Pseudo-steady State Hypothesis Research Articles

Kinetic Investigation for in-situ Epoxidation of Unsaturated Fatty Acid Based on the Pseudo-steady-state-hypothesis (PSSH).

Oleic acid is a mono-unsaturated fatty acid that can be found abundantly in various vegetable oils and potentially attractive to be used as raw material for epoxide chemical. In-situ epoxidation of oleic acid was conducted in batch reactor using peroxy-formic at 30-60°C. Pseudo-steady-state-hypothesis (PSSH) was applied to develop the kinetic model. Heterogeneous liquid-liquid system was chosen and four models which emphasized on the ring opening agent (ROA) and reversibility of the epoxidation reaction were proposed. It has been suggested that reversible model is well suited to represent the experimental data. Activation energy obtained from Arrhenius equation is in the range of 40-195 kJ/mol.

Heterogeneous catalytic reaction of glycerol with acetone for solketal production

The rapid growth of biodiesel industries has also increased the production of glycerol as side product. Without proper treatment, glycerol may cause serious problem for the environment. Glycerol can be reacted with acetone to produce solketal as a fuel additive. The aim of this research was to study the glycerol ketalization with acetone using Amberlyst-15 as catalyst. Experiments were undertaken in a batch reactor. A set of experiment was conducted at varying temperature (35 to 60oC), initial mole ratio of acetone to glycerol (2 – 6) and catalyst loading (1,3,5 and 7% w/w). Sample was analyzed every 30 minutes. The results showed that optimal condition was achieved at temperature of 60 °C, initial mole ratio of acetone to glycerol of 3, and the catalyst load of 3%. The highest glycerol conversion achieved was 87.41 % at 60oC for 3 hours reaction. The Pseudo Steady State Hypothesis (PSSH) has been developed as rnet =k4.CG.CAC/1+k5.CG. Parameter estimation of k4 and k5 were evaluated from experimental data at various temperatures. It appears that the model predicted the experimental data well at high conversion (above 80 min) and showed relatively poor prediction below 80 min.

Reaction Kinetics of CO2 with Monoethanolamine in n-Propanol. 1. Reaction Kinetic Data and Comparison with Existing Rate Law Expressions

The reaction kinetics of CO2 with monoethanolamine is of industrial significance with respect to both CO2 sequestration applications and characterizing the effective interfacial mass transfer area of packed separation columns. Reaction kinetic data were previously, by necessity, only measured under pseudo-first-order conditions with respect to CO2. Furthermore, mass-transfer limitations encountered by the heterogeneous techniques restricted the validity range of the reaction kinetic models developed from the data. New reaction kinetic data, independent of mass-transfer limitations and outside pseudo-first-order conditions, are presented. The data, collected via a previously developed novel, in situ FTIR technique, were subsequently compared with the predictions of two widely accepted rate expressions, the power rate law and pseudo-steady-state hypothesis (PSSH) rate law. The expressions were modeled on the data using a novel multiobjective goal attainment algorithm also developed in this study. The PSSH r...

Improvement of covalent immobilization procedure of β-galactosidase from Kluyveromyces lactis for galactooligosaccharides production: Modeling and kinetic study.

