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Technical Hole Deviation (THD) quantifies spatial differences between actual and planned well paths resulting in exclusive insight regarding directional steering decision making, performance monitoring, and post-evaluation. More specifically, THD provides:

  • ...the geologist with the ability to see the survey and the well plan and the geosteered beds, all together in the ***MD*** domain; thereby fully eliminating vertical section projection-dependent distortion issues. This enables most-informed directional steering monitoring and revised well path decision making.
  • ...the directional driller with crucial information to rationalize directional tool setting adjustments. A THD well log uniquely augments the visual tools available to the DD, especially for 3D/complex wellbores and within non-linear hole sections. 
  • ...the manager with enhanced directional control performance monitoring capabilities. Multiple relevant directional wellbore details cannot be determined from vertical section and plan view plots (e.g., dogleg-severity and wellbore inclination, and more importantly how they are changing absolutely and relative to the planned trajectory). THD logs present information at a scale that doesn't mask true details.
  • ...the systems designer with a firm basis upon which to evaluate overall directional drilling control performance. With THD, directional control performance can be quantified with various metrics.

Technical Hole Deviation (THD) is calculated at each survey station. THD may be fully presented with two well logs. Computing THD only requires a mathematical understanding of the "current" planned well path, and directional survey data. Employing THD technology doesn't require more "steering"; rather, it's an enhanced use of standard information to make more-informed directional control decisions at the same or less steering frequency.


Technical Hole Deviation (THD) is:

  • directly applicable to all types of directional drilling (ultra-short, short, medium, and long radii of curvature; slant; horizontal, etc.)
  • relevant to every type of directional drilling system (rotary, PDM, rotary steerable) and all industries (oil & gas, utilities/HDD, in-seam coal bed methane (CBM), and in-seam coal mine methane degasification)
  • mathematically valid as defined, with any planned well path profile (2D/3D circular arc, line, catenary, double circle, spline-in-tension, 3DStratBlock, earth model marker bed grid, "plan" defined by survey of offset well for relief well drilling, etc.)

Of critical importance to almost any system is how its state is changing. Actual directional well paths are "noisy". From an engineering/mathematical point of view, differentiating "noisy" data is useless. In effect, THD smoothes the data by associating the actual well path to the planned well path. The smoothed profile is then differentiated (differenced) to determine how it is changing relative to lineal and angular target path properties. This process provides the foundation for projecting future well path deviations, without explicitly assuming a model of directional drilling.


This document contains the following sections.



THD ComponentDescriptionDeviation "Sense"UnitOrderLineal DeviationAngular DeviationVerbal Descriptor
msVDvertical deviationVerticalft or m1stX High/Low
RCVDrelative change in vertical deviationVerticalft/1000ft or m/304.8m2ndX Positive/Negative
msIDinclinational deviationVerticaldeg1st XHigh/Low
RCIDrelative change in inclinational deviationVerticaldeg/100ft or deg/30.48m2nd XPositive/Negative
msHDhorizontal deviationHorizontalft or m1stX Left/Right
RCHDrelative change in horizontal deviationHorizontalft/1000ft or m/304.8m2ndX Positive/Negative
msADazimuthal deviationHorizontaldeg1st XHigh/Low
RCADrelative change in azimuthal deviationHorizontaldeg/100ft or deg/30.48m2nd XPositive/Negative


The planned well path defines the preferred location of the wellbore in 3D space. Every directional well has a planned path. In some cases as information is acquired while drilling, the planned path changes via geosteering. However, there is always a planned path in force at each survey station.


Technical hole deviation is defined with properties of the nearest point between "current TD" and the "current" planned path. Given the current actual location of the wellbore, there is one point along the planned path that minimizes the 3D distance between where the bottomhole location actually is, and where it is preferred.


This point along the planned path is called MD* ("measured depth star"). Associated with MD* is N*, E*, TVD*, Inc*, and Azi*, respectively, planned values North, East, True Vertical Depth, Inclination, and Azimuth. With a directional survey and a mathematical understanding of the planned path, MD* is found iteratively. (* always denotes a planned value)


Eight components collectively define technical hole deviation. They are based on lineal and angular differences—and the relative changes thereof—between the actual and planned well paths. Four THD components address hole deviation in the "vertical" sense, and four THD components address hole deviation in the "horizontal" sense. Other variables of interest include:


INC - actual wellbore inclination angle; (deg)

INC* - planned wellbore inclination angle; (deg)

DLS - actual wellbore dogleg-severity; (deg/100ft or deg/30m)

DLS* - planned wellbore dogleg-severity; (deg/100ft or deg/30m)

AZI - actual wellbore azimuth; (deg)

AZI* - planned wellbore azimuth; (deg)

DL - difference in MD* between two consecutive survey stations

b - subscript with reference to current wellbore total depth


A description and mathematical definition of each THD component follows.


msVD/msHD (1st Order, Lineal Deviation)


the math behind common senseVertical Deviation, msVD, and Horizontal Deviation, msHD, are the two most easily-visualized components of technical hole deviation. They convey where the wellbore exists in space, relative to the (current) preferred location.






