A CASE STUDY ON THE OPTIMIZATION OF HYDRAULIC HORSEPOWER FOR EFFICIENT BOTTOM HOLE CLEANING IN DRILLING By Orogun Humphrey Onome Submitted in Partial fulfillment of the requirements for the degree of Masters of Engineering Major Subject: Petroleum Engineering At Dalhousie University Halifax, Nova Scotia December, 2013 © Copyright by Orogun Humphrey Onome, 2013 i DALHOUSIE UNIVERSITY PETROLEUM ENGINEERING The undersigned hereby certify that they have read and recommend to the Faculty of Graduate Studies for acceptance a thesis entitled “A CASE STUDY ON THE OPTIMIZATION OF HYDRAULIC HORSEPOWER FOR EFFICIENT BOTTOM HOLE CLEANING IN DRILLING” by Orogun Humphrey Onome in partial fulfilment of the requirements for the degree of Master of Engineering. Dated: December 2, 2013 Supervisor: _________________________________ Reader: _________________________________ ii DALHOUSIE UNIVERSITY DATE: AUTHOR: TITLE: December 2, 2013 Orogun Humphrey Onome A CASE STUDY ON THE OPTIMIZATION OF HYDRAULIC HORSEPOWER FOR EFFICIENT BOTTOM HOLE CLEANING IN DRILLING DEPARTMENT OR SCHOOL: DEGREE: MEng. Petroleum Engineering CONVOCATION: May YEAR: 2014 Permission is herewith granted to Dalhousie University to circulate and to have copied for noncommercial purposes, at its discretion, the above title upon the request of individuals or institutions. _______________________________ Signature of Author The author reserves other publication rights. Neither the thesis nor extensive extracts from it may be printed or otherwise reproduced without the author’s written permission. The author attests that permission has been obtained for the use of any copyrighted material appearing in the thesis (other than the brief excerpts requiring only proper acknowledgement in scholarly writing), and that all such use is clearly acknowledged. iii DEDICATION This project report is dedicated to my lovely family, Mr. and Mr.’s Dennis Orogun, and to my siblings Desmond, Jane and Micheal Orogun for their support and understanding in making this project work a huge success. Also to my roommate and course mate in the department for their respective input. iv TABLE OF CONTENTS LIST OF TABLES ...................................................................................................................... xi LIST OF FIGURES .................................................................................................................... xii NOMENCLATURE ................................................................................................................... xiii ACKNOWLEDGEMENTS ...................................................................................................... xix ABSTRACT ..................................................................................................................................xx CHAPTER 1: INTRODUCTION .................................................................................................1 1.1 Study Objective ....................................................................................................................1 1.2 Problem Statement ...............................................................................................................1 1.3 Scope of Study .....................................................................................................................1 1.4 Limitations ...........................................................................................................................2 CHAPTER 2: LITERATURE REVIEW ....................................................................................3 2.1 Geomechanics ......................................................................................................................4 2.2 Pore Pressure ........................................................................................................................4 2.3 Causes of Over Pressure ......................................................................................................4 2.3.1 Depositional Effects ..................................................................................................5 2.3.2 Digenetic Processes ..................................................................................................5 2.3.3 Tectonic effect ..........................................................................................................5 2.3.4 Structural Causes ......................................................................................................6 2.3.5 Thermodynamic Effects ............................................................................................6 2.4 Fracture Pressure ..................................................................................................................6 2.5 Mud Weight Planning .........................................................................................................7 2.6 Factors Affecting Rate of Penetration..................................................................................7 2.6.1 Chip Hole Down Effect ...........................................................................................7 2.6.2 Effect of Bit Type ....................................................................................................8 2.6.3 Effect of Drilling Fluid Properties ..........................................................................9 2.6.4 Effect of Formation Characteristics .........................................................................9 2.6.5 Effect of Operating Conditions ................................................................................9 v 2.7 Factors Affecting Hole Cleaning ........................................................................................12 2.7.1 Drill Pipe Rotation ..........................................................................................…..13 2.7.3 Rheology ............................................................................................................…13 2.7.4 Drilling Rate.......................………………………………………………………13 2.7.5 Cutting Bed Characteristics…...…………………………………………………14 2.7.6 Hydraulics…………………………………………………………………...…...14 CHAPTER 3: PORE PRESSURE AND FRACTURE PRESSURE PREDICTION………15 3.1 Methods of Pore Pressure Predictions…………………………………………...............15 3.1.1 Resistivity Method of Pore Pressure Prediction…………………………………15 3.1.2 Sonic Methods of Pore Pressure Prediction……………………………………...17 3.1.3 Equivalent Depth Method……………………………………………………......18 3.1.4 Ratio Method.…………………………………………………………..…...…...19 3.1.5 Neutron Porosity Log…………………………………………………………….20 3.2 Methods of Fracture Pressure Predictions……………………………………………….22 3.2.1 The Hubbert and Willis Approach……………………………………………….23 3.2.2 The Mathews and Kelly Correlation…………………………………………......24 3.2.3 The Eaton’s Correlation………………………………………………………….25 3.2.4 The Macpherson and Berry Correlation……………………………………........25 3.3 Detection of Over Pressured Zone………………………………………………………..26 3.3.1 Detection of Over Pressure using Resistivity log………………………………...26 3.3.2 Detection of Over Pressure using Interval Transit Time…………………………29 vi CHAPTER 4: OPTIMIZATION OF DRILL BIT HYDRAULICS.......................................31 4.1 Hydraulic Power Requirement…………………………………………………………...31 4.1.1 Surface Connection Pressure Drop……………………………………………....32 4.1.2 Drill String Pressure Drop…...……………………………………………….….33 4.1.2.1 Newtonian Fluid………………………………………………………….34 4.1.2.2 Bingham Fluid……………………………………………………….......35 4.1.2.3 Power Law Fluid………………………………………………………...37 4.1.3 Annulus Pressure Drop………………………………………………………......38 4.1.2.1 Newtonian Fluid…………………………………………………………38 4.1.2.2 Bingham Fluid……………………………………………………...........39 4.1.2.3 Power Law Fluid…………………………………………………………40 4.1.2 Drill Bit Pressure Drop………………………………………………………......40 4.2 Flow Exponent and Optimum Flow Rate…………………………………………..........42 4.3 Drill Bit Hydraulic Horsepower Criterion…..…………………………………………...42 4.4 Hydraulic (Jet) Impact Force Criterion…………………………………………………..45 4.4.1 Shallow Well Bore Formation…………………………………………………....46 4.4.2 Deep well Bore Formation ……………………………………………………….49 4.5 Bit Nozzle Selection……………………………………………………………………..52 4.6 Drill Cuttings Transport………………………………………………………………….53 4.4.1 Cutting Slip Velocity……………………………………………………………..53 4.4.2 Annular Fluid Velocity…………………………………………………………...53 vii 4.4.3 Flow Regime……………………………………………………………………...54 CHAPTER 5: DESIGN METHODOLOGY………………………………………………...55 5.1 Estimation of Pore Pressure……………………………………………………………...56 5.2 Estimation of Fracture Pressure……………………………………………….................57 5.3 Mud Weight Selection…………………………………………………………………...58 5.3.1 Geological Mud Specific for Pore Pressure Line………………………………...58 5.3.2 Geological Mud Specific gravity for Fracture Pressure Line…………………….59 5.3.3 Design Mud Specific Gravity for Pore Pressure Line…………………………....59 5.3.4 Design Mud Specific Gravity for Fracture Pressure Line…………….….............59 5.4 Drilling Mud Rheology………………...…………………………………………...…....61 5.4.1 Introduction ……………………………………………………………………...61 5.4.2 Objective of Experiment……………………………………………………….....61 5.4.3 Equipment Used…………………………………………………………………..62 5.4.4 Mud Mixture……………………………………………………………………...63 5.4.5 Experimental Procedure…………………………………………………………..65 5.4.6 Composition of Mud additives Used……………………………………………..66 5.5 Pressure Drop Computation……………………………………………………...............68 5.5.1 Maximum and Minimum Flow Rate Calculation………………………………...68 5.5.2 Calculating Pressure Drop in Drill String……………………...…………………70 5.5.2.1 Pressure Drop Across the Drill Pipe ……………………...……………..70 5.5.2.2 Pressure Drop Across the Drill Collar…………………………………...72 viii 5.5.3 Calculating Pressure Drop in Surface connection………………………………..74 5.5.4 Calculating Pressure Drop in Annulus…………………………………................74 5.5.4.1 Pressure Drop Across the Annulus of the Drill Pipe ……………………74 5.5.4.2 Pressure Drop Across the Annulus Drill Collar………………………….77 5.6 Optimization using the Maximum Bit Horsepower Criterion…………………………...78 5.6.1 Optimum Flow Rate to Operate the Mud Pump………………………………….79 5.6.2 Optimum Nozzle Area of the Drill Bit…………………………………………...81 5.6.3 Maximum Hydraulic Horse Power on the Drill Bit……………………………..83 CHAPTER 6: RESULTS AND DISCUSSION………………………………………….......84 6.1 Frictional Pressure Loss of Mud Samples Result……………………………..................84 6.1.1 Using Mud Sample 1 ……………………………………………………….........84 6.1.2 Using Mud Sample 2……………………………………………………………..85 6.1.3 Using Mud Sample 3……………………………………………………………..86 6.2 Result for Mud Pump Operating Conditions………………………………….................87 CHAPTER 7: CONCLUSION AND RECOMMENDATION………………………..........88 7.1 Conclusion………………………………………………………………………………..88 7.2 Recommendation…………………………………………………………………………88 REFERENCES……………………………………………………………………………….....89 APPENDIX……………………………………………………………………………………...93 APPENDIX A……………………………………………………………………………………93 APPENDIX B……………………………………………………………………………………94 APPENDIX C……………………………………………………………………………………95 ix APPENDIX D……………………………………………………………………………………96 APPENDIX E……………………………………………………………………………………97 APPENDIX F………………………………………………………………………………..…..98 APPENDIX G………………………………………………………………………………..…..99 APPENDIX H………………………………………………………………………………..…100 APPENDIX I………………………………………………………………………………..….100 APPENDIX J………………………………………………………………………………..…109 x LIST OF TABLES Table 4.1: IADC Classes of Surface Equipment…………………………………………….....32 Table 5.1: Shale Conductivity Data……..…………………………………………………..….55 Table 5.2: API Densities of Mud Additives………...…...…………………………………...…64 Table 5.3: Composition of Mud Sample 1……………………………..…………………...…..66 Table 5.4: Composition of Mud Sample 2…………………………………..………….............67 Table 5.5: Composition of Mud Sample 3……………………………………………………...67 Table 5.6: Optimum Nozzle Area and Size Across Each Depth in the Over Pressure Zone………………………………………………………………………….……...82 Table 5.7: Optimum Hydraulic Horsepower Across the Drill Bit in the Over-Pressure Zone…………………………………………………………………………………83 Table 6.1: Frictional Pressures Losses in the Mud Circulatory System Using Mud Sample 1...84 Table 6.2: Frictional Pressures Losses in the Mud Circulatory System Using Mud Sample 2...85 Table 6.3: Frictional Pressures Losses in the Mud Circulatory System Using Mud Sample 3...86 Table 6.4: Optimum Hydraulic Conditions for Case Study……………………………...…......87 xi LIST OF FIGURES Figure 2.2: Chip Hole Down effect…………………...………………………………….......….8 Figure 2.3: Effect of weight on the drill bit…………………………………………………....10 Figure 2.4: Effect of rotary speed on the rate of penetration………………………..................11 Figure 3.2: Plot of porosity with depth………………………………………………...………18 Figure 3.3: Plot of porosity dependent parameter with depth……………………………….....20 Figure 3.4: Plot of porosity and pressure versus depth………………………………………...21 Figure 5.1: Semi log plot of shale resistivity versus depth………………………………….....56 Figure 5.2: Graph of specific gravity versus depth……………………………………….……60 Figure 5.3: Model 35 Viscometer………….………………………………………….….……60 Figure 5.4: Model 140 Mud Balance ………………………………….……………………....63 Figure 5.5: Critical Reynolds number for Bingham plastic fluids………………………...…...70 Figure 5.6: Hydraulic log-log plot of parasitic pressure losses with flow rate…………...…....80 xii NOMENCLATURE ROP Rate of Penetration CHDP Chip Hold Down Pressure PDC Polycrystalline Diamond Compacts IADC International Association of Drilling Contractors API American Petroleum Institute WOB Weight on bit RPM Revolution per Minute db Bit Diameter W0 Threshold Bit Weight K Constant of Proportionality S Compressive Strength of the Rock a5 Bit Weight Exponent t Interval Transit Time (sec) PP Pore Pressure (psia) ov Overburden Stress or Pressure (psia) PPN Normal pore pressure (psia) tN Normal Pore Pressure Trend Line Interval Transit time value at the point of Interest (s) tA Observed value of Interval Transit time at the depth of interest (sec) Ppeq Pore pressure at the equivalent depth (psia) Deq Equivalent Depth (ft) G Over Burden Pressure Gradient (psia/ft) D Depth (ft) DCN Normal Trend line of d Exponent DCO Observed d Exponent ΦD Porosity at a given Depth xiii ϕ0 Porosity in the mudline Z True Vertical Depth (ft) K Porosity Decline Constant C Compaction Constant Pf Fracture pressure (psia) min Minimum principal stress (psia) Poisson’s ratio h Horizontal stress (psia) F Stress Coefficient ( ma ) Vertical stress (psia) Kb Elastic Modulus (psia) b Bulk Density (Ibs/gal) RD Resistivity at a Reference Depth (Ω) R0 Resistivity at the Surface (Ω) Hh Hydraulic horse power (hp) P Pressure (psia) Q Flow rate (gpm) Pf Frictional Pressure Loss ( Pf ) s Surface Pressure Loss (psi) Ks Surface Pressure Coefficient m Mud Density (lb/gal) Pfdp Pressure drop in the drill pipe (psia) Lse Surface equipment equivalent length of drill pipe (ft) Ldp Length of drip pipe (ft) xiv Ldc Length of Drill Collar (ft) Va Average velocity (ft/sec) p Plastic Viscosity (cp) Di Internal diameter (in) Pipe Roughness (in) N RP Reynolds number f Frictional factor y Yield Point (Ibs/100ft) N He Hedstrom number N Re Reynolds Number Dop Outer diameter of the drill pipe or drill collar (in) Dh Diameter of the hole (in) Dp Diameter of the Pipe (in) De Equivalent Diameter of the Drill Collar (in) N Power law index K Equivalent centipoise PB Pressure drop across the drill bit (psia) A Area of Nozzle (in2) Cd Discharge coefficient Pdc Pressure Drop across Drill Collar (psia) xv Pfadp Pressure Drop in Annulus around Drill Pipe (psia) Padc Pressure Drop in Annulus around Drill Collar (psia) ( Pf ) D Parasitic Pressure Loss (psia) m Flow Exponent C Constant that depends on mud flow properties, hole geometry and Pipe geometry H HB Drill Bit Hydraulic Horse Power (hp) Pmax Maximum Pump Pressure (psia) P Optimum Parasitic Pressure Drop (psia) PBopt Optimum Pressure Drop on the Drill Bit (psia) HHPopt Optimum hydraulic horse power at the drill bit (hp) FJ Jet Impact Force (Ibf) H hp Maximum Pump Hydraulic Horse Power (hp) At opt Optimum Nozzle area (in2) Qopt Optimum Flow Rate (gpm) Qmax Maximum flow rate (gpm) Qmin Minimum flow rate (gpm) min Minimum Annular velocity (ft/sec) Volumetric Efficiency d N opt Optimum Nozzle Diameter (in) Rn Normal Shale Resistivity (Ω) f Dopt xvi R0 Observed shale Resistivity (Ω) pp Density from Pore Pressure (Ibm/gal) SG pp Specific Gravity from Pore Pressure w Density of water (Ibm/gal) fp Density from Fracture Pressure (Ibm/gal) SG fp Specific Gravity from Fracture Pressure dpp Design density from pore pressure (ibm/gal) SGdpp Design Specific gravity from pore pressure dpf Design Density from Fracture Pressure (Ibm/gal) SGdfp Design Specific gravity from fracture pressure mix Density of the mud mixture (g/cm3) M1 Mass of Barite (g) M2 Mass of Bentonite (g) M3 Mass of Water (g) 1 API Density for Barite (g/cm3 2 API Density for Bentonite (g/cm3) 3 API Density for Water (g/cm3) PV Plastic Viscosity (cP) YP Yield Point (ib/100ft) xvii 600 Dial reading at 600 rpm 300 Dial reading at 300 rpm xviii ACKNOWLEDGEMENT I would like to express my gratitude to my project supervisor Dr. Michael Pegg, for his contribution to this project work. I am also very thankful to my reader Dr. Steven Kuzak for taking the time to go over my work. I would also like to express my profound thanks and appreciation to Mr. Mumuni Amadu for his input, advice and support during the course of this project and to Mr.Matt Kujath for his assistance in using the laboratory equipment. xix ABSTRACT Drill cuttings in the well bore cause wear and tear to the drill string and this reduces the rate of penetration; therefore, there is need for efficient bottom hole cleaning. During drilling operation, optimization of hydraulic horsepower at the drill bit is adopted to enhance bottom hole cleaning and to increase the rate of penetration. Optimum drilling conditions are achieved using either the maximum horsepower criterion or the hydraulic jet impact force criterion. This project work focused on the application of optimization using the maximum horsepower criterion in an over pressure zone for bottom hole cleaning and for showing the effect of mud rheology on pressure losses in a mud circulatory system. In this work, optimum conditions for drilling were determined by estimating pore pressure and fracture pressure from conductivity data, selecting a suitable mud with an appropriate density based on the result of the conductivity data analysis, studying the rheological properties of mud samples, calculating the pressure losses in the mud circulatory system and finally applying the maximum horsepower criterion for optimization. Based on the results of conductivity data analysis, experimental analysis of the drilling mud rheology and pressure loss calculation in the mud circulatory system, conditions for optimum hydraulic horsepower across the drill bit in the problematic zone is presented in this case study. This study shows that pressure loss in the mud circulatory system depends on the mud and the circulating flow rate. Also, the operating conditions obtained in this study shows that the flow rate exceeds the minimum flow rate required for drill cuttings removal. One unique aspect of this project work is the integration of experimental work designed to generate rheological data for theoretical computation. xx CHAPTER 1: INTRODUCTION This project focuses on optimizing the hydraulic horsepower at the drill bit for the purpose of bottom hole cleaning and to enhance the rate of drilling. This work considers the effect of mud rheology on pressure losses in the mud circulatory system and then designing an hydraulics system for effective drill cutting removal during drilling operation by specify the operating conditions to maximize the power at the drill bit, using a case study where the target depth lies in an over pressure zone. 1.1 Study Objective The objective of this study aims at designing an hydraulic system to specify the operating conditions to operate the mud pump for drill cutting removal and to enhance the rate of penetration during drilling. The effect of mud rheology on the pressure losses in a mud circulatory system will also be considered in this study. 