M. Soledad Diaz

Determination of biogeochemical parameters in eutrophication models with simultaneous dynamic optimization approaches

This work addresses a parameter estimation problem in an ecological water quality model through a simultaneous dynamic optimization approach. The model is based on first principles and has a large number of parameters, which must be estimated based on data collected in the water body under study. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem, with a weighted least squares objective function. Main biogeochemical parameters have been obtained, which allow a close representation of the lake dynamics, as it is shown in the numerical results.

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.

Optimizing cyanobacteria metabolic network for ethanol production

This work addresses cyanobacteria Synechocystis PCC 6803 metabolic network optimization with potential gene knockouts for ethanol production as a Mixed Integer Lineal Programming problem. There is recent experimental evidence of ethanol production by fermentation of cyanobacteria, while sequestrating carbon dioxide as carbon source in photoautotrophic growth conditions. These issues make ethanol production by algae a promising alternative. The optimization of metabolic pathways gives useful insights on cellular metabolism for improving process yield by engineering cyanobacteria.

Developing A Lake Eutrophication Model And Determining Biogeochemical Parameters: A Large Scale Parameter Estimation Problem

This work addresses the dynamic parameter estimation problem for an eutrophication model, which is formulated within a simultaneous approach. Ecological processes are modeled through a set of complex nonlinear differential algebraic equations, with rate coefficients that must be estimated. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem. Main biochemical and chemical parameters have been obtained, which allow a close representation of the lake dynamics.

Water resources management with dynamic optimization strategies and integrated models of lakes and artificial wetlands

Abstract In this work, we propose an integrated mechanistic model for a freshwater eutrophic reservoir and an artificial wetland and within a dynamic optimization framework. A partial differential equation system results from dynamic mass balances for the main phytoplankton groups; two zooplankton groups and two size classes of zooplanktivorous fish in the reservoir, as well as dissolved oxygen and main nutrients in both the reservoir and wetland. Algebraic equations stand for forcing functions profiles, such as temperature, solar radiation, river inflows and concentrations, etc. The model is formulated as an optimal control problem within a control vector parameterization approach in gPROMS. Optimization variables are the fraction of nutrient rich water stream that is derived through the wetland and fish removal rates from the reservoir. The objective function is the minimization of a weighted sum of integrals along the entire time horizon: the quadratic difference between phytoplankton concentration and a desired value below eutrophication limits and the quadratic difference between phosphate concentration in the wetland outflows and a desired value. Numerical results provide optimal profiles for restoration actions and their effects on the studied ecosystem.

Biological Wastewater Treatment: Dynamic Global Sensitivity Analysis and Parameter Estimation in a System of Waste Stabilization Ponds

Abstract In this work, we propose a dynamic mathematical model describing main biochemical processes that take place within wastewater stabilization ponds. Mass balances for main microorganisms, nutrients, dissolved oxygen and biochemical demand of oxygen have been formulated. The wastewater biological treatment system under study is composed of two stages of oxygenated ponds in series. The first stage is aerobic oxygenated and the last one is facultative oxygenated. Global sensitivity analysis has been performed prior to the formulation of a parameter estimation problem, subject to the differential algebraic system describing the biological wastewater treatment system. Experimental data from a fruit juice plant have been collected throughout one year. Numerical results provide a deep insight on the complex relations among microorganisms, nutrients and organic matter concentration in wastewater treatment ponds.

Addressing Long-Term Biorestoration in Eutrophic Lakes as an Optimal Control Problem, Under Different Scenarios

Abstract In this work we propose an ecological water quality model for a reservoir, based on first principles, to study the response of main phytoplankton groups (algae) to temperature rise due to global warming and different nutrient (phosphate) loading scenarios in the middle and long term. An optimal control problem is formulated to determine optimal combination of restoration strategies, including nutrient loading reduction through inflows remediation within a wetland and in-lake biorestoration techniques. The dynamic optimization problem is formulated within a simultaneous approach.

Dynamic flux balance analysis in cyanobacteria for ethanol production with simultaneous optimization approaches

In this work we address dynamic optimization of ethanol production by Dynamic Flux Balance Analysis in an engineered cyanobacterium with autotrophic growth (i.e., using CO2 as substrate). The photobioreactor optimization model is integrated to the metabolic network one by replacing the inner problem by its first order optimality conditions. Complementarity constraints that arise associated to the optimality conditions are efficiently handled with a penalty function formulation. Numerical results suggest the possibility to activate the ethanol production pathway after 20 h in the batch run to enhance ethanol production.

Energy Consumption Minimization in Bioethanol Dehydration with Supercritical Fluids

Abstract In this work, we propose a rigorous model for bioethanol dehydration process with supercritical propane to minimize energy consumption. Thermodynamic predictions are performed with an upgraded Group Contribution with Association Equation of State, GCA-EOS. As compared to the basic scheme for dehydration with supercritical fluids, vapor recompression, as well as feed preconcentration could be highly energy efficient. We further consider alternative integration schemes between process streams, associated to different nonlinear programming problems. Special attention has been devoted to a new scheme that integrates the vapor recompression scheme to the preconcentration step, which provides additional reduction in total energy consumption. We demonstrate that bioethanol dehydration can be a sustainable alternative that is energetically competitive with molecular sieves in the production of this biofuel.

Middle term optimal control problem in eutrophic lakes through advanced mathematical programming approaches

Abstract In this work, we address lake biorestoration through the formulation of first principles models for water quality and advanced mathematical programming techniques. Dynamic mass balances have been formulated on main phytoplankton groups and nutrients, as well as other components available in lakes and reservoirs. Main parameters in the model have been estimated in previous work Estrada et al., 2008. The combined reductions in nutrient loading and inlake biorestoration strategies to control algae growth and reduce eutrophication have been formulated as an optimal control problem for a middle term time horizon (three years). The problem has been formulated within a simultaneous optimization framework and solving the large scale nonlinear program with an Interior Point method (Biegler et al., 2002). Numerical results give deep insight on the quantitative application of restoration strategies.