Life cycle network modeling framework and solution algorithms for systems analysis and optimization of the water-energy nexus

Abstract

The water footprint of energy systems must be considered, as future water scarcity has been identified as a major concern. This work presents a general life cycle network modeling and optimization framework for energy-based products and processes using a functional unit of liters of water consumed in the processing pathway. We analyze and optimize the water-energy nexus over the objectives of water footprint minimization, maximization of economic output per liter of water consumed (economic efficiency of water), and maximization of energy output per liter of water consumed (energy efficiency of water). A mixed integer, multiobjective nonlinear fractional programming (MINLFP) model is formulated. A mixed integer linear programing (MILP)-based branch and refine algorithm that incorporates both the parametric algorithm and nonlinear programming (NLP) subproblems is developed to boost solving efficiency. A case study in bioenergy is presented, and the water footprint is considered from biomass cultivation to biofuel production, providing a novel perspective into the consumption of water throughout the value chain. The case study, optimized successively over the three aforementioned objectives, utilizes a variety of candidate biomass feedstocks to meet primary fuel products demand (ethanol, diesel, and gasoline). A minimum water footprint of 55.1 ML/year was found, economic efficiencies of water range from -$1.31/L to $0.76/L, and energy efficiencies of water ranged from 15.32 MJ/L to 27.98 MJ/L. These results show optimization provides avenues for process improvement, as reported values for the energy efficiency of bioethanol range from 0.62 MJ/L to 3.18 MJ/L. Furthermore, the proposed solution approach was shown to be an order of magnitude more efficient than directly solving the original MINLFP problem with general purpose solvers.