Irreversible Second-order Reaction Research Articles

Modelling of Irreversible Homogeneous Reaction on Finite Diffusion Layers

The mathematical model proposed by Chapman and Antano (Electrochimica Acta, 56 (2010), 128–132) for the catalytic electrochemical–chemical (EC’) processes in an irreversible second-order homogeneous reaction in a microelectrode is discussed. The mass-transfer boundary layer neighbouring an electrode can contribute to the electrode’s measured AC impedance. This model can be used to analyse membrane-transport studies and other instances of ionic transport in semiconductors and other materials. Two efficient and easily accessible analytical techniques, AGM and DTM, were used to solve the steady-state non-linear diffusion equation’s infinite layers. Herein, we present the generalized approximate analytical solution for the solute, product, and reactant concentrations and current for the small experimental values of kinetic and diffusion parameters. Using the Matlab/Scilab program, we also derive the numerical solution to this problem. The comparison of the analytical and numerical/computational results reveals a satisfactory level of agreement.

Data-driven Nonlinear MPC using Dynamic Response Surface Methodology

Abstract For many complex processes, it is desirable to use a nonlinear model in the MPC design, and the recently proposed Dynamic Response Surface Methodology (DRSM) is capable of accurately modeling nonlinear continuous processes over semi-infinite time horizons. We exploit the DRSM to identify nonlinear data-driven dynamic models that are used in an NMPC. We demonstrate the ability and effectiveness of the DRSM data-driven model to be used as the prediction model for a nonlinear MPC regulator. This DRSM model is efficiently used to solve a non-equally-spaced finite-horizon optimal control problem so that the number of decision variables is reduced. The proposed DRSM-based NMPC is tested on a representative nonlinear process, an isothermal CSTR in which a second-order irreversible reaction is taking place. It is shown that the obtained quadratic data-driven model accurately represents the open-loop process dynamics and that DRSM-based NMPC is an effective data-driven implementation of nonlinear MPC.

Kinetics and mechanism of selenate and selenite removal in solution by green rust-sulfate.

This work investigated the removal of selenite and selenate from water by green rust (GR) sulfate. Selenite was immobilized by simple adsorption onto GR at pH 8, and by adsorption–reduction at pH 9. Selenate was immobilized by adsorption–reduction to selenite and zero valent selenium (Se0) at both pH 8 and 9. In the process, GR oxidized to a mixture of goethite (FeOOH) and magnetite (Fe3O4). The kinetics of selenite and selenate sorption at the GR–water interface was described through a pseudo-second-order model. X-ray absorption spectroscopy data enabled to elucidate the concentration profiles of Se and Fe species in the solid phase and allowed to distinguish two removal mechanisms, namely adsorption and reduction. Selenite and selenate were reduced by GR through homogeneous solid-phase reaction upon adsorption and by heterogeneous reaction at the solid–liquid interface. The selenite reduced through heterogeneous reduction with GR was adsorbed onto GR but not reduced further. The redox reaction between GR and selenite/selenate was kinetically described through an irreversible second-order bimolecular reaction model based on XAFS concentration profiles. Although the redox reaction became faster at pH 9, simple adsorption was always the fastest removal mechanism.

CHEMICAL INTERESTERIFICATION OF COTTON OIL WITH METHYL ACETATE ASSISTED BY ULTRASOUND FOR BIODIESEL PRODUCTION

In this study, research was performed on the interesterification reaction of cotton oil with methyl acetate, using potassium methoxide as catalyst, in the presence of ultrasonic waves. In order to obtain a better understanding of the process variables behavior, a response surface methodology was used along with statistical methods. The experiments were performed with molar ratio varying from 1:8 to 1:24, catalyst percentage of 0.1 to 1.3% (weight), ultrasonic nozzle amplitude varying from 30% to 90% (180 to 540 W) and vibration pulse varying from 50% to 90%. Process variables were optimized with the optimal molar ratio of 1:14.87, catalyst concentration of 1.17%, ultrasonic probe amplitude of 67.64% and vibration pulse of 67.30%. The average conversion of triglycerides was found to be 98.12% at the optimal conditions. The experimental data were adjusted to the second-order irreversible reaction approximation model, under optimized conditions, with temperatures of 30, 40 and 50 oC. Lastly, in comparison to the conventional methodology, a significant increase of 14% of triglycerides conversion utilizing ultrasonic waves was observed

A critical comparison of approximate solutions for enhancement factor for irreversible second-order reaction

In this paper, the exact numerical solution for the enhancement factor for mass transfer accompanied by an irreversible second-order reaction based on the film theory is presented. The accuracy of the numerical solution is enhanced by using non-uniform discretization steps and Richardson extrapolation. Approximate analytical solutions available in the literature for the enhancement factor for an irreversible second-order reaction were compared with presented numerical solution. All approximate solutions are able to predict the values of the enhancement factor with the relative deviations within 10% compared to the exact numerical solution for the film theory. However, the applicability of the model and some approximate solutions is limited to the fast reaction regime. The approximate solution of DeCoursey (1974), originally developed for the surface renewal theory, was adapted to the film theory by using a correction factor. The maximum relative deviation of the modified approximate solution is as low as 2.2% for entire range of parameters Ha and Ei (Hatta number and enhancement factor for instantaneous reaction), which is the best accuracy that has ever been reported for an explicit expression for the enhancement factor for an irreversible second-order reaction.

Theoretical modeling of transient reaction–diffusion dynamics in electrokinetic Y-shaped microreactors

We perform a theoretical study on transient reaction–diffusion kinetics in an electrokinetic Y-shaped microreactor. The flow is assumed to be both steady and fully developed. The governing equations are solved in dimensionless form utilizing a 3D finite-volume-based numerical algorithm, assuming a second-order irreversible reaction between the components. Analytical solutions are also obtained for cross-stream diffusion without reaction under a uniform velocity distribution. It is shown that the well-known butterfly-shaped form of the product concentration profile is not immediately created and it is established only after the system is sufficiently close to its steady-state. Furthermore, the inclination of the concentration peak toward the component of lower diffusivity or inlet concentration is less significant at the earlier stages of the production. Finally, it is demonstrated that the short-term influence of the parameters affecting the advection of mass on the total efficiency, defined as the ratio of the total production to the amount of the limiting reactant within the device, is quite the opposite of that at the steady-state.

Selective transport of zirconium (IV) and niobium (V) from hydrochloric media through a bulk liquid membrane

The selective transport of zirconium/niobium from hydrochloric medium has been investigated through a bulk liquid membrane (BLM) using tri-n-butyl-phosphate (TBP), tri-n-octylamine and dibenzo-18-crown-6 (DBC-6) as the extractants (carriers). The Optimization studies have been carried out by scrutinizing the effect of variables such as the hydrochloric acid concentration in the feed solution, membrane type and hydrochloric acid concentration in the strip solution using the Taguchi approach. The Quantitative transport of zirconium/niobium has been observed by 30% (v/v) TBP in 1200 min from the feed composed of a 9.0 M hydrochloric acid solution of Zr(IV), Nb(V) and lanthanide cations, while the transport of other cations, which have been presented along with Zr/Nb are less than 3% during the same time. Moreover, the possible mechanism of Zr(IV)/Nb(V) ion transport through the BLM has also been discussed and the results show a consecutive, irreversible second-order reaction at the interfaces. Transfer kinetics studies show that niobium transfer process exhibits slightly faster kinetics than zirconium.

Exploring electrochemical and sorptive aspects of interaction between dissolved sulfides and novel Fe-enriched aluminosilicate composites

Three types of functional ceramic composites were designed, synthesized and probed for effective sulfide removal from aqueous solutions. The main goal was to examine complex influence of graphite, surpluses of Fe (∼4%) and micro-additions of Cu (∼0.2%) on the functional features of the composites. The structural, textural, morphological and surface characteristics of the composites were examined in detail by XRD, nitrogen sorption, SEM and FTIR. It has been shown that all composites are solid heterogeneous systems containing amorphous and crystalline phases (graphite, hematite, montmorillonite, quartz, etc.) with pronounced redox activity in contact with sulfide aqueous solutions. Great enhancment of sulfide consumption was detected for composites which contained graphite and it was established that reaction kinetics is fitted to irreversible second-order batch reaction with two reactants. After the treatment of 1 mM S2− solution, using composite dossage of 1 g/dm3, concentration dropped down to 0.02 mM. In addition, cyclic voltammetry at 50 mV/s revealed the key role of dopants in electrochemical aspect of the process. Obvious boost of S2− uptake is ascribed to numerous electrochemical, chemical and sorption processes on the composite’s developed surface.

