Directional Drilling Fundamentals and Engineering Applications

Definition and Fundamentals of Directional Drilling

• Directional Wells: Defined as wells that are intentionally deviated from a vertical path to reach a specific subsurface target that cannot be accessed by drilling straight down.
• Methodology: Engineers control the wellbore’s direction and inclination to ensure the well intersects the reservoir at a planned location rather than drilling strictly vertically.
• Target Parameters: A predefined target is represented by two primary angles:     * Inclination Angle: The angle between the wellbore axis and the vertical.     * Azimuth (Direction Angle): Measured in the horizontal plane, corrected for True North.

Reasons for Drilling Directional Wells

• Side-tracking Existing Wells: Necessary due to hole problems, the presence of “fish” (lost equipment), or to reach new targets from an existing wellbore.
• Restricted Surface Locations: Used when the ideal surface location is unavailable due to topography or obstacles.
• Multiple Targets: Drilling one well to intercept several reservoir targets.
• Offshore Operations: To reduce the number of offshore platforms required by drilling multiple wells from a single site.
• Horizontal Drilling: To reach thin reservoirs using horizontal or multilateral drilling techniques.
• Environmental Footprint: Minimizing surface disturbance in sensitive areas.
• Salt Dome Drilling: Directing the well away from salt domes to avoid casing collapse problems associated with salt movement.
• Geological Requirements: To avoid gas or water coning problems and for intersecting specific fracture networks.
• Re-entering Existing Wells: Utilizing existing infrastructure for new production zones.
• Gas and Water Coning:     * Definition: A production problem in oil wells where unwanted fluids (gas or water) move toward the wellbore and are produced alongside oil.     * Mechanism: Occurs when the pressure drawdown near the well is too high, pulling gas or water toward the well faster than gravity causes them to settle.

Well Classification Systems

• Vertical Well: Wells with less than $10^{\circ}$ deviation from the vertical.
• High Inclination Well: Wells with an inclination between $60^{\circ}$ and $85^{\circ}$.
• Horizontal Well: Wells with more than $85^{\circ}$ deviation.
• Extended Reach Well: Wells where the Ratio of Horizontal Displacement to True Vertical Depth (TVD) is greater than $2.5$.
• Designer Well: Wells with a significant turn in the horizontal plane (ranging from $30^{\circ}$ to $180^{\circ}$) where the turn is not restricted by inclination.

Well Geographical Coordinates and Formats

• Reference Points: Coordinates are referenced to the wellhead for single wells or the central platform for offshore operations.
• Decimal Degrees (DD) Format: Represented as decimal numbers (e.g., Latitude: $48.858370^{\circ}$, Longitude: $2.294481^{\circ}$). This is the standard for modern digital applications.
• Degrees Minutes Seconds (DMS) Format: The traditional navigation format (e.g., $48^{\circ}51'30.1'' ext{N}$, $2^{\circ}17'40.1'' ext{E}$).     * Degrees: Whole number.     * Minutes: Whole number ranging from $0$ to $59$.     * Seconds: Decimal number ranging from $0$ to $59.999$.     * Direction: North/South for latitude, East/West for longitude.
• Conversion Formula: $\text{Decimal Degrees (DD)} = \text{Degrees} + (\frac{\text{Minutes}}{60}) + (\frac{\text{Seconds}}{3600})$.
• Standard System: The Global Positioning System (GPS) utilizes the World Geodetic System (WGS84) as the reference coordinate system.

Reference Systems for Well Planning

• Measured Depth (MD): The distance measured along the actual well path from a reference point to the survey point.
• True Vertical Depth (TVD): The vertical distance measured from a reference point (usually the rotary table or mean sea level) to the survey point.
• Inclination Reference: The angle formed between the wellbore axis and the vertical.
• Toolface: The angular orientation of a drilling tool relative to a fixed reference frame, typically expressed in degrees from a north reference point.
• Azimuth (Direction Angle): Measured in degrees from North ($0^{\circ}$) continuing clockwise to $360^{\circ}$ within the horizontal plane.     * Magnetic North: Measured via a magnetic compass; however, it is inconsistent due to the movement of magnetic poles and local field variations.     * True/Grid North: Although initial surveys with magnetic tools use Magnetic North, final coordinates are converted to True or Grid North.     * Gyroscopes: Used to measure azimuth because they maintain a preset direction independent of magnetic fields or outside disturbances.
• Magnetic Declination:     * The angle in degrees between True North and Magnetic North.     * Negative Declination: Magnetic North lies West of True North.     * Positive Declination: Magnetic North lies East of True North.     * Formula: $\text{True North} = \text{Magnetic North} \pm (\text{Declination})$.

Directional Well Trajectory and Profiles

• Kick Off Point (KOP): The point below the surface where the well is first deflected from the vertical trajectory. Its position depends on geology, well geometry, and the proximity of other wells.
• Build Up Rate (BUR) and Drop Off Rate (DOR):     * Conventional Range: $1.50^{\circ}$ to $3.0^{\circ}$ per $100\,\text{feet}$.     * High Rates: Used for horizontal and multilateral wells.     * Limitations: Determined by total depth, torque and drag limits, mechanical limits of drill strings or casing, and limitations of logging/production tools.
• Primary Well Profiles:     * Type I (Build and Hold): Consists of a KOP, one build-up section, and a tangent section leading to the target.     * Type II (S-Shape / Build-Hold and Drop): Consists of a vertical section, KOP, build-up section, tangent section, drop-off section, and a hold section to target.     * Type III (Deep Kick Off / Continuous Build): Consists of a vertical section, a deep KOP, and a build-up section directly to the target.     * Horizontal Profile: Can incorporate any of the above profiles plus a horizontal section (usually drilled at $90^{\circ}$) within the reservoir.

