(360d) Improved Fixed-Bed Transport Characteristics: A Shortcut Method to Optimize Catalyst Pellet Specifications

Highly efficient reactors are
fundamental for the resource- and energy efficient production of chemicals. The
basis to develop such optimal chemical reactors is the simultaneous
consideration of all possible design variables, leading to a perfectly tuned
system. In catalytic fixed-bed reactors, the catalyst pellet specifications
have a significant impact on the system behavior. Besides influencing the
catalytic activity and selectivity due to intraparticle transport phenomena,
the pellet also influences the fixed-bed transport characteristics such as heat
transfer and pressure drop. Hence, the simultaneous design of reactor and
catalyst pellet can lead to an improvement of the overall system performance.

For model-based reactor design via
dynamic optimization [1] a rigorous treatment of the catalyst pellet during
reactor design demands the discretization of the pellet balance equations in
addition to the reactor balance equations. The result is a complex heterogeneous
model leading to challenges in regard to the computational effort and the
numerical stability during optimization. Alternate approaches exist that enable
a consideration of the intrapellet mass transport effects via analytical
equations. However, these approaches either demand extensive pre-calculations
(e.g. Adomian decomposition method [2]) or are strongly limited in regard to their
applicability to certain reaction systems or reaction kinetic models (e.g.
Thiele-modulus concept [3]). To avoid the drawbacks of these approaches, in
this contribution a novel shortcut method is developed and applied. This approach
is applicable to arbitrary reaction networks and reaction kinetic models. It
enables the computationally cheap optimization of catalyst pellet specifications
to improve the bed transport characteristics during the simultaneous design of
reactor and catalyst pellet.

The principle of the method is to
linearize the rate of formation of each component influencing the reaction
rates at bulk conditions. These linear expressions are inserted into the
corresponding catalyst pellet component balances. The resulting set of identically
structured second order inhomogeneous differential equations is parametrized,
decoupled and then solved analytically. The solutions, differing only in the
values of their parameters, yield the component concentration profiles in the
pellet in dependency of the pellet specifications. Effective reaction rates,
calculated via integration, can be inserted into the reactor balance equations.
Hence, pellet specifications can be optimized without the need of a
heterogeneous model. To ensure a high accuracy of this approach, high catalyst
efficiencies should be targeted.

To
demonstrate the potential of a simultaneous reactor and catalyst pellet design with
the developed shortcut method, a fixed-bed reactor with constant coolant temperature
for the production of ethylene oxide is optimized. The objective is to minimize
the pressure drop while fulfilling other reactor performance constraints. Pellet
specifications in terms of pellet size and pellet heat conductivity are
optimized. A pressure drop reduction of 50 % compared to an optimized reactor
with prefixed pellet specifications is achieved. Figure 1 shows the optimized
catalyst heat conductivity as well as the resulting reaction temperature with
reaction progress.

Figure 1: Left: Optimal catalyst pellet heat
conductivity profile and resulting catalyst pellet component efficiencies
(E=Ethylene, O2=Oxygen, CO2= Carbon dioxide). Right: Resulting reaction
temperature profile and optimized coolant temperature.

The
presented method enables the design of tailored reactor-catalyst pellet systems
to improve the bed transport characteristics. Results with respect to the
pellet specifications can point to certain catalyst pellet types available
and/or give impulses to develop pellets fulfilling the optimal specifications, leading
to highly efficient reactor systems.

The
approach developed in this work is generally applicable, i.e., no limitations
exist regarding the applicability to certain reaction networks or specific
types of reaction rate models as compared to existing methods. At the same
time, since a high model complexity is avoided, the approach can be used for
efficient simulation and optimization of complex reaction systems.

References

[1]        Peschel,
A.; Freund, H.; Sundmacher, K.; Ind. Eng. Chem. Res. 49 (2010) 10535-10548

[2]        Adomian,
G.; J. Math. Anal. Appl. 135 (1988) 501-544

[3]        Thiele, E.W.; Ind. Eng. Chem. 31 (1929), 916-920

[4]        Aris, R.; Chem.
Eng. Sci. 13 (1960) 18-29