mass transfer to diffusion. There is exchange at the tray surface between the bed
and the headspace air. Within tray bioreactors several of factors appear to be
potentially able to limit bioreactor performance – heat transfer, oxygen transfer, and water transfer.
Heat transfer has been identified as the major problem in tray bioreactors, by
both experimental and modeling studies. Temperatures of the order of 20 °C
above the external incubation temperature have been noted for bed depths as
little as 8 cm [134]. This occurs because heat removal is essentially limited to
conduction through the bed. Note that natural convection within the bed might
also occur in response to the temperature profiles, and may affect not only heat
transfer but also CO 2 , oxygen, and water vapor transfer [100], but natural
convection has received no experimental or modeling attention. These high
temperatures cause corresponding low product yields. For example, Ghildyal et
al. [134] noted yields only 20% of those obtained in a bed with a 40-mm initial
bed depth when a bed depth of 80 mm or more was used.
The modeling study of Rajagopalan and Modak [87] confirms that bed
depths must be limited to the order of only a few centimeters, at least with
relatively fast growing organisms. The most easily manipulated design and
operating variables are the bed depth and the temperature of the surrounding
air. Note that decreasing the humidity of the surrounding air to promote
evaporation is not a feasible strategy because it will quickly lead to drying of the
exposed surfaces of the bed, and it is likely that these regions will dry to such
low values that growth and product formation will be limited. Best growth of
Aspergillus niger, which has an optimum temperature of 35 °C, was predicted
with relatively high surrounding air temperatures and relatively thin substrate
slabs. For example, temperatures of 35–40 °C and bed heights of 0.8–1.6 cm
gave maximal biomass yields at 100 h. At a bed height of 3.2 cm optimal growth
occurred with surrounding air temperatures of 30–35 °C. With a bed height of
6.4 cm the yield at 100 h was at best 55% of the maximum possible yield and
the optimum surrounding air temperature was 30 °C. At lower temperatures
some bed regions overcooled. At higher external temperatures too much of the
bed overheated. The model suggested that temperature gradients are more
important than oxygen gradients within trays, although oxygen limitations
were predicted at the bottom of an unperforated tray.
Szewczyk [135] modeled the effect of convective and evaporative heat
removal at the bed surface on tray performance. The mass transfer coefficient
for evaporation was assumed to be related to the surface-to-surroundings
convective heat transfer coefficient by the psychrometric ratio. The values of
these coefficients can potentially be increased by increasing the flowrate of air
past the tray surfaces, although the relationship was not explored. As the value
of the convective heat transfer coefficient increases, the predicted surface temperature initially falls sharply – from values as high as 45–60 °C with a coefficient of 2 W m
–2 K –1 to values around 35 °C with a coefficient of 10 W m –2 K –1 .
Further increases up to 50 W m –2 K –1 are relatively ineffective in reducing the
surface temperature further [135].
The importance of oxygen diffusion as a limiting factor depends on the
values of the thermal conductivity of the bed and the effective oxygen difBiochemical Engineering Aspects of Solid State Bioprocessing
105
and the headspace air. Within tray bioreactors several of factors appear to be
potentially able to limit bioreactor performance – heat transfer, oxygen transfer, and water transfer.
Heat transfer has been identified as the major problem in tray bioreactors, by
both experimental and modeling studies. Temperatures of the order of 20 °C
above the external incubation temperature have been noted for bed depths as
little as 8 cm [134]. This occurs because heat removal is essentially limited to
conduction through the bed. Note that natural convection within the bed might
also occur in response to the temperature profiles, and may affect not only heat
transfer but also CO 2 , oxygen, and water vapor transfer [100], but natural
convection has received no experimental or modeling attention. These high
temperatures cause corresponding low product yields. For example, Ghildyal et
al. [134] noted yields only 20% of those obtained in a bed with a 40-mm initial
bed depth when a bed depth of 80 mm or more was used.
The modeling study of Rajagopalan and Modak [87] confirms that bed
depths must be limited to the order of only a few centimeters, at least with
relatively fast growing organisms. The most easily manipulated design and
operating variables are the bed depth and the temperature of the surrounding
air. Note that decreasing the humidity of the surrounding air to promote
evaporation is not a feasible strategy because it will quickly lead to drying of the
exposed surfaces of the bed, and it is likely that these regions will dry to such
low values that growth and product formation will be limited. Best growth of
Aspergillus niger, which has an optimum temperature of 35 °C, was predicted
with relatively high surrounding air temperatures and relatively thin substrate
slabs. For example, temperatures of 35–40 °C and bed heights of 0.8–1.6 cm
gave maximal biomass yields at 100 h. At a bed height of 3.2 cm optimal growth
occurred with surrounding air temperatures of 30–35 °C. With a bed height of
6.4 cm the yield at 100 h was at best 55% of the maximum possible yield and
the optimum surrounding air temperature was 30 °C. At lower temperatures
some bed regions overcooled. At higher external temperatures too much of the
bed overheated. The model suggested that temperature gradients are more
important than oxygen gradients within trays, although oxygen limitations
were predicted at the bottom of an unperforated tray.
Szewczyk [135] modeled the effect of convective and evaporative heat
removal at the bed surface on tray performance. The mass transfer coefficient
for evaporation was assumed to be related to the surface-to-surroundings
convective heat transfer coefficient by the psychrometric ratio. The values of
these coefficients can potentially be increased by increasing the flowrate of air
past the tray surfaces, although the relationship was not explored. As the value
of the convective heat transfer coefficient increases, the predicted surface temperature initially falls sharply – from values as high as 45–60 °C with a coefficient of 2 W m
–2 K –1 to values around 35 °C with a coefficient of 10 W m –2 K –1 .
Further increases up to 50 W m –2 K –1 are relatively ineffective in reducing the
surface temperature further [135].
The importance of oxygen diffusion as a limiting factor depends on the
values of the thermal conductivity of the bed and the effective oxygen difBiochemical Engineering Aspects of Solid State Bioprocessing
105