Rotary steerable tools open the door for true automated downhole steering. A critical feature is the downhole brain, which could use fuzzy logic to make directional steering decisions.

Currently, there is no commercial directional drilling system that offers true steering automation. Such a system would incorporate wellpath inclination, azimuth and Cartesian coordinates to command the controllable components automatically. Today's few auto-modes cater only to the much simpler cases of either inclination/azimuth control or pre-defined lateral tool force magnitude control. Attending to the 3-D location of the well bore still requires manual steering.

Removing human intelligence from the steering control loop - albeit temporarily - is far from simple. This is true whether the directional drilling system is controlled from the surface (bent housing assembly) or downhole (rotary steerable tools).

Automation: Why and how?

The motivation for true automation is at least threefold. First, minimizing human expertise as the primary component for high-performance steering is desirable because the availability of such skill is always limited. Second, historical research and experience suggest imposing frequent, minor changes to operating conditions -the norm with a control system - produces a well bore with minimum dogleg severity (DLS) variance. A smooth well bore is less troublesome to drill and complete. A third motivation is to reduce in/out oscillations and thus, drill more pay zone.

A factor of critical importance for true steering automation is the algorithmic "brain" that governs the system. In general, a Fuzzy Logic controller defines a method by which observable system input is systematically mapped into controllable system output. In the 1980s, inaugural Fuzzy Logic controllers successfully removed full-time human dependency from the system's control loop. In multiple cases, the technology permitted automation for the first time. Commercial Fuzzy Logic applications include aircraft control, anti-lock brakes, cruise control and space shuttle docking.

A prerequisite for Fuzzy controller design is a human solution. For example, steering a vehicle is mentally rationalized with basic principles that are easily communicated with intuitive phrases and common sense (rules). With today's actively controlled directional drilling systems, this statement is similarly true for steering the direction in which a bit drills.

For rotary steerable systems, the system-specific mechanics of how lateral forces acting at or near the bit are controlled isn't vital to controller design. The consequence is the same in that lateral tool force magnitude and orientation (TFMO) is controllable for these systems.

Cognitive map of drilling direction

Actual wellbore trajectory results from system component interactions that are complex to model. Gleaned from many researchers' published works, the most critical system components that affect drilling direction are listed in Table 1.

A cognitive map, the concept of which originated in psychology and political science during the 1970s1, draws a causal picture of the association of components within a complex dynamic system. A cognitive map of drilling direction (CMDD) is presented in Figure 1.

The one-way and double-headed arrows show cause-and-effect relationships among the system components. The CMDD conveys in a simple snapshot the system complexity of directional wellbore steering. It also pictorially summarizes several decades worth of literature about the factors that affect drilling direction.

Technical hole deviation (THD)

The CMDD is academic. It helps to explain why directional steering decisions made at the rig site are not driven by directional drilling simulators. For simulators, output-sensitive input parameters are unknown, and the system is too complex to compute directly the value of TFMO - or if applicable, tool face orientation (TFO) - and still possess a consistently reliable solution. Rather, like most spatial steering applications, such decisions are founded in geometries.

Directional drillers mentally process tabular and graphical geometric data and rely on their experience to rationalize their steering decisions. Accordingly, an automated steering control system would require similar, relevant input.

THD is computed at each directional survey station with planned wellpath properties (inclination, azimuth and Cartesian coordinates) currently in effect and 3D-nearest to "current TD." THD is based on lineal and angular differences, and the relative changes thereof (summarized in Table 2). THD is collectively defined with eight components and is presented fully and graphically with two well logs. 2

Four THD components address hole deviation in the vertical sense, and four do so in the horizontal sense. At non-90-degree wellpath inclinations, "vertical" relates to wellbore high side (HS) as viewed perpendicular/upward to the vector currently in effect and defined by planned inclination and azimuth. For example, an actual well bore termed high and left matches common directional-driller sense (Figure 2). The mathematics of THD are presented in Reference 2.

When one or more of the nodes in the CMDD acts to alter drilling direction, the significance is manifested empirically via THD. With respect to wellbore trajectory control, the associated perturbation is addressed by changing directional tool settings, if necessary.

Fuzzy sets and systems

While chair of the Electrical Engineering and Electronics Department at the University of California at Berkeley, Russian-born Lotfi A. Zadeh founded fuzzy set theory with the paper "Fuzzy Sets." His definition: "A Fuzzy Set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership function that assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets." 3

Zadeh's 1965 paper spawned a processing technology that is now a science. "Fuzzy" typically infers rule-based methodologies wherein Fuzzy Sets and Fuzzy Logic are employed. With Fuzzy Logic, human knowledge via rules may be assimilated into a numerical structure that can be exploited with a computer.