1.2 Problem Statement Inadequate hole cleaning can lead to a number of problems, including hole fill, packing off, stuck pipe, and excessive hydrostatic pressure. Drill cuttings in the hole cause wear and tear of the drill string and also reduce the rate of penetration, thereby increasing the cost and time for drilling; hence, there is need to design a system that will efficiently remove the drill cuttings, transport them to the surface in a cost effective manner, prepare an appropriate drilling mud and maximize the hydraulic horse power at the drill bit. 1.3 Scope of Study The industry has made significant progress in hole cleaning. The ability of a drilling fluid to lift cuttings is affected by many factors, and there is no universally accepted theory which can account for all observed phenomena, Well bore cleaning can be achieved in a number of ways such as by increasing the drill pipe rotation, by improving the rheological properties of the mud, the cuttings bed properties. But this study will focus on drill cutting removal by preparing a 1 suitable mud from geological data, and using the concept of hydraulic optimization to maximize the drill bit hydraulic horsepower. 1.4 Limitations During the course of this project work, some of the limitations of this project work were as follows: 1. The use of conductivity data to estimate the abnormal pressure zone in this study has some degree of inaccuracy since conductivity is affected by salinity. However, seismic data is more accurate for detecting and quantifying abnormal pressure. 2. The Hottman and Johnson approach was used to estimate the pore pressure, which has some degree of inaccuracy since the approach does not account for the effect of overburden stress. 3. The Hubbert and Willis approach was used to estimate the fracture pressure, which has some degree of inaccuracy, since the approach assumes a poisson’s ratio of 0.25 and an over burden pressure gradient of 1psia/ft. 4. In this study, factors such as drill pipe eccentricity, drill pipe rotation and the weight on the drill bit that affect the rate of penetration were not accounted for, this study focussed on the mud rheology and hydraulics. 5. Due to unavailability of mud pump data, a theoretical flow exponent of 1.75 was used for the hydraulic design (Kendall and Goin, 1960), since the flow exponent can only be obtained by operating the mud pump on a drilling rig. 2 CHAPTER 2: LITERATURE REVIEW The rate of penetration is considered one of the prime factors in drilling a hydrocarbon well and it is therefore given a prime consideration when drilling an oil well. However, a lot of extensively analyzed on ways of increasing the rate of penetration from both theoretical and experimental standpoint has been carried out till date. Eckel (1967) was able to establish from laboratory and field experience that the rate of drilling using mud was increased from 30 to 70 percent of those obtainable with water under the same conditions. Eckel (1967) further stipulated that viscosity is a significant factor affecting the rate of drilling. Eckel (1967) used oil emulsion in his experiments and he observed that the rate of drilling was improved due to their lubricative properties. Eckel (1967) concluded that mud rheological properties have significant effect on the rate of penetration. Warren (1988) developed a rate of penetration (ROP) model for soft-formation bits under conditions where cuttings removal does not impede the rate of penetration. This model relates ROP to weight on bit (WOB), rotary speed, rock strength, and bit size. It is based on tests that were designed to provide basic information about the interaction between the bit and rock in the absence of complicating cuttings-removal effects. The practical application of this model to general ROP prediction is severely limited because it does not include cuttings-removal effects. Recently, Fear (1999) developed a method to identify the factors controlling ROP. He correlated mud logging data, geological information and drill bit characteristics against ROP and other drilling parameters. This statistical method suggested that factors affecting the rate of penetration are different for different cases and Fear (1999) recommends that the method be applied for each specific case to determine the applied drilling parameters. Numerous factors affect the rate of penetration, and the objective of this study is to design a hydraulic system to specifying the operating conditions to drill through the formation to effectively remove drill cuttings and enhance the rate of penetration in an over pressured zone. Enhancing the rate of penetration is the objective of an effective drilling program, as rate of penetration tends to decrease with depth. Therefore a detailed study of geomechanics, factors affecting the rate of penetration and bottom hole cleaning is discussed in this literature review. 3 2.1 Geomechanics Geomechanic involves the geologic study of the behavior of soil and rock under mechanical loading conditions (stresses, strain). The study of Geomechanics is paramount in predicting important reservoir parameters such as formation porosity, permeability, pore pressure, fracture pressure and bottom-hole pressure. This science provides us with vital knowledge of the reservoir properties which is essential in proper well planning and in completing a successful drilling project (Prassl, 2003). 2.2 Pore Pressure Pore pressure is the pressure acting on the fluids in the pore space of the rock (Rabia, 2002). This is the pressure due to the column of liquid occupying the pore space of a porous medium in a sedimentary basin. The magnitude of pore pressure can be described as either normal pressure or abnormal pressure. Rabia (2002) also stated that the magnitude of normal pore pressure varies with the following: concentration of dissolved salts, type of fluid, gases present and temperature gradient. Rabia (2002) further stated that as the concentration of dissolved salts increases the magnitude of normal pore pressure increases. Successfully predicting pore pressure within the formation to be drilled is one of the most critical parameters needed in planning and drilling a well. The estimates of formation pore pressure made before drilling are usually based on seismic data acquisition, analysis and interpretation. To estimate formation pore pressure from seismic data, the average acoustic velocity or the interval transit time as a function of depth must be determined. 2.3 Causes of Over Pressure Abnormal pore pressure can be said to be any pore pressure that is greater than the hydrostatic pressure of the formation fluid occupying the pore space. Over pressure can arise due to a combination of geological, geochemical, geophysical and mechanical process (Rabia, 2002). Rabia also stated some of the causes of over pressure which is show below. 4 2.3.1 Depositional Effects The deposition of evaporites can create high abnormal pore pressures in the surrounding zones with the pore pressure approaching the overburden gradient. When salt is deposited, the pore fluids in the underlying formations cannot escape and therefore become trapped and abnormally pressured (Rabia, 2002). 2.3.2 Digenetic Processes This is a process in which sediments undergo a process of chemical and physical changes collectively with increasing temperature and pressure (Rabia, 2002). Rabia (2002) further stated that Diagenetic processes could be as a result of the formation of new minerals, recrystallization and lithification. Diagenesis is the alteration of sediments and their constituent minerals during post-depositional compaction. Diagenesis may lead to volume changes and water generation, which if occurring in a seabed environment, may lead to both abnormal or sub-normal pore pressure. 2.3.3 Tectonic Effects Tectonic activity can result in the development of abnormal pore pressure as a result of a variety of mechanisms including: folding, faulting, uplift and salt diaparism (Rabia, 2002). In folding, abnormal pressure results when tectonic compression of a geological basin is produced. The additional horizontal tectonic stress created by folding compacts the clays laterally. For the formation to remain normally pressured, the increased compaction has to be balanced by pore water expulsion, but if the formation water cannot escape, abnormal pressure will result. Also, during faulting in sedimentary rocks, abnormal pressure is also caused by tectonic activities in which the sedimentary beds are broken up, moved up and down or twisted. Finally, if a normally pressured formation is uplifted to a shallower depth then the formation will appear to have an abnormal pressure due to the fact that the formation pressure has more hydrostatic pressure than a corresponding normally pressured zone at the same depth. 5 2.3.4 Structural Causes Abnormal pore pressure can also exist in both horizontal and non-horizontal reservoir structures which contain pore fluids of differing densities i.e. water, oil and gas Rabia (2002). Examples of structures in which this may occur are lenticular reservoirs, dipping reservoirs and anticlinal reservoirs. In dipping reservoirs, formation pressures which are normal in the deepest water zone of the reservoir will be transmitted to the up dip part of the structure. In large structures or gas reservoirs, the overpressure gradient contrast developed can be quite significant. Therefore, careful drilling practices should be adopted in order to minimize the risks associated with high overbalance as the reservoir is drilled down through the water zone. 2.3.5 Thermodynamic Effects Thermodynamic effects such as organic matter transformation can also result in abnormal pressure, at high temperatures and pressures associated with deep burial, complex hydrocarbon molecules (kerogen) will break down into simpler compounds, and that Kerogen alters to hydrocarbon at 90 0C (Rabia, 2002). Rabia (2002) stated that thermal cracking of the compound can result in two to three fold increases in the volume of the hydrocarbon. If this occurs in a sealed environment, high pore pressures could result. The pressures will be substantially increased if the hydrocarbon system becomes gas generative. 2.4 Fracture Pressure Fracture pressure is the amount of pressure it takes to permanently deform or fracture the formation. If the formations fracture pressure is exceeded, the wellbore will fracture, which may lead to loss of circulation as the fluids in the well are pushed into the formation through the fractures. The fracture pressure is dependent on the formation type, overburden pressure and on how the formation is compacted. If abnormal formation pressure is encountered, the density of the drilling fluid must be increased to maintain the wellbore pressure above the formation pore pressure to prevent the flow of fluids from permeable formations into the well. However, since the wellbore pressure must be maintained below the pressure that will cause fracture in the well 6 bore. Hence, there is a maximum drilling fluid density that can be tolerated in the well bore to maintain well bore stability. This means that there is a maximum depth into the abnormally pressured zone to which the well can be drilled safely without cementing another casing string in the well. Thus, the knowledge of the pressure at which formation fracture will occur at all depths in the well is essential for well planning and in drilling an oil well. 2.5 Mud Weight Planning Mud weight selection in a drilling program is a key factor in avoiding various borehole problems. It is essential to select the correct mud weight for drilling the individual sections. The following must be considered when selecting mud weight (Prassl, 2003): A very low mud weight may result in collapse and well cleaning problems. A very high mud weight may also result in mud losses or pipe sticking. Excessive variation in mud weight may also lead to borehole failure; as such a more constant mud weight must be aimed at. A median line concept is recommended generally for mud weight planning. The midpoint is between the pore pressure and fracture pressure. Hence keeping the mud weight within this median level causes least disturbance on the borehole wall. 2.6 Factors Affecting Rate of Penetration The rate of penetration is considered one of the primary factors affecting drilling costs and hence it is given consideration when planning for optimized drilling. Hence some of numerous factors that affect the rate of penetration of a formation are Chip hold-down, bit type, drilling fluid properties, formation characteristics, and the operating conditions (Rabia, 2002). 2.6.1 Chip Hole-Down Effect Chip hold-down occurs when a mud filter cake or fine solids block fractures produced by the bit. This prevents the liquid phase of the mud from invading the fractures, and results in a 7 positive pressure differential across the top surface of the chip. The chip hold-down force is equal to the area of the chip times the differential pressure Fig 2.1 Chip hole down effect (Rabia, 2002) The difference between the mud hydrostatic pressure and pore pressure is called Chip Hold down Pressure (CHDP) (Rabia, 2002). This pressure prevents formation fluids from entering the wellbore during drilling. However, this overbalance (CHDP) also acts to keep the rock cuttings held to the bottom of the wellbore. The effects of bit rotation and hydraulics offset this force and ensure that cuttings are lifted from the bottom of the hole. The CHDP (differential force) has one of the largest effects on rate of penetration especially in soft to medium strength formations (Rabia, 2002). 2.6.2 Effect Of Bit Type The bit type selected for drilling into a formation has a large effect on the rate of penetration. In the case of rolling cutter bits, the initial rate of penetration of a formation is optimum when using bits with long teeth and a large cone offset angle, but these bits are best used in soft formations because of a rapid tooth destruction and decline in penetration rate in hard formations. While the drag bits are designed to obtain a given penetration rate by producing a wedging type rock failure in which the bit penetration per revolution depends on the number of blades and the bottom cutting angle. The diamond and polycrystalline diamond compacts (PCD) bits are also designed for a given penetration per revolution by the selection of the size and number of diamonds or PCD blanks. The width and number of cutters can be used to compute the effective number of 8 blades. The lowest cost per foot drilled is usually obtained when using the longest tooth bit that will give a tooth life consistent with the bearing life at optimum bit operating conditions. 2.6.3 Effect of Drilling Fluid Properties The rate of penetration is also affected by the properties of drilling fluid used during drilling. These properties include: rheological properties, filtration characteristics, solids content and size distribution, and chemical composition. The rate of penetration tends to decrease with increasing fluid density, viscosity and solids content, and tends to increase with increasing filtration rate. The density, solid content, and filtration characteristics of the mud control the pressure differential across the zone of crushed rock beneath the bit. The fluid viscosity controls the system frictional losses in the drill string and thus the hydraulic energy available at the bit jets for cleaning. The most important factor out of the drilling fluid properties is the density, differential pressure tends to increase with increasing density, and the rate of penetration decreases with increasing differential pressure. 