Joseph M. Calo

Semi-global intrinsic kinetics for char combustion modeling†

This paper addresses the form of simple rate laws used to describe intrinsic char oxidation within practical combustion and gasification codes. The modern literature is surveyed for near-atmospheric kinetic studies that report global reaction order and/or activation energy. The resulting data set together with mechanistic insights drawn from fundamental surface studies are used to assess various semi-global kinetic models. There is strong evidence in the accumulated data for high reaction order (0.6–1) below 900 K, much weaker but significant evidence for low order above 1200 K, and some suggestion of transition toward another high-order regime at temperatures above about 1600 K. Neither global power-law kinetics nor semi-global Langmuir–Hinshelwood kinetics can describe this temperature-dependent behavior. A three-step semi-global mechanism is proposed whose simple rate law describes the major trends in reaction order, activation energy, and CO/CO2 ratio from 600 to 2000 K. The three-step model includes reaction between gaseous oxygen and surface complex, C(O), which is key to describing the high reaction orders widely reported in the low temperature Zone I regime.

Vibrational Relaxation and Electronic Quenching of the C 3Πu (υ′ = 1) State of Nitrogen

A molecular lifetime apparatus was used to study energy transfer processes of the C 3Πu state of nitrogen. Kinetic and luminosity measurements as a function of pressure indicate a cross section σ(3) = 2.5 ± 0.7 A2 for vibrational relaxation of N2(C 3Πu)υ′=1 by ground‐state nitrogen molecules. A useful result of the kinetic analysis is that although the observed lifetime (including quenching) decreases with υ′, vibrational relaxation reduces the gross C state luminescence decay to a single exponential, characteristic of the υ′ = 0 level. Natural radiative lifetimes and electronic quenching cross sections, σ(2), were determined for the υ′ = 0 and υ′ = 1 levels of the C state: υ′ = 0: τ = 40.5 ± 1.3 nsec and σ(2) = 1.98 ± 0.02 A2; υ′ = 1: τ = 44.4 ± 1.4 nsec and σ(2) = 1.42 ± 0.71 A2. Estimates of electronic and vibrational deactivation cross sections for the υ′ = 2 level are υ′ = 2: σ(2) = 3.9 ± 0.8 A2and σ(3) = 1.6 ± 0.4 A2. The efficiencies for excitation of the υ′ = 0 and υ′ = 1 levels by the secondary e...

The effects of hydrogen on thermal desorption of oxygen surface complexes

Abstract Temperature programmed desorption/reduction techniques have been applied to an investigation of the interaction of hydrogen with oxygen surface complexes and reactive sites on the surface of a resin char during thermal desorption. It is shown that the presence of hydrogen has a number of significant effects on the evolution patterns of the oxides of carbon and water vapor. A number of conclusions regarding the influence of hydrogen on oxidized carbon surfaces are presented, based upon analyses of the resultant TPD/TPR spectra for these samples. These results suggest that the interaction of hydrogen with oxygen surface complexes during temperature programmed experiments can be a useful “tool” in probing the nature and origin of surface species.

Generation of molecular clusters of controlled size

Abstract A novel gasdynamic source capable of producing small clusters of controlled size is described. Two versions of this Multiple Expansion Cluster Source (MECS) are discussed: one which produces transition metal clusters of interest in catalysis and one which produces water clusters of atmospheric interest. The clusters are formed as an aerosol supported in an inert gas flow. They can be isolated from the carrier gas by impingment on a surface or by expansion through a sonic orifice into a vacuum region to form a molecular beam. A controlled mean size ranging from the dimer up to several thousand of the monomer species is possible. The full width at half maximum of the distribution of cluster sizes that is produced is as small as is theoretically possible with a condensation type process. For a mean size greater than ≈50, the FWHM has a constant value in diameter space of approximately twice the diameter of the monomer.

Exact criteria for uniqueness and multiplicity of an nth order chemical reaction via a catastrophe theory approach

Abstract The development of a simple, generalized technique for the exact determination of regions of unique and multiple solutions to certain nonlinear equations via a catastrophe theory-implicit function theorem approach, is presented. The application of this technique to the nth order chemical reaction in the nonadiabatic and adiabatic CSTR yields exact, explicit bounds for all n ≥ 0. To our knowledge, this is the first report of exact, explicit bounds for these systems, except for n = 0, 1 for the adiabatic CSTR, and n = 1 for the nonadiabatic CSTR. For the nonadiabatic CSTR, these bounds show that the higher the reaction order, the smaller the region in parameter space for which multiplicity can occur for all γ and x2c, (dimensionless activation energy and coolant temperature, respectively). This behavior is similar to that reported by Van den Bosch and Luss[1] for the adiabatic CSTR. The zeroth order reaction in the nonadiabatic CSTR exhibits more complex behavior and assumes characteristics of both high and low reaction orders insofar as increasing and/or decreasing the uniqueness space, in comparison to all other n > 0. An exact implicit bound between regions of uniqueness and multiplicity is also derived for the nth order reaction in a catalyst particle with an intraparticle concentration gradient and uniform temperature, and is fully demonstrated for the first order reaction. In addition, explicit criteria, sufficient for uniqueness and multiplicity of the catalyst particle steady state, stronger than those of Van den Bosch and Luss, are also developed by combining the present technique with bounds suggested by these authors.

