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Compare operation, preservation and abandonment with explicit restart physics, then use evidence-based hysteresis to avoid fragile switching.
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 · Map the actions
Route 2 · Work the option band
Route 3 · Transfer and stress
Route 4 · Respect the limits
Route 5 · Verify and continue
CHAPTER 1 OF 12 · MAP THE ACTIONS
1. Why mothballing is a distinct thermodynamic decision
Closing a plant forever and preserving it for a possible restart are not the same action. Abandonment gives up the equipment, permits and organisational option. Mothballing pays preservation costs now so that a future operating state can still be reached.
The choice is exergoeconomic because future cash flows depend on physical condition. Corrosion protection, warm storage, catalyst care, insulation integrity, rotating-equipment preservation and retained operating knowledge change the exergy destruction and cost of the eventual restart.
A useful model therefore keeps three actions visible: operate, mothball and abandon. It also records which quantities are cash estimates, which are physical measurements and which are legal or safety constraints.
CHAPTER 2 OF 12 · MAP THE ACTIONS
2. A one-period map separates the three actions
Let q be the probability of a high-value market next period and let the discount rate be 8%. Immediate abandonment returns a salvage value A=150. Continued operation returns 300 in the high state and 20 in the low state. Its present value is C(q)=(20+280q)/1.08.
Mothballing costs 15 immediately. If the high state arrives, restart yields 260 after restart expense; if the low state arrives, the preserved plant can still be exited for 140. Its present value is M(q)=-15+(140+120q)/1.08.
These are decision values, not thermodynamic laws. They become defensible only when the payoffs are tied to fuel, product, maintenance, restart and exergy-cost evidence.
CHAPTER 3 OF 12 · WORK THE OPTION BAND
3. Worked ledger: mothballing wins in the middle region
At q=0.60, continued operation is (20+280×0.60)/1.08=174.07. Mothballing is -15+(140+120×0.60)/1.08=181.30. Immediate abandonment is 150. Mothballing has the greatest value in this worked case.
| Action | Present-value calculation | Value |
|---|---|---|
| Abandon | 150 | 150.00 |
| Operate | (20+280×0.60)/1.08 | 174.07 |
| Mothball | -15+(140+120×0.60)/1.08 | 181.30 |
The result is not “mothball whenever demand is uncertain”. It is a comparison under stated preservation, restart, salvage and market assumptions.
CHAPTER 4 OF 12 · WORK THE OPTION BAND
4. Two crossings create an action band
Set M(q)=A to find the lower crossing: -15+(140+120q)/1.08=150, giving q=0.3183. Below it, abandonment is worth more than preserving the option.
Set C(q)=M(q) to find the upper crossing. The equality 20+280q=123.8+120q gives q=0.64875. Above it, operating is worth more than mothballing.
| Probability q | Highest worked value | Interpretation |
|---|---|---|
| Below 0.318 | Abandon | Preservation cannot repay its cost |
| 0.318 to 0.649 | Mothball | Waiting retains useful restart flexibility |
| Above 0.649 | Operate | Immediate operating upside dominates |
CHAPTER 5 OF 12 · WORK THE OPTION BAND
5. Exergy costing changes the restart payoff
The high-state mothballing payoff of 260 should be built from a restart ledger. That ledger can include purchased fuel exergy, electricity, replacement parts, emissions obligations, labour, lost production during warm-up and the cost assigned to exergy destruction in each component.
An old compressor may restart safely yet consume more electricity. A heat exchanger may pass inspection yet suffer fouling that raises fuel use. A catalyst may need replacement before saleable product is reached. Each physical finding changes the economic payoff.
Exergoeconomic accounting is most useful here as a consistency check: it shows where resource costs enter and prevents an attractive market forecast from hiding a degraded conversion process.
CHAPTER 6 OF 12 · TRANSFER AND STRESS
6. Restart transients need their own boundary
Steady-state design data are not enough for restart. Heat-up, purge, pressure testing, synchronisation, off-spec production and minimum stable load can dominate the first hours or days.
Define the restart boundary before calculating value: start when preservation ends, stop when specified product and stable operating conditions are reached, and record discarded product and temporary utilities inside that boundary. If a restart crosses safety, emissions or equipment-life limits, the action may be infeasible regardless of its expected value.
A practical evidence pack links each restart cost to a work order, inspection result, measured energy quantity, vendor quotation or approved engineering estimate.
