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Petroleum Engineering Handbook
Larry W. Lake, Editor-in-Chief
Volume II - Drilling Engineering
Robert F. Mitchell, Editor
Copyright 2006, Society of Petroleum Engineers
Chapter 6 - Directional Drilling
Directional drilling is defined as the practice of controlling the direction and deviation of a wellbore to a predetermined underground target or location. This section describes why directional drilling is required, the sort of well paths that are used, and the tools and methods employed to drill those wells.
- Multiple wells from a single location. Field developments, particularly offshore and in the Arctic, involve drilling an optimum number of wells from a single platform or artificial island. Directional drilling has helped by greatly reducing the costs and environmental impact of this application.
- Inaccessible surface locations. A well is directionally drilled to reach a producing zone that is otherwise inaccessible with normal vertical-drilling practices. The location of a producing formation dictates the remote rig location and directional-well profile. Applications like this are where "extended-reach" wells are most commonly drilled.
- Multiple target zones. A very cost-effective way of delivering high production rates involves intersecting multiple targets with a single wellbore. There are certain cases in which the attitudes (bed dips) of the producing formations are such that the most economical approach is a directional well for a multiple completion. This is also applicable to multiple production zones adjacent to a fault plane or beneath a salt dome.
- Sidetrack. This technique may be employed either to drill around obstructions or to reposition the bottom of the wellbore for geological reasons. Drilling around obstructions, such as a lost string of pipe, is usually accomplished with a blind sidetrack. Oriented sidetrack is required if a certain direction is critical in locating an anticipated producing formation.
- Fault drilling. It is often difficult to drill a vertical well through a steeply inclined fault plane to reach an underlying hydrocarbon-bearing formation. Instead, the wellbore may be deflected perpendicular or parallel to the fault for better production. In unstable areas, a wellbore drilled through a fault zone could be at risk because of the possibility of slippage or movement along the fault. Formation pressures along fault planes may also affect hole conditions.
- Salt-dome exploration. Producing formations can be found under the hard, overhanging cap of salt domes. Drilling a vertical well through a salt dome increases the possibility of drilling problems, such as washouts, lost circulation, and corrosion.
- Relief-well drilling. An uncontrolled (wild) well is intersected near its source. Mud and water are then pumped into the relief well to kill the wild one. Directional control is extremely exacting for this type of application.
- River-crossing applications. Directional drilling is employed extensively for placing pipelines that cross beneath rivers, and has even been used by telecommunication companies to install fiber-optic cables.
- 1 Directional-Well Profiles
- 2 Directional Survey
- 3 BHA Design for Directional Control
- 4 Nomenclature
- 5 Acknowledgments
- 6 References
- 7 SI Metric Conversion Factors
A directional well can be divided into three main sections—the surface hole, overburden section, and reservoir penetration. Different factors are involved at each stage within the overall constraints of optimum reservoir penetration.
Most directional wells are drilled from multiwell installations, platforms, or drillsites. Minimizing the cost or environmental footprint requires that wells be spaced as closely as possible. It has been found that spacing on the order of 2 m (6 ft) can be achieved. At the start of the well, the overriding constraint on the well path is the presence of other wells. Careful planning is required to assign well slots to bottomhole locations in a manner that avoids the need for complex directional steering within the cluster of wells. At its worst, the opportunity to reach certain targets from the installation can be lost if not carefully planned from the outset. Visualizing the relative positions of adjacent wells is important for correct decisions to be made about placing the well path to minimize the number of adjacent wells that must be shut in as a safety precaution against collisions. The steel in nearby wells requires that special downhole survey techniques be used to ensure accurate positioning. This section is generally planned with very low curvatures to minimize problems in excessive torque and casing wear resulting from high contact forces between drillstrings and the hole wall.
Many directional wells are drilled from surface pads and offshore locations. Close surface locations always have the potential for collisions near the surface. Planning proper surface-hole surveying strategies to prevent collisions is critical in well planning. Gyro surveys (single/multiple shots) are often used to eliminate problems associated with close wellbore spacing. Modern well-planning software has used the survey uncertainty model in the anticollision calculations.
Perhaps the most important technique in collision avoidance is the traveling-cylinder diagram (TCD). The TCD provides an effective means of portraying the actual position of the well being drilled relative to its planned course and to adjacent wells. It also allows complex, 3D interwell tolerances on the allowable position of the borehole trajectory to be presented in a simple and unambiguous form. Because the original hand-drawn version was developed in 1968, various algorithms have been devised to produce the TCD in the well-planning software package. Among the three versions of the diagram commonly available, the normal-plane TCD is the most efficient tool. The normal-plane projection displays the intersection of wells with a plane constructed in space to be normal to the direction of the planned well at the point of interest. Because of its clear and simple presentation of a complex situation, the normal-plane TCD has recently been used at the wellsite to assist the simple go/no-go decision and the visualization of collision potential without making any interpretive judgments on well convergence or survey error values., , , , 
Overburden SectionHaving steered away from the congestion of the surface section, the main part of the well path through the overburden is specifically designed to put the well in the best possible position for penetrating the reservoir. There are three different overall shapes of the well, depending on the penetration requirements. These are build-and-hold, S-shaped, and continuous build. In practice, these generic shapes will be modified by local conditions. Getting the right well path through the overburden is a multidisciplinary task in which geologists advise the designer about the presence of faults, the precise shape of salt formations, mud diapirs, and other subsurface hazards. Understanding the interaction between the 3D well trajectory and the formation stresses, particularly in overthrust areas, is vital to ensuring that the well can be drilled safely and efficiently. See Fig. 6.1 for an illustration of these wellbores.
In general, a build-and-hold profile is planned so that the initial deflection angle is obtained at a shallow depth, and from that point on the angle is maintained as a straight line to the target zone. Once the angle and deflection are obtained, casing may be set through the deviated section and cemented. In general, the build-and-hold profile is the basic building block of extended-reach wells. These profiles can usually be employed in two distinct depth programs. These profiles can be used for moderate-depth drilling in areas where intermediate casing is not required and where oil-bearing strata are a single horizon. They can also be used for deeper wells requiring a large lateral displacement. In this case, an intermediate-casing string can be set to the required depth, and then the angle and direction can be maintained after drilling out below the string.
