(119b) Fixed Bed Local Structure Effects on Pressure Drop and Residence Time Distribution (RTD)

Steffen Flaischlen^1,2, Jan Martin^1,2, Jule Kersebaum¹, Gregor D. Wehinger^1,2

¹Institute of Chemical and Electrochemical Process Engineering, Clausthal University of Technology, Clausthal-Zellerfeld/Germany

² Research Center Energy Storage Technologies (EST), Clausthal University of Technology, Goslar/Germany

Introduction

In slender fixed beds, the local bed structure (morphology) has a great influence on the flow properties such as pressure drop and residence time distribution (RTD) as well as heat transport [1,2]. While the particles are randomly arranged at higher reactor-to-particle diameter ratios (D/d_p>10), the structure is highly influenced by the confining wall at small D/d_p<10. The effects on the flow can be shown, for example, by pressure drop (Δp) experiments, where only a small change in morphology can lead to large changes in pressure drop [1]. Consequently, classical pressure drop correlations, where bed-averaged values are incoropated, can reproduce some of the experimental values, while for some bed arrangements, they overpredict pressure drop due to channeling. In contrast to the use of correlations, particle-resolved computational fluid dynamic (PRCFD) simulations can deal with these effects by resolving the entire packed bed structure and calculating the flow in the interstice. Therefore, new insights can be gained into structural properties such as the radial void fraction as well as the tortuosity of the packed bed and its influence on the flow fields. In addition, RTD for packed beds can be simulated. In this context, even more complex particles seem to be of interest, since with increasing complexity the mapping with simple correlations becomes more difficult.

Methods

Since PRCFD simulations require an input geometry, a geometric image of a fixed bed is needed. Synthetic generation is one of the most commonly used methods to obtain such a fixed bed representation. With the rigid body approach (RBA), it is possible to generate the fixed bed under the same filling conditions as in the experimental setup, so that the obtained structure is as realistic as possible. The whole structure is meshed using the local-caps method, in which particle contacts are cut off and filled with fluid mesh cells, which prevents the formation of deformed volume cells and thus numerical problems [4]. In addition to the averaged void fraction, local resolution is also of interest. For the analysis of this axially averaged radial void fraction, the free surface on cylindrical planes in the fixed bed is calculated. The tortuosity can be obtained by a heat transfer simulation using the heat and mass transfer analogy [5]. The residence time distribution was obtained by using a passive scalar as a massless tracer in the fluid, using a transient simulation with a concentration step at the inlet [6]. By monitoring the outlet concentration, the RTD sum curve can be calculated. On the other hand, a qualitative analysis of RTD can be performed by monitoring the tracer concentration through the bed as a video file.

Results

The investigation of different D/d_p and different particle geometries shows a strong dependence of the flow properties on the local structure. This is particularly evident in the direct comparison of two fixed beds with nearly the same reactor-to-particle diameter ratios. While for a D/d_p of 2.68 common pressure drop correlations like the Ergun or Eisfeld-Schnitzlein equations overestimate the values, PRCFD can reproduce the experiments almost perfectly. Only a small change in the geometric dimensions (D/d_p = 2.7) leads to an agreement between correlation and simulation, while the local structure of the bed changes extremely. The reason for this behavior is the clearly visible channel in the center of the fixed bed, which reduces the flow resistance, while at D/d_p = 2.7 it is closed by a particle being positioned in the center of the free space [1]. This difference can also be quantified by comparing the tortuosity of the two packed beds. The D/d_p of 2.68 has a tortuosity of τ=1.27, which means that the fluid takes a 27% longer path through the reactor compared to an empty tube (τ=1.0). In comparison, a D/d_p of 2.7 has a tortuosity of τ=1.35, showing that a small change in diameter ratio results in an 8% higher detour. In contrast to the change in tortuosity, the change in total void fraction is smaller. While the fixed bed with D/d_p of 2.68 (with the open channel) has a mean bed void fraction of ε=0.54, the bed for D/d_p = 2.7 results in only a 3% lower void fraction of ε=0.51. Since the pressure drop correlations depend only on the mean bed void fraction, they cannot resolve the effect of tortuosity on flow behavior. To gain additional insight into the fixed-bed structure, the RTD is analyzed. Comparing the two packed beds at the same dimensionless time q, strong differences in the tracer distribution can be seen. The fixed bed channel results in higher tracer transport in the axial direction through the center, leading to a radially non-uniform distribution of the tracer. In contrast, the fixed bed without central channel shows a more random structure and thus a uniform concentration in the radial direction. A further description can be given by the RTD sum and density curves. While the fixed bed without channeling effect can be described by a Bodenstein number Bo = 80, which is close to the value of an ideal plug flow, the fixed bed with channel shows an early curve, which is a sign for stagnant zones in the fixed bed [7].

Conclusion

It is shown that the local structure of a slender fixed bed has a great influence on the flow behavior. While the structural changes may lead to an incorrect prediction of the pressure drop, PRCFD seems to be more promising. It can therefore be used for detailed quantification of local structural effects. While the results already shown apply to packed beds of spheres, the influence of more complex particles appears to be larger due to the additional degrees of freedom in particle orientation. In addition, only the influence on flow properties has been shown so far. It can be assumed that similar effects occur in heat and mass transport. In addition, the local structures are also expected to have strong effects on reactions and thus on the conversion rate, as well as on the overall performance of the reactor.

References

[1] Flaischlen, S., Kutscherauer, M., & Wehinger, G. D. (2021). Local structure effects on pressure drop in slender fixed beds of spheres. Chemie Ingenieur Technik, 93(1-2), 273-281.

[2] Dixon, A. G. (2021). Local Structure Effects on Heat Transfer in Very Low Tube-to-Particle Diameter Ratio Fixed Beds of Spheres. Industrial & Engineering Chemistry Research, 60(27), 9777-9786.

[3] Flaischlen, S., & Wehinger, G. D. (2019). Synthetic packed-bed generation for CFD simulations: blender vs. STAR-CCM+. ChemEngineering, 3(2), 52.

[4] Eppinger, T., Seidler, K., & Kraume, M. (2011). DEM-CFD simulations of fixed bed reactors with small tube to particle diameter ratios. Chemical Engineering Journal, 166(1), 324-331.

[5] Cooper, S. J., Eastwood, D. S., Gelb, J., Damblanc, G., Brett, D. J. L., Bradley, R. S., ... & Shearing, P. R. (2014). Image based modelling of microstructural heterogeneity in LiFePO4 electrodes for Li-ion batteries. Journal of Power Sources, 247, 1033-1039.

[6] Wehinger, G. D., Kreitz, B., Nagy, A., & Turek, T. (2020). Characterization of a modular Temkin reactor with experiments and computational fluid dynamics simulations. Chemical Engineering Journal, 389, 124342.

[7] Levenspiel, O. (1998). Chemical reaction engineering. John wiley & sons.