Gas transport in tight porous media: Gas kinetic approach

We describe the flow of gas in a porous medium in the kinetic regime, where the viscous flow structure is not formed in separate pores. Special attention is paid to the dense kinetic regime, where the interactions within the gas are as important as the interaction with the porous medium. The transport law for this regime is derived by means of the gas kinetic theory, in the framework of the model of “heavy gas in light one”. The computations of the gas kinetic theory are confirmed by the dimension analysis and a simplified derivation revealing the considerations behind the kinetic derivation. The role of the thermal gradient in the transport law is clarified.     

Characteristics of Elovich equation used for the analysis of adsorption kinetics in dye-chitosan systems

The Elovich equation has been widely used in adsorption kinetics, which describes chemical adsorption (chemical reaction) mechanism in nature. The approaching equilibrium parameter of Elovich equation (R_E) was used here to describe the characteristic curves of adsorption kinetics. Of 64 adsorption systems surveyed in this work, 80% of the R_E values were between 0.1 and 0.3 with an adsorption curve belonging to “mild rising”. The results of three examples revealed that the characteristic curve of Elovich equation was between those of Lagergren's first-order equation and intraparticle diffusion model. Chitosans prepared from prawn, lobster, and crab shells were used for the adsorption of a reactive dye. The mean deviation obtained from the three kinetic models revealed that Elovich equation was the most suitable one. All the adsorption systems were in the “mild rising” zone. The R_E value was related to the type of raw material but not to the particle size of chitosan, which agreed with chemical adsorption nature of the Elovich equation. According to an optimal adsorbent consumption of 85% coupled with its corresponding operating time (t_0.85) proposed, these two parameters could be used for engineering design.     

ISOTHERMAL AND NON-ISOTHERMAL MULTICOMPONENT ADSORPTION KINETICS

The model equations in the relaxation form for the multicomponent kinetics of isothermal and non-isothermal adsorption, taking into account all major distinctive features of the interphase heat and mass exchange inside porous grains and at their surface (see points 1 to 4 below) for P (“pore”) and S (“solid”) models of mass transfer within porous grains of the adsorbent, have been obtained.

First for isothermal and non-isothermal kinetics in the mixed kinetics region of mass and heat exchange in the absence natural mutual diffusion and natural thermal-diffusion the essential influence effective mutual diffusion and effective thermal-diffusion is shown.

Recommendations on the use of model equations of adsorption kinetics for describing isothermal and non-isothermal adsorption dynamics of multicomponent mixtures in the inner-diffusion and mixed (outer- and inner-diffusion) kinetic region of heat and mass exchange are made.     

Heuristic evolutionary synthesis with non-sharp separators

If, in undertaking a process separation task, such as separating the constituent minerals of an ore to the most profitable extent, we allow limited separation in each process unit (as against requiring a “perfect split”), the number and connection of the units have to be found. Here it is done by building up the required flowsheet unit by unit, stopping when further addition does not increase the profit. Recycle of streams is allowed, the extent being controlled by an arbitrary parameter over which a search may be made.Simulation is sequential modular, with convergence and the necessary process optimization of each intermediate flowsheet carried out by infeasible path successive quadratic programming.As heuristics guide the construction, “good”, not necessarily “the best”, flowsheets are obtained, which may be further ranked, such as by controllability and/or process flexibility.The approach is here developed for “homogeneous” flowsheets (all process units identical), with minerals flotation separation as an example, using a very simple first-order kinetic flotation model. While countercurrent circuits are synthesized as limiting cases of the heuristics, flowsheets more profitable than these are also obtained. The paper reviews critically the heuristics and their application.     

