SURFACE CASING DESIGN OF AN OIL WELL

By
MANISH PANT (R270307017)
SANDEEP BAHUGUNA (R270307032)

College of Engineering studies
University of Petroleum & Energy Studies
Dehradun
May, 2011

Surface casing design of an oil well
A thesis submitted in partial fulfilment of the requirements for the degree of
Bachelor of Technology
(Applied Petroleum Engineering, upstream)

Under the Guidance of
………………
Mr. Arun Chandel
(Mentor)
Approved

………….....
Dean
College of Engineering
University of Petroleum & Energy Studies
Dehradun
May, 2011
CERTIFICATE

This is to certify that Manish pant and Sandeep Bahuguna, students of B.Tech (APE)+ MBA(UAM) has written their thesis on “surface casing design for an oil Well” under my supervision and have successfully completed the project within stipulated time.
They have demonstrated high performance levels and dedication during the completion of their thesis.

……………
Mr. Arun Chandel (Mentor)

Acknowledgement

We would like to express our deepest gratitude to Dr. Shri Hari, Dean,
COES, UPES for allowing us to perform the project work. We have received maximum co-operation and help from UPES faculty members. We would also like to express our sincere thanks to Mr. Sabyasachi Maiti, Course Coordinator, B.Tech (APE Upstream+ MBA (UAM)), for giving his full support during our project work.
Lastly, we would like to thank our mentor, Mr. Arun Chandel for their kind attention and support and the valuable time they gave which lead to the accomplishment of this project.

UPES, Dehradun
ABSTRACT

Casing must be designed to resist various physical and chemical loads for the entire life cycle of the well. It is convenient to divide the life cycle into two separate phases; drilling and production because in general the loads encountered in these two phases are different to each other.

During the first phase, casing must ensure that * Wellhead and bop loads are supported without failure * Formation fluid do not migrate within the well or to the surface * Formation which are mutually exclusive are separated from each other in different hole section * Directional work is consolidated while drilling deeper * Drill bits, completion accessories and other tools can be run inside as required at various phases of the well

During second phase, casing must ensure that * Producing fluid are contained, even if the completion tubing string or downhole packers leak * Formation fluids do not migrate within the well or to the surface * Fluid do not corrode the casing to the point where the performance of casing is impaired * Cements do not degrade unduly overtime, either due to chemical reaction with formation fluid or by thermal degradation

Surface casing

This is normally the first pipe that can take a blowout preventer on top. The shoe must be set deep enough so that the formation fracture pressure is high enough for the well to be closed in on a kick while drilling for the casing string. Any gas encountered before a BOP can be nippled up is termed “shallow gas”.
As surface casing in some development area is set quite deep (sometime deeper than 3000 ft), shallow gas can be encountered fairly deep.
During the well life surface casing may be subject to be burst pressure from well kick, bad cement jobs, or to collapse pressure if the fluid level inside drops due to losses or if the bad cement jobs allow migration of gas outside the casing.
Surface casing is normal cemented to the surface or to the mud line.

Data Required for Design

A key component in developing the casing design for a well is the geo-technical document. This should ideally be completed before a well plan and casing design are generated and contain the following information:

* Type of well * Well location – onshore, water depth (if offshore), objective depths etc. * Geological information – formation tops, faults, structure maps etc. * Pore pressure, fracture pressure and temperature profile * Directional well plan * Offset well data – casing schemes, geological tie-in, operational problems, mud weights etc. * Hazards - shallow gas, faults etc. * Evaluation requirements * Hydrocarbon composition – gas or oil, corrosion considerations * Anticipated producing life of well and future well intervention * Tubing and downhole completion component sizes * Annulus communication, bleed off and monitoring policies, particularly for development wells * Constraints – licence block/lease line restrictions

Also to be considered in the design are any constraints due to rig capabilities, casing stocks, import restrictions etc.
Casing design methodology

There is a logical process for carrying out casing design for a well. The five steps of this basic process are * Step 1: data collection- certain information is required for the engineer to properly design casing for the life cycle of the well. During the life cycle, the well may undergo changes of use for instance a producing well being used as an injector or abandoning a lower zone and recompleting on a higher zone. Information is therefore required on all the different uses that the well will or may experience during the life cycle. * Step 2: preliminary design- defines the casing setting depth OD’s and the fluid densities for each hole section. * Step 3: detailed design- examine loads that the casing are subjected to and allow the casing weights, grades and connections to be defined * Step 4: triaxial analysis- is used to examine casing design and it’s examine all loads that act together on the casing. The result of these combined loads is compared to API minimum yield stress of the casing. It may identify cases where the design is inadequate when combine loads are considered, or where it is overdesigned and cheaper casing can be used. The calculation is done with a computer program stresscheck or TDAS. * Step 5: documentation of decisions- all decisions that are taken or all assumption that are made during the design process must be documented.

LIST OF FIGURES

S. NO. | FIGURE TITLE | PAGE NO. | 1 | The typical casing program | 16 | 2 | Burst design | 18 | 3 | Collapse criterion | 19 | 4 | Design factors for casing failure criteria | 24 | 5 | Casing setting depths bottom-up design | 51 | 6 | Casing setting depths top-down design | 52 | 7 | Collapse selection for casing (a) | 56 | 8 | Collapse selection for casing (b) | 56 | 9 | Casing selection on burst load | 57 | 10 | Casing selection on tensile load | 59 | 11 | Collapse selection for biaxial design | 61 |

LIST OF TABLES

S. NO. | TABLE TITLE | PAGE NO. | 1. | API steel grades | 64 | 2. | Non-API steel grades | 65 | 3. | Yield collapse pressure formula range | 66 | 4. | Formula factor and D/t range for plastic collapse | 67 | 5. | Formula factor and D/t range for transition collapse | 68 | 6. | D/t range for elastic collapse | 69 | 7. | Tensile property requirements | 70 | 8. | Buckling forces | 70 | *

CONTENTS
INTRODUCTION 14

LITERATURE REVIEW

1. INTRODUCTION TO CASING DESIGN 15

2.1 CASING STRINGS 2.2.1 CONDUCTOR CASING 2.2.2 SURFACE CASING 2.2.3 INTERMEDIATE CASING 2.2.4 PRODUCTION CASING 2.2.5 LINER 2.2.6 TIE BACK STRING

2.2 MECHANICAL PROPERTIES OF CASING 17 2.3.7 BURST STRENGTH 2.3.8 COLLAPSE STRENGTH 2.3.9.1 YIELD STRENGTH COLLAPSE 2.3.9.2 PLASTIC COLLAPSE 2.3.9.3 TRANSITION COLLAPSE 2.3.9.4 ELASTIC COLLAPSE 2.3.9.5 EQUIVALENT INTERNAL PRESSURE 2.3.9 AXIAL STRENGTH 21 2.3.10 COMBINED STRESS EFFECTS 2.3.11 COMBINED COLLAPSE AND TENSION 2.3.12 COMBINED BURST AND COMPRESSION LOADING 2.3.13 COMBINED BURST AND TENSION LOADING 2.3.14 USE OF TRIAXIAL CRITERION FOR COLLAPSE LOADING 2.3.15 FINAL TRIAXIAL STRESS CONSIDERATIONS

2. API CONNECTION RATING 28

3.3 COUPLING INTERNAL YIELD PRESSURE 3.4 ROUND-THREAD CASING-JOINT STRENGTH 3.5 BUTTRESS CASING-JOINT STRENGTH 3.6 EXTREME-LINE CASING-JOINT STRENGTH 3.7 PROPRIETARY CONNECTIONS 3.8 CONNECTION FAILURES 3.9 CONNECTION DESIGN LIMITS

3. LOADS ON CASING 34

4.10 EXTERNAL PRESSURE LOADS 4.11 INTERNAL PRESSURE LOADS 36 4.12.16 BURST 4.12.17 COLLAPSE 4.12.18 BURST 4.12.19 COLLAPSE ABOVE PACKER 4.12.20 COLLAPSE BELOW PACKER 4.12.21 COLLAPSE 4.12 MECHANICAL LOADS 40 4.13.22 CHANGES IN AXIAL LOAD 4.13.23 AXIAL 4.13.24 AIR WEIGHT OF CASING ONLY 4.13.25 BUOYED WEIGHT PLUS OVERPULL ONLY 4.13.26 SHOCK LOADS 4.13.27 SERVICE LOADS 4.13.28 BENDING LOADS 4.13 THERMAL LOAD AND TEMPERATURE EFFECTS 44

4. CASING DESIGN 46

5.14 DESIGN OBJECTIVES 5.15 DESIGN METHODS 5.16.29 PRELIMINARY DESIGN 5.16.30 DETAILED DESIGN 5.16 REQUIRED INFORMATION 47 5.17 PRELIMINARY DESIGN 5.18.31 MUD PROGRAM 5.18.32 HOLE AND PIPE DIAMETER 5.18.33 CASING SHOE DEPTH AND NO OF STRINGS 5.18.34 BOTTOM-UP DESIGN 5.18.35 TOP-DOWN DESIGN 5.18.36 HOLE STABILITY 5.18.37 DIFFERENTIAL STICKING 5.18.38 ZONAL ISOLATION 5.18.39 DIRECTIONAL DRILLING CONCERNS 5.18.40 UNCERTAINITY IN PREDICTED FORMATION PROPERTIES 5.18.41 DIRECTIONAL PLAN 5.18 DETAILED DESIGN 52 5.19.42 LOAD CASES 5.19.43 DESIGN FACTORS 5.19.44 OTHER CONSIDERATIONS

5. CASE STUDY 54 6.19 CASING DESIGN CALCULATION 6.20 BURST DESIGN CALCULATION 6.21 TENSILE LOAD DESIGN CALCULATION 6.22 BIAXIAL DESIGN CALCULATION 6.23 CONCLUSION

6. REFERENCES 63

7. APPENDIX 64

INTRODUCTION
AIM:

The aim of the project is to determine the various design loads on the given surface casing strings and select the most appropriate surface casing for the given well.

