🧊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.
Ex˙in and Ex˙out represent the exergy flows into and out of the system
Ex˙dest is the exergy destruction rate due to irreversibilities
ΔEx˙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
C˙P,k is the cost rate of the product exergy stream of component k
C˙F,k is the cost rate of the fuel exergy stream of component k
Z˙k is the cost rate associated with the investment and operating costs of component k
Exergy unit cost c is defined as the cost per unit of exergy (/kJor/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: min∑k(C˙F,k+Z˙k)
Maximizing the exergy efficiency: maxηex=Ex˙FEx˙P
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