First-order Irreversible Reaction Research Articles

Effects of Homogeneous and Heterogeneous Reactions on the Dispersion of a Solute for Immiscible Viscous Fluids between Two Plates

The paper presents an analytical solution for the dispersion of a solute of two immiscible viscous fluids in the presence of an irreversible first-order chemical reaction. The effects of both homogeneous and heterogeneous reactions on the dispersion are studied. The results are presented graphically and in tabular form for various values of viscosity ratio and pressure gradients on the volumetric flow rate and effective Taylor dispersion coefficient. It is found that for homogeneous chemical reaction, the effective Taylor dispersion coefficient decreases as reaction rate parameter increases. The validity of the results obtained from an analytical method for two fluid models is verified by comparison with the available one fluid model results, and good agreement is found.

Intermolecular Hydrogen Transfer in Isobutane Hydrate

Electron spin resonance (ESR) spectra of butyl radicals induced with γ-ray irradiation in the simple isobutane (2-methylpropane) hydrate (prepared with deuterated water) were investigated. Isothermal annealing results of the γ-ray-irradiated isobutane hydrate reveal that the isobutyl radical in a large cage withdraws a hydrogen atom from the isobutane molecule through shared hexagonal-faces of adjacent large cages. During this “hydrogen picking” process, the isobutyl radical is apparently transformed into a tert-butyl radical, while the sum of isobutyl and tert-butyl radicals remains constant. The apparent transformation from isobutyl to tert-butyl radicals is an irreversible first-order reaction and the activation energy was estimated to be 35 ± 3 kJ/mol, which was in agreement with the activation energy (39 ± 5 kJ/mol) of hydrogen picking in the γ-ray-irradiated propane hydrate with deuterated water.

Electric Current and Irreversible Faradaic Reaction on Electrode in Contact with Electrolyte

Electric current through a cathode in the form of a metal pipe with electrolyte flowing inside is studied experimentally. The electric current is measured at different flow rates for two liquids-highly conducting water, and oil with low conductivity. The results show the electric current saturation at high voltages in water and no saturation in oil. The physical origin of the electric current saturation in electrolytes is still debated. In macroscopic channels the saturation was once attributed to the diffusion-limited mechanism proposed by Levich. However, the saturation observed in the present experiments cannot be described by Levich's result and has a different nature. No other explanation of the electric current saturation in macroscopic channels is available, as to our knowledge. Our theoretical interpretation relates the electric current to a first-order irreversible faradaic reaction at the cathode surface and explains the dependence of the current density on the ion concentration and the electrolyte flow rate.

Cu(II) transport through soybean oil-based bulk liquid membrane: Kinetic study

Kinetic study of Cu(II) transport through a soybean oil-based bulk liquid membrane (BLM) containing di-2-ethylhexylphosphoric acid (carrier) and tributylphosphate (phase modifier) diluted in soybean oil (diluent) was conducted. Effects of initial Cu(II) concentration in the feed phase and temperature were investigated and their kinetic parameters were determined from the kinetic models of two consecutive irreversible first-order reactions. Various initial Cu(II) concentrations in the feed phase (50–500 mg/L (0.788–7.88 mM)) and temperatures (27–43 °C) were found not to affect the rate of extraction process significantly, but enhanced the rate of stripping process with decreasing initial Cu(II) concentration in the feed phase and increasing temperature. The rate-controlling steps of both extraction (diffusion-controlled) and stripping (chemical reaction-controlled) processes were determined and a plausible transport mechanism was proposed. The kinetics of Cu(II) transport through soybean oil-based BLM was then compared with that of a similar kerosene-based BLM and their extraction ( k 1) and stripping ( k 2) rate constants (soybean oil-based BLM: k 1 = 1.94 h −1, k 2 = 0.11 h −1; kerosene-based BLM: k 1 = 1.73 h −1, k 2 = 0.13 h −1) were determined. Application of soybean oil-based BLM in real industrial wastewater was also studied.