SCOPE OF THE PROJECT:

The project includes the various data which are required to determine during the design of surface casing. It also includes the various API and Non-API grades of casing used in drilling.
The project does not consider the surface casing design for high temperature and high pressure well. It does not contain the other casing string design i.e. conductor, intermediate and production.

LIMITATIONS:

The limitation of this project are the complete analysis of surface casing design in terms of burst, collapse, tensile loads and axial loads.

LITERATURE REVIEW
1. INTRODUCTION TO CASING DESIGN
Casing is the main part of the well construction. All wells drilled for the purpose of oil and gas production are cased with material with desired strength. Casing is the main structural part of a well. Casing is used to maintain borehole stability, prevent contamination of water sands, isolate water from producing formations, and control well pressures during drilling, production, and workover operations. Casing provides locations for the installation of blowout preventers, wellhead equipment, production packers, and production tubing. The cost of casing is a major part of the overall well cost, so selection of casing size, grade, connectors, and setting depth is a primary engineering and economic consideration.
1.1 Casing Strings: - There are basically six types of casing string:-
1.1.1 Conductor Casing: - It is the first string set below the structural casing. It separates unconsolidated formations and water sands and protects against shallow gas. Usually casing head is installed on to this string. A BOP is installed on this string. In offshore wells this string is cemented to the surface or to the mudline.
1.1.2 Surface Casing: - It is set to provide blowout protection, isolate water sands, and prevent lost circulation. It frequently provides sufficient shoe strength to drill into high-pressure transition zones. In deviated wells, the surface casing may cover the build section to prevent keyseating of the formation during deeper drilling. In offshore well this string is cemented to the surface or the mudline.
1.1.3 Intermediate Casing: - It is set to isolate unstable hole sections, lost-circulation zones, low-pressure zones, and production zones. It is frequently set in the transition zone from normal to abnormal pressure. The casing cement top must isolate any hydrocarbon zones. Some wells require multiple intermediate strings. Some intermediate strings may also be production strings if a liner is run beneath them.
Fig.1 the typical casing program
1.1.4 Production Casing: - This kind of casing is used to isolate production zones and contain formation pressure in caused due to tubing leak and contain. It may also be exposed to injection pressure from fracture jobs, downcasing or gas lift. A good Primary cement job is very critical for this string.

1.1.5 Liner: - This kind of Casing String that does not extend back to the wellhead but is hung from another casing string. They are used to reduce cost improve hydraulic performance while drilling deeper allow the use of larger tubing above the liner top and not represent tension limitation to the rig. Liners are either intermediate or production casings or are cemented throughout their length.

1.1.6 Tieback string: - It provides additional pressure integrity from the liner top to the wellhead. An intermediate tieback isolates a casing string that cannot withstand possible pressure loads if drilling is continued because of excessive wear or higher pressures. Similarly, a production tieback isolates an intermediate string from production loads. Tiebacks can be partially cemented or even uncemented.

1.2 Mechanical Properties of casing
1.2.1 Burst Strength: - If internal pressure is higher than the external pressure exerted on the casing it is exposed to burst pressure. Burst pressure conditions occur during well control operations, integrity tests and squeeze cementing. The burst strength of the pipe body is determined by the internal yield pressure formula
PB = 0.875 [2Yp t/ D] ……………………………………………………………………… (1.1)
Where, PB = minimum burst pressure (psi)
Yp = minimum yield strength (psi) t = nominal wall thickness (in)
And D = nominal outside pipe diameter (in)
This equation is the Barlow equation and is used to calculate the internal pressure at which the tangential stress at the inner wall of the pipe reaches the yield strength (YS) of the material.

FIG.2 BURST DESIGN

1.2.2 Collapse Strength: - Collapse happens when external pressure exceeds internal pressure. Such conditions may exist during cementing operations or well evacuation. Collapse strength is a function of the material’s yield strength and its slenderness ratio D/t.

FIG.3 COLLAPSE CRITERION
1.2.2.1 Yield Strength Collapse: - Yield strength collapse is based on yield at the inner wall using the Lamé thick wall elastic solution. This criterion does not represent a collapse pressure at all. For thick wall pipes (D/t < 15±) the tangential stress exceeds the yield strength of the material before a collapse instability failure occurs.
PY p = 2Yp [{(D / t) – 1}/ (D / t) 2]............................................................................................. (1.2)
Nominal dimensions are used in the collapse equations.
1.2.2.2 Plastic Collapse: - Plastic collapse is based on empirical data from 2,488 tests of K-55, N-80, and P-110 seamless casing. No analytic expression has been origined that accurately models collapse behaviour in this range. The minimum collapse pressure for the plastic range of collapse is calculated by equation
P p = Yp [{A/ (D / t)} – B] – C................................................................................................ (1.3)
1.2.2.3 Transition Collapse: - Transition collapse is obtained by a numerical curve fit between the plastic and elastic regimes. The minimum collapse pressure for the plastic-to-elastic transition zone PT is calculated with Equation
PT = Yp [{F/(D / t)} – G]......................................................................................................... (1.4)

1.2.2.4 Elastic Collapse: - Elastic Collapse is based on theoretical elastic instability failure this criterion is independent of yield strength and applicable to thin-wall pipe (D/t > 25±). The minimum collapse pressure for the elastic range of collapse is calculated with Equation
PE = (46.95 × 106) / [(D / t) {(D / t) – 1} 2]............................................................................. (1.5)
The applicable D/t range for elastic collapse is shown in Table.

1.2.2.5 Equivalent Internal Pressure: - If the pipe is subjected to both external and internal pressures, the equivalent external pressure is calculated as pe = po – [1 – 2/(D / t)]pi = Δ p + { 2/ (D / t )}pi ...................................................................... (1.6)
Where pe = equivalent external pressure, po = external pressure, pi = internal pressure,
And
Δp = po – pi.

Equation 1.6 can be written as peD = poD − pid, ....................................................................................................................... (1.7)
Where D = nominal outside diameter,
And d = nominal inside diameter.
In equation 1.7 we can see the internal pressure applied to the internal diameter and the external pressure applied to the external diameter. The equivalent pressure applied to the external diameter is the difference of these two terms.

1.2.3 Axial Strength: - The axial strength of the pipe body is determined by the pipe body yield strength formula.
Fy = π/4 (D2 − d2) Yp……….................................................................................................... (1.8)
Where
Fy = pipe body axial strength (units of force),
Yp = minimum yield strength,
D = nominal outer diameter,
And d = nominal inner diameter.
Axial strength is the product of the cross-sectional area and the yield strength.
1.2.4 Combined Stress Effects: - All the pipe-strength equations previously given are based on a uniaxial stress state (i.e. a state in which only one of the three principal stresses is nonzero). This idealized situation never occurs in oilfield applications because pipe in a wellbore is always subjected to combined loading conditions. The fundamental basis of casing design is that if stresses in the pipe wall exceed the yield strength of the material a failure condition exists.
Therefore the yield strength is a measure of the maximum allowable stress. To evaluate the pipe strength under combined loading conditions the uniaxial yield strength is compared to the yielding condition. The triaxial safety factor is the ratio of the material’s yield strength to the triaxial stress.
The yielding criterion is stated as σV M E = (1/√2) √{(σz − σθ)2 + (σθ − σr)2 + (σr − σz)2 }≥ Yp........................................................(1.9) where Yp = minimum yield stress (psi), σVME = triaxial stress(psi), σz = axial stress (psi), σθ = tangential or hoop stress (psi),
And σr = radial stress (psi).

