How Survey Interval Affects Wellbore Tortuosity Analysis

A tortuosity metric does not measure the wellbore independently of the survey used to describe it. Survey resolution, interval consistency, and resampling can materially change the result.

Imagine drilling one wellbore and surveying it twice.

The first survey records inclination and azimuth every few feet.

The second records the same trajectory every 90 or 100 feet.

Physically, there is only one hole.

Yet a numerical measure of wellbore tortuosity can produce different results from the two datasets.

Nothing changed downhole.

What changed was how much of the geometry was visible to the calculation.

That creates an important issue whenever tortuosity is used to compare:

• BHAs,
• directional drilling performance,
• wells,
• rigs,
• service providers,
• or historical drilling programs.

Before deciding that one well was smoother than another, an engineer has to ask a more basic question:

Were the two trajectories measured in a sufficiently comparable way?

A detailed investigation published in SPE-196020 examined this problem using high-resolution gyro surveys that were deliberately downsampled to different survey intervals.[1]

The results illustrate a broader data-analysis principle that applies far beyond directional drilling:

A performance metric can contain information about both the physical system and the way that system was measured.

The physical wellbore does not change when survey spacing changes, but the geometric information available to a tortuosity calculation does.

Why Measure Tortuosity at All?

Traditional lateral BHA performance metrics usually focus on outcomes such as:

• ROP,
• total drilling time,
• number of bit or BHA runs,
• ability to reach planned TD,
• casing or liner placement,
• and the percentage of the wellbore placed in the desired target.

Those are all important.

But they do not directly quantify the quality of the trajectory that was created.

SPE-196020 emphasizes this distinction and notes that the highest-ROP well is not necessarily the best well from the standpoint of subsequent well construction or completion.[1]

Excessive tortuosity can be associated with operational consequences including:

• erratic torque and drag,
• reduced drilling performance,
• poor hole cleaning,
• difficult casing or liner runs,
• and complications during subsequent operations.

A tortuosity metric therefore tries to answer a different question from ROP:

How smooth is the path that was actually drilled?

That makes tortuosity potentially valuable for evaluating BHA design and directional performance.

But before the metric can be used for benchmarking, we need to understand what affects the metric itself.

Survey interval turns out to be one of those factors.

A Directional Survey Is a Sampled Representation of the Hole

A wellbore trajectory is continuous.

A conventional directional survey is not.

It consists of discrete observations along measured depth:

• measured depth,
• inclination,
• azimuth.

The trajectory between those stations is reconstructed mathematically, commonly using the minimum curvature method.

This distinction matters.

The survey does not contain every local variation in the physical wellbore.

It contains the variations that can be observed at the locations where measurements were taken.

Consider a hypothetical lateral that contains several small directional oscillations.

A high-resolution survey might contain enough points to reveal each one.

A conventional survey with stations approximately one stand apart may see only some of them.

A still coarser representation could connect points on either side of several local variations and effectively hide them from the trajectory calculation.

The physical path did not become smoother.

The measured representation became smoother.

As survey spacing increases, local trajectory features can disappear from the sampled representation even though they remain in the actual wellbore.

Tortuosity Depends on Features Detected in the Path

The tortuosity approach evaluated in SPE-196020 considers geometric characteristics of turns within the trajectory.[1]

Two concepts are particularly useful for understanding its behavior.

Frequency

How many directional turns are identified along the section?

A higher-resolution trajectory can expose smaller changes that may not appear when stations are widely spaced.

As the high-resolution gyro surveys in the study were sampled at progressively different intervals, the number of identifiable curve turns changed substantially.[1]

Sharpness

How different is the actual path through a turn from the direct path between the turn's endpoints?

One way to represent that geometrically is to compare:

• the arc length through a turn,
• with the chord length connecting its endpoints.

For a nearly straight interval, the two distances are almost equal.

For a sharper or more complicated turn, the path along the curve becomes longer relative to the straight-line connection.

