Thermodynamics II

🧊Thermodynamics II Unit 15 – Exergy and Thermoeconomic Analysis

Exergy and thermoeconomic analysis are powerful tools for evaluating and optimizing energy systems. These methods go beyond traditional energy analysis, considering the quality of energy and its potential for useful work. By combining thermodynamic principles with economic factors, engineers can make more informed decisions about system design and operation. This unit covers key concepts like exergy, anergy, and dead state, as well as practical applications in power plants, refrigeration systems, and chemical processes. Students will learn how to perform exergy balances, calculate exergy destruction, and use thermoeconomic principles to optimize system performance and minimize costs.

Key Concepts and Definitions

  • Exergy represents the maximum useful work that can be obtained from a system as it reaches equilibrium with its surroundings
  • Anergy is the portion of energy that cannot be converted into useful work due to irreversibilities and losses
  • Dead state refers to the reference environment conditions (usually ambient temperature and pressure) at which a system has zero exergy
  • Exergy destruction quantifies the irreversible losses in a system caused by friction, heat transfer, and other irreversible processes
  • Exergy efficiency measures the ratio of useful exergy output to the total exergy input in a system or process
    • Provides a more accurate assessment of the thermodynamic performance compared to energy efficiency
  • Thermoeconomics combines thermodynamic analysis with economic principles to optimize the design and operation of energy systems
  • Exergy costing assigns monetary values to exergy streams and quantifies the cost of exergy destruction in a system

Exergy: Fundamentals and Applications

  • Exergy is a state function that depends on the system's properties and the reference environment conditions
  • Exergy balance equation: Ex˙inEx˙outEx˙dest=ΔEx˙system\dot{Ex}_{in} - \dot{Ex}_{out} - \dot{Ex}_{dest} = \Delta \dot{Ex}_{system}
    • Ex˙in\dot{Ex}_{in} and Ex˙out\dot{Ex}_{out} represent the exergy flows into and out of the system
    • Ex˙dest\dot{Ex}_{dest} is the exergy destruction rate due to irreversibilities
    • ΔEx˙system\Delta \dot{Ex}_{system} is the change in exergy of the system
  • Exergy of a closed system consists of physical exergy (due to temperature and pressure differences) and chemical exergy (due to composition differences)
  • Exergy of an open system includes physical, chemical, kinetic, and potential exergy components
  • Exergy analysis helps identify the location, magnitude, and sources of thermodynamic inefficiencies in a system
  • Applications of exergy analysis include power plants, refrigeration systems, heat exchangers, and chemical processes
    • Allows for the optimization of system design and operation to minimize exergy destruction and improve efficiency

Exergy Analysis of Thermodynamic Systems

  • Exergy analysis involves performing an exergy balance on each component of a thermodynamic system
  • Exergy destruction in a component is calculated as the difference between the exergy input and output
  • Exergy efficiency of a component is defined as the ratio of exergy output to exergy input
  • Exergy analysis of a power plant helps identify the components with the highest exergy destruction (usually the boiler and turbine)
    • Provides insights for improving the plant's overall efficiency
  • Exergy analysis of a refrigeration system reveals the exergy losses in the compressor, condenser, and evaporator
    • Helps optimize the system design and operating conditions to minimize exergy destruction
  • Exergy analysis of a heat exchanger quantifies the exergy destruction due to finite temperature differences and pressure drops
    • Allows for the selection of optimal heat exchanger configurations and operating parameters
  • Exergy analysis of chemical processes identifies the sources of inefficiencies in reactors, separators, and other process units

Thermoeconomics: Basics and Principles

  • Thermoeconomics integrates thermodynamic analysis with economic principles to optimize energy systems
  • Exergy costing assigns monetary values to exergy streams based on their quality and potential for generating useful work
  • Specific exergy costing (SPECO) method allocates costs to exergy streams in proportion to their exergy content
  • Exergoeconomic analysis combines exergy analysis with economic evaluation to assess the cost-effectiveness of system improvements
  • Exergoeconomic optimization aims to minimize the total cost (investment and operating costs) while maximizing the system's exergy efficiency
  • Thermoeconomic evaluation helps in the selection of optimal system configurations, operating conditions, and component sizes
  • Thermoeconomic diagnosis identifies the components with the highest cost impact on the system's overall performance