The main reasons for drilling an S-shaped well are completion requirements for the reservoir; for example, when a massive stimulation operation is required during the completion. An S-shaped well also sets the initial deflection angle near the surface. After the angle is set, drilling continues on this line until the appropriate lateral displacement is attained. The hole is then returned to vertical or near vertical and drilled until the objective depth is reached. Surface casing is set through the upper deviated section and cemented. The wellbore is then continued at the desired angle until the lateral displacement has been reached and then returns to vertical. Intermediate casing is set through the lower vertical-return section. Drilling then continues below the intermediate casing in a vertical hole. The S-shaped well is often employed with deep wells in areas where gas troubles, saltwater flows, etc. dictate the setting of intermediate casing. It permits more-accurate bottomhole spacing in a multiple-pay area. The deflection angle may be set in surface zones in which drilling is fast and round-trip costs can be held to a minimum.
A continuous-build well starts its deviation well below the surface. The angle is usually achieved with a constant build to the target point. The deflection angles may be relatively high, and the lateral distances from vertical to the desired penetration point are relatively shorter than other well types. Typical applications would be in exploring a stratigraphic trap or obtaining additional geological data on a noncommercial well. Because deflection operations take place deep in the hole, trip time for such operations is high, and the deflected part of the hole is not normally protected by casing. The continuous-build profile may also commonly be found in old fields in which development of bypassed oil is carried out by means of sidetracks from existing wells that have ceased to produce economically from the original completion.
The penetration of the reservoir is the realization of the whole purpose of drilling the well, whether a producer or an exploration well. Therefore, correct placement of the well within the target zone is of utmost importance. Designing the penetration is clearly a major multidisciplinary task involving not only the drilling team but also geologists and reservoir engineers. As indicated previously, for some wells, a simple straight-line penetration may suffice to provide an economical flow. Sometimes the path should be brought back to vertical to assist in stimulation operations or to keep the well within a fault block. Increasingly, though, target penetrations can be very complex undertakings in high-cost, Arctic, onshore extended-reach, and offshore-platform operations. At its most basic is the horizontal well; at the other extreme is the designer well.
There are two important aspects of reservoir penetration. First is allowing for the effects of a wellbore position error on defining the target location; the other is placing the wellbore within the formation for maximum production efficiency. The surveys used to calculate the well position always contain some errors. These errors result in a difference between the apparent location of the well, as derived from the survey data, and the actual location, which, by definition, is never known. The likely size of these errors can be quantified for different well locations, surveying methods, and wellbore shapes. These errors must be taken into account when defining the boundaries, or tolerances, around the target location. In extreme cases, such as extended-reach wells in the Arctic, the errors can be much greater than the size of the target unless special surveying techniques are employed. Under these conditions and even though the apparent position of the well is within the target, the actual location may be outside. When undetected, this misleading information can have a significant impact on understanding the geological model and can result in substantial losses of reserves. If detected, there may be the need to undertake a costly sidetracking operation to place the well correctly.
Horizontal wells are high-angle wells (with an inclination of generally greater than 85°) drilled to enhance reservoir performance by placing a long wellbore section within the reservoir. This contrasts with an extended-reach well, which is a high-angle directional well drilled to intersect a target point. There was relatively little horizontal drilling activity before 1985. The Austin Chalk play is responsible for the boom in horizontal drilling activity in the U.S. Now, horizontal drilling is considered an effective reservoir-development tool., , , 
The advantages of horizontal wells include:
1. Reduced water and gas coning because of reduced drawdown in the reservoir for a given production rate, thereby reducing the remedial work required in the future.
2. Increased production rate because of the greater wellbore length exposed to the pay zone.
3. Reduced pressure drop around the wellbore.
4. Lower fluid velocities around the wellbore.
5. A general reduction in sand production from a combination of Items 3 and 4.6. Larger and more efficient drainage pattern leading to increased overall reserves recovery.
Horizontal wells are normally characterized by their buildup rates and are broadly classified into three groups that dictate the drilling and completion practices required, as shown in Table 6.1.
The "build rate" is the positive change in inclination over a normalized length (e.g., 3°/100 ft.) A negative change in inclination would be the "drop rate." A long-radius horizontal well is characterized by build rates of 2 to 6°/100 ft, which result in a radius of 3,000 to 1,000 ft. This profile is drilled with conventional directional-drilling tools, and lateral sections of up to 8,000 ft have been drilled. This profile is well suited for applications in which a long, horizontal displacement is required to reach the target entry point. The use of rotary-steerable systems (RSSs) may be required to drill an extra-long lateral section because slide drilling may not be possible with the conventional steerable motors.
Medium-radius horizontal wells have build rates of 6 to 35°/100 ft, radii of 1,000 to 160 ft, and lateral sections of up to 8,000 ft. These wells are drilled with specialized downhole mud motors and conventional drillstring components. Double-bend assemblies are designed to build angles at rates up to 35°/100 ft. The lateral section is often drilled with conventional steerable motor assemblies. This profile is common for land-based applications and for re-entry horizontal drilling. In practical terms, a well is classified as medium radius if the bottomhole assembly (BHA) cannot be rotated through the build section at all times. At the upper end of the medium radius, drilling the maximum build rate is limited by the bending and torsional limits of API tubulars. Smaller holes with more-flexible tubulars have a higher allowable maximum dogleg severity (DLS).
Short-radius horizontal wells have build rates of 5 to 10°/3 ft (1.5 to 3°/ft), which equates to radii of 40 to 20 ft. The length of the lateral section varies between 200 and 900 ft. Short-radius wells are drilled with specialized drilling tools and techniques. This profile is most commonly drilled as a re-entry from any existing well.
Multilateral wells are new evolution of horizontal wells in which several wellbore branches radiate from the main borehole. In 1997, Technology Advancement for Multi-Laterals (TAML), an industry consortium of operators and service companies, was formed to categorize multilateral wells by their complexity and functionality. The designated categories (levels) are as follows.
- Level 1—openhole junction.
- Level 2—cased-hole exit.
- Level 3—junction with connection but no seal.
- Level 4—sealed junction.
- Level 5—mechanical sealed junction with reduced inside diameter (ID).
- Level 6—mechanical sealed junction with full ID.
- Level 6S—downhole splitter.
An extended-reach well is one in which the ratio of the measured depth (MD) vs. the true vertical depth (TVD) is at least 2:0. The current world record is Brintnell Well 2-10 (Amoco in Canada), with the highest MD/TVD ratio of 8.00. The top four wells are as follows.
- Amoco Brintnell 2-10 (Wabasca): MD/TVD = 8.00.
- Amoco Brintnell 1-18 (Wabasca): MD/TVD = 7.39.
