IADO   05364
INSTITUTO ARGENTINO DE OCEANOGRAFIA
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Dynamic Optimization Approaches for the Determination of Bottom-up and Top-down Control In Lakes and Reservoirs
Autor/es:
ESTRADA, V.; PARODI, E.R; DÍAZ, M.S.
Lugar:
Philadelphia, USA
Reunión:
Congreso; AIChE Annual Meeting; 2008
Institución organizadora:
AIChE
Resumen:
Biogeochemical processes that take place in water bodies can be represented through a
set of complex nonlinear partial differential algebraic equations resulting from dynamic
mass balances for phytoplankton and nutrients. Once calibrated, the model can be
integrated into a dynamic optimization framework for the determination of optimal control
policies to prevent eutrophication of the water body.
In this work, we develop a dynamic optimization model for a water body to determine
optimal concentrations of zooplankton required to decrease phytoplankton concentration
in the lake, associated to fish removal, as well as optimal limiting nutrient inflow profiles to
the lake, with the associated flowrate of the inflows that has to be derived to a nearby
wetland for remediation.
The model is based on horizontally averaged concentrations and its main parameters
have been previously estimated (Estrada et al., 2007) based on collected data sets
corresponding to an entire year (Parodi et al., 2004). Dynamic mass balances in
phytoplankton (in the form of diatoms, green algae and cyanobacteria), dissolved oxygen
and nutrients, which include nitrate, ammonium, organic nitrogen, phosphate and organic
phosphorus, have been formulated. Biogeochemical processes include growth, respiration
and death processes for phytoplankton, as well as mineralization, nitrification and uptake
and release of nutrients. Algebraic equations represent profiles for temperature, solar
radiation and river inflows, in addition to the calculation of most factors that affect rate
equations. The resulting partial differential algebraic equations (PDE) model is
transformed into an ordinary differential equations system by spatially discretizing the
PDE into sets of ordinary differential-algebraic equations (DAE). The objective function is
the minimization of the offset between phytoplankton concentration and the desired
concentration in the water body along the first year, subject to the previously described
DAE system and upper bounds on phytoplankton and nutrients concentrations, to remain
below eutrophication levels.
The dynamic optimization problem is solved through a simultaneous approach by
transforming it into a large-scale nonlinear programming (NLP) problem discretizing state
and control variables applying collocation over finite elements (Raghunathan et al., 2004).
The discretized NLP model has more than 17,000 variables and it has been solved with a
reduced successive quadratic programming algorithm (Kameswaran and Biegler, 2006).
The study has been performed on Paso de las Piedras Lake, which supplies drinking
water for more than 400,000 inhabitants in Bahia Blanca (Argentina).