In the design of a fluidising bed system it is necessary to establish the re- quired residence time of the particles. This information is then contributed to the size and geometric specification of the bed. Residency time required in a pyrolysis bed is simply the time it takes for the pyrolysis reaction to occur in an average particle. For the purposes of the present study, the assumption is made that pyrol- ysis occurs the moment that the material is brought to the required temperature for pyrolysation. Therefore, as heat is transferred from the surface of a particle, to the particle’s centre, the particle is progressively pyrolysed.
The assumption makes calculation of pyrolysation rate a first approximation only. This is because in reality there is not a single temperature at which pyrolysis occurs, there is a range. However, due to the lack of homogeneity in the feedstock particles, this is an appropriate approximation.
The following presents a series of calculations for heat transfer and thus residency time in the pyrolysis bed:
Conduction in a particle: Radius of particle = 0.01 m Surface area = 1.3×10−3 m2 Initial temp = 12◦C Final temp = 906◦C dT = 894◦C
Heat flow from surface to centre of particle = 13.48 W
Internal energy change of particle:
Volume of particle = 4.19×10−6m3
Mass of particle = 2.09×10−3kg (assuming particle is a sphere)
U2-U1 = 2583 J
Time to transfer heat = 192 sec
Time to transfer heat = 3.19 min
Effect on Bed:
Residency time in pyrolysis bed = 38 sec
Mass of biomass in pyrolysis bed = 4.15 kg
Packed bed volume of biomass = 0.02 m3
Percentage packed bed of total bed volume = 24%
The particle radius, specified in appendix J, is based on an assumption made on the average particle dimension. Assuming a spherical particle, this value is then used to determine surface area of the particle. Initial temperature, final
temperature and thus change in temperature are values taken from the energy and mass balance calculations, as discussed previously. A value for heat flow from the surface to the centre of the particle is then derived using Fourier’s law shown in equation 13.14.
˙
Qx =−κA
dT
dx (13.14)
[Moran and Shapiro, 2000]
Where: Q˙x = Heat transfer in the x direction (W)
κ = Thermal conductivity within the particle (W/mK)
A = Surface area (m2)
dT = Change in temperature (K)
dx = Distance in x direction (radius of particle) (m)
The thermal conductivity for wood is defined in appendix J.
The volume of the particle is calculated from the radius, assuming that the particle is spherical. The mass of the particle is calculated using the volume and an assumed particle density, defined in appendix J.
The following equation is therefore used to calculate the change in internal energy in the particle:
cv =
du
dT (13.15)
[Moran and Shapiro, 2000]
Where: cv = Specific heat (J/kgK)
du = Change in specific internal energy (J/kg)
Solving forduand multiplying mass therefore provides a value for the change
Since the units for ˙Qare Watts, or Joules per second, the change in internal
energy is divided by ˙Q to provide a value for time in seconds. This is the time
that it takes for heat to be transferred from the surface of the particle to its centre, through conduction. As was mentioned earlier, it is assumed that pyrolysis occurs instantaneously as the material reaches the required temperature. We can therefore assume that as the particle is entirely pyrolysed in the time it takes for the heat to transfer to its centre. That is the time calculated above.
The energy and mass balance calculations define a value for the percentage of biomass that is gasified (or pyrolysed). By taking this percentage and multiplying it by the time it takes for a particle to be pyrolysed, a value for the residency time in the bed is calculated. The approximation that pyrolysis occurs linearly with time is a close enough approximation for the purposes of the present study. Following from this, since the mass flow rate of biomass into the bed is defined, the bulk mass of biomass in the bed can be calculated. Assuming a bulk density for the biomass, as defined in appendix J, a volume is calculated and thus, based on the volume of the bed calculated in the fluid dynamics section of this chapter, the percentage packed bed of the total volume of the bed may be calculated. That is, under non-fluidisation conditions, the percentage of the bed that contains biomass. The volume of the bed must allow for expansion of the biomass under fluidi- sation conditions. This information is therefore used to verify that the designed and specified bed size and geometry is appropriate.
A similar procedure is then followed for the combustion bed where the fol- lowing calculations are relevant:
Conduction in a particle: Radius of particle = 2.5×10−4 m Surface area = 7.9×10−7 m2 Initial temp = 600◦C Final temp = 906◦C dT = 306◦C
Heat flow from surface to centre of particle = 2.88 W
Internal energy change of particle:
Volume of particle = 6.54×10−11m3
Mass of particle = 9.82×10−8kg (assuming particle is a sphere)
U2-U1 = 2.40×10−2J
Time to transfer heat = 8.33×10−3sec (taken as instantaneous)
Effect on Bed:
Flow rate sand = 20 kg/sec
Mass of sand in combustion bed = 0.17 kg
Packed bed volume of biomass = 1.16×10−4m3
Packed bed of total bed volume = 0.143%
Here the particle of interest is the sand rather than the biomass. It is a much smaller particle with different characteristics to that of the biomass. The resultant time to transfer heat is very small and can thus be taken as instanta- neous. Therefore, there is not a minimum required residency time for the sand in the combustion bed to ensure that the sand is sufficiently heated. The size and geometry of the combustion bed is therefore dependant only on the fluid dynamics, as was discussed previously.
The percentage packed bed of the total volume of the bed is calculated and is essentially negligible. The sand will therefore be in the combustion bed for longer than required to heat it.