By design, their definitions are such that being High or Low, and Left or Right, match common directional-driller sense. The terminology and equations apply to ALL curvilinear and linear well plans (i.e., not just circular-arc). In the mind's eye, if you were to "walk" along the planned path at MD* as the well is drilled and point to the current wellbore TD, the components of that pointing vector, relative to the high side of the planned hole, would be msVD and msHD.


The relevancy of industry's "vertical section" deteriorates when the current planned azimuth is different from the vertical section azimuth. In other words, projecting well path departure onto a single vertical plane (i.e., to compute vertical section) can sometimes have little meaning over thousands of feet of hole. EVERY well with "turn" built into the plan, to some degree, suffers from this fact. It's not an issue with msVD and msHD.


click to enlarge Log strip discussion


RCVD/RCHD (2nd Order, Lineal Deviation)


The Relative Change in Vertical Deviation, RCVD, and the Relative Change in Horizontal Deviation, RCHD, are less intuitive than are msVD and msHD. However, they contain much information, including "predictive" qualities. We say predictive because, for example, RCVD leads msVD (or conversely msVD lags RCVD).


    RCVD        RCHD

*Note: For metric, use 304.8 in place of 1000 in the equations above.


Consider two examples of technical hole deviation in the vertical sense, as sketched below.


CaseA        CaseB


Current msVD is identical in both cases, that is, the wellbore is low of the plan by the same amount. Current RCVD is positive in both cases but the magnitude of RCVD for Case B is clearly higher. Thus, the plan is being approached more quickly in Case B than in Case A, which may have significant influence on the next directional tool setting decision.


RCVD provides insight as to how msVD is changing. RCHD provides insight as to how msHD is changing. The signs and magnitudes of RCVD and RCHD are important for real-time tool-setting purposes. For example, if the wellbore is high, then RCVD must be made negative before the wellbore will begin to approach the plan. Typically, this will happen long before the planned path is approached or intersected, hence, the "predictive" quality as mentioned above. RCVD and RCHD are also used for projecting msVD and msHD.


click to enlarge Log strip discussion

msID/msAD (1st Order, Angular Deviation)


Inclinational Deviation, msID, and Azimuthal Deviation, msAD, are differences in actual and preferred wellbore angles. For example, if the current wellbore inclination is 91.6 degrees while the plan is horizontal, msID = 1.6 degrees.


    msID        msAD


Visualizing msID or msAD in space is not simple. Nevertheless, both their signs and magnitudes contain important directional control information, especially when combined with other technical hole deviation components and while considering the task at hand. In all cases, controlling msID (or msAD) is easier to accomplish than controlling msVD (or msHD), because sooner or later msVD depends on msID.


While drilling the upper hole section of a directional well, maintaining msID and msAD close to zero is usually more important than minimizing msVD and msHD. Why? Because it means the wellbore is headed in the planned directions and drilling is taking place at the planned DLS. For example, you may be drilling that 45 degree tangent section 35 feet low, but you're drilling it at 45 degrees, which may be perfect in the practical sense.


However, landing and drilling the payzone "perfectly" requires minimization of all 8 components of hole deviation. In the vertical sense, this includes, msVD, RCVD, msID, and RCID. In the horizontal sense, this includes, msHD, RCHD, msAD, and RCAD. Typically, "being on depth", that is, minimizing hole deviation in the vertical sense is most important.


It is entirely possible for msVD ~ 0, RCVD ~ 0, and msID be significantly greater-than or less-than 0. In other words, even though you're currently on-depth, msVD won't stay zero for long and the wellbore will soon be either high or low. Collectively analyzing technical hole deviation in the vertical sense can help eliminate the foregoing situation.


RCID/RCAD (2nd Order, Angular Deviation)


The Relative Change in Inclinational Deviation, RCID, and the Relative Change in Azimuthal Deviation, RCAD, are similar in design to RCVD and RCHD. They quantify how msID and msAD are changing as the hole is drilled.


    RCID        RCAD

*Note: For metric, use 30.48 in place of 100 in the equations above.


As was the case with 2nd order lineal deviation, both the signs and magnitudes of RCID (or RCAD) have relevancy and insight into controlling msID and msVD (or msAD and msHD).




Most directional drillers employ some sort of forecasting scheme to assist in determining their directional tool-setting control actions. Some methods are quantitative (e.g., linear projection, path projection, etc.), while others are purely qualitative and include simply "mental processing" of numeric and/or graphed information. No method is perfect, since what lies ahead of the bit and how it will affect drilling direction is unknown beforehand.


