Calculating effectiveness factors in non-uniform washcoat shapes

This paper describes a method for the determination of effectiveness factors in a monolith washcoat of non-uniform thickness. The method is based on the previously reported slice concept, in which the monolith is divided into a series of slices, each of which is analysed using a one-dimensional approach. In each one-dimensional slice, an apparent characteristic length is used to compute the Thiele modulus. In the approach described here, the apparent characteristic length is determined by conducting a single two-dimensional simulation for a first-order reaction in the kinetically controlled region. The characteristic length is then calculated from the flux at the surface using an analytical solution. Results are shown for the idealized circular washcoat in a square channel, as well as for a real washcoat in a square channel and a sinusoidal shape. Results for first-order and LHHW kinetics show good agreement between the one-dimensional approximation and the true solution. Both average and local effectiveness factors can be calculated within acceptable range for monolith reactor simulations.     

The effect of washcoat geometry on mass transfer in monolith reactors

This paper reports the results of a numerical investigation of the diffusion and reaction in the washcoat of a catalytic monolith reactor. Both idealized shapes and real geometries are tested. It is shown that for non-uniform washcoat thickness, the Sherwood number varies along the channel/washcoat interface. The internal diffusion resistance, expressed in terms of an effectiveness factor, cannot be represented in terms of a unique curve using the generalized Thiele modulus approach. The most significant deviation occurs when the washcoat has the greatest variation in thickness. The internal diffusion affects the magnitude of the external mass transfer resistance. Three factors significantly affect the rates and role of mass transfer. These are (1) the washcoat thickness, (2) the channel radius, including its non-uniformity around the channel, and (3) the angular diffusion in the washcoat caused by variable thickness.     

A robust iterative method of computing effectiveness factors in porous catalysts

A robust, efficient numerical method for computing the effectiveness factor of a heterogeneous reaction in a catalyst is developed in this study. The method is based on shooting at the outer surface of the catalyst and is optimized for an accurate estimation of the concentration gradient at the outer surface. The shooting at the outer surface, however, is inherently unstable for a cylindrical or a spherical catalyst, and it also can become unstable with an increasing Thiele modulus even for a slab catalyst. From an analysis of the governing equation, however, three criteria are developed to make the method work efficiently in the presence of instability. The numerical method is shown to be effective for diverse kinetic expressions, from simple power-law to sophisticated Langmiur-Hinselwood kinetics, and for isothermal or non-isothermal catalysts. The method is also shown to be easily applicable to a more complex case of multiple steady states, estimating all the corresponding effectiveness factors. In this method, a simple rule that determines the stability of each steady state is proposed.     

Two-parameter model for evaluating effectiveness factor for immobilized enzymes with reversible Michaelis-Menten kinetics

A two-parameter mathematical model was developed to calculate the effectiveness factor for immobilized enzymes in porous spherical particles. The model was resolved for reversible Michaelis-Menten kinetics, including simple Michaelis-Menten and product competitive inhibition kinetics. Since only two dimensionless moduli are involved in the model, the effectiveness factor for the three kinetic equations considered can be estimated by using only one generalized graph.     

High temperature stable magnesium oxide catalyst for catalytic combustion of methane: A comparison with manganesesubstituted barium hexaaluminate

The activity of magnesium oxide for catalytic combustion of methane was examined and the results were compared with experimental results for manganese-substituted barium hexaaluminate. The catalysts were calcined at temperatures up to 1 500°C and the effects of temperature, space velocity and calcination temperature were examined. The catalysts were also characterized with BET and XRD. For magnesium oxide calcined at 1 100°C the ignition temperature T_10% was decreased by 270°C compared to the non-catalyzed reaction. For the same catalyst T_50% was measured to be 795°C. The corresponding temperature for the hexaaluminate was 640°C. The difference between the two catalysts decreased after calcination at 1 500°C. For the magnesium oxide the influence of catalytically initiated homogeneous gas phase reactions was studied by varying the post catalytic volume of the reactor (and hence the residence time in the heated zone after the catalyst). It was shown that these catalytically initiated homogeneous gas phase reactions are significant for the methane conversion.     

A method for measuring the kinetics of organically associated inorganic contaminant vaporization during coal combustion

A novel method is presented for the direct measurement of kinetic parameters under conditions that simulate the vaporization of inorganic material during coal combustion. This method will ultimately be used to generate key physical property data necessary to model and assess the vaporization behavior of trace elements (TEs) during coal combustion. The method uses a graphite furnace atomic absorption spectrometer (GFAAS) as the experimental platform for vaporization measurements for temperatures up to 2800 K. The method was used to model vaporization during coal pyrolysis for one of the three key contaminant domains: organically associated material. Significant testing was conducted for selected TEs under varied instrumental operational conditions that could affect activation energies, such as GFAAS ashing and atomization temperatures, TE concentration, and carrier gas flow rate. The vaporization activation energies determined were found to be independent of these operating conditions despite a significant difference in the degree of analyte vaporization observed at varied ashing temperatures.     

A test method for measuring chloride diffusion coefficients through partially saturated concrete. Part II: The instantaneous plane source diffusion case with chloride binding consideration

A test method is proposed for measuring chloride diffusion coefficients through partially saturated concrete specimens with well characterized water contents. It includes an experimental procedure for supplying a limited amount of Cl⁻ to the tested concrete surface, and two mathematical models for processing the experimental Cl⁻ content profiles obtained at selected diffusion times. The use of the more refined model, taking into account the chloride binding by concrete, allows to increase the reliability of the determined diffusion coefficients. For the two tested Portland cement concretes, (water/cement ratios 0.6 and 0.5), the Cl⁻ diffusion coefficient decreases about two orders of magnitude, from 6 · 10^− 12 to 2 · 10^− 14 m²/s, when the relative humidity of the atmosphere in equilibrium with concrete is lowered from 95% to 54% approximately.