Chapter 2: Casing Design Open Hole Completions
The first decision on casing the pay zone is not of size or weight but whether or not to run casing at all. Open hole completions represent the simplest type of completions and have some very useful traits. They also present some problems. An open hole or barefoot completion is usually made by drilling to the top of the pay, then running and cementing casing. After these operations, the pay is drilled with a nondamaging fluid. Since the other formations are behind pipe, the drilling fluid overbalance is only that needed to control the reservoir pressure. This creates less damage. Open hole completions have the largest possible formation contact with the wellbore, allowing injection or production with every part of the contacted interval. The effect of the open hole on stimulated operations depends on the type of job. Fracturing operations are often easier in the open hole than through perforations by less possibility of perforation screenouts, but the perforations may make the zone easier to break down since a crack (the perforation) has already been placed. Matrix acidizing can more evenly contact the entire zone in an open hole but is more difficult to direct by straddle packer than in a cased hole. Hydraulic jetting is most effective in the open hole. Productivity of open hole gravel packs, especially the underreamed open holes are usually much higher than cased hole gravel packs. Why then, are casing strings even used? Part of the answer is in formation (wellbore) stability concerns and part is unfamiliarity with completing and producing the open hole completions. A decision must be reached on the merits of the completions on the pay in question. If the pay is prone to brittle failures during production that leads to fill, most operators choose to case and cement. In areas of water coning or zone conformance problems, casing may make isolation of middle or top zones possible. With the advent of improved inflatable packers and matrix sealants, however, isolation is also possible in open holes, although wellbore diameter may be severely restricted. Cased Hole Completions A casing string is run to prevent the collapse of the wellbore and to act in concert with the cement sheath to isolate and separate the productive formations. The size of the casing is optimized on the expected productivity of the well and must be designed to withstand the internal and external pressures associated with completion, any corrosive influences, and the forces associated with running the casing.
An optimum design for a casing string is one designed from "the inside out", a design that is based on supplying a stable casing string of a size to optimize total fluid production over the life of the well (including possibility of secondary or tertiary floods). The effective design of a casing string for any well consists of four principal steps. 1. Determine the length and size of all casing strings that are needed to produce the well to its
maximum potential. 2. Calculate the pressure and loads from predicted production and operations such as stimulation,
thermal application and secondary recovery. 3. Determine any corrosive atmosphere that the casing string will be subjected to and either select alloys which can resist corrosion or design an alternate corrosion control system.
2- 1
4. Determine the weight and grade of casing that will satisfactorily resist all of the mechanical,
hydraulic, and chemical forces applied. The sizing of a casing string must be complete before finalizing the bit program during the planning of the well. A casing string can be visualized as a very long telescoping tube with the surface casing or conductor pipe as the first segment and the deepest production string or liner as the smallest, most extended section. Each successive (deeper) segment of the casing string must pass through the last section with enough clearance to avoid sticking. Figure 2.1 illustrates the way the casing string fits together. The drill bits used for each section are usually 1.5 to 3 in. or more larger than the casing 0.d. to be run. When one section is cased and cemented, a bit just small enough to pass through the casing drift ID is run to drill to the next casing seat (casing shoe set depth). During drilling, departing from the bit program is often required, especially in a wildcat when the fluid pressures in the formations cannot be controlled with a single mud weight without either breaking down some formations by hydraulic fracturing with the mud, or allowing input of fluid from other formations because of low hydrostatic drilling mud pressure (a kick). Ideally, just before this noncontrollable point is reached, the “casing point” is designated and a casing string is run. Economics of drilling and cementing dictate that these casing points be as far apart as formation pressures and hole stability will allow. Use of as few casing strings as possible also permits larger casing to be used across the production zone without using extremely large diameter surface strings.
ii
7
,
-.;$:$$,y;. ........ ........ .......... .. ;,........... : .........
F .......... x:;,.+;:<: ..:.::::::.
......:>. ...,...>~..:2!:...:,
E.iZ:.:i;i
,
i.....
0.
i
“YDRO-PRESSURE3
WEUS
b. GEO- PRESSURED
WELLS
(Buzarde et al., SPE, 1972)
Figure 2.1:
Typical casing strings for normal and high pressure wells. In the high pressure wells, the multiple strings in the overlap section will likely be cemented in the annulus, clear back to the liner top or to surface on a casing string.
Use of small casing severely restricts the opportunities for deepening the well or using larger pumps. Use of small casing to save on drilling costs is usually a poor choice in any area in which high production rates (including water floods) are expected. Description of Casing Strings
There are several different casing strings that are run during the completion of a well. These strings vary in design, material of construction and purpose. The following paragraphs are brief descriptions of the common required strings and specialty equipment.