The calculated axial stress, σz, at any point along the cross-sectional area should include the effects of self-weight, buoyancy, pressure loads, bending, shock loads, frictional drag, point loads, temperature loads, and buckling loads. Except for bending/buckling loads, axial loads are normally considered to be constant over the entire cross-sectional area.
The tangential and radial stresses are calculated with the Lamé equations for thick-wall cylinders. σθ =[{ (1 + ro2 / r2)/ (ro 2 − ri 2 )} ri 2 pi ]−[{ (1 + ri 2 / r2) (ro 2 − ri2)} ro2po.]............................ (1.10)
And
σr = [{(1 – ro 2 / r2)/ (ro 2 − ri2)} ri 2 pi ]– [{(1 − ri 2 / r2)/ (ro2 − ri2)} ro2 po]...............................(1.11)
Where pi = internal pressure, po = external pressure, ri = inner wall radius, ro = outer wall radius, and r = radius at which the stress occurs.
The absolute value of σθ is always greatest at the inner wall of the pipe and that for burst and collapse loads, where |pi – po| >> 0, then |σθ| >> |σr|. For any pi and po combination, the sum of the tangential and radial stresses is constant at all points in the casing wall. Substituting equation 1.10 and equation 1.11 into Equation 1.9 after rearrangements yields σVME =√{ ( f1 f2)2 + f3 2 }………..............................................................................................(1.12)

Where f1 = (ri /r) 2 (√3 /2) (po − pi), f2 = (1/2) [(D/t )2/ {(D/t) – 1}] ,
And
f3 = σz – {(ri 2 pi – ro 2 po ) /(ro2 − ri 2 )}
Where
D = outside pipe diameter,
And
t = wall thickness.
Equation 1.12 calculates the equivalent stress at any point of the pipe body for any given pipe geometry and loading conditions.
1.2.5 Combined Collapse and Tension: - Let σz > 0 and σθ >> σr and setting the triaxial stress equal to the yield strength.
Yp = √[σz 2 − σzσθ + σθ 2]………………………………….................................................... (1.13)
This equation represents an ellipse.
This is the biaxial criterion used in API Bull.5C3, Formulas and Calculations for Casing, Tubing, Drillpipe and Line Pipe Properties, considering the effect of tension on collapse.
Ypa = [√{1 − 0.75(Sa Yp )2 − 0.5 (Sa /Yp )}]Yp………………............................................... (1.14)
Where
Sa = axial stress based on the buoyant weight of pipe,
And
Yp = yield point.
From the above equation we can say that as the axial stress Sa increases, the pipe collapse resistance decreases.

FIG.4 DESIGN FACTORS FOR CASING FAILURE CRITERIA.
Plotting this ellipse, Fig. 1.2 allows a direct comparison of the triaxial criterion with the API ratings. Loads that fall within the design envelope meet the design criteria. The curved lower right corner is caused by the combined stress effects, as described in Equation 1.14.
1.2.6 Combined Burst and Compression Loading: - Combined burst and compression loading corresponds to the upper left-hand quadrant of the design envelope. This is the region where triaxial analysis is most critical because reliance on the uniaxial criterion alone would not predict several possible failures. For high burst loads (i.e., high tangential stress and moderate compression), a burst failure can occur at a differential pressure less than the API burst pressure. For high compression and moderate burst loads, the failure mode is permanent corkscrewing i.e. plastic deformation because of helical buckling). This combined loading typically occurs when a high internal pressure is experienced (because of a tubing leak or a buildup of annular pressure) after the casing temperature has been increased because of production. The temperature increase, in the uncemented portion of the casing, causes thermal growth, which can result in significant increases in compression and buckling. The increase in internal pressure also results in increased buckling.
1.2.7 Combined Burst and Tension Loading: - Combined burst and tension loading corresponds to the upper right-hand quadrant of the design envelope. This is the region where reliance on the uniaxial criterion alone can result in a design that is more conservative than necessary. For high burst loads and moderate tension, a burst yield failure will not occur until after the API burst pressure has been exceeded. As the tension approaches the axial limit, a burst failure can occur at a differential pressure less than the API value. For high tension and moderate burst loads pipe body yield will not occur until a tension greater than the uniaxial rating is reached.
Taking advantage of the increase in burst resistance in the presence of tension represents a good opportunity for the design engineer to save money while maintaining wellbore integrity. Similarly, the designer might wish to allow loads between the uniaxial and triaxial tension ratings. However, great care should be taken in the latter case because of the uncertainty of what burst pressure might be seen in conjunction with a high tensile load (an exception to this is the green cement pressure test load case). Also, connection ratings may limit your ability to design in this region.

1.2.8 Use of Triaxial Criterion for Collapse Loading
For many pipes used in the oil field, collapse is an inelastic stability failure or an elastic stability failure independent of yield strength. The triaxial criterion is based on elastic behaviour and the yield strength of the material and, therefore should not be used with collapse loads. The one exception is for thick-wall pipes with a low D/t ratio, which have an API rating in the yield strength collapse region. This collapse criterion along with the effects of tension and internal pressure (which are triaxial effects) result in the API criterion being essentially identical to the triaxial method in the lower right hand quadrant of the triaxial ellipse for thick-wall pipes.
For high compression and moderate collapse loads experienced in the lower left-hand quadrant of the design envelope, the failure mode may be permanent corkscrewing because of helical buckling. It is appropriate to use the triaxial criterion in this case. This load combination typically can occur only in wells that experience a large increase in temperature because of production. The combination of a collapse load that causes reverse ballooning and a temperature increase acts to increase compression in the uncemented portion of the string.
Most design engineers use a minimum wall for burst calculations and nominal dimensions for collapse and axial calculations. Arguments can be made for using either assumption in the case of triaxial design. Most importantly, more so than the choice of dimensional assumptions, is that the results of the triaxial analysis should be consistent with the uniaxial ratings with which they may be compared.
Triaxial analysis is perhaps most valuable when evaluating burst loads. Therefore, it makes sense to calibrate the triaxial analysis to be compatible with the uniaxial burst analysis. This can be done by the appropriate selection of a design factor. Because the triaxial result nominally reduces to the uniaxial burst result when no axial load is applied, the results of both of these analyses should be equivalent. Because the burst rating is based on 87.5% of the nominal wall thickness, a triaxial analysis based on nominal dimensions should use a design factor that is equal to the burst design factor multiplied by 8/7. This reflects the philosophy that a less conservative assumption should be used with a higher design factor. Therefore, for a burst design factor of 1.1, a triaxial design factor of 1.25 should be used.

1.2.9 Final Triaxial Stress Considerations: - Fig. 7.3 graphically summarizes the triaxial, uniaxial and biaxial limits that should be used in casing design along with a set of consistent design factors.
Because of the potential benefits that can be realized a triaxial analysis is recommended for all well designs. Specific applications include saving money in burst design by taking advantage of the increased burst resistance in tension; accounting for large temperature effects on the axial load profile in high-pressure, high temperature wells, accurately determining stresses when using thick-wall pipe (D/t < 12) (conventional uniaxial and biaxial methods have imbedded thin-wall assumptions); and evaluating buckling severity (permanent corkscrewing occurs when the triaxial stress exceeds the yield strength of the material).
While it is acknowledged that the von Mises criterion is the most accurate method of representing elastic yield behavior, use of this criterion in tubular design should be accompanied by a few precautions.
First, for most pipe used in oilfield applications, collapse is frequently an instability failure that occurs before the computed maximum triaxial stress reaches the yield strength. Therefore, triaxial stress should not be used as a collapse criterion. Only in thick-wall pipe does yielding occur before collapse.
Second, the accuracy of triaxial analysis is dependent upon the accurate representation of the conditions that exist both for the pipe as installed in the well and for the subsequent loads of interest. Frequently, it is the change in load conditions that is most important in stress analysis. Therefore, an accurate knowledge of all temperatures and pressures that occur over the life of the well can be critical to accurate triaxial analysis.

2. API CONNECTION RATING
While a number of joint connections are available, the API recognizes three basic types:
1. Coupling with rounded thread (long or short);
2. Coupling with asymmetrical trapezoidal thread buttress; and
3. Extreme-line casing with trapezoidal thread without coupling. Threads are used as mechanical means to hold the neighboring joints together during axial tension or compression. For all casing sizes, the threads are not intended to be leak resistant when made up. API Spec. 5C2, Performance Properties of Casing, Tubing, and Drillpipe, provides information on casing and tubing threads dimensions.

