(258d) 2D Optimization of Fixed-Bed Reactors: Additional Degrees of Freedom for the Reactor Design to Increase Efficiency

Highly efficient reactors are
fundamental for resource- and energy efficient production of chemicals. To
enable high reactor efficiencies, the reactor design aims to realize optimal
reaction conditions along the reaction route [1]. In this regard, the reaction
temperature plays a superior role due to its strong influence of the reaction
rates.

For
heterogeneously catalyzed reactions with a pronounced energy release, the
state-of-the-art approach is the use of tube bundle reactors with axial
dilution zones to approximate the optimal temperature [2]. However, a significant
deviation from the optimal temperature can still exist in radial direction of
the tubes due to the radial heat transport resistances as shown in figure 1.

Figure
1:
Exemplary demonstration of the (system specific) optimal reaction temperature along
the tube (a) compared to the resulting reaction temperature profile due to heat
transport resistances in a fixed-bed reactor with an optimal axial catalyst bed
dilution profile (b) and a fixed-bed reactor with an optimal axial and radial
catalyst bed dilution profile (c) for the air-based production of ethylene
oxide.

This deviation can be reduced by further
increasing the surface-to-volume ratio of the tubes, thereby reducing the
radial transport pathways. To maintain the necessary residence time, this
approach requires either longer tubes or an increase of the number of tubes. Both
options lead to an increase of investment and operation costs as a result of a
higher pressure drop and higher material and/or installation costs.

As
an alternative, the concept of the radial optimization of tubular reactors is
introduced for the model-based reactor design. This is an extension to the
state-of-the art approach of optimizing suitable design variables such as the
catalyst bed dilution or the catalyst pellet specifications in axial direction
of the tube [3]. The radial coordinate is additionally considered as a degree
of freedom for the chosen design variables, leading to a superior approximation
of the optimal reaction temperature as shown in figure 1 c). The optimization
results give a quantitative indication of the potential reactor performance gain
by introducing radial profiles of the chosen design variables. It can then be
investigated to which extent these profiles can be technically approximated.
Furthermore, the optimization results can indicate the potential of suitable alternate
reactor concepts (e.g. catalytic foam reactors or monolithic reactors).

The
concept of the radial optimization is presented and illustrated by optimizing a
tubular reactor for the air-based production of ethylene oxide in a case study.
To reduce the computational effort for the resulting large-scale nonlinear
optimization problem, pseudo-homogeneous reactor balance equations are used to
describe the reactor. The solutions of the catalyst pellet equations are
approximated via analytical approximations [4]. A suitable model basis is
identified that is compatible with the dynamic optimization approach, yet
considers changes of design variables in radial direction of the tube. The
objective function is to maximize the conversion of ethylene while fulfilling
other reactor performance constraints in terms of selectivity towards ethylene
oxide and space-time yield. Results show that by introducing a 2D dilution
profile, the yield of ethylene oxide can be increased by 2 %. Furthermore, the 2D
optimization results indicate that a novel alternate reactor concept consisting
of a catalytic foam reactor followed by a classical particle packed fixed-bed
reactor holds significant potential for process intensification.

References

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

[2]        Eigenberger, G.; Ruppel, W.;
Ullmann’s Encycl. Ind. Chem. Online ed. Wiley-VCH, Weinheim, 2012

[3]        Hwang, S.; Smith, R.; Chem.
Eng. Sci. 59 (2004) 4229-4243

[4]        Pietschak, A.; Kaiser, M.;
Freund, H.; Chem. Eng. Res. Des. (2018) submitted