Galactooligosaccharides (GOS) are prebiotics produced from lactose through an enzymatic reaction. Employing an immobilized enzyme may result in cost reductions; however, the changes in its kinetics due to immobilization has not been studied. This study experimentally determined the optimal reaction conditions for the production of GOS from lactose by β-galactosidase (EC 3.2.1.23) from Kluyveromyces lactis covalently immobilized to a polysiloxane-polyvinyl alcohol (POS-PVA) polymer activated with glutaraldehyde (GA), and to study the transgalactosylation kinetics. Yield immobilization was 99 ± 1.1% with 78.5 ± 2.4% enzyme activity recovery. An experimental design 24 with 1 center point and 2 replicates was used. Factors were lactose [L], enzyme concentration [E], pH and temperature (T). Response variables were glucose and galactose as monosaccharides [G1], residual lactose [Lac]r and GOS as disaccharides [G2] and trisaccharides [G3]. Best conditions were pH 7.1, 40 °C, 270 gL-1 initial lactose concentration and 6 U mL-1 enzyme concentration, obtaining 25.46 ± 0.01 gL-1 yield of trisaccharides. Although below the HPLC-IR detection limit, tetrasaccharides were also identified after 115 min of reaction. The immobilization protocol was then optimized by diminishing total reactant volumes : support ratio, resulting in improved enzyme activity synthesizing 43.53 ± 0.02 gL-1 of trisaccharides and 13.79 ± 0.21 gL-1 of tetrasaccharides, and after four cycles remaining relative activity was 94%. A reaction mechanism was proposed through which a mathematical model was developed and rate constants were estimated, considering a pseudo steady-state hypothesis for two concomitant reactions, and from this simplified analysis, the reaction yield could eventually be improved. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1568-1578, 2017.

Modeling interporosity flow functions and shape factors in low-permeability naturally fractured reservoir

A new method is proposed to derive interporosity flow functions (also called transfer functions) and shape factors between the fracture and low-permeability matrix in naturally fractured reservoirs with dual porosity model. The differential form of single-phase seepage equation and the analytical solution for pressure diffusion equation are adopted to deduce the analytical solution for shape factors in transient pressure diffusion equation. By employing this approach, the limitations resulting from the process of deducing interporosity flow function and shape factors under many assumptions are avoided, and the no-linear pressure gradients in the matrix can be well explained. The defects of the interporosity flow function and shape factors mostly are generated under the pseudo-steady state hypothesis, in which no-linear pressure gradients in the matrix cannot be accurately captured. The interporosity flow function, constant shape factors and time-varying shape factors considering threshold pressure in one, two and three dimensional fractures are derived for low permeability fractured reservoirs under no pseudo-steady state hypothesis. The newly developed analytical solution is useful in compressible fluid productivity prediction and transient well testing application. The field case study shows that those shape factors are able to provide more accurate parameters for compressible fluid productivity prediction and more reasonable theoretical basis for the correct interpretation of well testing.

Kinetics of oxidative cracking of n‐hexane to olefins over VOx/Ce‐Al2O3 under gas phase oxygen‐free environment

The kinetics of oxidative cracking of n‐hexane to olefins using lattice oxygen of VOx/Ce‐Al2O3 is investigated. The TPR/TPO analysis shows a consistent reducibility (79%) of VOx/Ce‐Al2O3 in repeated redox cycles. The total acidity of the sample is found to be 0.54 mmol/g with 22% are strong acid sites that favors olefin selectivity. The oxidative cracking of n‐hexane in a fluidized CREC Riser simulator gives approximately 60% olefin selectivity at 30% n‐hexane conversion. A kinetic model is developed considering (1) cracking, (2) oxidative dehydrogenation (ODH), and (3) catalyst deactivations. The proposed cracking mechanism considers adsorption, C–H and C–C bond fission and desorption as elementary steps and implemented by pseudo steady state hypothesis. A Langmuir‐Hinshelwood mechanism is found to represent the ODH reactions. The developed model fits the experimental data with favorable statistical indicators. The estimated specific reaction rate constants are also found to be consistent with the product selectivity data. © 2016 American Institute of Chemical Engineers AIChE J, 63: 130–138, 2017

BET adsorption reaction model based on the pseudo steady-state hypothesis for describing the kinetics of adsorption in liquid phase

A multilayer adsorption reaction model in liquid phase based on BET isotherm fundamentals has been developed from the pseudo steady-state hypothesis of adsorption on the accumulating adsorbate layers. The model accurately reproduces the adsorption isotherms and kinetic profiles of different adsorption systems reported in the literature, and especially those of mesoporous carbon materials used to adsorb organic compounds in aqueous solutions. The kinetic rate constant evaluated for each of the adsorption systems permitted them to be sorted according to the adsorption rate, regardless of the operation parameters employed in the experiments. The model also allowed the effect of the equilibrium parameters and operation variables on the adsorption rate to be analyzed. The analysis yielded similar trends to those reported in literature.