2.1 Coupling Internal Yield Pressure: - The internal yield pressure is the pressure that initiates yield at the root of the coupling thread.
PCIY = Yc({W − d1}/W )……………………………….......................................................... (1.15)
Where
PCIY = coupling internal yield pressure (psi)
Yc = minimum yield strength of coupling (psi)
W = nominal outside diameter of coupling (in) d1 = diameter at the root of the coupling thread in the power tight position (in) This dimension is based on data given in API Spec. 5B, Threading, Gauging, and Thread Inspection of Casing, Tubing, and Line Pipe Threads and other thread geometry data. The coupling internal yield pressure is typically greater than the pipe body internal yield pressure. The internal pressure leak resistance is based on the interface pressure between the pipe and coupling threads because of makeup.
PILR = ETN pt(W 2 − Es 2 ) /2ESW 2………………………..................................................... (1.16)
Where
PILR = coupling internal pressure leak resistance (psi)
E = modulus of elasticity,
T = thread taper (in),
N = a function of the number of thread turns from hand-tight to power-tight position, as given in API Spec. 5B, threading, gauging and thread inspection of casing, tubing, and line pipe threads. pt = thread pitch (in)
And
Es = pitch diameter at plane of seal, as given in API Spec. 5B threading, gauging and thread inspection of casing, tubing, and line pipe threads.
This equation accounts only for the contact pressure on the thread flanks as a sealing mechanism and ignores the long helical leak paths filled with thread compound that exist in all API connections.
2.2 Round-Thread Casing-Joint Strength: - The round-thread casing-joint strength is given as the lesser of the fracture strength of the pin and the jump-out strength. The fracture strength is given by
Fj = 0.95AjpUp......................................................................................................................... (1.17)
The jump-out strength is given by
Fj = 0.95AjpL [{(0.74D−0.59Up )/(0.5L + 0.14D)} + {Yp /(L + 0.14D)}] ................................(1.18)
Where
Fj = minimum joint strength (lbf),
Ajp = cross-sectional area of the pipe wall under the last perfect thread (in2) = π/4[(D – 0.1425)2 – d2]
D = nominal outside diameter of pipe (in) d = nominal inside diameter of pipe (in)
L = engaged thread length (in) as given in API Spec. 5B, Threading, Gauging, and Thread Inspection of Casing, Tubing, and Line Pipe Threads.
Yp = minimum yield strength of pipe (psi)
And
Up = minimum ultimate tensile strength of pipe (psi)
These equations are based on tension tests to failure on 162 round-thread test specimens. Both are theoretically derived and adjusted using statistical methods to match the test data. For standard coupling dimensions, round threads are pin weak (i.e., the coupling is noncritical in determining joint strength).
2.3 Buttress Casing Joint Strength: - The buttress thread casing joint strength is given as the lesser of the fracture strength of the pipe body (the pin) and the coupling (the box). Pipe thread strength is given by
Fj = 0.95ApUp [1.008 − 0.0396{1.083 – (Yp / Up) D}]........................................................... (1.19)
Coupling thread strength is given by Fj = 0.95AcUc.......................................................................................................................... (1.20)
Where
Uc = minimum ultimate tensile strength of coupling (psi)
Ap = cross-sectional area of plain-end pipe (in2)
And
Ac = cross-sectional area of coupling (in2) = π/4(W2 – d12).
These equations are based on tension tests to failure on 151 buttress-thread test specimens. They are theoretically derived and adjusted using statistical methods to match test data.
2.4 Extreme-Line Casing-Joint Strength: - Extreme-line casing-joint strength is calculated as
Fj = AcrUp ……………………………………………….........................................................(1.21)
Where
Fj = minimum joint strength (lbf)
And
Acr = critical section area of box, pin, or pipe, whichever is least (in2)
When performing casing design, it is very important to note that the API joint-strength values are a function of the ultimate tensile strength. This is a different criterion from that used to define the axial strength of the pipe body, which is based on the yield strength. If care is not taken, this approach can lead to a design that inherently does not have the same level of safety for the connections as for the pipe body. This is not the most prudent practice, particularly in light of the fact that most casing failures occur at connections. This discrepancy can be countered by using a higher design factor when performing connection axial design with API connections.
The joint-strength equations for tubing given in API Bull 5C3 Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties are very similar to those given for round-thread casing except they are based on yield strength. Therefore, the UTS/YS discrepancy does not exist in tubing design.
If API casing connection joint strengths calculated with the previous formulae are the basis of a design, the designer should use higher axial design factors for the connection analysis. The logical basis for a higher axial design factor (DF) is to multiply the pipe body axial design factor by the ratio of the minimum ultimate tensile strength Up to the minimum yield strength Yp.
DFconnection = DFpipe × (U p/Yp )………………………………............................................... (1.22)
Tensile property requirements for standard grades are given in API Spec. 5C2 Performance Properties of Casing, Tubing, and Drillpipe and are shown in Table for reference along with their ratio.
2.5 Proprietary Connections: - Special connections are used to achieve gas-tight sealing reliability and 100% connection efficiency (joint efficiency is defined as a ratio of joint tensile strength to pipe body tensile strength) under more severe well conditions. Severe conditions include high pressure (typically > 5,000 psi) high temperature (typically > 250°F) a sour environment, gas production, high-pressure gas lift, a steam well and a large dogleg (horizontal well). Also efficiency in flush joint integral joint or other special clearance applications improves connections; a large diameter (> 16 in) pipe improves the stab-in and makeup characteristics galling should be reduced (particularly in CRA applications and tubing strings that will be re-used) and connection failure under high torsional loads (e.g., while rotating pipe) should be prevented.
The improved performance of many proprietary connections results from one or more of these features not found in API connections: more complex thread forms; resilient seals; torque shoulders; and metal-to-metal seals. The premium performance of most proprietary connections comes at a premium cost. Increased performance should always be weighed against the increased cost for a particular application. As a general rule, it is recommended to use proprietary connections only when the application requires them. Premium performance may also be achieved using API connections if certain conditions are met. Those conditions are tighter dimensional tolerance; plating applied to coupling; use of appropriate thread compound; and performance verified with qualification testing.
The performance of a proprietary connection can be reliably verified by performing three steps: audit the manufacturer’s performance test data (sealability and tensile load capacity under combined loading); audit the manufacturer’s field history data; and require additional performance testing for the most critical applications. When requesting tensile performance data, make sure that the manufacturer indicates whether quoted tensile capacities are based on the ultimate tensile strength (i.e., the load at which the connection will fracture, commonly called the “parting load”) or the yield strength (commonly called the joint elastic limit). If possible it is recommended to use the joint elastic limit values in the design so that consistent design factors for both pipe-body and connection analysis are maintained. If only parting load capacities are available, a higher design factor should be used for connection axial design.
2.6 Connection Failures: - Most casing failures occur at connections. These failures can be attributed to improper design or exposure to loads exceeding the rated capacity failure to comply with makeup requirements failure to meet manufacturing tolerances damage during storage and handling; and damage during production operations (corrosion, wear, etc.).
Connection failure can be classified broadly as leakage structural failure galling during makeup yielding because of internal pressure jump-out under tensile load fracture under tensile load and failure because of excessive torque during makeup or subsequent operations. Avoiding connection failure is not only dependent upon selection of the correct connection but is strongly influenced by other factors, which include manufacturing tolerances storage (storage thread compound and thread protector) transportation (thread protector and handling procedures) and running procedures (selection of thread compound, application of thread compound and adherence to correct makeup specifications and procedures).
The overall mechanical integrity of a correctly designed casing string is dependent upon a quality assurance program that ensures damaged connections are not used and those operations personnel adhere to the appropriate running procedures.
2.7 Connection Design Limits: -The design limits of a connection are not only dependent upon its geometry and material properties but are influenced by surface treatment phosphating metal plating (copper, tin, or zinc) bead blasting thread compound makeup torque use of a resilient seal ring (many companies do not recommend this practice) fluid to which connection is exposed (mud, clear brine, or gas) temperature and pressure cycling and large doglegs (e.g., medium- or short-radius horizontal wells).

3. LOADS ON CASING 1. In order to evaluate a given casing design a set of loads is necessary. 2. Casing loads result from running the casing, cementing the casing, subsequent drilling operations, production and well workover operations. 3. Casing loads are principally pressure loads, mechanical loads, and thermal loads. 4. Pressure loads are produced by fluids within the casing, cement and fluids outside the casing, pressures imposed at the surface by drilling and workover operations, and pressures imposed by the formation during drilling and production. 5. Mechanical loads are associated with casing hanging weight, shock loads during running, packer loads during production and workovers, and hanger loads. 6. Temperature changes and resulting thermal expansion loads are induced in casing by drilling, production, and workovers and these loads might cause buckling loads in uncemented intervals.
Next we discuss casing loads that are typically used in preliminary casing design. However each operating company usually has its own special set of design loads for casing based on their experience. If you are designing a casing string for a particular company this load information must be obtained from them. Because there are so many possible loads that must be evaluated most casing design today is done with computer programs that generate the appropriate load sets evaluate the results and sometimes even determine a minimum-cost design automatically. 3.1 External Pressure Loads 1. Pressure Distributions: - Pressure distributions are typically used to model the external pressures in cemented intervals. 2. Mud/Cement Mix-Water: - Fluid pressure is given by the mud gradient above the top-of-cement (TOC) and by the cement gradient below TOC. 3. Permeable Zones: Good Cement: - Again, fluid pressure is given by the mud gradient above TOC and by the cement gradient below TOC. The exception is that formation pore pressure is imposed over the permeable zone interval. This pressure profile is discontinuous. 4. Permeable Zones: Poor Cement, High Pressure: - In this case, the formation pore pressure is felt at the surface through the poor cement. This pressure profile is continuous with depth. 5. Permeable Zones: Poor Cement, Low Pressure: - In this case, the mud surface drops so that the mud pressure equals the formation pressure. This pressure profile is continuous with depth. 6. Openhole Pore Pressure: TOC Inside Previous Shoe: - In this case, fluid pressure is given by mud gradient above TOC, cement gradient to the shoe, and the minimum equivalent mud weight gradient of the openhole below the shoe. This pressure profile is not continuous with depth; it is discontinuous at the previous shoe. 7. Openhole Pore Pressure: TOC Below Previous Shoe, Without Mud Drop: - In this case, fluid pressure is given by the mud gradient above TOC and by the minimum equivalent mud weight gradient of the openhole below the shoe. This pressure profile is not continuous with depth but is discontinuous at TOC. 8. TOC below Previous Shoe, With Mud Drop: - In this case, the mud surface drops so that the mud pressure equals the minimum equivalent mud weight gradient of the openhole at the TOC. This pressure profile is continuous with depth. 9. Above/Below TOC External Pressure Profile: - In this case, fluid pressure is given by mud gradient above TOC, cement gradient to the shoe, and a specified pressure profile below a specified depth. This external pressure distribution may be discontinuous at the specified depth. If a pressure gradient is specified, the pressure profile may also be continuous at the specified depth.