2-2
The conductor pipe is the first casing which is run in the well. This casing is usually large diameter and may be set with the ”spudding” arm on the rig (The spudding arm drives in the casing.). The primary purpose of the conductor casing is as a flow line to allow mud to return to the pits and to stabilize the upper part of a hole that may be composed of loose soil. The depth of the conductor pipe is usually in the range of 50-250 ft with the depth set by surface rocks and soil behavior. It also provides a point for the installation of a blow-out preventer (BOP) or other type of diverter system. This allows any shallow fluid flows to be diverted away from the rig, and is a necessary safety factor in almost all areas. In areas with very soft and unconsolidated sediments, a temporary outer string, called a stove pipe, may be driven into place to hold the sediment near the surface. The well is drilled out from the conductor pipe to a depth below the shallow fresh water sands. The surface casing string is run through the conductor pipe and has three basic functions: (1) it protects shallow, fresh-water sands from contamination by drilling fluids, (2) prevents mud from being cut with brines or other water that may flow into the wellbore during drilling, and (3) it provides sufficient protection of the zone to avoid fracturing of the upper hole so that the drilling may proceed to the next casing point. This surface casing is cemented in place over the full length of the string and is the second line of safety for sealing the well and handling any high pressure flow. The intermediate string is the next string of casing, and it is usually in place and cemented before the higher mud weights are used. It allows control of the well if subsurface pressure higher than the mud weight occurs and inflow of fluids is encountered. This inflow of well fluids during drilling or completion of the well is called a kick and may be extremely hazardous if the flowing fluids are flammable or contain hydrogen sulfide (sour gas). The intermediate casing may or may not be cemented in place and, if not cemented, may be removed from the well if an open-hole completion is desired. If a casing string is not hung from the surface, but rather hung from some point down hole, it is called a “liner”. In most wells, the top of the liner is cemented in place to provide sealing. The top of the liner is set inside an upper casing string. The section where the liner runs inside another string is the overlap section.
Production liners are permanent liners that are run through the productive interval. On some occasions] they may be run back to surface in a liner tieback operation. The tieback consists of a downhole mechanical sealing assembly in a hanger into which a linear string or the tie back string is “stabbed” to complete the seal. A cement job seals the liner into place in the casing and prevents leakage from the formation into the casing. The lower part of the casing string, into which the liner is cemented, is called the overlap section. Overlap length is usually only enough to insure a good seal, typically 300 to 500 ft. Overlap length may be longer where water or gas channeling would create a severe problem. Liners are run for a variety of reasons. If the operator wants to test a lower zone of dubious commercial quality, a liner can be set at less expense than a full casing string. Also, in lower pressure areas where multiple strings of pipe up to the surface are not necessary to control corrosion or pressure, the liner can be an expense-saving item. In wells that are to be pumped by ESP’s (Electric Submersible Pumps), the liner through the production section leaves full hole diameter in the casing string above the pay for setting large pumps and equipment. The production casing, or the final casing run into the well, is a string across the producing zone that is hung from the surface and may be completely cemented to the surface. This string must be able to withstand the full wellhead shutin pressure if the tubing or the packer fails. Also, it must contain the full bottomhole pressure and any mud or workover fluid kill weight when the tubing or packer is removed or replaced during workovers. The decision on whether to cement the full string is based on pressure control, economics, corrosion problems, pollution possibilities and government regulations. Casing Clearance The necessary clearance between the outside of the casing and the drilled hole will depend on the hole and mud condition. In cases where mud conditioning is good or the mud is lightweight and the formations are competent, a clearance of 1.5 in. total diameter difference is acceptable. For this clearance to be usable, the casing string should be short. Primary cementing operations may not be suc-
2-3
cessful in this clearance and cementing backpressures will be high. A better clearance for general purpose well completions is 2 to 3 in. For higher mud weights, poorer mud conditioning, poor quality hole and higher formation pressures, clearance should be increased. For more information on hole quality and sticking, review the chapter on Drilling the Pay. Excessive clearances should also be avoided. If the annular area is too large, the cement cannot effectively displace the drilling mud. A reference for hole size and casing size for single or multiple string operations are shown in
Figure 2.2.2The solid lines indicate the common biffcasing combinations with adequate clearance for most operations. The dashed lines indicate less common (tighter) hole sizes or bitkasing combinations. Long runs of casing through close clearance holes usually leads to problems. Tight clearances should be avoided where possible.
(Oil and Gas Journal)
Figure 2.2:
This chart can be used to select the casing bit sizes required to drill most drilling programs. To use the chart, select the casing or liner sire to be used and enter the chart at that sire. Follow the solid lines to select the applications. The holelcasing combinations linked by the dashed lines are close clearance and require special techniques. They should be avoided. The deepest casing is chosen first and the bit and casing program is built in reverse (toward the surface from the maximum depth).
2-4
Connections The threaded connection of casing or tubing is important because of strength and sealing considerations. The connections are isolated pressure vessels that contain threads, seals and stop shoulder^.^ The fluid seal produced by a connection may be created in the threads by a pipe dope fluid or by a metal or elastomer seal within the connection. Strength of the connection may range from less than pipe body strength to tensile effciencies of over 115% of pipe body ~ t r e n g t hThreads .~ are tapered and designed to fit a matching thread in a particular collar. In the API round thread series, the connection may be either short thread and coupling (ST&C) or long thread and coupling (LT&C) as illustrated in Figure 2.3. If the thread is an eight round, it means eight threads per inch. The length description refers to the relative length of the coupling and the amount of pipe that is threaded (the pin). Creation of a pressure tight seal with an API round thread requires filling the voids between the threads with a sealing compound (thread dope) during makeup of the joint.
Figure 2.3:
Left: Cut away coupling view of a long thread and coupling joint (LT&C), round thread. Right: Close-up of the joint connection showing relative thickness of metal and position of threads. Seal is formed with pipe dope in the threads.