Mathematical analysis of reduction of copper oxide pellets by hydrogen using the shrinking core model

Reduction of copper oxide by hydrogen at high temperatures to metallic copper is one of the ways of removing hydrogen gas or its isotopes from its mixture with an inert gas like helium which is the coolant for plasma facing first wall of tritium breeding blanket modules in fusion reactor systems. The kinetics of the reaction of hydrogen with copper oxide was obtained from literature and it was used to model the reduction of a single particle of copper oxide using the well-known shrinking core model along with the pseudo-steady state hypothesis. No controlling regime was assumed a priori and the various interfacial gas concentrations were calculated by an iterative procedure based on the pseudo steady state hypothesis as function of the core radius at any time and for given operating conditions. The time required for complete reaction of the pellet was then calculated by numerical integration. A spherical geometry was considered in this work for the purpose of illustrating the technique, but the method is applicable to any kinetic model and any geometry of the pellets after simple modifications to the governing equations.

Mathematical analysis of the hydrogen–uranium reaction using the shrinking core model for hydrogen storage application

The reaction of metallic uranium particles with hydrogen at ambient or above ambient temperature has been used as the basis for the solid state storage of hydrogen in the form of uranium hydride for various applications in the nuclear industry. This work models the reduction of a single particle of metallic uranium to uranium hydride using available kinetic data, the well known shrinking core model and the pseudo-steady state hypothesis. No single rate controlling regime was assumed apriori and the various interfacial gas concentrations were calculated by an iterative procedure as function of the core radius at any time and for given operating conditions. The volumetric expansion or increase in the outer radius of the uranium particle as it is progressively hydrided was also considered in this work. The time required for complete conversion of the pellet to the hydride was then calculated by numerical integration and the rate controlling regime was identified. A spherical geometry was considered in this work for illustrating the technique, but the method is applicable to any kinetic model and any geometry of the pellets after simple modifications to the governing equations.

Experimental Conditions for Valid Langmuir-Hinshelwood Kinetics

Users of Langmuir-Hinshelwood kinetics often neglect that it invokes the pseudo-steady state hypothesis (PSSH) for all adsorbed species, and they do not check that the PSSH is validly used. However, with solid catalyzed reactions, the validity of the PSSH must often be based on the concentration of active sites being very small. With a high site concentration catalyst, the PSSH would be incorrect for adsorbates with significant coverages, which would make the deduced kinetic parameters lose their physical meaning and be only the parameters of curve fitting. It is estimated that many catalysts do not meet the criterion for their site concentration to be less than one-tenth the highest reactant concentration.

Kinetic Study of Synthesizing Dimethoxydiphenylmethane under Phase-Transfer Catalysis and Ultrasonic Irradiation

The synthesis of dimethoxydiphenylmethane (DMODPM) from the reaction of methanol and dichlorodiphenylmethane (DCDPM) was successfully carried out in a liquid−liquid phase-transfer catalytic (LLPTC) reaction assisted by ultrasonic irradiation. Little of the desired product DMODPM was obtained from the reaction in the presence of only potassium hydroxide and quaternary ammonium salts. The production of the DMODPM product was greatly enhanced when the reaction system was irradiated by ultrasonic waves. Two sequential reactions in the organic-phase solution proceed to produce the desired product. However, the second rate of the organic-phase reaction was faster than the first. Therefore, the first intermediate product, chloromethoxydiphenylmethane (CMODPM), was not detected during or after the reaction. A kinetic model was developed based on the experimental data. A pseudo-steady-state hypothesis (PSSH) was employed to describe the characteristic behaviors of the kinetic data. The results were finally described by a pseudo-first-order rate law, from which the apparent rate constant (kapp,1) of the first organic-phase reaction was obtained. The effects of the reaction conditions on the conversion of DCDPM and the reaction rate were investigated in detail, including the agitation speed; the amounts of methanol, DCDPM, water, chlorobenzene, potassium hydroxide, and tetrabutylammonium bromide (TBAB); the ultrasonic power and frequency; the organic solvents; the quaternary ammonium salts; and the temperature. Rational explanations are provided for the experimental results.

