# Application of Minimum Curvature Method to Wellpath Calculations

on January 27, 2023

### ABSTRACT

A major drawback of directional and horizontal well drilling is the numerous complex computations required to be done while planning a well. These computations are very stressful and time consuming especially when done manually.

One of the objectives of this study was to develop a user friendly Excel Spreadsheet program that would make the computations of these well trajectory parameters easier, faster and accurate.

An Excel Spreadsheet program was developed employing the Minimum Curvature method (and for other five methods) for wellpath design and planning. This would help increase the usage of these trajectory methods especially the Minimum Curvature method.

The program is able to provide pictorial views both in the vertical and horizontal plane of the trajectory of the drilling bit’s position in the wellbore. This would therefore help to minimize risk and uncertainty surrounding hitting predetermined target.

This is possible because deviations can easily be detected and the necessary directional corrections or adjustment be initiated to re-orient the drilling bit to the right course before (planning process) and during the drilling operations.

ABSTRACT ……… iii
LIST OF FIGURE …… vii
LIST OF TABLES ……….. x
LIST OF APPENDICES …… xi
ACKNOWLEDGMENTS …. xii
DEDICATION ……… xiii
DECLARATION ……… xiv

CHAPTER  FORMULATION OF THE PROBLEM

1.1 Introduction ……. 1
1.2 Problem Definition …….. 1
1.3 Objectives of Study ………. 2
1.4 Methodology and Scope of Study …… 2
1.5 Organization of the Study ……………… 2

CHAPTER 2

THEORETICAL BACKGROUND ON DIRECTIONAL DRILLING ……………. 4
2.1 Directional Drilling 4
2.1.1 History of Directional Drilling ….…… 4
2.1.2 Reasons for Directional Drilling ……… 5
2.2 Fundamental Concepts/Basis of Directional Drilling .…. 10
2.3 Well Trajectory Planning …….. 11
2.3.1 Type A: Build and Hold …………….. 11
2.3.2 Type B: Build, Hold and Drop …………. 12
2.3.3 Type C: Build, Hold and Build or ‘S’ shape Trajectory . 12
2.3.4 Type D: Continuous Build …….. 12
2.4 Planning the Well Survey Parameters ………. 12
2.4.1 Planning the Kickoff and Trajectory Change ……. 14
2.4.2 Directional Surveying ………………. 15
2.4.2.1 Reference Systems and Coordinates … 15
2.5 Methods for Calculating Wellbore Trajectory ……… 17
2.5.1 Tangential Method …… 22
2.5.2 Balanced Tangential Method .… 22
2.5.3 Mercury Method ……….. 22
2.5.4 The Averaging Method …………… 22
2.5.5 Radius of Curvature Method ……. 23
2.5.6 Minimum Curvature Method … 23
2.5.7 Comparison of the Six Methods ……… 24
2.6 The Minimum Curvature Method ……. 24
2.6.1 Introduction ……… 24

CHAPTER 3 PROGRAM DEVELOPMENT IN EXCEL SPREADSHEET

3.1 Introduction. 28
3.2 Data Input Interface ..……… 28
3.3 The Computational Procedure for the Wellpath Trajectory Design …. 29
3.3.1 Data Input Interface ………… 28
3.4 Derivation of Associated Equations for the various Wellpath Trajectory Methods used for the development of the Excel Spreadsheet Program … 32

CHAPTER 4 COMPUTATION, COMPARISON AND ANALYSIS OF RESULTS

4.1 Introduction …….. 54
4.2 Validation of the Excel Spreadsheet Program ….. 56
4.3 Summary of Observations and Analysis of Results using hr Adams, (1985) Data … 66
4.4 Summary of Observations and Analysis of Results using Bourgoyne et al, (1991) Data . 86
4.5 General Discussion … 86

CHAPTER 5 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary …. 87
5.2 Conclusions . 87
5.3 Recommendations …………….. 88
NOMENCLATURE ………. 89
REFERENCES ……. 90
APPENDICES ……… 91

Directional drilling is the science and art of deviating a wellbore along a planned course to a subsurface target whose location is a given lateral distance and direction from the vertical (Bourgoyne et al, 1991).

Directional drilling and horizontal wells represent an efficient way to achieve or hitting special targets that may or are very difficult to reach using vertical wells (Tarek, 2000).

Directional drilling is relatively done to increase production rates, control water and gas conning, control sand production and increase recovery rate (Bourgoyne et al, 1991).

There are many reservoirs which can not be tapped by vertical wells or would be uneconomical to exploit with vertical wells (Bourgoyne et al, 1991).

Other reservoirs are also characterized by vertical permeability or the pay zones may be very thin and producing with vertical wells would require quiet a number of them which would make vertical wells to be very uneconomical in such situations.

The application of vertical wells in such formations could also result in lower ultimate recovery (Tarek, 2000). In such low permeability formations, the only way out is to use directional and horizontal well technology which has over the years proved to enhance ultimate recovery (Bourgoyne et al, 1991).

### REFERENCES

Adams J. Neal and Charrier Tommie, Drilling Engineering, A Complete Well Planning Approach, PennWell Publishing Company, Tulsa, Oklahoma, 1985.
Baker Hughes INTEQ, Drilling Engineering Workbook, A Distributed Learning Course, December 1995.
Bourgoyne, Millheim, Chenvert, Young: Applied Drilling Engineering, SPE Textbook Series, Vol. 2, 1991.
BP Amoco, Directional Survey Handbook, 1999.
Chukwu A. Godwin, Drilling and Well Completion Lecture material, African University of Science and Technology, Abuja-Nigeria, 2008.
Molvar E.M., 2003. Drilling smarter: Using minimum-footprint directional drilling to reduce oil and gas impacts in the Intermountain West.  Laramie, WY: Biodiversity Conservation Alliance, 32 pp, 2003.