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Technical Hole Deviation (THD) was a building block that resulted from searching for a solution to control logic for truly automated rotary steerable directional drilling systems. Just like the cruise-control in cars and the auto-pilot mode in aircraft, so too will true "auto-guidance" really enter directional drilling operations.


This page and Next present an overview of our patented Fuzzy Logic controller for directional steering. For reference we'll call it the Fuzzy Drilling Direction (FDD) Controller. The discussions will convey how Technical Hole Deviation plays a vital role in assessing the current state of the directional drilling system and how Fuzzy-processing such information leads to an informed change in "current" directional tool settings.


This document contains the following sections.

If Technical Hole Deviation (THD) in general is new for you, we kindly suggest you first read this.




In 1996, Stoner Engineering attacked the following problem: design a controller for truly automated directional drilling. At that time, 3D rotary steerable directional drilling systems--the ones that provide direct control of lateral force magnitude AND direction close to the bit--were very new. However, given the many published benefits gained by imposing inclinational and azimuthal directional control while rotating, we guessed these systems would eventually become standard for long and medium radii directional drilling.


Tool Force Magnitude and OrientationGiven a 3D rotary steerable directional drilling system, controller OUTPUT was the change in the effective Tool Force Magnitude AND Orientation (TFMO) acting at the adjustable stabilizer (or otherwise near the bit, depending on system specifics); with respect to the adjacent sketch, this is vector components DTFy and DTFx. To keep the controller practical, DTFMO must be determined from only the current actual well path and the current preferred well path, that is, no models of directional drilling were to be employed. The far from simple challenge was to create a controller--the logic implemented as software in a computer chip--that could "do" what a "good" directional driller does.


openheadThe direction in which a bit drills cannot accurately be predicted. Thus, a drilling direction controller based on a rigorous (or otherwise) model of drilling is in the practical sense, futile. That doesn't mean simulators don't have value; it means that using classical control theory to design a controller for directional drilling is severely limited in the best it can ever do. To think that the mental data-processing capabilities of a directional driller can be "temporarily" replaced with one or a few linear equations is far-fetched. Thus, in our opinion a "good" controller actually mimics--what we think are--the thought processes of a directional driller. One way to attempt this is with Fuzzy control theory. Fuzzy control theory provides a means to design a controller for highly complex dynamic systems, with a structure that can be entirely explained with words and intuitive phrases we can understand. Fuzzy control theory is also based on mathematical concepts that better model how humans think and convey information.




There are two primary reasons for directional steering automation:

  1. Less 24/7 dependency on "human touch"


    • Directional  driller control performance must at times vary. Even if "you" have the best of the best directional drillers, they can't be everywhere all of the time, and they must sleep.


  2. Better well bore for the operator


    • Pioneering technical analyses of bottomhole assemblies began with the published works of Arthur Lubinski in the 1950's. He showed that imposing minor changes to controllable operating parameters produces a well bore with minimum dogleg severity variance. This equates to a "smooth", usable well bore. If system controller software (the "brains") is sufficient to "temporarily" compete with the directional control performance of the best directional drillers, then the software can reside in the downhole tool or otherwise be made to automatically process frequently.

Why automation? A better well bore, drilled on the preferred's that simple.




(Some portions of this page may be outdated.)


Before we continue with a very brief introduction to Fuzzy Logic, we would like to summarize commercial state-of-the-art automated rotary steerable directional drilling systems. Let us begin by defining (truly) automated rotary steerable directional drilling:

  • A directional drilling system possessing a drilling mode whereby tool settings (e.g., TFMO) are automatically determined by system software, and frequently and automatically changed/controlled by system hardware, while drilling.

  • Furthermore, the system controller software addresses angular deviation AND lineal deviation, and only requires "knowledge" of the actual and planned well path trajectories. Thus, the system controller software temporarily assumes the role of a traditional directional driller. 