An improved computational method for sensitivity analysis: Green's function method with ‘AIM’

Sensitivity analysis of initial value models via the calculation of linear sensitivity coefficients is quite important for model evaluation and validation. Direct solution of the sensitivity equations for n -dimensional, m -parameter systems of ordinary differential equations requires the solution of m × n differential equations, which can become quite expensive for large-scale models. When m > n (the usual case for chemical kinetic systems, for example), the Greens function method (GFM), which requires solutions of n 2 differential equations with m × n subsequent numerical quadratures, is the most efficient computational technique for determining linear sensitivity coefficients. Even so, associated computing costs can still become quite large. In the current work, an algorithm, known as the analytical integrated Magnus (AIM) modification of the GFM, is presented which dramatically reduces the computational effort required to determine linear sensitivity coefficients. The technique employs the piecewise Magnus method for more efficient calculation of Greens function kernels, and treats the sensitivity integrals analytically. An application of this technique to a chemical kinetics system is presented in which the computational effort is reduced by an order of magnitude in comparison to the unmodified GFM.

Sensitivity analysis of oscillatory systems

Abstract Methods of sensitivity analysis are extended to find the parametric dependencies of systems of ordinary differential equations which exhibit limit cycle oscillations. The quantitative relations between the system parameters and the observable period, amplitude, phase and cycle shape are developed. These formulae, presented for both the first and second order, are applicable to systems of arbitrary size and complexity. The techniques are used here to develop correlations for period and amplitude in a non-isothermal oscillating stirred-tank chemical reactor, and to find and optimize a beneficial periodic operating strategy for a lumped-parameter catalytic reacting system.

Dimer formation in supersonic water vapor molecular beams

An experimental and theoretical study of dimer formation in supersonic water vapor molecular beams is presented. Terminal dimer mole fractions, as a function of source pressure, temperature, and orifice diameter, were measured by sampling fully expanded jets with a quadrupole mass spectrometer employing a phase‐sensitive pulse counting technique. The results are in good agreement with a termolecular formation and bimolecular destruction kinetic model for the dimer if a sudden cessation is assumed for the reverse reaction at low reduced temperatures. The model makes use of an expression developed for the equilibrium dimer mole fraction of polar molecules, and takes into account the increase in collision diameter for water molecules due to the reduced kinetic energy of relative motion at low temperatures. The source pressure at which the terminal dimer mole fraction attains a maximum is found to be proportional to D−0.630 and T3.50, where D0 is the orifice diameter and T0 is the source temperature.

Some aspects of the thermal annealing process in a phenol-formaldehyde resin char

Abstract It is well known that chars and carbons lose reactivity as a function of the severity of their heat treatment in inert environments. In this study, phenol-formaldehyde resins of low impurity contents were prepared and heat treated at heat treatment temperatures (HTT) ranging from 1273 K to 1673 K. The low-temperature oxygen reactivity of the chars was then measured, both in the oxygen chemisorption regime (423 K, 101 kPa O2) and the oxygen gasification regime (573–673 K, 0.5 to 101 kPa O2). The oxygen gasification reactivity varied with heat treatment by an order of magnitude. It was concluded that this was not entirely attributable to changes in total surface area with heat treatment. The variation of the reactivity to active surface ares (ASA) ratio with burnoff was small in 1273 K char and large in 1673 K char. The kinetics of annealing were explored, and it was found that a single firstorder deactivation reaction model was unable to describe the variation of either reactivity or ASA with HTT. A first-order distributed activation energy model was found to fit the data reasonably, and implied that the deactivation reactions that are of relevance under these conditions have a preexponential factor of between 1013 and 1014 s−1, and activation energies in excess of 450 kJ/mole.

Explaining the optical fuse

Experiments show that the characteristic periodic damage pattern that results from the optical fuse can be produced by purely thermal means by heating the fiber to temperatures in the 700-1000 degrees C range in the absence of light. The nature of the damage region bubbles suggests local temperatures high enough to soften the fiber core. The additional energy required may be supplied by an exothermic mechanism. Consideration of activated interstitial diffusion of various potential oxidants: unoxidized sites with O(2) could be responsible.