3.2 Exergy Balance for Closed and Open Systems

Exergy balance for closed and open systems is crucial for understanding energy efficiency and system performance. It helps us quantify the maximum useful work obtainable from a system as it interacts with its environment, considering heat, work, and mass flows.

By analyzing exergy destruction and losses, we can identify inefficiencies in thermodynamic processes. This knowledge allows us to optimize energy systems, reduce waste, and improve overall performance, ultimately leading to more sustainable and efficient energy utilization.

Exergy balance for closed systems

Fundamentals of exergy in closed systems

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• Exergy represents the maximum useful work obtainable from a system as it interacts with the environment to reach equilibrium
• The exergy balance for a closed system considers the change in exergy of the system, exergy transfer associated with heat and work interactions, and exergy destruction
• The exergy balance equation for a closed system: ΔX = X_heat - X_work - X_destruction
  • ΔX denotes the change in exergy of the system
  • X_heat represents the exergy transfer associated with heat
  • X_work represents the exergy transfer associated with work
  • X_destruction represents the exergy destruction within the system

Exergy transfer and destruction in closed systems

• Exergy transfer associated with heat (X_heat) is calculated using the Carnot efficiency, which relates the temperature at which the heat transfer occurs to the temperature of the environment: X_heat = (1 - T_0/T) × Q
  • T_0 represents the temperature of the environment
  • T represents the temperature at which the heat transfer occurs
  • Q represents the heat transfer
• Exergy transfer associated with work (X_work) equals the work done by the system on the surroundings, as work is a form of organized energy that can be fully converted to useful work (shaft work, electrical work)
• Exergy destruction (X_destruction) represents the irreversible losses within the system due to entropy generation and always remains greater than or equal to zero, as per the second law of thermodynamics (friction, heat transfer across finite temperature differences)

Exergy balance for open systems

Exergy associated with mass flow in open systems

• Open systems involve mass flow across the system boundaries, and the exergy balance equation must account for the exergy associated with the mass entering and leaving the system
• The exergy balance equation for an open system: ΔX = Σ(ṁ_in × ψ_in) - Σ(ṁ_out × ψ_out) + X_heat - X_work - X_destruction
  • ṁ_in and ṁ_out represent the mass flow rates entering and leaving the system, respectively
  • ψ_in and ψ_out represent the specific exergies of the mass flows entering and leaving the system
• The specific exergy (ψ) of a mass flow is the sum of its physical exergy (ψ_ph), kinetic exergy (ψ_ke), potential exergy (ψ_pe), and chemical exergy (ψ_ch): ψ = ψ_ph + ψ_ke + ψ_pe + ψ_ch
  • Physical exergy (ψ_ph) represents the maximum useful work obtainable when the system is brought from its initial state to the environmental state through reversible processes
  • Kinetic exergy (ψ_ke) and potential exergy (ψ_pe) are associated with the velocity and elevation of the mass flow, respectively
  • Chemical exergy (ψ_ch) represents the maximum useful work obtainable when the system is brought from its initial chemical composition to the reference environment composition through reversible processes

Work interactions in open systems

• Exergy transfer associated with work interactions (X_work) in open systems includes shaft work, electrical work, and flow work
  • Shaft work involves the transfer of mechanical energy through a rotating shaft (turbines, compressors)
  • Electrical work involves the transfer of electrical energy (generators, motors)
  • Flow work represents the work required to push the fluid into or out of the system (pumps, valves)

Exergy destruction in thermodynamic processes

Causes of exergy destruction and losses

• Exergy destruction and losses occur due to irreversibilities in real thermodynamic processes and systems
  • Friction leads to the dissipation of mechanical energy into heat (bearings, fluid flow)
  • Heat transfer across finite temperature differences results in a reduction of the available thermal energy (heat exchangers)
  • Mixing of fluids with different compositions or temperatures leads to a decrease in the potential for work extraction (combustion chambers, condensers)
  • Chemical reactions may involve irreversibilities due to the generation of entropy (combustion, electrochemical processes)

Quantifying exergy destruction and losses

• Exergy destruction (X_destruction) can be calculated using the exergy balance equation for closed or open systems by accounting for all exergy transfers and changes in the system's exergy
• Exergy loss (X_loss) refers to the exergy that is transferred to the environment without being used
  • Heat transfer to the surroundings represents a loss of exergy that could have been utilized for useful work
  • Exergy associated with the exhaust gases or waste streams leaving the system is considered an exergy loss
• The total exergy destruction and loss in a system is the sum of exergy destruction and exergy loss: X_total_loss = X_destruction + X_loss
• Identifying and quantifying sources of exergy destruction and losses in thermodynamic processes and systems helps in understanding the inefficiencies and potential for improvement (power plants, refrigeration systems)

Exergetic performance evaluation

Exergetic efficiency and loss ratios

• Exergetic efficiency (ε) is the ratio of the useful exergy output to the exergy input of a component or system: ε = X_useful_output / X_input
  • Useful exergy output (X_useful_output) represents the desired exergy transfer or change in the system's exergy that contributes to the intended purpose of the component or system (mechanical work output, cooling effect)
  • Exergy input (X_input) represents the total exergy supplied to the component or system, including exergy associated with mass flow, heat, and work interactions
• Exergy destruction ratio (y_D) is the ratio of exergy destruction within a component or system to the total exergy input: y_D = X_destruction / X_input
  • It quantifies the fraction of the input exergy that is destroyed due to irreversibilities (friction, heat transfer, mixing)
• Exergy loss ratio (y_L) is the ratio of exergy loss to the total exergy input: y_L = X_loss / X_input
  • It quantifies the fraction of the input exergy that is lost without being utilized (heat loss to the environment, exergy in exhaust streams)

Application of exergetic performance analysis

• Exergetic performance analysis helps identify the components or processes with the highest exergy destruction and losses, guiding efforts to improve the overall efficiency and sustainability of energy systems
  • Analyzing the exergetic efficiency and loss ratios of individual components in a power plant (boiler, turbine, condenser) can pinpoint the areas with the greatest potential for improvement
  • Comparing the exergetic performance of different designs or operating conditions for a refrigeration system can help select the most efficient configuration
• By minimizing exergy destruction and losses, the utilization of energy resources can be optimized, leading to reduced environmental impact and increased sustainability (reduced fuel consumption, lower greenhouse gas emissions)