- Maersk Qatar BA-26 (Al Shaheen): MD/TVD = 7.04.
- BP Wytch Farm M16z: MD/TVD = 6.89.
- BP Wytch Farm Well M16z still holds the world record MD and horizontal departure (MD = 37,001 ft, and departure = 35,197 ft).
Other notable extended-reach-drilling (ERD) achievements in pushing the horizontal departure limit are:
- 9,000 to 10,000 ft TVD: Phillips (Xijiang, China) = 8 km, Norsk Hydro (Oseberg, Norway) = 7.8 km, Woodside (Goodwyn, Australia) = 7.4 km, and Statoil (Sleipner, Norway) = 7.4 km.
- 13,000 to 15,000 ft TVD: Woodside (Goodwyn, Australia) = 7.4 km, and Statoil (Sleipner, Norway) = 7.4 km.
- More than 20,000 ft TVD: Shell (Auger, U.S.A.) = 3.9 km.
Extended-reach wells are expensive and technically challenging., , ,  However, they can add value to drilling operations by making it possible to reduce costly subsea equipment and pipelines, by using satellite field development, by developing near-shore fields from onshore, and by reducing the environmental impact by developing fields from pads.
There have been more than 1,700 extended-reach wells drilled to date, as shown in Fig. 6.2.
Fig. 6.3 shows the evolution of extended-reach wells in the 1990s and the future. With new technology, the goal is to see the TVD push to 30,000 ft and the horizontal departure to 50,000 ft in the 21st century. As of this printing, we are still waiting to see that goal achieved.
Design WellsToday, most directional-well planning is done on the computer. Modern computer technologies, such as 3D visualization and 3D earth models, have provided geoscientists and engineers with integrated and interactive tools to create, visualize, and optimize well paths through reservoir targets, as shown in Fig. 6.4. Furthermore, recently developed geosteering systems and RSSs allow more-complex directional-well trajectories that are designed to drain more of the reservoir. The future is the real-time integration of the drilling and logging-while-drilling (LWD) data with geosteering and the earth model. The 3D visualization of real-time data, together with the earth model, would allow integrated knowledge management and real-time decision making.
The method used to obtain the measurements needed to calculate and plot the 3D well path is called directional survey. Three parmeters are measured at multiple locations along the well path—MD, inclination, and hole direction. MD is the actual depth of the hole drilled to any point along the wellbore or to total depth, as measured from the surface location. Inclination is the angle, measured in degrees, by which the wellbore or survey-instrument axis varies from a true vertical line. An inclination of 0° would be true vertical, and an inclination of 90° would be horizontal. Hole direction is the angle, measured in degrees, of the horizontal component of the borehole or survey-instrument axis from a known north reference. This reference is true north, magnetic north, or grid north, and is measured clockwise by convention. Hole direction is measured in degrees and is expressed in either azimuth (0 to 360°) or quadrant (NE, SE, SW, NW) form.
Each recording of MD, inclination, and hole direction is taken at a survey station, and many survey stations are obtained along the well path. The measurements are used together to calculate the 3D coordinates, which can then be presented as a table of numbers called a survey report. Surveying can be performed while drilling occurs or after it has been completed.
The purposes of directional survey are to:
- Determine the exact bottomhole location to monitor reservoir performance.
- Monitor the actual well path to ensure the target will be reached.
- Orient deflection tools for navigating well paths.
- Ensure that the well does not intersect nearby wells.
- Calculate the TVD of the various formations to allow geological mapping.
- Evaluate the DLS, which is the total angular inclination and azimuth in the wellbore, calculated over a standard length (100 ft or 30 m).
- Fulfill requirements of regulatory agencies, such as the Minerals Management Service (MMS) in the U.S.
Survey instruments can be set up in several different variations, depending on the intended use of the instrument and the methods used to store or transmit survey information. Basically, there are two types of survey instruments: magnetic and gyroscopic. Depending on the method used to store the data, there are film and electronic systems. Survey systems can also be categorized by the methods used to transmit the data to the surface, such as wireline or measurement while drilling (MWD).
Magnetic Sensors. Magnetic sensors must be run within a nonmagnetic environment [i.e., in uncased hole either in a nonmagnetic drill collar(s) or on a wireline]. In any case, there must not be any magnetic interference from adjacent wells. Magnetic sensors can be classified into two categories—mechanical and electronic compasses.
A mechanical compass uses a compass card that orients itself to magnetic north, similar to a hiking-compass needle. Inclination is measured by means of a pendulum or a float device. In the pendulum device, the pendulum is either suspended over a fixed grid or along a vernier scale and is allowed to move as the inclination changes. The float device suspends a float in fluid that allows the instrument tube to move around it independently as the inclination changes. The only advantage of mechanical compasses is the low cost, while several disadvantages have limited them from being used widely in directional surveys. The drawbacks are high maintenance costs, a need to choose inclination range, limited temperature capability, the possibility of human error in reading film, and the inability to use them in MWD tools.
The electronic compass system is a solid-state, self-contained, directional-surveying instrument that measures the Earth ’ s magnetic and gravitational forces. Inclination is measured by gravity accelerometers, which measure the Earth’ s gravitational field in the x, y, and z planes. The z plane is along the tool axis, x is perpendicular to z and in line with the tool’ s reference slot, and y is perpendicular to both x and z.From this measurement, the vector components can be summed to determine inclination. Hole direction is measured by gravity accelerometers and fluxgate magnetometers. Fluxgate magnetometers measure components of the Earth’ s magnetic field orthogonally (i.e., in the same three axes as the accelerometers). From this measurement, the vector components can be summed to determine hole direction.
Depending on the packaging of the electronic sensors, the electronic-compass system can be employed in different modes, such as single-shot, multishots, and MWD, in which data are sent to surface in real time through the mud-pulse telemetry system.
The electronic magnetic single-shot records a single survey record while drilling the well. The sensors measure the Earth’ s magnetic and gravitational forces with fluxgate magnetometers and gravity accelerometers, respectively. The components of this survey system include the probe and a battery stack that supplies power to the probe. The raw data are stored downhole in the memory and retrieved at the surface to calculate the hole direction, inclination, and tool face. The electronic magnetic multishot uses the same components as the electronic single-shot; the only difference is that electronic multishots record multiple survey records. The MWD acquires downhole information during drilling operations that can be used to make timely decisions about the drilling process. The magnetic survey information is obtained with an electronic compass, but, unlike previous systems that stored the information, the MWD encodes the survey data in mud pulses that are sent up and decoded at the surface. The real-time survey information enables the drillers to make directional-drilling decisions while drilling. The sensors used in MWD tools are the same design as those used in electronic magnetic single-shot and multishots (i.e., gravity accelerometers and fluxgate magnetometers).