MULTIPLICITY AND STABILITY ANALYSIS OF AGGLOMERATION CONTROLLED PRECIPITATION

The possibility of multiplicity in continuous isothermal MSMPR precipitators has been explored for agglomeration controlled conditions and general criteria, independent of nucleation kinetics, are developed for stability and multiplicity of the steady states. For the Volmer model of primary nucleation and the magma dependent power law model of secondary nucleation, parameter regions are determined in which multiple steady states exist, and their linear stability is analyzed. The analysis holds in general for all types of agglomeration kernel. For the Volmer nucleation kinetics three steady states exist in the region of multiplicity with the “middle” one always being unstable. The analysis for magma dependent power law model showed multiplicity regions having as many as four steady states, the number depending on magma and kinetic order. Unlike the case of molecular growth control, limit cycle behaviour is not possible, and the approach to the steady state is always asymptotic     

An evaluation of the macro-homogeneous and agglomerate model for oxygen reduction in PEMFCs

The kinetics of oxygen reduction reaction on platinum/carbon powders in a Nafion film were evaluated with rotating disk electrode and gas diffusion electrode. The effects of the activation, mass transport and ohmic overpotentials were simulated via an “effectiveness factor” approach. The macro-homogeneous model was suitable to simulate the ORR kinetics at the RDE. On the other hand, it was found that the macro-homogeneous model does not simulate the operation of a porous gas diffusion cathode in PEMFC. With this model, the diffusion overpotential in the cathode is considerably overestimated. Conversely, the good agreement between calculated and experimental Tafel plots demonstrates the validity of the agglomerate model, even though the active layers of the PEMFC electrodes were thin and contained no PTFE. These results provided evidence for a two step transport process in the active layer of PEMFC electrodes.     

A kinetic study of the electrocatalytic oxidation of reduced glutathione at Prussian blue film-modified electrode using rotating-disc electrode voltammetry

In this work a thorough study of the oxidation of reduced glutathione (GSH) by electro-generated Berlin Green (BG) at Prussian blue (PB) film-modified glassy carbon electrode (GCE) was attempted by employing cyclic voltammetry (CV) and rotating-disc electrode (RDE) techniques. It has been shown that oxidation of GSH occurs at the potential coinciding with that of Fe^II(CN)₆ to Fe^III(CN)₆ transformation in the PB film, where no oxidation signal is observed at a bare GCE. The kinetics of catalytic reaction was investigated using a rotating-disc electrode voltammetry. The results obtained for various thicknesses of film and GSH concentrations are explained using the theory of electrocatalytic reactions at chemically modified electrodes (Andrieux–Saveant model) and it was concluded that the reaction has a “surface” reaction mechanism in which a few monolayers at film/solution side engaged in the catalytic process. However, the “surface” reaction tends to a saturation limit with increasing GSH concentration was observed and the behavior has been explained by using Michealis–Menten inner sphere kinetics. Tafel plots for various concentrations of GSH have been drawn and the slope values of 95–110 mV/decade indicate that the first electron transfer is not rate limiting process. The reaction order with respect to GSH and H⁺ were calculated as 0.6 and −0.4, respectively.     

UCKRON II TEST PROBLEM THE EFFECTS OF PORE DIFFUSION

The UCKRON I test problem was reworked with the inclusion of diffusional limitations to the kinetics. For this purpose, the rate expressions, i.e. the full kinetic model and the Langmuir-Hinshelwood model, proposed in the previous workshop, were assumed to represent the true kinetics.

A simple mathematical model based on simplified effective diffusivities and the “Dusty-Gas” model were used to take account of pore diffusion resistance within the catalyst particle. These models predicted effectiveness factors based on the reaction at the bulk conditions. The effectiveness factors were then correlated against temperature and the partial pressure of reacting species.

These correlations were then used to predict the temperature profiles within the water cooled plug flow reactor for various values of cooling media temperature.     