Highly efficient and selective transport of methylene blue through a bulk liquid membrane containing Cyanex 301 as carrier

A bulk liquid membrane (BLM) system contained bis(2,4,4-trimethyl pentyl) dithiophosphinic acid (cyanex 301) as carrier and Triton-X-114 as nonionic surfactant was utilized for transport of methylene blue (MB). Cyanex 301 was an efficient and selective carrier for the uphill transport of MB through chloroform and n-hexane in the bulk liquid membrane. Maximum extraction (85%) was observed at 0.0002 M concentration of Cyanex 301 in the membrane phase and 0.2 M concentration of H 2SO 4 in the receiving phase after 7 h. The selectivity and efficiency of MB transport from aqueous solutions contained mixtures of methylene blue (cationic dye) and methyl orange (anionic dye) were studied. The effect of parameters influencing the transport of MB such as pH and concentration of dye in the feed solution, carrier and surfactant concentrations in the membrane, type of organic solvent, nature and composition of the receiving phase, stirring speed and transport time on kinetic parameters of MB transport were elucidated for the interface assuming two consecutive, irreversible first-order reactions. The analysis of the accumulation of MB in the liquid membrane phase and the rate-controlling step under different experimental conditions were discussed. Finally, the proposed liquid membrane was successfully applied for MB separation from waste water.

Time/depth dependent diffusion and chemical reaction model of chloride transportation in concrete

This study focuses on the physical and chemical processes that control the transport of chloride ions into concrete structures. An analytical solution of a diffusion reaction model is presented for determining the time/depth dependent chloride diffusivities considering both diffusion process and binding mechanism of chloride occur simultaneously. The diffusion-reaction model, which is based on the Fick’s second law of diffusion and a mathematical formulation for an irreversible first-order chemical reaction, is used to precisely describe the diffusion mechanism of chloride diffusion process. When the chemical reaction is considered, the free chloride concentration is slowly reduced since some of the free chloride ions have reacted with cement paste such that the diffusion coefficient is also reduced simultaneously. The diffusion-reaction model predicts a longer service life than the total and free chloride diffusion models that do not consider the effect of the chemical reaction during the chloride diffusion process.

Mathematical Modeling of the Amperometric Response to Glucose of Glucose Oxidase Films Deposited by AC-Electrophoresis

Previous work illustrated that glucose oxidase (GOx) could be deposited on conducting substrates using asymmetrical alternating current electrophoretic deposition (AC-EPD) to form thick enzyme layers suitable for the manufacturing of highly active biosensors. Here, we modeled the amperometric response of GOx layers to glucose as a function of the thickness of the enzyme layer. The model is based on reaction-diffusion equations with irreversible first-order catalytic reactions. The numerical results displayed qualitative and reasonable quantitative agreement with the experimental data obtained for oxidation currents due to glucose, which increase with the enzyme thickness.

EFFECTS OF THE REACTION RATE AND THE LARGE SIZE DEFORMABLE AEROSOLS ON DISPERSION IN ATMOSPHERIC FLOW REGARDED AS THE TURBULENT FLUID SATURATED POROUS MEDIA

This paper describes the use of Taylor's analysis to study the dispersion of large size aerosols as the mixture of deformable agglomeration and coalescence of aerosols in the atmosphere. A proper theory is developed incorporating the resistance offered by sparsely packed aerosols following the Darcy-Brinkman model, including elastic deformation. Analytical solutions for velocity are obtained using a regular perturbation technique. Concentration distribution is determined using the advection of concentration by the atmospheric turbulent fluid in the presence of an irreversible first-order chemical reaction and a source in the boundary condition. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric turbulent fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, D β, called the Taylor dispersion coefficient. This D β is numerically computed and the results reveal that D β increases with an increase in Re and Pe, but decreases with an increase in σρ, β1, and R1, where Re is the Reynolds number, σρ is the porous parameter, R1 is the deformation parameter, and β1 is the reaction rate parameter. This decrease in D β, with an increase in the porous parameter and an increase in the reaction rate parameter is favorable for the formation of clouds in the atmosphere.

Kinetic studies of xylan hydrolysis of corn stover in a dilute acid cycle spray flow-through reactor

Xylan of corn stover was pretreated with 1%, 2% and 3% (w/w) sulfuric acid at relatively low temperatures (90°C, 95°C and 100°C) in a dilute acid cycle spray flow-through reactor (DCF). The hydrolysis of xylan to its monomeric xylose was modeled by a series of first-order reactions. Both biphasic and Saeman hydrolysis models were applied to fit the experimental data. The results confirmed that the kinetic data of xylan hydrolysis fitted a first-order irreversible reaction model and the experimental data. The reaction rates of xylose monomer formation and degradation were sensitive to catalyst concentration and temperature. Higher catalyst concentration and lower reaction temperature result in high xylose yield. The activation energy for xylose formation and degradation were determined to be 112.9 and 101.0 kJ·mol-1, respectively. Over 90% theoretical xylose obtained from corn stover can be used to produce ethanol, xylitol and fumaric acid by fermentation.

