Diffusion Control Regime Research Articles

An apparent kinetic model for the carbonation of calcium oxide by carbon dioxide

For the apparent kinetics of the carbonation reaction of calcium oxide by carbon dioxide, as a kind of noncatalytic gas–solid reaction, a model equation has been proposed as follows: X= kbt/( b+ t), where X is the conversion of CaO; k, a kinetic rate constant (time −1); b, a constant (time) equivalent to the time taken to attain half the ultimate conversion of CaO, and t, the time. As a result of analyses for some literature-reported data of CaO-carbonation conversion, it has been found that the rate of the carbonation can be well represented by d X/d t= k(1− X/ X u) 2, where X u is the ultimate conversion of CaO, which is given by the product of two parametric constants, k and b. The constants k and b in the two rate control regimes of CaO-carbonation, chemical reaction control and diffusion control, have been determined as functions of temperature, respectively. The activation energy in the carbonation of surface CaO with CO 2 is estimated to about 72 kJ/mol regardless of the sources of CaO, however, that in the diffusion control regime appears differently as 102.5 (mesoporous CaO) or 189.3 kJ/mol (commercial-available CaO), possibly due to the morphological differences of the two CaO samples. From a practical point of view, the simple model equation proposed in this study deserves attention in that the CaO-carbonation behavior at working temperatures higher than 700 °C could be closely predicted.

An electrochemical study of copper cementation of gold(I) thiosulfate

In the present study, copper cementation was evaluated as a method for the recovery of gold from thiosulfate leach solutions. It was found that it is possible to achieve appreciable cementation rates of gold onto a copper substrate. The presence of 0.4 M ammonia had a positive effect on cementation, shifting the reaction from the chemical reaction control regime to the diffusion control regime. This effect is explained by the shift in the anodic reaction, copper oxidation, as ammonia was added. Electrochemical studies of the cathodic reaction, gold deposition, were also carried out. It was found that a high overpotential is required to deposit gold onto a gold substrate. However, the presence of copper, either as metallic copper or as Cu(I) thiosulfate, dramatically enhances the gold deposition half reaction. Without this enhancement, the cementation reaction would occur at a very low rate.

Effect of eccentricity and interaction between kinetics and mass transfer on the behaviour of catalytic annular reactors: a comparison between lumped and distributed models

A numerical investigation has been carried out on an isothermal annular reactor for kinetic studies under laminar flow conditions. The scope was to investigate the effects of eccentricity in the annular reactor and the adequacy of using lumped models when modelling such cases. 1D-models were compared with the corresponding 3D-models for different values of eccentricities and for different kinetic rate laws. In the case of linear kinetics, the solutions of the lumped models agreed satisfactorily with the solutions of the distributed models for all eccentricity values investigated. However, for non-linear kinetics, especially for LHHW rate expressions, significant differences in conversion between the models were observed during a mixed chemical diffusion-control regime. The differences became progressively larger as the eccentricity was increased. An enhanced 1D-model, with compensation for those non-linear effects, was designed and gave satisfactory agreement with the 3D-models. For conditions when the 1D-model could predict multiple steady states, a higher eccentricity produced a wider temperature range over which multiplicity occurred. This was so even in the cases where the multidimensional models did not predict any multiple steady states. It is not in general possible to rely on evaluating kinetic data from an eccentric annular reactor by using a 1D-model. In order to be sure to obtain accurate data from this type of reactor, an eccentricity of less than 10% is allowed.

Expressing nth Order Char-Oxygen Reaction Initial Rate under Elevated Pressure.

Char combustion is investigated in the temperature range of 559–1273 K and pressure range of 0.1–1.6 MPa in a 0.5th-order reaction (a lignite coal char) and a first-order reaction (a bituminous coal char).The intrinsic combustion constant kv and the reaction order n do not vary with pressure, but the char combustion initial rate varies with the pressure in the chemical kinetics control and the internal diffusion influence regimes. The variation of initial rate with pressure was also sensitized to the reaction order n. In the chemical kinetics control regime, the char combustion initial rate was proportional to Pn with the exponent n, the reaction order. In the internal diffusion influence regime, the apparent dependency of char combustion initial rate on pressure changed with the exponent range from n to n/2. The reaction initial rate in the external diffusion control regime was invariant with pressure. A rate expression was developed for predicting the initial rate of nth-order char combustion under elevated pressure.

Modeling of gas-carbon reaction in pore diffusion control regime

A model is developed for pore diffusion controlled gas-carbon reactions where the reaction is limited to a narrow region on the exterior surface of the carbon particle. A planar geometry is used and an isothermal condition is assumed. However, the effects of pore structure change with conversion are included. The model can predict the penetration depth, the porosity profile, the reaction surface area profile and the concentration profile in the reaction zone. The model is an extension of Gavalas model[l] and an improvement over Desai and Yang’s model[2]. The model predictions are compared with available experimental data and wilh those of Desai and Yang’s model.

Pressure changes during diffusion with chemical reaction in a porous pellet

A method is proposed for evaluation of the pressure change in an isothermal porous pellet within which a single chemical reaction takes place, accompanied by mass transfer by Knudsen diffusion, bulk diffusion and viscous convective flow of the reacting mixture. The dimensionless pressure is expressed as a function of two dimensionless parameters which characterize transport mechanism and mixture properties respectively. The pressure change also depends on the reaction and on the mixture composition on the pellet surface. The method requires numerical integration of an initial-value problem. A simple analytical method is also proposed for estimation of the maximum possible pressure changes in the system, both for the Knudsen diffusion control regime and for the bulk diffusion with viscous convective flow control regime. Both methods are illustrated by the computed results for a general two-molecule reaction and for the ammonia synthesis reaction.

Slow spinodal decomposition in binary liquid mixtures of polymers

Isothermal demixing process of binary polymer mixtures of SBR (styrene–butadiene random copolymer) and polybutadiene at deep quench depths was investigated by time-resolved light scattering technique. The results indicated that the systems undergo extremely slow spinodal decomposition of the type as adequately characterized by Cahn’s linearized theory in the early stage and in the small q regime (q≲qmax≂105 cm−1) covered in this experiment where q is wave number of growing fluctuations and qmax is the q value having maximum growth rate. The spinodal decomposition studied in this work was that in the diffusion-control regime, and in the slowest case of the decomposition, the early stage was found to extend up to about 80 min, corresponding to the reduced time τ about 2.7. The shortest reduced time achieved in this experiment is about 0.03.

The effect of diffusion and bulk gas flow on the thermal oxidation of porous carbons—III. Ungraphitised carbons

A previously published mathematical model of the effect of in-pore mass transport resistance on the kinetics of reactions between porous solids and gases has been verified by a study of the oxidation of a baked carbon tube at temperatures in the range 300–420°C. The baked carbon used in these studies had a higher reactivity than the nuclear graphite employed in earlier work. Evidence of the diffusional effect was obtained from gas concentrations in the bore and at the external surface. The effect of superimposed bulk flow of gas through the walls of the carbon tube was examined. Good agreement between the observed results and those calculated from the theory was obtained. An energy of activation of 55.2 kcal/g. atom was determined for the carbon oxygen reaction. The value of the energy of activation fell markedly at the lower temperatures examined. This reduction was tentatively ascribed to catalysis of the oxidation by the impurities in the carbon which is more important at these lower temperatures. The order of reaction was determined as 0.78 from measurements carried out at 450°C in the inpore diffusion control regime.