Time preserves operational sequence; depth preserves location in the well. Converting one into the other changes weighting, eligibility, and resolution, so it must be treated as an engineering transformation rather than a plotting option. The raw time record and its depth-derived products should remain linked and auditable.
Time and depth are not one-to-one
The most important complication is that time and depth do not have a simple one-to-one relationship. During rotary drilling:
- time advances,
- hole depth increases,
- bit depth generally increases.
During a connection:
- time advances,
- hole depth stays constant,
- bit depth may change slightly or remain static.
During a trip:
- time advances,
- hole depth stays constant,
- bit depth can move thousands of feet.
During reaming:
- bit depth changes,
- but new hole may not be created.
During circulation off bottom:
- time advances,
- neither hole depth nor bit depth necessarily changes much.
Time continues through drilling, connections, reaming, circulation, and trips while hole depth and bit depth respond differently.
Several depth axes are available:
| Coordinate | Represents | Common uses |
|---|---|---|
| Hole depth | Deepest drilled extent | As-drilled ROP, drilling performance, and formation comparison |
| Bit depth | Current bit location | Tripping, reaming, mechanical events, and torque-and-drag analysis |
| TVD | Vertical position | Geology and pressure relationships |
| Formation-relative depth | Position from a common geological marker | Equivalent intervals across wells |
The correct depth variable depends on the question.
“Plot it by depth” is therefore incomplete unless the type of depth has also been defined.
Apply operating-state eligibility first
If all real-time samples are grouped by hole depth, a 14,000-ft bin might contain:
- 15 minutes drilling,
- 5 minutes reaming,
- 4 minutes circulating,
- 6 minutes making a connection.
Every sample may inherit approximately the same hole depth. Averaging them into one bin then mixes physically different operations. The bin is numerically valid; the engineering population is not. Validate the data, identify rig state, select the eligible population, and only then convert or aggregate by depth.
For a drilling-performance analysis: drilling data → depth is much more meaningful than all time-series data → depth. This is one reason operational-state classification is such important infrastructure for depth-based analytics.
Weighting changes average ROP
Take a simple hypothetical section:
| Interval | Footage | ROP | Drilling time |
|---|---|---|---|
| 1 | 100 ft | 100 ft/hr | 1.0 hr |
| 2 | 100 ft | 200 ft/hr | 0.5 hr |
The 200-ft section took 1.5 hours, so its delivered drilling rate was 133.3 ft/hr. The equal-footage average of the two interval ROP values is 150 ft/hr.
Both numbers arise legitimately from the same drilling. But they answer different questions.
The 133-ft/hr result answers:
How quickly was the section actually drilled?
It reflects the fact that more time was spent in the slower interval.
The 150-ft/hr result answers something closer to:
What was the average ROP across equally weighted footage intervals?
The difference is not a mathematical error. It is a weighting decision. This is why every drilling-performance KPI should define whether its population is weighted by:
- time,
- footage,
- stands,
- events,
- or another unit.
Time-weighted and equal-footage ROP averages can both be valid, but they answer different engineering questions.
Binning can remove the event
Once drilling data is transformed to depth, another choice appears:
How large should the depth interval be?
Possible intervals might include:
- 1 ft,
- 5 ft,
- 10 ft,
- one stand,
- 100 ft,
- formation interval.
Smaller bins preserve more detail; larger bins suppress variability and simplify comparison. A 100-ft median may nearly hide a dysfunction that persists for 20 ft, while a 1-ft statistic may be unnecessarily noisy for evaluating a BHA across several thousand feet. Resolution should match the physical scale of the question.
- Bit failure: stand-level trends may be appropriate.
- Formation benchmarking: tens or hundreds of feet may be appropriate.
- Survey response: individual survey intervals may matter.
- Short mechanical event: the time domain may be more useful than depth aggregation at all.
Imagine a 30-ft interval drilled in ten minutes. For nine minutes, torque is stable. For thirty seconds, severe oscillation occurs. Then drilling stabilizes again. A depth-based median may make the interval look completely normal. A time-series view immediately exposes the event. This does not make depth aggregation bad. It means the representation has intentionally compressed time-domain information. That leads to an important practical rule: Use depth to locate the problem; use time to investigate the event.
Choose windows for the physical question
SPE-186166 describes filtering its drilling-efficiency indicator with moving averages defined over time or depth.[1] The two windows change differently with ROP:
| Window | At 60 ft/hr | At 240 ft/hr | Constant scale |
|---|---|---|---|
| 5 minutes | 5 ft | 20 ft | Time |
| 20 ft | 20 minutes | 5 minutes | Depth |
A time window is generally more defensible for equipment dynamics; a depth window better preserves formation scale.
Preserve provenance through transformation
If one dataset contains a value every 10 ft and another every foot, interpolation may be necessary for plotting or numerical comparison. The distinction must remain clear: interpolated values are estimates between measurements, not additional observations. Increasing the row count does not increase measured information. Depth transformation should therefore preserve:
- original source resolution,
- interpolation,
- binning method,
- aggregation method.
A defensible workflow is:
| Stage | Requirement |
|---|---|
| Define the question | Decide whether the analysis needs sequence, location, section performance, geological comparison, or event investigation. |
| Validate and synchronize | Resolve bad sensors, missing intervals, timestamp problems, and known source latency. |
| Classify state | Separate drilling, sliding, reaming, tripping, connections, and circulation. |
| Choose the coordinate | Use hole depth, bit depth, TVD, or formation-relative depth according to the question. |
| Choose the unit and statistic | Define the sample, foot, interval, stand, or formation and the median, mean, maximum, or percentile used. |
| Preserve provenance | Record source frequency, state filter, depth basis, bin size, aggregation, and interpolation. |
| Retain time linkage | Keep every depth-derived KPI traceable to the underlying time interval. |
The same interval answers different questions in time and depth views; keeping them linked preserves the operational event behind the depth trend.
Related technical resources
- Two Clocks, One Well: Modeling Time- and Depth-Indexed Data
- The Average Trap: Comparing Drilling Performance With Distributions
- Why Rig-State Classification Is Foundational to Real-Time Drilling Analytics
References
- Ambrus, A., Ashok, P., Chintapalli, A., Ramos, D., Behounek, M., Thetford, T. S., and Nelson, B. A Novel Probabilistic Rig Based Drilling Optimization Index to Improve Drilling Performance. SPE-186166-MS, SPE Offshore Europe Conference & Exhibition, Aberdeen, United Kingdom, 2017.