Transport and separation of iron(III) from nickel(II) with the ionic liquid trihexyl(tetradecyl)phosphonium chloride

Abstract Iron(III) was efficiently extracted from a 6 M hydrochloride solution with the ionic liquid trihexyl(tetradecyl)phosphonium chloride, Cyphos ® IL101, dissolved in chloroform. Spectroscopical data revealed that iron exists as tetrachloroferrate species in the organic phase. In contrast, nickel(II) was not extracted under experimental conditions. Satisfying back extraction of Fe(III) was achieved with a 0.5 M HCl solution. Consequent time-dependent transport studies with Cyphos IL101 as ionic liquid carrier in chloroform (0.01 M), showed a successful quantitative transport of 0.1 M Fe(III) from a 6 M hydrochloride source phase to a 0.5 M hydrochloride receiving phase and a favorable separation from Ni(II). The transport of Fe(III) through the bulk liquid membrane (BLM) was assumed to follow a nonsteady kinetic regime with two consecutive and irreversible first-order reactions. With an initial Fe(III)/Cyphos IL101 concentration ratio of 10, an apparent rate constant k s of 31.4 × 10 −3 min −1 was obtained for the Fe(III) transport from the membrane- to the receiving phase, whereas the rate constant k f for the Fe(III) transport from the source- to the membrane phase was 11.8 × 10 −3 min −1 .

On the continuum approximation of large reaction mixtures

In analyzing a reaction mixture of very many components, treating the mixture as a continuum can produce results of generality. In many practical situations (e.g., hydrodesulfurization), it is highly desirable to predict the overall behavior of the mixture at large times (high conversions) with minimum information on the mixture property. For irreversible first-order reactions in a plug-flow reactor, it was previously shown that the continuum approximation cannot be valid at arbitrarily large times. This work is an investigation of the validity of the approximation for mixtures with complex kinetics. It is found that the approximation can be conditionally or universally valid, depending on kinetics, reactor type, pore diffusion, and mixture properties. The validity conditions for a variety of situations, nontrivial as they may seem, take a power-law form. Backmixing and pore diffusion widen the range of validity. The underlying physics and some dichotomies/subtleties are discussed. The results are applied to catalytic hydroprocessing in petroleum refining. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Turbulent plumes with heterogeneous chemical reaction on the surface of small buoyant droplets

A model is developed for a turbulent plume with heterogeneous chemical reaction rising in an unbounded environment. The chemical reaction, which may generate or deplete buoyancy in the plume, occurs at the interface between two phases, a continuous phase and a dispersed one. We study the case in which a buoyant reactant is released at the source and forms the dispersed phase, consisting of very small bubbles, droplets or particles. Once in contact with the ambient fluid, a first-order irreversible reaction takes place at the surface of the, for example, droplets. The behaviour of this plume in a uniform and stratified environment is examined. We show that the dynamics of a pure plume with such heterogeneous reaction is completely determined by the ratio of the environmental buoyancy frequency N and a frequency parameter associated with the chemical reaction, G. The group G is a measure of the ability of the reaction to generate buoyancy in the plume. In a uniform environment, the sign of parameter G fully determines the plume motion. When the reaction generates buoyancy (positive G) the motion is unbounded, whilst when reaction depletes buoyancy (negative G) the plume reaches a level of neutral buoyancy. A relation for this neutral buoyancy level as a function of the initial buoyancy flux of the plume and G is calculated. Our theoretical predictions compared well with experimental results using a plume of calcium carbonate particles descending in an acidic aqueous solution. In a stratified environment, the motion of the plume is always bounded, irrespective of the magnitude of G, and we determine the level of maximum buoyancy flux, as well as those of zero buoyancy and zero momentum as a function of N/G. Finally, our model is applied to study the dynamics of a localized release of carbon dioxide in the ocean.