The Geomagnetic Field. Both types of magnetic sensors rely upon detecting the Earth’ s magnetic field to determine hole direction. The Earth can be imagined as having a large bar magnet at its center, laying (almost) along the north/south spin axis (see Fig. 6.5). The normal lines of the magnetic field will emanate from the bar magnet in a pattern such that at the magnetic north and south poles, the lines of force (flux lines) will lay vertically, or at 90° to the Earth’ s surface, while at the magnetic equator, the lines of force will be horizontal, or at 0° to the Earth’ s surface. At any point on the Earth, a magnetic field can be observed having a strength and a direction (vector). The strength is called magnitude and is measured in units of tesla. Usual measurements are approximately 60 microtesla at the magnetic north pole and 30 microtesla at the magnetic equator. The direction is always called magnetic north. However, although the direction is magnetic north, the magnitude will be parallel to the surface of the Earth at the equator and point steeply into the Earth closer to the north pole. The angle that the vector makes with the Earth’
The prevailing models used to estimate the local magnetic field are provided by the British Geological Survey (BGS) or, alternatively, by the U.S. Geological Soc. (USGS). These models carry out a high-order spherical harmonic expansion of the Earth’
s magnetic field and provide a very accurate global calculation of the magnetic field rising from the Earth’
s core and mantle. The models are based on measurements from hundreds of magnetic stations on the surface of the earth, airborne magnetic surveys, and magnetic-field data gathered by satellites. Because even the field of the Earth’
s core and mantle varies with time, these models are updated on an approximately annual basis. Note that these models include neither effects from materials near the surface of the earth (termed "crustal anomalies"), which can be quite significant, nor separate effects from various electrojets in the Earth’
s atmosphere, the effects of solar storms, or the diurnal variation in the earth’
s magnetic field. At high latitudes, these effects can be quite significant. A way of getting around this problem is to make magnetic-observatory-quality measurements directly at the wellsite; however, this is rarely possible. A very useful alternative is to interpolate the field at a given location and time, as measured by at least three nearby magnetic observatories, the triangle of which preferably includes the wellsite being surveyed. This is referred to as interpolated in-field referencing. Scientists who use this technique on surveys taken at high latitudes and with axial magnetic interference report achieving an accuracy approaching that otherwise attainable only with gyros.
Gyroscopic Sensors. Gyroscopic surveying instruments are used when the accuracy of a magnetic survey system may be corrupted by extraneous influences, such as cased holes, production tubing, geographic location, or nearby existing wells. A rotor gyroscope is composed of a spinning wheel mounted on a shaft, is powered by an electric motor, and is capable of reaching speeds of greater than 40,000 rev/min. The spinning wheel (rotor) can be oriented, or pointed, in a known direction. The direction in which the gyro spins is maintained by its own inertia; therefore, it can be used as a reference for measuring azimuth. An outer and inner gimbal arrangement allows the gyroscope to maintain its predetermined direction, regardless of how the instrument is positioned in the wellbore.
Gyroscopic systems (gyros) can be classified into three categories—free gyros, rate gyros, and inertial navigation systems.
- Free gyros. There are three types of free gyros: tilt scale, level rotor, and stable platform. The tilt scale and level rotor are film systems, while the stable platform uses the electronic system, which has shorter run time, faster data processing, and monitors continuously. Thus, most free gyros are the stable-platform type, which uses a two-gimbal gyro system like the level-rotor gyro, but the gimbals remain perpendicular to each other, even when the instrument is tilted during use. The inner gimbal remains perpendicular to the tool axis (platform) instead of perpendicular to the horizon.
- Rate gyros (north-seeking gyros). These use the horizontal component of the Earth’
s rotational rate to determine north. The Earth rotates 360° in 24 hours, or 15° in 1 hour. The horizontal component of the Earth’ s rate decreases with the cosine of latitude; however, a true-north reference will always be resolved at a latitude of less than 80° north or south. Therefore, the rate gyro does not have to rely on a known reference direction for orientation. Inclination is measured by a triaxial gravity-accelerometer package. Rate gyros have a very precise drift rate that is small compared to the Earth’ s spin rate. The Earth’ s spin rate becomes less at higher latitudes, affecting the gyro’ s ability to seek north. This effect also increases the time required to seek north accurately and decreases the accuracy of the north reference.
- Inertial navigation systems. This is the most accurate surveying method. Inertial navigation systems use groups of gyros to orient the system to north. It can measure movement in the x, y, and z axes of the wellbore with gyros and gravity accelerometers. Because of the sensor design, this instrument can survey in all latitudes without sacrificing accuracy.
There are several known methods of computing directional survey. The five most commonly used are: tangential, balanced tangential, average angle, curvature radius, and minimum curvature (most accurate).
- Tangential. This method uses the inclination and hole direction at the lower end of the course length to calculate a straight line representing the wellbore that passes through the lower end of the course length. Because the wellbore is assumed to be a straight line throughout the course length, it is the most inaccurate of the methods discussed and should be abandoned completely.
- Balanced Tangential. Modifying the tangential method by taking the direction of the top station for the first half of the course length, then that of the lower station for the second half can substantially reduce the errors in that method. This modification is known as the balanced-tangential method. This method is very simple to program on hand-held calculators and in spreadsheets and gives accuracy comparable to the minimum-curvature method.
- Average Angle. The method uses the average of the inclination and hole-direction angles measured at the upper and lower ends of the course length. The average of the two sets of angles is assumed to be the inclination and the direction for the course length. The well path is then calculated with simple trigonometric functions.
- Curvature Radius. With the inclination and hole direction measured at the upper and lower ends of the course length, this method generates a circular arc when viewed in both the vertical and horizontal planes. Curvature radius is one of the most accurate methods available.
- Minimum Curvature. Like the curvature-radius method, this method, the most accurate of all listed, uses the inclination and hole direction measured at the upper and lower ends of the course length to generate a smooth arc representing the well path. The difference between the curvature-radius and minimum-curvature methods is that curvature radius uses the inclination change for the course length to calculate displacement in the horizontal plane (the TVD is unaffected), whereas the minimum-curvature method uses the DLS to calculate displacements in both planes. Minimum curvature is considered to be the most accurate method, but it does not lend itself easily to normal, hand-calculation procedures.