Although the standard 8-round threaded connection is reasonably strong, it does not approach the strength of the body of the pipe. As tensile loads increase toward the limit of the pipe, the connection will normally fail by shearing off the threads from the pipe or by thread jumpout caused by pipe deformation under severe loads. To make a stronger joint in tubing, a thicker (larger outside diameter) section is left at the end of the pipe so that threads can be cut without making the wall thickness of the pipe thinner than in the body. This form of connection is called external upset or EUE, Figure 2.4. Its inside diameter is the same as the pipe. A nonupset, or NU pipe and several other joint types are shown in Figure 2.5 The outside diameter of the EUE joint is larger than the NU connection, and the coupling or collar is normally manufactured on the pipe. Another method of increasing the strength of the threaded connection is by upsetting the connection to the inside of the pipe. This internal upset restricts the inside diameter of the pipe at every joint and is only used in drill pipe where a constant outside diameter is necessary. Other sealing surfaces are available in special connections and have found popularity where rapidly made, leak free sealing is important. The two-step thread connection uses two sets of threads with a metal sealing surface between. In other connections, a groove at the base of the box may contain an elastomer seal. A variety of connection types and sealing surfaces are available, Figure 2.5. The disadvantage to the numerous thread and sealing combinations is that the connections cannot be mixed
2-5
pin end
r
box end
outside of pipe
- - - * A + " ~ .
constant inside diameter
Figure 2.4:
Cut away drawing of an external upset connection (EUE).
(World Oil Tubing Tables)
Figure 2.5:
Examples of patented or specialty pipe connectors. Tubing and Casing examples are shown.
in a string without crossovers (adaptors). A more detailed discussion of connections are available from other sources.14 Casing Weights and Grades
Common casing diameters range from less than 4-1/2 in. to over 20 in., and common tubing sizes are from 3/4 in. to over 4-1/2 in. In some high rate wells, tubing may be 5-1/2 in. to over 7 in. and 2-7/8 in. casing is run in tubingless completions. After the size is determined, the grade of the steel must be selected. The grades, along with weight, are based on pressure and corrosion requirements. The grades of steel used in oil industry tubulars are shown in the following table for API and non-API sizes. The letters are assigned only to avoid confusion. Grades N-80 and stronger are considered high strength steels. Use of the higher strength steels increases cost and decreases resistance to some forms of corrosion. Use of the very hard
2-6
alloys, such as V-150, makes packer setting difficult since the slips have difficulty setting in the very hard steel of the casing. API Grades
Minimum Strength (psi) Yield
I
Ultimate
The yield and burst strength values for each casing size and weight are available from detailed tables are used for selection of casing once the necessary strength calculations are made. Often, because of economics or efforts to lighten the casing string, lower grade or lighter weight casing may be considered. Because the weight and pressure loads on a casing string change from top to bottom, a well designed string may incorporate several weights and grades of casing. Casing Design Safety Factors
The design criteria for casing strings depends on the intended use and anticipated stresses. Because variance exists in both pipe manufacture and formation properties, safety factors must be incorporated into a design. The common ranges for safety factors in normal completion are shown b e l ~ w . ~ ~ ~ ~ Factors such as salt flows,7 very high pressures, sour service,8 reservoir compaction loads,g and thermal cycling'0 may change the safety factors. tension burst collapse
1.6 to 1.8
1.25 to 1.30 1.O to 1.25
Earth shift forces, such as salt movement or other faulting and folding events caused by tectonic movement or are very difficult to address with a traditional safety factor. These forces have been successfully offset in some cases by designs using very heavy wall pipe or concentric pipe (casing cemented inside casing) over the affected zone. These types of casing designs are rare and most are generated by a series of trail and error approaches. Load Description
The casing string must be designed for any load encountered from mud or reservoir fluids in placement or during any phase of stimulation or production. The common forces are tension during running, internal pressures during drilling, completion or production, and external pressures caused by drawdown, mechanical loads, and zone pressures. These loads are tension, burst, and collapse. The loads are often applied simultaneously in different parts of the string, and the forces may interact. The tension design of the casing string is made as if it were hanging free in air. A safety factor of 1.6 to 1.8 is applied to make allowances for a number of other tension factor^.^*^^'' These factors are briefly discussed in the following paragraphs. Collapse, burst, and tension forces are explained separately, but all must be satisfactorily accounted for in the final design. The design methods in this book
2-7
result in a conservative design. Each design method is based on the worst possible case that could occur during running.
’
Collapse loading is force applied from outside the casing by either fluid pressure in a zone or earth shift forces. Forces from fluid pressure are collapse loadings while earth shift forces produce mechanical crush loadings. The largest collapse load from fluid pressure will usually be exhibited at the bottom of the string where hydrostatic pressure is greatest. The exception is an isolated, very high pressure zone. These zones are usually noted on the drilling record as places where kicks are taken. The occurrence of earth shift zones from faults or salt movement are much harder to locate, especially on wildcats but may often show up on the drilling record as sticking points (not associated with mud cake buildup) or zones that have to be reamed or redrilled to get back to gauge hole size. The occurrence of salt zones are a very important tip to potential casing problem^.