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.
Highlights
Sustainability is a key area of interest in both academia and industry
Where fcfj is the fixed cost factor for technology j, cchf is the capital charge factor required to annualize the capital cost for appropriate calculation of the net present value (NPV), CCj is the capital cost of technology j, Xj is the capacity of technology j, refcj is the reference capacity for technology j, refocj is the reference operating cost for technology j, Pi is the quantity purchased of material/compound i, fpi is the feedstock price of compound i, vtci is the variable transportation cost of feedstock i, ftci is the fixed transportation cost of feedstock i, ec is the cost of electricity, uej is the unit energy consumption of technology j, Si is the quantity sold of final product i, and spi is the selling price of final product i
Three optimal processing pathways were identified from the extreme points of the Pareto-optimal surface
Summary
Sustainability is a key area of interest in both academia and industry. This state of affairs has not always been the case, especially in the industrial sector, and its recent emergence has guided thought and galvanized efforts to understand, quantify, and optimize sustainability indicators in an industrial context [1,2]. While hydroelectric dams have clear connections to the water-energy nexus and have been the subject of key studies to determine their water footprints [14], most water consumption in the energy sector is used for cooling demands of power plants. Ahmetović et al optimized energy and water consumption of a corn grain to ethanol facility [19] These studies found that recycling of water streams and minimizing energy consumption were critical to reducing the water footprint of bioconversion technologies that utilize corn or corn stover feedstocks. This work aims to provide a new product and process network-focused water-energy nexus optimization strategy This task is accomplished first by building a comprehensive process and product network model that can account for both the economics and water footprints of each technology and throughout the processing pathways. The construction of the network model and its formulation is described followed by a discussion of the results
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