Together, these concepts attempt to capture both:

how often the path changes direction

and

how significant those changes are.

Comparing the path through a turn with the direct chord between its endpoints provides a geometric measure of turn severity.

The Survey-Interval Experiment

The particularly useful part of SPE-196020 is that the authors did not merely speculate that resolution might matter.

They tested it.

The study used five gyro surveys originally available at approximately 1-ft resolution.[1]

Those trajectories were progressively downsampled by removing survey points, producing representations with intervals ranging from very high resolution to intervals as large as approximately 120 ft.

The tortuosity calculation was then repeated on each representation.

That creates an unusually clean experiment.

The wellbore stays the same.

The underlying high-resolution survey stays the same.

Only the number and spacing of points provided to the calculation changes.

If the tortuosity metric were completely independent of survey resolution, the calculated result should remain essentially unchanged.

It did not.

The calculated tortuosity varied as survey interval changed.[1]

The behavior was also not as simple as assuming:

More survey points always produce proportionally more tortuosity.

The interaction between the number of identified turns and the geometric severity of those turns created more complicated behavior.

This is exactly why survey resolution deserves attention before tortuosity values are compared across wells.

Synthetic example showing why the relationship between survey interval and calculated tortuosity should not be assumed to follow one universal correction.

More Resolution Reveals More Features—but the Metric May Not Respond Linearly

At first glance, one might expect an obvious relationship.

A finer survey reveals more geometric detail.

Therefore:

higher resolution → more detected tortuosity.

The first part is reasonable.

SPE-196020 found that the number of detected curve turns increased dramatically as the survey representation became more detailed.[1]

But the calculated tortuosity metric did not simply increase in direct proportion to that additional detail.

Why?

Because the formulation did not weight the number of turns and the sharpness of those turns equally.

The frequency component reduced the influence of simply detecting additional turns, while the sharpness component could dominate the result.[1]

The authors investigated modifying the frequency term to give the number of turns more direct influence.

That did not produce a universal solution either.

In some cases the frequency component then became dominant, while in others the different terms offset one another.[1]

This is an important lesson.

The problem is not merely:

"What correction factor should we apply for survey spacing?"

The deeper issue is that changing resolution changes the actual geometric information available to the calculation.

Why a Simple Correction Factor Is Tempting

If a KPI changes systematically with survey interval, the obvious data-science response is to normalize it.

For example:

1. calculate the relationship between survey spacing and tortuosity,
2. fit a trend,
3. remove the trend,
4. compare the corrected values.

SPE-196020 tested a version of this idea.[1]

For the specific dataset examined, removing general trends reduced the variation in tortuosity across survey intervals by approximately 50%.

That sounds encouraging.

But the authors explicitly cautioned against treating the correction as a general solution.[1]

The reason is fundamental.

The difference between a 30-ft survey and a 100-ft survey is not simply a scale difference.

The lower-resolution survey has actually lost information about the trajectory.

A linear correction can adjust a number.

It cannot reconstruct geometric features that were never sampled.

That is why the paper ultimately argues that using reasonably consistent survey intervals is preferable, where possible, to relying on a universal correction factor.[1]

This principle applies to many drilling KPIs:

Normalization works best when the measurement processes are fundamentally comparable.

It cannot always repair missing information.

Consistency May Matter as Much as Absolute Spacing

There is another complication.

A directional survey may not even use the same spacing through the entire well.

For example:

• vertical section surveys may be widely spaced,
• the curve may contain much tighter survey spacing,
• the lateral may return to wider and more consistent intervals.

That creates another source of bias.

In the SPE-196020 analysis, conventional surveys included intervals around 95 ft in some sections and intervals as short as approximately 30 ft in the curve.[1]

The researchers compared:

1. the original conventional survey,
2. a conventional survey resampled to a consistent interval,
3. a high-resolution gyro survey downsampled to a comparable interval.