Fuzzy drilling direction controller

A directional drilling simulator was developed to investigate a methodology for automated directional steering. The simulator was a 3-D finite element model and incorporated a drill-ahead model.4 The modeled control feature was eccentricity settings (and thus, force settings) of a non-rotating, near-bit adjustable stabilizer. This work instigated the CMDD, created the necessity for THD, and produced a patent5 related to using Fuzzy Logic for directional steering.

The Fuzzy Drilling Direction Controller (FDDC) systematically maps THD into change in TFMO (?TFMO). The vector ?TFMO is determined by Fuzzy processing to compute the components ?TFy and ?TFx, where positive y and x point to the hole high side and right side, respectively (Figure 3).

?TFMO has direct application to rotary steerable systems and auxiliary application to bent housing assemblies via TFO and drilling mode (rotary/slide). The FDDC could also serve as expert advisory software for directional drillers for either system type. Final "new" values of tool settings are computed by vector adding prior settings to the new ? values.

The FDDC is comprised of numerous Fuzzy rules that are organized with multiple rule matrices. Each rule within a rule matrix addresses a basic steering scenario, such as those presented in Figure 4. Three rule matrices use msVD, RCVD, msID and RCID to systematically compute ?TFy; identical symmetry is used to compute ?TFx.

Six well paths generated with the simulator and with the FDDC in command are presented in Figure 5. The examples demonstrate a horizontal well with an immediate true-vertical-depth change in the planned path. Such applications occur frequently when directionally drilling thin pay zones in faulted reservoirs.
As observed in Figure 5, the FDDC "produced" desirable wellpath trajectories. Controller generality is suggested because in all examples the identical FDDC was employed. That is, the many parameters, functions and rules that comprise the FDDC were the same for all simulations, while initial conditions were varied. Simulations from kick-off-point through the toe of horizontal wells with a build gradient of 2° to 6°/100 ft were also conducted; equivalent performance and stability - with the identical controller - were observed.

An example THD log and qualitative FDDC output using real data is presented in Figure 6. Again, the identical controller as that in Figure 5 was employed. Neither THD nor the FDDC were available while drilling this well, which was drilled with a rotary steerable system.

The vertical THD log presents a 2°/100 ft 2-D drop section at 8,000 ft measured depth. A snapshot at two different times in the progression of drilling is displayed. In the center between these snapshots, qualitative FDDC output is displayed. Green and red horizontal arrows at each survey station represent how to change settings with respect to borehole high side. Arrow lengths are directly proportionate to the ?TFMO magnitude computed by the FDDC.

It appears as though the directional driller, who can directly affect RCID, didn't begin to lower msID (RCID made negative) until after 8,750 ft; this is after the overshoot was under way. Overcompensation follows as purposeful steering is enacted (excess DLS is the smoking gun) to attempt to regain control. The FDDC output was suggesting drilling low side hundreds of feet prior to the overshoot.

THD logs expose important details that are impossible to observe from standard directional plots. Even without focus on automation or advisory software, it is thought that THD can assist the directional driller to better assess the situation and make more-informed steering decisions.

If directional well bores are drilled that produce less drill string torque and drag because of less tortuosity and minimized DLS variance, then limits of reach can be extended, and running casing is more likely to be uneventful. If geo-driven changes in the planned path can be implemented smoothly and quickly, fewer sidetracks will be necessary. If technology (automated or not) can produce a better well bore for the operator, then eventually that technology will become standard.

Other fuzzy control applications

Directional steering is one of the most obvious drilling control applications to warrant investigation of Fuzzy Logic control. Several other control applications within drilling operations exist:

• choke and mud pump control during well control operations;
• rotary speed and hook load control for minimum vibration or optimized ROP;
• flow rate control for air or underbalanced drilling operations;
•drilling diagnostics and alarm systems;
• liquid mixing systems for density control; and
• dynamic positioning for drillships.

Acknowledgments

The author wishes to thank Jonathan Lightfoot, a technical services coordinator for Scientific Drilling International, for providing the directional survey and plan data for Figure 6.

References

1. Kosko, Bart. Fuzzy Thinking: The New Science of Fuzzy Logic. Hyperion, 1993.

2. Stoner, Michael S. "Deviation log, new formulae aid directional drillers," Oil & Gas Journal, pp. 64-70, Aug. 9, 1999.

3. Zadeh, Lotfi A. "Fuzzy Sets," Information and Control, Volume 8, pp. 338-353, 1965.
4. Stoner, Michael S. A Fuzzy Logic Controller for Drilling Directionally, T-4667. Colorado School of Mines, 1997.

5. Stoner, Michael S. Numerical control unit for wellbore drilling, United States Patent #6,101,444. Aug. 8, 2000.

6. McNeill, Daniel, and Paul Freiberger. Fuzzy Logic. The Revolutionary Computer Technology That Is Changing Our World. Simon & Schuster Inc., 1994.

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