^ In one study area, 87% of the wells around a salt dome suffered some casing diameter reduction due to external, earth shift force. In the collapse design for fluid pressure, the worst case loading occurs with the unlikely combination of an empty casing string in a hole full of mud. A proper design, for effects of collapse only, would be a casing string that is strongest at the bottom and weakest at the top. Collapse is also affected by the effects of tension, which reduces the collapse rating or the “set depth limit” of the casing. As an object is pulled, it is more likely to lose diameter as it stretches in length. This thinning is a force in the same direction as collapse forces. Fortunately, the point at which the effect of tension induced “narrowing” of the string is at maximum is at the surface where effects of collapse pressure from hydrostatic pressure are the lowest. Burst pressure is a force applied from inside the casing by produced fluid pressures, hydrostatic mud load or addition of surface pressure during stimulation or workover operations. Since there is usually mud hydrostatic pressure along the outside of the casing before and during cementing, the net pressure or the difference between the pressure inside the casing and outside the casing will be used in the design of the casing. Unlike collapse, however, the shallower casing section is also important in the burst calculations from a safety standpoint. Burst pressures exerted by produced fluids are maximum at the surface (no offsetting hydrostatic load), while those exerted by mud is maximum at the bottom of the well. During fracturing, high burst loads may be exerted all along the string. Because collapse loads offset the burst load at the bottom of the string, the burst calculation is usually important above the “buoyancy neutral point.” This will be developed later. Tension is a force produced by the weight of the casing, the pressure differential, and the mud weights inside and outside the casing. It is largest at the top of the string and decreases with depth toward the bottom of the string. The tension load is partially offset by the buoyancy of the string in mud and is affected by pressure. When the pressure inside the tube rises, the pipe diameter is expanded and the length shortened or the tension is increased in a pipe that is anchored to prevent upward movement. When the pressure outside of a tube rises, the tube is elongated or the compression is increased if the ends are fixed, Figure 2.6. Buckling failure in casing usually results from axial compression (lengthwise) overloading. The load produces ridges in the casing walls or corkscrewing of the tube. Either of these actions relieve compression, but the pipe is usually permanently yielded. The effects of buckling, Figure 2.7, is critical on the design of the casing string. The neutral point, Figure 2.8, is the dividing line between where buckling may occur and where it cannot occur in a tube that is evenly loaded around its radius. Above the neutral point, the tube is in tension and will not buckle. Below the neutral point, the upward buoyancy of the mud and other forces including pressure and mechanical loading place the tube in compression. Buckling can occur if the compressive load is more than the pipe can tolerate in the wellbore surroundings. The following information describes the neutral point, first in a theoretical manner and then in a practical way. There can be a neutral point in the casing or tubing string described by the formula:’*
2-8
-HIGH
-LOW PRESSURE
PRESSURE
REVERSE W N I N G The tubing will rhomn if k Is frw to mow or it will c m t i I tinsion forts on thr packer if it Is m strainad from moving.
Th. tubing will kngchrn if k I$ fm to mow or It will cram I mmp d v e f o m on thr packer if k Ir mtraind from moving.
(Guiberson)
Figure2.6:
Effects of external and internal pressure on length change in a tube. NEUTRAL
COIN7
U 111
Figure 2.7:
(Harnrnerlindl, 1977)
Exaggerated view of tube buckling below the neutral point.
Fz $ PiAi- PoAo where:
(or axial force rating of the tubular)
Fz
= true axial force
Pi
= pressure inside tubular, psi
Ai
= cross-sectional area of ID, in.*
2-9
Y
Figure 2.8:
(Hammerlindl, 1980) Stress distributions of a tube under various conditions.
PO
= pressure outside tubular, psi
A,
= cross-sectional area of OD, in.*
When F, is algebraically greater than the right-hanc side of the equation, the pipe tends to be straldht. When F, is less than the equation, the pipe tends to buckle. When F, is equal to the equation, the neutral point is reached. The right-hand side of Eqn. (2.1) may also be referred to as the stability force. The true axial force will vary from point to point in the string, and will also vary over the life of the well. Typical considerations necessary to compute F, include the conditions at the time of cementing the casing or setting the packer in the case of tubing, as well as changes in the environment (temperature and pressure) to which the tubular is exposed. For casing, buckling primarily affects wear, particularly for intermediate strings through which additional drilling will occur. In extreme cases, splitting may also be common. For tubing, the radial clearance between tubing and casing is usually sufficient to allow corkscrewing, often producing permanent deformation of the buckled portion of the string. A special case expression for F, uses Poisson's ratio:
Fz = 2pPiAi where:
p
= Poisson's ratio, about 0.3 for this application
This equation is only appropriate for an open ended tube, clamped at both ends, with PO= 0 and A T = 0 , and ignoring weight. Under the unlikely conditions of a weightless string with no outside pressure, buckling in tension is possible. To illustrate the impact of Eqn. 2.2, consider a weightless tube that is open ended and subject to internal pressure only. For this loading, the only axial force is that due to ballooning given by Eqn. 2.2 and shown previously in Figure 2.6. As the inside pressure is increased, F, increases as 2pPjAis but the right hand side of Eqn. 2.1 increases as PjAi. The tube will not only buckle immediately, but will also buckle in tension. The stability equation is also reported as:12 =
Fa+ PiAi- PoAo
where:
2-10
Fs Fa
= stability force = axial load
In relating this equation to Eqn. 2.1, Fs = -[F, - (PiAi) - (PoAo)]and F, = -Fa. Each zone or section of the casing string is checked for tensile requirements following collapse and burst calculations. In case of corrections made to a string design to compensate for tension load requirements, the order of selection is usually: (1) stronger connection, (2) higher grade (stronger steel), and (3) higher weight. Increasing connection strength and steel grade is preferred since they increase total string strength without adding significant weight. There are so many “premium” connections available that it is difficult to present a comprehensive data set. Tables of connection specifics are published yearly.37 For the sole purpose of casing collapse strength derating due to the effects of tension, a practical “buoyancy neutral point”, designated N.P., can be estimated by Eqn. (2.4) where:
N.P.
=
.(I-&) (2.4)
where: N.P. = the “neutral point” for tension effects on casing collapse, ft 0, = settling depth of casing string, ft prn = mud density, Ib/gal 65.4 is the weight of steel in Ib/gal based on a density of 489.5 Ib/ft3 The collapse resistance values given in the manufacturer tables are for casing that is not affected by axial load. In a well, the casing will be stressed by fluid pressures, Figure 2.9, mechanical bending forces, Figure 2.10, and tensile forces produced by the hanging weight of the casing. In collapse calculations, axial tension produces a reduction in collapse resistance. For purposes of this example, the axial tension is assumed to be from tension loads on a straight, free hanging pipe and not from bending loads.