3.2 Internal Pressure Loads
Pressure Distributions: - Pressure distributions are typically used to model the internal pressures. These pressure distributions are discussed next.
3.2.1 Burst:
(a- Gas Kick: - This load case uses an internal pressure profile, which is the envelope of the maximum pressures experienced by the casing while circulating out a gas kick using the driller’s method. It should represent the worst-case kick to which the current casing can be exposed while drilling a deeper interval. Typically, this means taking a kick at the total depth (TD) of the next openhole section. If the kick intensity or volume cause the fracture pressure at the casing shoe to exceed, the kick volume is frequently reduced to the maximum volume that can be circulated out of the hole without exceeding the fracture pressure at the shoe. The maximum pressure experienced at any casing depth occurs when the top of the gas bubble reaches that depth.
(b- Displacement to Gas: - This load case uses an internal pressure profile consisting of a gas gradient extending upward from a formation pressure in a deeper hole interval or from the fracture pressure at the casing shoe. This pressure physically represents a well control situation, in which gas from a kick has completely displaced the mud out of the drilling annulus from the surface to the casing shoe. This is the worst-case drilling burst load that a casing string could experience, and if the fracture pressure at the shoe is used to determine the pressure profile, it ensures that the weak point in the system is at the casing shoe and not the surface. This, in turn, precludes a burst failure of the casing near the surface during a severe well-control situation.
(c- Maximum Load Concept: - This load case is a variation of the displacement-to-gas load case that has wide usage in the industry and is taught in several popular casing design schools. It has been used historically because it results in an adequate design (though typicall quite conservative, particularly for wells deeper than 15,000 ft), and it is simple to calculate. The load case consists of a gas gradient extending upward from the fracture pressure at the shoe up to a mud/gas interface and then a mud gradient to the surface. The mud/gas interface is calculated in a number of ways—the most common being the “fixed endpoint” method. The interface is calculated on the basis of surface pressure typically equal to the BOP rating and the fracture pressure at the shoe and assuming a continuous pressure profile.
(d- Lost Returns With Water: - This load case models an internal pressure profile, which reflects pumping water down the annulus to reduce surface pressure during a well-control situation in which lost returns are occurring. The pressure profile represents a freshwater gradient applied upward from the fracture pressure at the shoe depth. A water gradient is used, assuming that the rig’s barite supply has been depleted during the well-control incident. This load case typically dominates the burst design when compared to the gas-kick load case. This is particularly the case for intermediate casing.
(e- Surface Protection: - This load case is less severe than the displacement-to-gas criteria and represents a moderated approach to preventing a surface blowout during a well-control incident. It is not applicable to liners. The same surface pressure calculated in the “lost returns with water” load case is used, but in this load case, a gas gradient from this surface pressure is used to generate the rest of the pressure profile. This load case represents no actual physical scenario; however, when used with the gas-kick criterion, it ensures that the casing weak point is not at the surface. Typically, the gas-kick load case will control the design deep, and the surface-protection load case will control the design shallow, leaving the weak point somewhere in the middle.
(f- Pressure Test: - This load case models an internal pressure profile, which reflects a surface pressure applied to a mud gradient. The test pressure typically is based on the maximum anticipated surface pressure determined from the other selected burst load cases plus a suitable safety margin. For production casing, the test pressure is typically based on the anticipated shut-in tubing pressure. This load case may or may not dominate the burst design depending on the mud weight in the hole at the time the test occurs. The pressure test is normally performed prior to drilling out the float equipment.
3.2.2Collapse:
(a- Cementing: - This load case models an internal and external pressure profile, which reflects the collapse load imparted on the casing after the plug has been bumped during the cement job and the pump pressure bled off. The external pressure considers the mud hydrostatic column and different densities of the lead and tail cement slurries. The internal pressure is based on the gradient of the displacement fluid. If a light displacement fluid is used, the cementing collapse load can be significant. (b- Lost Returns with Mud Drop: - This load case models an internal pressure profile which reflects a partial evacuation or a drop in the mud level because of the mud hydrostatic column equilibrating with the pore pressure in a lost-circulation zone. The heaviest mud weight used to drill the next openhole section should be used along with a pore pressure and depth that result in the largest mud drop. Many operators make the conservative assumption that the lost-circulation zone is at the TD of the next openhole section and is normally pressured. A partial evacuation of more than 5,000 ft because of lost circulation during drilling, is normally not seen. Many operators use a partial evacuation criterion in which the mud level is assumed to be a percentage of the openhole TD. (c- Other Load Cases (Full Evacuation): - This load case should be considered when drilling with air or foam. It may also be considered for conductor or surface casing where shallow gas is encountered. This load case would represent all of the mud being displaced out of the wellbore (through the diverter) before the formation bridged off.
Water Gradient: - For wells with a sufficient water supply, an internal pressure profile consisting of a freshwater or seawater gradient is sometimes used as a collapse criterion. This assumes a lost-circulation zone that can only withstand a water gradient.
3.2.3 Burst:
(a- Gas Migration (Subsea Wells): - This load case models bottomhole pressure applied at the wellhead (subject to fracture pressure at the shoe) from a gas bubble migrating upward behind the production casing with no pressure bleedoff at the surface. The pressure is the minimum of the fracture pressure at the shoe and the reservoir pressure plus the mud gradient. The load case has application only to the intermediate casing in subsea wells where the operator has no means of accessing the annulus behind the production casing.
(b- Tubing Leak: - This load case applies to both production and injection operations and represents a high surface pressure on top of the completion fluid because of a tubing leak near the hanger. A worst-case surface pressure is usually based on a gas gradient extending upward from reservoir pressure at the perforations. If the proposed packer location has been determined when the casing is designed, the casing below the packer can be assumed to experience pressure, based on the produced fluid gradient and reservoir pressure only. (d- Injection down Casing: - This load case applies to wells that experience high-pressure annular injection operations such as a casing fracture stimulation job. The load case models a surface pressure applied to a static fluid column. This is analogous to a screenout during a fracturing job.
3.3.4 Collapse above Packer: (a- Full Evacuation:- This severe load case has the most application in gas lift wells. It is representative of a gas filled annulus that loses injection pressure. Many operators use the full evacuation criterion for all production casing strings regardless of the completion type or reservoir characteristics. (b- Partial Evacuation: - This load case is based on a hydrostatic column of completion fluid equilibrating with depleted reservoir pressure during a workover operation. Some operators do not consider a fluid drop but only a fluid gradient in the annulus above the packer. This is applicable if the final depleted pressure of the formation is greater than the hydrostatic column of a lightweight packer fluid.
3.3.5 Collapse below Packer: (a- Full Evacuation: - This load case applies to severely depleted reservoirs, plugged perforations, or a large drawdown of a low-permeability reservoir. It is the most commonly used collapse criterion. (b- Fluid Gradient: - This load case assumes zero surface pressure applied to a fluid gradient. A common application is the underbalanced fluid gradient in the tubing before perforating (or after if the perforations are plugged). It is a less conservative criterion for formations that will never be drawn down to zero. 3.3.6 Collapse : (a- Gas Migration (Subsea Wells): - This load case models bottomhole pressure applied at the wellhead (subject to fracture pressure at the prior shoe) from a gas bubble migrating upward behind the production casing with no pressure bleedoff at the surface. The pressure distribution is the minimum of the following two pressure distributions. The load case has application only in subsea wells where the operator has no means of accessing the annulus behind the production casing. An internal pressure profile consisting of a completion fluid gradient is typically used. (b- Salt Loads: - If a formation that exhibits plastic behavior, such as a salt zone, is to be isolated by the current string, then an equivalent external collapse load (typically taken to be the overburden pressure) should be superimposed on all of the collapse load cases from the top to the base of the salt zone.

3.3 Mechanical Loads
3.3.1Changes in Axial Load: - In tubing and over the free length of the casing above TOC changes in temperatures and pressures will have the largest effect on the ballooning and temperature load components. The incremental forces because of these effects are-
ΔFbal = 2υ(Δ pi Ai − Δ po Ao) + υLgc(Δρi Ai − Δρo Ao)............................................................(1.47)
Where
ΔFbal = incremental force because of ballooning (lbf) υ = Poisson’s ratio (0.30 for steel) gc = gravity constant = 1 lbf/lbm
Δpi = change in surface internal pressure (psi)
Δpo = change in surface external pressure (psi)
Ai = cross-sectional area associated with casing inside diameter (in)
Ao = cross-sectional area associated with casing outside diameter (in)
L = free length of casing (in)
Δρi = change in internal fluid density (lbm/in3) and Δρo = change in external fluid density (lbm/in3)
ΔFtemp = − αE AsΔT….......................................................................................................... (1.48)
Where
ΔFtemp = incremental force because of temperature change (lbf) α = thermal expansion coefficient (6.9 × 10–6 °F–1 for steel) (°F–1)
E = Young’s modulus (3.0 × 107 psi for steel) (psi)
As = cross-sectional area of pipe (in2)
And
ΔT = average change in tempera-ture over free length (°F)

