(395a) Filtered Models for Reacting Gas-Solid Flows

Particle laden flows are used in a wide variety of industrially relevant processes that span applications ranging from the synthesis of specialty chemicals to the refining of petroleum products. The gas-solid flows exhibit persistent large fluctuations in velocities and particle volume fraction that cover a wide range of length and time scales. These gas-solid flow structures arise as a consequence of the instability of the uniformly fluidized state [1], and can be predicted via continuum models that treat the particle and fluid phases as interpenetrating continua [2]. These models commonly take the form of balance equations for mass, momentum, and energy associated with fluctuating motion of particle and fluid phases. While the continuum model framework is capable of predicting these flow structures, the ability to accurately resolve all relevant length scales requires very fine grid resolution (on the order of 10 particle diameters) [3]. Such fine resolution is rarely affordable when simulating gas-solid flows large devices, and traditionally, a much coarser grid resolution is generally employed.

Recently, filtered models have been developed for the accurate simulation of non-reacting gas-solid flows on coarse numerical grids without neglecting the consequences of fine scale structure [4]. The present study is concerned with the extension of previous work to reacting gas-solid flows. Coarse-grid simulations of reacting multiphase flows require filtered species and energy balances, in addition to filtered hydrodynamic equations. In the present study we construct filtered balance equations for gaseous reactants participating in catalytic reactions on the solid surface. Such filtered equations call for filtered chemical reaction rates, which should account for modification of the reaction rates brought about by mesoscale inhomogeneous structures. The goal of the present study is to understand when the effectiveness factor associated with transport limitations caused by the mesoscale structures can be appreciably smaller than unity.

To this end we have performed highly resolved simulations of gas-solid flow in the presence of a solid catalyzed, irreversible, first order, isothermal, gas phase reaction. Our simulations reveal that the effectiveness factor associated with mesoscale structures decreases systematically with increasing filter size and reaction rate constant. This implies that coarse-grid simulations of reacting multiphase flows will overestimate conversions if proper allowances are not made for the decreased effectiveness factors. Strategies to model the filter-size dependent effectiveness factors will be discussed in the presentation.

[1] Sangani A, Koch, DL. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid. Mech. 1999; 400: 229-263.

[2] Jackson R, The Dynamics of Fluidized Particles. Cambridge University Press: Cambridge, 2000.

[3] Agrawal K, Loezos, PN, Syamlal, M, Sundaresan, S. The role of meso-scale structures in rapid gas-solid flows. J. Fluid. Mech. 2001; 445: 151-185

[4] Igci, Y, Andrews, AT, Sundaresan, S, Pannala, S, O'Brien, T. Filtered two-fluid mod- els for fluidized gas-particle suspensions. AIChE J. 2008; 54: 1431-1448