The equivalent yield strength, Ypal is:’5 x
Y,,,
[ ( 1 - 0.75 ( o,/ Y,,) 2,
’
’2
- 0.5 (CTJ Y,,) ] Yp
where: CT, = axial
stress, psi
Yp = minimum rated yield strength of casing, psi The percent of yield stress may be calculated by:
Yr =
st -
Yrn
2-11
Figure 2.9:
Schematic of the location 0.Jxial (03,tangential (03 and radial (or) stresses on a vertical suspended tube exposed to fluid pressure. tension from hook loads
!
Figure 2.10:
Loads on a casing string during running and on casing landed in a curved section of the borehole.
where: Y,
= percent of yield stress
S,
= unit tensile stress, psi
2-12
tension fmhook loads !
i tension from casing below
Ym
= minimum yield stress of casing body, psi
The percent yield stress is related to percent of full collapse pressure by the curve of Figure 2.11. The product of the percent of collapse and the collapse rating is the effective collapse strength (derated for effects of tension). Because of buoyancy effects, tension only exists above the buoyancy neutral point calculated by Eqn. 2.4. The effects of compression below the buoyancy neutral point increase the casing collapse resistance although the increase is not accounted for in this design.
K
gr0 f
'.
TENSION LOAD BODY YIELD STREETH
(from Halliburton)
Figure 2.11:
Effect of axial tension on collapse strength of casing. The Y,vaiue is used in the collapse derating calculation.
2-13
Designing for forces involving earth shifts, highly deviated hole, sticking, reciprocating and rotating casing while cementing or running stresses, involves field optimization and the criteria for design differ from company to company. Earth shift design usually involves multiple strings of pipe or very heavy wall pipe across the problem zone. Problem zone recognition can often be made from drilling records where bit dragging (nonassociated with mud cake buildup) occurs long after a zone is drilled. Wells near salt domes or flows are considered likely prospects for formation movement.
Casing String Design A complex solution (API method) requiring computer solution is discussed first, followed by a practical, hand calculated method. API Equations
Collapse strength rating is the external pressure required to collapse the casing. There are several methods for designing casing strings that will produce an acceptable casing design. Most methods use an x-diagram graphical approach or a calculated design based on a single strength concern in each area of design. The API procedure recognizes the changes in steel behavior in elastic, transition, plastic, and ultimate yield. The procedure illustrated here for determining the collapse strength is defined in API Bulletin 5C3.15 This casing design section is merely an introduction to the process. For a complete treatment, refer to Rabia's Fundamentals of Casing Design.14 When exposed to external pressure from mud or reservoir fluids and the effects of axial tension from the weight of the casing below any point (plus other loads)," a piece of casing may fail in one of three possible collapse mechanisms: elastic collapse, plastic collapse, and failure by exceeding the ultimate strength of the material. Each failure mode is bounded by limits of the ratio of casing diameter to thickness, plus a transition collapse formula was added arbitrarily since the API minimum elastic and rninimum plastic curves do not intersect. The transition formula covers this area. The API minimum collapse resistance equations are shown in Figure 2.12.15 Figure 2.1215
Applicable D range
1. Elastic
t
46.95x 1O6 p c = D ( D ,)2
D,2+
BIA
t - 3BIA
t 7-
2. Transition
YP(A-F) D<2+BIA <-C+ Y P ( B - G ) - t 3BIA
2-14
3. Plastic [(A-2)2+8(B+C/YP)]1/2+
(A-2)
2 ( B + C/YP)
pp
D
575
YP(A-F) C + YP(B-
G)
(2.9)
4. Ultimate Yield (A-2)2+8(B+CIYP)1/2+(A-2) 2(B+ClYP)
l i l
1 (2.1 0)
where:
A
=
2.8762 + 0.10679 x 10-6 YP+ 0.21301 x lO-'OYP
B
YP
C
=
=
=
- 0.53132 x 10-l6 YP3
0.026233 + 0.50609 x 10-6 Y P
(2.11) (2.12)
minimum yield strength of the pipe, lb
- 465.93 + 0.030867 YP- 0.10483 x 10-7 Y p - 0.36989 x 10-13 YP3
(2.1 3)
-
(2.1 4)
G
=
FBIA
(2.1 5)
The effect of addition of axial tension to a casing string has a net effect of reducing the yield stress of the pipe. The reduction may be severe enough to cause a derating of the pipe by a full grade, e.g., N80 to C-75. The yield strength, Ypa, of the axial stress equivalent grade is:14
Ypa = ( ( 1 - 0.75 (oa/Y P )2,
1 / 2 - 0.5
where: Ypa
= yield strength of axial stress equivalent, psi
2-15
(Gal YP) ) YP
(2.1 6)
YP
= minimum body yield strength of the pipe, Ib
0,
= axial stress, psi
Axial loads generally result from two forces: 1. hanging weight of the casing string 2. temperature induced forces in thermal wells and in nonthermal wells where operating tempera-
tures may change by over 100°F. Buoyancy
When the hole is filled with cement or mud, there is a buoyancy force exerted on the casing by the fluid in the hole and opposed by the fluid in the casing. Buoyant force acts on the entire casing string and results in a reduction in hanging weight. The amount of buoyant force exerted by the mud is equal . to the weight of the mud displaced by the submerged casing. The weight of steel at 489.5 Ib/ft3 or 65.4 Ib/gal, is several times the heaviest mud weight, yet the buoyant contribution of the mud is a significant factor in the hook load during running and cementing of the casing. Hook loads change dramatically during running and cementing operations and conditions do exist (running closed end casing, dry) where hook load could diminish to zero (the casing floats). Buoyant weight, Wb, for an open-ended casing string of air weight W,, filled and surrounded by one fluid. is:
(2.17) where: pf
= density of the fluid
ps
=
density of the steel, 489.5 Ib/ft3 or 65.4 Ib/gal