Studies on the oxidation reaction of l-cysteine in a confined matrix of layered double hydroxides

The amino acid l-cysteine (l-Cys) was intercalated into a MgAl layered double hydroxide (LDH), and its oxidation reaction by hexacyanoferrate (III) (Fe(CN)₆³⁻) in the confined region between sheets of LDH has been studied in detail. Based on the measurement results of XRD, Raman and FT-IR, it was found that the interlayer l-Cys was oxidized to cystine by Fe(CN)₆³⁻. Furthermore, the kinetics of this reaction was investigated in batch mode. The influences of initial Fe(CN)₆³⁻concentration, l-Cys-LDH quantity and reaction temperature on the interlayer oxidation reaction have been studied, respectively. The reaction follows a diffusion-controlled mechanism represented by Crank-Ginstling and Brounshtein kinetic model with the apparent activation energy of 29.93 kJ/mol. Therefore, this layered material may have prospective application as a novel “molecular reactor” for confined chemical reactions.     

Catalytic oxidation of CO on CuOx revisited: Impact of the surface state on the apparent kinetic parameters

Analysis of kinetic features of the copper oxides reduction by CO pulses as related to mechanism of CO catalytic oxidation by oxygen combined with monitoring the state of the surface by an electrochemical technique using a solid electrolyte—Pyrex glass and high resolution TEM data on the defect structure of CuO allowed us to suggest a partially “flexible” model of CuO surface. This model, with a due regard for the data of FTIR spectroscopy of adsorbed CO test molecules, assigns the most active surface sites able to coordinate highly reactive CO and O forms to clusters of Cu⁺ cations located at outlets of extended defects (dislocations, twins). Variation of the number, size and structure of these clusters under the reaction medium effect allows explaining the difference between quasi-steady and true steady states of copper oxides in catalytic CO oxidation reaction as well as the difference between kinetic parameters of reaction estimated at quasi-steady and constant states of the surface following Boreskov's approach. Kinetic features of the reaction agree with the Langmuir–Hinshelwood reaction mechanism operating for clustered defect centers of CuO.     

A new kinetic model for titanium dioxide mediated heterogeneous photocatalytic degradation of trichloroethylene in gas-phase

This paper focuses on the kinetics of photocatalytic removal and carbon mineralization of gaseous trichloroethylene (TCE) on near-UV irradiated TiO₂ Degussa P25. Experiments were carried out in a flat-plate photoreactor at TCE inlet concentrations of 100–500 ppmv, relative humidities (RH) of 0–62% and gas residence times of 2.5–60.3 s. Gas residence time distribution (RTD) curves revealed an axial dispersed plug flow in the photoreactor with Peclet numbers above 59.4. For all experimental conditions, the carbon mineralization efficiency (5.1–73.0%) was lower than the removal efficiency (8.6–99.9%) and dichloroacetylchloride (DCAC) was detected as a gas-phase degradation product. TCE removal efficiencies increased with lower TCE inlet concentrations, lower RH and higher gas residence times. Evaluating different kinetic models by least squares analysis, it was shown that the Langmuir–Hinshelwood (LH) model could not give an adequate fitting to the experimental results. A new kinetic model, explicitly taking into account electron–hole pair reactions, was developed based on linear TCE adsorption–desorption equilibrium and first order reaction kinetics. The new kinetic model described the experimental results in a more accurate way, as exemplified by a more randomly distributed set of residuals and by a reduction of the sum of squares (SSQ) by a factor 1.7–8.5. The effect of TCE gas-phase concentration, RH and light intensity on adsorption–desorption kinetics, electron–hole concentrations and chemical conversion rates is discussed.     

Latent variable projections of sensitivity data for experimental screening and kinetic modeling