The survey results are compared against those from the minimum-curvature method, as shown in Table 6.2. Large errors are seen in the tangential method for only approximately 1,900 ft of deviation. This demonstrates that the tangential method is inaccurate and should be abandoned completely. The balanced-tangential and average-angle methods are more practical for field calculations and should be used when sophisticated computational equipment or expertise may not be available. These should be noted as "Field Results Only."
Sources of Errors in Directional Survey
Survey Instruments. The survey instrument ’ s performance depends on the package design elements, calibration performance, and quality control during operation. System performance will functionally depend on the borehole inclination, azimuth, geomagnetic-field vector, and geographical position. Because of the dependency on sensing Earth’ s spin rate, the performance of gyro compassing tools is inversely proportional to the cosine of the latitude of wellbore location. The sensor systems’ performance generally degrades as the inclination increases, especially in an east/west direction at higher latitudes. For magnetic tools, high latitudes result in weaker horizontal components of Earth’ s field. For two-axis gyro tools, the approach to east/west at high inclinations places the sensor axes increasingly parallel to Earth’s spin. With magnetic tools, errors increase at high east/west inclinations because of the progressive difficulty in compensating for the effect of drillstring magnetism.
Gyros suffer from the additional problem of time-related drift uncertainty. The time component may be significant for gyro systems, particularly in horizontal wells and possibly in east/west orientation. The survey duration inevitably extends beyond the average survey-duration period. Long survey duration means larger drift uncertainty and more exposure to the wellbore environment, which may potentially reduce the accuracy of directional data.
The ability of the tool to freefall into the well will decrease substantially at approximately 60°. Consequently, gyro performance degrades at 60°, and most gyros cannot be used to survey at greater than 70°.
Tool Misalignment. The misalignment of the survey instrument with the wellbore results in errors in measuring wellbore-axis direction and inclination. (Note: inclination and azimuth are affected.) Sources of this kind of error are detailed in Table 6.3. Sensor-to-instrument error is independent of inclination, which is an important variable for both instrument to drillstring/casing and drillstring to wellbore. Misalignments have long been recognized as significant error sources in directional surveying.
MD Error. Sources of depth error depend on the type of survey system used. Drillpipe-conveyed tools (MWD, multishots, and single-shot) suffer from errors in the physical measurement of drillpipes and the differential effects of drillstring compression and stretch. Because of wellbore friction, drillstring compression and stretch are not easily calculated, particularly in inclined wells. Depth errors can account for the relatively large angular errors frequently observed when comparing overlapping, high-accuracy surveys in deviated wells.
Wireline survey tools generally have smaller depth errors than drillstring-conveyed tools, provided adequate quality-control measures have been taken. Errors on the order of 1/1,000 for gyroscopic tools and 2/1,000 for drillstring tools are commonly quoted. However, this may not apply to horizontal-well situations.
Magnetic Interference. Magnetic interference may be defined as corruption of the geomagnetic field by a field from an external source. This can cause serious errors in measuring hole direction (azimuth). Potential sources of magnetic interference are:
- Adjacent wells.
- Casing shoes.
- Magnetic formations.
- "Hot spots" in nonmagnetic drill collars.
Although all the previous error sources may compromise the magnetic survey ’ s quality, drillstring (axial) interference is probably the most common and frequent cause of errors in hole direction. The drillstrings may be regarded as a steel-bar, dipole magnet. The normal approach for magnetic survey tools is to place the survey sensor within sufficient quantity of nonmagnetic drill collars in the BHA. Azimuth measurement errors are minimized by virtue of their distance from the interference source. Magnetic interference diminishes proportionally with the inverse of the square of the distance from the source. The bar-dipole-magnet analogy is simplistic. There is evidence that downhole drillstring magnetism may be much more complex, even dynamic in nature. In practice, it may be hard to remove interference completely. The magnitude of the effect of magnetic interference depends on the strength of the interference field as well as the inclination and direction of the wellbore and its geographical latitude. Highly deviated wells drilled in an east/west direction are likely to suffer greater magnetic-interference errors, especially in higher latitudes., 
There are several techniques to correct the effects of magnetic interference. These tend to be proprietary, but at least two are based upon a common hypothesis. The corrupted sensor measurements can be replaced with values calculated from a model of the local geomagnetic parameters, which allows azimuth estimation without interference errors. The techniques have been proved to be sound, in theory. In practice, the available geomagnetic models are imperfect, resulting in potentially significant errors in the calculated azimuth. If good geomagnetic-field information is available, then these correction routines can provide accurate azimuth data. In some cases, the hole direction’ s (azimuth’ s) accuracy has approached gyro quality.
Cross-Axial Interference. This can arise from hot spots or from close proximity to magnetic elements in the drillstring. Cross-axial magnetic interference can cause significant survey errors, especially when the well being surveyed is in an east/west direction or approximately horizontal. A few companies have devised means for dealing with this type of interference, and at least one company combines this with an axial interference correction. These techniques also rely on knowing the magnitude of the local magnetic field and the dip angle. As with axial interference corrections, performance can be affected significantly by the imperfections in commonly available geomagnetic models.
Wellbore Position Error
The survey errors described previously must be translated into positional errors so that geoscientists can assess the impact of those errors on their understanding of the subsurface model and behavior of the well when on production. In extreme cases, these errors, if not recognized, can result in a well missing its target completely. Thus, the wellbore position error is a multidisciplinary problem and should be considered during well planning. Also, drillstring magnetic interference affects hole-direction measurements most severely at high inclinations when the well is traveling close to east or west. Planning the drainage of a field with wells oriented not along east or west greatly improves the accuracy of the directional MWD surveys.
To quantify the effects of the instrument errors described previously on bottomhole location, Walstrom et al. introduced the concept of survey uncertainty by generating 2D ellipses of uncertainty. An ellipse is used because the greatest survey errors are usually azimuth errors rather than inclination ones. The ellipse is expressed as an ellipsoid with the long axis at right angles to the wellbore direction. These calculations were based on the assumption that most survey errors were random. It later became evident that the calculated ellipses were too small and generally would not overlap.