3.3.2 Axial
Running in Hole: - This installation load case represents the maximum axial load that any portion of the casing string experiences when running the casing in the hole. It can include effects such as- self-weight, buoyancy forces at the end of the pipe and at each cross-sectional area change, wellbore deviation, bending loads superimposed in dogleg regions, shock loads based on an instantaneous deceleration from a maximum velocity and frictional drag.
Overpull While Running: - This installation load case models an incremental axial load applied at the surface while running the pipe in the hole. Casing designed using this load case should be able to withstand an overpull force applied with the shoe at any depth if the casing becomes stuck while running in the hole. Certain effects must be considered, such as self-weight; buoyancy forces at the end of the pipe and at each cross-sectional area change; wellbore deviation; bending loads superimposed in dogleg regions; frictional drag; and the applied overpull force.
Green Cement Pressure Test: - This installation load case models applying surface pressure after bumping the plug during the primary cement job. Because the cement is still in its fluid state, the applied pressure will result in a large piston force at the float collar and frequently results in the worst-case surface axial load. The effects that should be considered are self-weight; buoyancy forces at the end of the pipe and at each cross-sectional area change;\ wellbore deviation; bending loads superimposed in dogleg regions; frictional drag; and piston force because of differential pressure across float collar.
3.3.3 Air Weight of Casing only: - This axial load criterion has been used historically because it is an easy calculation to perform, and it normally results in adequate designs. It still enjoys significant usage in the industry. Because a large number of factors are not considered, it is typically used with a high axial design factor (e.g. 1.6+).
3.3.4 Buoyed Weight plus overpull only: - Like the air weight criterion, this load case has wide usage because it is an easy calculation to perform. Because a large number of factors are not considered, it is typically used with a high axial design factor (e.g. 1.6+).
3.3.5 Shock Loads: - Shock loads can occur if the pipe hits an obstruction or the slips close while the pipe is moving. The maximum additional axial force because of a sudden deceleration to zero velocity is given by the equation,
Fshock = (vrun As/12)√(Eρs/gc)……………………………........................................................ (1.49)
Where
Fshock= shock loading axial force (lbf) νrun = running speed (ft/sec)
As = pipe cross-sectional area (in2)
E = Young’s modulus for pipe (lbf/in2) ρs = density of pipe (lbm/ft3)
And
gc = gravity constant (ft/sec2)
The shock load equation is frequently expressed as
Fshock =(wa/gc ) vrun vsonic………………………………........................................................... (1.50)
Where
wa = pipe weight per unit length in air (lbm/ft)
And
vsonic = speed of sound in pipe (ft/sec) = √(144E gc / ρs) (For steel, vsonic is 16,800 ft/sec)
For practical purposes, some operators specify an average velocity in this equation and multiply the result by a factor that represents the ratio between the peak and average velocities (typically 1.5).
3.3.6 Service Loads: - For most wells, installation loads will control axial design. However, in wells with uncemented sections of casing and where large pressure or temperature changes will occur after the casing is cemented in place, changes in the axial load distribution can be important because of effects such as self-weight, buoyancy forces, wellbore deviation, bending loads, changes in internal or external pressure, temperature changes and buckling.
3.3.7 Bending Loads: - Stress at the pipe’s OD because of bending can be expressed as σb = ED/2R …………………………….…………................................................................ (1.51)
Where
σb = stress at the pipe’s outer surface (psi)
E = modulus of elasticity (psi)
D = nominal outside diameter (in)
And
R = radius of curvature (in)
This bending stress can be expressed as an equivalent axial force as
Fbnd = (Eπ/360) D (α/L) As………………………………...................................................... (1.52)
Where
Fbnd = axial force because of bending (lbf) α /L = dogleg severity (°/unit length)
And
As = cross-sectional area (in2)
The bending load is superimposed on the axial load distribution as a local effect.

3.3 Thermal Loads and Temperature Effects: -
In shallow normal-pressured wells temperature will typically have a secondary effect on tubular design. In other situations loads induced by temperature can be the governing criteria in the design. Next we discuss how temperature can affect tubular design.
Temperature Effects on Tubular Design: - 1) Annular Fluid Expansion Pressure: - Increases in temperature after the casing is landed can cause thermal expansion of fluids in sealed annuli and result in significant pressure loads. Most of the time these loads need not be included in the design because the pressures can be bled off. However in subsea wells the outer annuli cannot be accessed after the hanger is landed. The pressure increases will also influence the axial load profiles of the casing strings exposed to the pressures because of ballooning effects. 2) Tubing Thermal Expansion: - Changes in temperature will increase or decrease tension in the casing string because of thermal contraction and expansion respectively. The increased axial load because of pumping cool fluid into the wellbore during a stimulation job can be the critical axial design criterion. In contrast the reduction in tension during production because of thermal expansion can increase buckling and possibly result in compression at the wellhead. 3) Temperature Dependent Yield: - Changes in temperature not only affect loads but also influence the load resistance. Because the material’s yield strength is a function of temperature, higher wellbore temperatures will reduce the burst, collapse, axial, and triaxial ratings of the casing. 4) Sour Gas Well Design: - In sour environments, operating temperatures can determine what materials can be used at different depths in the wellbore. 5) Tubing Internal Pressures: - Produced temperatures in gas wells will influence the gas gradient inside the tubing because gas density is a function of temperature and pressure.

4. CASING DESIGN
To design a casing string we should know the purpose of the well, the geological cross section, available casing and bit sizes, cementing and drilling practices, rig performance, as well as safety and environmental regulations. To get the optimal solution the design engineer must consider casing as a part of a whole drilling system.
4.1 Design Objectives
To develop the well plan and casing design is faced with a number of tasks that can be done are - 1) Ensure the well’s mechanical integrity by providing a design basis that accounts for all the loads that can be encountered during the life of the well. 2) Design strings to minimize well costs over the life of the well. 3) Provide clear documentation of the design basis to operational personnel at the well site.
While the intention is to provide reliable well construction at a minimum cost at times failures occur. Most documented failures occur because the pipe was exposed to loads for which it was not designed. These failures are called “off-design” failures. “On-design” failures are rather rare. This implies that casing-design practices are mostly conservative. Many failures occur at connections. This implies that either field makeup practices are not adequate or the connection design basis is not consistent with the pipe-body design basis.
4.2 Design Method
The design process can be divided into two different phases.
4.2.1 Preliminary Design: - The largest opportunities for saving money are present while performing this task.
This design phase comprises- 1) Data gathering and interpretation, 2) Determination of casing shoe depths and number of strings, 3) Selection of hole and casing sizes, 4) Mud-weight design and directional design.
The quality of the gathered data will have a large impact on the appropriate choice of casing sizes and shoe depths and whether the casing design objective is successfully met.

4.2.2 Detailed Design: -The detailed design phase comprises- 1) Selection of pipe weights and grades for each casing string. 2) Connection selection. 3) The selection process consists of comparing pipe ratings with design loads and applying minimum acceptable safety standards (i.e. design factors).
A cost-effective design meets all the design criteria with the least expensive available pipe.
4.3 Required Information: - The items listed next are a checklist which is provided to aid the well planners/casing designers in both the preliminary and detailed design. 1) Formation properties:- pore pressure, formation fracture pressure, formation strength (borehole failure), temperature profile, location of squeezing salt and shale zones, location of permeable zones, chemical stability/sensitive shales (mud type and exposure time), lost-circulation zones, shallow gas, location of freshwater sands, and presence of H2S and/or CO2. 2) Directional data:- surface location, geologic target and well interference data. 3) Minimum diameter requirements:- minimum hole size required to meet drilling and production objectives, logging tool OD, tubing size, packer and related equipment requirements, subsurface safety valve OD (offshore well) and completion requirements. 4) Production data:- packer-fluid density, produced-fluid composition and worst-case loads that might occur during completion, production and workover operations. 5) Other: - available inventory, regulatory requirements and rig equipment limitations.
4.4 Preliminary Design: -The purpose of preliminary design is to establish casing and corresponding drill-bit sizes, casing setting depths and consequently, the number of casing strings. Casing program (well plan) is obtained as a result of preliminary design. Casing program design is accomplished in three major steps. First mud program is prepared, second the casing sizes and corresponding drillbit sizes are determined and next the setting depths of individual casing strings are found.
4.4.1 Mud Program: - The most important mud program parameter used in casing design is the mud weight. The complete mud program is determined from: pore pressure, formation strength (fracture and borehole stability), lithology, hole cleaning and cuttings transport capability, potential formation damage, stability problems, and drilling rate, formation evaluation requirement, and environmental and regulatory requirements.

