A mathematical model has been formulated to describe the pyrolysis of biomass in a bubbling fluidized-bed reactor. The reactor is a vertical cylinder that contains a mixture of biomass particles and sand. Superheated steam enters the reactor through holes in the bottom and flows out freely at the top. The sand is a high heat capacity medium used for heating the biomass. The biomass particles, initially at room temperature, are introduced into the already hot reactor and become heated primarily through contact with the sand. Upon reaching a threshold temperature, the biomass particles undergo chemical reactions, the gaseous products of which are carried away by the flow of steam. The "bubbles" are regions of the fluidized bed that are mostly devoid of particles; these regions occur as a result of the interaction of the turbulent gaseous flow with the particles.

The mathematical model is one of multiphase flow. The mixture of biomass and sand is regarded as a particulate phase divided into two classes of particles that interact with a flowing gas phase. Initially, the solid biomass is regarded as consisting of three chemical species: cellulose, hemicellulose, and lignin. From each of these initial species, two new solid species are generated during pyrolysis: an "active" species and a char. The gas phase is regarded as consisting of the original carrier gas (steam), plus tar and gas that are generated through pyrolysis.

The model includes equations for the conservation of mass, momentum, enthalpy, and chemical species. The conservation equations for the particles are derived from the Boltzmann equations through ensemble averaging. The particulate-phase stresses are expressed as a tensor sum of collisional and Reynolds contributions; contributions from collisions between particles of different classes are included. The conservation equations for the gaseous phase are the Navier-Stokes equations augmented by the species and energy equations and by the perfect gas law. A distinctive feature of these equations are the source/sink terms portraying the dynamic interaction between particles and gas phase.

Stresses in the gaseous phase are expressed as the sum of Newtonian and Reynolds (turbulent) contributions. Transfer of heat between phases, and between particles in various classes (e.g., as a result of collisions between biomass and sand particles) is taken into account.

Unlike most models of turbulent flows of gases in fluidized beds, this model does not contain the Boussinesq approximation, which would imply that the stress and strain-rate tensors are aligned. Such alignment is not consistent with the recirculating flows that occur in fluidized beds. Instead, in this model, turbulence is represented by the equations of the full differential Reynolds stress model (DRSM) for two-phase flows. Some of the terms in the DRSM equations are mathematical submodels that have yet to be defined. It will be necessary to complete the modeling of Reynolds stresses for both the gaseous and the particulate phases in order to close the system of governing equations.

The model is extremely complex because of the coupled nature of the dynamic and thermodynamic evolution of the phases, and because of the turbulent features of the gaseous carrier and particulate flows. Because many of the aspects of the model are novel, it is expected that the first numerical simulations to be performed by use of the model will be those of sand/biomass dynamics in absence of heat transfer, turbulence, or chemical reactions. The results of the first simulations should enable the validation of the parts of the model that represent the dynamic interaction between phases and the particulate stress tensor.

*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.nasatech.com/tsp *under the Physical Sciences category. NPO-20708*

##### NASA Tech Briefs Magazine

This article first appeared in the June, 2001 issue of *NASA Tech Briefs* Magazine.

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