In 1981, Wolff and de Wardt introduced an alternative method of determining wellbore uncertainty by suggesting that most survey errors were systematic rather than random. This method, or similar ones that also use systematic error sources, has become the accepted method of computing error source. While work was done in this area during the late 1980s, there was little standardization in computational technique. This caused many problems within the industry. To address these issues, a number of individuals created the Industry Steering Committee on Wellbore Survey Accuracy (ISCWSA) in 1995. The committee ’ s objective is to produce and maintain standards relating to wellbore-survey accuracy for the industry. ISCWSA published a paper describing in detail how errors in sensor bias, scale factor, and misalignment propagate into errors in measured inclination and azimuth. Readers interested in survey accuracy and error models should contact ISCWSA for more information.
Survey Quality Control
The nature of downhole directional surveying is that it can never be independently verified. It is very difficult to go down the well to check if the bottom is located where the calculations claim. Practically, the best way of verifying survey results is to have surveys obtained from two different sources, preferably from two different sensor types, such as a magnetic MWD survey checked by a rate gyro or inertial navigation system.
Survey-tool performance often is dependent on how it is run. Regardless of the system or sensor type, the quality of the survey is controlled by the surveyor. The surveyor must follow the procedures and verification checks specified by the survey company and possibly even apply additional procedures and checks, as specified by the operating company, to ensure the best possible survey. Unless the proper procedures and checks are adhered to, the quality of the survey is questionable. These checks should include pre- and post-job calibration checks and paperwork and procedures verification by someone other than the original surveyor.
BHA Design for Directional Control
Design Principles—Bit Side Force and Tilt
The BHA is a portion of the drillstring that affects the trajectory of the bit and, consequently, of the wellbore. In general, the factors that determine the drilling tendency of a BHA are bit side force, bit tilt, hydraulics, and formation dip. The BHA design objective for directional control is to provide the directional tendency that will match the planned trajectory of the well.
The bit side force is the most important factor affecting the drilling tendency. The direction and magnitude of the bit side force determine the build, drop, and turn tendencies. A drop assembly is defined as when the bit side force acts toward the low side, whereas a build assembly is when the bit side force acts toward the high side of the hole. A hold assembly is when the inclination side force at the bit is zero. The bit tilt angle is the angle between the bit axis and the hole axis and affects the drilling direction because a drill bit is designed to drill parallel to its axis.
Rotary assemblies are designed to build, drop, or hold angle. The behavior of any rotary assembly is governed by the size and placement of stabilizers within the first 120 ft from the bit. Additional stabilizers run higher on the drillstring will have limited effect on the assembly
s performance. Rotary assemblies are not "steerable"; first, the azimuth behavior (right/left turn) of a rotary assembly is nearly uncontrollable. Second, each rotary assembly has its own unique build/drop tendency that cannot be adjusted from the surface. Thus, tripping for the assembly change is required to correct the wellbore course.
Commonly used stabilizer types are sleeve, welded blade, and integral blade. For long wear life, geology is the most important consideration when selecting one type of stabilizer vs. another. Sleeve stabilizers are most economical, but ruggedness often is an issue. Welded-blade stabilizers are best suited to large holes in soft formations. Integral-blade stabilizers are the most expensive but very rugged, making them the ideal choice in hard and abrasive formations. Roller reamers are sometimes used with stabilizers to open the hole to full gauge, extend bit life, and prevent possible sticking problems.
Building Assemblies: Fulcrum Principle. Building assemblies use the fulcrum principle—a near-bit stabilizer, closely placed above the bit, creates a pivot point wherein the bending drill collars force the near-bit stabilizer to the low side of the hole and create a lateral force at the bit to the high side of the hole. Experience has shown that the more limber the portion of the assembly just above the fulcrum, the faster the increase in angle.
A typical build assembly uses two to three stabilizers. The first (near-bit) stabilizer usually connects directly to the bit. If a direct connection is not possible, the distance between the bit and the first stabilizer should be less than 6 ft to ensure it remains an angle-building assembly. The second stabilizer is added to increase the control of side force and to alleviate other problems. Build rates can be increased by increasing the distance between the first and second stabilizers. When the distance between the stabilizers increases enough to cause the drill collar sag to touch the low side of the hole, the bit side force and bit tilt reach their maximum build rate for the assembly. Generally, the drill collars will sag to touch the borehole wall when the distance between the stabilizers is greater than 60 ft. The amount of sag will also depend on the hole and collar sizes, inclination, stabilizer gauge, and weight on bit (WOB).
Other important factors for the fulcrum assemblies are inclination, WOB, and rotary speed. The build rate of a fulcrum assembly increases as inclination increases because the larger component of the collar’ s own weight causes them the bend. Increasing the WOB will bend the drill collars behind the near-bit stabilizer even more, increasing the build rate. A higher rotary speed tends to straighten out the drill collars, thus reducing the build rate. Therefore, low rotary speeds (70 to 100 rev/min) are generally used with fulcrum assemblies. Sometimes, in soft formations, a high flow rate can lead to formation washout, resulting in decreased stabilizer contacts and, thus, a reduced build tendency.
Holding Assemblies: Packed Hole. The packed-hole assemblies contain three to five stabilizers properly spaced to maintain the angle. The increased stiffness on the BHA from the added stabilizers keeps the drillstring from bending or bowing and forces the bit to drill straight ahead. The assembly may be designed for slight build or drop tendency to counteract formation tendencies.
Dropping Assemblies: Pendulum Principle. The pendulum effect is produced by removing the stabilizer just above the bit while retaining the upper ones. While the remaining stabilizers hold the bottom drill collar away from the low side of the wall, gravity acts on the bit and the bottom drill collar and tends to pull them to the low side of the hole, thus decreasing the hole angle. Pendulum assemblies sometimes can be run slick (without stabilizers). Although a slick assembly is simple and economical, it is difficult to control and maintain the drop tendency.
A dropping assembly usually contains two stabilizers. As the distance between the bit and the first stabilizer increases, gravity pulls the bit to the low side of the hole, increasing the downward bit tilt and bit side force. If the distance between the bit and the first stabilizer is too large, the bit will begin to tilt upward, and the drop rate will reach a maximum. With a higher WOB, the drop assembly could even start building angle. Generally, the distance between the bit and the first stabilizer will be approximately 30 ft. The second stabilizer is added to increase control of the side force.
Initially, low WOB should be used to avoid bending the pendulum toward the low side of the hole. Once a dropping trend has been established, moderate WOB can be used to achieve a higher penetration rate.
Deviation ToolsThe most common deviation tools for directional drilling are steerable motor assemblies (or so-called positive-displacement motors [PDMs]) and RSSs. Adjustable-gauge stabilizers, known as "2D rotary systems," have become quite popular to run with the rotary and PDM assemblies to control inclination. Whipstocks, especially casing whipstocks, are used routinely to sidetrack out of cased wellbores. Other tools, such as turbines, are used mainly in Russia, and jetting bits are seldom used today.