2.6.4 Effecting of Formation Characteristics The elastic limit and ultimate strength of the formation are important formation properties that affect the rate of penetration. The permeability of the formation also has a significant effect on the ROP. In permeable rocks, the drilling fluid filtrate can move into the rock ahead of the bit and equalize the pressure differential acting on the chips formed beneath each tooth. This would tend to promote the more explosive elastic mode of crater formation. The mineral composition of the rock also affects the rate of penetration. Rocks containing hard, abrasive minerals can cause rapid dulling of the bit teeth. Rocks containing gummy clay minerals can cause the bit to ball up and drill in a very inefficient manner. 2.6.5 Effect of Operating Conditions Operating conditions such as the weight on the drill bit, the rotary speed have significant effect on the rate of penetration. The rate of penetration has been observed to increase rapidly with an 9 increase in the weight on the drill bit. In some cases, a decrease in rate of penetration is observed at extremely high value of weight on the drill bit. This type of behaviour is often called bit floundering. This poor response of ROP at high values of bit weight is usually attributed to less efficient bottom hole cleaning at higher rates of cuttings. Figure 2.2 shows the effect of the weight on the drill bit on the rate of penetration (Prassl, 2003) Fig 2.2: Effect on weight on the drill bit (Prassl, 2003) Figure 2.2 shows that the rate of penetration increases from point a to point d with an increase in the weight on the drill bit, but a decrease in the rate of penetration is suddenly observed from point d to point e with increase in the weight on the drill bit. The rate of penetration also increases with the rotary speed while other drilling variables held constant. The rate of penetration usually increases linearly with low rotary speed, but at higher values of rotary speed the rate of penetration begins to decreases. The reason for decrease in the rate of penetration is due to poor hole cleaning. Figure 2.3 shows the effect of rotary speed on the rate of penetration (Prassl, 2003). 10 Fig 2.3: Effect of rotary speed on the rate of penetration (Prassl, 2003) Figure 2.3 shows that the rate of penetration increases from point a to point b with an increase in the rotary speed, but a decrease in the rate of penetration is suddenly observed from point b to point c with futher increase in the rotary speed. Maurer (1980) developed a theoretical equation for rolling cutter bits relating ROP to WOB, revolution per minute (RPM), bit size, and rock strength. The equation was derived from the following observation made in single tooth impact experiments: (1) the crater volume is proportional to the square of the depth of cutter penetration, and (2) the depth of cutter penetration is inversely proportional to the rock strength. 2 K R 2 S W W N db db t (1.1) Where R= rate of penetration (ft/h) K = constant of proportionality S = compressive strength of the rock (ib/in2) W = bit weight (ib) W0 = threshold bit weight (ib) db = bit diameter (in) N = rotary speed(rev/min) 11 The theoretical equation of Maurer (1980) can be verified using experimental data obtained at relatively low bit weight and rotary speeds corresponding to segment ab in Figures (2.3). Bingham suggested the following drilling equation on the basis of considerable laboratory and field data. a5 W R K N db (1.2) Where R= rate of penetration (ft/h) K = constant of proportionality that includes the effect of rock strength W = bit weight (ib) db = bit diameter (in) a5 = bit weight exponent N = rotary speed (rev/min) In this equation the threshold bit weight was assumed to be negligible and the bit weight exponent must be determined experimentally for the prevailing conditions. 2.7 Factors Affecting Hole Cleaning To effectively remove drill cuttings during drilling, a number of factors must be put in place to achieve optimal bottom hole cleaning. To efficiently transport cuttings out of the hole, there must be enough energy to push the solids out of the hole and the drilling fluid must be able to suspend the solid particles. Some of the factors that affect hole cleaning are drill pipe rotation, drill pipe eccentricity, rheology, drilling Rate, Cutting Bed Properties, and hydraulics (Tobenna, 2010). 12 2.7.1 Drill Pipe Rotation Pipe rotation tends to make flow turbulent and this turbulence causes an increase in shear stress on the cutting bed surface. This increased shear stress will assist in cuttings removal. But the impact if drill pipe rotation on hole cleaning is relatively small in vertical well but more significant in inclined wells. 2.7.2 Rheology Rheology refers to the study of flow properties and characteristics of a drilling fluid. These Properties of the circulation fluid have an effect on solids transport. Bottom hole cleaning is more effective in a vertical well bore, when a high viscosity fluid is pumped in the well in a laminar flow regime rather than a low viscosity fluid in a turbulent flow, but for a horizontal well bore, bottom hole cleaning is more efficient when a low viscosity fluid is pumped in a turbulent flow regime. The rheological properties of a fluid can be described using models that provide assistance in characterising fluid flow. These models include the Bingham plastic model, and the Herschel-Bulkley model. The rheological properties of the mud will go a long way in determining its flow rate and suspension characteristics. Mud rheology will be an integral part of this project work. 2.7.3 Drilling Rate The rate of drilling has an important effect on cuttings transport, since as the drill rate increases, the cuttings concentration in the annulus also increases. Hence for effective removal of drilled cuttings, as the drilling rate increases the hydraulic requirement should also increase. To ensure good hole cleaning during high rate of penetration (ROP) drilling, the flow rate and/or pipe rotation have to be adjusted. If the limits of these two variables are exceeded, the only alternative is to reduce the ROP. Although a decrease in ROP may have a detrimental impact on drilling costs, the benefit of avoiding other drilling problems, such as mechanical pipe sticking or excessive torque and drag, can outweigh the loss in ROP. 13 2.7.4 Cutting Bed Properties The size, distribution, shape, and specific gravity of the cuttings affect their dynamic behavior in a flowing media. The properties of the cutting bed has a significant effect on hole cleaning, if the bed is loose or highly porous, then it may be necessary to remove single cutting particles that are not adhered to the bed. In which case removing the bed becomes easy. But if the cutting bed is highly consolidated with no cutting particle free to be removed alone from the bed by the flow, hole cleaning will be difficult. 2.7.5 Hydraulics Mud hydraulics is a crucial aspect of effective drilling. A drilling mud hydraulics program consist of specifying the operating conditions to operate such as the minimum mud flow rate in the annular space required to ensure efficient drill cuttings removal .This means that for a given flow rate an increase in mud density beyond the desired level will impose additional hydraulic requirement on the hydraulic system, which can impact on the optimum pump power requirement. Experimental work shows that for a given pump flow rate requirement, the density and viscosity of the mud are important parameters that affect the overall hydraulics of the system. 14 CHAPTER 3: PORE PRESSURE AND FRACTURE PRESSURE PREDICTION In well planning, it is important to estimate the pore pressure and fracture pressure to be encountered in the subsurface. These predictions are important to ensure the safety of personnel, equipment, specify operating conditions to follow during drilling. These prediction facilities effective well planning and in selecting the required materials required for the entire drilling operations. Also with respect to the reservoir, the right drilling mud weight is important. If it is too low, a blowout might occur and conversely, if it is too high, the formation might be damaged by invasion of the drilling fluid. Pore pressure and fracture pressure prediction cannot be over emphasised in drilling. 3.1 METHODS OF PORE PRESSURE PREDICTIONS There are different methods of pore pressure prediction currently used in the oil and gas industry for pore pressure prediction. Over-pressure is an important geological problem in many regions of the world; hence the detection of pore pressure is important in drilling of well bore, in studying hydrocarbons migrations, and also in the formation of oil and gas fields. The most effective method of estimating geological conditions before drilling is seismic prospecting. The zones of over-pressure are frequently characterized by an abnormal intense condition of rocks such as abnormal porosity, resistivity and density. These factors are the physical preconditions for overpressure prediction from seismic data. Eaton’s method is one of the most widely used quantitative methods for pore pressure evaluation. This method applies a regionally defined exponent to an empirical formula, which has resulted in the development of equations that may be used for the prediction of geopressure from well logs and seismic data. Equations are given for use with resistivity plots, conductivity plots, sonic travel-time plots, and corrected "d" exponent plots. All equations have the same theoretical basis (Eaton, 1975). The methods of pore pressure predictions are resistivity method, sonic method, equivalent depth method, ratio method, and neutron porosity log. 3.1.1 Resistivity Method of Pore Pressure Prediction Resistivity method is based on the electrical resistivity of the sample, which includes the rock matrix and the fluid filled porosity. Shale resistivity increases with depth. The resistivity of the sample depends on factors such as porosity and salinity (Hussain Rabia, 2002). If a zone that has 15 abnormally high porosity and high pressure is penetrated, the resistivity of the rock will be reduced due to greater conductivity of water. This approach involves plotting shale resistivity with depth. Hottman and Johnson (1965) developed a technique based on empirical relationships whereby an estimate of formation pressure could be made by noting the ratio between the observed and normal rock resistivity. The following steps are necessary to estimate the pore pressure The normal trend is established by plotting the logarithm of shale resistivity with depth. The top of the pressure interval is found by noting the depth at which the plotted points diverge from the trend. The pressure gradient at any depth is found by taking the ratio of the extrapolated normal shale resistivity to the observed shale resistivity, and then the formation pressure corresponding to the calculated ratio is found. Eaton (1975) also developed an equation using resistivity data for pore pressure predictions. This equation is given as R Pp ov ov PPN o RN 1.2 (3.1) Where PP = pore pressure (psia) ov = overburden pressure (psia) PPN = normal pore pressure (psia) RN= normal resistivity (Ω) RO = observed resistivity (Ω) 16 3.1.2 Sonic Method of Pore Pressure Prediction To estimate formation pore pressure from seismic data, the average acoustic velocity as a function of depth must be determined. The sonic log is provides the most reliable estimate of pore pressure. Sonic log are usually more accurate because they are relatively unaffected by borehole size, formation temperature and pore water salinity (Rabia, 2002). Sonic logs measure the transit time for a compressional sonic wave to travel through the formation from a transmitter to a receiver. The time to travel one foot is termed the interval transit time (IIT). In a shale sequence showing a normal compact profile the transit time should decrease with depth due to decreased porosity and increased density. Abnormal pressure shales tend to have higher porosity and lower density than normally pressured shales at the same depth; Hence, ITT values will be higher. By plotting ITT against linear depth, a normal pressure trend line can be established through clean shales. Abnormally pressured shales will therefore show an increased ITT above normal trend line values. Rabia (2002) developed the following procedure to estimate pore pressures knowing the acoustic travel time for shale formations: The normal compaction trend for the area of interest is established by plotting the logarithm of interval transit time versus depth. The top of the over pressure formation is found by noting the depth at which the plotted Points diverge from the trend line. The fluid pressure gradient of a reservoir at any depth is found as follows: The divergence of adjacent shales from the extrapolated normal line is measured. The pore pressure gradient corresponding to the interval transit time value is found from a figure showing the relationship between the shale acoustic parameter and the reservoir pressure gradient. The pore pressure is then obtained by multiplying the pore pressure gradient by the depth to obtain the reservoir pore pressure. Eaton (1975) also developed a similar equation to that used in resistivity, to be used with interval transit time data this equation can be used for both sonic and seismic data. 17 t Pp ov ov PPN N tA 3 (3.2) Where PP = pore pressure (psia) ov = overburden pressure (psia) PPN = normal pore pressure (psia) t N = normal pore pressure trend line interval transit time value at the point of interest(s) t A = observed value interval transit time at the depth of interest (s) 3.1.3 Equivalent Depth Method The equivalent depth method (Ham, 1966) is based on the reasonable assumption that formations with the same physical properties such as resistivity, interval velocity, density or porosity would have the same effective vertical stress irrespective of the depth. Figure 3.1 shows that every point A in an under compacted clay is associated with a normally compacted point B. The compaction at point A is assumed to be identical to that at point B. The depth of point B, ZB, is called the equivalent depth, which is also called the isolation depth (Soufi, 2009). Fig 3.2: Plot of porosity with depth (Soufi, 2009) 18 The pore pressure is given as Pp Ppeq G( D Deq ) (3.3) Ppeq 0.465Deq (3.4) Where Pp = pore pressure (psia) Ppeq = pore pressure at the equivalent depth (psia) Deq= equivalent depth (ft) G = over burden pressure gradient (psia/ft) D = depth (ft) 3.1.4 Ratio Method The ratio method is based on the concept that the difference between the observed and normal values of formation parameters is proportional to the increase in pressure (Soufi, 2009). Thus the ratio of the observed (dco) to the normal (dcn) value is Proportional to the formation pressure. D P p PPN * CN DCO (3.5) Where PP = pore pressure gradient (Psia/ft) PPN = normal pore pressure gradient (psia/ft), DCN = normal trend line of d exponent DCO = observed d exponent. 19 Fig 3.2: Plot of porosity dependent parameter with depth (Soufi, 2009) The ratio method is considered unsuitable for use in most shale sequences. However, it has been found to give accurate results in interpreting pore pressures from elastic limestone data in the Middle East. 3.1.5 Neutron Porosity Log Pore pressure can also be predicted from the neutron porosity log. The under-compaction of sediments is the primary cause of formation overpressure, which occurs primarily in rapidly subsiding basins and in rocks with low permeability. Pore pressure and formation porosity are higher in under-compacted sediments than those in the normal compaction condition. It is commonly accepted that porosity decreases exponentially as depth increases in normally compacted formations. One commonly used relationship between porosity and depth is given by the equation below (Athy, 1930) D 0e KD (3.6) 20 Where D = porosity at a given depth ϕ0 = porosity in the mudline D = true vertical depth (ft) K = porosity decline constant. Therefore porosity is a function of effective stress and pore pressure, particularly for the overpressures generated from under-compaction and hydrocarbon cracking. Therefore, pore pressure can be estimated from formation porosity. In a formation with under-compaction, porosity and pore pressure are higher than those in a normally compacted one. Fig 3.4: Plot of porosity and pressure with depth (Athy, 1930) Figure 3.3 shows the schematic porosity (a) and corresponding pore pressure (b) in a sedimentary basin. The dashed porosity profile in (a) represents a normally compacted formation. In the over-pressured section in (a), a porosity reversal occurs. In the over -pressured section, there is a deviation from the trend line (ϕn) which indicates an abnormal pressure. Heppard (1998) used an empirical porosity equation similar to Eaton's sonic method to predict pore pressure using shale porosity data. Heppard (1998) derived a theoretical equation for pore pressure prediction shown in the relationship below: 21 Pp ov ov PPN ln o ln cz (3.7) Where PP = pore pressure (psia) ov = over burden pressure (psia) ϕ = porosity in shale ϕ0 = porosity in the mudline Z = true vertical depth below the mudline (ft) C = compaction constant (1/ft) Porosity tends to decrease with depth in the wellbore, but when there is a sudden increase in porosity with depth, under compaction is said to have occurred which indicates an abnormal pressure zone. Compaction occurs in a normally pressured zone. 3.2 METHOD OF FRACTURE PRESSURE PREDICTIONS Formation fracture pressure predictions are made based on empirical correlations. Formation fracture pressure is deduced from formation pore pressure. The commonly used fracture pressure prediction equations are Hubbert and Willis equation, Mathews and Kelly equation and Eaton’s correlation. 