Computational fluid dynamics (CFD) simulation has become a routine tool for understanding the multiphase behavior in bubble column reactors. Process industry has a strong desire for reliable and accurate CFD models to aid the design, scaleup, optimization and troubleshooting of reactors. But CFD simulation has been reported to be sensitive to a number of closure models such as drag, lift and turbulence models, boundary conditions and numerical algorithms, and one may have to adjust model parameters to achieve the consistency with experiments. This issue is first relevant to the complexity of multi-scale flow structure and the difficulty in describing the effects of meso-structures in physical and mathematical models. 

In our previous work, we have developed the Energy-Minimization Multi-Scale (EMMS) approach for gas-solid fluidization, and the EMMS drag model could improve the accuracy of CFD simulation. Then an extended EMMS approach for gas-liquid flow, i.e. the Dual-Bubble-Size (DBS) model, featuring a stability condition reflecting the compromise of two dominant mechanisms, was developed for bubble column reactors. The drag model (termed as DBS-Global) was incorporated into CFD simulation through the ratio of effective drag coefficient to bubble diameter (C_D/d_b). The ratio as a function of global hydrodynamic parameters was used in CFD simulation, and the simulation showed reasonable agreement with experiments compared to other drag models. In this work, we further extend this model to each computational cell to calculate the average drag force (termed as DBS-Local). Hence the lumped ratio of drag coefficient to bubble diameter is linked with local hydrodynamic parameters. 

Several bubble column cases with different inlet types (non-uniformity and uniformity) and column diameters operated at different superficial gas velocities have been simulated to test the performance of three drag models, i.e., the DBS-Global drag model, the DBS-Local drag model, and the correlation of Schiller-Naumann.

We find that the Schiller-Naumann drag model under-estimated the local and overall gas holdup as well as the axial liquid distribution for the lower superficial gas velocity, both for the uniform and non-uniform gas aeration, and for the columns of small and large diameters. By contrast, the calculation of DBS-Global drag model shows significant improvements than the Schiller-Naumann drag model, and the DBS-Local shows the best agreement with the experimental data. 

On the other hand, the DBS-Local drag model looks better for the simulation of columns of large diameters, especially for the uniform gas aeration. The DBS-Global and Schiller-Naumann drag models can hardly acquire the parabolic radial gas holdup profile for the transition and heterogeneous flow regimes, whereas the DBS-Local drag model can accomplish this because the DBS-Local model can give a reasonable C_D/d_b in radial direction. We find that the C_D/d_b in radial direction calculated by these three drag models are nearly constant for the homogeneous regime, which eventually led to the uniform spatial distribution of gas holdup. But for the transitional and heterogeneous flow regimes, the bubbles of a size distribution at radial direction (large bubbles at center and smaller bubbles near wall) are of different ratio of C_D/d_b. DBS-Local drag model can give the reaonable distribution of C_D/d_b, and hence capture the parabolic radial gas holdup profile. Note the DBS-Global drag model can also capture the parabolic radial gas holdup profile for the small diameter column, but it may be related to the wall effect. 

On the whole, the DBS-Local drag model can well predict the radial gas holdup distribution, axial liquid velocity and total gas holdup, showing great potential and advantage in understanding the complex nature of multi-scale structure of gas-liquid flow in bubble column reactors.