First-order Irreversible Reaction Research Articles

Control of hot spots in plug flow reactors

This paper addresses the problem of suppressing the magnitude of hot spots in plug flow reactors by manipulating the jacket coolant temperature. A nonlinear control law is derived which guarantees that the hot spot temperature remains below a pre-specified bound for all times after an initial transient, under relatively mild assumptions on the inlet conditions. The performance and robustness of the derived control law are evaluated for the case of a first-order irreversible exothermic reaction.

Transport of Hg2+ through bulk liquid membrane using a bis-calix[4]arene nitrile derivative as carrier: kinetic analysis

The transport of Hg(II) ions from an aqueous solution into an aqueous receiving solution through a bulk liquid membrane containing a bis-calix[4]arene nitrile derivative (1) as a carrier was examined. The kinetic parameters were analyzed assuming two consecutive, irreversible first-order reactions. The influence of temperature, the solvent and stirring rate on the kinetic parameters (k1, k2, Rmmax, tmax, Jdmax, Jamax) has also been investigated. The membrane entrance rate, k1, and the membrane exit rate, k2, increased with increasing temperature and stirring rate. The membrane entrance and exit rate constants are found to vary in the order CH2Cl2 > CHCl3 > CCl4. For the maximum membrane exit flux, Jamax, the activation energy was found from the slope of the linear Arrhenius relationship to be 9.95 kcal mol−1, which indicates that the process is controlled by species diffusion.

Analysis of the Operation of a Nonisothermal Flow Reactor in Terms of the Relaxation Model of Longitudinal Dispersion

A set of equations and additional conditions for the relaxation model of longitudinal dispersion are proposed to describe the operation of a nonisothermal reactor. The near-perfect-mixing, adiabatic, and near-isothermal steady-state modes of operation of a mixing apparatus are analyzed. The analysis is performed for a irreversible first-order chemical reaction. For the adiabatic mode, the problem formulation is relevant to an isothermal reactor with a modified mass source. The perfect-mixing mode is illustrated by analytical and graphical data on the number of solutions of the model equations.

Catalyst performance testing: Radial and axial dispersion related to dilution in fixed-bed laboratory reactors

The effect of different distributions of catalyst particles and diluent particles on the conversion in gas–solid systems for an irreversible first-order reaction was investigated in a laboratory microreactor. Vertically and horizontally segregated beds, as well as mixed beds were considered. The experimental investigations were performed by employing catalysed N 2O decomposition over two different catalysts: FeZSM-5 and Co-La, Al mixed oxide. If the catalyst and the dilution are not well-mixed, the conversion may reduce significantly due to bypassing and axial dispersion. The effects are the strongest at high conversions. Since a completely homogeneous distribution of catalyst and diluent is difficult to achieve, the use of data obtained at high conversions with diluted fixed beds should preferentially be avoided, since it can lead to a wrong interpretation of kinetic data, e.g. the apparent activation energies may vary considerably. The radial and axial dispersion coefficients were estimated from the experiments, all in the laminar-flow regime, using the random particle distribution (RPD) model. The bed tortuosity derived using the model corresponds well with values reported in literature.

Effect of kinetic synergist on transport of copper(II) through a liquid membrane containing P507 in kerosene

A new kinetic synergism system for copper(II) transport through a bulk liquid membrane containing mono(2-ethyhexyl)-2-ethyhexyl phosphate and Manoxol OT (OT) was examined. The influence of stripping agent, anion, pH in feed phase, and carrier concentration were investigated. The kinetics of Cu(II) transport could be analyzed in the formalism of two consecutive irreversible first-order reactions, considering both extraction and stripping. The pseudo-first-order apparent rate constants of interfacial reactions in membrane transport are determined by altering the temperature. The activation energy values are 38.1 kJ mol–1 for extraction and 32.8 kJ mol–1 for stripping. The experiments demonstrated that Manoxol OT is a good kinetic synergist for Cu(II) transport through liquid membranes in this study. The kinetic synergism of OT for extraction of Cu2+ ions is analyzed.Key words: copper ions, kinetic synergist, liquid membrane.