3.2.1 The Hubbert and Willis Approach The Hubbert and Willis (1957) approach states that the minimum wellbore pressure required to fracture a formation is the sum of the pore pressure and the minimum principal stress ( min ). The Hubbert and Willis equation is given below (Hubbert and Willis, 1957): Pf min Pp (3.8) Where Pf = fracture pressure (psia) min = minimum principal stress (psia) 22 Pp = pore pressure (psia) The minimum principal stress occurs in the horizontal plane and if this horizontal stresses ( h ) are equal to the local stress concentration at the borehole wall. Thus, the pressure required to initiate fracture in a homogeneous, isotropic Formation is given in the relationship below: Pf 2 h PP (3.9) Where Pf = fracture pressure (psia) h = horizontal stress (psia) Pp = pore pressure (psia) The horizontal stress is given as 1 2 1 h ov (3.10) Where h = horizontal stress (psia) Pp = pore pressure (psia) ov = over burden pressure (psia) = passion ratio Since the earth is so inhomogeneous and anisotropic, with many existing joints and bedding planes, fracture pressure is generally used for well planning and casing design. Furthermore Hubbert and Willis (1965) also concluded that the minimum stress in the shallow sediments is approximately one-third the vertical matrix stress resulting from the weight of the overburden. Therefore the formation fracture pressure is shown as (Hubbert and Willis, 1957) 23 Pf ov 2 Pp 3 (3.11) Where Pf = fracture pressure (psia) Pp = pore pressure (psia) ov = over burden pressure (psia) h = horizontal stress (psia) 3.2.2 The Mathews and Kelly correlation Mathews and Kelly in 1976 established that the assumption made by Hubbert and Willis that the minimum stress was one-third the matrix stress is not valid for deeper formation, as formation fracture gradient tends to increase with depth. They provided an equation for calculating the minimum stress ( min ). min F ma (3.12) Where min = minimum stress (psia) F = Stress coefficient ma = vertical stress (psia) Where the stress coefficient ( F ) is determined empirically from field data in a normally pressured formation. The vertical stress ( ma ) at the normally pressured zone is calculated with the relationship below ma ov Ppn (3.13) Where ma = vertical stress (psia) 24 ov = over burden pressure (psia) Ppn = normal pressure gradient (psi/ft) Matthews and Kelly assumed that the average overburden stress ( ob ) is 1psi/ft and the average normal pressure gradient ( Ppn ) is 0.465psi/ft. Then the fracture pressure of the formation is calculated with the Hubbert and Willis equation given in equation (3.7). 3.2.3 The Eaton Correlation Eaton’s (1957) fracture prediction approach is the most widely used strategy. Eaton’s correlation can be used anywhere in the world as long as the area specific over-burden stress gradient, the pore pressure of the well and the area-specific Poisson’s ratio is known. Eaton’s equation for fracture pressure is given below (Eaton, 1975): Pf D ov PP PP 1 D D D (3.14) Where Pf = fracture pressure (psia) = poisson’s ratio D = depth (ft) Pp = formation pore pressure (psia) OV = overburden stress (psia) 3.2.4 The MacPherson and Berry correlation Macpherson and Berry (1972) were able to estimate formation fracture pressure by developing a correlation between elastic modulus for a compressional wave and formation fracture pressure. They made the following conclusion from studies on the prediction of fracture pressure. They 25 made measurements of the interval transit time by means of a sonic log. The elastic modulus is computed using the relationship below: Kb 1.345 *1010 b t2 (3.15) The fracture pressure is then obtained from the Macpherson and Berry empirical correlation between Kb ov and the fracture pressure. Where Kb = elastic modulus (psia) b = the bulk density (ib/gal) t = the interval transit time (s) ov = the overburden stress (psia) 3.3 DETECTION OF OVER PRESSURED ZONE The over-pressure zone can be detected using a number of approaches; each approach relates formation properties such as porosity, resistivity, interval transit time, and density with depth. These empirical relationships are obtained using Athy’s equation, which relates porosity and depth. 3.3.1 Detection of Over-Pressure Using Resistivity Log An over pressured zone can be detected from resistivity data by relating resistivity to porosity. A basis for most rock resistivity studies was provided by Archie (1942) who examined the relationship between resistivity and porosity in sandstone cores from the U.S. Gulf Coast region. He empirically established that the resistivity is inversely proportional to porosity. Archie 26 established an exponential empirical relationship between resistivity and the porosity which can be described by the equation below R K (3.16) Where R = resistivity at a reference depth (Ω) K = compaction factor which depends on the formation = porosity At the surface of the well bore R0 K 0 (3.17) This can be written as 0 K R0 (3.18) At a given depth in the well bore RD K D (3.19) This can be written as D K RD On substituting both equation (3.18) and equation (3.19) into equation (3.5) Therefore, 27 K K 0e KD RD R0 1 1 0e KD RD R0 Taking the logarithm of both side of the equation 1 1 Log KD Log RD R0 This can also be written as Log1 LogRD Log1 LogR0 KD Therefore LogRD LogR0 KD (3.20) Where RD = resistivity at a reference depth (Ω) R0 = resistivity at the surface (Ω) D = depth (ft) K = compaction factor which depends on the formation Equation (3.20) shows that the resistivity is expected to increase linearly with depth; hence overpressured zone is detected when there is an abnormal deviation from the normal trend line in a semi-log plot of resistivity with depth. 28 3.3.2 Detection of Over Pressure Using Interval Transit Time The interval transit time depends on the elastic properties of the rock matrix, the properties of the fluid in the rock, and the porosity of the rock. Wyllie (1958) proposed that the interval transit time can be represented as the sum of the transit time in the matrix fraction and the transit time in the liquid fraction and that this interval transit time is directly proportional to porosity. The Wyllie relationship between interval transit time and porosity can be written as: t K (3.21) Where t = interval transit time (sec) K = compaction factor or porosity decline factor = porosity At the surface of the well bore t0 K0 This can be written as 0 t0 K (3.22) At a given depth in the well bore t D KD This can be written as D t D K (3.23) 29 On substituting equation (3.22) and equation (3.23) into equation (3.16) Therefore, t D t0 KD e K K t D t0e KD Taking the logarithm of both side of the equation LogtD Logt0 KD Therefore LogtD Logt0 KD (3.20) Where t D = interval transit time at a reference depth (s) t0 = interval transit time at the surface (s) D = depth (ft) K = compaction factor which depends on the formation The equation above shows that the interval transit time is expected to increase linearly with depth. An over pressured zone is detected when there is an abnormal deviation from the normal trend line in a semi-log plot of interval transit time with depth. 30 CHAPTER 4: OPTIMIZATION OF DRILL BIT HYDRAULICS The hydraulic power from mud pump must be efficiently utilized for efficient drilling operation to be achieved. Hence, the hydraulic power across the drill bit needs to be maximized at the point of contact between the drill bit and the formation so as to provide enough jet impact force to transport the cuttings as the formation is been drilled. Therefore, to efficiently remove drill cuttings and transport cuttings up the annulus, it is important to minimize power loss in the mud circulatory system so has to have adequate hydraulic horsepower across the drill bit. 4.1 Hydraulic Power Requirement The power involved in the mud circulating system is made up of the mechanical horse power which is the power needed to drive the mud pump, the fluid hydraulic horsepower, which is the fluid power which will provide a jet impact force and the bit hydraulic horse power, which is the power at the drill bit. The fluid hydraulic horsepower and the bit hydraulic horse power are the main design parameter for an effective hydraulic program design needed for effective bottom hole cleaning, and improved rate penetration. The main component of a hydraulic system is the mud pump at the surface, the surface connection, the drill pipe, the drill collars, the drill bit, and mud tank at the surface. However, the mud pump is the main source of circulating drilling fluid in the mud circulating system. Hydraulic power is define as the product of pressure and the corresponding flow rate (Azar and Robello 2007) Hh P * Q (4.1) In field unit this relationship is given Hh P *Q 1714 (4.2) Where Hh = hydraulic horse power (hp) 31 P = pressure (psia) Q =flow rate (gpm) 4.1.1 Surface Connection Pressure Drop In the mud circulation system the first pressure drop is experienced in the surface equipment. The surface equipment of a drilling rig includes the standpipe, rotary hose, swivel wash pipe, along with the gooseneck and Kelly bushing. The pressure drop in the surface connection is substantial during drilling fluid circulation and this loss depends on the type of surface connection. Surface equipment has been grouped into four classes by the International association of drilling contractors (IADC).Table 4.1 shows IADC classes of surface equipment of a drilling rig. Table 4.1 IADC Classes of Surface Equipment (Baker-Huges Drilling Engineering Workbook, 1995) Class #1(Coefficient 19) Class #2 (Coefficient 7) Class #3 (Coefficient 4) Class #4 (Coefficient 3) 40 ft & 3 in. I.D. standpipe 40 ft &3.5 in. I.D. Standpipe 5 ft & 2.5 in. I.D. Swivel 6 ft & 3 in. I.D. Swivel 45 ft & 2 in. I.D. Hose 55 ft & 2.5 in. I.D. Hose 45 ft & 4 in. I.D. Standpipe 45 ft & 4 in. I.D.Standpipe 4 ft & 2 in. I.D. Swivel 5 ft & 2.5 in. I.D. Swivel 40 ft & 3.25 in. I.D. Kelly 40 ft & 4 in. I.D. Kelly 40 ft & 2.25 in I.D. Kelly 40 ft & 3.25 in. I.D. Kelly 55 ft & 3 in. I.D. Hose 55 ft & 3 in. I.D.Hose Therefore, when calculating surface pressure losses, the surface pressure coefficient that corresponds to the surface equipment on the rig is chosen and the following relationship below is used (Baker Huges drilling engineering workbook 1995). Pfs 105 * K s * m * Q1.86 (4.3) 32 Where Pfs = surface pressure loss (psia) Ks = surface pressure coefficient m = mud density (lb/gal) Q = flow rate (gal/min) However, the surface connection pressure loss can also be obtained from the equivalent length of surface equipment of drill pipe. The surface connection pressure loss can also be calculated by Pfs Pfdp * Lse Ldp (4.4) Where Pfs = surface pressure loss (psi) Pfdp = pressure drop in the drill pipe (psia) Lse = surface equipment equivalent length of drill pipe (ft) Ldp = length of drip pipe (ft) 4.1.2 Drill String Pressure Drop After the drilling fluid passes through the surface connection it flows through the drill string. As the drilling fluids flow through the drill pipe and the drill collar, the walls of the drill strings create a resistance against fluid flow. This drag force from the drill string walls and irregularities caused by the drill string joints and sudden contractions of the internal diameter from the drill pipe to the drill collar produce eddies in the drill string. These eddies cause cross-flow and countercurrents, which create frictional resistance. This frictional resistance results in pressure loss in the drill string. The pressure drop in the drill pipe and the drill collar can be calculated for 33 laminar and turbulent flow criteria depending on the drilling fluid type used. The correlations for pressure drop in the drill string for both laminar and turbulent flow regimes are given below ( Bourgoyne, 1991) : 4.1.2.1 Newtonian Fluid For a Newtonian fluid in a laminar flow the pressure drop in the drill pipe and the drill collar is given below Pf L * p * Va 2 1500 * Didp Va Q 2 2.45 * Didp (4.5) (4.6) Where Pf = frictional pressure loss in the drill pipe or the drill collar (psia) Di = internal diameter of the drill pipe or drill collar (in) Va = average velocity of the drill pipe or drill collar (ft/min) Q = flow rate (gpm) L = length of the drill pipe or the drill collar (ft) p = plastic viscosity (cP) The equation for pressure drop using a Newtonian fluid in a turbulent flow regime, in the drill pipe and the drill collar is given by the equation below (Bourgoyne, 1991): 34 Pf f * m * Va2 25.8 * Di (4.7) Where the friction factor as given by Colebrook’s equation 21.25 1 2.28 4 Log 0.9 N RP f Di (4.8) Where Pf = friction pressure loss in the drill pipe or the drill collar (psia) f = friction factor m = mud density (ib/gal) Di Va = internal diameter of the drill pipe or drill collar (in) = average velocity of the drill pipe or drill collar (ft/min) = pipe roughness (in) N RP = reynolds number 4.1.2.2 Bingham Fluid For a Bingham fluid in a laminar flow regime the pressure drop in the drill pipe and the drill collar is given by the relationship below (Bourgoyne, 1991): Pf L * p * Va 2 idp 1500 * D y *L 225 * Di (4.9) Where P f = frictional pressure loss in the drill pipe or the drill collar (psia) Di = internal diameter of the drill pipe or drill collar (in) 35 Va = average velocity of the drill pipe or drill collar (ft/min) Q = flow rate (gpm) L = length of the drill pipe or the drill collar (ft) y = yield point (ib/100ft) p = mud plastic viscosity (cP) For turbulent flow, a turbulence criterion for fluids that follows the Bingham plastic model was presented by Hanks (1967) which he calls the Hedstrom number. The Hedstrom number equation is given as N He 37100 * m * y * d 2 p2 (4.10) Where N He = hedstrom number m = density of mud (ib/gal) p = plastic viscosity (cP) d = diameter of drill pipe or drill collar (in) Hanks (1967) also found that the Hedstrom number could be correlated to the critical Reynolds number from a chart. A turbulent flow is said to exist when this critical number is less than the Reynolds number .The pressure drop across the drill pipe for a turbulent flow can be calculated using the relationship given below (Bourgoyne, 1991): 36 Pf m0.75 * V 1.75 * 0p.25 * L (4.11) 1.25 1800 * Di Where P f = frictional pressure loss in the drill pipe or the drill collar (psia) Di = internal diameter of the drill pipe or drill collar (in) Va = average velocity of the drill pipe or drill collar (ft/min) L = length of the drill pipe or the drill collar (ft) m = density of mud (ib/gal) p = plastic viscosity (cP) 4.1.2.3 Power Law Fluid For a Power law fluid in a laminar flow the pressure drop in the drill pipe and the drill collar is given by the relationship below (Bourgoyne, 1991): Pf L * K * V n 3n 1 143700 * Dipn 1 0.0416 n (4.13) Where K = equivalent centipoise n = power law index L = length of the drill pipe of drill collar (ft) V = velocity (ft/min) Dip = Internal diameter (in) of drill pipe or drill collar 37 4.1.3 Annulus Pressure Drop The pressure drop in the annulus of the drill pipe and the drill collar mainly depend on the external diameters of the drill collar and the drill pipe, the bore hole size, the internal diameter of the casing and the drilling fluid flow rate. The cross-sectional fluid flow area in the annulus is larger compared to inside the drill string. The flow in the annulus is usually assumed to be laminar due to low fluid pressure and velocity. The frictional pressure loss in the annulus of the drill pipe and the drill collar can be calculated for both laminar and turbulent flow criteria depending on the type of drilling fluid used. The correlations for pressure drop in the annulus of the drill pipe and drill collar for both laminar and turbulent flow regimes are given below (Bourgoyne, 1991): 4.1.3.1 Newtonian Fluid For a Newtonian fluid in a laminar flow the pressure drop in the annulus of the drill pipe and the drill collar is given by the relationship below (Bourgoyne, 1991): p * Va * L Pa 1500 2 D 2 Do2 Dh Do2 h in ( Dh / Do ) (4.14) Where Va Q 2.45 * ( Dh2 D02 ) (4.15) Where Pa= frictional pressure loss in the annulus of the drill pipe or the drill collar (psia) Di = internal diameter of the drill pipe or drill collar (in) 38 Va = average velocity of the drill pipe or drill collar (ft/gal) Q = flow rate (gpm) L = length of the drill pipe or the drill collar (ft) Dh = diameter of the hole (in) Do = outer diameter of the drill collar or drill pipe (in) p = Plastic viscosity (cP) For a Newtonian fluid in a turbulent flow regime the pressure drop in the drill pipe and the drill collar is calculated using equation (4.7) where the internal diameter ( Di ) is replaced with the equivalent diameter ( De )of the drill pipe or drill collar. 