8.4 Exergy balance for closed and open systems

Exergy balance is a powerful tool for analyzing energy systems, helping us understand how efficiently they use available energy. It goes beyond traditional energy analysis by considering the quality of energy and its potential to do useful work.

For closed and open systems, exergy balance reveals where energy is wasted and helps identify areas for improvement. By minimizing exergy destruction and loss, we can design more efficient systems that make better use of our energy resources.

Exergy balance for closed systems

Exergy and its components

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• Exergy represents the maximum useful work obtainable from a system as it reaches equilibrium with a reference environment
• The exergy of a closed system consists of physical exergy (associated with temperature and pressure) and chemical exergy (related to composition)
• Physical exergy quantifies the system's potential to perform work due to its deviation from the reference environment's temperature and pressure
• Chemical exergy accounts for the work potential arising from the difference in chemical composition between the system and the reference environment

Exergy balance equation and terms

• The exergy balance equation for a closed system describes the change in exergy over time, considering heat transfer, work interactions, and internal irreversibilities (exergy destruction)
• The exergy transfer associated with heat transfer depends on the boundary temperature ($T_b$) and the reference environment temperature ($T_0$), given by $\dot{Ex}_{heat} = (1 - \frac{T_0}{T_b})\dot{Q}$
• The exergy transfer associated with work is equal to the work itself, as work is a form of pure exergy
• The exergy destruction term represents the irreversible losses within the system due to friction, heat transfer across finite temperature differences, mixing, and chemical reactions
• The exergy balance equation for a closed system is expressed as $\frac{dEx}{dt} = \sum (1 - \frac{T_0}{T_b})\dot{Q} - \dot{W} - \dot{Ex}_{destruction}$

Exergy analysis of closed systems

Exergy efficiency and system performance

• Exergy efficiency is defined as the ratio of the useful exergy output to the total exergy input, quantifying the effectiveness of the system in utilizing the available exergy
• By comparing the actual work output of a closed system to its maximum theoretical work potential (exergy), the degree of departure from ideal performance can be assessed
• Exergy analysis helps identify the locations and magnitudes of irreversibilities within a closed system, pinpointing areas for potential improvements in system design and operation
• Minimizing exergy destruction is crucial for enhancing the overall efficiency of closed systems

Applications of exergy analysis in closed systems

• Exergy analysis can be applied to various closed systems, such as batch reactors (chemical processing), energy storage devices (batteries, thermal storage), and closed-cycle power systems (Stirling engines, closed-cycle gas turbines)
• In batch reactors, exergy analysis can evaluate the thermodynamic performance of chemical reactions and identify inefficiencies related to heat transfer and mixing
• For energy storage devices, exergy analysis assesses the efficiency of charging and discharging processes, considering the exergy losses associated with temperature gradients and internal resistance
• In closed-cycle power systems, exergy analysis helps optimize the system design by minimizing exergy destruction in components like heat exchangers, turbines, and compressors

Exergy balance for open systems

Exergy associated with mass flows

• Open systems involve mass and energy interactions with the surroundings, requiring the consideration of exergy associated with mass flows in addition to heat and work interactions
• The specific exergy of a mass flow consists of physical exergy (temperature and pressure), chemical exergy (composition), kinetic exergy (velocity), and potential exergy (elevation)
• The exergy transfer due to mass flow is determined by the difference between the specific exergy of the incoming and outgoing streams, multiplied by their respective mass flow rates
• The specific exergy of a mass flow is given by $ex = (h - h_0) - T_0(s - s_0) + \frac{1}{2}(V^2 - V_0^2) + g(z - z_0) + ex_{chemical}$

Steady-state exergy balance equation

• The steady-state exergy balance equation for open systems assumes no change in exergy over time, simplifying the analysis
• The steady-state exergy balance equation is expressed as $0 = \sum (1 - \frac{T_0}{T_b})\dot{Q} - \dot{W} + \sum \dot{m}_{in} ex_{in} - \sum \dot{m}_{out} ex_{out} - \dot{Ex}_{destruction}$
• The equation accounts for the exergy transfer associated with heat ($\dot{Q}$) and work ($\dot{W}$), the exergy of incoming ($\dot{m}_{in} ex_{in}$) and outgoing ($\dot{m}_{out} ex_{out}$) mass flows, and the exergy destruction ($\dot{Ex}_{destruction}$)
• The steady-state exergy balance equation allows for the evaluation of exergy destruction and loss in open systems, guiding the optimization of system performance

Exergy destruction and loss in open systems

Sources and quantification of exergy destruction and loss

• Exergy destruction represents the irreversible losses within the system boundaries due to internal processes, such as friction, heat transfer, mixing, and chemical reactions
• Exergy loss refers to the exergy discarded to the surroundings through waste heat or mass flows, representing a loss of potential work that cannot be recovered
• The exergy destruction and loss in open systems can be quantified using the steady-state exergy balance equation, considering the exergy of incoming and outgoing flows, as well as the exergy transfer associated with heat and work
• Exergy destruction is calculated as $\dot{Ex}_{destruction} = \sum (1 - \frac{T_0}{T_b})\dot{Q} - \dot{W} + \sum \dot{m}_{in} ex_{in} - \sum \dot{m}_{out} ex_{out}$

Strategies for minimizing exergy destruction and loss

• Minimizing exergy destruction and loss is crucial for improving the overall efficiency of open systems
• Process optimization techniques, such as pinch analysis and process integration, can be employed to minimize exergy destruction by reducing heat transfer across large temperature differences and optimizing mass and energy flows
• Heat integration strategies, like heat exchanger networks and cogeneration systems, help recover waste heat and minimize exergy loss to the surroundings
• Utilizing waste heat and mass flows for additional processes or power generation can further reduce exergy loss and enhance overall system efficiency
• Optimizing chemical processes by selecting appropriate operating conditions (temperature, pressure, catalyst) and reactor configurations can minimize exergy destruction due to chemical reactions and mixing
• Reducing pressure drops and friction losses in fluid flow systems, such as pipelines and turbomachinery, contributes to lower exergy destruction