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A component malfunction does not stop at the component boundary. The productive structure carries its extra resource demand upstream and its penalty downstream into the final product.
Open the chapter contents · Thermodynamics root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the question, or read from Chapter 1 for the complete argument. The teaching chapters remain open; these grouped routes form the index.
Route 1 · Build the productive chain
Route 2 · Work the fuel impact
Route 3 · Stress the diagnosis
Route 4 · Check limits and evidence
Route 5 · Transfer and continue
CHAPTER 1 OF 12 · BUILD THE PRODUCTIVE CHAIN
1. A local malfunction becomes a system fuel penalty
A component can consume the same named fuel and still perform worse because fouling, leakage, erosion, off-design control or heat-transfer degradation changes its resource requirement. Thermoeconomic diagnosis asks more than “which component is inefficient?” It traces how that local malfunction changes resource consumption through the productive structure.
Fuel impact is the increase in the system’s external resource needed to deliver the same specified final product. Malfunction cost assigns an economic value to that impact. Product penalty expresses the consequence at the output boundary. The boundary, product definition and reference condition therefore come before the arithmetic.
This article extends the Thermodynamics root, thermoeconomic cost formation and multi-product exergy allocation.
CHAPTER 2 OF 12 · BUILD THE PRODUCTIVE CHAIN
2. The productive structure is a map of dependencies
Represent each component by fuels it consumes and products it supplies. A boiler may turn chemical exergy into steam exergy; a turbine may turn steam exergy into shaft work while supplying extraction steam; a compressor may consume shaft work to support the cycle. The thermoeconomic graph makes these dependencies explicit.
Reference operation supplies the baseline coefficients: how much upstream product is required per unit of downstream product. Actual operation supplies the changed coefficients. Their differences are malfunctions in the thermoeconomic sense. A malfunction in one component can induce extra production in upstream components even if those upstream components have not degraded.
This distinction separates origin from propagation. The component where extra irreversibility appears is not always the component carrying the largest final cost penalty.
CHAPTER 3 OF 12 · WORK THE FUEL IMPACT
3. Worked example: a two-component productive chain
Consider an original teaching system with component A producing an intermediate exergy stream for component B. At reference operation, A needs 1.25 units of external fuel per unit of intermediate product. B needs 80 units of intermediate product to deliver 50 units of final product, so the reference external fuel is 1.25 × 80 = 100 units.
| Case | A fuel coefficient | B intermediate demand | External fuel | Fuel impact versus reference |
|---|---|---|---|---|
| Reference | 1.25 | 80 | 100.0 | 0.0 |
| B malfunction only | 1.25 | 84 | 105.0 | 5.0 |
| A malfunction only | 1.30 | 80 | 104.0 | 4.0 |
| Both malfunctions | 1.30 | 84 | 109.2 | 9.2 |
B’s local malfunction adds four units of intermediate demand, but the external fuel impact is five because A needs 1.25 fuel units per intermediate unit. The productive chain amplifies and translates the local change.
CHAPTER 4 OF 12 · WORK THE FUEL IMPACT
4. Direct, induced and interaction terms must reconcile
With B degraded alone, its extra intermediate demand causes a five-unit fuel impact. With A degraded alone, the coefficient increase from 1.25 to 1.30 on the reference intermediate flow causes four units. Adding those single-malfunction impacts gives nine units, but the both-degraded case needs 9.2.
The extra 0.2 is an interaction: B’s extra four units are produced at A’s degraded coefficient, adding (1.30 – 1.25) × 4 = 0.2. A complete ledger must reconcile to the observed system impact.
| Contribution | Calculation | Fuel-impact units |
|---|---|---|
| B-origin impact through reference A | 1.25 × 4 | 5.0 |
| A-origin impact on reference B demand | 0.05 × 80 | 4.0 |
| Interaction of both changes | 0.05 × 4 | 0.2 |
| Total | 5.0 + 4.0 + 0.2 | 9.2 |
Ignoring the interaction would understate the measured system penalty. Assigning the entire 9.2 to the most visibly degraded component would confuse origin with propagated consequence.
CHAPTER 5 OF 12 · WORK THE FUEL IMPACT
5. Malfunction cost applies a declared resource price
If the external fuel exergy costs $0.06 per unit-hour, the 9.2-unit fuel impact costs $0.552 per hour. Spread over the fixed 50-unit final product, the incremental product penalty is $0.01104 per product-unit-hour.
That number is not a market price unless the cost model says so. Thermoeconomic unit costs can represent resource-accounting costs, monetary costs or a hybrid objective. State the basis, currency year, fuel price, operating period and treatment of capital and environmental charges.
The product denominator must remain fixed for a fair comparison. If actual production falls, a cost-per-product increase combines efficiency loss and capacity loss. That may be the operational question, but it is different from the same-product fuel impact.