4.4.2 Hole and Pipe Diameters: - 1) Production: - The production equipment requirements include tubing, subsurface safety valve, submersible pump and gas lift mandrel size, completion requirements (e.g., gravel packing) and weighing the benefits of increased tubing performance of larger tubing against the higher cost of larger casing over the life of the well. 2) Evaluation: - Evaluation requirements include logging interpretation and tool diameters. 3) Drilling: - Drilling requirements include a minimum bit diameter for adequate directional control and drilling performance, available downhole equipment, rig specifications and available BOP equipment.
These requirements normally impact the final hole or casing diameter. Because of this, casing sizes should be determined from the inside outward starting from the bottom of the hole. Usually the design sequence is as described next.
Based upon reservoir inflow and tubing intake performance, proper tubing size is selected. Then, the required production casing size is determined considering completion requirements. Next the diameter of the drill bit is selected for drilling the production section of the hole considering drilling and cementing stipulations. Next one must determine the smallest casing through which the drill bit will pass and the process is repeated. Large cost savings are possible by becoming more aggressive during this portion of the preliminary design phase. This has been one of the principal motivations in the increased popularity of slimhole drilling.
4.4.3 Casing Shoe Depths and the Number of Strings: - Following the selection of drillbit and casing sizes, the setting depth of individual casing strings must be determined. In conventional rotary drilling operations, the setting depths are determined principally by the mud weight and the fracture gradient, as schematically depicted in Fig. 7.5, which is sometimes called a well plan. Equivalent mud weight (EMW) is pressure divided by true vertical depth and converted to units of lbm/gal. EMW equals actual mud weight when the fluid column is uniform and static. First, pore and fracture gradient lines must be drawn on a well-depth vs. EMW chart. These are the solid lines in Fig. 7.5. Next, safety margins are introduced, and broken lines are drawn which establish the design ranges. The offset from the predicted pore pressure and fracture gradient nominally accounts for kick tolerance and the increased equivalent circulating density (ECD) during drilling. There are two possible ways to estimate setting depths from this figure.
4.4.4 Bottom-Up Design: - This is the standard method for casing seat selection. From Point A in Fig. 7.5 (the highest mud weight required at the total depth) draw a vertical line upward to Point B. A protective 7⅝-in. casing string must be set at 12,000 ft corresponding to Point B to enable safe drilling on the section AB. To determine the setting depth of the next casing draw a horizontal line BC and then a vertical line CD. In such a manner Point D is determined for setting the 9⅝-in. casing at 9,500 ft. The procedure is repeated for other casing strings usually until a specified surface casing depth is reached.
4.4.5 Top-Down Design: - From the setting depth of the 16-in. surface casing draw a vertical line from the fracture gradient dotted line Point A to the pore pressure dashed line Point B. This establishes the setting point of the 11¾-in. casing at about 9,800 ft. Draw a horizontal line from Point B to the intersection with the dotted fracture gradient line at Point C then draw a vertical line to Point D at the pore pressure curve intersection. This establishes the 9⅝-in. casing setting depth. This process is repeated until bottom hole is reached.
There are several things to observe about these two methods. First they do not necessarily give the same setting depths. Second they do not necessarily give the same number of strings.
In the top-down design the bottomhole pressure is missed by a slight amount that requires a short 7-in. liner section. This slight error can be fixed by resetting the surface casing depth.
The top-down method is more like actually drilling a well in which the casing is set when necessary to protect the previous casing shoe. This analysis can help anticipate the need for additional strings given that the pore pressure and fracture gradient curves have some uncertainty associated with them. In practice a number of regulatory requirements can affect shoe depth design.
4.4.6 Hole Stability: - This can be a function of mud weight, deviation and stress at the wellbore wall or can be chemical in nature. Frequently hole stability problems shows time-dependent behaviour. The plastic flowing behavior of salt zones must also be considered.
4.4.7 Differential Sticking: - The probability of becoming differentially stuck increases with increasing differential pressure between the wellbore and formation, increasing permeability of the formation and increasing fluid loss of the drilling fluid (i.e. thicker mudcake).
4.4.8 Zonal Isolation: - Shallow freshwater sands must be isolated to prevent contamination. Lost circulation zones must be isolated before a higher-pressure formation is penetrated.
4.4.9 Directional Drilling Concerns: - A casing string is frequently run after an angle building section has been drilled. This avoids keyseating problems in the curved portion of the wellbore because of the increased normal force between the wall and the drill pipe.
4.4.10 Uncertainty in Predicted Formation Properties: - Exploration wells frequently require additional strings to compensate for the uncertainty in the pore pressure and fracture gradient predictions. Another approach that could be used for determining casing setting depths relies on plotting formation and fracturing pressures vs. hole depth rather than gradients. This procedure however typically yields many strings and is considered to be very conservative. See the chapter on geoscience principles in this volume of the handbook.

FIG.5 CASING SETTING DEPTHS BOTTOM-UP DESIGN
The problem of choosing the casing setting depths is more complicated in exploratory wells because of shortage of information on geology, pore pressures and fracture pressures. In such a situation a number of assumptions must be made. Commonly the formation pressure gradient is taken as 0.54 psi/ft for hole depths less than 8,000 ft and taken as 0.65 psi/ft for depths greater than 8,000 ft. Overburden gradients are generally taken as 0.8 psi/ft at shallow depth and as 1.0 psi/ft for greater depths.
4.4.11 Directional Plan: - For casing design purposes establishing a directional plan consists of determining the wellpath from the surface to the geological targets. The directional plan influences all aspects of casing design including mud weight and mud chemistry selection for hole stability, shoe seat selection, casing axial load profiles, casing wear, bending stresses, and buckling. It is based on factors that include geological targets, surface location, interference from other wellbores, torque and drag considerations, casing wear considerations, bottomhole assembly (BHA is an assembly of drill collars, stabilizers, and bits) and drill-bit performance in the local geological setting. To account for the variance from the planned build, drop and turn rates which occur because of the BHAs used and operational practices employed, higher doglegs are frequently superimposed over the wellbore. This increases the calculated bending stress in the detailed design phase.

4.5 Detailed Design
4.5.1 Load Cases: - In order to select appropriate weights, grades and connections during the detailed design phase using sound engineering judgment, design criteria must be established. These criteria normally consist of load cases and their corresponding design factors that are compared to pipe ratings. Load cases are typically placed into categories that include burst loads, drilling loads, production loads, collapse loads, axial loads, running and cementing loads and service loads.

FIG.6 CASING SETTING DEPTHS TOP- DOWN DESIGN
4.5.2 Design Factors: - In order to make a direct graphical comparison between the load case and the pipe’s rating, the DF must be considered.
DF = SFmin ≤ SF = pipe rating/applied load……………...……............................................. (1.53)
Where
DF = design factor (the minimum acceptable safety factor) and
SF = safety factor.
It follows that
DF × (applied load) ≤ pipe rating............................................................................................ (1.54)
Therefore by multiplying the load by the DF a direct comparison can be made with the pipe rating. As long as the rating is greater than or equal to the design load the design criteria have been satisfied.
4.5.3 Other Considerations: - After performing a design based on burst, collapse and axial considerations an initial design is achieved. Before a final design is reached design issues (connection selection, wear, and corrosion) must be prepared. In addition other considerations can also be included in the design. These considerations are triaxial stresses because of combined loading —this is frequently called service life analysis, temperature effects and buckling.

5. CASE STUDY

Proposed well SW-1 is scheduled as an oil producer (36°API) anticipated to flow at ±25,000b/d. SW-1 is central in a cluster of a twelve well-slot land drilling centre. Six wells have already been drilled and completed. Slot centres are 2 metres apart and surface casing string (13-3/8”) has to be set at ±3500 feet (TVD) at inclinations of no more than 1°.

Following data is given: 1. Formation fluid density = 9 ppg;
2. Fracture gradient at 3500 ft = 0.78 psi/it;
3. Mud weight when casing run = 9.5 ppg;
4. Cement density (back to surface) = 12 ppg;5. Gas gradient expected = 0.115 psi/ft.
6. Formation temperature = 3500F
7. Design factors to be used:
Burst and Collapse, both = 1.1;
Tension = 1.6 plus 100,000 lbs pull.
It is desired to do burst design, collapse design, tensile load design and biaxial design for the surface casing to be set in the well. Finally, based on the design calculations, it is required to select an appropriate casing from the list of casings given below:

5.1 Collapse design calculation ∆Pshoe = 0.052×ϒmud×h

Where, ϒ=specific wt of the mud,ppg

h=depth,ft

collapse load at 3500ft

∆Pshoe = 0.052×ϒmud×h =0.052×12×3500=2184 lbf/in2

∆Psurf = 0 lbf/in2

collapse design at 3500ft

∆Pshoe = 1.1×2184 =2402.4 lbf/in2

∆Psurf = 0 lbf/in2

5.2 Burst design calculation

Burst load at 3500ft Internal pressure = (0.78/0.052 +1) × 3500 × 0.052 = 2912 lbf/in2 Surface pressure = 2912 – (0.115×3500) = 2509.5 lbf/in2

Shoe pressure = 0.052×9×3500 = 1638 lbf/in2

Burst desgin at 3500ft

∆Psurf = 1.1×2509.5 = 2760.45 lbf/in2

∆Pshoe = 1.1×1638 = 1801.8 lbf/in2

5.3Tensile load design calculation

W1 = 650×72 = 46800 lbs

W2= 2850×68 = 193800 lbs

F= P × A

P = 0.052×9.5×3500 = 1729 psi

A = π/4 (13.3752-12.3472) =20.77 in.

F1 = 1729×20.77 = 35911.33 lbf

P = 0.052×9.5×2850 = 1470.9 psi

A= π/4 (12.4152-12.3472) =1.32 in2

F2 = 1470.9×1.32 = 1941.6 lbf

Tension = - PoAo + PoA1 + ∑ Pi(Ai+1 - Ai) + ∑ WiLi

| DEPTH | TENSION | D.F. = 1.6 | OVERPULL(100,000lbs) | N80 | 3500 | -35911 | - | 64089 | | 2850 | 36089 | 57742 | 136089 | K55 | 2850 | 38031 | 60850 | 138031 | | 0 | 208031 | 332850 | 308031 |

5.4 Biaxial design calculation

Calculation of Y Fclps= √(1-0.75(F/AtY)2) – 0.5(F/AtY)

Calculation of X

Using ellipse equation,

(x2/a2)+ (y2/b2) =1

TENSION | PIPE BODY YIELD | X | Y | DERATE COLLAPSE | -35911 | 1661000 | 0 | 1 | 2670 | 36089 | 1661000 | 0.020 | 0.99 | 2643 | 38031 | 1069000 | 0.040 | 0.98 | 1961 | 208031 | 1069000 | 0.456 | 0.89 | 1736 |

5.5 CONCLUSION
While design a surface casing we can begin with either burst or collapse and it is really immaterial where we start. For most surface casing string collapse usually is more critical than burst and the initial selection for collapse often satisfies the requirements for burst too. In the above case we have two casing string of same grade and different collapse and burst strength. Of these two strings we select the string which has more collapse strength. One of the advantages of this selection is that we can use the string for more vertical depth. Using one string will also decrease the complexity and the cost of casing design. After selection of this string we calculate burst strength, tensile strength and biaxial design.

