Leakage Cost Scenario Calculator

It deliberately separates leak-flow estimation from cost calculation so uncertainty is visible and auditable.

1. Purpose and Engineering Decision

A leak has two different engineering questions: how much air is escaping, and what that lost air costs to produce. The preferred input is measured leak flow from a verified survey, flow test or system balance. Where measured flow is unavailable, the calculator may estimate flow from an equivalent orifice, upstream pressure, temperature and discharge coefficient, but must label that result as an estimate rather than a measured fact.

The economic output is built from compressor specific power, operating hours and electricity tariff. This prevents the calculator from assuming that every plant requires the same kW to produce a unit of compressed air. The result can then be extended into repair-rate, recurrence, verification and payback scenarios.

2. Core Cost Equations

Leak power (kW) = Q_leak,ref x Specific Power

Annual leakage energy (kWh) = Leak power x Operating hours

Annual leakage cost = Annual leakage energy x Electricity tariff

Q_leak,ref must use the same flow reference basis as the specific-power value. Specific power should ideally come from a measured compressor-system operating point or validated performance data at a relevant pressure.

3. Measured Leak Flow Takes Priority

The highest-confidence cost estimate uses measured leak flow. A leak detector that only gives an acoustic severity index is not automatically a volumetric flow meter; if the survey vendor provides a calibrated flow estimate, that estimate should be recorded with its method and confidence.

4. Optional Orifice-Flow Estimate

At typical compressed-air pressures discharging to atmosphere, the flow is often choked. The calculator must test the pressure ratio before using the choked-flow equation.

Critical pressure ratio = [2 / (gamma + 1)]^(gamma / (gamma - 1))

If P_down/P_up <= critical ratio, flow is choked

m_dot = Cd x A x P_up x sqrt(gamma/(R x T_up)) x [2/(gamma+1)]^((gamma+1)/(2(gamma-1)))

The mass flow is then converted to reference volumetric flow using the reference-state density. Cd is the discharge coefficient, A is equivalent orifice area, P_up is absolute upstream pressure, T_up is absolute temperature, gamma is the heat-capacity ratio and R is the gas constant for air. A real leak can be a crack, thread path, fitting gap or damaged hose, so an equivalent-hole result is only an approximation.

5. Input Model

6. Specific Power - Do Not Use Motor Nameplate Alone

Leak cost should be tied to the incremental electrical power needed to supply the lost air. Motor nameplate kW is not the same thing as actual input power, and rated compressor flow may not match the current pressure or part-load operating state.

Specific Power = Electrical input power / Reference air flow

Where a plant has multiple compressors, the marginal compressor or fleet response can differ from the fleet average. The calculator should allow a base specific-power case and an alternative marginal-power case for scenario comparison.

7. Reference Test Case A - Measured Plant Leakage

A verified leakage survey totals 2.5 m3/min on the same reference basis as a measured plant specific power of 6.5 kW per m3/min. The leakage exists during 6,000 operating hours/year. Electricity tariff is INR 8.50/kWh.

Annual cost = 2.5 x 6.5 x 6,000 x 8.50 = INR 828,750

8. Reference Test Case B - Equivalent 2 mm Leak at 7 bar(g)

Estimate a circular equivalent leak of 2.0 mm diameter from 7.0 bar(g), 25 C air to atmosphere. Use Cd = 0.65, gamma = 1.4 and a reference state of 1.01325 bar(a), 20 C. The pressure ratio confirms choked flow under these assumptions.

This is an equivalent-orifice estimate, not a substitute for field measurement. Crack geometry, fittings, partial obstruction and local temperature can materially change actual leakage.

9. Reference Test Case C - Repair Campaign, Recurrence and Payback

A plant baseline survey identifies 8.0 m3/min of leakage. The repair campaign is expected to eliminate 70% initially. Of the repaired flow, 15% is expected to recur before the next verification cycle. Repair campaign cost is INR 180,000.

Retained saving flow = Baseline x Repair fraction x (1 - Recurrence fraction)

This makes the value of post-repair verification and a repeating leak-management cycle visible rather than assuming every repaired leak remains permanently closed.

10. Pressure Reduction Scenario

For a choked equivalent orifice with similar temperature and Cd, mass flow is approximately proportional to upstream absolute pressure.

Q2 / Q1 approximately equals P2,abs / P1,abs for the same choked orifice and temperature

Example: reducing a zone from 7.0 to 6.5 bar(g), at the same atmospheric pressure, changes the absolute-pressure ratio from 8.01325 to 7.51325 bar(a). The simple choked-orifice estimate predicts leakage of about 93.8% of the original flow. This is a scenario estimate; process minimum pressure and equipment behaviour remain governing constraints.

11. Scenario Matrix

12. Portfolio / Leak Register Mode

A useful plant implementation should support multiple leak records. Each leak retains its own location, source method, pressure zone, measured/estimated flow, confidence, repair status and verification date. The calculator then aggregates only compatible flow bases and clearly separates measured from estimated totals.

13. Optional Carbon Output

The calculator must not hard-code a universal carbon factor.

Avoided emissions = Avoided electricity (kWh) x User-entered emission factor

14. Validation and Guardrails

15. Output Specification