Sustainability: Humanity Perspective - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 771

Let

X H ¼ X 0 exp½m G ðt H t L Þ (15.16)

be the standing biomass at harvest, then

1
t H t L ln

X H
X 0

m G ¼ (15.17)

Thus, the average standing biomass for a managed forest is given by

t L
t H þ

X H X 0
lnðX H =X 0 Þ

t L
t H

X av ¼ X 0 1 (15.18)

Let the average life span of the biomass harvested and their derived products together be t PS
before degraded to CO 2 and emitted to the atmosphere. The total “biomass storage” for an
optimally managed forest is then

t L
t max þ

X max X 0
lnðX max =X 0 Þ

t L
t max

X max X 0
t max

X ST ¼ X av þ P X t PS ¼ X 0 1 þ t PS (15.19)

If the growth follows the logistic growth rate, the average standing biomass for a managed
forest is given by

t L
t H þ

X N t L

t H

X av ¼ X 0 1 (15.20)

lnðX H =X 0 Þ
ln½ðX N X 0 Þ=ðX N X H Þ

1 þ

and the total “biomass storage” for an optimally managed forest is

t L
t max þ X N

X max X 0 t L

t max

X max X 0
t max

X ST ¼ X 0 1 þ t PS (15.21)

lnðX max =X 0 Þ
ln½ðX N X 0 Þ=ðX N X max Þ

1 þ

Depending on the life span of the final product, the effect of forest biomass management
on the carbon storage can be either positive or negative as compared with an unmanaged
undisturbed forest. For longer product life span or CO 2 capture and storage after biomass
conversion, a managed forest for biomass can turn the forest into a net CO 2 sink.
The biomass storage beneath the ground (i.e. roots) is dependent on the biomass species,
location, climate, and harvesting frequencies and methods. For trees, the roots or beneath
ground biomass is usually proportional to the above ground biomass. If new shoots and/or
new trees can be restarted from harvested stump and/or roots, the reduction in the beneath
ground biomass storage is small after harvest. In some species, however, the complete unit
will die after the above ground biomass is removed, resulting in the decomposition of beneath
ground biomass (after certain time). There is thus a great loss of biomass storage after
harvesting. The softwood species commonly belong to this category. For hardwood, the
loss of beneath ground biomass is minimal after harvesting the above ground biomass if
the disturbance is not extensive enough to cause the whole system to die.
Therefore, in general as depicted by Fig. 15.13 , the carbon storage will decrease and CO 2 in
the atmosphere will increase when we start to manage forest for energy, chemicals, and