6. REFERENCES 1) TED G. BYROM: Casing and liners for drilling and completion. 2) Crandall, S.H. and Dahl, N.C.: An Introduction to the Mechanics of Solids, McGraw-Hill Book. 3) ISO 2394; International Standard for General Principles on Reliability of Structures. 4) Kapur, K.C. and Lamberson, L.R.: Reliability in Engineering Design, John Wiley & Sons. 5) Hussain Rabia: well engineering & construction.

7. APPENDIX

API STEEL GRADE | API GRADE | YIELD STESS(PSI) | MINIMUM ULT TENSILE (PSI) X(1000) | MINIMUM ELONGATION(%) | | MINIMUM X(1000) | MAXIMUMX(1000) | | | H-40 | 40 | 80 | 60 | 29.5 | J-55 | 55 | 80 | 75 | 24.0 | K-55 | 55 | 80 | 95 | 19.5 | N-80 | 80 | 110 | 100 | 18.5 | L-80 | 80 | 95 | 95 | 19.5 | C-90 | 90 | 105 | 100 | 18.5 | C-95 | 95 | 110 | 105 | 18.5 | T-95 | 95 | 110 | 105 | 18.0 | P-110 | 110 | 140 | 125 | 15.0 | Q-125 | 125 | 150 | 135 | 18.0 |

NON- API STEEL GRADES | NON-API GRADE | MANUFACTURER | YIELD STENGTH(PSI) | MINIMUM ULT TENSILE(PSI) X(1000) | MINIMUMELONGATION(%) | | | MINIMUMX(1000) | MAXIMUMX(1000) | | | S-80 | Lone Star | 75 | | 75 | 20 | | Longitudinal | 55 | | | | modN-80 | Mannesmann | 80 | 95 | 100 | 24 | C-90 | Mannesmann | 90 | 105 | 120 | 26 | SS-95 | Lone Star | 95 | | 95 | 18 | | Longitudinal | 75 | | | | SOO-95 | Mannesmann | 95 | 110 | 110 | 20 | S-95 | Lone Star | 95 | | 110 | 16 | | Longitudinal | 92 | | | | SOO-125 | Mannesmann | 125 | 150 | 135 | 18 | SOO-140 | Mannesmann | 140 | 165 | 150 | 18 | V-150 | US Steel | 150 | 180 | 160 | 14 | SOO-155 | Mannesmann | 155 | 180 | 165 | 20 |

YIELD COLLAPSE PRESSURE FORMULA RANGE | GRADE | MAXIMUM (D/t) | H-40 | 16.40 | -50 | 15.24 | J-K-55 | 14.81 | -60 | 14.44 | -17 | 13.85 | C-75&E | 13.60 | L-N-80 | 13.38 | C-90 | 13.01 | C-T-95&X | 12.85 | -100 | 12.70 | P-105&G | 12.57 | P-110 | 12.44 | -120 | 12.21 | Q-125 | 12.11 | -130 | 12.02 | S-135 | 11.92 | -140 | 11.84 | -150 | 11.67 | -155 | 11.59 | -160 | 11.52 | -170 | 11.37 | -180 | 11.23 |

FORMULA FACTOR AND D/t RANGE FOR PLASTIC COLLAPSE | GRADE | FORMULA FACTOR | D/t RANGE | | A | B | C | | H-40 | 2.950 | 0.0465 | 754 | 16.40-27.0 | -50 | 2.976 | 0.0515 | 1056 | 15.24-25.63 | J-K-55 | 2.991 | 0.0541 | 1206 | 14.81-25.01 | -60 | 3.005 | 0.0566 | 1356 | 14.44-24.42 | -70 | 3.037 | 0.0617 | 1656 | 13.85-23.38 | C-75&E | 3.054 | 0.0642 | 1806 | 13.60-22.91 | L-N-80 | 3.071 | 0.0667 | 1955 | 13.38-22.47 | C-90 | 3.106 | 0.0718 | 2254 | 13.01-21.69 | C-T-95&X | 3.124 | 0.0743 | 2404 | 12.85-21.33 | -100 | 3.143 | 0.0768 | 2553 | 12.70-21.00 | P-105&G | 3.162 | 0.0794 | 2702 | 12.57-20.70 | P-110 | 3.181 | 0.0819 | 2852 | 12.44-20.41 | -120 | 3.219 | 0.0870 | 3151 | 12.21-19.88 | Q-125 | 3.239 | 0.0895 | 3301 | 12.11-19.63 | -130 | 3.258 | 0.0920 | 3451 | 12.02-19.40 | S-135 | 3.278 | 0.0946 | 3601 | 11.92-19.18 | -140 | 3.297 | 0.0971 | 3751 | 11.84-18.97 | -150 | 3.336 | 0.1021 | 4053 | 11.67-18.57 | -155 | 3.356 | 0.1047 | 4204 | 11.59-18.37 | -160 | 3.375 | 0.1072 | 4356 | 11.52-18.19 | -170 | 3.412 | 0.1123 | 4660 | 11.37-17.82 | -180 | 3.449 | 0.1173 | 4966 | 11.23-17.47 |

FORMULA FACTOR AND D/t RANGE FOR TRANSITION COLLAPSE | GRADE | FORMULA FACTOR | D/t RANGE | | F | G | | H-40 | 2.063 | 0.0325 | 27.01-42.64 | -50 | 2.003 | 0.0347 | 25.63-38.83 | J-K-55 | 1.989 | 0.0360 | 25.01-7.21 | -60 | 1.983 | 0.0373 | 24.42-5.73 | -70 | 1.984 | 0.0403 | 23.38-33.17 | C-75&E | 1.990 | 0.0418 | 22.91-32.05 | L-N-80 | 1.998 | 0.0434 | 22.47-1.02 | C-90 | 2.017 | 0.0466 | 21.69-29.18 | C-T-95&X | 2.029 | 0.0482 | 21.33-28.36 | -100 | 2.040 | 0.0499 | 21.00-27.60 | P-105&G | 2.053 | 0.0515 | 20.70-26.89 | P-110 | 2.066 | 0.0532 | 20.41-26.22 | -120 | 2.092 | 0.0565 | 19.88-25.01 | Q-125 | 2.106 | 0.0582 | 19.63-24.46 | -130 | 2.119 | 0.0599 | 19.40-23.94 | S-135 | 2.133 | 0.0615 | 19.18-23.44 | -140 | 2.146 | 0.0632 | 18.97-22.98 | -150 | 2.174 | 0.0666 | 18.57-22.11 | -155 | 2.188 | 0.0683 | 18.37-21.70 | -160 | 2.202 | 0.0700 | 18.19-21.32 | -170 | 2.231 | 0.0734 | 17.82-20.60 | -180 | 2.261 | 0.0769 | 17.47-19.93 |

D/t RANGE FOR ELASTIC COLLAPSE | GRADE | MINIMUM D/t RANGE | H-40 | 42.64 | -50 | 38.83 | J-K-55 | 37.21 | -60 | 35.73 | -70 | 33.17 | C-75&E | 32.05 | L-N-80 | 31.02 | C-90 | 29.18 | C-T-95&X | 28.36 | -100 | 27.60 | P-105&G | 26.89 | P-110 | 26.22 | -120 | 25.01 | Q-125 | 24.46 | -130 | 23.94 | S-135 | 23.44 | -140 | 22.98 | -150 | 22.11 | -155 | 21.70 | -160 | 21.32 | -170 | 20.60 | -180 | 19.93 |

TENSILE PROPERTY REQUIREMENTS | GRADE | YP(PSI)X(1000) | UP(PSI)X(1000) | UP/YP | H-40 | 40 | 60 | 1.50 | J-55 | 55 | 75 | 1.36 | K-55 | 55 | 95 | 1.73 | N-80 | 80 | 100 | 1.25 | L-80 | 80 | 95 | 1.19 | C-90 | 90 | 100 | 1.11 | C-95 | 95 | 105 | 1.11 | T-95 | 95 | 105 | 1.11 | P-110 | 110 | 125 | 1.14 | Q-125 | 125 | 135 | 1.08 |

DEVIATION ANGLE (0) | BUCKLING FORCES(lbf) | | MINIMUM LATERAL | MAXIMUM LATERAL | MINIMUM HELICAL | 0 | 0 | 0 | 0 | 5 | 2201 | 6226 | 3113 | 10 | 3107 | 8788 | 4394 | 15 | 3793 | 10729 | 5365 | 30 | 5272 | 14913 | 7456 | 60 | 6939 | 19626 | 9813 | 90 | 7456 | 21090 | 10545 |