SPE/IADC 140183

A Comparison of Collision Avoidance Calculations Shola Okewunmi, SPE, Chevron; Andrew Brooks, SPE, Pathfinder, a Schlumberger company

Copyright 2011, SPE/IADC Drilling Conference and Exhibition This paper was prepared for presentation at the SPE/IADC Drilling Conference and Exhibition held in Amsterdam, The Netherlands, 1–3 March 2011. This paper was selected for presentation by an SPE/IADC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers or the International Association of Drilling Contractors and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers or the International Association of Drilling Contractors, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers or the International Association of Drilling Contractors is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE/IADC copyright.

Abstract This paper will describe procedures commonly used in the industry for avoiding unwanted wellbore collisions. Unwanted collisions may occur if the actual position of a wellbore differs from its presumed position. Such differences may arise from errors in positioning the wellhead, errors in directional survey measurements, or incorrect assumptions regarding the survey errors or the trajectory between survey stations.

Normal practice is to assign an error model to each survey. The presumed position of the well then consists of a wellpath centerline and an associated envelope of uncertainty which is derived from the error model. Collision avoidance practices may be based on specifying minimum clearance between the centerlines or between the envelopes of uncertainty, or they may be based on estimates of collision probability.

Exercises have been conducted to compare uncertainty envelopes and estimates of collision probability, calculated by different service companies using different software packages. The exercises showed substantial variation among the results obtained, given the same input data. These results highlight the need for detailed specification of the problem, oversight of the process by suitably qualified personnel, and for clear annotation of all results to indicate the methods employed and assumptions made.

In spite of the complicated error models which are now available, it must be remembered that the values and error distributions assigned to several critical input parameters are little more than educated guesses. Under these circumstances, there are limits to how far it is worth proceeding with refining the details of error modeling, and the use of ample safety factors should be encouraged. Genesis of the study The Industry Steering Committee on Wellbore Survey Accuracy (ISCWSA) was established in 1995, following some concern within the industry that service companies had been claiming widely disparate accuracies for their MWD surveys, despite the facts that all tools operated on similar principles and the dominant error sources were external and therefore common to all. As a result, a set of standard error models was proposed (Williamson 2000) and has now been accepted as a de facto standard by most major MWD service companies. Although the steering committee is now the SPE Wellbore Positioning Technical Section, the standard error model is commonly referred to as the ISCWSA model, and that convention will be followed in this paper.

More recently, concerns have again arisen that different service companies may report substantially different survey accuracy while using nominally identical ISCWSA error models. A particularly disturbing example is shown in Fig. 1. The figure plots three components of the ellipsoid of uncertainty (EoU) semi-axis dimensions, as obtained by two companies for the same well, through application of a standard ISCWSA model. It is evident that there are wide differences in the reported ellipsoid dimensions in all three directions. This study was therefore initiated to determine the cause of such discrepancies. Estimation of collision probability Estimation of collision probability is intimately related to estimation of position uncertainty. Standard error models for MWD were described by Williamson 2000, following earlier work by Harvey 1971, Wolff 1981, and Thorogood 1990. Various collision avoidance methods have been described (Thorogood 1991, Williamson 1998a, McNair 2005, Poedjono 2007, Brooks 2010); most of these which are in common usage rely on calculation of a clearance factor which is based on the sizes of error ellipsoids at a specified significance level. A collision avoidance work group within the ISCWSA has described and compared several such methods (ISCWSA 2010).

2 SPE/IADC 140183

Common to most estimation methods is an assumption that sources of survey uncertainty are independent and follow Gaussian distributions. It is well understood that the latter approximation is a poor one in the case of uncertainty in the earth’s magnetic field (Macmillan 2010) and drillstring magnetization (Grindrod 1983). Unfortunately, these two error sources frequently make dominant contributions to survey azimuth uncertainty.

