The kinetic model of the fluidized bed gasifier consists of reactor hydrodynamics, which define the transport phenomena of the gasification medium through the system and solid mixing behavior. There are several versions of fluidized bed hydrodynamic models [91-93]:

1. The two-phase model in a bubbling fluidized bed, which considers bubble and emulsion phases.

2. The three-phase model in a bubbling fluidized bed consists of bubbling, cloud, and emulsion phases.

3. The core-annulus model for circulating fluidized beds where the core is the upward flow of gas and solid in the center and the annulus is the downward flow of gas and solid close to the wall.

4. The compartment models in which the fluidized bed is divided into slices or horizontal sections.

These types of fluidized bed models avoid the complexity of gas-solid dynamics but still keep the fluid-dynamic effects by considering different regions and phases throughout the reactor, which are described by semi-empirical correlations [91, 92, 93, 94 and 95].

Gas flow through the bed can be modeled as follows:

1. Bubble phase as plug flow and emulsion phase as ideally mixed gas.

2. Both phases as ideally mixed gases.

3. Both phases as plug flow with mass transfer between two phases.

4. Upward gas in the core as plug flow and solid backflow in the annulus [95].

There are three ways to describe conversion models for single char particles:

1. Shrinking core model;

2. Shrinking particle model; and

3. Uniform conversion model [96, 97].

Shrinking core and shrinking particle models are both surface reaction models where the fast reaction takes place as soon as the reactant gas reaches the external surface of the particle. In the shrinking particle model, however, the ash peels off instan­taneously and the particle shrinks during reaction. In the shrinking core model, the particle size stays constant since the ash remains attached to the particle and becomes an additional heat and mass resistance. In the uniform conversion model the reaction takes place all over the char particle uniformly.

Different types of fluidized bed modeling have been applied for coal and biomass gasifiers [90, 98-102]. The following section presents essential equations for a one­dimensional steady-state model of a bubbling fluidized bed gasifier. The fluidized bed is divided into two regions, a dense zone and a free board. The gas flow in the dense part consists of bubble and emulsion phases, which deals with drying, pyrolysis, and gasification of biomass. The freeboard is free of solid particles and only gas phase reactions continue from the bed. The mass balance for the emulsion and bubble phases can be expressed as (10.1) and (10.2):

Emulsion phase:

— (1 — 8b)smfdz (CieUe) — Kbe(Cib — Cie) + (1 — Sb)(1 — Smf )’Lg-sRi + (10 1) (1 — Sb)Smf^g-gRi = 0 (.)

Bubble phase:

d

Sb (Cibub) + Kbe(Cib

d z

(1 — Yb)Sb^g-gRi = 0

The boundary conditions for the above equations are defined in the feeding zone, which is the gas composition, predicted using the pyrolysis kinetics.

For solid hydrodynamics, a concurrent back mixing model is considered [95]. Based on the CCBM, (10.3) could be written for the char particles.

Char balance in the ascending phase:

Char balance in the descending phase:

-Fds,0 ^ + Kw(Cas, c — Cds, c)Afas + A(1 — fas)^g-sRi = 0 dz

The bubble and emulsion equations, which give the gas concentration profile in the bed, and the char balance equation, which provides the char conversion profile in the bed, will be solved simultaneously for all gas species to obtain produced gas compositions and yields in the bed.

Based on this assumption there won’t be any solid in the freeboard and it will be considered as a plug flow reactor. The mass balance for each gas species in this region can be written as (10.5):