Air Demand Duration Curve Tool

It preserves data coverage, missing intervals and measurement basis so the curve can support capacity, trim, fleet, rental and energy decisions without disguising gaps as real demand.

1. Purpose and Engineering Decision

A chronological trend answers when demand changed. A duration curve answers how often high, medium and low demand occurred. This separates short peaks from persistent base demand and exposes the portion of the operating year that occupies each demand band.

The tool is useful for compressor-capacity review, base/trim selection, fleet-dispatch studies, peak-rental planning, storage screening and energy modelling. It must not be used to infer chronology, event sequence or recovery time; those remain properties of the original time-series data.

2. Required Asset - Duration Curve Generator and Missing Data Rules

The curve cannot be considered complete unless the user can see how much of the scheduled period was actually represented by valid data.

3. Data Input Model

4. Time Weighting

Duration curves must represent time, not row count. For regularly sampled data, each valid record receives the sampling interval as its time weight. For irregular data, the tool assigns each point a valid interval only up to the configured maximum gap threshold.

Weight_i = Valid Time represented by sample i

T_valid = Sum(Weight_i)

If a timestamp-to-next-timestamp interval exceeds the maximum allowed gap, the excess interval is recorded as missing rather than credited to the preceding measurement. This prevents a stale value from being carried across an instrumentation outage.

5. Missing-Data Rules

Recommended imputation choices are none, forward-hold for very short stable gaps, or linear interpolation for short gaps where the user explicitly accepts the assumption. The tool must never interpolate across a known plant start/stop, shift boundary, compressor trip or major process transition without explicit user action.

6. Coverage Metrics

Coverage (%) = Valid Observed Time / Scheduled Analysis Time x 100

Missing Time = Scheduled Analysis Time - Valid Observed Time

The primary duration curve uses valid observed time as its denominator. If the user elects an imputation method, an additional imputed-coverage figure is shown separately rather than overwriting the raw coverage result.

7. Duration Curve Construction

Each accepted flow value is paired with its time weight. The engine sorts pairs by demand from highest to lowest, then accumulates hours. Equal demand values may be grouped to reduce output size without changing total represented time.

Cumulative Hours_j = Sum(Weight_i for all Q_i >= Q_j)

Exceedance_j (%) = Cumulative Hours_j / T_valid x 100

The x-axis therefore represents hours or percent of valid observed time for which demand was equaled or exceeded; the y-axis represents demand flow on the declared reference basis.

8. Exceedance Demand Metrics

The tool should use the E-prefix to avoid confusion with statistical percentile naming conventions.

9. Demand Volume and Mean Flow

Total Reference Volume = Sum(Q_i x Weight_i)

Q_mean = Total Reference Volume / T_valid

When Q is in m3/min and time is in minutes, the integrated result is m3 on the same reference basis. The calculator should convert time units internally so that volume integration remains dimensionally correct.

10. Load Factor and Peak Definition

Load Factor = Q_mean / Q_peak_basis

The user chooses the peak basis: maximum observation, Q_E1, Q_E5 or another declared exceedance level. Using a robust peak metric can prevent one isolated meter spike from making the load factor appear artificially low. The selected peak definition must be printed with the result.

11. Reference Test Case A - Regular 15-Minute Data

Assume eight valid 15-minute readings: 40, 35, 30, 30, 25, 20, 15 and 5 m3/min. Total valid time is 2 hours. The sorted sequence is already descending.

Time-weighted average demand is 25.0 m3/min. The maximum 40 m3/min occurs for only 0.25 h, while demand of at least 20 m3/min persists for 1.50 h.

12. Reference Test Case B - Missing Interval

A 24-hour analysis window contains 22.5 hours of valid observations, 0.5 hour of explicitly accepted short-gap interpolation and 1.0 hour of unresolved missing data.

The raw duration curve is based on 22.5 observed hours.

13. Reference Test Case C - Capacity Exceedance Hours

A plant has 6,000 valid annual operating hours. Its duration curve shows demand above 55 m3/min for 240 hours and above 45 m3/min for 1,050 hours.

This information can support decisions such as whether permanent capacity should cover the full peak, whether a trim machine is justified, or whether short seasonal peaks could be handled by temporary capacity.

14. Reference Test Case D - Robust Peak vs Single Spike

A dataset contains one isolated 85 m3/min point, while Q_E1 is 63 m3/min and mean demand is 38 m3/min.

15. Demand Bands for Fleet and Energy Analysis

Band boundaries are user inputs or imported from compressor operating envelopes. They should not be hard-coded.

16. Pressure and Quality Segmentation

Where the plant operates multiple pressure or air-quality systems, a single combined duration curve can be misleading.

17. Chronology Warning

Sorting destroys the original order of events. Two plants can have the same duration curve but very different transient behaviour.

18. Data Quality and Outlier Review

19. Input Validation and Guardrails

20. Output Specification