The whole-well analysis showed meaningful differences between the representations.[1]

But when the analysis was limited to laterals that already had relatively consistent survey spacing, the differences were much smaller.

That suggests an important practical rule:

Before comparing tortuosity values, inspect not only the average survey interval but the distribution and consistency of survey intervals over the section being compared.

Two wells can both have an "average survey interval" of 90 ft and still be sampled very differently.

Two surveys can have similar average spacing while representing the trajectory with very different sampling consistency.

Resampling Does Not Automatically Improve the Data

Once inconsistent survey spacing is recognized, resampling to a common interval seems like an obvious solution.

Sometimes that helps.

Sometimes it does not.

The key question is whether resampling is:

standardizing existing information

or

creating interpolated points between sparse measurements.

SPE-196020 found that resampling an already consistently sampled lateral did not necessarily improve the agreement with higher-resolution reference data.[1]

One reason was point placement.

A newly generated regular grid can fall at locations that miss geometric features captured by the original stations.

Another reason is the trajectory reconstruction itself.

The minimum curvature method produces a smooth mathematical path between survey stations.

When sparse data are interpolated onto a new grid, that reconstructed path can appear smoother than the underlying high-resolution trajectory.

The important distinction is:

More rows in a resampled dataset do not mean more measured information.

If a 100-ft survey is interpolated to 10-ft spacing, it now contains ten times as many rows.

It does not contain ten times as much directional information.

Resampling can standardize a dataset, but it cannot recreate trajectory information that was never measured.

A Practical Example

Suppose two motor BHAs drilled comparable laterals.

BHA A

• average ROP: 145 ft/hr
• surveys generally every 90–100 ft
• calculated tortuosity index: 18

BHA B

• average ROP: 135 ft/hr
• surveys generally every 30 ft
• calculated tortuosity index: 24

A quick conclusion might be:

BHA A drilled faster and produced the smoother hole.

That may ultimately be true.

But the tortuosity comparison is not yet fair.

BHA B was observed at approximately three times the directional resolution.

It had far more opportunities for small turns to appear in the trajectory.

The analysis should first ask:

• Are the sections geometrically comparable?
• Are planned trajectory differences being accounted for?
• What are the survey-interval distributions?
• Are intervals reasonably consistent within each well?
• Can both surveys be evaluated at a common defensible resolution?
• Will resampling remove information from the higher-resolution survey or merely manufacture interpolated points in the lower-resolution one?

Only after those questions are addressed should the tortuosity ranking be interpreted as BHA performance.

A defensible BHA comparison requires controlling the measurement basis before interpreting differences in tortuosity.

The Comparison Section Matters

Another useful observation from SPE-196020 was the difference between whole-well and lateral-only analysis.[1]

The whole well contains distinctly different geometric regimes:

• vertical,
• build,
• potentially tangent,
• landing,
• lateral.

These sections often have different planned curvature and different survey practices.

Combining them into one metric can therefore mix:

• intended geometry,
• directional execution,
• and measurement-resolution differences.

For BHA performance analysis, a section-specific comparison is often more defensible.

A lateral BHA should generally be evaluated against other comparable lateral intervals.

A curve BHA should be evaluated with consideration for the planned build geometry.

This also connects to the distinction between:

• planned tortuosity,
• as-drilled tortuosity,
• and unplanned tortuosity.

A well that intentionally builds at a high rate is geometrically curved.

That does not mean the directional execution was poor.

The useful metric depends on the engineering question being asked.

Tortuosity Should Be a Controlled KPI, Not Just a Calculated Column

Once a tortuosity function exists in software, it is easy to calculate the value for every well in a database.

That can create a false sense of comparability.

A more defensible analytics workflow should store supporting information with the metric, including:

• section analyzed,
• survey source,
• median survey interval,
• minimum and maximum interval,
• interval variability,
• whether the data were resampled,
• resampling method,
• whether the survey is conventional or high resolution,
• and the tortuosity formulation used.

