(203e) Bioremediation Costs Estimation in Lakes and Reservoirs through Dynamic Optimization Based On Hybrid Eutrophication Models

Long-term studies on Europe and North American eutrophic lakes showed that even when reduction of external nutrient loading has had successful results, eutrophication symptoms, like harmful algal blooms (HAB) development, are retained even for decades after restoration (Jeppensen et al., 2005, Søndergaard et al 2007). Biological and chemical process can delay the recovery of water quality (Gulati and van Donk, 2002; Søndergaard, Jensen and Jeppesen, 2003) mainly due internal phosphorus recycling (the limiting nutrient in freshwater ecosystems) from sediments. In order to accelerate lake recovery, several in-lake restoration methods have been applied (e.g. sediment removal by dredging, hypolimnetic oxygenation, and alum treatment). Bio-manipulation has been one of the most extensive strategies used to prevent algal blooms in European lakes and reservoirs. This method is based on the trophic chain theory and consists of keeping a high grazing pressure on phytoplankton populations performing zooplanktivorous fish removal (Shapiro & Wright, 1984; Jeppesen et al., 1990). Many restoration projects have been reported in the literature in the past decades, some of which were successful (Hansson et al., 1998; Søndergaard et al., 2000; Gulati and Van Donk 2002), whereas others had not obtained the expected results (Hansson et al., 1998).

In this work, we estimate biorestoration costs through simultaneous dynamic optimization based on a hybrid ecological water quality that determines bio-manipulation policies in a currently eutrophic water body, which is the drinking water source for more than 450,000 inhabitants in Argentina. The model considers four biogeochemical cycles, i. e., carbon, nitrogen, phosphorus and dissolved oxygen, three functional groups of phytoplankton (cyanobacteria, diatoms and chlorophyta) and three of zooplankton (cladocerans, copepods and rotifers). The model takes into account different food quality for each phytoplankton group. Previous work (Estrada et al., 2008) showed that in-lake restoration techniques, as well as the reduction of external nutrient load, are needed in order to avoid the appearance of recurrent algal blooms that are occurring for several years.

To solve the model, the partial differential algebraic equations model is transformed into an ordinary differential equations system by spatial discretization into horizontal layers. The objective function is to minimize the offset between total phytoplankton concentration and a desired value below eutrophication limit, and the optimization variable is the zooplanktivorous fish biomass to be removed. The best candidate for bio-manipulation at Paso de las Piedras Reservoir is silverside (Odontesthes bonaeriensis).

The optimal control problem is solved with a simultaneous approach (Raghunathan et al., 2004) applying an Interior Point method with reduced successive quadratic programming techniques, within program IPOPT (Kameswaran and Biegler, 2006).

References

Estrada V., Parodi, M.S. Diaz (2008). A simultaneous dynamic optimization approach for addressing the control problem of algae growth in water reservoirs through biogeochemical models, submitted.

Gulati, R.D. and Van Donk, E. (2002). Lakes in the Netherlands, their origin, eutrophication and restoration: stateof-the-art review. Hydrobiologia, 478, 73?106.

Hansson, L.-A., Annadotter, H., Bergman, E., Hamrin S. F., Jeppesen, E., Kairesalo, T., Luokkanen, E., Nilsson, Søndergaard, M. and Strand, J. (1998) Biomanipulation as an application of food-chain theory: constraints, síntesis, and recomendations for temperate lakes. Ecosystems 1, 558-574.

Kameswaran, S., L.T. Biegler (2006), Simultaneous dynamic optimization strategies: Recent advances and challenges, Comp. Chem. Eng., 30, 1560.

Raghunathan A., S. Diaz, L.T. Biegler, 2004, An MPEC Formulation for Dynamic Optimization of Distillation Operations, Comp. Chem.Eng., 28, 2037.