Entfernung von Pb(II) aus wässrigen Lösungen mit Kohlenstoffen gewonnen aus Salholz (Shorea robusta)

In the present work, physically and chemically activated carbons are prepared using Sal wood (Shorea robusta) sawdust by thermal process and using sulfuric acid as the activation agent to remove Pb(II) from aqueous solutions. Adsorption equilibrium studies have been done at a pH of 4 and a room temperature of 30 °C. It was found that the adsorption isotherms are favorable and chemically activated carbons are better than physically activated carbon in terms of adsorption capacity. Various two-parameter adsorption isotherm models, viz. Freundlich, Langmuir, Temkin and Dubinin-Radushkevich, were used to fit the equilibrium data and it was found that the Freundlich adsorption model provided best-fit. The first-order irreversible unimolecular reaction model and the pseudo-second-order kinetic models were used to fit the kinetic data and it was found that both the models provided good fit. Kinetic and film diffusion studies show that the adsorption of lead(II) on the activated carbons tested in this work are both intra-particle and film diffusion controlled.

Kinetic study of chromium(VI) facilitated transport through a bulk liquid membrane using tri-n-butyl phosphate as carrier

Abstract The facilitated transport of Cr(VI) through a bulk liquid membrane (BLM) is investigated, using the commercially available solvent tri- n -butyl phosphate (TBP) as mobile carrier. The influences of the carrier concentration in the liquid membrane phase, the HCl concentration of the feed phase, and the stripping concentration on the mass transfer process are studied. The transport rate of Cr(VI) increases with increasing the TBP concentration and HCl concentration. The increasing of the stripping concentration improves the stripping process until a plateau is reached. A kinetic model is used to describe the Cr(VI) transport behavior, assuming that it obeys the kinetic laws of two consecutive irreversible first-order reactions. The experimental data fits reasonable well with the derived model. The analysis of the accumulation of Cr(VI) in the liquid membrane phase and the discussion of the rate-controlling step under different experimental conditions are carried out. The magnitude of the value of k e and k s is found to be 10 −4 –10 −5 s −1 , and is well in agreement with other studies.

Multiplicity and Stability of Chemical Reactors with Evaporative Cooling

This work characterizes the dynamic behavior of reactors with evaporative cooling. The process under consideration is a continuous stirred tank reactor used to carry out an exothermic irreversible first-order reaction with heat removal through the wall as well as by partial evaporation of the reacting liquid followed by return of the condensate to the reactor. Bifurcation analysis is used to classify the stability character and the types of multiplicity and oscillatory behavior to be expected. A variety of practical situations is examined, including cases of volatile reactant, volatile or nonvolatile product (liquid or solid), and volatile solvent. For a fixed vapor flowrate to the condenser, the dynamic structure of reactors with evaporative cooling is qualitatively similar to the case with wall cooling alone. Other cases show significantly different structures. Cases with five steady states and two regions of three steady states are found with evaporative cooling operation, and for some conditions even seven steady states may be possible. A rich variety of dynamic behavior is predicted.

Study of the kinetics of the transport of Cu(II), Cd(II) and Ni(II) ions through a liquid membrane

The coupled transport of Cu(II), Cd(II) and Ni(II) ions through a bulk liquid membrane (BLM) containing pyridine-2-acetaldehyde benzoylhydrazone (2-APBH) as carrier dissolved in toluene has been studied. Once the optimal conditions of extraction of each metal were established, a comparative study of the transport kinetics for these metals was performed by means of a kinetic model involving two consecutive irreversible first-order reactions. The kinetic parameters (apparent rate constants of the metal extraction and re-extraction reactions (k(1), k(2)), the maximum reduced concentration of the metal in the liquid membrane (R(o)max), the time of the maximum value of R(o)(t(max)) and the maximum entry and exit fluxes of the metal through the liquid membrane (J(f)max and J(s)max) of the extraction and stripping reactions were evaluated and results showed good agreement between experimental data and theoretical predictions. Complete transport through the membrane took place according to the following order: Cd(II)>Cu(II)>Ni(II), with similar kinetic parameters obtained for Cu(II) and Cd(III). The transport behaviour of Ni(II) was different to that of Cu(II) and Cd(III), probably due to the different stoichiometry of the nickel complex compared to those of the other metal ions and the different chemical conditions required for its formation. The influence of the sample salinity on the transport kinetics was studied. k(1) values decreased slightly when the feed solution salinity was increased for Cu(II) and Ni(II), but not for Cd(II). Values of k(2) were practically unaffected. The proposed BLM was applied to the preconcentration and separation of metal ions (prior to their determination) in water samples with different saline matrices (CRM, river water and seawater), and good agreement with the certified values was obtained.

