A Strategy for Bioremediation of Marine Shorelines by Using Several Nutrient Release Points - Mathematical Modelling and Numerical Simulation of Oil Pollution Problems - page 51

Fig. 2.8 Optimal discharge
rates Q i

1500

) = ʳ i Q i ( ( t t ) ,

Q 1

i 2 and 3, for the

critical concentrations
c 1

= 1 ,

1250

= 19 . 0, c 2 = 0 . 8and

c 3 = 0 . 8, and slack variables

1000

ʱ = ʲ = 0 . 1and 1 1

ʱ = ʲ = 0 ( i = 2 , 3 ) i i

750

500

250

Q 3

0

0 0.5 1 1.5 2 2.5 3 3.5 Q 2 4

t

Note that Q 2 is practically zero, and hence, the discharge rate Q 1 is responsible for
the concentration reached in zone ʩ 2 .

2.8 Conclusions

The main objectives of the mathematical modelling in the environment protection
are the identification of emission rates of sources and their positions, the prediction
of concentrations of different substances (pollutants, cleanears, nutrients, etc.), the
development of themethods which help to prevent dangerous pollution levels (control
of emissions) and the search of new strategies for the remediation of polluted zones.
In this chapter, we have presented a method for the cleanup of the oil-polluted marine
environment through bioremediation. It is assumed that oil is stranded in some zones
at the shoreline and the goal is to release a nutrient into aquatic system in order to
increase the amount of indigenous microorganisms which degrade the pollutants in
such zones. Thus, the specific objective is to determine the appropriate parameters
of releasing the nutrient, namely, the discharge sites and the discharge rates, in order
to reach critical (necessary) concentrations of the nutrient in the polluted zones. All
the unknown parameters are chosen for minimizing the total mass of the released
nutrient, with the aim to minimize the impact on the environment and the cost of
remediation.
To this end, the problem is solved in two stages. In the first stage, each zone ʩ i is

considered separately from other and contains just one source. In order to reach the
critical concentration c i in each polluted zone

, a variational problem
is posed and solved with the aim to find both the optimal location of release point r i

ʩ i ( 1 ≤ i ≤ N )