Exergy Costing and Valuation

  • Exergy costing assigns monetary values to exergy streams based on their potential for generating useful work
  • Specific exergy costing (SPECO) method allocates costs to exergy streams in proportion to their exergy content
    • Assumes that the cost of an exergy stream is directly proportional to its exergy value
  • Fuel-Product-Loss (F-P-L) approach defines the fuel (input), product (desired output), and loss (waste) exergy streams for each component
    • Helps in formulating cost balance equations and determining the unit exergy costs
  • Exergy cost balance equation: C˙P,k=C˙F,k+Z˙k\dot{C}_{P,k} = \dot{C}_{F,k} + \dot{Z}_{k}
    • C˙P,k\dot{C}_{P,k} is the cost rate of the product exergy stream of component kk
    • C˙F,k\dot{C}_{F,k} is the cost rate of the fuel exergy stream of component kk
    • Z˙k\dot{Z}_{k} is the cost rate associated with the investment and operating costs of component kk
  • Exergy unit cost cc is defined as the cost per unit of exergy (/kJor/kJ or /kWh)
    • Calculated by dividing the cost rate by the corresponding exergy flow rate
  • Exergy costing provides a rational basis for allocating costs in a multi-product system (cogeneration plants, desalination systems)

Optimization Using Thermoeconomic Analysis

  • Thermoeconomic optimization aims to minimize the total cost (investment and operating costs) while maximizing the system's exergy efficiency
  • Objective function for optimization typically includes the total cost rate and the exergy efficiency
    • Minimizing the total cost rate: mink(C˙F,k+Z˙k)\min \sum_{k} (\dot{C}_{F,k} + \dot{Z}_{k})
    • Maximizing the exergy efficiency: maxηex=Ex˙PEx˙F\max \eta_{ex} = \frac{\dot{Ex}_{P}}{\dot{Ex}_{F}}
  • Decision variables for optimization include design parameters (component sizes, operating conditions) and economic parameters (interest rate, equipment costs)
  • Optimization methods such as genetic algorithms, particle swarm optimization, and gradient-based techniques can be applied
  • Thermoeconomic optimization helps in the selection of optimal system configurations, operating conditions, and component sizes
    • Balances the trade-off between thermodynamic performance and economic feasibility
  • Sensitivity analysis investigates the impact of varying input parameters on the optimal solution
    • Identifies the most influential parameters and their effect on the system's performance and cost

Real-World Applications and Case Studies

  • Thermoeconomic analysis of a combined cycle power plant
    • Identifies the components with the highest exergy destruction and cost impact
    • Optimizes the plant's design and operation to minimize the levelized cost of electricity (LCOE)
  • Exergoeconomic optimization of a cogeneration system producing electricity and heat
    • Determines the optimal allocation of resources between power generation and heat production
    • Minimizes the total cost while meeting the demand for both products
  • Thermoeconomic evaluation of a desalination plant
    • Compares different desalination technologies (multi-stage flash, reverse osmosis) based on their exergy efficiency and unit cost of water production
    • Identifies the most cost-effective and energy-efficient desalination process
  • Exergy analysis and optimization of a refrigeration system
    • Quantifies the exergy destruction in each component and identifies the main sources of inefficiencies
    • Optimizes the system's design and operating conditions to minimize exergy destruction and improve the coefficient of performance (COP)
  • Thermoeconomic analysis of a chemical process plant
    • Assigns costs to the exergy streams in the process and identifies the cost-intensive units
    • Optimizes the process design and operating parameters to minimize the production cost while meeting the product quality requirements

Problem-Solving Techniques and Examples

  • Exergy analysis of a gas turbine power plant
    • Given: Ambient temperature and pressure, fuel composition and flow rate, component efficiencies, and power output
    • Calculate the exergy destruction and exergy efficiency of each component (compressor, combustion chamber, turbine)
    • Determine the overall exergy efficiency of the plant and identify the components with the highest exergy destruction
  • Exergoeconomic analysis of a steam power plant
    • Given: Ambient conditions, fuel cost, component costs, and operating parameters
    • Perform exergy analysis to calculate the exergy flows and exergy destruction in each component
    • Apply the SPECO method to assign costs to the exergy streams and determine the unit exergy costs
    • Calculate the exergoeconomic performance indicators (exergy destruction cost, exergoeconomic factor) for each component
    • Identify the components with the highest cost impact and suggest improvements based on the exergoeconomic analysis
  • Thermoeconomic optimization of a cogeneration system
    • Given: Demand for electricity and heat, fuel cost, component costs, and operating constraints
    • Formulate the objective function (minimize total cost) and constraints (meet demand, component limitations)
    • Define the decision variables (component sizes, operating conditions) and their bounds
    • Apply an optimization algorithm (genetic algorithm, particle swarm optimization) to find the optimal solution
    • Analyze the optimal system configuration, performance, and cost breakdown
    • Conduct sensitivity analysis to investigate the impact of varying input parameters on the optimal solution


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© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.