3D modeling of reaction-diffusion dynamics in an electrokinetic Y-shaped microreactor

We perform a 3D numerical modeling of reaction-diffusion dynamics in a Y-shaped microreactor, considering a fully developed combined electroosmotic and pressure-driven flow. The governing equations, based on a second-order irreversible reaction, are solved invoking a finite-volume approach for a non-uniform grid system. We demonstrate that the reaction is highly position dependent: more production is observed adjacent to the horizontal walls for a favorable pressure gradient, whereas both the wall and centerline are the regions of highest production when a back pressure is applied. We further show that, to achieve the maximum production rate, the EDL should be thick enough, the pressure gradient should be unfavorable, and both the diffusiveties and the inlet concentrations of the reacting components should be identical. Although the same is true for the production efficiency, defined to be the ratio of the average production concentration to the inlet concentration of the limiting component, there is a main difference: when the inlet concentrations are the same the efficiency is minimal. Moreover, the concentration pick is inclined toward the component with either less diffusivity or less inlet concentration; the inclination is magnified when either the Debye length increases or an unfavorable pressure gradient is employed.

Numerical analysis of dialysis with chemical reaction at steady state. Irreversible second-order reaction

In the present work, the effect of chemical reaction on the rate of dialysis is analysed. The attention is paid to an irreversible second-order chemical reaction at steady state. A simple scheme, in which component A is transported through the membrane by diffusion and reacts with component B diffusing in the opposite direction, is considered. The analogy between the solution-diffusion model in the membrane transport and mass transfer in gas-liquid systems described by the film theory, both accompanied by chemical reactions, is taken into consideration. A numerical solution scheme is presented and the effect of chemical reaction is evaluated in terms of the enhancement factor for a wide range of parameters. The analysis of limiting cases is carried out and the applicability of the existing approximate solutions for the mass transfer accompanied by chemical reaction is examined. An effort was made to develop new correlations for the enhancement factor in the case that no approximate solution is available in literature.

Transesterification of Castor Oil with Methanol – Kinetic Modelling

Abstract In this research work, transesterification of castor oil with methanol and sulphuric acid catalyst has been carried out in a lab reactor of capacity 500 mL at various operating conditions (reaction temperature=35–65°C, pressure=1 atm, methanol/oil ratio=6:1 and 600 rpm). The effect of reaction temperature is considered, followed by the determination of kinetics of the production of biodiesel. Experimental results have been analysed with respect to three types of reaction kinetics, namely first-order irreversible reaction, second-order irreversible reaction and reversible reaction. For each of the schemes, the activation energy and Arrhenius constants were determined. The experimental data fits very well to second-order reversible reaction kinetics. Properties of fatty acid methyl ester (biodiesel) produced from castor oil have been experimentally determined and compared with standard values as given in EN 14214 norms.

The effect of tetrahydrofuran on the base-catalyzed sunflower oil methanolysis in a continuous reciprocating plate reactor

The homogeneous base-catalyzed methanolysis of sunflower oil in the presence and absence of tetrahydrofuran (THF) as a co-solvent was studied in a continuous cocurrent upflow reciprocating plate reactor (RPR). The measurements of the dispersed phase drop size demonstrated the effects of the THF concentration on the Sauter-mean drop diameter and the drop size distribution in both non-reactive (methanol/oil) and reactive (methanol/KOH/oil) systems. The presence of THF shifted both heterogeneous systems to the stable homogeneous emulsion consisted of small dispersed phase drops. The triacylglycerol (TAG) conversion degree was measured in the reactive system. The sigmoidal kinetics was observed in the absence and presence of THF at lower THF concentrations (≤10% of the oil mass). This shape was explained by the existence of the initial TAG mass transfer controlled region followed by the irreversible second-order reaction controlled region. However, at the highest THF concentration (30% of the oil mass) the irreversible and reversible second-order reaction kinetics was used to describe the variation of TAG conversion degree with time. The proposed kinetic models satisfactorily fitted the experimental data.