Because collisions are low-probability events, quantitative estimates of collision probability are extremely sensitive to EoU dimensions and also to the type of distribution chosen to model error probability. For example, in the case of a one-dimensional problem with a Gaussian distribution, a 10% change from 1 to 1.1 standard deviations changes the corresponding probability of an out-of-range event by 17% from 1 in 3.2 to 1 in 3.7, while a 10% change from 3 to 3.3 standard deviations changes the probability by 179% from 1 in 370 to 1 in 1034. In the case of wellbore collisions, it is not uncommon to work at the five or six standard deviation level, where the sensitivity of event probability to EoU dimensions is even greater. Status of published error models Although standard MWD error models have been available for many years, it is recognized that they are imperfect, and they are continuing to evolve. A number of revisions have been issued, including:

• Rev. 0: The original MWD error model (Williamson 2000), with some minor corrections. • Rev. 1: Misalignment terms revised to the same form as the gyro error model (Torkildsen 2008). In deep near-

vertical drilled wells, this revision can increase the size of horizontal ellipsoid dimensions, which were considered to be unreasonably small using Rev. 0.

• Rev. 2: Correction to some of the values assigned to depth uncertainty terms. • Rev. 3: Replacement of toolface-dependent sensor bias and scale factor terms by terms independent of toolface,

similar to those in the gyro error model (Torkildsen 2008). With this revision, weighting functions for all standard MWD terms become independent of toolface.

Several error terms and survey procedures have been the subject of recent discussions or revision proposals, without yet giving rise to a new revision of the model. These include:

• In-field referencing (Russell 1995) and interpolation in-field referencing (Williamson 1998b). • Aeromagnetic inversion and downward continuation (Waag 1999). • Continuous MWD surveys, and survey station position or interval (Stockhausen 2003). • Sag, which may dominate TVD uncertainty in horizontal or extended reach wells (Studer 2006). • Multi-station analysis (Nyrnes 2009). • Geomagnetic reference field, including declination (Macmillan 2010).

As a result of continuing model development and varying survey practices, the standard MWD error model has bred a large number of variations. Different service companies may prefer to use different error model variations to reflect their own practices. It is important for the operator to understand these issues rather than to depend on a black box solution from a service company, and to demand that the error model assigned to a survey be appropriate to the well geometry and the particular survey techniques and quality control (QC) procedures in use. Recent publications (Ekseth 2006, 2007) have emphasized the need for survey quality control and the intimate relationship which must be demonstrated between an error model and its corresponding QC checks. Initial investigation Following an examination of the results presented in Fig. 1, three MWD service companies agreed to assist in determining the cause of the discrepancies. A number of factors were quickly identified as contributing to the discrepancies in Fig. 1, among them:

• One company had used the original ISCWSA error model (Rev. 0), while the other had used a later version (Rev. 2), which included the revised treatment of misalignment errors described above under Rev. 1. This was a major factor contributing to the difference in major and minor axis EoU dimensions.

• The original ISCWSA error model (Williamson 2000) permits a number of options, including fixed versus floating rig, sag corrected or not, and symmetric or biased treatment of drillstring magnetization (AMID) and depth (DST) terms; the two companies had used different default settings. The use of a biased depth term by one company was resulting in zero uncertainty due to stretch, contributing to the difference in the vertical EoU dimension.

• The two companies had presented their results at differing confidence levels; their ellipsoids were scaled to a different number of standard deviations.

• One company had presented ellipsoid dimensions referenced to a north - east - vertical (NEV) coordinate system, while the other was using highside - lateral - along-hole (HLA) coordinates.

• Instructions had not specified whether surface location uncertainty should be included in the EoU dimensions. • Slightly different results could be obtained depending on whether intermediate stations were inserted in long

gaps in the survey record, such as the gap from rig datum to sea floor in deep water wells.

SPE/IADC 140183 3

Second comparison Survey listings from three wells were then distributed to the three participating service companies, with instructions to compute survey uncertainty using a standard ISCWSA MWD error model, and with detailed specifications intended to resolve the problems noted above. In addition to the deep near-vertical well which was the source of Fig. 1, the second was an extended-reach well, and the third followed a complex high-angle designer well profile. One well was drilled on land, and the other two were in deep water, one of them to be modeled as drilled from a semisubmersible and one from a tension leg platform (TLP). Results were requested using two different versions of the ISCWSA error model (Rev. 0 and Rev. 2).

