Developing a lake eutrophication model and determining biogeochemical parameters: a large scale parameter estimation problem

VANINA ESTRADA; ELISA PARODI; MARIA SOLEDAD DIAZ

Computer Aided Chemical Engineering

Elsevier

Año: 2008 vol. 25 p. 1113 - 1118

1570-7946

Eutrophication models represent biogeochemical processes that take place in water bodies through a set of complex nonlinear partial differential algebraic equations, with specific parameters that require calibration to suit site-specific conditions. The parameter estimation problem in eutrophication models has been recently addressed by Zhang et al. (2004), they have proposed a sequential procedure to determine phytoplankton and zooplankton parameters using exergy as the objective function and calibrating both physical and chemical parameters by trial and error. Shen (2006) proposed a least squares objective function and an ad-hoc procedure to solve the dynamic parameter estimation problem. In this work, we develop an eutrophication model for Lake Paso de las Piedras, an artificial lake which supplies drinking water for more than 400,000 inhabitants in Bahia Blanca (Argentina). The model is based on horizontally averaged concentrations (Estrada et al., 2007). 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. Not only is the gradient concentration along the water column taken into account, but throughout the sediment. 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). We have formulated a parameter estimation problem with a weighed least-squares objective function subject to the previously described DAE system. Previously collected data sets corresponding to an entire year, with a frequency of twice a week have been used (Parodi et al., 2004). The parameter 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 15,000 variables and it has been solved with a reduced successive quadratic programming algorithm (Biegler et al., 2002). We have determined kinetic and biological parameters and their values are in agreement with those from the literature. We are currently collecting data sets from the lake for validation of numerical results. References Biegler L.T., Cervantes A, Waechter A., 2002; Advances in Simultaneous Strategies for Dynamic Process Optimization. Chem. Eng. Sci. 57: 575-593. Estrada V., E. Parodi, S. Diaz, Hydrodynamic Studies and Dynamic Parameter Estimation for Eutrophication Models, ECCE-6, Denmark, September 2007. Parodi, E.., Estrada, V., Trobbiani, N., Argañaraz Bonini, G., 2004, Análisis del estado trófico del Embalse Paso de las Piedras (Buenos Aires, Argentina). Ecología en tiempos de Cambio. 178. Raghunathan A., S. Diaz, L.T. Biegler, 2004, An MPEC Formulation for Dynamic Optimization of Distillation Operations, Comp. & Chem. Eng., 28, 2037. Shen, J., 2006, Optimal estimation of parameters for aestuarine eutrophication model, Ecol. Model. 191, 521–537.