When the fluid in the casing is different from the fluid outside the casing, the volumes contained in the casing and displaced by the casing must be calculated and the weights summed against the air weight of the casing. For the special case of an additional surface pressure such as holding pressure on the mud in the casing while cement sets in the annulus, the surface pressure is incorporated with the load produced by the mud. The buoyant force, FB,applied to the air weight of the casing becomes:
FB
=
[ (Pis- 0.052pjd)Ai- (PO,+ O.052p0d) A,]
where: FB
= buoyancy force, Ib
= surface pressure on fluid inside casing, psi (usually zero) pi, PO, = surface pressure on fluid outside casing, psi (usually zero) = density of fluid inside casing, Ib/gal pi
2-16
(2.1 8)
po
= density of fluid outside casing, Ib/gal
Ai
= inside area of casing, in.2
A,
= outside area of casing, in.2
d =depth, ft The pressure terms affect buoyancy much the same way as pressure affects tubing forces. Example 2.1
A 10,000 ft string of 7 in., 26 Ib/ft, N-80 casing is run in a hole filled with 12 Ib/gal mud. The string is equipped with a float shoe. Calculate: a. hook load of an empty, closed end, casing string in mud. air weight = (10,000 ft)(26 Ib/ft) = 260,000 Ib displaced volume of mud = E ( d ) X depth = 4 displaced weight of mud = (2673 ft3)
[12$)(
a( &)'
(1 0,000)
=
2673 ft3
7 . 4 8 5 ) = 239, 928 Ib
The displaced weight of the mud is a force acting upward on the casing, trying to float it out of the well. It has the effect of trying to lighten the total load. hook load = 260,000 - 239,928 = 20,062 Ib (this ignores the weight of air) b. hook load of a mud filled string in mud (same mud weights inside and outside). Since the only action is on the cross section of the steel body, the buoyancy factor difference formula is adequate.
6,- [I-:)
=
1-
=
0.817
489.5-lb
ft3
wb = (260,000
lb) (0.817)
=
212,420 lb
c. hook load of 16 Ib/gal cement filled string in mud. total buoyant wt. = wt. of casing in air + wt. of cement - buoyancy of displaced mud. wt. cement = (x/4)(6.276 in.)2 (16 Ib/gal) (0.052 gal/ft in.2)(10,000 ft) = 257,382 Ib
2-17
buoyancy force = 239,928Ib (from part a) total buoyant wt. = 260,000 + 257,382- 239,928= 277,455Ib The effect of gas density is usually ignored for hanging weight or buoyancy calculations. It will be considered, however, in hydrostatic calculations.
-
Collapse Design Non-API Method A practical method that considers burst, collapse, and tensile forces is also available. This method may be worked by equations or by graphical methods. The design is conservative in collapse resistance because of the basic assumptions of an empty string in a hole full of mud. In practice, most casing strings are filled with mud as they are run. The design begins at the bottom of the string. The collapse force produced by fluid pressure from a homogeneous fluid in the well and an empty casing string is:
(2.1 9) where: Pcx = collapse pressure at a depth D,, psi = density of the fluid on the outside of the pipe, Ib/gal pf = depth at the point of calculation, ft D,
The forces can be visualized graphically by the methods of Figures 2.13 through 2.18.35 b
(Hills) Figure 2.13: Graphical collapse force analysis.
When the effects of a different fluid, such as cement, inside the pipe is considered, the equation becomes:’ 6*1
P, Pcx PO
( P O+ D,G,)
- ( P i + D,GJ
= collapse pressure at a depth Dx, psi
= external surface pressure, psi (usually zero)
2-18
(2.20)
(Hills)
Figure 2.14: Graphical burst force analysis.
Figure 2.15: X-Graph design method. Alternative casing design.
(Hills)
Figure 2.16:
Graphical method for tension analysis.
D,
= depth of calculation, ft
Go
= pressure gradient exerted by the fluid outside the pipe, psi/ft
pi
= internal surface pressure, psi
Gi
= pressure gradient exerted by fluid inside pipe, psi/ft
The external surface pressure, PO,is used where there is an outer casing string and an annular pressure will be exerted. This technique is commonly used to “back up the tubing” and increase burst
2-19
(Hills) Figure 2.17: Graphical method for over-pull analysis.
(Hills)
Figure 2.1 8: Graphical buoyancy analysis.
resistance of the inner string. It may also be used in some casing designs. Because outside surface pressure is rare, the term is generally dropped. It is customary to design the primary strings for the worst possible case. Since the worst possible case will be when the pipe is empty, the equation reduces to:
(2.21) The outside surface pressure is assumed to be zero. The design on an empty pipe string may seem excessive but it is done to eliminate consideration of triaxial forces produced by hole irregularities and other factors3 The worst possible case design, therefore, covers a multitude of other forces. Because of buoyancy produced by changes in axial load following setting of the cement, portions of the casing string may be in compression rather than tension. Casing above the point of zero axial tension has less collapse resistance, and casing below the point of zero axial tension has more collapse resistance since it is in compression. The collapse forces on a casing are usually visualized as being applied by the pressure of the mud in which the string is
2-20
run. The effect of tension in reducing the collapse strength of the casing is generally considered, but the effects of ballooning, ovality, and temperature changes during circulating are often neglected. These effects can be severe, especially in high collapse resistance casing such as some 95-grades. For the burst calculations, one of two API approved formulas may be used. For plain end (nonthreaded) pipe and pipe with premium couplings (couplings stronger than the pipe body), Barrow's formula is used.