Unsteady heat and/or mass transfer from a fluid sphere in creeping flow

The transient heat and/or mass transfer from a fluid sphere with internal circulation into a flowing fluid are investigated. The temperature and/or concentration inside the sphere are considered uniform. Two cases are studied: the physical mass and/or heat transfer and the mass transfer accompanied by an isothermal, first-order irreversible chemical reaction in the continuous phase. Steady, creeping flow is assumed around and inside the sphere. The problem is solved by a finite difference method in the range of parameters, 10⩽ Pe⩽1000, 0.01⩽H (Φ h )⩽100 , 0.1⩽ Da⩽1000. The influence of distribution coefficient ( H) or volume heat capacity ratio ( Φ h) on the transfer rate and thermal wake phenomenon is analysed.

Hydrogen atom abstraction by radical cations. The reactions of 9-substituted acridine radical cations with cyclohexa-1,4-diene†

9-Substituted acridine radical cations undergo facile hydrogen atom abstraction reactions with cyclohexa-1,4-diene in dichloromethane–Bu4NPF6 (0.2 M). The kinetics of the reaction were studied by derivative cyclic voltammetry and observed to conform to the EC mechanism (charge transfer followed by irreversible first-order reaction). The products of the reactions are the protonated acridine substrate and dimer–substrate adducts of cyclohexa-1,4-diene. A comparison is made between the reactions of 9-phenylacridine and 9-phenylanthracene radical cations. The former undergoes rapid hydrogen atom abstractions, while the latter slowly dimerizes in the absence of nucleophiles. It is suggested that localization of the odd electron in a p-orbital on nitrogen imparts the hydrogen abstraction activity of the radical cation. Since there are no free p-orbitals on the carbon atoms of the aromatic rings in arene radical cations the hydrogen atom abstraction reaction pathway is not observed.

EFFECT OF INTERPHASE MASS TRANSFER ON UNSTEADY CONVECTIVE DIFFUSION:PART I, PLANE-POISEUELLE FLOW OF A POWER-LAW FLUID IN A CHANNEL

The paper presents an all-time analysis of unsteady convective diffusion of solute undergoing an irreversible first-order chemical reaction at the bounding walls of a parallel-plate channel. The heterogeneous chemical reaction significantly influences the convective and diffusive coefficients. A new coefficient arises exclusively due to the incorporation of wall reaction. The effects of wall-catalysed reaction and power-law index ‘N’ on dispersion are investigated against the background of the no-reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when.reaction is absent. The Taylor [1 ] and Ans [2] regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis.

Effect of paraffin and surfactant on coupled transport of cadmium(II) ions through liquid membranes

The transport of Cd(II) ions from an aqueous feed chloride solution to an ammonium acetate stripping solution through a supported liquid membrane containing tri- n-octylamine (TOA) in xylene has been examined. The influence of stirring rate, carrier concentration, stripping agent and H + concentration in the feed solution was investigated. The transport of Cd(II) ions is coupled by the co-transport of protons. The kinetics of transport could be analyzed in the formalism of two consecutive irreversible first-order reactions, considering both extraction and stripping reactions. The pseudo-first-order rate constants of interfacial reactions in membrane transport are determined with a bulk liquid membrane based on paraffin and the surfactant Span-80. The experimental results show that the effect of paraffin or surfactant in the membrane is different for the interfacial reactions of extraction and stripping.

Effect of process modeling on the nonlinear behaviour of a CSTR Reactions A→ B→ C

In this work the nonlinear behaviour of a CSTR in which two exothermic irreversible first-order reactions in series A→ B → C take place, when the jacket energy balance is incorporated in the CSTR mathematical model, is analyzed. Catastrophe theory is used to study the parameters with respect to which output multiplicities, input multiplicities, isola formation and disjoint bifurcations may exist. One main objective of this work is to address the effect of including the jacket energy balance on the nonlinear behaviour of the CSTR. The results show that the steady-state open-loop nonlinear behaviour of CSTRs, modeled without and with the jacket energy balance, is quite different. Using the software XPP-AUTO different bifurcation maps were obtained. Five operating regions were characterized.