CHAPTER 6 OF 12 · STRESS THE DIAGNOSIS
6. Changed context: final product is not held constant
Suppose B’s degradation reduces final output from 50 to 46 while external fuel remains 100. The fuel impact at fixed product cannot be read directly from the observed fuel difference, because there is none. The unit resource use has worsened from 2.0 to about 2.174 fuel units per product unit.
Choose a comparison convention: restore the actual system mathematically to the reference product, reduce the reference system to the actual product, or use a marginal production model. Different conventions answer different questions.
Do not label lost production as extra fuel without stating the equivalence rule. Capacity degradation, efficiency degradation and dispatch change can occur together.
CHAPTER 7 OF 12 · STRESS THE DIAGNOSIS
7. Changed context: an upstream component is forced off design
B’s malfunction increases A’s load. Even if A has no intrinsic degradation, its efficiency may change because it moves to another operating point. The resulting upstream penalty is induced, not necessarily an A malfunction.
A fair diagnosis therefore needs characteristic curves or a reference model across load. Comparing actual A at 84 units with reference A at 80 units can falsely accuse A of degradation when the difference is load-driven.
Use like-for-like environmental conditions, boundary states and control settings. Exergy analysis corrects energy quality, but it does not remove the need for a defensible operating reference.
CHAPTER 8 OF 12 · STRESS THE DIAGNOSIS
8. Multi-product components need explicit allocation rules
A turbine may produce shaft work and process steam. A heat-recovery system may supply several pressure levels. One cost balance is not enough to assign costs to all products; auxiliary equations or a productive-structure rule close the system.
Changing the auxiliary rule changes product costs while leaving physical balances untouched. That sensitivity is not an algebra mistake; it exposes a value judgement about joint production. Review product specifications and fair separation benchmarks before treating one allocation as uniquely physical.
For diagnosis, report both system fuel impact and the allocation rule used to distribute the penalty among products. A stable system total can coexist with unstable product-specific costs.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Dissipative components require careful product definitions
Condensers, throttling valves and pollution-control devices may not have a saleable exergy product. Their function can be enabling, constraining or environmental. Forcing every component into a simple fuel-to-product ratio can produce misleading unit costs.
The productive structure may allocate their costs to the components or final products they support. The chosen rule should preserve the system balance and remain understandable to operators.
Exergy destruction still has physical meaning through the Gouy–Stodola relation, but cost assignment is an additional model. Continue with exergy destruction and lost work to keep those layers separate.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Limits and misconceptions
Fuel impact is not simply the sum of local irreversibility changes. Propagation coefficients, induced operation and interaction terms matter. A component with a small local malfunction can create a large system penalty if it sits early in an expensive productive chain.
Thermoeconomic diagnosis does not prove a mechanical cause. It localises and values abnormal resource use; vibration, chemistry, inspection and control data are still needed to identify fouling, leakage or erosion.
Reference choice can dominate the result. Weather, load, fuel composition, maintenance state and product specifications must be normalised or declared. Cost numbers are conditional on prices and allocation rules, not universal physical constants.
CHAPTER 11 OF 12 · TRANSFER AND CONTINUE
11. Evidence and verification route
Valero and colleagues develop the vocabulary, mathematical principles and fuel-impact formula in On the thermoeconomic approach to the diagnosis of energy system malfunctions. Lazzaretto and Tsatsaronis present the SPECO framework in SPECO: A systematic and general methodology for calculating efficiencies and costs in thermal systems. The foundations of exergetic cost are developed in Theory of the exergetic cost90006-Y).
Verification should close the physical exergy balances, close the cost balances, reproduce the productive coefficients, reconcile origin plus induced plus interaction terms to total fuel impact, and rerun the result under plausible reference and allocation choices. Keep units and signs visible at every step.
CHAPTER 12 OF 12 · TRANSFER AND CONTINUE
12. Frequently asked questions
Is malfunction cost the repair bill?
No. It values additional resource use under the chosen cost basis. Repair cost, downtime and risk require separate data.
Why can an upstream component show a penalty without being damaged?
It may be producing extra intermediate product or operating off design because a downstream malfunction changed demand.
Can the same physical plant have different product penalties?
Yes. Product definitions, auxiliary equations, prices and boundary choices can change allocation while the physical balances remain the same.
What should be held constant?
Usually the specified final product and comparable external conditions, unless the study explicitly targets capacity loss or dispatch performance.
Final transfer check and connected reading
Before accepting a diagnosis, ask: Is the reference comparable? Are fuel and product definitions explicit? Does the productive structure show propagation? Do local, induced and interaction terms reconcile to the system impact? Are monetary penalties separated from physical causation and repair decisions?
Continue through the Thermodynamics root, thermoeconomic cost formation and structural uniqueness, and multi-product exergy allocation. The transferable skill is to trace every local change through a declared productive chain until the system fuel impact and product penalty reconcile.
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