Sustainability: Humanity Perspective - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 769

Stationary phase

20

Pinch line

Pinch point

15

P

10

Maximum Growth

5

I

0

Lag phase

0

10 20 30 40 50 60 70 80 90 100

Time, year

FIGURE E15-5.1 Finding the optimum biomass production from a growth curve.

To solve the problem graphically, we first plot the growth curve (X, t). Locate the starting
(or initial) point of growth (after harvest and on new batch of growth) I, in this case is t ¼ 0

and X 0 Mg-C. Starting from point I, plot a straight line that only touch the growth curve

once at a time after the growth started (t

¼

0). We call this line the Pinch Line. The pinch point
P is the intercept of the pinch line and the growth curve.
We can read from Fig. E15-5.1 that the pinch point P is at 44.2 years, when the CO 2 seques-
trated is 12.88 Mg-C. That is, the optimum point of harvest is at a 7.12 Mg-C deficiency as
compared with the initial harvest (of 20 Mg e C). The biomass production rate is given by

>

X max X 0
t max

¼ 12:88 0
44:2

P X max ¼ Mg-C = year ¼ 0:2914 Mg-C = year

Therefore, the optimum biomass yield on the given lot is to harvest the biomass at
a 44.2-year cycle, which produces 12.88 Mg-C biomass each cycle, and the biomass produc-
tion rate is 0.2914 Mg-C/year.
Example 15-5 shows that the optimum harvesting time is not near the time when the
maximum standing biomass or saturation biomass level is reached. In this case, the biomass
yield at optimum harvesting time is only about 65% of the saturation biomass or the biomass
carrying capacity. The optimum utilization of woody biomass will result in a reduced level of
standing biomass on the ground.
Fig. 15.13 illustrates the effect of biomass utilization as compared with fossil utilization. If
there is no human disturbance, the level of CO 2 in the atmosphere and the standing biomass
are stable or at a sustainable value as shown on the left portion of the Fig. 15.13 . When fossil is
used for energy by mankind, the atmospheric CO 2 increases monotonously with time (as
shown also in Fig. 15.9 ). When biomass is used for energy, there is a higher rate of increase
of CO 2 in the atmosphere initially (than using fossil for energy instead). There is also
a decrease in the standing biomass at short times. However, when a longer time is elapsed,
the atmospheric CO 2 is stabilized to a constant (or sustainable) level, which is higher than if