Kinetics of Cadmium(II) Transport through a Liquid Membrane Containing Tricapryl Amine in Xylene

Coupled transport of Cd(II) ions through a supported liquid membrane containing tricapryl amine in xylene has been examined. The influences of stirring rate, carrier concentration, stripping agent, and H+ concentration in the feed solution were investigated. The transport of Cd(II) ions is coupled by cotransport of protons. The kinetics of Cd(II) transport could be analyzed in the formalism of two consecutive irreversible first-order reactions. The pseudofirst-order apparent rate constants of interfacial reactions in membrane transport were determined with bulk liquid membrane at various temperatures. The activation energy values are 14.7 kJ·mol−1 for extraction and 12.4 kJ·mol−1 for stripping.

Cell model for gas absorption with first-order irreversible chemical reaction and heat release in gas-liquid bubbly media

A model for mass and heat transfer during physical gas absorption in gas-liquid bubbly medium suggested in [1] is generalized for a case of chemical absorption accompanied by heat release. Diffusion and thermal interactions between bubbles are taken in to account in the approximation of a cellular model of a bubbly medium whereby a bubbly medium is viewed as a periodic structure consisting of identical spherical cells with periodic boundary conditions at a cell boundary. Distribution of concentration of the dissolved gas, temperature distribution in liquid and rates of mass and heat transfer during nonisothermal chemical absorption of a soluble pure gas from a bubble by liquid are determined. In the limiting case of chemical absorption without heat release the derived formulas recover the expressions for isothermal chemical absorption. In the limiting case of physical absorption with heat release the derived formulas recover the expressions for nonisothermal absorption obtained in [1].

Analytical solution for networks of irreversible first-order reactions

A new analytical solution technique for networks of irreversible chemical reactions in batch reactors with first-order kinetics is presented. The solution technique involves the iterative calculation of a coefficient matrix that is then applied for direct calculation of species concentrations at any time. The derivation, which is based on Laplace transforms of an arbitrary network, is presented in the appendix. Several examples and extensions to the solution are discussed. Extensions made to the solution include the consideration of phase equilibria, first-order and zero-order sources and sinks, common reaction products outside the network, and combined networks of reactions and CSTRs. Rate-limited mass transfer effects and reversible reactions were not considered. The solution is general, compact, easy to use, and allows several extensions that will likely aid scientists and engineers in solving problems related to the dynamics of these networks.

Linear sweep voltammetry in flooded porous electrodes at low sweep rates

Abstract A theoretical analysis of linear sweep voltammetry (LSV) in flooded-porous electrodes is treated for reversible (Nernstian) and first-order irreversible reactions. At low sweep rates, the ohmic potential drop within the electrode is negligible and concentration gradients are predominantly in the axial direction. The solution to the reversible case is mathematically simple, but the results are presented to understand the influence external mass-transfer resistance has on the voltammogram. For irreversible kinetics, a Green’s function technique is used to obtain an analytical solution to the diffusion equation. An analytical solution for the current as a function of the electrode dimensions, sweep rate and reaction kinetic parameters allows one to predict the voltammogram over a wide range of conditions. The analytical solution is used to develop correlations that enable the kinetic parameters (i.e. exchange current density per unit volume and the transfer coefficient) to be easily extracted from experimental data.

Determination of kinetic parameters for both reversible and irreversible first-order reactions

Two methods of calculating the rate constant(s) and the total amount of final product for both irreversible and reversible first-order reactions have been developed. These methods are based on the analytical solution (for a special case) of the system of transcendental equations, which describe the reaction kinetics. The methods are simpler and more convenient to use than the earlier proposed graphic methods of Guggengeim and Kezdy-Swinbourne.

The Photophobic Receptor from Natronobacterium pharaonis: Temperature and pH Dependencies of the Photocycle of Sensory Rhodopsin II

The photocycle of the photophobic receptor sensory rhodopsin II from N. pharaonis was analyzed by varying measuring wavelengths, temperature, and pH, and by exchanging H 2O with D 2O. The data can be satisfactorily modeled by eight exponents over the whole range of modified parameters. The kinetic data support a model similar to that of bacteriorhodopsin (BR) if a scheme of irreversible first-order reactions is assumed. Eight kinetically distinct protein states can then be identified. These states are formed from five spectrally distinct species. The chromophore states S i correspond in their spectral properties to those of the BR photocycle, namely pSRII 510 (K), pSRII 495 (L), pSRII 400 (M), pSRII 485 (N), and pSRII 535 (O). In comparison to BR, pSRII 400 is formed ∼10 times faster than the M state; however, the back-reaction is almost 100 times slower. Comparison of the temperature dependence of the rate constants with those from the BR photocycle suggests that the differences are caused by changes of ΔS. The rate constants of the pSRII photocycle are almost insensitive to the pH variation from 9.0 to 5.5, and show only a small H 2O/D 2O effect. This analysis supports the idea that the conformational dynamics of pSRII controls the kinetics of the photocycle of pSRII.