CHAPTER 7 OF 12 · TRANSFER AND STRESS
7. Changed context: a higher restart cost removes the band advantage
Suppose restart cost rises by 40, reducing the high-state mothballing payoff from 260 to 220. At q=0.60, the mothball value becomes -15+(0.60×220+0.40×140)/1.08=159.07. Continued operation remains 174.07, so the preferred action changes.
This is a transfer check. Nothing about the market probability changed; the decision moved because the physical and economic restart burden changed. Recalculate both crossings rather than carrying the original band into the new context.
The exercise also shows why a single “mothballing value” is misleading. Preservation standard, downtime, restart scope and equipment condition must travel with the number.
CHAPTER 8 OF 12 · TRANSFER AND STRESS
8. Hysteresis prevents fragile switching
If management switches action whenever an estimated probability touches a single boundary, small revisions can trigger repeated shutdown and restart plans. Real plants also have mobilisation lead times, minimum run periods and cycling damage.
A hysteresis policy uses separated entry and exit triggers. For example, operate only after the upper evidence threshold is crossed, but do not mothball an operating plant until a lower threshold is crossed and the expected saving exceeds shutdown and cycling costs.
The width of a hysteresis band should come from forecast error, transaction costs, physical cycling evidence and decision delay. It should not be an arbitrary buffer added after the model is built.
CHAPTER 9 OF 12 · RESPECT THE LIMITS
9. Evidence checks before approving preservation
Check market probabilities against dated scenarios rather than a single forecast. Stress fuel and product prices together when they are correlated. Reconcile the asset register with the preservation scope, and verify that the salvage estimate applies after the proposed storage period.
On the physical side, inspect critical rotating equipment, pressure boundaries, electrical systems, catalysts, control systems and stored spares. Record statutory inspection dates, environmental obligations, insurance conditions and retained staffing assumptions.
Finally, test whether the ranking survives plausible changes in discount rate, restart time, exergy destruction, preservation cost and salvage value. A decision that reverses under tiny evidence changes needs more investigation or a staged commitment.
CHAPTER 10 OF 12 · RESPECT THE LIMITS
10. Limits and common misconceptions
Expected value does not represent every risk attitude, financing constraint or bankruptcy exposure. A one-period model compresses a sequence of learning, inspection and recommissioning choices. Correlated failures and market states can make the simple state tree optimistic.
Mothballing is not “doing nothing”. Poor preservation can destroy the restart option. Nor is exergy cost an observed market price by itself; it is an allocation that must be traced to declared fuel and product rules.
Hysteresis does not justify ignoring new safety evidence. Legal, environmental and integrity constraints override a financial band. The model supports accountable judgement; it does not replace competent engineering approval.
Evidence, sources and reproducibility
The economic logic of delayed exit is developed in Entry and Exit Decisions under Uncertainty. Evidence on mothballing as an operational flexibility decision appears in Mothballing, reopening and exit decisions. The physical-cost connection follows the exergoeconomic foundations in Exergoeconomic analysis and evaluation of energy-conversion plants90020-9).
Archive the dated state tree, probability sources, price scenarios, discount convention, preservation plan, restart work scope, exergy model, salvage evidence, constraint register and sensitivity results. Keep the spreadsheet or code that reproduces both crossings and every value in the worked tables.
CHAPTER 11 OF 12 · VERIFY AND CONTINUE
11. Frequently asked questions
Is mothballing always reversible?
No. Permits, staff, suppliers, degradation and obsolescence can make reopening slower, dearer or impossible. Model those losses explicitly.
Why include salvage after mothballing?
Preservation can retain a later exit route. The value must reflect realistic disposal timing and condition, not today’s headline salvage quote.
Should cycling damage be a cash cost or a constraint?
It can be both. Price measurable life consumption and maintenance, but retain hard integrity and safety limits as constraints.
Can the probabilities come from one forecast?
Use scenarios and calibration evidence. A single point forecast hides uncertainty that is central to an option decision.
What should a decision note report?
Report all three actions, crossing values, state payoffs, physical boundaries, exclusions, constraint checks, sensitivity ranges and the next evidence review date.
CHAPTER 12 OF 12 · VERIFY AND CONTINUE
12. Final transfer check and connected reading
Keep the original payoffs but raise the preservation cost from 15 to 30. Recalculate the two crossings, identify the new mothballing band, and explain whether it widens or narrows. Then name one physical observation that could justify the change.
Continue through the Thermodynamics root, abandonment-options guide, real-options guide, compound-options guide, Monte Carlo guide and expected-regret guide. Together they connect physical condition, operating flexibility and accountable investment decisions.
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