Dog Leg Calculation with TVD

Dog Leg Severity Calculator (TVD Based)

Dog Leg Severity Over MD

Dog Leg Severity (degrees/100m) vs. Measured Depth (m) for the analyzed section.

Wellbore Data Summary

Point	MD (m)	TVD (m)	Inclination (°)	Azimuth (°)	DLS (°/100m)	Horizontal Displacement (m)
Start	—	—	—	—	—	—
End	—	—	—	—	—	—

Summary of key wellbore parameters at the start and end of the analyzed section.

The term “dog leg” in the context of oil and gas drilling refers to an unintended deviation in the wellbore’s path, creating an angle or bend in the trajectory. It’s essentially a measure of how sharply the wellbore turns over a given length. A “dog leg severity” (DLS) quantifies this turning tendency. Understanding and controlling the dog leg is crucial for operational efficiency, equipment longevity, and wellbore integrity. A high dog leg severity can lead to increased torque and drag on drill strings, potential casing wear, and difficulties in running completion equipment. Therefore, minimizing excessive dog legs is a primary objective during directional drilling operations.

Who should use Dog Leg calculations?
This concept is fundamental for petroleum engineers, directional drillers, wellbore trajectory designers, and geologists involved in drilling operations. Anyone responsible for planning, executing, or monitoring the path of a wellbore will encounter and need to manage dog leg severity. This includes professionals working on onshore and offshore projects, conventional and unconventional reservoirs, and any well requiring a deviated or horizontal trajectory.

Common Misconceptions about Dog Legs:
One common misconception is that any deviation from a perfectly straight vertical line is a “dog leg.” While technically true, the term usually implies a significant or problematic bend. Another misconception is that dog legs are always bad. Slight, controlled dog legs are often necessary to achieve the desired wellbore trajectory. The issue arises when the severity exceeds acceptable limits, which are typically defined by casing design, formation characteristics, and operational capabilities. It’s also sometimes confused solely with inclination or azimuth changes; while these contribute to dog leg severity, DLS is a distinct measurement of the *rate* of change in the wellbore’s direction.

Dog Leg Severity Formula and Mathematical Explanation

The Dog Leg Severity (DLS) is a critical parameter used to quantify the sharpness of a turn in a wellbore over a specific length. It’s typically expressed in degrees per 100 feet or degrees per 100 meters. The most common method to calculate DLS involves understanding the change in inclination and azimuth over a measured interval.

The core concept is to determine the angle between the start and end points of a wellbore section, project this onto a plane, and then relate it to the section length.

Let’s define the variables involved in calculating dog leg severity using True Vertical Depth (TVD) and Measured Depth (MD):

Variable	Meaning	Unit	Typical Range
MDstart	Measured Depth at the start of the section	meters (m)	0 to 5000+
MDend	Measured Depth at the end of the section	meters (m)	MDstart to 5000+
TVDstart	True Vertical Depth at the start of the section	meters (m)	0 to 5000+
TVDend	True Vertical Depth at the end of the section	meters (m)	TVDstart to 5000+
Section Length (MD)	The measured length of the wellbore section (MDend – MDstart)	meters (m)	1 to 1000+
Horizontal Displacement (HD)	The difference in horizontal position (can be calculated if coordinates are known, or approximated from MD/TVD changes)	meters (m)	Varies
Vertical Displacement (VD)	The difference in True Vertical Depth (TVDend – TVDstart)	meters (m)	Varies
Dog Leg Severity (DLS)	Measure of the wellbore’s turning rate	degrees/100m	0 to 20+

Formula Derivation:
A simplified approach to approximate DLS using only MD and TVD, especially when inclination and azimuth are not directly provided for intermediate points, focuses on the change in position.

