(356e) Mesoscale Modeling of Multiphase Reactors: Theory and Applications
In this paper, we highlight a heuristic mesoscale modeling approach for multiphase reactor systems, starting from a conceptual Energy-Minimization Multiscale (EMMS) model and ending at the stability-constrained multifluid CFD model. While the stability condition determines the direction of system evolution, the stability-constrained CFD further describes the dynamics of structure evolution. Then this theory is applied to the simulation of gas-solid fluidization and gas-liquid bubble column reactors, with further extension to gas-liquid-solid three phase flow and stirred tanks. Several industrial applications on meso-scale modeling in liquid-solid polyethylene reactors and liquid-liquid emulsification systems will also be highlighted.
Taking the gas-liquid flow in bubble column reactors as an example, these reactors have found widespread applications in chemical and energy-related industries, such as coal liquefaction, waste water treatment and CO2 utilization, in view of their advantage in mixing, mass and heat transfer. CFD is playing important roles in the understanding of complex multi-phase fluid dynamics, phase holdup and bubble size distribution. However, the CFD simulation for gas-liquid flow based on Eulerian framework is reported to be sensitive to a number of constitutive equations. The accuracy or reliability of CFD prediction cannot be guaranteed and empirical correlations or parameters are always needed. Actually the CFD simulation is usually based on the Eulerian-Eulerian framework in which the complex meso-scale physics is averaged out and hidden in the so-called constitutive equations of two-fluid models, though the governing equations are rigorously derived from continuum mechanics or kinetic theory. The difficulty and challenging issue is therefore technically shifted to the constitutive models to describe the phase interaction forces (drag, lift and virtual mass forces) for momentum conservation equations, the turbulence coupling terms for turbulence modeling and the bubble breakup and coalescence kernel functions for population balance equations(PBM) of bubble number density. But physically the constitutive models relies on the understanding of mesoscale transport mechanisms. In the new model, a stability condition is formulated as the minimization of the sum of two energy dissipations, reflecting the compromise of a liquid-dominant regime at which smaller bubbles prevail and a gas-dominant regime favoring the existence of larger bubbles. It supplies a mesoscale constraint for conservation equations, and a mesoscale perspective to understand the macroscale regime transition. With the zero-dimensional conceptual model, we obtain a jump change after a gradual increase of gas holdup with superficial gas velocity. The jump change corresponds to the regime shift from the homogeneous regime to the fully-developed heterogeneous regime, and the regime shift can be physical interpreted through the stability condition: transition of the minimum of the sum of two energy dissipations from one local minimum point to the other leads to the dramatic variation of structure parameters and finally gives rise to the regime shift. The model calculation for gas-liquid and gas-solid systems demonstrates the intrinsic similarity of the two systems: the system evolution at macroscale is driven by stability conditions.
Theoretically stability condition may offer closure laws for CFD simulation. While direct integration is difficult, we propose various simplified approaches which are able to derive new closure models for drag, bubble-induced turbulence and corrections for kernel functions of coalescence or breakage rates in population balance equations. The stability-constrained multifluid CFD model shows much advantage over traditional closure models. We also tentatively extended this model to gas-liquid-solid flows for slurry bubble columns. More details can be found the publications (Li et al., 2016; Yang et al., 2015, 2017; Zhou et al., 2017).
Yang, N.*, Xiao, Q., A mesoscale approach for population balance modeling of bubble size distribution in bubble column reactors, Chemical Engineering Science, 2017, in press.
Zhou, R., Yang, N.*, Li, J., CFD simulation of gas-liquid-solid flow in slurry bubble columns with EMMS drag model, Powder Technology, 2017, in press
Li, J., Ge, W., Wang, W., Yang, N., Huang, W., Focusing on mesoscales: from the energy-minimization multiscale model to mesoscience, Current Opinion in Chemical Engineering, 2016, 13, 10-23
Yang, N.*, Mesoscale transport phenomena and mechanisms in gas-liquid reaction systems. In: Guy B. Marin and Jinghai Li, eds., Advances in Chemical Engineering (book chapter), 46, 245-280.