At least three commercial 3D rotary steerable directional drilling systems exist. They are: 

  • Baker Hughes Inteq's AutoTrak
  • Halliburton's Geo-Pilot
  • Schlumberger's PowerDrive

Baker Hughes Inteq's AutoTrak can only attempt to automatically control angular deviation in "hold mode", and otherwise requires manual "steer mode" to attempt to control lineal deviation. In other words, their system automatically tries to be "on inclination" and "on azimuth"--be they changing or constant--but not necessarily also "on depth". AutoTrak for example is certainly a big step towards true automated directional drilling. However, a comparable analogy is this: "the car is headed straight, just like you asked; however, it's in the river instead of on the road." We are not aware of the "automation" features of PowerDrive or Geo-Pilot, but surmise they are similar to AutoTrak.


If drilling the payzone at the best trajectory is important, then controlling lineal deviation is of utmost concern. Controlling angular deviation alone is far easier than controlling lineal deviation, because controlling lineal deviation inherently requires the ability to also control angular deviation.




"Fuzzy" is a catch-all term that refers to a system or methodology that to some degree employs Fuzzy sets. A Fuzzy set is a general mathematical concept that describes how an element belongs to a particular notion (set) of some domain of definition. Classical, or Boolean set theory declares that membership of an element to a set is either completely true or completely false (black/white, on/off, 1/0, binary). Alternatively, Fuzzy set theory declares that the degree of membership (DOM) of an element within a set lies within a continuum from true to false [1.0, 0.0]. Additionally, and unlike Boolean set theory, an element can "belong" to more than one set...even its opposite!


What does this mean? Consider drilling a horizontal well bore. A hypothetical Fuzzy rule that relates vertical deviation and the change in the vertical tool force component is the following:


  •     IF msVD is VERY HIGH, THEN DTFy should be NEGATIVE BIG


five fuzzy setsLet us examine the "IF" part of the rule. msVD represents an Input variable defined over a domain (e.g., -40 feet to +40 feet). msVD could be described with 5 sets, named VERY LOW, LOW, RIGHT-ON, HIGH, and VERY HIGH. The adjacent figure presents an example "fuzzification" of msVD, in which the preceding 5 fuzzy sets are defined. If they were Boolean sets, discrete true/false boundaries would exist that separate the various notions about vertical deviation.


Let us consider msVD = 16 ft, for example. The graph shows that +16 ft belongs to the set of HIGH vertical deviation to a degree of 0.5, while it also belongs to the set of VERY HIGH vertical deviation to a degree of 0.5 (and to a degree of 0 for VERY LOW, LOW, AND RIGHT-ON). With Boolean sets, DOM is binary; move an infinitesimal amount from the boundary (e.g. to 16.00001 ft) and set membership flips. generic control systemClearly, Boolean sets do not model how humans--including directional drillers (ha)--categorize elements and process information. A black and white world is rare; typically it's many shades of gray.


How do Fuzzy rules work? In short, the consequent ("THEN" part) is true to the same degree as the antecedent ("IF" part) is true, and all rules are "fired" (computed). The ending result is a modified/scaled fuzzification of the respective OUTPUT variable, which is then defuzzified to arrive at a discrete result (e.g., DTFy = -100 LB).




Literally, multiple 10,000's of documents have been published about Fuzzy Logic theory and applications. It is not our intention to even begin to teach Fuzzy Control Theory to you. A query with search string "Fuzzy Sets" at returns over 400 books! What should be retained from this primer on Fuzzy Logic is that it's not just theory. Several industries have successfully applied Fuzzy technology to solve real problems for monetary benefit. See the (dated) table below that lists a few commercial applications that employ Fuzzy Logic. The sources are:

