Pore-Scale Simulation for the Fully-Developed Flow Through a Fixed-Bed Reactor Regularly Packed with Mono-Sized Spheres with Extension to Random Packing

This work conducts pore-scale numerical computations to reveal the hydrodynamic characteristics of the fully-developed flow through a fixed-bed reactor regularly packed with mono-sized spheres. One of the main purposes is to obtain invariant standard values which can be used as the benchmarks for those results from randomly packing methods such as Monte Carlo or DEM. Also, a repeatable and verifiable process is introduced to forecast the pressure drop and the mass flow rate in a packed bed without running any numerical simulation.

The mono-sized spheres in the present simulations are in FCC, BCC, or SC arrangement. For each packing, different Reynolds numbers and lattice angles are considered. For these regular arrangements, it is revealed that the cross-section of the reactor can be clearly separated into two regions: the more loosely-packed near-wall region and the densely-packed core region, with a boundary at a half-sphere diameter distance from the wall. The mass flow rates into the two regions will self-adjust themselves in proportion. Consequently, separate average Reynolds numbers in the near-wall, Re_w, and the core region, Re_co, are defined. Comparison of our computational results for fully-developed conditions with the experimental data for regular packings is presented. However, the inevitable presence of the entrance effect in the experiments on insufficiently-long regular packed beds forbids pertinent comparison. This work then continues to present a simplified model to predict the pressure drop through a reactor randomly packed with mono-sized spheres. The empirical correlations of C_D \(\times\) $\times$ d/L with Re_w or Re_co in respective regions are derived. These correlations can be used to evaluate the pressure drop through a reactor at a given total mass flow rate, which is proportioned in each region. A linear interpolation or extrapolation procedure is proposed to evaluate the \(\Delta\) $\mathrm{\Delta }$ P based on the \((1/\Delta\) $(1/\mathrm{\Delta }$ P_FCC)- \({\varepsilon }_{\text{FCC}}\) ${\epsilon }_{\text{FCC}}$ , \((1/\Delta P\text{BCC}\) $(1/\mathrm{\Delta }P\text{BCC}$ )- \({\varepsilon }_{\text{BCC}}\) ${\epsilon }_{\text{BCC}}$ , and \((1/\Delta\) $(1/\mathrm{\Delta }$ P_SC)- \({\varepsilon }_{\text{SC}}\) ${\epsilon }_{\text{SC}}$ relations, with given average void fraction \(\varepsilon\) $\epsilon$ , diameter and length of the container, particle diameter, and total mass flow rate. The reliability of the simplified model has been validated through the comparison with empirical correlations and Monte Carlo simulation in the literature.