Analytical solution of isothermal semi-batch reactor with proceeding irreversible second-order reaction of Class II: A + B → PROD

A formulation of the time dependent molar balance equations, one of which is a nonlinear Bernoulli differential equation, is a preliminary step to modeling an isothermal semi-batch reactor with irreversible second-order reactions. The molar balance equations obtained in this fashion are classified as first order nonlinear ODEs. This paper presents a methodology to replace the nonlinear ODE that characterizes the molar composition of the reactants with an equivalent, linear ODE derived from a Bernoulli ODE to obtain an analytical solution. This approach leads to a general solution. The analytical results using this methodology are subsequently compared to numerical solutions to verify the accuracy of the model.

Kinetics of rapeseed oil transesterification over a heterogeneous barium-aluminum oxide catalyst with the methanol pressure taken into account

Use of heterogeneous catalysts in the synthesis of biodiesel from vegetable lipids via transesterification with alcohols has certain advantages over use of homogeneous catalysts. Commercialization of this process needs investigation of its kinetics. Here, we report, for the first time, the kinetics of transesterification of rapeseed oil with gaseous methanol over a heterogeneous catalyst with methanol partial pressure taken into account. Experiments have been carried out in a flow reactor with a fixed bed of a barium-aluminum oxide catalyst at 200°C and a methanol pressure of 0.1–2.5 MPa. Experimental data have been processed in terms of a simplified kinetic model involving one irreversible second-order reaction (first-order reaction with respect to both oil and methanol). Service life tests have been carried out for the catalyst calcined at 700°C.

Connecting the Chemical and Biological Properties of Nitric Oxide

Nitric oxide (NO(•); nitrogen monoxide) is known to be a critical regulator of cell and tissue function through mechanisms that utilize its unique physicochemical properties as a small and uncharged free radical with limited reactivity. Here, the basic chemistry and biochemistry of NO(•) are summarized through the description of its chemical reactivity, biological sources, physiological and pathophysiological levels, and cellular transport. The complexity of the interactions of NO(•) with biotargets, which vary from irreversible second-order reactions to reversible formation of nonreactive and reactive nitrosyl complexes, is noted. Emphasis is placed on the kinetics and physiological consequences of the reactions of NO(•) with its better characterized biotargets. These targets are soluble guanylate cyclase (sCG), oxyhemoglobin/hemoglobin (HbO(2)/Hb) and cytochrome c oxidase (CcOx), all of which are ferrous heme proteins that react with NO(•) with second-order rate constants approaching the diffusion limit (k(on) approximately 10(7) to 10(8) M(-1) s(-1)). Likewise, the biotarget responsible for the most described pathophysiological actions of NO(•) is the superoxide anion radical (O(2)(•-)), which reacts with NO(•) in a diffusion-controlled process (k approximately 10(10) M(-1) s(-1)). The reactions of NO(•) with proteins containing iron-sulfur clusters ([FeS]) remain little studied and the reported rate constants of the first steps of these reactions are considerable (k approximately 10(5) M(-1) s(-1)). Not surprisingly, the interactions of proteins containing iron-sulfur clusters with NO(•) remain ambiguous and have been associated with both physiological and pathophysiological effects. Overall, it is emphasized that any claimed biological action of NO(•) should be connected with its interaction with kinetically relevant biotargets. Although reactivity toward biotargets is only one of the factors contributing to cellular and tissue responses mediated by short-lived species, such as NO(•) and other oxygen-derived species, it is a critical factor. Therefore, taking reactivity into account is important to advancing our knowledge on redox signaling mechanisms.