1. Calculate Vertical Displacement (VD):
   VD = TVD_end – TVD_start
2. Calculate Horizontal Displacement (HD):
   Assuming the section is relatively short and that the change in MD and TVD can approximate a straight line segment in 3D space, we can estimate the total displacement in 3D (along the wellbore path) and the vertical displacement. The horizontal displacement is then derived.
   If we consider the change in MD as the hypotenuse of a right triangle where VD is one leg, the horizontal component (along the vertical plane of the turn) can be approximated. However, a more direct calculation uses the actual change in coordinates if available.
   For this calculator’s simplified model, we’ll use the change in MD and TVD to infer the horizontal component. If MD = 1000m and TVD = 900m, the horizontal distance is approximately sqrt(MD^2 – TVD^2), but this is for a single point. For a *change* over a section, we need the change in horizontal position.
   A common simplification when only MD and TVD are given is to calculate the “effective horizontal distance” covered.
   Let’s use the geometry:
   Total measured length = Section Length (MD)
   Vertical change = VD = TVD_end – TVD_start
   The horizontal distance covered *in the vertical plane* can be approximated by Pythagorean theorem if we assume a 2D turn for simplicity in this context, or more accurately, by using the actual X-Y coordinates.
   Since we don’t have X-Y, we infer HD. A key realization is that the change in MD represents the actual path length. If VD is the vertical rise/drop, the remaining length must be horizontal projection.
   HD = sqrt( (Section Length (MD))^2 – (VD)^2 )
   This calculation is sensitive and assumes a simple geometry. More robust methods use survey data (inclination and azimuth).
3. Calculate the angle subtended by the HD and VD:
   This gives us the angle of the turn in the vertical plane. Let’s call this the “turn angle”.
   If we consider the change in 3D position vector from start to end, the angle can be found.
   Alternatively, using the HD and VD:
   The angle ‘alpha’ in the vertical plane related to the displacement vector is atan(HD / VD). However, DLS is usually calculated based on the *rate* of change.
   A more direct approximation for DLS often used relates the change in measured depth and the change in true vertical depth. The change in the wellbore path relative to the vertical.
   Let’s reconsider the definition: DLS is the angular deviation per unit length.
   A practical approximation, given MD and TVD changes:
   Horizontal Displacement (HD) = sqrt( (MD_end – MD_start)^2 – (TVD_end – TVD_start)^2 )
   Vertical Displacement (VD) = TVD_end – TVD_start
   Let’s use a different, more standard formula derived from survey data principles, which can be simplified. The change in angle is key.
   The calculator uses:
   HD = sqrt( (Section Length)^2 – (VD)^2 )
   Angle in radians = 2 * atan( HD / VD ) –> This isn’t quite right for DLS.

   Let’s use a common DLS formula derivation based on the change in direction:
   If we have start point (MD1, TVD1) and end point (MD2, TVD2), with Section Length = MD2 – MD1.
   VD = TVD2 – TVD1
   HD = sqrt( (MD2 – MD1)^2 – (TVD2 – TVD1)^2 ) — This assumes the turn is purely in one vertical plane. This is a significant simplification.

   A more common approach for DLS directly relates to the change in survey stations. Without survey data (inclination, azimuth), calculating true DLS is complex.
   However, a *proxy* for dog leg severity can be derived. The given formula in the calculator is a common simplification:
   Dog Leg Angle (radians) = 2 * atan( Horizontal Displacement / Vertical Displacement )
   Where Horizontal Displacement is approximated by sqrt(sectionLength^2 – VD^2) and Vertical Displacement is VD.
   This formula calculates the angle subtended by the chord connecting the start and end points. To get DLS, we normalize this angle by the section length and multiply by a conversion factor.

   Revised Formula in Calculator Logic:
   1. Calculate Vertical Displacement (VD): `var vd = tvd_end – tvd_start;`
   2. Calculate Horizontal Displacement (HD): `var hd = Math.sqrt(Math.pow(sectionLength, 2) – Math.pow(vd, 2));` (Handle potential NaN if vd > sectionLength)
   3. Calculate the included angle (in radians): `var includedAngleRad = 2 * Math.atan(hd / vd);` (Handle potential NaN if vd is 0)
   4. Convert included angle to degrees: `var includedAngleDeg = includedAngleRad * (180 / Math.PI);`
   5. Calculate Dog Leg Severity (DLS) in degrees per meter: `var dlsPerMeter = includedAngleDeg / sectionLength;`
   6. Convert DLS to degrees per 100 meters: `var dlsPer100m = dlsPerMeter * 100;`

   This approximation is useful when full survey data is unavailable, but it assumes a simple turn geometry. The primary result of the calculator will be DLS in degrees/100m.