In microkinetic modeling the number of kinetic parameters is large and the precision of the “known” parameters is often very low. The standard approach is then to fit only the most uncertain parameters while regarding the fixed parameter as “true”. This assumption will have consequences also on the fitted parameters since the correlation structure often is quite significant. In this study we have taken the approach to fit many parameters and then try to use more efficient experimental designs to break the correlation structure and thus obtain more precise parameter estimation despite the large number of fitted parameters. After performing sensitivity analysis of many candidate experiments, a latent variable model (PCA) is made from the resulting sensitivity matrix and the score matrix is used as a candidate set prior to experiment selection. Due to the correlation structure in the sensitivity matrix, the number of components from the PCA model is fewer than the number of parameters. The columns in the score matrix are furthermore orthogonal whereas the columns in the original sensitivity matrix are not. Different designs were generated using the original sensitivity matrix, the score matrix as well as using a space-filling design and performing a sequential approach. Both steady state and transient experiments were evaluated. These different designs were used to fit kinetic parameters to a simulated dataset made using published parameter values. The results show no significant difference when using the original sensitivity matrix or the score matrix. However, since the score matrix has fewer columns than the full sensitivity matrix, the use of designs based on the score matrix enables more efficient designs when few experiments are required. The number of components in the PCA model also gives the rank of the parameter space induced by the candidate experiments. This is useful information when fitting many parameters in a microkinetic model and provides an assessment of the value of every candidate experiment before it is even performed.     

Simplified model for calculation of devolatilization in fluidized beds

A devolatilization model based on simplification of the earlier model has been developed for fluidized bed conditions. It is simple and computationally fast enough to be incorporated as a submodel into a CFD code, but accurate enough to be suitable for different fuels including biomass with varying particle size, moisture, reactivity and shape. In this new model, the partial differential equation describing heat and mass transfer inside the particle is approximately converted to two differential equations. Drying is described to take place on a shrinking core and pyrolysis, which can take place simultaneously with drying, is described to take place at a specific “characteristic pyrolysis temperature”. The dependence of this temperature on parameters for the kinetics of pyrolysis, bed temperature and particle size can be determined. The model can be extended to include the case, where pyrolysis is considered to consist of parallel reactions of different components.     

The photocatalytic activity and kinetics of the degradation of an anionic azo-dye in a UV irradiated porous titania foam

A porous organic–inorganic hybrid titania foam, prepared from a long chain organic surfactant, hexadecylamine (HDA) and a semiconductor powder was characterized by microscopic and spectroscopic techniques and photocatalytically evaluated for the solution phase decomposition of methyl orange under alkaline conditions. Kinetic data obtained indicate conformity with Langmuir–Hinshelwood kinetic model at the initial stages of the degradation reaction. An attempt was made to study the effect of experimental parameters including catalyst loading and dye concentration on photocatalytic degradation of MO. Results indicate that the rate of reaction is governed by adsorption of azo-dye into the surface of the photocatalyst materials and suggests an optimum catalyst load and dye concentration for the degradation reaction. Light absorption and scattering within the substrate reaction zone and arising from differences in optical properties of catalyst material, made it impossible to interpret entire kinetic data on the basis of a simple Langmuir–Hinshelwood kinetics. However, kinetic data obtained at the initial stages of the reaction suggest conformity with first-order kinetics. The foam promises to be a versatile material in that it can be used for the treatment of low concentrations of pollutants of biological, organic and inorganic origins in water and air.     

Interaction of vanadium containing catalysts with microwaves and their activation in oxidative dehydrogenation of ethane

Microwave (MW)-activated oxidative dehydrogenation of ethane is studied using kinetic approach. It consists in the comparison of kinetic dependencies (shape of kinetic equations, “selectivity or yield vs. conversion” curves) and apparent parameters (activation energies) obtained in thermal and MW modes. In the case of VMo and VMoNb oxides a distinct difference between ethane yields was observed at given conversion of limiting reactant (oxygen). It was proven by X-ray diffraction that MW activation changes the catalyst microstructure forming phase distribution different from that formed under a conventional heating and thus changing catalytic behavior of VMo and VMoNb oxides.     

ADDITION OF PORE DIFFUSION LIMITATION TO THE “UCKRON-I” KINETIC RATE OF METHANOL SYNTHESIS

Kinetic data with pore diffusion limitation on methanol synthesis were generated by extending the “UCKRON-I” kinetic rate expression. The best fit model and the extended “true” model were compared using their respective rates to simulate temperature profiles in a non-isothermal plug flow tubular reactor.