Survey Calculation Methods

• Tangential Method:     * Assumes the well path follows a straight line with constant inclination and azimuth equal to those measured at the lower survey station.     * Pros/Cons: Easy for quick calculations but results in greater lateral displacement and less vertical displacement error.     * Equations:         * $\Delta\text{VD} = \Delta\text{MD} \times \cos(I_2)$         * $\Delta\text{HD} = \Delta\text{MD} \times \sin(I_2)$         * $\Delta\text{E} = \Delta\text{HD} \times \sin(A_2) = \Delta\text{MD} \times \sin(I_2) \times \sin(A_2)$         * $\Delta\text{N} = \Delta\text{HD} \times \cos(A_2) = \Delta\text{MD} \times \sin(I_2) \times \cos(A_2)$
• Balanced Tangential Method:     * Uses measured angles at both the top and bottom of the course to create a smoother wellbore profile.     * Equations:         * $\Delta\text{HD} = (\frac{\Delta\text{MD}}{2}) \times (\sin(I_1) + \sin(I_2))$         * $\Delta\text{VD} = (\frac{\Delta\text{MD}}{2}) \times (\cos(I_1) + \cos(I_2))$         * $\Delta\text{N} = (\frac{\Delta\text{MD}}{2}) \times (\sin(I_1) \times \cos(A_1) + \sin(I_2) \times \cos(A_2))$         * $\Delta\text{E} = (\frac{\Delta\text{MD}}{2}) \times (\sin(I_1) \times \sin(A_1) + \sin(I_2) \times \sin(A_2))$
• Angle Averaging Method:     * Inclination angles ($I_1, I_2$) and direction angles ($A_1, A_2$) are simplified by averaging.     * Equations:         * $\Delta\text{VD} = \Delta\text{MD} \times \cos(\frac{I_1 + I_2}{2})$         * $\Delta\text{HD} = \Delta\text{MD} \times \sin(\frac{I_1 + I_2}{2})$         * $\Delta\text{N} = \Delta\text{MD} \times \sin(\frac{I_1 + I_2}{2}) \times \cos(\frac{A_1 + A_2}{2})$         * $\Delta\text{E} = \Delta\text{MD} \times \sin(\frac{I_1 + I_2}{2}) \times \sin(\frac{A_1 + A_2}{2})$
• Radius of Curvature Method:     * The well path is generated as a space curve with a spherical arc shape.     * Equations for Departure (AD): $\Delta\text{D} = \frac{360 \times \Delta\text{MD}}{2 \times \pi \times (I_2 - I_1)} \times (\cos(I_1) - \cos(I_2))$     * Equations for Northing (AN): $\Delta\text{N} = \frac{360 \times \Delta\text{MD} \times (\cos(I_1) - \cos(I_2)) \times (\sin(A_2) - \sin(A_1))}{4 \times \pi^2 \times (A_2 - A_1) \times (I_2 - I_1)}$
• Minimum Curvature Method:     * The most accurate method; it minimizes total curvature to produce a smooth circular arc using a Ratio Factor ($RF$).     * Dog-leg Angle (DL): $\cos(DL) = \cos(I_2 - I_1) - \sin(I_1) \times \sin(I_2) \times (1 - \cos(A_2 - A_1))$     * Ratio Factor (RF): $\text{RF} = (\frac{2}{\beta}) \times \tan(\frac{\beta}{2})$, where $\beta$ is the dog-leg angle in radians.

Dog-Leg Severity (DLS)

• Definition: Any sudden change in hole inclination and/or direction.
• Severity: Described as the dog-leg angle over a specified interval (typically $100\,\text{ft}$ or $10\,\text{m}$).
• Unit: $\text{degrees} / 100\,\text{ft}$.
• Consequences: Excessive DLS causes fatigue failure in drill pipe, drill collars, and tool joints.

MWD and LWD Technologies

• MWD (Measurement While Drilling):     * Known as the "Ears" of the operation.     * Provides real-time data on direction, inclination, and toolface orientation.     * Uses magnetometers and accelerometers within the Bottom Hole Assembly (BHA).
• LWD (Logging While Drilling):     * Known as the "Eyes" of the operation.     * Measures petrophysical properties: porosity, hydrocarbon saturation, and resistivity.     * Enables Geosteering: Drilling a horizontal or deviated well based on real-time geologic and reservoir data to optimize the path within the target zone.
• Operational Benefits: LWD provides a real-time log, often replacing the need for separate wireline logs. Tools are primarily constrained by high temperatures (causing circuit malfunction) and extreme doglegs.

Operational Challenges and Advances

• Borehole Geometry Control: Difficulty in maintaining the planned trajectory can lead to missing the target or collision with adjacent wells.
• Key Seating: Occurs when the drill string rubs one side of the borehole, cutting a groove. This leads to the pipe getting stuck and difficulty pulling out.
• Wellbore Instability: Caused by weak shale, incorrect mud weight, or stress redistribution. Results in hole collapse, tight spots, or lost circulation.
• Differential Sticking: High mud pressure pushes the pipe against permeable rock, making rotation or pulling impossible.     * Backing Off: If the pipe remains stuck, a section is unscrewed and abandoned.
• Fishing Operations: The use of special tools to retrieve broken or lost equipment from the wellbore; very time-consuming and risky.
• Recent Advances:     * Extended Reach Drilling (ERD): Extremely long horizontal distances to access remote reserves from one surface location.     * Slant Hole Drilling: Starting the well at an angle from the surface.     * Plasma Drilling: Non-mechanical technology using hot plasma to fracture/melt rock. No bit wear, faster penetration, and suitable for ultra-hard formations.     * Laser Drilling: Experimental technology using high-power laser beams to vaporize rock, resulting in a smooth wellbore and reduced fluid use.