Technical hole deviation provides a superior foundation upon which to form opinions about hole deviations and thus, directional tool-setting control actions. THD projections forecast msVD and msHD and are model-free. Furthermore, when viewed on a THD well log, THD projections significantly compliment the other graphed information that is "mentally processed" by the directional driller.


The equations for projecting THD in the vertical sense (msVD) and in the horizontal sense (msHD) are provided below. In either case, delMD represents a projection length (e.g., 100 feet measured depth) beyond the current known values (i.e., at the deepest survey station "n"). 


    msVDn+1         msHDn+1

*Note: For metric, use 304.8 in place of 1000 in the equations above.


Although the THD projection equations are linear, it does not mean the planned or actual well paths are assumed linear, circular, or of any specific shape. What is assumed is that the relative change in deviation is constant over delMD; over short distances this assumption is often completely valid. Obviously, forecasting and subsequent visual interpretation influences the tool-setting control actions taken by the directional driller, which will affect the actual well path and thus, the actual THD profiles that unfold.






In spite of numerous attempts (& millions of dollars) to develop mathematical models that could directly assist directional drillers in how to steer--particularly in the 1970's and 1980's--drilling direction cannot be predicted with significant certainty. The core picture that captures the complexity of drilling direction is conveyed in the cognitive map, pictured above. A cognitive map draws a causal picture of the association of components within a complex dynamic system. All that may be directly controlled while drilling (e.g., hookload, rotary speed, pump rate, directional tool settings/orientations, mud characteristics) rests in the node "Operating Conditions".


Even with a complex model that attempts to address the drilling system as a whole, the effort can't help for live practical purposes because there are too many significant unknowns. While drilling, the 3D circumferential shape of the wellbore or the true dynamic hole diameter profile with depth is unknown, along with multiple other factors that directly or indirectly affect drilling direction! This is one of many reasons why directional drillers have never required a simulator to do their job. The system is too complex to be modeled with any relevancy, and what lies ahead of the bit is even more uncertain. Instead, directional drillers make real-time decisions regarding steering with quantitative information that is accessible. Such information is predominantly geometric-based.


When one or more of the sub-system nodes in the cognitive map alters drilling direction, its significance is manifested empirically via Technical Hole Deviation. Thus, knowing the precise cause of changed drilling direction—a change in the compressive strength of the formation being drilled or hole enlargement, for examples—is of hindsight value for real-time operations.


A planned drilling trajectory exists for a reason. While tolerances vary by application and within application, having the ability to control the drilling direction is important to the oil and gas industry.


While it is true that drilling direction cannot be predicted, that doesn't mean to say it can't be controlled (i.e., steered). A similar analogy is that you can't predict the precise path your vehicle will travel while driving down a street, however, you still manage to steer your vehicle to its destination by continually acting, reacting, and processing many forms of information. In general, steering for humans is a relatively simple task. Just consider driving a car, playing a video game, or watching a 3 year old on a tricycle. Placing our human steering logic into a computer system, however, is a challenge.




Automation is coming to drilling. The context to which this statement refers is similar to when cars began to have cruise controls and aircraft began to have auto-pilot mode. One of the first steps in designing a control algorithm/methodology for a directional drilling control system is to identify observables and controllables. Relevant observables are metrics (inputs) that quantify the current state of the system, while controllables represent--as one may easily guess--that which may be directly controlled. For example, wellbore inclination is an observable, while effective directional tool force magnitude and orientation (TFMO) is a controllable for rotary steerable directional drilling systems.


Stoner Engineering patented a Fuzzy-Logic-based controller for auto/guided directional drilling and for general steering guidance at surface. In its infancy in 1996, the project began with identifying the system observables of directional drilling trajectory control. This work led to what is now called Technical Hole Deviation. Since Technical Hole Deviation is important "input" to an auto/guided directional drilling control system, we feel THD has significant potential to assist the directional drilling industry in general by directly assisting directional drillers and conveying information to operators. A more-informed human (or system) is more likely to make better decisions.


Discovering new technology from "standard data" is a welcomed occurrence. Numerically defining geometric hole deviation extracts an abundance of information, simply from directional survey data and a planned well path. The details of directional control performance are no longer hidden. THD well logs convey the actual and planned well path properties in a manner far superior than path projections onto static vertical and horizontal planes and tables of numbers alone.


Directional drilling trajectory control requires minimization in at least 4 x 2 = 8 dimensions. This helps to convey its complexity. Minimizing 8 variables is not simple for man or machine. Much value exists in simply identifying what needs minimized! It is our opinion that the THD state variables msVD, msID, msHD, msAD, and the respective THD state-transition variables RCVD, RCID, RCHD, and RCAD, collectively and sufficiently quantify how a directional well path differs from its planned trajectory.


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