Kinetics of Ethyl Acetate Synthesis Catalyzed by Acidic Resins

A low-cost experiment to carry out the second-order reversible reaction of acetic acid esterification with ethanol to produce ethyl acetate is presented to illustrate concepts of kinetics and reactor modeling. The reaction is performed in a batch reactor, and the acetic acid concentration is measured by acid–base titration versus time. The experimental data are used to optimize the specific rate constant of the direct reaction, which is the unique parameter of the model; the rate constant for the inverse reaction is expressed in terms of the equilibrium constant. Good representations are generally obtained: the absolute average relative deviation found in this work is only 2.86%. After the experiment, students may carry out simulations for distinct operating conditions. The experimental data for short times are also analyzed approximately by using the classical approach for irreversible second-order reactions.

Designing and analysing parallel control for multifeed ternary systems

This paper explores a parallel control structure for improving the behaviour of a chemical plant having recycling and multiple feed streams; a ternary system is taken as an example, having an A+B→C second-order irreversible reaction. Material recycling dynamics can induce the so-called snowball effect in the presence of disturbance in the feed stream. The snowball effect can be prevented by distributing load through the parallel control scheme. A control structure was thus proposed where product composition was regulated by means of simultaneous feedback manipulation of final column vapour boilup rate and reactor temperature. An extension was made for one reactor, one distillation column and recycle stream configuration. Nonlinear simulations showed that effective composition control could be obtained with moderate vapour boilup control efforts.

Kinetics of the base-catalyzed sunflower oil ethanolysis

The kinetics of the sunflower oil ethanolysis process using NaOH as a catalyst was studied at different reaction conditions. The reaction system was considered as a pseudo-homogeneous one with no mass transfer limitations. It was also assumed that the chemical reaction rate controlled the overall process kinetics. A simple kinetic model consisting of the irreversible second-order reaction followed by the reversible second-order reaction close to the completion of the ethanolysis reaction was used for the simulation of the triglyceride conversion and the fatty acid ethyl ester formation. The proposed kinetics model fitted the experimental data well.

Secondary Organic Aerosol-Forming Reactions of Glyoxal with Amino Acids

Glyoxal, the simplest and most abundant alpha-dicarbonyl compound in the atmosphere, is scavenged by clouds and aerosol, where it reacts with nucleophiles to form low-volatility products. Here we examine the reactions of glyoxal with five amino acids common in clouds. When glyoxal and glycine, serine, aspartic acid or ornithine are present at concentrations as low as 30/microM in evaporating aqueous droplets or bulk solutions, 1,3-disubstituted imidazoles are formed in irreversible second-order reactions detected by nuclear magnetic resonance (NMR), aerosol mass spectrometry (AMS) and electrospray ionization mass spectrometry (ESI-MS). In contrast, glyoxal reacts with arginine preferentially at side chain amino groups, forming nonaromatic five-membered rings. All reactions were accompanied by browning. The uptake of 45 ppb glyoxal by solid-phase glycine aerosol at 50% RH was also studied and found to cause particle growth and the production of imidazole measured by scanning mobility particle sizing and AMS, respectively, with a glyoxal uptake coefficient alpha = 0.0004. Comparison of reaction kinetics in bulk and in drying droplets shows that conversion of glyoxal dihydrate to monohydrate accelerates the reaction by over 3 orders of magnitude, allowing these reactions to occur at atmospheric conditions.

Kinetics of sunflower oil methanolysis at low temperatures

The kinetics of the sunflower oil methanolysis process was studied at lower temperatures (10–30 °C). The sigmoidal kinetics of the process was explained by the mass transfer controlled region in the initial heterogenous regime, followed by the chemical reaction controlled region in the pseudo-homogenous regime. A simple kinetic model, which did not require complex computation of the kinetic constants, was used for simulation of the TG conversion and the FAME formation in the latter regime: the fast irreversible second-order reaction was followed by the slow reversible second-order reaction close to the completion of the methanolysis reaction. The mass transfer was related to the drop size of the dispersed (methanol) phase, which reduced rapidly with the progress of the methanolysis reaction. This was attributed to the formation of the emulsifying agents stabilizing the emulsion of methanol drops into the oil.