4.1.3.2 Bingham Fluid For a Bingham fluid in a laminar flow the pressure drop in the annulus of the drill pipe and the drill collar is given below (Melrose, 1985). Pf L * p * Va 1000 * Dh Dod 2 y *L 200 * Dh Dod (4.16) Where P f = frictional pressure loss in the drill pipe or the drill collar (psia) Di = internal diameter of the drill pipe or drill collar (in) Va = average velocity of the drill pipe or drill collar (ft/min) Q = flow rate (gpm) L = length of the drill pipe or the drill collar (ft) y = yield value (ib/100ft) p = plastic viscosity (cP) 39 4.1.3.3 Power Law Fluid For a power law fluid in a laminar flow the pressure drop in the annulus of the drill pipe and the drill collar is given below (Dodge and Metzner, 1957): L * K *V n 2n 1 Pf n 1 143700 * Dh Do 0.0208 n (4.17) Where P f = frictional pressure loss in the annulus of the drill pipe or the drill collar (psia) K = equivalent centipoise n = power law index L = length of the drill pipe of drill collar (ft) V = velocity (ft/s) Do = outer diameter of the drill pipe or drill collar (in) Dh = diameter of the hole (in) 4.1.4 Drill Bit Pressure Drop The pressure drop across the drill bit is the most important element in a hydraulics equation and is mainly due to the change of fluid velocities in the nozzles and the flow rate of the drilling fluid. The amount of hydraulic horsepower available at the drill bit is influenced by the size of nozzles used, the mud density and the flow rate. The pressure drop across the bit is given by the relationship below (Azar and Samuel, 2007): 8.3 *105 * m * Q Pb A2 * Cd2 2 (4.18) 40 Where Pb = pressure drop across the drill bit (psia) Q = flow rate (gpm) A = area of nozzle (in2) Cd = discharge coefficient m = density of mud (ib/gal) Thus, the total pressure coming from the mud pump system consists of the pressure drop across surface connections (Pfs), the pressure drop across the drill bit (PB), the pressure drop across drill pipe (Pdp), the pressure drop across drill collar (Padc), the pressure drop in the annulus of the drill pipe (Padp) and the pressure drop in the annulus of the drill collar (Padc). The total circulating pressure (Pmax) Pmax Pfs Pdp Pdc padp Padc PB (4.19) The sum of all pressure drops except the pressure drop across the drill bit is called the parasitic pressure drop ( Pf ) D ( Pf ) D Pfs Pdp padp Padc (4.20) Hence the Total circulating standpipe pressure ( Pmax ) Pmax ( Pf ) D PB (4.21) 41 4.2 Flow Exponent and Optimum Flow Rate The flow exponent (m) between two points is deduced from the relationship between frictional pressure loss and flow rate. The flow exponent has a theoretical value of 1.75 (Bourgoyne, 1991): ( Pf ) D CQ m (4.22) Where ( Pf ) D = Parasitic pressure loss (psia) Q = Flow rate (gpm) m = Flow exponent C = constant that depends on mud flow properties, hole geometry and pipe geometry On taking the logarithm of both side of the equation log( Pf ) D log C m log Q (4.23) The plot of equation (4.23) is a straight-line with a slope of m and an intercept of log C . Therefore, if the mud pump is operated at two different flow rates, the flow exponent (m) can be obtained. There are two basic criteria that are used in analyzing bit hydraulics for hole cleaning either the drill bit hydraulics horsepower or the hydraulic jet impact force 4.3 Drill Bit Hydraulic Horsepower Criterion Drill bit hydraulic horsepower criterion is based on the fact that cuttings are best removed from beneath the bit by delivering the most power to the bottom of the hole. The amount of pressure lost at the bit, or bit pressure drop, is essential in determining the hydraulic horsepower. This criterion states that the optimum hole cleaning is achieved if the hydraulic horsepower across the bit is maximized with respect to the flow rate (Azar and Samuel, 2007). 42 H HB PB * Q . (4.24) Where H HB = drill bit hydraulic horse power (hp) PB = pressure across the drill bit (psia) Q = flow rate (gpm) Kendall and Goins (1960) derived an equation for calculating optimum parasitic pressure loss this is given below. On substituting equation (4.21) into equation (4.22) and making P B subject of the formula PB Pmax CQ m (4.25) On substitution equation (4.26) into equation (4.25) H HB Pmax Q CQ m 1 For maximum condition to occur dH HB 0 dQ Hence dH HB Pmax (m 1)CQ m 0 dQ (4.26) 43 But recall that ( Pf ) D CQ m Therefore dH HB Pmax (m 1)( Pf ) D 0 dQ Therefore the optimum parasitic pressure loss is given by the equation below (Kendall and Goins, 1960) ( Pf ) Dopt Pmax m 1 On the basis of the maximum bit hydraulic horsepower criterion, the optimum bit hydraulic will be achieved if frictional pressure loss in the circulating system is maintained at an optimum value given below (Kendall and Goins, 1960). ( Pf ) Dopt Pmax m 1 (4.27) Where Pmax = maximum pump pressure (psia) m = flow exponent ( Pf ) Dopt = optimum parasitic pressure drop (psia) The resulting optimum pressure drop across the drill bit is derived below (Kendall and Goins, 1960): But recall from equation (4.21) ( Pf ) Bopt Pmax ( Pf ) Dopt On substituting equation (4.28) 44 ( Pf ) Bopt m Pmax m 1 (4.28) Where ( Pf ) Bopt = optimum pressure drop on the drill bit (psia) Pmax = maximum pump pressure (psia) m = flow exponent Using the optimum hydraulic horsepower criteria, the hydraulic horse power at the bit can be determined from the relation below (Kendall and Goins, 1960): HHPopt PBoptQopt 1714 (4.29) Where HHPopt = optimum hydraulic horse power at the drill bit (hp) PBopt = optimum pressure drop across the drill bit (psia) Qopt = optimum flow rate (gpm) 4.4 Hydraulic (Jet) Impact Force Criterion Hydraulic (jet) impact force criterion is based on the fact that drill cuttings are best removed from beneath the bit when the force of the fluid leaving the jet nozzles and striking the bottom of the hole is very high. The maximum jet impact force criterion states that the bottom-hole cleaning is achieved by maximizing the jet impact force with respect to the flow rate. The jet impact force at the bottom of a wellbore can be derived from Newton’s second law of motion and is given by the equation below (Azar and Samuel, 2007): 45 FJ 0.01823Cd Q PB m (4.30) Where FJ = jet impact force (ibf) Cd = discharge coefficient m = mud density (ib/gal) Q = flow rate (gpm) PB= pressure on the drill bit (psia) But recall from equation (4.26) PB Pmax CQ m On substituting equation (4.37) FJ 0.01823Cd Q m ( Pmax CQ m ) (4.31) The hydraulic jet impact force criteria has two basic limitations which are due to the maximum available pump hydraulic horsepower and the maximum allowable surface operating pressure 4.4.1 Shallow Well Bore Formation When drilling a shallower portion of a wellbore formation, the frictional pressure loss is usually low and the flow rate requirement is large. Therefore, the hydraulic jet impact force is limited only by the limited pump hydraulic horse power. This relationship is relationship is derived below (Azar and Samuel, 2007): Pmax H H max Q (4.32) 46 Where Pmax = maximum pump pressure (psia) Q = flow rate (gpm) H H max = maximum pump hydraulic horsepower (hp) On substituting equation (4.33) into equation (4.32) FJ 0.01823Cd m ( H P max Q CQ m 2 ) (4.33) For maximum condition to occur dFJ 0 dQ On differentiating the equation (4.34) dFJ 0.009115Cd m ( H H max (m 2)CQ m 1 ) 0 dQ m ( H H max Q CQ m 2 ) To obtain a valid solution of the differential equation above, the numerator must be equal to zero. Hence 0.009115Cd m ( H H max (m 2)CQm 1 ) 0 Therefore ( H H max (m 2)CQm 1 ) 0 (4.34) But recall H H max Pmax Q On substituting into equation (4.35) 47 Pmax Q (m 2)CQmQ 0 Also recall that ( Pf ) D CQ m Hence, Pmax Q (m 2)( Pf ) D Q 0 This gives ( Pf ) Dopt Pmax m2 Therefore the optimum frictional pressure loss that can be obtained using the jet impact force criterion for a shallow portion of the well is given below (kendall and Goins, 1960): ( Pf ) Dopt Pmax m2 (4.35) Where Pmax = maximum pump pressure (psia) m = flow exponent ( Pf ) Dopt = optimum parasitic pressure drop (psia) The resulting optimum flow drop across the drill bit for a shallow depth based on the jet impact force criterion of optimization is given below (kendall and Goins, 1960): But recall, ( Pf ) Bopt Pmax ( Pf ) Dopt (4.36) Where 48 ( Pf ) Bopt = optimum pressure drop on the drill bit (psia) Pmax = maximum pump pressure (psia) ( Pf ) Dopt = optimum parasitic pressure drop (psia) On substituting equation (4.35) into equation (4.36) ( Pf Bopt ) m 1 Pmax m2 (4.37) Where ( Pf Bopt ) = optimum pressure drop on the drill bit (psia) Pmax = maximum pump pressure (psia) m = flow exponent 4.4.2 Deep Well Bore Formation When drilling a deeper portion of the wellbore, the frictional pressure loss increases while the flow rate requirement decreases. Therefore, the hydraulic jet impact force will be limited by the limited maximum allowed pump pressure Pmax. This relationship is derived as shown below (Azar and Samuel, 2007): From equation (3.32) FJ 0.01823Cd Q m ( Pmax CQ m ) This can also be written as FJ 0.01823Cd m ( Pmax Q2 CQ m 2 ) (4.38) For the maximum condition to occur, 49 dFJ 0 dQ On differentiating equation (4.39) dFJ 0.009115Cd m (2 Pmax Q (m 2)CQ m 1 ) _ 0 dQ m ( Pmax Q 2 CQ m 2 ) To obtain a valid solution of the differential equation above, the numerator must be equal to zero. Hence 0.009115Cd m 2Pmax Q (m 2)CQm 1 0 2Pmax Q (m 2)CQ m 1 0 Recall that ( Pf ) D CQ m Therefore 2Pmax Q (m 2)( Pf ) D Q 0 This gives ( Pf ) Dopt 2 Pmax m2 Therefore the optimum frictional pressure loss that can be obtained using the jet impact force criterion for a deeper portion of the well is given below (kendall and Goins, 1960): ( Pf ) Dopt 2 Pmax m2 (4.39) Where ( Pf ) Dopt = optimum parasitic pressure drop (psia) 50 Pmax = maximum pump pressure (psia) m = flow exponent The resulting optimum flow drop across the drill bit based on the jet impact force criterion of optimization is given below Recall, (Pf ) Bopt Pmax (Pf ) Dopt (4.40) On substituting equation (4.39) into equation (4.40) ( Pf ) Bopt m Pmax m2 (4.41) Where ( Pf ) Bopt = optimum pressure drop on the drill bit (psia) Pmax = maximum pump pressure (psia) m = flow exponent Using the optimum jet impact force criteria for both cases, the hydraulic jet impact force is given below: m FJ 0.01823Cd * Qopt m ( Pmax C * Qopt ) (4.42) Where FJ = jet impact force (ibf) Cd = discharge coefficient m = mud density (ib/gal) 51 Qopt = optimum flow rate (gpm) PB= pressure on the drill bit (psia) 4.5 Bit Nozzle Selection The process of bit nozzle selection involves running a circulating pressure test at the rig site, while keeping the rotary speed and weight-on-bit constant. This usually involves varying the mud pump speed and recording the pump pressure and circulating rate at each speed. The objective is to determine the optimum pressure drop across the bit nozzles and the optimum flow rate as discussed above and from thence determine the nozzle sizes to support these optimum conditions. The necessary conditions for attaining optimal bottom hole cleaning below a drill bit is usually approximated via the optimization of the two design criteria. The optimum nozzle area and optimum nozzle diameter is given by the relationship below (Azar and Samuel, 2007): ( At )opt 2 8.311 *105 * m * Qopt 2 Cd * Pbopt (4.43) Where ( At ) opt = optimum nozzle area (in2) Qopt = optimum flow rate (gpm) m = flow exponent Pbopt = optimum pressure on the drill bit (psia) Cd = discharge coefficient m = mud density (ib/gal) If there are three nozzles and of equal diameter the optimum nozzle diameter is given below (d N )opt 4( At )opt 3 (4.44) 52 Where (d N ) opt = optimum nozzle diameter (in) ( At ) opt = optimum nozzle area (in2) 4.6 Drill Cutting Transport Drill cuttings in the annular space are subjected to numerous forces such as gravitational forces, buoyancy, drag inertia, friction and interparticle contact. The flow of cuttings in the annulus is dictated by these forces. Some of the factors that affect the capacity of drilling fluids to transport drilled cuttings through the annular space are cutting slip velocity, annular fluid velocity and flow regime. 4.6.1 Cutting Slip Velocity The cutting slip velocity is the rate at which drill cuttings fall. For the fluid to lift the drill cuttings to the surface, the fluid annular average velocity must be in excess of the cuttings average slip velocity. To maintain good hole cleaning, the velocity of the drilling fluid has to be greater than the slip velocity of the cuttings. The slip velocity depends on the difference in densities, viscosity of the fluid and the size of the cuttings. Several empirical correlations such as the Chien correlation, the Moore correlation and theWalker and Mayes correlation have been developed to predict the slip velocity. 4.6.2 Annular Fluid Velocity The annular fluid velocity when drilling a vertical well has to be sufficiently high to avoid cuttings from settling and to transport these cuttings to the surface. The increasing radial component of a particle slip velocity pushes the particles towards the lower wall of the annulus, causing cuttings bed to form. Therefore the annular velocity has to be sufficiently high to avoid bed formation. 53 4.6.3 Flow Regime Flow regime describes the manner in which a drilling fluid behaves when flowing. The flow regime could be laminar or turbulent. Fluid flow may also be predominantly laminar at very low pump rates, but can become turbulent either at high pump rate or during pipe rotation. The characteristics of laminar flow that is useful to the drilling engineer are the low frictional pressures and minimum hole erosion. Laminar flow can be described as individual layers moving through the pipe or annulus. The center layers moves at rates greater than the layers near the well bore or pipe. The variations in velocity of this layer are controlled by the shear-resistant capability of the mud. A high yield point for the mud tends to make the layers move at more uniform rates. Cuttings removal is often discussed as being more difficult with laminar flow. Turbulence occurs when increased velocities between the layers create shear stresses exceeding the capacity of the mud to remain in laminar flow. Turbulence occurs commonly in the drill string and occasionally around the drill collars. Reynolds number can be used to determine flow regime. 54 CHAPTER 5: DESIGN METHODOLOGY The aim of a drill bit hydraulic design is to provide sufficient hydraulic horsepower to the drill bit for efficient bottom hole cleaning and to ensure an effective rate of penetration during drilling. Hence for a drill bit hydraulic design, the pump operating requirements, appropriate drilling mud, optimum flow rate and the corresponding optimum drill bit nozzle size are necessary to ensure optimum drilling conditions. In this project work a case study will be considered in the design of a hydraulic system to enhance the rate of penetration in an overpressured zone and to also enhance bottom hole cleaning by providing the optimum operating conditions. In this case study the reservoir interval lies in an over-pressured zone; therefore, it is critical to drill efficiently and safely in this zone. This project work will involve estimation of pore pressure and fracture pressure using geological data, mud weight selection, laboratory work on drilling fluid rheology as well as calculations of pressure drop across the hydraulic system using the maximum horse power criterion for optimization purposes. The geological data available for this study is the Frio shale conductivity data (Mian,1991) acquired from an offshore well drilled in Nueces County in Texas. Table 5.1 below shows of shale conductivity data obtained from a vertical well. Table 5.1 Shale Conductivity Data from Nueces County Texas (Mian, 1991) Conductivity (m/Ωm2) Depth(ft) 7400 7500 7550 8300 8350 8400 8500 9200 9300 9550 9600 9700 9750 9900 9950 710 780 790 710 690 680 690 600 590 570 590 610 621 700 830 Conductivity (m/Ωm2) Depth(ft) 10000 10050 10150 10200 10300 10500 10600 10650 10850 11000 11050 11200 11300 11500 950 1100 1200 1240 1310 1250 1350 1370 1500 1280 1400 1650 1840 1920 55 5.1 Estimation of Pore Pressure The pore pressure from geological data (well log) is obtained using the Hottman and Johnson procedure (Mian, 1991), by making a semi-log plot of shale resistivity versus depth using the well data given. The plot of resistivity versus depth for the well is shown in Fig 5.1. In(R) 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 7000 7500 8000 Normal Presssure Zone 8500 Depth(ft) 9000 9500 Top of Over Pressure 10000 10500 Over Pressure Zone Normal Shale Resistivity Trend Line(Rn) 11000 11500 Observed shale Resistivity Trend Line (R0) 12000 Fig 5.1 – Semi log plot of shale resistivity versus depth 56 From Figure 5.1, it shows that the point of entry into the overpressure zone occurs at a depth of 9550 ft. Therefore the over pressure zone of interest extends with depth from this point. Figure 5.1 also shows that the normal pore pressure trend is defined by the traditional semi log plot characterised by a straight line that extends from 7400ft to 9550ft. This has a pore pressure gradient 0.465psia/ft. The pore pressure at each depth is obtained using the relationship below Pp GD (5.1) Where G = pore pressure gradient (psia/ft) D = depth (ft) PP = pore pressure (psia) The pore pressure values in the normally pressured zone is shown in Appendix A The pore pressure in the over pressure zone that lies from 96000 ft to 11500 ft is obtained from the Hottman and Johnson procedure using equation 5.1 by taking the ratio of the observed shale resistivity ( R0 ) and the normal shale resistivity ( Rn ) from Figure 5.1 at each depth. The pore pressure gradient at each depth in the overpressure zone is obtained from the chart of shale resistivity ratio versus pore pressure gradient given in Appendix E. The estimates of the pore pressure at each depth in the well are shown in appendix A. 5.2 Estimation of Fracture Pressure The fracture pressure of the formation in this case study is estimated using the Hubbert and Willis equation. The Hubbert and Willis approach assumes that overburden pressure gradient G= 1psia/ft and Poisson’s ratio = 0.25 (Bourgoyne, 1991). 57 The semi-log plot of resistivity versus depth shows that the over pressure zone starts from a depth of 9600 ft. Fracture pressure at the normal pressure zone which lies from 7400 ft to 9600 ft is and the over pressure zone which lies between 9600 ft to 11500 ft is obtained using the Hubbert and Willis equation (Hubbert and Willis, 1957) given in equation (3.9) and equation (3.10).The estimates of the fracture pressure at each depth in the well are shown in Appendix A. 5.3 Mud Weight Selection The mud weight to be selected for this design work is obtained by plotting a graph of specific gravity versus depth. The calculation approach of specific gravity from pore pressure and fracture pressure data for each depth is outlined in the following section. 5.3.1 Geological Mud Specific Gravity from Pore Pressure Geological mud specific gravity from pore pressure is the specific gravity calculated from well log data. The relationship below is given below ( Bourgoyne, 1991): p PP 0.052 * D SG p p p 8.33 (5.2) (5.3) w Where p = density from pore pressure (ib/gal) D = depth (ft.) SG p = specific gravity from pore pressure w = density of water (ib/gal) PP = pore pressure (psia) 58 5.3.2 Geological Mud Specific Gravity for Fracture Pressure Geological mud specific gravity from fracture pressure is the specific gravity calculated from fracture pressure data obtained using well log data. This can be calculated using equation (5.2) and (5.3) where the pore pressure is replaced with fracture pressure and the specific gravity for pore pressure is replaced with specific gravity for fracture pressure. 