This exercise produced the results shown in Figs. 2 through 4; for clarity, only results for the Rev. 2 model are shown. For the well shown in Fig. 3, the three companies were in close agreement along the major axis. However, in spite of care being taken to specify the model parameters, it is apparent that some significant differences existed among the results from the three companies. Further investigation revealed the following contributing factors:

• Different companies were using different defaults, either rig datum or seafloor, for ellipse start depth on offshore locations.

• There was some inconsistency in computation of depth terms in deep water, if the ellipse start depth was substantially below the depth datum. Published models do not explicitly define where depth weighting functions should originate in this case.

• Some confusion remained as to whether a TLP should be modeled as a fixed or floating installation. • One company had incorrectly set up the grid convergence term. • One company identified and subsequently fixed a program bug which had caused grid convergence to be mis-

applied in the calculation of error term weighting functions. After resolving these additional issues, the three companies were finally able to achieve an acceptable degree of

agreement for all three wells. The process of investigating and resolving ISCWSA error model implementation differences was beneficial both to the

operator and to the service companies involved; however, it proved to require an unexpectedly long and tedious effort. The following are among the reasons why this was the case: error propagation is not rigorously defined for tie-ons or cases where uncertainties begin below the survey datum, published test cases do not exercise the models fully, operators do not always specify the problem precisely, and service companies may not be annotating their results completely. Unresolved issues There remains some debate in the survey community concerning proper computation of vertical or depth uncertainty in cases where error ellipses start at a point below the rig datum. Such cases have not been included in published descriptions of the ISCWSA error model or in example test cases. This normally makes only a minor contribution to the overall error budget, but it may need to be taken into consideration when comparing error model results.

Although the ISCWSA has taken the position that the use of biased error terms is to be discouraged, the published error models continue to include a biased depth stretch (DST) term with zero associated uncertainty. It is suggested that a preferable procedure would be to apply a depth correction (Chia 2006), and model the residual stretch uncertainty with a reduced but non-zero value.

The larger issue is management of the many options and revisions available within ISCWSA models, and additional tool-specific terms introduced by service companies to differentiate their products. A minimum requirement is that a position uncertainty report should clearly indicate which model terms were used in its preparation. Conclusions

• ISCWSA models provide a common framework for modeling positional uncertainty, but the results are very dependent on detail, and many different variations of the “standard” ISCWSA model are now in use.

• The behaviors of some error terms are incompletely defined in published models, particularly when surveys are tied on or when error ellipses are generated starting below the depth datum.

• Use of an inappropriate model or version can cause a survey to appear to be better than reality. Service companies must resist the temptation to select a model based on this criterion, while operators should be sufficiently knowledgeable to demand use of an appropriate model.

• Position uncertainty reports should be annotated with sufficient detail to allow replication of the results by another party.

Acknowledgements The authors would like to thank the managements of Chevron and Pathfinder for permission to publish this paper, Bill Calhoun for initiating and encouraging the study, and Nadeem Adeleke for his assistance in preparing results. Thanks are also due to survey specialists in the participating MWD service companies.

4 SPE/IADC 140183

References Brooks, A.G. 2010 “A New Look at Wellbore Collision Probability” SPEDC June 2010, 223-229. Chia, C. et al. “A New Method for Improving MWD Logging Depth” paper SPE 102175, presented at SPE Annual Technical Conference

and Exhibition, San Antonio, 24-27 September 2006. Ekseth, R., et al. 2006 “The Reliability Problem Related to Directional Survey Data” paper SPE 103734 presented at IADC/SPE Asia

Pacific Drilling Technology Conference and Exhibition, Bangkok, 13-15 November 2006. Ekseth, R., et al. 2007 “High-Integrity Wellbore Surveys: Methods for Eliminating Gross Errors” paper SPE 105558 presented at

SPE/IADC Drilling Conference, Amsterdam, 20-22 February 2007. Grindrod, S.J. and Wolff, C.J.M. 1983 “Calculation of NMDC Length Required for Various Latitudes Developed From Field

Measurements of Drill String Magnetization” paper SPE 11382, presented at IADC/SPE Drilling Conference, New Orleans, 20-23 February 1983.

