James Wei

The stability of a reaction with intra-particle diffusion of mass and heat: The Liapunov methods in a metric function space

Abstract For a chemical reaction in a porous catalyst particle in the presence of heat and mass diffusion, the stability of steady state solutions is analysed by extending the two methods of Liapunov to a function space with a suitable metric.

Adsorption and cracking of n-alkanes over ZSM-5: Negative activation energy of reaction

Abstract The heat of adsorption of normal-paraffins on ZSM-5 is a linear function of the number of carbon atoms on the paraffin n, and is approximately half of the latent heat of consation. The rate of cracking of n-paraffins over ZSM-5 increases exponentially with n, which is consistent with a linear dependence of Δ G° with n. As temperature is increased, the cracking rate increases when n is less than 16, but decreases when n is greater than 16. This phenomenon is contrary to normal expectations, and is a consequence of the competition between two effects: the increase of intrinsic kinetics with temperature, and the decrease of adsorption strength and the concentration of active intermediates with temperature. The heat of adsorption becomes larger than the activation energy of the intrinsic kinetics when n=16.

On the maximum temperature inside a porous catalyst

Abstract In the presence of an exothermic reaction, the interior temperature of a porous catalyst may greatly exceed the surface temperature. It is shown here that under transient conditions the temperature difference may be considerably greater than the steady-state temperature difference of Prater, but must be less than an upper bound derived here.

Note on the Global Validity of the Baker‐Hausdorff and Magnus Theorems

The Baker‐Hausdorff theorem states that for two given elements x and y in an associative algebra, the equation exey = ez has a solution z which lies in the Lie algebra generated by x and y. The Magnus continuous analog gives an exponential solution to a linear operator differential equation. Both theorems are valid globally for free Lie algebras of formal power series. For algebras that are not free, however, both theorems are locally but not globally valid. Some examples are given. Necessary and sufficient conditions for global validity are discussed. A superior representation in terms of a finite product of exponentials is also given.

On the structure and analysis of complex systems of first-order chemical reactions containing irreversible steps—I general properties

Abstract The mathematical structures of systems of first-order reactions containing some irreversible steps are considerably more complicated than the structures of completely reversible systems because the principle of detailed balancing does not apply to the entire system. Characteristic vectors occur that do not correspond to directly responsible straight line reaction paths and the rate constant matrix cannot always be diagonalised. A decomposition of this system into subsystems of reversible reactions interconnected by irreversible steps allows one to introduce the principle of detailed balancing and leads to the development of theorems that should greatly increase ones ability to study such systems.

On the structure and analysis of complex systems of first-order chemical reactions containing irreversible steps—II Projection properties of the characteristic vectors

Abstract In systems of first-order reactions containing some irreversible steps, characteristic vectors occur that do not correspond to directly observable straight line reaction paths. A projection technique is presented and discussed that will transform such characteristic vectors into artificial straight line reaction paths that can be directly observed.

On the structure and analysis of complex systems of first-order chemical reactions containing irreversible steps — III Determination of the rate constants

Abstract The use of parallel ray projection in the determination of the characteristic vectors and rate constants of first-order reaction systems containing both reversible and irreversible steps is described.

The critical plume

The Gaussian plume model describes the dispersion of a pollutant from a point source. The region at risk is where the concentration c exceeds a critical concentration c∗, and we call this region the critical plume. In a steady-state windless situation, the critical plume is spherically symmetric. When the wind is blowing steadily, the critical plume is reduced in size in all directions except downwind, where the wind has no effect, contrary to physical intuition. Thus the wind reduces the risk of all the points not directly downwind, but has no effect on points directly downwind. In a transient situation with an instantaneous point source, the instantaneous critical plume is always spherical in shape, and the union of all the instantaneous critical plumes with time forms a shape similar to that of the steady-state critical plume. The overall exposure at a fixed point downwind, i.e. the integral in time of the concentration at that point, is independent of the wind speed, again contrary to physcial intuition but in agreement with the steady-state results.