Robust nonlinear control of continuous stirred tank reactors

This paper deals with the temperature tracking control problem of continuous stirred tank reactors (CSTRs) widely used in chemical engineering. Design of robust tracking controller for a class of CSTRs plant with uncertainties is presented using input-output feedback linearization techniques. The control scheme has been applied to a first-order irreversible exothermic reaction process carried out in a CSTR, and simulation results show that it is effective.

Conjugate Heat and Mass Transfer from a Solid Sphere in the Presence of a Nonisothermal Chemical Reaction

This paper analyzes the influence of the conductivity ratio, Φ λ , the volume heat capacity ratio, Φ h , and the diffusivity ratio, Φ D , on the conjugate heat and mass transfer from a particle in the presence of a chemical reaction. The nonisothermal, first-order irreversible chemical reaction takes place in the particle. Both exothermic and endothermic reactions are studied. The creeping flow and the moderate Reynolds number domain are the hydrodynamic regimes considered. For the exothermic reaction, the particle average temperature and concentration and the effectiveness factor are strongly influenced by the variation of the physical properties ratios. For the endothermic reaction, these effects are considerably less significant. The change of the hydrodynamic regime did not lead to any new or spectacular result. The interphase heat- and mass-transfer coefficients are equal and independent of the physical properties ratios.

Kinetic Modeling of Enzyme Inactivation: Kinetics of Heat Inactivation at 90−110 °C of Extracellular Proteinase from Pseudomonas fluorescens 22F

The kinetics of heat inactivation at 90−110 °C of the extracellular proteinase from Pseudomonas fluorescens 22F was studied. The activation enthalpy ΔH⧧ and activation entropy ΔS⧧ of the inactivation reaction, when analyzed with a first-order kinetic inactivation model, were found to be 84.5 kJ mol-1 and −83.2 J mol-1 K-1. Because the fit was not adequate, alternative inactivation models were proposed and modeled to fit the data. The model with the fewest parameters being statistically acceptable consisted of two sequential irreversible first-order reactions and could be used for predictive modeling of the inactivation of the proteinase. A model consisting of two consecutive irreversible reactions, in which the first reaction leads to a partially inactivated enzyme molecule with a relative specific activity of ≈0.6, was statistically better and also appeared to be more in accordance with the mechanism of inactivation. Keywords: Kinetic modeling; heat inactivation; (metallo)proteinase; Pseudomonas fluorescens

A method for calculating the activation energy distribution for desorption of ammonia using a TPD spectrum obtained under desorption control conditions

A method, called the dc-TPD method, was presented for calculating the density distribution function of the activation energy for ammonia desorption by utilizing the temperature-programmed desorption (TPD) spectrum of ammonia from solid catalysts measured under desorption control conditions. TPD spectra were measured in a helium stream under low pressure (about 0.13 kPa) to realize desorption control conditions by removing ammonia desorbed from a catalyst quickly. The measured TPD spectra showed only one peak corresponding to stronger acid sites, and were found to be dependent not on the time factor (ratio of the catalyst weight to the gas flow rate), but only on the heating rate. The TPD spectrum thus obtained was assumed to be the sum of the spectra from a series of acid sites with different acid strengths distributed on the catalyst. The desorption of ammonia from the acid sites was approximated as an irreversible first-order reaction rate equation with the activation energy and frequency factor whose values correspond to the acid strength of the acid sites. Using these assumptions, the relation between the TPD spectrum and the activation energy distribution for desorption was derived. The distribution functions obtained can be used for characterizing the acidic properties of solid catalysts. The shape of the distribution function was found to have little dependence on the heating rate in the TPD experiment. The acidic properties of silica-alumina, H-mordenite, and HY-type and MFI-type zeolites were well characterized by the distribution function of the activation energy for ammonia desorption.