KINETIC STUDY OF SYNTHESIZING 1-PHENYl-3-PROPYL ETHER UNDER LIQUID-LIQUID PHASE-TRANSFER CATALYTIC CONDITIONS

The etherification of 1-bromo-3-phenylpropane with phenol to synthesize 1-phenyl-3-propyl ether by phase-transfer catalytic conditions was successfully carried out in an alkaline solution of KOH/organic solvent two-phase medium. In this work, quaternary ammonium salts acted as the phase-transfer catalysts. The main purpose of this study was to investigate the kinetic behavior, mechanism, and activation energy of the reaction system. A rational mechanism for the etherification is proposed according to the experimental evidence. The reaction follows a pseudo first-order rate law. A pseudo steady-state hypothesis (PSSH) was proposed to describe the kinetic behaviors from which the apparent rate constant of the two-phase reaction (kapp) was obtained via experimental data. Kinetics of the reaction including the effects of agitation speed, amount of potassium hydroxide, volume of water, temperature, amount of tetrabutylammonium bromide, quaternary ammonium salts, volume of chlorobenzene, and organic solvents on the reaction rate were investigated in detail. Rational explanations to account for the unique results, especially for the water volume effect on the reaction rate, are also provided.

KINETIC STUDY OF S-ALKYLATION OF 2-MERCAPTOBENZIMIDAZOLE CATALYZED BY TETRABUTYLAMMONIUM BROMIDE

The S-alkylation of 2-mercaptobenzimidazole (MBI) by α-bromo-m-xylene (RBr) under phase transfer catalytic reaction condition was successfully carried out in an aqueous solution of KOH/organic solvent two-phase medium. No product was obtained from N-alkylation during or after the reaction period by using a limited quantity of α-bromo-m-xylene. The reaction is greatly enhanced by adding a small amount of tetrabutylammonium bromide (TBAB) and/or potassium hydroxide. Based on the experimental evidence, a rational reaction mechanism is proposed. A kinetic model is derived, from which a pseudo steady-state hypothesis (PSSH) is applied to the reaction system. The kinetic behaviors and the characteristics of the reaction are sufficiently described by the pseudo first-order rate law. The effects of the reaction conditions, including agitation speed, amount of TBAB catalyst, amount of KOH, quaternary ammonium salts, volume of water, volume of dichloromethane, amount of 2-mercaptobenzimidazole, amount of α-bromo-m-xylene, inorganic salts, organic solvents, and temperature on the conversion of the reactant and the apparent rate constants (kapp) were investigated in detailed. Rational explanations are provided for the observed phenomena from experimental results.

Two-Phase Catalyzed S-Substitution of 2-Mercaptobenzimidazole by Tributylamine in the Presence of Potassium Hydroxide

The catalyzed S-substitution of 2-mercaptobenzimidazole (MBI or RSH) by tributylamine (TBA) was carried out in an alkaline solution of KOH/organic solvent two-phase medium. Tributylamine (TBA) reacts in situ with the organic-phase reactant, α-bromo-m-xylene (R′Br) to produce a quaternary ammonium salt ((C4H9)3R′NBr or QBr) which is used as the phase transfer catalyst. The reaction is greatly enhanced by adding a small amount of TBA in the presence of KOH. By appropriately controlling α-bromo-m-xylene (limited compound) at low KOH concentration, only the hydrogen atom connecting to the sulfur atom of 2-mercaptobenzimidazole was substituted byα-bromo-m-xylene. A kinetic model was developed in conjunction with the mass transfer of the catalyst (QBr) and the active intermediate (RSQ), as well as the reactions in both the aqueous and organic phases. The two-film theory is used to account for the mass transfer of QBr and RSQ between two phases. The experimental data verify that the mass transfer rate of the species between the two phases is larger than the reaction rate in the organic phase. The organic-phase reaction is the rate-controlling step for the whole two-phase reaction. A pseudo-steady-state hypothesis (PSSH) is employed to simplify the kinetic model, from which a pseudo-steady-state rate law is sufficiently used to describe the experimental data. Effects of the reaction conditions on the reaction rate and the conversion were investigated in detail.