5.3.3 Design Mud Specific Gravity from Pore Pressure Line In designing for mud specific gravity a safety factor called the trip margin is considered. The trip margin is necessary to compensate for swab pressure. Redmann (1991) suggested a trip margin of 0.5 ib/gal for pore pressure. The relationship below was used: dp p 0.5 (5.4) Where dp = design mud density from pore pressure (ib/gal) p = mud density from pore pressure (ib/gal) The design mud specific gravity can then be calculated using equation (5.3) where the mud density from pore pressure is replaced with the design mud density from pore pressure. 5.3.4 Design Mud Specific Gravity from Fracture Pressure In designing for the specific gravity, a kick tolerance of 0.5 ib/gal is used as kick margin for fracture pressure (Redmann, 1991). To avoid fracturing the formation Redmann (1991) recommended a kick tolerance of 0.5 ib/gal. The design mud specific gravity for fracture pressure can be calculated using equation (5.3) where the specific gravity from pore pressure is replaced with design specific gravity from fracture pressure and mud density from pore pressure is replaced with design mud density from fracture pressure. 59 The design mud density from pore pressure and design mud density from fracture pressure used for this work are shown in Appendix A. Figure 5.2 shows a plot from Appendix B that gives the design mud specific gravity from pore pressure and fracture pressure. Specific gravity 0.5 1 1.5 2 2.5 3 3.5 4 4.5 7000 7500 8000 8500 Depth(ft) 9000 9500 10000 10500 11000 11500 Geological specific gravity for pore pressure line Design specific gravity for fracture pressure line Geological specific gravity for fracture preesure line Design specific gravity for pore pressure line 12000 Fig 5.2: Graph of specific gravity versus depth 60 Figure 5.2 shows that the mud density required to drill through the formation lies between the pore pressure and fracture pressure line. The density of the drilling mud affects the rate of penetration. Therefore based on fig 5.2, a mud specific gravity ( SGm ) of 1.5 will be chosen to drill effectively and efficiently through the formation at a faster rate and to avoid the chip hole down problem. Hence the mud density is given below: Mud density ( m ) = mud specific gravity ( SGm )*density of water ( w ) 1.5*8.33= 12.495 ib/gal 5.4 DRILLING MUD RHEOLOGY 5.4.1 Introduction Based on the mud density (12.495 ib/gal) obtained from the geological data of this case study as given above, the drill mud rheology properties were studied. It is important to study the rheological properties of the mud to be used. This study will enable the determination of the rheological properties of the mud, such as the plastic viscosity and the yield point of the drilling mud to be used in the mud circulatory system. These rheological properties are vital in determining the flow regime in the mud circulatory system. These rheological properties are also essential in calculating the entire pressure drop in the mud circulatory system. 5.4.2 Objective of Experiment The aim of the experimental part of this project work is to prepare a suitable drilling mud based on the result of the mud density obtained from the geological data. This requires the determination of the Plastic viscosity and the yield point of the drilling mud. A rotational viscometer was used to acquire the plastic viscosity and yield strength of the drilling mud. Mud samples with varying concentration of mud additives were prepared to achieve a suitable mud with suitable rheological properties, since pressure losses strongly depend on the rheological properties of the drilling mud. Based on the geological data of my case study a water-based mud with a density of 12.5 ib/gal was prepared in the laboratory using a mixture of barite, bentonite and water. A water-based mud was chosen for this work because the rate of penetration with water-based mud is generally slightly faster than with oil-base mud for both roller cutting bits 61 and diamond bit (Cheatham, 1985). Three mud samples were prepared for this purpose in order to determine the mud sample with the smallest parasitic pressure losses. 5.4.3 Equipment Used Viscometer: A model 35 Fann viscometer manufacture by Fann Instrument Company was used for this experiment, this viscometer was used to determine the viscosity and yield point of the mud sample that was prepared for this project work. The diagrammatic representation of the model 35 viscometer can be seen in the Figure 5.3. Fig 5.3: Model 35 Viscometer Mud Balance: A model 140 Mud balance manufactured by NL Bariod was used for mud density measurement which has an accuracy of ±0.05ib/gal.The mud density test for each mud sample was conducted using a mud balance, which consists of a base and a balance arm with cup, lid, knife edge, rider, level glass, and counterweight. The cup is attached to one end of the balance 62 arm and the counterweight is at the opposite end. The diagrammatic representation of the mud balance can be seen in the Figure5.4. Fig 5.4: Model 140 Mud Balance 5.4.4 Mud Mixture: The mud composition used in preparing a water based mud for this experimental work is barite, bentonite and water. The equation below was used in preparing the mud samples to obtain a mud density of 12.5 ib/gal (Mian, 1991): mix M1 M 2 M 3 M1 M 2 M 3 1 2 (5.5) 3 Where mix = density of the mud mixture (g/cm3) M 1 = mass of barite (g) M 2 = mass of bentonite (g) M 3 = mass of water (g) 1 = API density for barite (g/cm3 2 = API density for bentonite (g/cm3) 3 = API density for water (g/cm3) 63 Table 5.2 shows the American Petroleum Institute (API) density for the additives used for this work. Table 5.2 API Densities of Mud Additives (Bourgoyne, 1991) Mud Additive Density ( ib/gal) Barite 35 Bentonite 2.7 Water 8.33 5.4.5 Experimental procedure The following test procedures were carried out in the laboratory at a temperature of 220c The masses of barite, bentonite and water were each measured using the mass balance The barite, bentonite and water were mixed and poured in the mud cup of the mud balance and the mud density was measured by adjusting the rider in the balance arm until a point of equilibrium was achieved. The mud density was then read from the level glass indicator of the mud balance. More additives was added to the mixture because the laboratory mud density of the mixture was less than the theoretical mud density, until the mud density of 12.5 ib/gal was obtained using the mud balance. The mud mixture with a density of 12.5 (ib/gal) was filled in the stainless steel sample test cup of the viscometer to the scribed line and placed on the instrument stage. The lock nut of the viscometer was loosened and the instrument stage with the stainless steel in it was raised until the rotor was immersed to the proper immersion depth of the stainless steel cup and the lock nut was tightened. The rotor of the viscometer was operated in a high speed position of 600 rpm with the gear shifted down. The dial reading on the viscometer is recorded when the indicator became steady. The rotor of the viscometer was then switched to 300 rpm speed with the gear still shifted down. The dial reading on the viscometer is also recorded when the indicator became steady. 64 The plastic viscosity and the yield of the mud sample was obtained using the relationship below (Model 35 viscometer instruction manual) : PV 600 300 YP 300 PV (5.6) (5.7) Where PV = plastic viscosity (cP) YP = yield point ib/100ft 600 = dial reading of viscometer at 600 rpm 300 = dial reading of viscometer at 300 rpm 5.4.6 Composition of Mud Additives used Table 5.3 shows the composition of mud additives used in the laboratory for preparing the three mud samples. Table 5.3: Composition of Mud Sample 1 Mud Additives Barite Bentonite Water Mass (g) 250 25 400 Taking measurements from the viscometer while running the viscometer at 600 rpm and 300 rpm 600 43 300 24 The plastic viscosity was obtained using equation (5.6) PV 600 300 65 PV 19cP The Yield point is obtained using equation (5.7) YP 300 PV YP 5ib / 100 ft 2 Table 5.4: Composition of Mud Sample 2 Mud Additives Barite Bentonite Water Mass (g) 350 40 550 Taking measure from the viscometer running the viscometer at 600 rpm and 300 rpm 600 80 300 46 The Plastic viscosity for this mud sample is obtained using equation (5.6) PV 600 300 PV 34cP The Yield point for this mud sample is obtained using equation ( 5.7) YP 300 PV YP 12ib / 100 ft 2 Table 5.5: Composition of mud sample 3 Mud Additives Barite Bentonite Water Mass (g ) 560 90 795 66 Taking measure from the viscometer running the viscometer at 600rpm and 300rpm 600 85 300 72 The Plastic viscosity for this mud sample is obtained using equation (5.6) PV 600 300 PV 15cP The Yield point for this mud sample is obtained using equation (5.7) YP 300 PV YP 57 Ibs / 100 ft 2 5.5 PRESSURE DROP COMPUTATIONS The pressure drop computation in the mud circulatory system for this work was done based on the result obtained from the experimental work. The pressure drop across the mud circulatory system comprises the pressure drop across the surface connection, the pressure drop in the drill pipe and drill collar, the pressure drop in the annulus of the drill pipe and the drill collar and the pressure drop across the drill bit. The pressure losses in the mud circulatory system will be calculated using the properties of the three mud samples prepared in the laboratory. The mud pump data, drill string data, drill bit and hole data used in the minimum flow rate, maximum flow rate and pressure losses computation are given in appendix C. 5.5.1 Maximum and Minimum Flow Rate Calculation The optimum flow rate to be used in drilling must be between the maximum and minimum flow rates. The maximum flow rate in the well can be achieved at maximum mud pump pressure with maximum pump horse power and pump efficiency. The minimum flow rate is a critical parameter that should be high enough to carry the cuttings from the bottom hole. The minimum flow are depends on the minimum annular velocity. Laboratory and field work carried out by Williams and Bruce (1951) show that the minimum annular velocity necessary to remove drill cuttings from a hole ranges from 100 to 125 ft per min (Williams and Bruce, 1951). 67 Maximum flow rate can be calculated with the relationship given as (Bourgoyne, 1991): Qmax 1714 * * H hp Pp max (5.8) Where Qmax = maximum flow rate (gpm) H hp = hydraulic horse power (hp) Pp max = maximum allowed operating pressure of the pump (psia) = volumetric efficiency Therefore the maximum flow rate in the well can be calculated using the given pump data as shown below: Qmax 1714 * 0.8 * 1765 4000 Qmax = 605.04 gpm Minimum flow rate can be calculated with the relationship given as (Bourgoyne, 1991): Qmin 2.448 * ( Dh2 Dp2 ) * vmin (5.9) Where Qmin = minimum flow rate (gpm) Dh = diameter of the hole (in) Dp = diameter of the pipe (in) vmin = minimum annular velocity (ft/s) A minimum annular velocity of 120 ft/min is used for this design in according with Williams and bruce (1951). 68 Therefore the minimum flow rate in the well can be calculated as shown below: 120 Qmin 2.448 * (7.8752 42 ) * 60 Qmin = 378.35 gpm Therefore, the operating flow rate ranges from the minimum (378.35 gpm) to maximum (667.4 gpm). Hence the parasitic pressure losses will be computed at a flow rate between the maximum and minimum flow rate (Bourgoyne, 1991). A flow rate of 400 gpm (Bourgoyne, 1991) will be chosen for the parasitic pressure losses computation in this work. 5.5.2 Calculating Pressure Drop in the Drill String In calculating the pressure drop in the drill string it is very important to know the flow pattern in the drill pipe and in the drill collar. The pressure drop across the drill pipe and drill collar was calculated for each depth starting from the point of entry into the over pressured zone which is at a depth of 9600 ft. 5.5.2.1 Pressure Drop Across the Drill Pipe The flow regime drilling at a depth of 9600ft was determined using the Hedstrom number criterion using a Mud Sample 1 which has a viscosity of 19 cP and yield point of 5 ib/100ft. The Hedstrom number given in equation (4.10) N He 37100 *12.495 * 5 * 42 102728.97 192 69 The critical Reynolds number is obtained using the graph below : Fig 5.5 Critical Reynolds number Bingham plastic fluids (Bourgoyne, 1991) The Critical Reynolds number = 7000 as seen in Figure 5.5, using the Hedstrom Number ( 102728.97 ) The Reynolds number is given by (Bourgoyne, 1991): N Re 928 * m * * d p (5.10) Where N Re = reynolds number m = density of mud (ib/gal) p = mud plastic viscosity (cP) = mean fluid velocity (ft/s) d = diameter of drill pipe (in) The mean fluid velocity in the drill pipe is given as (Bourgoyne, 1991): 70 V Q 2 2.45 * Didp (5.11) Where V = mean fluid velocity in the drill pipe (ft/s) Q = flow rate (gpm) Didp = internal diameter of the drill pipe or drill collar (in) V Q 400 10.2 ft / s 2 2.45 * Didp 2.45 * 42 Hence, N Re 928 *12.495 *13.28 * 4 24899.487 19 The critical Reynolds number is less than the Reynolds number; therefore the flow regime in the drill pipe is turbulent. The frictional pressure loss in the drill pipe for turbulent flow is given in equation (4.11). Pdp Pdp m0.75 * 1.75 * 0p.25 * Ldp 1.25 1800 Didp 12.4950.75 *10.21.75 *190.25 * (9600 1000) 1800 * 41.25 Therefore the pressure drop in the drill pipe at a depth of 9600 ft is given as Pdp 682.33 psia 71 The same procedure is repeated for the pressure drop across the drill pipe at subsequent depth in the over pressure zone. This calculation is also repeated using Mud Samples 2 and 3 which is given in Appendix G and H. 5.5.2.2 Pressure Drop across the Drill Collar The flow regime will be determined using the Hedstrom number criteria using a Mud Sample 1 Hedstrom number equation is given by equation (4.10) as shown below: N He N He 37100 * m * y * de2 p2 37100 *12.495 * 5 * 4.52 130016.36 192 From Figure 5.5, The Critical Reynolds number =22000 is obtained using the Hedstrom number (130016.36). The mean velocity in the drill pipe is obtained using equation (5.11), replacing the diameter of the drill pipe with the diameter of the drill collar. The fluid velocity in the drill collar is given below. V Q 2 2.45 * Didc V Q 400 8.06 ft / s 2 2.45 * Didc 2.45 * 4.52 Therefore the Reynolds number is given below: 72 N Re 928 *12.495 * 8.06 * 4.5 22134.93 19 The Critical Reynolds number is less than the Reynolds number therefore the flow regime in the drill collar is turbulent. The frictional pressure loss in the drill collar for a turbulent flow is given in equation (4.11) Pdc m0.75 * 1.75 * 0p.25 * Ldc 1.25 1800 Didc 12.4950.75 * 8.061.75 *190.25 *1000 Pdc 48.54 psia 1800 * 4.51.25 Therefore the pressure drop across the drill collar is: Pdc 48.54 psia This calculation is repeated using mud sample 2 and 3 which is given in Appendix G and H. 5.5.3 Calculating Pressure Drop in Surface Connection The surface connection pressure drop will be calculated using the relationship below since the equivalent surface equipment length of drill pipe is known. The equation for calculating pressure drop in surface connection in equation (4.4) is given below. Pf S Pdp * Lse Ldp Pf S 682.33 * 340 (9600 1000) Pf S 26.98 psia 73 5.5.4 Calculating Pressure Drop in Annulus In calculating the pressure drop in the annulus it is very important to know the flow regime in the annulus of the drill pipe and in the drill collar. The pressure drop across the annulus of the drill pipe and drill collar will then be calculated for each depth starting from the point of entry into the over pressured zone which is at a depth of 9600ft. 5.5.4.1 Pressure Drop across the Annulus of Drill Pipe The flow regime will be determined using the Hedstrom number criteria using Mud Sample 1.The Hedstrom number equation which is given by equation (4.10) where the internal diameter is replaced with the equivalent diameter. N He 37100 * m * y * de2 p2 The equivalent diameter de is given as (Bourgoyne, 1991): de 0.816 * (dh dodp) (5.12) Where d e = equivalent diameter (in) d h = diameter of the hole (in) d odp = outer diameter of the drill pipe (in) de 0.816 * (7.875 5.25) 74 de 2.142in N He 37100 *12.495 * 5 * 2.1422 29458.59 192 Figure 5.5, the critical Reynolds number =10000 is obtained using the Hedstrom number (29458.59) The mean velocity in the drill pipe is given as (Bourgoyne, 1991): V Q 2 2.45 * ( Dh2 Dodp ) (5.13) Where Va = average velocity of fluid in the drill pipe (ft/s) Q = flow rate (gpm) Dodp = outer diameter of the drill collar (in) Dh = diameter of the hole (in) Va Q 400 4.74 ft / s 2 2 2.45 * ( Dh Dodp ) 2.45 * (7.8752 5.252 ) N Re 928 *12.495 * 4.74 * 2.142 6196.24 19 The critical Reynolds number is greater than the Reynolds number, therefore the flow regime in the drill collar is laminar. The frictional pressure loss in the annulus of the drill pipe for a laminar flow regime starting at a depth of 9600 ft is calculated by the relationship given in equation (4.16). 