All of the problems mentioned for the intrapellet model (12/13/2013) and the effectiveness factor method (12/21/21013) can be avoided by measuring the kinetics using the commercial catalyst.
The catalyst particle: the perfect integrator
If your model is based on kinetics that used the commercial catalyst, then the catalyst has done the integration into the pellet for you! This integration has been done with the actual distribution of pore sizes, tortuosity and activity. It has been done with the actual catalyst shape and size. No knowledge of the location of the internal boundary condition is required. All that is required is a kinetic model based on the catalyst surface concentrations and temperature. In the reactor model, the surface variables can be easily determined without iteration.
There is no need to assume the particle is isothermal
Although the catalyst particle often is nearly isothermal, that is not a requirement for this method. All that is required is knowledge of the particle surface temperature. The interior temperatures are assumed to be uniquely related to this temperature (see Multiple steady states below).
The surface conditions in the kinetic experiments
Given a reasonable estimate or measurement of the fluid velocity around the catalyst, say catalyst in a Berty or Carberry reactor, then the heat and mass transfer coefficients across the fluid film can be estimated.
With the computed transport parameters and the measured reaction rates (determined easily by material balance around a CSTR reactor), then the surface conditions can be computed by equating the mass and energy production rates with the film transfer rates. No effectiveness factor is required.
The surface conditions in the reactor model
A reactor model can be developed for both the fluid and the catalyst particle phases. The particle phase balances will include (1) the heat or mass production rates using the surface variables, and (2) the film transport to the bulk fluid, and (3) heat dispersion through the solid phase. The fluid balances will include the film transport, and the convection, and dispersion terms for the moving fluid. Accumulation terms can be added for dynamic models.
Numerical method for reactor model
With many numerical methods, iteration may be required between the solution of the fluid balances and the particle balances. However, the hopscotch method (see postings 9/24 and 9/29/2013) solves all of the balances simultaneously, without iteration.
Multiple steady states
There is one requirement for this method to work: there must be a unique reaction rate for a given set of surface conditions. Multiple steady states will be the subject of the next posting.