Steerable Motor Assemblies or PDMs. The most important advancements in trajectory control are the steerable motor assemblies, which contain PDMs with bent subs or bent housing. The PDM is based on the Moineau principle. The first commercial PDM was introduced to the petroleum industry in the late 1960s. Since then, PDM use has been accelerated greatly for directional-drilling applications. Steerable motor assemblies are versatile and are used in all sections of directional wells, from kicking off and building angle to drilling tangent sections and providing accurate trajectory control. Among the PDM assemblies, the most commonly used deviation tool today is the bent-housing mud motor.
The bent sub and bent housing use bit tilt (misalignment of bit face away from the drillstring axis) and bit side force to change the hole direction and inclination. Bent housing is more effective than the bent sub because of a shorter bit-to-bend distance, which reduces the bit offset and creates a higher build rate for a given bend size. A shorter bit-to-bend distance also reduces the moment arm, which, in turn, reduces the bending stress at the bend. As a result, the bent-housing PDM is easier to orient and allows for a long rotation period. Larger hole sizes (22 to 26 in.) are the only application for a bent sub. The requirement for bent subs is obsolete in most applications, particularly with the introduction of the adjustable bent housing.
Before the personal computer become widely available, the simple "three-point curvature" calculation was used to predict the build rates of the motor assemblies as
in which rb = build rate in degrees/100 ft, θ = bend angle in degrees, L1 = distance from the first contact point (bit) to the second (bend) in ft, and L2 = distance from the second contact point to the third (motor top stabilizer) in ft.
For more-accurate results, a BHA-analysis program is often used to calculate the build/drop/turn rates of the motor assemblies. Fig. 6.6 shows the expected DLS and the bit side forces for a two-stabilizer motor assembly.
Bent-Housing Motor Components. A typical bent-housing motor contains the following four sections: dump sub, power unit, transmission/bent-housing unit, and bearing section.
- Dump sub. Located on top of the motor assembly, the dump sub contains a valve that is ported to allow fluid flow between the drillstrings and the annulus. This allows the drillstrings to fill when tripping in the hole and empty when tripping out of the hole. The dump sub also permits low-rate circulation bypassing of the motor, if required.
- Power unit. Most motor assemblies use the Moineau pump principle to convert hydraulic energy to mechanical energy: a rotor/stator pair converts the hydraulic energy of the pressurized circulating fluid to mechanical energy for a rotating shaft. The rotor and stator are of lobed design. Both rotor- and stator-lobe profiles are similar, with the steel rotor having one less lobe than the elastomeric stator. The rotor and stator lobes are helical in nature, with one stage equating to the linear distance of a full "wrap" of the stator helix. Power units may be categorized with respect to the number of lobes and the effective stages. The speed and torque of a power section is linked directly to the number of lobes on the rotor and stator. The greater the number of lobes, the greater the torque and the lower the rotary speed. Typical rotor/stator configurations range from 1:2 to 9:10 lobe, as shown in Fig. 6.7. The power section should be matched to the bit and the formation being drilled for best performance.
- Transmission bent-housing/unit. The universal couplings inside the transmission/bent-housing unit eliminate all eccentric rotor motion and accommodate the misalignment motion of the bent housing while transmitting torque and down thrust to the drive shaft, which is held concentrically by the bearing assembly.
- Bearing section. The bearing assembly consists of multiple thrust-bearing cartridges, radial bearings, a flow restrictor, and a drive shaft. The thrust bearings support the down thrust of the rotor, the hydraulic down thrust from bit pressure loss, and the reactive upward thrust from the applied WOB. For larger-diameter motors, the thrust bearings are usually of multistack ball- and track-design. Small-diameter motors use carbide/diamond-enhanced friction bearings. Metallic and nonmetallic radial bearings are employed above and below the thrust bearings to absorb lateral side loading of the drive shaft. The flow restrictor allows approximately 5 to 8% of the circulating fluid to flow through the bearing section to cool and lubricate the bearing assembly. On the basis of planned bit hydraulics, the type of flow restrictor used is preselected and set in the motor shop; it cannot be changed at the rig site. The drive shaft transmits both axial load and torque to the bit. The drive shaft is a forged component designed such that fatigue, axial, and torque strengths are maximized. It has a threaded connection at the bottom to facilitate connection to the drill bit.
- Power delivered to the bit. Eqs. 6.2 and 6.3 are used to calculate the horsepower delivered to the bit from the motor. Note T (torque) is in the unit of lbf-ft (not lbf/ft).
in which hp = horsepower, T= torque in lb-ft, and N = speed of rotation in rev/min.
PDM Applications in Directional Drilling. Sidetrack. The most common method of sidetracking out of casing, especially when considerable drilling is to follow, is milling a length of casing with a section mill, then diverting the trajectory with a bent-housing motor assembly. The assembly usually contains a stabilizer on the motor and possibly another one above the motor.
Steerable Drilling and Kickoff. The essential requirement for a steerable drilling system is that it be capable of making both inclination and azimuth changes. Thus, this is the most commonly used configuration because:
- An average planned curvature can be adhered to by a combination of orienting and rotating.
- After completing the buildup, the assembly can be rotated ahead to hold the angle with minor corrections to inclination and azimuth as necessary.
- Extended intervals can be drilled through different formations without tripping for assembly changes.
- Drilling performance is maximized by efficiently delivering the torque and horsepower at the bit.
This system usually consists of a bent-housing motor and a stabilizer on the bearing housing. To enhance the motor ’ s sliding capability, the stabilizer has wide, straight blades that are tapered at either end and is undergauge relative to the hole size (typically ⅛ to ½ in.). Depending on the application, additional stabilizers may be used above the motor. Although these stabilizers are generally spiral, the blades should be tapered and undergauge.
The overall design of this steerable assembly will depend on its application. The important considerations are as follows:
- The expected build rate in oriented mode should be slightly greater than (typically 1 to 2°/100 ft) that required to guarantee the planned build rate.
- The number of stabilizers used should be kept to a minimum to reduce drag in the oriented mode.
- If the drillstring is rotated in a curved section, bending stresses around the bent housing should be checked to ensure that they are less than the endurance limit.
s Wytch Farm (U.K.) extended-reach wells.