An integrated dynamic model for reaction kinetics and catalyst deactivation in fixed bed reactors: skeletal isomerization of 1-pentene over ferrierite

Catalyst deactivation in fixed beds is a critical issue in many industrial processes. A general dynamic model for fixed bed reactors involving catalyst deactivation was presented and simplified. The simplifications were based on the pseudo-steady state hypothesis for the fluid phase. Catalyst deactivation was treated by a linear model with respect to surface intermediates. A semi-analytical solution was obtained for the surface intermediates. The approach was applied to skeletal isomerization of 1-pentene over ferrierite. The comparison of experimental results and model predictions revealed that the model is able to describe the essential features of catalyst deactivation in skeletal isomerization and it can be useful for process scale-up.

KINETIC STUDY OF THE PHASE TRANSFER CATALYTIC EPOXIDATION OF DICYCLOPENTADIENE IN A TWO-PHASE MEDIUM

The epoxidation of dicyclopentadiene catalyzed by quaternary ammonium salt in the presence of hydrogen peroxide, sodium tungstate, and phosphoric acid was successfully carried out in an acidic aqueous solution/organic solvent two-phase medium. The epoxidation of dicyclopentadiene is dramatically enhanced in the presence of quaternary ammonium salt, hydrogen peroxide, sodium tungstate, and phosphoric acid of appropriate quantities. Based on the experimental results, a rational reaction mechanism was proposed and a pseudo steady-state hypothesis was applied to describe the kinetic data. The organic-phase reactions were found to be the rate-determining step of the entire phase transfer catalysis. Four reactions, which include the epoxidation of two single-site double bonds and one two-site double bond of dicyclopentadiene molecule, were obtained, i.e., two primary and two secondary sequential reactions in the organic phase. The purpose of this work is to investigate the effects of the reaction conditions such as agitation speed, quaternary ammonium salt, amount of Aliquat 336 catalyst, sodium tungstate, phosphoric acid, active catalyst, hydrogen peroxide, pH value, organic solvents, volume of chloroform, and temperature on the conversion of dicyclopentadiene. The apparent rate constants of the two primary reactions in the organic phase were determined.

Epoxidation of Dicyclopentadiene under Phase Transfer Catalysis Conditions: Pseudo Steady State Hypothesis Approach.

Epoxidation of dicyclopentadiene via phase transfer catalysis was successfully carried out in an acidic solution/organic solvent two-phase medium. The reaction is greatly enhanced in the presence of quaternary ammonium salt using hydrogen peroxide as the oxidizing agent, and sodium tungstate and phosphoric acid as the cocatalyst. Three products, which include epoxidation of two single-site double bonds and epoxidation of one two-sites double bonds, were obtained. The organic-phase reaction was found to be the rate-determining step. Thus, the organic-soluble methyltrioctylammonium chloride (Aliquat 336) was chosen as the phase transfer catalyst to enhance the reaction rate. The purpose of this work is to build up a rational reaction mechanism in which an active oxidation catalyst was synthesized from the reaction of hydrogen peroxide, sodium tungstate, phosphoric acid and quaternary ammonium salt. Based on the experimental data, a pseudo steady state hypothesis (PSSH) approach was considered for the variation of the concentration of the active oxidation catalyst during the reaction. The apparent rate constants of the organic-phase reactions were obtained. Factors which influenced the apparent rate constants were discussed in detail.

Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation

Tumour angiogenesis is the process whereby a capillary network is formed from a preexisting vasculature in response to tumour secreted growth factors (TAFs). The capillary network is largely composed of migrating endothelial cells (EC) which organise themselves into dendritic structures. In this paper, we model angiogenesis via the theory of reinforced random walks, whereby the chemotactic response of the endothelial cells to TAF and their haptotactic response to the matrix macromolecule fibronectin is accomplished through transition probability rate functions. These functions essentially assign directional probabilities for the movement of endothelial cells. Under a pseudosteady state hypothesis, whereby the TAF and fibronectin gradients are specified a priori, simulations in one, two, and three space dimensions are performed. Realistic elementary capillary networks are obtained and analysed. In addition, even without EC proliferation, the formation of microloops or anastomoses is observed. The model provides a “bridge” linking microcellular and macrocellular events. As such, it indicates a new step towards understanding tumour angiogenesis and possible mechanisms for its control.

The destruction of N 2O in a pulsed corona discharge reactor

The removal of N 2O by a pulsed corona reactor (PCR) was investigated. Gas mixtures containing N 2O were allowed to flow in the reactor at various levels of energy input, and for different background gases, flow rates, and initial pollutant concentrations. The reactor effluent gas stream was analyzed for N 2O, NO, NO 2, by means of an FTIR spectrometer. It was found that destruction of N 2O was facilitated with argon as the background gas; the conversion dropped and power requirements increased when nitrogen was used as the background gas. Reaction mechanisms are proposed for the destruction of N 2O in dry argon and nitrogen. Application of the pseudo-steady state hypothesis permits development of expressions for the overall reaction rate in these systems. These reaction rates are integrated into a simple reactor model for the pulsed corona discharge reactor. The reactor model brings forth the coupling between reaction rates, electrical discharge parameters, and fluid flow within the reactor. Comparison with experiment is encouraging, though the needs for additional research are clearly identified.

Kinetics of hydrogen peroxide decomposition with complexed and ?free? iron catalysts

The hydrogen peroxide decomposition kinetics were investigated for both “free” iron catalyst [Fe(II) and Fe(III)] and complexed iron catalyst [Fe(II) and Fe(III)] complexed with DTPA, EDTA, EGTA, and NTA as ligands (L). A kinetic model for free iron catalyst was derived assuming the formation of a reversible complex (Fe–HO2), followed by an irreversible decomposition and using the pseudo-steady-state hypothesis (PSSH). This resulted in a first-order rate at low H2O2 concentrations and a zero order rate at high H2O2 concentrations. The rate constants were determined using the method of initial rates of hydrogen peroxide decomposition. Complexed iron catalysts extend the region of significant activity to pH 2–10 vs. 2–4 for Fenton's reagent (free iron catalyst). A rate expression for Fe(III) complexes was derived using a mechanism similar to that of free iron, except that a L–Fe–HO2 complex was reversibly formed, and subsequently decayed irreversibly into products. The pH plays a major role in the decomposition rate and was incorporated into the rate law by considering the metal complex specie, that is, EDTA–Fe–H, EDTA–Fe–(H2O), EDTA–Fe–(OH), or EDTA–Fe–(OH)2, as a separate complex with its unique kinetic coefficients. A model was then developed to describe the decomposition of H2O2 from pH 2–10 (initial rates = 1 × 10−4 to 1 × 10−7 M/s). In the neutral pH range (pH 6–9), the complexed iron catalyzed reactions still exhibited significant rates of reaction. At low pH, the Fe(II) was mostly uncomplexed and in the free form. The rate constants for the Fe(III)–L complexes are strongly dependent on the stability constant, KML, for the Fe(III)–L complex. The rates of reaction were in descending order NTA > EGTA > EDTA > DTPA, which are consistent with the respective log KMLs for the Fe(III) complexes. Because the method of initial rates was used, the mechanism does not include the subsequent reactions, which may occur. For the complexed iron systems, the peroxide also attacks the chelating agent and by-product-complexing reactions occur. Accordingly, the model is valid only in the initial stages of reaction for the complexed system. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 24–35, 2000