Pv
=
0.875-
2 Y"t DO
(2.22)
where: Py Y, Do
= minimum internal yield pressure, psi
t
= nominal wall thickness, in.
= minimum yield strength, psi = nominal outside diameter, in.
The 0.875 factor allows for a 12.5% variation in wall thickness as permitted by API manufacturing specifications. For threaded and coupled pipe, the internal yield is about the same as for plain end pipe, except where low clearance couplings are used or where the coupling has less strength than the tube. In the case of lower strength couplings:
(2.23) = minimum yield of coupling material, psi Y, Do = nominal outside diameter of coupling, in. = diameter at root of coupling when pipe has been fully tightened. Di The design for the upper part of the casing string is dominated by the burst consideration. The safety aspect of controlling kicks and blowouts places a large amount of importance on controlling full well pressure in the upper sections of the string. The worst case is when a blowout occurs and the hole contains only gas. The maximum surface pressure then is the maximum formation pressure minus the hydrostatic load created by gas. As a simplification, the mud hydrostatic pressure is taken as the reservoir pressure (unless the reservoir pressure in known).
(2.24) Ps prn Dt
Gg
= maximum well shut-in pressure = density of mud, Ib/gal
= depth of kick, ft = gas gradient, psi/ft (varies from 0.1 to 0.15 psi/ft based on pressure)
In most cases, the potential problem area will be at the casing shoe. The pressure at the shoe can be calculated from:
2-21
‘bx
=
(2.25)
Pbx = burst pressure exerted at depth D,, psi Q = formation breakdown gradient, usually from 0.7 to 1.O psi/ft D, = casing setting depth, ft D, = depth where fb, is being determined, ft
To determine the worst case burst pressure exerted during a blowout with gas in the hole, the external pressure is subtracted from the previous equation. pbx = GbdDc-
GgC D,- Dx)- 0.052p,Dx
(2.26)
where po equals external fluid density in Ib/gal. Burst force design may also be considered graphically, Figure 2.14.35 Eqn. 2.26 can be used to make the start of the X diagram of Figure 2.1 5. The X diagram is constructed by collapse and burst c a l c ~ l a t i o n s . ’The ~ ~ ~maximum ~ burst line is drawn between the calculated burst at the surface and the calculated burst at the casing shoe. The collapse line is drawn between U and the maximum collapse pressure at the casing shoe, calculated by Eqn. 2.24 or 2.25. Tension design is the last step for each section of the casing string. The top of each section should be checked to see that the tensile ratings are not exceeded. The common safety factor is 1.6 to 1.8. When the tensile limits are exceeded, a change to a higher strength joint should be made. Tension limits may be gathered from a table of casing properties or calculated by dividing the API 5C3 value for joint strength by the safety factor.
-
Example 2.2 Single String Casing Design
Design an economical casing string that will satisfy the pressure requirements of collapse and burst, and the load requirements of tensile force. Strings increase in cost with increasing grade and weight. A packer will be set within 100 ft of the bottom of the well. The string must be designed to allow packer running and setting. It must also allow efficient well operations. Design for an annulus full of mud and an empty string; these are the worst normal conditions. Casing Safety Factors: Collapse 1.l, Burst 1.25, Tensile 1.7 Data from Well file: A 10-3/4 in. surface string has been landed and cemented at 450 ft. Depth = 7600 ft Mud wt = 12 Ib/gal bit size = 8.75 in. Frac gradient = 0.77 psi/ft straight gauge hole Reservoir pressure = 0.56 psi/ft water base mud Buoyancy Neutral Point for collapse calc.
2-22
Bottom hole pressure
=
( 12) (0.052) (7600 ft)
=
4742psi
Maximum collapse pressure (from the mud column) is:
P
=
(12 lb/gal) (0.052 gal/in.2/ft) (7600 ft)
~ ~ X B H
2-23
=
4742 psi
Pick a casing grade and weight that has a collapse rating in excess of [(4742) (1.1)] = 5216 psi The casing data on size, weight, grade, burst, collapse, body tensile and joint tensile are obtained from pipe books. A partial table for 7 in. casing from one pipe manufacturer is shown in Figure 12.1 9.