Harvey, R.P, Walstrom, J.E. and Eddy, H.D. 1971 “A Mathematical Analysis of Errors in Directional Survey Calculations” JPT November 1971, 1368-1374.

ISCWSA 2010 “Collision Avoidance Calculations - Current Common Practice” report by the Collision Avoidance Work Group, September 2010.

Macmillan, S., and Grindrod, S. 2010 “Confidence Limits Associated With Values of the Earth’s Magnetic Field Used for Directional Drilling” SPEDC June 2010, 230-238.

McNair, G.A. et al. 2005 “Implementation of a New Risk Based Well Collision Avoidance Method” paper SPE 92554 presented at SPE/IADC Drilling Conference, Amsterdam, 23-25 February 2005.

Nyrnes, E., Torkildsen, T. and Wilson, H. 2009 “Minimum Requirements for Multi-Station Analysis of MWD Magnetic Directional Surveys” paper SPE 125677, presented at SPE/IADC Middle East Drilling Technology Conference and Exhibition, Manama, 26-28 October 2009.

Poedjono, B. et al. 2007 “Minimizing the Risk of Well Collisions in Land and Offshore Drilling” paper SPE 108279 presented at SPE/IADC Middle East Drilling and Technology Conference and Exhibition, Cairo, 22-24 October 2007.

Russell, J.P., Shiells, G., and Kerridge, D.J. 1995 “Reduction of Well-Bore Positional Uncertainty Through Application of a New Geomagnetic In-Field Referencing Technique” paper SPE 30452 presented at SPE Annual Technical Conference and Exhibition, Dallas, 22-25 October 1995.

Stockhausen, E.J. and Lesso, W.G. 2003 “Continuous Direction and Inclination Measurements Lead to an Improvement in Wellbore Positioning” paper SPE 79917, presented at SPE/IADC Drilling Conference, Amsterdam, 19-21 February 2003.

Studer, R. and Macresy, L. 2006 “Improved BHA Sag Correction and Uncertainty Evaluation Brings Value to Wellbore Placement” paper SPE 102088, presented at SPE Annual Technical Conference and Exhibition, San Antonio, 24-27 September 2006.

Thorogood, J.L. 1990 “Instrument Performance Models and Their Application to Directional Surveying Operations” SPEDE December 1990, 294-298.

Thorogood, J.L., Hogg, T.W. and Williamson, H.S. 1991 “Application of Risk Analysis Methods to Subsurface Well Collisions” SPEDE December 1991, 299-304.

Torkildsen, T. et al. 2008 “Prediction of Wellbore Position Accuracy When Surveyed With Gyroscopic Tools” SPEDC March 2008, 5-12. Waag, T.I. et al.1999 “Local Geomagnetic Field Monitoring Closes the Gap Between MWD and Gyro Directional Surveying” paper SPE

56699, presented at SPE Annual Technical Conference and Exhibition, Houston, 3-6 October 1999. Williamson, H.S. 1998a “Towards Risk-Based Well Separation Rules” SPEDC March 1998, 47-51. Williamson, H.S. et al. 1998b “Application of Interpolation In-Field Referencing to Remote Offshore Locations” paper SPE 49061,

prepared for SPE Annual Technical Conference and Exhibition, New Orleans, 27-30 September 1998. Williamson, H.S. 2000 “Accuracy Prediction for Directional Measurement While Drilling” SPEDC December 2000, 221-233. Wolff, C.J.M. and de Wardt, J.P. 1981 “Borehole Position Uncertainty - Analysis of Measuring Methods and Derivation of Systematic

Error Model” JPT December 1981, 2338-2350.

SPE/IADC 140183 5

Figures

Fig. 1. Original EoU comparison, near-vertical well.

Fig. 2. Second EoU comparison, near-vertical well.

6 SPE/IADC 140183

Fig. 3. EoU comparison, deep extended-reach well.

Fig. 4. EoU comparison, designer well.