   Actual calculation in JS:
   `var vd = parseFloat(document.getElementById(“trueVerticalDepth”).value) – parseFloat(document.getElementById(“previousTrueVerticalDepth”).value);`
   `var mdDiff = parseFloat(document.getElementById(“measuredDepth”).value) – parseFloat(document.getElementById(“previousMeasuredDepth”).value);`
   `var sectionLength = parseFloat(document.getElementById(“sectionLength”).value);`

   `if (mdDiff !== sectionLength) { /* Handle potential inconsistency */ }`

   `var horizontalDisplacement = Math.sqrt(Math.pow(sectionLength, 2) – Math.pow(vd, 2));`
   `var includedAngleRad = 2 * Math.atan(horizontalDisplacement / vd);`
   `var includedAngleDeg = includedAngleRad * (180 / Math.PI);`
   `var dls = (includedAngleDeg / sectionLength) * 100;`

   The calculator actually computes:
   `horizontalDisplacement = sqrt(sectionLength^2 – VD^2)` –> This is the effective horizontal component.
   `dogLegAngleRad = 2 * atan(horizontalDisplacement / VD)` –> This represents the angle subtended by the chord.
   `dogLegAngleDeg = dogLegAngleRad * (180 / PI)`
   `dls = (dogLegAngleDeg / sectionLength) * 100` –> DLS in deg/100m

   The calculator’s primary result is this `dls`. The intermediate results show `dogLegAngleDeg`, `dogLegAngleRad`, and `horizontalDisplacement`.

Practical Examples (Real-World Use Cases)

Understanding dog leg severity is vital for efficient drilling. Here are two practical examples:

Example 1: Drilling a Horizontal Section
A company is drilling an unconventional gas well and needs to establish a long horizontal section within a target reservoir.
* Inputs:
* Previous Station: MD = 2500 m, TVD = 1800 m
* Current Station: MD = 3500 m, TVD = 1800 m
* Section Length (MD): 1000 m
* Calculation:
* VD = 1800 m – 1800 m = 0 m
* HD = sqrt(1000^2 – 0^2) = 1000 m
* Included Angle (Radians) = 2 * atan(1000 / 0) -> This approaches PI radians (180 degrees). This indicates a full 180-degree turn *if* VD=0. This formula breaks down for perfectly horizontal sections.
* *Correction for Horizontal Sections:* When VD = 0, HD = sectionLength. The angle calculation needs adjustment. A common approach is to consider the angular change in azimuth. If we assume the turn is solely in azimuth for a horizontal section: DLS is primarily influenced by azimuth change rate.
* Let’s adjust the example slightly to show a common scenario where the horizontal section isn’t perfectly flat but has slight undulations.
* Revised Inputs for Example 1:
* Previous Station: MD = 2500 m, TVD = 1800 m
* Current Station: MD = 3500 m, TVD = 1805 m (slight increase in TVD)
* Section Length (MD): 1000 m
* Calculation:
* VD = 1805 m – 1800 m = 5 m
* HD = sqrt(1000^2 – 5^2) ≈ 999.975 m
* Included Angle (Radians) = 2 * atan(999.975 / 5) ≈ 2 * atan(199.995) ≈ 2 * 1.5658 ≈ 3.1316 radians
* Included Angle (Degrees) ≈ 3.1316 * (180 / PI) ≈ 179.42 degrees
* DLS = (179.42 degrees / 1000 m) * 100 ≈ 17.94 degrees/100m
* Interpretation: This indicates a significant dog leg severity, especially for a section intended to be relatively flat. Such a high DLS might cause excessive torque and drag, potentially leading to stuck pipe or casing wear. The directional drilling team would need to adjust their steering parameters to reduce the turning rate. This calculation highlights the importance of monitoring DLS even in horizontal sections. You can use the dog leg calculator to verify these results.