The objective of this work was to add pore diffusion resistance to the UCKRON-1 kinetic rate for methanol synthesis (Berty, et al. 1983). Kinetic modeling of the data with 5% experimental error added, showed the best model to be that developed from a previous kinetic model (Shalabi, et al. 1983) with apparent activation energy approximately one-half the activation energy at no pore diffusion.

Methods used in this work to determine and evaluate pore diffusion parameters can be utilized for other reaction systems where pore diffusion may play a role in reaction rate.

Temperature profiles estimated from reactor simulation studies showed good argeement between ideal and predicted models for temperature.     

Numerical calculations of field enhancement and field amplification factors for a vertical carbon nanotube in parallel-plate geometry

Three types of models, with various emitter shapes in planar electrodes, have been employed to investigate field electron emission characteristics by finite element method. With the model of “hemisphere on a post”, two definitions of field enhancement and field amplification factors and their relation have been discussed systemically at different anode locations. The field distribution in the gap, between emitter apex and anode, is quantified by a field saturation factor. Simulation indicates that field distribution is an important aspect for explaining the nonlinear variation of field amplification factor at different anode locations. Furthermore, the field saturation factor can reflect the saturation degree of field amplification factor. The findings can be used not only in the model of “hemisphere on a post” but also approximately in the models of “two-stage hemisphere on a post” and “hemi-ellipsoid on plane”. Therefore, the fact can be approximately applied to every protruding shape of emitter that is supposed. Comparisons with previously reported experimental and theoretical results are also given.     

A kinetic model for the combustion of carbon in a porous medium

A model is proposed for infiltration combustion, which incorporates the reaction kinetics more fully. Calculations have been performed on a multicomponent system with complicated kinetics, which show that the kinetic parameters have a marked effect on the basic working ones. It has been shown by varying the water-air ratio for wet combustion that the completeness of the conversion of the fuel increases with the initial water concentration, and that the speed of the combustion front and the combustion temperature increase.Chernogolovka. Translated from Fizika Goreniya i Vzryva, Vol. 29, No. 3, pp. 136–139, May–June, 1993.     

Oxidation of titanium carbide–graphite hetero-modulus ceramics with low carbon content: II. Physico-chemical interpretation of the ridge effect

Hetero-modulus ceramics (HMC) present the combination of a ceramic matrix with the inclusions of a dispersed phase with considerably lower Young's modulus, resulting in a material with significantly improved properties. An interpretation of the so-called “ridge effect” observed during the isobaric-isothermal oxidation of 93 vol% TiC–7 vol% C (graphite) HMC at temperatures of 400–1000 °C and oxygen pressures of 0.13–65 kPa is given. Established in Part I of this study, the meanings of a ridge temperature and ridge oxygen pressure, which are served as boundaries between prevailing oxidation mechanisms in phenomenological kinetics model, are considered on the basis of X-ray diffraction (XRD) and microscopy analyses. The oxidation mechanisms, essentially different within the studied ranges of temperatures and oxygen pressures are identified according to the developed general model. These results can be used for the preparation of special protective coatings on the surface of refractory carbide–carbon HMC parts applied in severe environments, e.g. chemically active, high-enthalpy gaseous flows.     

Cinetique de graphitisation d'un coke de brai et d'un pyrocarbone suivie in situ par diffraction de rayons X

An X-ray spectrometer has been adapted to allow the recording of relatively fast transformations “in situ”. The experimental set-up was used to measure the changes in d₀₀₂ occurring with time for two kinds of carbon samples (a pitch coke sample and a pyrocarbon) while the sample was maintained at a constant temperature HTT. Methods to smooth out the scatter are applied to the graphitization kinetic curves and the dangers involved in using these methods are shown and discussed. Thus it turned out not yet possible to follow “in situ” small d₀₀₂ variations with a precision needed to establish the presence of step processes in graphitization.