  • 1) Kosko, Bart. 1993. Fuzzy Thinking: The New Science of Fuzzy Logic. New York, New York: Hyperion.
  • 2) McNeill, Daniel, and Paul Freiberger. 1994. Fuzzy Logic. The Revolutionary Computer Technology That Is Changing Our World. New York, New York: Simon & Schuster Inc.
Product DescriptionCompany
air conditionerHitachi, Matsushita, Mitsubishi, Sharp
aircraft controlRockwell Corp.
anti-lock brakesNissan
auto engineNissan
auto transmissionHonda, Mitsubishi, Nissan, Saturn, Subaru
cement kiln controlMitsubishi Chemical
chemical mixerFuji Electric
copy machineCanon
cruise controlIsuzu, Nissan, Mitsubishi
elevator controlFujitec, Mitsubishi Electric, Toshiba
factory controlOmron
golf diagnostic systemMaruman Golf
handwriting recognitionSony
health management systemOmron
iron mill controlNippon Steel
kerosene heaterMatsushita
microwave ovenHitachi, Matsushita, Sanyo, Sharp, Toshiba
plasma etchingMitsubishi Electric
refrigeratorMatsushita, Sharp
rice cookerMatsushita, Sanyo
shower systemMatsushita
still cameraCanon, Minolta
space shuttle dockingNASA
stock tradingYamaichi
subway control systemHitachi
televisionGoldstar, Hitachi, Samsung, Sony
traffic control systemMatsushita
vacuum cleanerHitachi, Matsushita, Toshiba
video camcorderCanon, Matsushita, Sanyo
washing machineGoldstar, Hitachi, Matsushita, Samsung, Sanyo, Sharp


Fuzzy set theory was invented by Dr. Lotfi Zadeh in 1965. The first commercial applications of Fuzzy Logic addressed control problems (e.g., controller for a cement kiln; controller for a high-speed train). A few Fuzzy systems exist within the Petroleum Industry, and most of those are fuzzy expert systems (e.g., fluid selection for stimulation). As of 1996, we were not aware of any commercial Fuzzy applications in the drilling business, which is why we applied Fuzzy technology to one of the best control problems we have: directional drilling.




Before we continue with an explanation of the FDD controller, let us "jump to the bottom line" to recognize why we believe our work has significant value. We created a directional drilling simulator with which to test and design the FDD controller. The simulator was a 3D finite element model incorporated with a drill-ahead model. The finite element model was a static analysis of a typical rotary-steerable bottom hole assembly. Our drill-ahead model was based on laboratory data and a simulation model, proposed by Millheim and Warren in 1978, and Brett et al. in 1986, respectively. We setup many formation types by altering the respective parameters and stochastically varied those parameters to implement extra complexities with which the controller would have to deal. For example, directional control is different when drilling at 200 feet per hour versus 10 feet per hour.


Progress was slow. In the beginning, we experienced all the common problems associated with complex controllers: (well path) instability and controller-parameter sensitivity. Of course, Technical Hole Deviation and the FDD controller were being invented simultaneously. However, "in the end", we produced a controller that possessed very important characteristics.


Consider the following two vertical section views, which were created with the simulator and the FDD controller. The first one presents six TVD corrections for a horizontal well, where initial vertical deviations varied from 3 feet to 8 feet in one foot increments, and initial well bore inclinations were 90 degrees. The second vertical section view below presents 3 entire horizontal wells, modeled from the KOP through the horizontal section. The significance of these plots is given below!


Section View for six TVD Corrections

Same controller. Different initial conditions. WOW!

Section View for three Horizontal Wells

Same controller. Different well plans. WOW!

All nine smooth well bores were "drilled" with the identical Fuzzy controller! By identical, we mean the controller parameters were kept constant in all cases, while initial conditions, well plans, and formation parameters were significantly varied.


What does this mean? It means GENERALITY--a systems engineer's dream. This technology has performed for so many other industries!

Every controller has control parameters that directly affect the computed OUTPUT, and those parameters must be tuned. Classical controllers (e.g., P, PI, PID) typically have a very small number of parameters, therefore, "choosing" or tuning to find the "right ones" usually does not result in a general controller. In other words, take a tuned classical controller and simply change the initial conditions; directional control performance becomes heavily degraded.


The FDD controller has more than one hundred control parameters, but common-sense human intelligence gets most of them "close-enough" and the remaining few are tuned. That's the power of Fuzzy. Academia cares about theoretical correctness, while industry cares about solving problems efficiently and effectively, period; for this reason, Fuzzy Logic still (after 40+ years) is sometimes met with criticism in Academia.


To view more details of the FDD controller, click NEXT.

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