Quantity and Quality: A Proposed Exergy-Based Reporting Framework for Energy Systems

Abstract

First-law scalar energy accounting, expressed in joules, kilowatt-hours, megawatt-hours, quads, barrels-of-oil-equivalent, and related quantities, does not encode the second-law distinction between energy magnitude and accessible work potential unless an additional quality field is provided. Classical exergy analysis restores that distinction, but routine adoption has been limited by reference-state dependence, carrier-specific terminology, data requirements, and the perceived burden of full thermodynamic accounting. The result is a persistent operational gap between thermodynamic rigor and the low-overhead reporting interfaces used by plant engineers, utility managers, regulators, market designers, and investors.

This paper proposes a dual-layer framework for closing that gap. The physics layer preserves carrier-level thermodynamics. It defines the intensive carrier potential as the exergy voltage, ∆Φ(C) A =dXA/dC, and uses it to recover the carrier-current relation ̇XA = ̇C∆Φ(C) A , which can be written at a reporting boundary as ̇XA = fX ̇E. The interface layer compresses that physics into a practical reporting token, (Ecarrier,fX), where Ecarrier is a first-law energy quantity with explicit carrier and basis context, such as MWh_e, MWh_th, or MWh_HHV_CH4, and fX is the Exergy Factor, the accessible work potential per unit reported energy at the declared boundary.

Five Fidelity Tiers, F0 through F4, allow the notation to scale from conventional scalar reporting, through presumptive lookup factors, asset-specific metadata, dynamic interval com putation, and full state-vector engineering analysis without changing the public interface. The paper also defines optional diagnostics: Exergy Capital Efficiency for capital screening, and the Exergy Loss Angle, θloss = atan2(Xlost,Xuseful,out), as a bounded display coordinate derived from second-law efficiency. The angle is not a new thermodynamic property; it is a visualization of retained versus lost useful work potential over a declared boundary and interval.

The framework is demonstrated with public XAI4HEAT district-heating telemetry. Four pro cessed substations, covering 51,592 synchronized 15-minute intervals from the 2024–2025 heating season, are converted into dynamic F3 Exergy Factor records using measured primary supply temperature, measured ambient temperature, and the reported thermal-delivery field as an inter val weight. The delivery-weighted portfolio Exergy Factor is 0.216 with a dynamic ambient sink and 0.173 with a fixed 20◦C sink. A supply-return sensitivity check shows that an integrated primary water-stream model gives 0.172, while a secondary-side proxy gives 0.125, reinforcing that the public token must carry method and tier metadata. The empirical demonstration is limited to thermal district-heating telemetry and does not validate the chemical-carrier registry or optional diagnostic metrics. The central practical claim is therefore narrow and operational: every reported energy quantity should carry an Exergy Factor, and supply, demand, storage, and conversion pathways should be matched by both quantity and quality.