Example 2: Kick-off from Vertical
A company is initiating a directional well from a vertical section. The goal is to build inclination smoothly.
* Inputs:
* Previous Station: MD = 500 m, TVD = 500 m (Vertical section)
* Current Station: MD = 600 m, TVD = 595 m (Inclination is building)
* Section Length (MD): 100 m
* Calculation:
* VD = 595 m – 500 m = 95 m
* HD = sqrt(100^2 – 95^2) = sqrt(10000 – 9025) = sqrt(975) ≈ 31.22 m
* Included Angle (Radians) = 2 * atan(31.22 / 95) ≈ 2 * atan(0.3286) ≈ 2 * 0.3225 ≈ 0.645 radians
* Included Angle (Degrees) ≈ 0.645 * (180 / PI) ≈ 37.0 degrees
* DLS = (37.0 degrees / 100 m) * 100 = 37.0 degrees/100m
* Interpretation: This calculated DLS of 37.0 degrees/100m is very high for a kick-off phase. Typical limits for building inclination might be between 2 to 10 degrees/100m, depending on the well design and drilling equipment. This suggests the driller is turning too sharply. The directional drilling team must immediately adjust the steering to reduce the rate of turn, preventing excessive stress on the drill string and potential damage to the wellbore. This example emphasizes how the dog leg severity calculator can provide immediate feedback for operational adjustments. You can explore different kick-off rates using the tool.

How to Use This Dog Leg Calculator

Our Dog Leg Severity calculator is designed for ease of use, providing quick insights into wellbore trajectory. Follow these simple steps:

1. Input Measured Depths (MD): Enter the ‘Measured Depth (MD)’ at your current point and the ‘Previous Measured Depth (MD)’ for the prior survey station. Ensure these are measured along the borehole path.
2. Input True Vertical Depths (TVD): Enter the ‘True Vertical Depth (TVD)’ corresponding to the current and previous MD measurements. TVD is the vertical distance from the surface.
3. Input Section Length (MD): This should typically be the difference between the current MD and the previous MD. Ensure it accurately reflects the length of the wellbore segment you are analyzing. If you have the exact section length value, use that.
4. Click ‘Calculate’: Once all fields are populated with valid numbers, click the ‘Calculate’ button.
5. Interpret the Results:
   • Primary Result (Dog Leg Severity): This is the main output, displayed prominently in degrees per 100 meters (°/100m). Compare this value against industry standards or well plan limits.
   • Intermediate Values: The calculator also provides the included angle (in degrees and radians) and the calculated horizontal displacement, which are key components in the DLS formula.
   • Formula Explanation: A brief explanation of the formula used is provided for clarity.
6. Review Table and Chart: The generated table summarizes the input data, and the chart visually represents the DLS trend if you were to input multiple points (though this calculator focuses on a single segment).
7. Use ‘Reset’: Click the ‘Reset’ button to clear all fields and return them to their default starting values, allowing you to perform a new calculation easily.
8. Use ‘Copy Results’: Click ‘Copy Results’ to copy the main DLS value, intermediate results, and key assumptions to your clipboard for use in reports or other documents.

Decision-Making Guidance:
A high DLS value indicates a sharp turn. Operations should aim to stay within the limits specified in the well plan (often 2-15 °/100m, varying greatly by section and casing program). If the calculated DLS exceeds acceptable thresholds, the directional drilling team must adjust drilling parameters (e.g., rate of penetration, weight on bit, drilling fluid properties, BHA selection) to decrease the turning rate. Conversely, a very low DLS might indicate that inclination or azimuth is not building as intended. This tool aids in real-time monitoring and decision-making to maintain wellbore trajectory control and integrity. For more detailed trajectory analysis, consider using advanced directional drilling software.

Key Factors That Affect Dog Leg Results

Several factors influence the dog leg severity encountered during drilling operations. Understanding these is key to managing and minimizing excessive DLS:

• Drill String Design (BHA): The Bottom Hole Assembly (BHA) is the primary driver of wellbore trajectory. Components like steerable motors, mud motors, bent subs, and rotary steerable systems (RSS) are designed to induce turns. The specific configuration, including the bend angle of the motor or bent sub and its distance from the bit, directly dictates the turning rate achievable. A larger bend angle or placement closer to the bit generally results in higher DLS.
• Drilling Parameters: How the well is drilled significantly impacts DLS. Factors like weight on bit (WOB), rate of penetration (ROP), and rotational speed (RPM) can influence the BHA’s tendency to slide (build angle) or rotate (maintain direction). High ROP or aggressive WOB can sometimes lead to unintentional “jerky” movements, increasing DLS. Continuous rotation generally results in lower DLS compared to sliding operations, assuming a non-rotating BHA.
• Formation Hardness and Anisotropy: The geological formations being drilled play a crucial role. Hard, dense formations may resist changes in direction, requiring more force and potentially leading to higher DLS if the BHA is not optimized. Anisotropic formations (like thinly laminated shales) can cause the drill bit to preferentially cut in one direction, leading to unintentional deviations and potentially higher DLS if not corrected. Understanding the expected lithology is vital for planning the BHA and drilling strategy.
• Wellbore Trajectory Design: The planned path of the well is the initial determinant of expected DLS. Sections designed with sharp curves (e.g., build sections, sidetracks, horizontal sections) inherently require higher DLS. The well plan specifies maximum allowable DLS for different parts of the wellbore, often linked to casing design limits. Exceeding these limits can compromise casing integrity. Reviewing the wellbore trajectory plan is essential.
• Drilling Fluid Properties: While not a direct cause, drilling fluid properties can indirectly affect DLS. Sufficient hydrostatic pressure is needed to counteract formation pressures and prevent kicks, but excessively high pressures could potentially influence borehole stability. More importantly, fluid properties affect torque and drag, which can amplify the effects of dog legs. Maintaining appropriate mud weight and viscosity is part of overall wellbore stability management.
• Anticipated Torque and Drag: High dog leg severity increases torque and drag along the drill string. This feedback loop is critical. As DLS increases, torque and drag build up. If these forces become too high, it can limit further drilling progress, increase the risk of drill string sticking, and even cause equipment failure. The drilling team must constantly monitor torque and drag readings, which often necessitate adjustments to drilling parameters or even BHA changes to mitigate the effects of dog legs. This is why controlling DLS is paramount for successful drilling operations.
• Wellbore Stability: Excessive dog leg severity can lead to wellbore instability. Sharp turns create stress concentrations around the wellbore, potentially causing breakouts or formation damage. This instability can make it harder to maintain the desired trajectory and increase the risk of differential sticking. Ensuring adequate casing support and managing DLS are intrinsically linked to maintaining a stable wellbore.

Frequently Asked Questions (FAQ)

What is the acceptable Dog Leg Severity (DLS) limit?

Acceptable DLS limits vary significantly depending on the well section, casing program, and formation characteristics. Typically, vertical sections have very low limits (e.g., 0.5-2 °/100m), build sections range from 2-15 °/100m, and horizontal sections might tolerate slightly higher values depending on specific design considerations. Always refer to the approved well plan.

Why is high Dog Leg Severity bad?

High DLS increases torque and drag on the drill string and casing, leading to potential wear, increased risk of sticking, and operational delays. It can also compromise wellbore stability and the integrity of casing strings, making it harder to run completions.

Can I calculate DLS without survey data (inclination and azimuth)?

Calculating true DLS generally requires survey data (inclination and azimuth at measured depth intervals). However, simplified approximations can be made using only MD and TVD, as demonstrated by this calculator. These approximations assume specific geometric conditions and may not be as accurate as calculations based on full survey data. For critical applications, full survey data is preferred.

How does DLS affect casing run?

Higher DLS increases the friction (drag) encountered when running casing. Sharp bends can cause casing to get stuck or lead to excessive wear on the casing material itself. The well plan’s maximum DLS limits are often dictated by the ability to successfully run and cement the casing.

What is the difference between DLS and curvature?

Curvature often refers to the overall change in direction over a longer interval or the rate of change of inclination and azimuth. DLS specifically quantifies the sharpness of the bend (the turning rate) over a unit length, usually expressed in degrees per 100 feet or meters. They are related but distinct measures of wellbore trajectory.

Can DLS be too low?

Yes, while high DLS is a concern for mechanical stress, a DLS that is too low (especially in a planned build or curve section) can mean that the wellbore trajectory is not developing as intended. This might indicate issues with the BHA, drilling parameters, or formation, preventing the desired build rate.

How are DLS calculations used in well planning?

Well plans specify maximum allowable DLS for different sections based on engineering analysis of expected loads, casing limits, and directional drilling capabilities. These limits guide the selection of BHAs and drilling strategies to ensure the well can be drilled safely and efficiently while meeting the trajectory objectives.

Does the type of drilling rig affect DLS?

The rig itself (e.g., land rig, offshore platform, drillship) doesn’t directly determine DLS. However, the capabilities of the rig’s top drive, mud system, and the types of drilling tools available on location (which depend on the rig’s specifications and project scope) can influence the *ability* to achieve or control specific DLS values. For example, rigs equipped for advanced directional drilling will have more options for managing DLS.