Medium-Radius Applications (6 to 15°/100 ft DLS). The vast majority of medium-radius drilling is undertaken in hole sizes of 12¼ in. and less with 8-in. (and less) -diameter motors for build rates of 6 to 15°/100 ft. There are a number of motor configurations used to drill medium-radius wells, each with its own merits—single bent-housing motor, single bent housing with offset pad, double-bend motor, bent-housing motor with bent sub positioned on top of the motor and aligned with the bend, and double bent-housing motor.
Intermediate- and Short-Radius Applications. Intermediate-radius drilling systems are used to achieve build rates from 15 to 65°/100 ft. The build and lateral sections are drilled with a short-bearing pack motor. When the build rate exceeds 45°/100 ft, an articulated motor and flexed MWD tool should be used. Both system types can be used for new or re-entry wells.
Two types of motors are used to drill the short-radius wells with build rates ranging from 65 to 125°/100 ft: a "build" articulated motor used to drill the build section and a "hybrid lateral" motor for the horizontal lateral section. The articulated MWD tool is used on both the build and lateral sections.
RSS. The RSS is an evolution in directional-drilling technology that overcomes the drawbacks in steerable motors and in conventional rotary assemblies. To initiate a change in the wellbore trajectory with steerable motors, the drilling rotation is halted in such a position that the bend in the motor points in the direction of the new trajectory. This mode, known as the sliding mode, typically creates higher frictional forces on the drillstring. In extreme ERD, the frictional force builds to the point at which no axial weight is available to overcome the drag of the drillstring against the wellbore, and, thus, further drilling is not possible. To overcome this limitation in steerable motor assemblies, the RSS was developed in the early 1990s to respond to this need from ERD. The first RSS was used in BP plc ’
RSSs allow continuous rotation of the drillstring while steering the bit. Thus, they have better penetration rate, in general, than the conventional steerable motor assemblies. Other benefits include better hole cleaning, lower torque and drag, and better hole quality. RSSs are much more complex mechanically and electronically and are, therefore, more expensive to run compared to conventional steerable motor systems. This economic penalty tends to limit their use to highly demanding extended-reach wells or the very complex profiles associated with designer wells. Additionally, the technology is still very new. As a result, the current generation of systems (2002) is climbing a very steep learning curve in regard to run length, performance, and mechanical reliability.
There are two steering concepts in the RSS—point the bit and push the bit. The point-the-bit system uses the same principle employed in the bent-housing motor systems. In RSSs, the bent housing is contained inside the collar, so it can be oriented to the desired direction during drillstring rotation. Point-the-bit systems claim to allow the use of a long-gauge bit to reduce hole spiraling and drill a straighter wellbore. The push-the-bit system uses the principle of applying side force to the bit, pushing it against the borehole wall to achieve the desired trajectory. The force can be hydraulic pressure or in the form of mechanical forces. In general, either a point-the-bit or a push-the-bit RSS allows the operator to expect a maximum build rate of approximately 6 to 8°/100 ft for the 8½-in.-hole-sized tool.
Adjustable-Gauge Stabilizers (AGSs). In the late 1980s, the industry developed AGSs, the effective blade outer diameter (OD) of which could be changed while the tool was downhole. With AGSs, the drillers could change the stabilizer OD without making time-consuming and costly trips out of the hole. AGSs run in rotary assemblies were often placed near the bit or positioned approximately 15 to 30 ft from the bit. In these positions, changes in their gauge could effectively control the build or drop tendency of the assembly. Because they could control inclination while in the rotary mode, these assemblies became known as "2D rotary systems." AGSs can also be run with steerable motor systems. Running AGSs with the steerable motor assemblies makes it possible to control inclination with the stabilizer while drilling in the rotary mode. If the wellbore requires a change in azimuth, one would have to revert to a sliding mode.
AGSs have been widely used recently, particularly in drilling the horizontal section with a geological steering or pay-zone steering device that usually consists of an LWD tool. With its deep investigation depth, a resistivity sensor can detect a geological change many feet before the bit penetrates that boundary. This ability may allow the drilling assembly to be held in the reservoir and steered away from either an upper or lower boundary.
Whipstocks. Openhole whipstocks are the first type of deflection tool used to change the wellbore trajectory but are seldom used today. Bent-housing motors have replaced openhole whipstocks as the most commonly used deviation tool in openhole sidetracking. Casing whipstocks, on the other hand, are routinely used to sidetrack out of cased wellbores. Whipstocks can be either retrievable or nonretrievable. Retrievable ones are ideal for drilling multiple laterals from a single wellbore. A typical casing-sidetracking operation involves multiple trips to set the cement plug and the whipstock, start the window mill, complete the mill, and clean up. To save time, recently developed systems can accomplish all these tasks in one trip. Note that the gyro survey is usually required for setting the whipstock and for initial tool orientations.
Turbines. Turbines, commonly known as turbodrills, are powered by a turbine motor, which has a series of rotors/stators (stages) connected to a shaft. As the drilling fluid is pumped through the turbine, the stators deflect the fluid against the rotors, forcing the rotors to rotate the drive shaft to which they are connected. Turbines are designed to run on high speed and low torque; thus, they are suited for running with diamond or polycrystalline-diamond compact bits. Turbines are not only less flexible and efficient than PDMs but are also more expensive, so they are not as widely used, except in Russia.
Jetting Bits. Jetting bits can be used to change the trajectory of a borehole, with the hydraulic energy of the drilling fluid used to erode a pocket out of the bottom of the borehole. The tricone bit with one large nozzle is oriented to the desired hole direction to create a pocket. The drilling assembly is forced into the jetted pocket for a short distance. This procedure continues until the desired trajectory change is achieved. Jetting is seldom used today because of its slow penetration rate and its limitations in soft formations.
|L1||= distance from the first contact point to the second, ft|
|L2||= distance from the second contact point to the third, ft|
|N||= speed of rotation, rev/min|
|rb||= build rate, ft|
|T||= torque, lbf-ft|
|θ||= bend angle, degrees|
aunoy, and Paul Rodney, for their review and comments.
The author is deeply grateful to John Thorogood for his guidance and inspiration during the preparation of this work. He would also like to thank BP plc for providing the ERD database as well as his colleagues, Alpar Cseley, Steve D ’
SI Metric Conversion Factors
|ft||× 3.048*||E–01||= m|
|hp||× 7.46*||E–01||= kW|
|lbm||× 4.535 924||E–01||= kg|
|lbf||× 4.448 222||E+
Conversion factor is exact.