75 Pfadp Pfadp Ldp * p * Va 1000( Dh Dodp) 2 y * LdP 200( Dh Dodp) (9600 1000) *19 * 4.74 5 * (9600 1000) 2 1000 * (7.875 5.25) 200 * (7.875 5.25) Pfadp 194.30 psia The same procedure is repeated for the pressure drop across the annulus of the drill pipe at subsequent depths in the over pressure zone. This calculation is also repeated using Mud Samples 2 and 3 which is given in Appendix G and H. 5.5.4.2 Pressure Drop across the Annulus of the Drill Collar The flow regime will be determined using the Hedstrom number criteria using mud sample 1. Hedstrom number equation is given by equation (4.10). N He 37100 * m * y * de2 p2 The equivalent diameter de is calculated using equation (5.12) where the outer diameter of the drill pipe is replaced with the other diameter of the drill collar. de 0.816 * (dh dodc) de 0.816 * (7.875 6.5) de 1.122in 76 N He 37100 *12.495 * 5 *1.1222 8082.74 192 From Figure 5.5, the Critical Reynolds number =3200 is obtained using the Hedstrom number (8082.72).The Reynolds number is given by equation (5.10). The mean velocity in the annulus of the drill collar is calculated using equation (5.13) where the outer diameter of the drill pipe is replaced with outer diameter of the drill collar given below. Va Q 2 2.45 * ( Dh2 Dodc ) Va Q 400 8.26 ft / s 2 2 2.45 * ( Dh Dod ) 2.45 * (7.8752 6.52 ) N Re 928 *12.495 * 8.26 *1.122 5655.92 19 The critical Reynolds number is less than the Reynolds number, therefore the flow regime in the drill collar is turbulent. Since the flow is turbulent the frictional pressure loss in the annulus of the drill collar is calculated using equation (4.11) where the internal diameter is replaced with equivalent diameter as shown below. Padc Padc m0.75 * 1.75 * 0p.25 * Ldc 1800 * De1.25 12.4950.75 * 8.261.75 *190.25 *1000 268.63 psia 1800 *1.1221.25 Therefore the pressure drop across the drill collar is given below: 77 Padc 268.63 psia This calculation is also repeated using Mud Samples 2 and 3 which are given in Appendix G and H. 5.6 Optimization using the Maximum Drill Bit Horsepower Criterion The condition for maximum drill bit horse power derived by Kendal and Goins (1960) states that bit hydraulic horse power is maximum when the parasitic pressure loss is given by the equation (4.28) shown below. ( Pf ) Dopt Pmax m 1 Kendal and Goins (1960) stated that the theoretical value for the flow exponent (m) is 1.75 Therefore the optimum parasitic pressure loss using the maximum bit horsepower criteria for this case study is given below: ( Pf ) Dopt Pmax 4000 m 1 1.75 1 ( Pf ) Dopt 1454.55 psia Kendal and Goins further stated that for bit hydraulic horse power to be maximum the pressure across the drill bit is given by the relationship below. ( Pf ) Bopt Pmax ( Pf ) Dopt (5.14) Where ( Pf ) Bopt = optimum pressure drop on the drill bit (psia) ( Pf ) Dopt = optimum Parasitic pressure drop (psia) Pmax = maximum pump pressure (psia) 78 Therefore for optimum condition to be achieved the pressure across the drill bit must be maintained, in this case study the pressure across the drill bit is given below : ( Pf ) Bopt 4000 1454.55 2545.45 psia In other to maintain the optimum pressure across the drill bit in this case study, the pump must be operated at the optimum flow rate to the target depth of 11500 ft. 5.6.1 Optimum Flow Rate to Operate the Mud Pump Pressure drop increases with depth, hence in order to drill at the optimum condition the pump must be operated at the optimum flow rate at each depth as the well is being drilled to the target depth. In other to achieve this objective in this case study a graphical approach is used. The optimum flow rate across each depth in the overpressure zone is obtained from the hydraulic plot. The hydraulic plot is a log-log plot of parasitic pressure loss against flow rate. The data for the parasitic pressure drop and flow rate used for the hydraulic plot is given in Appendix D. 79 3.185 Line extends to maximum mud pressure Log(Pmax)= 3.6 Optimum Parasitic pressure loss log(Pdopt) =3.163 3.165 11500ft 3.145 y = 1.75x - 1.295 Log Pd 11300ft 11200ft 10850ft 3.125 Optimum hydraulic plot 11050ft 11000ft m= 1.75 10650ft 10600ft 10500ft Over pressure zone line of interest 10300ft 10200ft 10150ft 3.105 10050ft 10000ft 9950ft 9900ft 9750ft 9700ft 3.085 2.45 9600ft Qmin 2.55 2.65 Log Q Qmax 2.75 Fig 5.6: Hydraulic log-log plot of parasitic pressure losses versus flow rate using Appendix D 80 The optimum flow at each depth in the over pressured zone is obtained by taking a straight line with a slope =1.75 across each depth on the over pressure line, and recording the point where the line hits the optimum hydraulic path line, which gives the optimum flow rate at each depth. This is given in Appendix F. 5.6.2 Optimum Nozzle Area of Drill Bit The optimum nozzle area and diameter is obtained at optimum conditions to drill to the target depth of 11500ft. It is obtained by using the equation below (Azar and Samuel, 2007): ( At )opt 2 8.311 *105 * m * Qopt 2 Cd * Pbopt (5.15) Where ( At ) opt = optimum nozzle area (in2) Qopt = optimum flow rate (gpm) m = flow exponent Pbopt = optimum pressure on the drill bit (psia) Cd = discharge coefficient m = mud density (ib/gal) The optimum nozzle area is calculated using the equation below assuming that the three nozzles of the drill bit are of equal area. d N opt 4( At )opt 3 (5.16) 81 Where d N opt = optimum nozzle diameter (in) ( At ) opt = optimum nozzle area (in2) Table 5.6 shows the optimum nozzle area and optimum nozzle size of the drill bit using equation 5.15 and 5.16. Table 5.6: Optimum Nozzle Area and Size Across Each Depth in the Overpressure zone. Depth(ft) Qopt(gpm) Aopt(sq in) Dopt(in) 9600 439.54 0.364 0.393 9700 438.53 0.363 0.392 9750 438.53 0.363 0.393 9900 434.51 0.36 0.39 9950 433.51 0.36 0.39 10000 432.51 0.358 0.389 10050 431.52 0.358 0.389 10150 429.54 0.356 0.389 10200 428.55 0.355 0.388 10300 426.58 0.354 0.388 10500 421.69 0.349 0.385 10600 420.73 0.349 0.385 10650 419.75 0.348 0.384 10850 416.87 0.345 0.383 11000 413.99 0.343 0.382 11050 412.09 0.342 0.381 11200 410.21 0.34 0.38 11300 408.32 0.338 0.379 11500 403.65 0.335 0.377 In other to drill at optimum conditions in the over pressured zone to the target depth of 11500 ft using the maximum hydraulic horse power criterion, the flow rates at which the pump must be operated are given in the Table 5.6 as obtained from the hydraulic plot of Figure 5.6. 82 5.6.3 Maximum Hydraulic Horse Power on the Drill Bit Using the optimum hydraulic horsepower criteria, the hydraulic horse power at the bit can be determined from the relationship given in equation (4.29) as shown below (Kendall and Goins, 1960): HHPopt PBopt * Qopt 1714 Table 5.7: Optimum Hydraulic Horsepower at Each Depth in the Overpressure zone. Depth(ft) Qopt(gpm) Aopt(sq in) Dopt(in) HHPbopt(hp) 9600 439.54 0.364 0.393 652.76 9700 438.53 0.363 0.392 651.26 9750 438.53 0.363 0.393 651.26 9900 434.51 0.36 0.39 645.29 9950 433.51 0.36 0.39 643.8 10000 432.51 0.358 0.389 642.32 10050 431.52 0.358 0.389 640.85 10150 429.54 0.356 0.389 637.91 10200 428.55 0.355 0.388 636.44 10300 426.58 0.354 0.388 633.51 10500 421.69 0.349 0.385 626.25 10600 420.73 0.349 0.385 624.82 10650 419.75 0.348 0.384 623.37 10850 416.87 0.345 0.383 619.09 11000 413.99 0.343 0.382 614.81 11050 412.09 0.342 0.381 611.99 11200 410.21 0.34 0.38 609.2 11300 408.32 0.338 0.379 606.39 11500 403.65 0.335 0.377 599.46 83 CHAPTER 6: RESULT AND DISCUSSION The results of this project work are based on experimental work carried out and pressure loss calculation. 6.1 Frictional Pressure Loss of Mud Samples Result Frictional pressure losses are observed to increase with depth across the drill pipe, and the annulus of the drill pipe, but the frictional pressure drop across the surface connection, drill collar and the annulus of the drill collar remain the same. 6.1.1 Using mud sample 1 Mud Sample 1 has a viscosity of 19 cP and a yield point of 5 lb/100ft2. Table 6.1 shows the pressure losses in the mud circulatory system when Mud Sample 1 was used in the design work with an assumed flow rate of 400 gpm. This results shows that a larger percentage of the pressure loss in the mud circulatory system was found to occur in the drill pipe which is as a result of turbulent flow in the drill pipe. Table 6.1 shows all the frictional pressure losses observed when using this mud. Table 6.1 Frictional Pressures Losses in the Mud Circulatory System Using Mud Sample 1 Depth (ft) Ps (psia) Pdp (psia) Pdc (psia) Padp (psia) Padc (psia) Pd (psia) 9600 9700 9750 9900 9950 10000 10050 10150 10200 10300 10500 10600 10650 10850 11000 11050 11200 11300 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 26.98 682.33 690.26 694.23 706.13 710.09 714.06 718.03 725.96 729.93 737.86 753.73 761.66 765.63 781.5 793.4 797.37 809.27 817.2 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 48.54 194.3 196.56 197.69 201.08 202.21 203.34 204.47 206.73 207.86 210.11 214.63 216.89 218.02 222.54 225.93 227.06 230.45 232.71 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 268.63 1220.78 1230.96 1236.06 1251.35 1256.45 1261.54 1266.64 1276.83 1281.93 1292.12 1312.51 1322.7 1327.8 1348.19 1363.48 1368.57 1383.86 1394.06 Ps = pressure losses in surface connection (psia) Pdp = pressure losses in the drill pipe (psia) Pdc = pressure losses in the drill collar (psia) 84 Padp = pressure losses across the annulus of the drill pipe (psia) Padc = pressure losses across the annulus of the drill collar (psia) Pd = parasitic pressure loss (psia) is the summation of the above losses. 6.1.2 Using mud sample 2 Mud Sample 2 has a viscosity of 34cP and a yield point of 12 ib/100ft2. Table 6.2 shows the pressure losses in the mud circulatory system when Mud Sample 2 was used in the design work with an assumed flow rate of 400 gpm. This result also shows that a larger percentage of the pressure loss in the drill pipe. However Mud Sample 2 has a higher parasitic pressure loss compare to Mud sample 1 which is due to the difference in viscosity and yield point. Table 6.2 shows all the frictional pressure losses observed when using this mud. Table 6.2 Frictional Pressures Losses in the Mud Circulatory System using Mud Sample 2 Depth(ft) Ps (psia) Pdp (psia) Pdc (psia) Padp (psia) Padc (psia) Pd (psia) 9600 31.19 789.1 56.14 558.35 310.66 1745.44 9700 31.19 798.27 56.14 564.84 310.66 1761.1 9750 31.19 802.86 56.14 568.08 310.66 1768.94 9900 31.19 816.63 56.14 577.82 310.66 1792.44 9950 31.19 821.21 56.14 581.07 310.66 1800.27 10000 31.19 825.8 56.14 584.31 310.66 1808.11 10050 31.19 830.39 56.14 587.56 310.66 1815.94 10150 31.19 839.56 56.14 594.05 310.66 1831.61 10200 31.19 844.15 56.14 597.3 310.66 1839.44 10300 31.19 853.33 56.14 603.79 310.66 1855.11 10500 31.19 871.68 56.14 616.78 310.66 1886.45 10600 31.19 880.86 56.14 623.27 310.66 1902.11 10650 31.19 885.44 56.14 626.52 310.66 1909.95 10850 31.19 903.79 56.14 639.5 310.66 1941.28 11000 31.19 917.56 56.14 649.24 310.66 1964.79 11050 31.19 922.14 56.14 652.48 310.66 1972.62 11200 31.19 935.91 56.14 662.22 310.66 1996.12 11300 31.19 945.08 56.14 668.71 310.66 2011.79 11500 31.19 963.43 56.14 681.7 310.66 2043.13 Ps = pressure losses in surface connection (psia) Pdp = pressure losses in the drill pipe (psia) Pdc = pressure losses in the drill collar (psia) Padp = pressure losses across the annulus of the drill pipe (psia) 85 Padc = pressure losses across the annulus of the drill collar (psia) Pd = parasitic pressure loss (psia) is the summation of the above losses. 6.1.3 Using mud sample 3 Mud Sample 3 has a viscosity of 15 cP and a yield point of 57 ib/100ft2. Table 6.3 shows the pressure losses in the mud circulatory system when Mud Sample 3 was used in the design work with an assumed flow rate of 400gpm. A larger percentage of the pressure loss was found to occur in the annulus of the drill pipe using this mud sample which is due to a high yield point of the mud. Table 6.3 shows all the frictional pressure losses observed when using this mud. Table 6.3 Frictional Pressures Losses in the Mud Circulatory System Using Mud Sample 3 Depth (ft) Ps (psia) Pdp (psia) Pdc (psia) Padp (psia) Padc (psia) Pd (psia) 9600 25.32 640.53 45.57 1020.96 271.71 2004.09 9700 25.32 647.98 45.57 1032.83 271.71 2023.41 9750 25.32 651.7 45.57 1038.77 271.71 2033.07 9900 25.32 662.87 45.57 1056.57 271.71 2062.05 9950 25.32 666.6 45.57 1062.51 271.71 2071.71 10000 25.32 670.32 45.57 1068.45 271.71 2081.37 10050 25.32 674.04 45.57 1074.38 271.71 2091.03 10150 25.32 681.49 45.57 1086.25 271.71 2110.35 10200 25.32 685.22 45.57 1092.19 271.71 2120.01 10300 25.32 692.66 45.57 1104.06 271.71 2139.32 10500 25.32 707.56 45.57 1127.8 271.71 2177.96 10600 25.32 715.01 45.57 1139.67 271.71 2197.28 10650 25.32 718.73 45.57 1145.61 271.71 2206.94 10850 25.32 733.62 45.57 1169.35 271.71 2245.58 11000 25.32 744.8 45.57 1187.16 271.71 2274.56 11050 25.32 748.52 45.57 1193.09 271.71 2284.22 11200 25.32 759.7 45.57 1210.91 271.71 2313.2 11300 25.32 767.14 45.57 1222.78 271.71 2332.52 11500 25.32 782.04 45.57 1246.52 271.71 2371.16 Ps = pressure losses in surface connection (psia) Pdp = pressure losses in the drill pipe (psia) Pdc = pressure losses in the drill collar (psia) Padp = pressure losses across the annulus of the drill pipe (psia) Padc = pressure losses across the annulus of the drill collar (psia) 86 Pd = parasitic pressure loss (psia) is the summation of the above losses. 6.2 Results for Pump Operating Conditions Based on the analysis from the three mud samples, mud sample 1 was selected for this design work, because it has the lowest parasitic pressure losses and it produces the least strain on the mud pump. To optimize the hydraulic power across the drill bit to the target depth of 11500 ft, in order to maintain an optimum parasitic pressure loss of 1454.55psia and an optimum pressure drop of 2545.55psia across the drill bit, mud pump must be operated at the drilling conditions given in Table 6.4. Table 6.4 Optimum Hydraulic Conditions for This Case Study Depth(ft) Qopt(gpm) Aopt(sq in) Dopt(in) HHPbopt(hp) 9600 439.54 0.364 0.393 652.76 9700 438.53 0.363 0.392 651.26 9750 438.53 0.363 0.393 651.26 9900 434.51 0.36 0.39 645.29 9950 433.51 0.36 0.39 643.8 10000 432.51 0.358 0.389 642.32 10050 431.52 0.358 0.389 640.85 10150 429.54 0.356 0.389 637.91 10200 428.55 0.355 0.388 636.44 10300 426.58 0.354 0.388 633.51 10500 421.69 0.349 0.385 626.25 10600 420.73 0.349 0.385 624.82 10650 419.75 0.348 0.384 623.37 10850 416.87 0.345 0.383 619.09 11000 413.99 0.343 0.382 614.81 11050 412.09 0.342 0.381 611.99 11200 410.21 0.34 0.38 609.2 11300 408.32 0.338 0.379 606.39 11500 403.65 0.335 0.377 599.46 Qopt = optimum flow rate (gpm) Aopt = optimum nozzle area (in2) Dopt = optimum nozzle diameter (in) HHPbopt= optimum hydraulic horsepower across the drill bit (hp) 87 CHAPTER 7: CONCLUSIONS AND RECOMMENDATION 7.1 Conclusions Drilling is the most capital intensive stage of hydrocarbon exploration projects and as such requires geological, technical and economic evaluations. The basis for optimization studies in this project work was geological data based on conductivity measurement in a potential hydrocarbon basin. In this project, a laboratory based approach was used for mud rheology determination for pressure loss computations. In the petroleum industry, optimization techniques are based on the maximum horse power criterion and the jet impact force criterion, however this project work considers the maximum bit horse power criterion. The following are the principal conclusions of this study. 1. The results for pore pressure and fracture pressure predictions obtained are in accordance with correlations used in the industry and in other published works. 2. The mud sample with a density of 12.5 ib/gal, a viscosity of 19 cP and a yield point of 5 ib/100ft2 gave the least parasitic pressure loss. 3. The optimum flow (403.65 gpm) rate required to operate the mud pump to the target depth lies within the minimum flow rate (378.35 gpm) and maximum flow rate (605.04 gpm) which is in accordance with industry standard for bottom hole cleaning. 7.2 Recommendation Pore pressure and fracture pressure prediction is the basis for well planning, hence it is not sufficient to make accurate prediction of pore pressure and fracture pressure using only conductivity data as carried out in this work. Hence, an integrated approach using other well logging data should be incorporated to deduce pore pressure and fracture pressure; this would help in understanding the uncertainty in each method. Also, the flow exponent should be obtained directly by operating the mud pump on a drilling rig instead of using a theoretical flow exponent as carried out in this study. 88 REFERENCES Archie, G. E. (1942). The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics. 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Standford: American Geological Institute. 