Facilitated transport of copper through bulk liquid membranes containing different carriers: compared kinetic study

The discharge of heavy metals into the environment is a serious problem facing numerous industries. Heavy metals tend to accumulate in living organisms causing various diseases and disorders. So the search for extraction techniques to remove those heavy metals are of increasing interest. Liquid membranes have shown great potential in this way, especially in cases where metal concentrations are relatively low and other techniques cannot be applied efficiently. A comparative kinetic study of the facilitated counter transport of copper ion through bulk liquid membranes containing D2EHPA, CYANEX 272 and LIX 984N as carriers and protons as counter ions is carried out is this paper. The transport kinetic was analysed by means of a kinetic model involving two consecutive irreversible first-order reactions. The rate constants of the extraction and stripping reactions and the maximum transport fluxes of copper(II) through the bulk liquid membrane were determined for the three carriers.

Generic Optimal Temperature Profiles for a Class of Jacketed Tubular Reactors

This paper deals with the optimal and safe operation of jacketed tubular reactors. Despite the existence of advanced distributed controllers, optimal steady-state reference profiles to be tracked are often unknown. In Logist et al. [2008], a procedure which combines analytical and numerical optimal control techniques, has been proposed for deriving optimal analytical (and thus generic) references, and it has been illustrated for plug flow reactors. The aim of this paper is to illustrate the general applicability of this procedure by allowing dispersion. As dispersion significantly complicates a possible solution process (due to second-order derivatives and split boundary conditions), hardly any generic results are known. Nevertheless, the dispersive plug flow reactor model is important for practice, since varying the dispersion level allows to mimic an entire reactor range, i.e., from plug flow to perfectly mixed reactors. As an example a jacketed tubular reactor in which an exothermic irreversible first-order reaction takes place is adopted. It is shown that the procedure yields generic reference solutions for (i) three different cost criteria, and (ii) different dispersion levels.

Mass transfer enhancement by chemical reaction in turbulent tube flow

Abstract Section 21.4 of Transport Phenomena (BSL2 after its three authors: Bird, Stewart, and Lightfoot; second ed.; full reference given in [1]) addresses the problem of mass transfer enhancement by a homogeneous and irreversible first-order chemical reaction in turbulent tube flow. The authors discuss several solution approaches of historical interest, and provide a complete transport model for solute A based on the laws of conservation of mass and momentum, from which the local Sherwood number, Sh , can be obtained as a function of the dimensionless axial distance into the mass transfer zone and the Damkohler number, Da . The latter accounts for the effect of reaction kinetics on solute transport. However, BSL2 is very sketchy in the solution details of their model, and does not validate the key results relative to other studies. Thus, the usefulness of the authors’ modelling approach cannot be properly assessed. In this work, a fully documented numerical solution of the original transport problem is given, along with comprehensive results such as velocity and concentration profiles, as well as Sh values outside the range of axial positions given in BSL2. Mass transfer enhancement factors (ratio of Sh with chemical reaction/ Sh without reaction) are also calculated and compared with the literature. Our results show that accurate estimates of enhancement factors in turbulent tube flow with chemical reaction can be obtained using the straightforward BSL2 modelling approach, which may be readily adapted to examine other situations relevant to chemical engineering.

Kinetic analysis of chromium(VI) ions transport through a bulk liquid membrane containing p- tert-butylcalix[4]arene dioxaoctylamide derivative

A kinetic study of chromate ions (Cr 2O 7 2−) transport from an aqueous donor phase into an aqueous acceptor phase through a bulk liquid membrane containing p- tert-butylcalix[4]arene dioxaoctylamide derivative as a carrier was studied. The influence of pH on donor and acceptor phase, effect of chromate and carrier concentration, type of solvent, stirring speed and temperature were investigated. The kinetic parameters ( k 1, k 2, R m max , t max, J d max , J a max ) were calculated for the interface reactions assuming two consecutive, irreversible first-order reactions. The activation energy values are calculated as 16.89 and 10.34 kJ mol −1 for extraction and reextraction, respectively. The values of calculated activation energy indicate that the process is diffusionally controlled by chromate ions. The experiments demonstrated that p- tert-butylcalix[4]arene dioxaoctylamide derivative is a good carrier for Cr(VI) transport through liquid membranes in this study.