The Catalyst Review April 2020 - 10

SPECIAL FEATURE
Examples of Working Reaction Kinetic Models
Figure 1 illustrates the use of reaction kinetic models for scaling up to a full-size plant to produce a product. However, there are a
number of other specific applications of sophisticated, validated reaction kinetic models including: (1) mathematical prediction of
catalyst life, activity and selectivity over a wide range of conditions at a significantly lower cost and time expenditure than for actual
process development tests; (2) optimization of catalyst life and process economics; and (3) estimates of reactor size and cost for design
and scale-up.
Development of kinetic models in the new paradigm requires a significantly higher level of sophistication than the present practice.
The objective is to develop a robust, comprehensive, physically realistic, fundamental model. Robust means that the model is general,
flexible, and applicable to related but distinctly different process conditions, catalysts, and reactor geometries. A comprehensive
model considers every important facet of a process, e.g., reaction chemistry, heat and mass transport, pore diffusion, and fluid
mechanics. A realistic model incorporates the most physically meaningful submodels for reaction, transport and thermodynamics,
while 'fundamental' implies a basic description of each subprocess of the model, such as kinetics of elementary steps or LangmuirHinshelwood expressions, so that data can be extrapolated over a wide range.
Example 1: 1D Reactor Model

The principal components of a reasonably simple but adequate, 1D
fundamental kinetic model for a heterogeneous catalytic reaction
are listed in Table 1. The equations and symbols are described in
textbooks by Davis and Davis (2003) and by Bartholomew and Farrauto
(2006). The principal equations are the differential equations (1-3)
for mass, energy and momentum balances (Davis and Davis 2003).
They relate changes in concentration, temperature, and pressure with
axial direction z through the tubular reactor. Equations 1-3 are solved
simultaneously using a stiff differential equation solver. In addition,
50-150 auxiliary algebraic equations, initial and final conditions, and
constants define the variables in the differential equations and are also
solved simultaneously. These auxiliary equations include Equations
4 through 10 defining the enthalpy of reaction, heat capacity, rate
equations, and pore diffusional resistance. Note that there are two rate
equations, one describing the rate of disappearance of the Species A in
the main reaction and a second accounting for changes in Normalized
Activity with time due to catalyst deactivation (Bartholomew and
Farrauto 2006); it is assumed in this model that deactivation is slow
relative to reaction - thus, the main reaction is at steady state. Rates
and pore diffusional parameters are calculated through the bed for
incremental values of z. In addition, molar balances yielding mole
fractions and partial pressures of each species and for the sum of all
species are carried out for incremental values of z (not shown). An
example of a molar balance for methanol synthesis is provided in
Chapter 6 of Bartholomew and Farrauto (2006).

Table 1. Basic design equations for 1D reactor design of a tube-shell
heat exchange reactor.

Unfortunately, several important features were missing in a number of previously developed kinetic models. Future modeling efforts will
need to be more rigorous and complete in order to meet new and more demanding standards of engineering practice. A few published
examples of robust, comprehensive, and fundamental models that have covered a range of space and temporal scales are addressed here.
Several other examples involving a deactivating catalyst are presented in Chapter 5 of Bartholomew and Farrauto (2006).
Brunner et al. (2012) developed a comprehensive, fundamental 1D trickle fixed-bed reactor model for Fischer-Tropsch synthesis (FTS)
applicable to both cobalt and iron catalysts which accounts for gas and liquid recycle. The model predicts temperature, gas and liquid
species, and conversion as a function of bed length. Four intrinsic rate models each for both iron and cobalt catalysts are included in
the reactor model and their effects on model predictions are compared. Reaction rates were determined for quasi-average radial bed
temperatures and correlations are used to account for radial thermal conductivity and radial convective heat transfer, the later of which
enables the radial temperature profile to be estimated. Traditional pressure drop calculations for a packed column were modified with
a correlation to account for trickle-flow of the liquid product. This paper does three things: (1) describes the model in great detail; (2)
shows results of varying fundamental, theoretically-based parameters (e.g., effective diffusivity, Prandtl number, and friction factor); and
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The Catalyst Review

April 2020

The Catalyst Review April 2020

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