J. Szekely

A structural model for gas—solid reactions with a moving boundary

Abstract Gas—solid reactions involving a moving boundary are generally described in terms of the shrinking core model, where structural parameters are incorporated into an empirical reaction rate constant. ln the paper an alternative representation is proposed by describing the progress of the reaction in terms of the porosity, grain size, gas phase and solid state diffusivities and a heterogeneous reaction rate constant, which is now independent of structure. By taking “reasonable values” for these parameters the model was found to reproduce the general trends exhibited by the experimental data of other investigators.

A structural model for gas-solid reactions with a moving boundary—III: A general dimensionless representation of the irreversible reaction between a porous solid and a reactant gas

Abstract A general structural model is developed for the description of non-catalytic gas-solid reactions; which allows for spherical and flat plate like pellets, made up of spherical or flat plate-like grains. The numerical solution of the dimensionless form of the governing equations results in a plot of the dimenionless time to achieve complete reaction against a gas-solid reaction modulus, which is valid for all the geometries considered. The use of this plot could be useful for the planning of experiments or for the interpretation of experimental data, in terms of structural models, without the need for digital computation. It is shown that for extreme values of the gas-solid reaction modulus, the results of the model reduce to the asymptotic solutions corresponding to the “shrinking core” and the “uniform reacting pellet” models respectively. Thus the “gas-solid reaction modulus” is helpful for the quantitative definition of the range of these asymptotic regimes, in terms of the chemical and structural parameters of the system.

A structural model for gas-solid reactions with a moving boundary-II: The effect of grain size, porosity and temperature on the reaction of porous pellets

Abstract A structural model is presented for the non-catalytic reaction between a porous solid and a gas stream. The model incoporates parameters such as solid grain size, porosity, effective pore diffusion coefficient and allows the quantitative assessment of the role played by these in determining the overall reaction rate. The model was found to predict reasonably well the reaction of porous nickel oxide pellets with hydrogen within an intermediate temperature range. In the paper an approximate allowance is made for the effects of sintering and it is suggested that there may exist an optimum combination of grain size, porosity and reaction temperature which would give the fastest overall reaction rate.

A structural model for gas—solid reactions with a moving boundary—V an experimental study of the reduction of porous nickel-oxide pellets with hydrogen

Abstract Experimental results are reported on the reduction of porous nickel-oxide pellets with hydrogen within the temperature range 224–412°C. The experimental data were interpreted using a previously published model for gas—solid reactions. The measurements taken with small specimens provided information on the intrinsic kinetic parameters and on the shape of the solid grains, whereas the data taken using large specimens allowed the authors to determine the diffusional parameters of the system. The kinetic and the diffusional parameters obtained in the two asymptotic regims were used to predict the behavior of the system in the intermediate region.

Natural convection transients and their effects in unidirectional solidification

A formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot. It was found that appreciable fluid velocities may be produced by natural convection, the values of which could be comparable to the terminal rising velocities of typical nonmetallic inclusions. The simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500,i.e., to narrow slots or to low values of the superheat; nonetheless, the results should be indicative of the effects of convection at much higher values of GrPr.

The role of natural convection in ladles as affecting tundish temperature control in continuous casting

An approximate analysis is presented to describe the flow field in molten steel held in a ladle, as caused by natural convection. It is shown that a thick (say 8 to 14 in.) slag layer is required to suppress extensive vertical mixing within the ladle. It is also shown that natural convection caused by the contact of the metal with the cold ladle walls may produce mass flow rates of the order of 2 to 3 tons per min for typical 100 to 150 ton ladles. If ladles are tapped at comparable rates, then this pehnomenon can effectively prevent mixing in the bulk. The resultant stratification may be desirable in tundish temperature control.

Non-equilibrium effects in the growth of spherical gas bubbles due to solute diffusion

Abstract A formulation and computed results are presented for the growth of a spherical gas bubble in a supersaturated liquid, due to solute diffusion. The computed results are given in a dimensionless form and the appropriate dimensionless parameters allow a more general representation of the effects of surface tension, viscosity and liquid inertia. An approximate assessment is also made of the range, over which certain asymptotic solutions are valid. The computed results were found to agree quite well with experimental data obtained in the region where liquid inertia played an important role in controlling the overall growth rate.

A structural model for gas—solid reactions with a moving boundary—IV. Langmuir—Hinshelwood kinetics

Abstract The Langmuir—Hinshelwood type of kinetic expression has been incorporated into the “general structural model” for the reaction of a porous solid with a gas. Thus the system occupies the domain between the asymptotes corresponding to first-order and zeroth-order kinetics. The effect of the form of the rate expression is found to be the largest in the intermediate regime where both chemical reaction and diffusion play important roles in determining the overall rate. A “gas—solid reaction modulus” generalized for the Langmuir—Hinshelwood type of rate expression was developed to define the regimes of the different controlling mechanisms.

Stirring and its Effects on Aluminum Deoxidation in the ASEA-SKF Furnace : Part II, Mathematical Representation of the Turbulent Flow Field and of Tracer Dispersion

A mathematical formulation is presented describing fluid flow and tracer dispersion in an ASEA-SKF furnace. The statement of the problem required the simultaneous solution of the turbulent Navier-Stokes equations together with a simplified form of Maxwell’s equations. The resultant partial differential equations were solved numerically using a digital computer. Computed results are presented describing the streamline pattern, the velocity field, the spatial distribution of turbulent energy within the system, together with the rate at which a tracer is dispersed. For a 50 ton furnace, with a coil current of 1300 A the computed linear velocities ranged up to 150 cm/s and the mean values of the eddy diffusivity were of the order of 300 to 500 cm2/s. The computed results were found to be in reasonable agreement with previously reported tracer dispersion measurements. However, there is a disparity between the predicted circulation rates and those deduced from the measurements in an earlier paper using a simple one dimensional model for the interpretation of the results.

Reactions between solids through gaseous intermediates—I reactions controlled by chemical kinetics

Abstract A formulation is presented for the reaction between two solid species which proceeds through gaseous intermediates, involving the net generation of gases. Problem of this type are of considerable practical interest in the reduction of metal oxides with carbon. The system is characterized by two dimensionless parameters which include the reaction rate constants, the shape, size and the relative amount of the solid reactants. Through the use of these parameters it is possible to identify the asymptotic regimes where the overall rate is controlled by the reaction of one of the solid species. These dimensionless parameters also allow the definition of the criteria for the complete conversion of both solid reactants. In case of multiple reactions both stoichiometry and the kinetic factors must be taken to consideration in the establishment of these criteria.