2 Dynamic Modelling of Reactive Fluidized Bed Systems Using …
49
operation, this carbon slip is kept to a minimum. The combustion of char in the air
reactor is described with reaction (7):
O 2 + C char
k 7
→ CO 2
(R7)
For the reaction rate constant k 7 a value that high is chosen so that all char,
which has entered the air reactor via carbon slip, is converted. With reaction (7) a
conventional combustion with air in the fuel reactor can be simulated as well.
The reaction of the solid (Cu, CuO or C char ) j with the respective gas component
l is described by the reaction rate r s,j,l :
r s, j,l = −c v, j · ρ m, j ·
d X s, j,l
dt
(15)
Here, c v,j is the volumetric concentration of a solid reactant j in a reactor volume
element. It is taken by multiplying the total solids concentrations c v and the fraction
of active reactant on and inside the particles. This is relevant since most oxygen
carriers consist only partly of reactive material. Moreover, ρ m,j is the molar density
of the solids reactant j and dX s,j,l /dt is the solids conversion rate of reactant j with
respect to the fuel gas l. The solids conversion rate is usually determined experimentally. From the obtained data, Arrhenius-type reaction rates for each reaction
can be obtained. Since metallic OCs differ from the structure and reaction behavior,
several heterogenous reaction models were proposed for the solid conversion [9].
For the mentioned gas-solid reactions a shrinking-core model with active, spherical
grains is used. Abad et al. [24] found out that this model is well suited to describe the
reaction behavior of a CuO/Al 2 O 3 oxygen carrier. A general form of the Arrhenius
type reaction kinetics is described as follows.
d X s, j,l
dt
= k
C
n
l , T
· f (X )
(16)
Here, the reaction rate constant k is a function of the molar concentration of the
reacting gas l, with the reaction order n and the temperature T. If the gas concentration
C l is constant over the course of the reaction in a discretized volume element A r · dh,
the reaction rate constant can be described with the Arrhenius equation:
k = k 0 · e
−Ea
RT
(17)
In the Arrhenius equation, k 0 is a pre-exponential factor and E a is the activation
energy for the reaction, both are determined experimentally. The factor R is the
universal gas constant. The rate of conversion also changes with the conversion X
itself. For this simulation, an algebraic expression for spherical grains and a reaction
limitation is used. This model assumes active round grains which shrink over time.
With a declining surface area over the course of the reaction, the reaction rate declines
as well [9]:
49
operation, this carbon slip is kept to a minimum. The combustion of char in the air
reactor is described with reaction (7):
O 2 + C char
k 7
→ CO 2
(R7)
For the reaction rate constant k 7 a value that high is chosen so that all char,
which has entered the air reactor via carbon slip, is converted. With reaction (7) a
conventional combustion with air in the fuel reactor can be simulated as well.
The reaction of the solid (Cu, CuO or C char ) j with the respective gas component
l is described by the reaction rate r s,j,l :
r s, j,l = −c v, j · ρ m, j ·
d X s, j,l
dt
(15)
Here, c v,j is the volumetric concentration of a solid reactant j in a reactor volume
element. It is taken by multiplying the total solids concentrations c v and the fraction
of active reactant on and inside the particles. This is relevant since most oxygen
carriers consist only partly of reactive material. Moreover, ρ m,j is the molar density
of the solids reactant j and dX s,j,l /dt is the solids conversion rate of reactant j with
respect to the fuel gas l. The solids conversion rate is usually determined experimentally. From the obtained data, Arrhenius-type reaction rates for each reaction
can be obtained. Since metallic OCs differ from the structure and reaction behavior,
several heterogenous reaction models were proposed for the solid conversion [9].
For the mentioned gas-solid reactions a shrinking-core model with active, spherical
grains is used. Abad et al. [24] found out that this model is well suited to describe the
reaction behavior of a CuO/Al 2 O 3 oxygen carrier. A general form of the Arrhenius
type reaction kinetics is described as follows.
d X s, j,l
dt
= k
C
n
l , T
· f (X )
(16)
Here, the reaction rate constant k is a function of the molar concentration of the
reacting gas l, with the reaction order n and the temperature T. If the gas concentration
C l is constant over the course of the reaction in a discretized volume element A r · dh,
the reaction rate constant can be described with the Arrhenius equation:
k = k 0 · e
−Ea
RT
(17)
In the Arrhenius equation, k 0 is a pre-exponential factor and E a is the activation
energy for the reaction, both are determined experimentally. The factor R is the
universal gas constant. The rate of conversion also changes with the conversion X
itself. For this simulation, an algebraic expression for spherical grains and a reaction
limitation is used. This model assumes active round grains which shrink over time.
With a declining surface area over the course of the reaction, the reaction rate declines
as well [9]: