A mathematical model has been developed for describing the thermofluid dynamics of a dense, chemically reacting mixture of solid particles and gases. As used here, "dense" signifies having a large volume fraction of particles, as for example in a bubbling fluidized bed. The model is intended especially for application to fluidized beds that contain mixtures of carrier gases, biomass undergoing pyrolysis, and sand. So far, the design of fluidized beds and other gas/solid industrial processing equipment has been based on empirical correlations derived from laboratory- and pilot-scale units. The present mathematical model is a product of continuing efforts to develop a computational capability for optimizing the designs of fluidized beds and related equipment on the basis of first principles. Such a capability could eliminate the need for expensive, time-consuming predesign testing.

The present model includes components in common with models described in several previous NASA Tech Briefs articles, including, most notably, "Model of Pyrolysis of Biomass in a Fluidized-Bed Reactor" (NPO-20708), NASA Tech Briefs, Vol. 25, No. 6 (June 2001), page 59; "Multiphase-Flow Model of Fluidized-Bed Pyrolysis of Biomass" (NPO-20789), NASA Tech Briefs, Vol. 26, No. 2 (February 2002), page 56; and "Model of a Fluidized Bed Containing a Mixture of Particles" (NPO-20937), NASA Tech Briefs, Vol. 26, No. 4 (April 2002), page 56. The model distinguishes among multiple particle classes on the basis of physical properties (e.g., diameter or density) and/or through thermochemical properties (e.g., chemical reactivity or nonreactivity). The formulation of the model follows a multifluid approach in which macroscopic equations for the solid phase are derived from a kinetic-like theory considering inelastic-rigid-sphere submodels in accounting for collisional transfer in high-density regions. The gas phase equations are derived using ensemble averaging.

The Tar Yield of a Fluidized Bed as a function of time was computed, for various temperatures of fluidizing gas, by use of the model described in the text.
Separate transport equations are constructed for each of the particle classes, providing for the separate description of the acceleration of the particles in each class, of interactions between particles in different size classes, and of the equilibration processes in which momentum and energy are exchanged among the particle classes and the carrier gas. The kinetic-like theory is based on a Gaussian approximation of the velocity distribution, assuming that spatial gradients of mean variables are small and particles are nearly elastic. Each class of particles is characterized by its own granular temperature, which represents the mean kinetic energy associated with fluctuations in the velocities of the particles. The stress tensor is augmented by a frictional-transfer submodel of stress versus strain: The separate equations of the dynamics of the various particle classes are coupled through source terms that describe such nonequilibrium processes as transfer of mass, momentum, and energy, both between particles and between gas and particles.

In one of several test cases, the model was applied to the pyrolysis of biomass particles in a laboratory fluidized bed reactor and used to compute yields of reaction products (especially tar). The results indicate that at fixed initial particle size, the temperature of the fluidizing gas is the foremost parameter that influences the tar yield and can be chosen to maximize the tar yield (see figure). The temperature of the biomass feed, the nature of the feedstock, and the fluidization velocity were all found to exert only minor effects on the tar yield.

This work was done by Josette Bellan and Danny Lathouwers of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Physical Sciences category. NPO-30163.

This Brief includes a Technical Support Package (TSP).
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Model of Fluidized Bed Containing Reacting Solids and Gases

(reference NPO-30163) is currently available for download from the TSP library.

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