption kinetics at solid/aqueous solution interfaces. However, its validity boundaries still remain faint. Here, they are set on the basis of the predictions of the well-established Langmuir model, cast in terms of the relevant kinetic variables; i.e., the initial concentrations of the adsorbing species and of the free surface sites. It is shown that the pseudo-second order rate equation becomes valid when the adsorption equilibrium constant is large (larger than ca. 5×105 M-1), the initial concentrations of the reactants are nearly equal, and they surpass a certain critical value. For systems characterized by typical adsorption equilibrium constants, the pseudo-second order model seldom applies within the usually explored experimental conditions. This latter finding alerts on the significance of the reported rate constants that derive from the lax use of the pseudo-second order rate equation.

A library of BASIC scripts of reaction rates for geochemical modeling using phreeqc

Rate equations and kinetic parameters for about 100 minerals were programmed into a library of callable Basic language scripts for the geochemical modeling program Phreeqc (version 3.5.0) to facilitate the application of kinetics in geochemical modeling. For most minerals, the following general equation is used: rnet=SA∑jAje−Ea,j/RT∏iai,jni(1−Ωpj)qjwhere rnet stands for the net dissolution rate of a mineral phase (mol kgw−1 s−1); j the jth reaction mechanism; SA the surface area per unit water mass (m2 kgw−1); Aj the Arrhenius pre-exponential factor (mol m−2 s−1); Ea,j the apparent reaction activation energy (J mol−1); R the universal gas constant (8.31446 J mol−1 K−1); T the temperature (K); ai the activity of aqueous species i; Ω the mineral saturation quotient. pj and qj are empirical fitting parameters. j stands for the specific mechanisms of reaction. Other forms of rate equations and associated parameters programmed in the library include parallel mechanisms, Langmuir adsorption isotherm, and empirical rate equations that apply to a specific reaction mechanism or geochemical system. A separate file of PHASEs, which define the chemical stoichiometry of the phases, dissolution reactions, and equilibrium constants of the dissolution reactions, is also provided. PHREEQC requires that the names in PHASES and RATES blocks match with each other.The Basic language scripts can also be used as templates for writing other rate equations which users might wish to use. To illustrate the application of the script library, we simulated the reaction path of albite dissolution at 25 °C and 1 bar, using three rate equations and compared the results. The script and phase library and supporting materials can be downloaded from https://github.com/HydrogeoIU/PHREEQC-Kinetic-Library and doi.org/10.5967/41gq-yr13.

Study on the Removal of Thiosulfate from Wastewater by Catalytic Oxidation

Wastewater streaming from industrial plants, including petroleum refineries, chemical plants, pulp and paper plants, mining operations, electroplating operations, and food processing plants, can contain offensive substances such as cyanide, sulfides, sulfites, thiosulfates, mercaptans and disulfides that tend to increase the chemical oxygen demand (COD) of the streams. In the present work, removal of thiosulfate from wastewater by catalytic oxidation using aluminum oxide as a catalyst was studied. Four main factors were considered, namely the initial thiosulfate concentration, the hydrogen peroxide concentrations, the amount of the catalyst and the operating temperatures. The analysis of thiosulfate and sulfate was carried out by using UV Visible Spectrophotometer. An empirical rate equation was developed.

Methanation at Very Low COx/H2 Ratio: Effect of Ce on Ni–Ce–Al Catalyst Properties and Empirical Kinetics

The effect of CeO2 on catalytic properties of Ni–Al COx methanation catalyst obtained by co-precipitation and thermal processing of hydroxycarbonate precursors was discussed. A series of model Ni–Ce–Al catalysts with variable content of cerium oxide were synthetized and the effect of modifier on physicochemical properties and on methanation rate was studied with regard to the temperature and the concentration of carbon oxides. Values of activation energy and turn-over frequencies and exponents in empirical kinetic power rate equations were determined. The analysis of exponents values provided information about probable changes of carbon oxides sorption. A higher activity of Ni–Al–Ce catalysts in methanation reaction was found as compared to reference Ni–Al catalyst. Ce modified Ni–Al catalysts also showed higher TOF values which proves the formation of more active centers.

Kinetics of nitric acid leaching of cerium from oxidation roasted Baotou mixed rare earth concentrate

The kinetics of nitric acid leaching of cerium was investigated for the oxidation roasted Baotou mixed rare earth concentrate. The effects of leaching temperature, HNO3 concentration, liquid–solid ratio (L/S) and stirring rate on rare earth extraction were studied. The XRD and SEM mapping analysis of the samples before and after acid leaching shows that the roasted bastnaesite is completely leached. Besides, the decomposition process of oxidizing roasting was also obtained by TG–MS and XRD. Different kinetics models were applied in this leaching process. The results of dynamic fitting show that the leaching process can be described by a new variant of the shrinking-core model. And the leaching rate is controlled by both the interfacial transfer and diffusion through the product layer. The apparent activation energy is calculated as 76.78 kJ/mol and the reaction orders with respect to HNO3 concentrations and liquid–solid ratio are determined to be 7.609 and 2.516, respectively. Besides, an empirical rate equation is obtained to describe the process.

PRODUCTION OF HYDROGEN BY WATER-GAS SHIFT REACTION ON Ru/C CATALYST

This work explores the catalytic performance of a 2% ruthenium carbon (Ru/C) catalyst in the low temperature water-gas shift reaction (WGSR). The catalyst synthetized was characterized with X-ray diffraction (XRD) and specific surface area (BET) methods. The gas mixture of 15% carbon monoxide + argon and water were used as reagents. The operations catalytic were performed in a fixed bed reactor over a temperature range of 453–553 K. A numerical fitting algorithm was developed for the estimation of the kinetic parameters in a power-law model for the rate velocity. At 553K, 80% CO conversion was achieved, under steady state. For the empirical rate equation, the activation energy determined from the experimental data, was 190 kJ/mol.

Attrition in the kimberlite system

The sustained transportation of particles in a suspension commonly results in particle attrition leading to grain size reduction and shape modification. Particle attrition is a well-studied phenomenon that has mainly focussed on sediments produced in aeolian or fluvial environments. Here, we present analogue experiments designed to explore processes of attrition in the kimberlite system; we focus on olivine as it is the most abundant constituent of kimberlite. The attrition experiments on olivine use separate experimental set-ups to approximate two natural environments relevant to kimberlites. Tumbling mill experiments feature a low energy system supporting near continual particle-particle contact and are relevant to re-sedimentation and dispersal processes. Experiments performed in a fluidized particle bed constitute a substantially higher energy environment pertinent to kimberlite ascent and eruption. The run-products of each experiment are analysed for grain size reduction and shape modification and these data are used to elucidate the rates and extents of olivine attrition as a function of time and energy. Lastly, we model the two experimental datasets with an empirical rate equation that describes the production of daughter products (fines) with time. Both datasets approach a fines production limit, or plateau, at long particle residence times; the fluidized system is much more efficient producing a substantially higher fines content and reaches the plateau faster. Our experimental results and models provide a way to forensically examine a wide range of processes relevant to kimberlite on the basis of olivine size and shape properties.