Then the tortuosity number has provenance.

Without that information, a fleet-wide ranking can accidentally become a ranking of survey practices rather than just wellbore quality.

DrillingMetrics tortuosity views compare unplanned-curvature index across wells and depth.

When Should Surveys Be Resampled?

There is no universal rule that every trajectory must be resampled.

The source study actually argues against unnecessary resampling in sections that already have reasonably consistent survey intervals.[1]

A practical decision process might be:

1. Inspect the raw interval distribution

Do not begin with the average.

Plot or summarize the actual spacing between stations.

2. Define the section being compared

Whole-well comparisons may mix very different survey practices and planned geometries.

3. Determine whether interval inconsistency is material

Small differences may have little practical effect.

Large differences between sections or wells deserve more attention.

4. Preserve genuine measurements where possible

Do not replace measured survey points with interpolated values merely to make the table aesthetically uniform.

5. If downsampling is necessary, downsample the higher-resolution dataset

This at least creates a comparison in which both datasets contain similar levels of geometric information.

It does not recover information missing from the lower-resolution survey.

6. Document the transformation

A tortuosity value calculated from the original survey and one calculated after normalization should not silently overwrite each other.

The processing history matters.

The Same Problem Appears in Many Drilling Metrics

The larger lesson is not limited to tortuosity.

Drilling engineers routinely compare metrics generated from datasets with different:

• sampling frequencies,
• averaging windows,
• sensor quality,
• filtering methods,
• depth increments,
• state-classification rules,
• and reporting practices.

Examples include:

• ROP,
• connection times,
• vibration indices,
• MSE,
• torque variability,
• trip speeds,
• and dysfunction statistics.

Whenever a KPI changes, there are two possibilities:

1. the physical drilling performance changed,
2. the measurement or processing method changed.

Sometimes both changed.

Tortuosity provides an unusually clear demonstration because we can hold the physical path conceptually fixed and change only the sampling interval.

That makes the analytical problem easy to see.

Use Tortuosity to Ask Better Questions

The conclusion should not be that tortuosity is unreliable.

The opposite is more useful.

Tortuosity can add an important dimension to BHA and directional performance analysis that ROP alone cannot provide.

SPE-196020 used tortuosity across a historical database of more than 300 BHA runs and found relationships between wellbore quality, ROP, BHA characteristics, and other operational metadata.[1]

But for those comparisons to be meaningful, the measurement basis needs to be understood.

The strongest use of tortuosity is therefore not:

BHA A has TI = 18 and BHA B has TI = 22, so BHA A is better.

It is:

After controlling for trajectory section, planned geometry, survey resolution and interval consistency, does BHA A repeatedly produce lower unplanned tortuosity than comparable alternatives?

That is a much stronger engineering question.

And it leads to a broader rule for drilling analytics:

Before comparing the answer produced by a metric, make sure you are comparing the information that went into the metric on a consistent basis.

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References

1. Shahri, M., James, M., Vasicek, A., De Napoli, R., White, M., Behounek, M., D'Angelo, J., Ashok, P., and van Oort, E. Case Studies: Optimizing BHA Performance by Leveraging Data and Advanced Modeling. SPE-196020-MS, SPE Annual Technical Conference and Exhibition, Calgary, Alberta, Canada, 2019.

Additional papers referenced in SPE-196020

2. D'Angelo, J., Ashok, P., van Oort, E., Shahri, M., Thetford, T., Nelson, B., et al. Unplanned Tortuosity Index: Separating Directional Drilling Performance from Planned Well Geometry. SPE-194099-MS, 2019.

3. Gaynor, T., Hamer, D., Chen, D. C.-K., and Stuart, D. Quantifying Tortuosities by Friction Factors in Torque and Drag Model. SPE-77617-MS, 2002.

4. Chen, D. C.-K., Gaynor, T., and Comeaux, B. Hole Quality: Why It Matters. SPE-74403-MS, 2002.