True vertical depth
True vertical depth (TVD) refers to the perpendicular vertical distance from a reference point at the surface—often the wellhead or mean sea level—to a specific point along the wellbore in drilling operations.[1] This measurement is essential in the oil and gas industry, where wells are frequently deviated or horizontal rather than straight vertical paths, distinguishing it from measured depth (MD), which represents the actual length of the wellbore along its trajectory and is always greater than TVD due to curvature.[2] TVD is typically calculated using directional survey data to account for the well's inclination and azimuth, ensuring accurate assessments of subsurface positions.[3] In practical applications, TVD plays a critical role in various drilling and reservoir engineering calculations, such as determining hydrostatic pressure, estimating formation temperatures, and evaluating kill weight mud requirements for well control.[2] It is often expressed as TVDSS (true vertical depth subsea) when referenced to sea level, which is particularly useful for offshore operations and comparing depths across different wells or fields.[3] Unlike MD, which is used for volume computations like annular or drill string capacities, TVD provides a standardized vertical metric that aligns with geological strata and pressure gradients, facilitating precise formation evaluation and seismic correlations.[1] Accurate TVD determination is vital for safety and efficiency, as errors can lead to miscalculations in drilling fluids and blowout prevention strategies.[2]Fundamentals
Definition
True vertical depth (TVD) is defined as the straight-line vertical distance from a fixed reference point at the surface, such as ground level or the kelly bushing, to a subsurface point, measured perpendicular to the Earth's surface or a horizontal plane.[1][3] This measurement captures the pure vertical component without regard to any horizontal displacement.[2] TVD plays a critical role in representing the actual geological depth of formations and targets, remaining independent of the wellbore's trajectory or inclination.[4] This independence ensures that TVD provides a standardized vertical reference for correlating subsurface data across different wells, facilitating accurate geological interpretation and resource evaluation.[1] In contrast to measured depth, which tracks the total length along the borehole path, TVD focuses solely on the vertical dimension.[2] The concept of TVD emerged in the early 20th century alongside the development of directional drilling techniques in oil exploration, addressing the need to standardize depth reporting for deviated or slanted wells beyond traditional vertical drilling.[5] Prior to this, depth measurements in straight wells equated measured and vertical depths, but increasing well deviations in the 1920s necessitated distinct vertical metrics for reliable subsurface mapping.[5] TVD is typically expressed in units of feet in the United States or meters internationally, aligning with prevailing engineering and geological standards in the petroleum industry.[2][1]Relation to Measured Depth
Measured depth (MD) refers to the total length of the wellbore path from the surface location to a specific point of interest, accounting for all deviations, curves, and horizontal displacements along the trajectory.[2][6] In perfectly vertical wells, true vertical depth (TVD) is equivalent to MD, as the borehole follows a straight perpendicular path to the surface.[7] However, in deviated or horizontal wells, TVD is always less than or equal to MD because the actual path length incorporates inclined and lateral components that exceed the straight-line vertical distance.[7][6] For instance, a well with an MD of 10,000 ft drilled at a constant 45-degree inclination would have a TVD of approximately 7,071 ft, illustrating how deviation shortens the vertical component relative to the total path length.[6] The ratio of MD to TVD serves as a key metric for evaluating well tortuosity—the unintended undulations or excess curvature in the borehole—and overall drilling efficiency, with ratios exceeding 2:1 often indicating extended-reach conditions that amplify challenges like torque and drag.[8][9] Higher ratios highlight potential inefficiencies from path irregularities, guiding optimizations in trajectory planning.[8]Measurement and Calculation
Survey Methods
Survey methods for determining true vertical depth (TVD) in well operations primarily involve specialized tools that capture inclination and azimuth data at discrete points along the wellbore. These methods enable the derivation of TVD as the vertical component of the trajectory from measured depth.[10] Measurement while drilling (MWD) tools provide real-time trajectory information during active drilling. These systems integrate arrays of accelerometers to detect gravitational components, yielding precise inclination measurements, and magnetometers to sense magnetic fields for azimuth determination. The sensors are typically housed in non-magnetic drill collars to minimize interference, transmitting data via mud pulse telemetry or electromagnetic signals to the surface.[11][12] For post-drilling verification, wireline logging tools are deployed into the completed wellbore. These include multi-shot cameras or electronic survey instruments that record inclination and azimuth at multiple depths. In environments with significant magnetic interference, such as near casing or in areas with high drillstring magnetization, gyroscopic surveys are preferred for their independence from magnetic fields, offering high-accuracy inertial measurements using rate gyros or ring laser gyros.[13][14] The surveying process follows a standardized procedure: tools are positioned at survey stations spaced at regular intervals, commonly every 90 feet (27 meters), though denser intervals like every 30 feet may be used in complex trajectories. At each station, the drilling is paused, and the tool records inclination, azimuth, and toolface orientation relative to the high-side of the hole. Data from consecutive stations are then used to model the well path between points.[15][16] Several error sources can impact TVD accuracy in these surveys. Dogleg severity, representing abrupt changes in well direction, challenges the assumption of constant curvature between survey points, potentially leading to positional offsets. Magnetic interference from the drillstring or nearby steel structures distorts azimuth readings in MWD tools, while sag effects—caused by the gravitational bending of the bottom-hole assembly—introduce inclination errors. Typical TVD accuracy from standard MWD surveys achieves about ±0.5-1% of total depth after applying common corrections, though gyro methods can reduce this to under 0.1% in controlled conditions.[17][18][19]Mathematical Formulas
The computation of true vertical depth (TVD) in directional wells relies on survey data consisting of measured depth (MD), inclination (I), and azimuth (A) at discrete stations. The basic formula for incremental TVD assumes a straight-line path tangent to the borehole at the survey station, known as the tangential method:\Delta \text{TVD} = \Delta \text{MD} \times \cos I
where \Delta \text{MD} is the incremental measured depth between stations, and I is the inclination angle at the lower station in degrees.[20] This method is suitable for low-deviation wells but accumulates errors in highly deviated trajectories due to its assumption of constant inclination over the interval.[20] For more accurate calculations in deviated wells, the average angle method averages the inclination and azimuth at the upper and lower stations to approximate the path:
\Delta \text{TVD} = \Delta \text{MD} \times \cos \left( \frac{I_1 + I_2}{2} \right)
where I_1 and I_2 are the inclinations at the upper and lower stations, respectively.[20] This serves as a simple approximation for moderate deviations, improving on the tangential method by considering both endpoints.[21] The industry-standard minimum curvature method models the borehole path as a circular arc between survey stations, minimizing curvature assumptions and providing higher accuracy for complex trajectories. The incremental TVD is calculated as:
\Delta \text{TVD} = \frac{\Delta \text{MD}}{2} (\cos I_1 + \cos I_2) \times \text{RF}
where RF is the ratio factor, given by \text{RF} = \frac{2}{\delta} \tan \left( \frac{\delta}{2} \right), and \delta is the dogleg angle in radians. The dogleg severity (DLS), which quantifies trajectory change, is:
\text{DLS} = \frac{100 \times \acos \left( \cos I_1 \cos I_2 + \sin I_1 \sin I_2 \cos(A_2 - A_1) \right)}{\Delta \text{MD}}
in degrees per 100 ft, with A_1 and A_2 as azimuths at the upper and lower stations.[22] This method, originally developed by Craig and Randall, accumulates TVD iteratively from the surface by summing increments and is recommended for most applications. Software such as Halliburton Landmark's COMPASS implements these algorithms iteratively, incorporating minimum curvature for TVD computation along with anti-collision analysis and 3D visualization.[23]