91 APPENDIX Appendix A Depth (ft) C 7400 710 7500 780 7550 790 8300 710 8350 690 8400 680 8500 690 9200 600 9300 590 9550 570 9600 590 9700 610 9750 621 9900 700 9950 830 10000 950 10050 1100 10150 1200 10200 1240 10300 1310 10500 1250 10600 1350 10650 1370 10850 1500 11000 1280 11050 1400 11200 1650 11300 1840 11500 1920 R 0.00141 0.00128 0.00127 0.00141 0.00145 0.00147 0.00145 0.00167 0.00169 0.00175 0.00169 0.00164 0.00161 0.00143 0.0012 0.00105 0.00091 0.00083 0.00081 0.00076 0.0008 0.00074 0.00073 0.00067 0.00078 0.00071 0.00061 0.00054 0.00052 ln R PP FP MDPP DMDPP MDFP 6.56526 3441 13312.6 8.94231 9.44231 34.5962 6.65929 3487.5 13492.5 8.94231 9.44231 34.5962 6.67203 3510.75 13582.5 8.94231 9.44231 34.5962 6.56526 3859.5 14931.7 8.94231 9.44231 34.5962 6.53669 3882.75 15021.7 8.94231 9.44231 34.5962 6.52209 3906 15111.6 8.94231 9.44231 34.5962 6.53669 3952.5 15291.5 8.94231 9.44231 34.5962 6.39693 4278 16550.8 8.94231 9.44231 34.5962 6.38012 4324.5 16730.7 8.94231 9.44231 34.5962 6.34564 4440.75 17180.5 8.94231 9.44231 34.5962 6.38012 4464 17270.4 8.94231 9.44231 34.5962 6.41346 4510.5 17450.3 8.94231 9.44231 34.5962 6.43133 4533.75 17540.3 8.94231 9.44231 34.5962 6.55108 4603.5 17810.1 8.94231 9.44231 34.5962 6.72143 4975 18248.3 9.61538 10.1154 35.2692 6.85646 5100 18440 9.80769 10.3077 35.4615 7.00307 5326.5 18733.2 10.1923 10.6923 35.8462 7.09008 5379.5 18919.6 10.1923 10.6923 35.8462 7.12287 5508 19114.8 10.3846 10.8846 36.0385 7.17778 5562 19302.2 10.3846 10.8846 36.0385 7.1309 5775 19782 10.5769 11.0769 36.2308 7.20786 6042 20182.4 10.9615 11.4615 36.6154 7.22257 6070.5 20277.6 10.9615 11.4615 36.6154 7.31322 6184.5 20658.4 10.9615 11.4615 36.6154 7.15462 6270 20944 10.9615 11.4615 36.6154 7.24423 6409 21149.7 11.1538 11.6538 36.8077 7.40853 6608 21548.8 11.3462 11.8462 37 7.51752 6667 21741.2 11.3462 11.8462 37 7.56008 6785 22126 11.3462 11.8462 37 MDPP= Mud Density from Pore Pressure (psia) MDPF= Mud Density from Fracture Pressure (psia) DMDPP= Design Mud Density from Fracture Pressure (psia) R= Resistivity (Ω) C=Conductivity (1/Ω) PP = Pore Pressure (psia) FP =Fracture Pressure (psia) DMDFP 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.0962 34.7692 34.9615 35.3462 35.3462 35.5385 35.5385 35.7308 36.1154 36.1154 36.1154 36.1154 36.3077 36.5 36.5 36.5 92 Appendix B Depth (ft) MDPP 7400 8.942308 7500 8.942308 7550 8.942308 8300 8.942308 8350 8.942308 8400 8.942308 8500 8.942308 9200 8.942308 9300 8.942308 9550 8.942308 9600 8.942308 9700 8.942308 9750 8.942308 9900 8.942308 9950 9.615385 10000 9.807692 10050 10.19231 10150 10.19231 10200 10.38462 10300 10.38462 10500 10.57692 10600 10.96154 10650 10.96154 10850 10.96154 11000 10.96154 11050 11.15385 11200 11.34615 11300 11.34615 11500 11.34615 DMDPP 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 9.442308 10.11538 10.30769 10.69231 10.69231 10.88462 10.88462 11.07692 11.46154 11.46154 11.46154 11.46154 11.65385 11.84615 11.84615 11.84615 MDFP 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 34.59615 35.26923 35.46154 35.84615 35.84615 36.03846 36.03846 36.23077 36.61538 36.61538 36.61538 36.61538 36.80769 37 37 37 DMDFP 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.09615 34.76923 34.96154 35.34615 35.34615 35.53846 35.53846 35.73077 36.11538 36.11538 36.11538 36.11538 36.30769 36.5 36.5 36.5 SG-PP 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.073506 1.154308 1.177394 1.223566 1.223566 1.246653 1.246653 1.269739 1.315911 1.315911 1.315911 1.315911 1.338997 1.362083 1.362083 1.362083 DSG-PP 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.13353 1.214332 1.237418 1.28359 1.28359 1.306677 1.306677 1.329763 1.375935 1.375935 1.375935 1.375935 1.399021 1.422107 1.422107 1.422107 SG-FP 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.1532 4.234001 4.257087 4.30326 4.30326 4.326346 4.326346 4.349432 4.395604 4.395604 4.395604 4.395604 4.418691 4.441777 4.441777 4.441777 DSG-FP 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.093176 4.173977 4.197063 4.243236 4.243236 4.266322 4.266322 4.289408 4.33558 4.33558 4.33558 4.33558 4.358667 4.381753 4.381753 4.381753 MDPP= Mud Density from Pore Pressure (psia) MDPF= Mud Density from Fracture Pressure (psia) DMDPP= Design Mud Density from Fracture Pressure (psia) SG-PP= Specific gravity from Pore pressure DSG-PP=Design Specific gravity from Pore pressure SG-FP= Specific gravity from Fracture pressure DSG-FP=Design Specific gravity from Fracture pressure 93 Appendix C In this case study, the following data’s were used for (Azar and Samuel, 2007). Given the following well data: TARGET DEPTH (TM): 11500 ft Hole size to TD = 7 7/8 in DRILL PIPE OD = 5 ¼ in ID = 4 in Air weight = 26.66 ib/ft DRILL COLLAR Length = 1000 ft OD = 6 ½ in ID = 4.5 in MUD PROGRAM Bingham plastic model Mud density= 12.459 ppg PUMP Maximum allowed Operating Pressure = 4000psia Hydraulic Horsepower = 1765hp Volumetric Efficiency = 80% Drill bit 12 7/8 in tricon with 3-14 nozzles to 9600ft Minimum required annular fluid velocity: 120ft/min Surface Equipment: Equivalent to 340ft of drill pipe Field data: using the 8 7/8 tricone 3-14 Nozzle 94 Appendix D Using Mud Sample 1 D(ft) Ps(psia) Pdp(psia) Pdc(psia) 9600 26.976 682.33 48.54 9700 26.976 690.258 48.54 9750 26.976 694.225 48.54 9900 26.976 706.126 48.54 9950 26.976 710.093 48.54 10000 26.976 714.06 48.54 10050 26.976 718.027 48.54 10150 26.976 725.961 48.54 10200 26.976 729.928 48.54 10300 26.976 737.862 48.54 10500 26.976 753.73 48.54 10600 26.976 761.664 48.54 10650 26.976 765.631 48.54 10850 26.976 781.499 48.54 11000 26.976 793.4 48.54 11050 26.976 797.367 48.54 11200 26.976 809.268 48.54 11300 26.976 817.202 48.54 11500 26.976 833.07 48.54 Padp(psia) Padc(psia) Pd(psia) LOG Pd Q (gpm) LOG Q 194.3 268.63 1220.78 3.0866 400 196.5591 268.63 1230.96 3.0902 400 197.6888 268.63 1236.06 3.092 400 201.0777 268.63 1251.35 3.0974 400 202.2074 268.63 1256.45 3.0991 400 203.337 268.63 1261.54 3.1009 400 204.4667 268.63 1266.64 3.1027 400 206.726 268.63 1276.83 3.1061 400 207.8556 268.63 1281.93 3.1079 400 210.1149 268.63 1292.12 3.1113 400 214.6335 268.63 1312.51 3.1181 400 216.8928 268.63 1322.7 3.1215 400 218.0225 268.63 1327.8 3.1231 400 222.5411 268.63 1348.19 3.1297 400 225.93 268.63 1363.48 3.1346 400 227.0597 268.63 1368.57 3.1363 400 230.4486 268.63 1383.86 3.1411 400 232.7079 268.63 1394.06 3.1443 400 237.2265 268.63 1414.44 3.1506 400 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 Ps loss = Surface connection pressure loss (psia) Pdopt =Optimium parasitic loss =1454.55 psia Pdp loss =Drill Pipe pressure loss Pbopt =Optimum drill bit pressure =2545.45psia Pdc loss =Drill Collar Pressure loss (psia) Padp loss = Annulus of the Drill Pipe pressure loss (psia) Qmin =Mimimum flow rate =378.35gpm Padc loss = Annulus of the Drill Collar pressure loss (psia) Qmax =Maximum flow rate= 605.04gpm Pd Loss = Parasitic Pressure loss (psia) Viscosity = 19CP Q= Assumed Flow Rate (gpm) Yield Point = 5 D =Depth (ft) P max= Maximum pump pressure =4000psia LOG Qmin = 2.576 LOG Qmax = 2.782 LOG Pdopt = 3.163 LOG Pmax = 3.6 95 Appendix E Hottman and Johnson relationship between formation pore pressure gradient with shale resistivity ratio (Bourgoyne, 1991). Plot of formation pore pressure gradient with shale resistivity ratio (Bourgoyne, 1991) 96 Appendix F Depth(ft) Log Qopt Qopt(gpm) 2.643 439.54 2.642 438.53 2.642 438.53 2.638 434.51 2.637 433.51 2.636 432.51 2.635 431.52 2.633 429.54 2.632 428.55 2.63 426.58 2.625 421.69 2.624 420.73 2.623 419.75 2.62 416.87 2.617 413.99 2.615 412.09 2.613 410.21 2.611 408.32 2.606 403.65 Qopt = Optimum flow rate obtained by taking the antilog Log Qopt= obtained from the hydrualic plot 9600 9700 9750 9900 9950 10000 10050 10150 10200 10300 10500 10600 10650 10850 11000 11050 11200 11300 11500 97 Appendix G Mud Sample 2 Depth(ft) Ps loss(psia) Pdp loss (psia) Pdc loss (psia) Padp loss (psia) Padc loss (psia) Pd loss(psia) 9600 31.19 789.1 56.14 558.35 310.66 1745.44 9700 31.19 798.28 56.14 564.84 310.66 1761.1 9750 31.19 802.86 56.14 568.08 310.66 1768.94 9900 31.19 816.63 56.14 577.82 310.66 1792.44 9950 31.19 821.21 56.14 581.07 310.66 1800.27 10000 31.19 825.8 56.14 584.31 310.66 1808.11 10050 31.19 830.39 56.14 587.56 310.66 1815.94 10150 31.19 839.56 56.14 594.05 310.66 1831.61 10200 31.19 844.15 56.14 597.3 310.66 1839.44 10300 31.19 853.33 56.14 603.79 310.66 1855.11 10500 31.19 871.68 56.14 616.78 310.66 1886.44 10600 31.19 880.85 56.14 623.27 310.66 1902.12 10650 31.19 885.44 56.14 626.52 310.66 1909.95 10850 31.19 903.79 56.14 639.5 310.66 1941.29 11000 31.19 917.56 56.14 649.24 310.66 1964.79 11050 31.19 922.15 56.14 652.49 310.66 1972.62 11200 31.19 935.91 56.14 662.22 310.66 1996.12 11300 31.19 945.08 56.14 668.72 310.66 2011.79 11500 31.19 963.43 56.14 681.7 310.66 2043.13 Ps loss = Surface connection pressure loss (psia) Pdp loss =Drill Pipe pressure loss Pdc loss =Drill Collar Pressure loss (psia) Padp loss = Annulus of the Drill Pipe pressure loss (psia) Padc loss = Annulus of the Drill Collar pressure loss (psia) Pd Loss = Parasitic Pressure loss (psia) 98 Appendix H Mud Sample 3 Depth(ft) Ps loss(psia) Pdp loss (psia) Pdc loss (psia) Padp loss (psia) Padc loss (psia) Pd loss(psia) 9600 25.32 640.53 45.57 1020.96 271.71 2004.09 9700 25.32 647.98 45.57 1032.83 271.71 2023.4 9750 25.32 651.7 45.57 1038.77 271.71 2033.07 9900 25.32 662.87 45.57 1056.57 271.71 2062.05 9950 25.32 666.6 45.57 1062.52 271.71 2071.71 10000 25.32 670.32 45.57 1068.45 271.71 2081.37 10050 25.32 674.04 45.57 1074.38 271.71 2091.03 10150 25.32 681.49 45.57 1086.25 271.71 2110.35 10200 25.32 685.22 45.57 1092.19 271.71 2120.01 10300 25.32 692.66 45.57 1104.06 271.71 2139.33 10500 25.32 707.56 45.57 1127.8 271.71 2177.97 10600 25.32 715.01 45.57 1139.68 271.71 2197.28 10650 25.32 718.73 45.57 1145.61 271.71 2206.94 10850 25.32 733.63 45.57 1169.35 271.71 2245.58 11000 25.32 744.8 45.57 1187.16 271.71 2274.56 11050 25.32 748.52 45.57 1193.1 271.71 2284.22 11200 25.32 759.7 45.57 1210.91 271.71 2313.2 11300 25.32 767.14 45.57 1222.78 271.71 2332.52 11500 25.32 782.04 45.57 1246.52 271.71 2371.16 Ps loss = Surface connection pressure loss (psia) Pdp loss =Drill Pipe pressure loss Pdc loss =Drill Collar Pressure loss (psia) Padp loss = Annulus of the Drill Pipe pressure loss (psia) Padc loss = Annulus of the Drill Collar pressure loss (psia) Pd Loss = Parasitic Pressure loss (psia) 99 Appendix I Calculating the Pore Pressure in the Over-Pressure Zone Over pressure at 9600 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=6.34 Rn=6.34 R0 Rn 6.34 1 6.34 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P D 0.465 psi / ft Hence Pore pressure = 4464 psia Over pressure at 9700 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=6.42 Rn=6.32 R0 Rn 6.42 6.32 1.01 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.465 psi / D ft 100 Hence Pore pressure = 4510.5 psia Over pressure at 9750 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=6.44 Rn=6.3 R0 Rn 6.44 1.02 6.3 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P D 0.465 psi / ft Hence Pore pressure = 4533.75psia Over pressure at 9900 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=6.56 Rn=6.28 R0 Rn 6.56 1.04 6.28 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.465 psi / D ft 101 Hence Pore pressure = 4603.5psia Over pressure at 9950 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=6.72 Rn=6.27 R0 Rn 6.72 6.27 1.07 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.5 psi / D ft Hence Pore pressure = 4975 psia Over pressure at 10000 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=6.86 Rn=6.26 R0 Rn 6.86 1.09 6.26 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.51 psi / D ft 102 Hence Pore pressure = 5100psia Over pressure at 10050ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7 Rn=6.25 R0 Rn 7 1.12 6.25 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.53 psi / D ft Hence Pore pressure = 5326.5psia Over pressure at 10150ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.08 Rn=6.24 R0 Rn 7.08 1.13 6.24 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.53 psi / ft D Hence Pore pressure = 5379.5 psia 103 Over pressure at 10200 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.12 Rn=6.22 R0 Rn 7.12 1.14 6.22 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.54 psi / D ft Hence Pore pressure = 5508 psia Over pressure at 10300 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.18 Rn=6.21 R0 Rn 7.18 1.16 6.21 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship chart Pore pressure gradient P 0.55 psi / D ft Hence Pore pressure = 5562 psia 104 Over pressure at 10500 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.13 Rn=6.21 R0 Rn 7.13 1.15 6.21 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.55 psi / D ft Hence Pore pressure = 5775 psia Over pressure at 10600 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.2 Rn=6.16 R0 Rn 7.2 6.16 1.17 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.57 psi / D ft Hence Pore pressure = 6042 psia Over pressure at 10650 ft 105 From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.22 Rn=6.14 R0 Rn 7.22 1.18 6.14 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.57 psi / D ft Hence Pore pressure = 6070.5 psia Over pressure at 10850 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0 = 7.31 Rn = 6.2 R0 Rn 7.31 1.18 6.2 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.57 psi / ft D Hence Pore pressure = 6184.5 psia Over pressure at 11000 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.16 Rn=6.08 106 R0 Rn 7.16 1.18 6.08 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.57 psi / D ft Hence Pore pressure = 6270 psia Over pressure at 11050 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.24 Rn=6.07 R0 Rn 7.24 1.19 6.07 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P D 0.58 psi / ft Hence Pore pressure = 6409 psia Over pressure at 11200 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.41 Rn=6.04 R0 Rn 7.41 1.23 6.04 107 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P 0.59 psi / ft D Hence Pore pressure = 6608 psia Over pressure at 11300 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0 =7.52 Rn = 6.03 R0 Rn 7.52 1.25 6.03 From Hottman and Johnson Pore pressure gradient and shale resistivity relationship Pore pressure gradient P D 0.59 psi / ft Hence Pore pressure = 6667 psia Over pressure at 11500 ft From Figure 5.1 the normal shale resistivity and observed shale resistivity is given below R0=7.56 Rn=6 R0 Rn 7.56 1.26 6 Pore pressure gradient P D 0.59 psi / ft Hence Pore pressure = 6785 psia APPENDIX J Calculating the Fracture Pressure in the Over Pressured Zone Fracture pressure at the normal pressure zone which lies from 9600ft to11500 is obtained using the Hubbert and Willis equation. 108 Pf 2 h PP Recall that 1 2 h o v 1 Where pore pressure at 9600 ft is given as 0.465 psia/ft PP PP *D D PP= 0.465*9600= 4464 psia Also ov G * D ov =1*9600=9600 psia 1 2(0.25) = 6403.2 psia h 1 (0.25) 9600 Hence Pf = 2(6403.2) +4464 = 17270.4 psia Therefore the Fracture pressure at a depth of 9600 ft = 17270.4 psia Fracture pressure at 9700 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 9700 ft = 4510.5 psia 109 Also ov G * D ov =1*9700=9700 psia 1 2(0.25) h 1 (0.25) 9700 6469.9 psia Hence Pf = 2(6469.9) +4510.5= 17450.3 psia Therefore the Fracture pressure at a depth of 9700 ft = 17450.3 psia Fracture pressure at 9750 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 9750 ft =4533.75 psia Also ov G * D ov =1*9750=9750 psia 1 2(0.25) h 1 (0.25) 9750 6503.25 Hence Pf = 2(6503.25) +4533.75 = 17540.25 psia Therefore the Fracture pressure at a depth of 9750 ft = 17540.25 psia 110 Fracture pressure at 9900ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 9900ft =4603.5psia Also ov G * D ov =1*9900=9900psia 1 2(0.25) h 1 (0.25) 9900 6603.3 psia Hence Pf = 2(6603.3) +4603.5= 17810.1psia Therefore the Fracture pressure at a depth of 9900ft = 17810.1psia Fracture pressure at 9950 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 9950 ft =4975 psia Also 111 ov G * D ov =1*9950=9950psia 1 2(0.25) h 1 (0.25) 9950 6636.65 psia Hence Pf = 2(6636.65) +4975= 18248.3 psia Therefore the Fracture pressure at a depth of 9950 ft = 18248.3 psia Fracture pressure at 10000 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 10000 ft =5100 psia Also ov G * D ov =1*10000=10000 psia 1 2(0.25) h 1 (0.25) 10000 6670 psia Hence Pf = 2(6670) +5100= 18540 psia Therefore the Fracture pressure at a depth of 10000 ft = 18440 psia Fracture pressure at 10050 ft 112 Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 10050 ft =5326.5 psia Also ov G * D ov =1*11000=10050 psia 1 2(0.25) h 1 (0.25) 10050 6703.35 psia Hence Pf = 2(6703.35) +5326.5= 18733.2 psia Therefore the Fracture pressure at a depth of 10050 ft = 18733.2 psia Fracture pressure at 10150 ft Pf 2 h PP Recall that 1 2 o v 1 h Where Pore pressure at 10150 ft =5379.5 psia Also ov G * D ov =1*10150=10150 psia 113 1 2(0.25) 10150 6770.05 psia 1 (0.25) h Hence Pf = 2(6770.05) +5379.5= 18919.6 psia Therefore the Fracture pressure at a depth of 10150 ft = 18919.6psia Fracture pressure at 10200 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 10200 ft =5508 psia Also ov G * D ov =1*10200=10200 psia 1 2(0.25) 10200 6803.4 psia h 1 (0.25) Hence Pf = 2(6803.4) +5508= 19114.8 psia Therefore the Fracture pressure at a depth of 10200 ft = 19114.8 psia Fracture pressure at 10300ft Pf 2 h PP 114 Recall that 1 2 h o v 1 Where Pore pressure at 10300 ft =5562 psia Also ov G * D ov =1*10300=10300psia 1 2(0.25) h 1 (0.25) 10300 6870.1 psia Hence Pf = 2(6870.1) +5562= 19302.2 psia Therefore the Fracture pressure at a depth of 10300 ft = 19302.2 psia Fracture pressure at 10500 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 10500ft =5775psia Also ov G * D ov =1*10500=10500psia 115 1 2(0.25) h 10500 7003.5 psia 1 (0.25) Hence Pf = 2(7005.5) +5775= 1978.2 psia Therefore the Fracture pressure at a depth of 10500 ft = 1978.2 psia Fracture pressure at 10600 ft Pf 2 h PP Recall that 1 2 o v 1 h Where Pore pressure at 10600 ft =6042 psia Also ov G * D ov =1*10600=10600 psia 1 2(0.25) h 1 (0.25) 10600 = 7070.2 psia Hence Pf = 2(7070.2) +6042=20182.4 Therefore the Fracture pressure at a depth of 10600 ft = 20182.4 psia Fracture pressure at 10650 ft Pf 2 h PP 116 Recall that 1 2 h o v 1 Where Pore pressure at 10650 ft =6070.5 psia Also ov G * D ov =1*10650=10650 psia 1 2(0.25) h 1 (0.25) 10650 7103.55 psia Hence Pf = 2(7103.55) +6070.5= 20277.6 psia Therefore the Fracture pressure at a depth of 10650 ft = 20277.6 psia Fracture pressure at 10850ft Pf 2 h PP Recall that 1 2 1 h ov Where Pore pressure at 10850 ft =6184.5 psia Also ov G * D ov =1*10850=10850psia 117 1 2(0.25) 10850 7236.95 psia h 1 (0.25) Hence Pf = 2(7236.95) +6184.5= 20658.4 psia Therefore the Fracture pressure at a depth of 12100 ft = 20658.4 psia Fracture pressure at 11000 ft Pf 2 h PP Recall that 1 2 ov 1 h Where Pore pressure at 11000ft =6270 psia Also ov G * D ov =1*11000=11000 psia 1 2(0.25) h 1 (0.25) 11000 = 7337 psia Hence Pf = 2(7337) +6270= 20944 psia Therefore the Fracture pressure at a depth of 11000 ft = 20944 psia Fracture pressure at 11050 ft 118 Pf 2 h PP Recall that 1 2 ov 1 h Where Pore pressure at 11050 ft =6409 psia Also ov G * D ov =1*11050=11050 psia 1 2(0.25) h 1 (0.25) 11050 = 7370.35 psia Hence Pf = 2(7370.35) +6409= 21149.7 psia Therefore the Fracture pressure at a depth of 11050 ft = 21149.7 psia Fracture pressure at 11200 ft Pf 2 h PP Recall that 1 2 ov 1 h Where Pore pressure at 11200 ft =6608 psia Also ov G * D 119 ov =1*11200=11200 psia 1 2(0.25) = 7470.4 psia h 1 (0.25) 11200 Hence Pf = 2(7470.4) +6608= 21548.8 psia Therefore the Fracture pressure at a depth of 11200 ft = 21548.8 psia Fracture pressure at 11300 ft Pf 2 h PP Recall that 1 2 h o v 1 Where Pore pressure at 11300 ft =6667 psia Also ov G * D ov =1*11300=11300psia 1 2(0.25) h 1 (0.25) 11300 = 7537.1 psia Hence Pf = 2(7537.1) +6667= 21741.2 psia Therefore the Fracture pressure at a depth of 11300 ft = 21741.2 psia Fracture pressure at 11500 ft 120 Pf 2 h PP Recall that 1 2 ov 1 h Where Pore pressure at 11500 ft =6785 psia Also ov G * D ov =1*11500=11500 psia 1 2(0.25) h 11500 7670.5 psia 1 (0.25) Hence Pf = 2(7670.5) +6785= 22126 psia Therefore the Fracture pressure at a depth of 13300 ft = 22126 psia 121