L80* 5595s 595. CYS95* C95* PllO
4320 5250 5410 5410 7800 7800 7800 5070 6210
4980 6790 7240 7240 1240 8600 8600 8600 9950
4980 6790 7240 7240 7240 8600 8600 8600 9960
364' 401 489 519 511 510 602 602 593 693
592 631 667 641 696 747 747 122 853
29.00 C75 N00* 29.00 29.00 LOO* 29.00 SS95* S95* 29.00 29.00 CYS95* 29.00 C95+ 29.00 5105. 29.00 PllO 29.00 V150
6760 7020 7020 9200 9200 9200 7820 9700 8510 9800
7650 8160 8160 8160 9690 9690 9690 9690 11220 15300
7650 7650 8160 8160 8160 8160 8160 8160 9690 9690 9690 9690 9690 9690 9690 9690 11220 11220 15300 15300
562 597 587 655 692 692
707 746 718 779 036 836 800 859 955 1243
32.00 C75 32.00 N80* LEO* 32.00 32.00 SS95* 32.00 S95* 3 2 - 0 0 CYS95S 32.00 C95* 32.00 S105* 32.00 PllO 32.00 V150
8230 8600 8600 10400 10400 10400 9730 11340 10760 13020
8490 9060 9060 9060 10760 10760 10760 10760 12460 16990
8490 9060 9060 9060 10760 10760 10760 10760 12460 16990
7930 8460 0460 8460 10050 10050 10050 10050 11640 15870
35.00 C75 35.00 N8O* 35.00 100* 35.00 SS95* 35.00 S95* 35.00 CYS95* 35.00 C95* 35.00 SlOS* 35.00 PllO 35.00 Vl50
9710 10180 10180 11600 11600 11600 11640 12780 13010 16230
9340 9960 9960 9960 11030 11830 11830 11830 13690 18670
8660 9240 9240 9240 10970 10970 10970 10970 12700 17320
7.000 7.000
38.00
7.000
38.00 38.00
10680 11390 11390 12700 12700
10120 10800 10800 10800 12820 12820 12820 12820 14850 20250
8660 9240 9240 9240 10970 10970 10970 10910 i2700 17320
7.COO 7.000 7.000 7.000 7.000 7.000 7.000 7.000 7.000
26.00 26.00 26.00 26.00 26.00 26.00 26.00 26.00 26.00
7.000 7.000
7.000 7.000 7.000 7.000 7. COO 7.COO 7.000 7.000
7.000 7.000 7.000
7.000 7.000
7.000 7.000 7.000 7.000 ?.COO 7.000 7.000 7.000 7.000
7.000 7.000 7.000 7.000 7. COO 7.000
7.000 7. coo 7.000 7.COO
38.00 38.00 38.00
7.000
38.00 38.00
7.000 7.000
38.00
K55* C75
N8O*
C75 N8O* L8O* 5595. 595. CYS95* C95* S105*
38-00 P l l O V150
12700 13420 14040 15110 19240
4980
.
4980 6790 7240 7240 7240 8600 8600 8600 9960
415 -362 566 -362 604' -362 60* -362 601 -362 717 -362 717 -362 117 - 3 6 2 830 -362
6.276 6.276 6.276 6.276 6.276 6.276 6.276 6.276 6.276
6.151 6.151 6.151 6.151 6.151 6.151 6.151 6.151 6.151
634 676 676 676 803
929 - 4 0 8 1267 - 4 0 8
6.184 6.184 6.184 6.184 6.184 6.184 6.184 6.104 6.184 6.184
6.059 6.059 6.059 6.059 6.059 6.059 6.059 6.059 6.059 6.059
812 891 768 947 897 1053 1180 1370
'699 745 745 745 885 985 805 885 1025 1398
6.094 6.094 6.094 6.094 6.094 6.094 6.094 5.094 6.094 6.094
5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969
7930 8460 8460 8460 10050 10050 10050 10050 11640 15870
703 833 746 076 734 833 819 876 865 964 865 964 853 920 901 964 996 1096 1 3 1 1 1402
814 814 814 966 966 966 966 1119 1526
-498 -498 .498 -498 -498 -498 .490 -498 -498
7930 8460 8460 0460 10050 10050 10050 10050 11640 15870
767 833 814 876 8 0 1 833 894 876 944 964 944 964 931 920 983 964 1087 i 0 9 6 1430 1402
822 877 877 077 1041 1041 1041 1041 I205
-540 -540 -540
C83 721 797 1049
633 672 661
779
823 791 860 922 922
738 779 779
.
,
-408 -408
-408 -408 -408 803 - 4 0 8 803 -408 803 - 4 0 0
-453 .453 -453 .453 -453 .453 -459 .453 -453 -453
763 - 4 9 8
-240
-540 -540 .540 -540 -540 1644 -540
6.004
6.604 6.004 6.004 6.004 6.004 6.004 6.004 6.004 6.004
I
'
,
5.879 5.879 5.879 5.879 5.879 5.079 5.879 5.079 5.879 5.879
5.920 5.795 5.920 5.795 5.920 5.795 5.920 : 5.795 5.920 5.795 5.920 5.795 5.920 5.795 5.920 5.795 5.920 5.795 5.920 5.795
(Lone Star Steel)
Figure 2.19: Casing strength tables from one manufacturer. The largest casing that can easily be run in the 8.75 in. hole is 7 in. To satisfy collapse pressure requirements, pick 26 Ib/ft C-75 as a first choice, collapse = 5250 psi. The first casing will extend from the bottom of the well upwards to a point where a weaker (lower grade or lighter weight) and cheaper string can be run. That point depends on the pressure rating of the second string. Several small jumps in weight or grade can be made or just a few large changes. The route depends more on economics and inventory available than on a scientific selection process. Second casing pick is 23 Ib/ft C-75, = 3427 psi. How deep can the 23 Ib/ft casing collapse = 3770 psi derate for safety factor = [3770/1.l] be set? D, = 3427/(12)(0.052) = 5492 ft.
2-24
The 26 Iblft C-75 (the bottom string) has an initial design length of from 5492 ft to 7600 ft; however, the collapse rating of the upper string (the 23 Ib/ft C-75), must be derated for the effects of tension since it is above the neutral point. The 26 Ib/ft casing is not derated for collapse since maximum collapse pressure is exerted at the bottom of the well where the casing is below neutral point and in axial compression (which opposes collapse forces). To derate the collapse rating of the upper string for effects of tension: 1. Derate the set depth of 5492 ft slightly; typically 2% to 4% will do. 5400 ft will be used here.
2. Calc. unit tensile stress, St = (6206 ft - 5400 ft) (26 Ib/ft) = 20,956 Ib. 3. Axial load factor, X, = (20,956/499,000) = 0.042, derating factor, Yr, = 0.99 (from Figure 2.11) 4. The derated collapse (for effects of tension) of the 23 Ib/ft = 3427 x 0.99 = 3392. 5. Collapse pressure at 5400 ft = (5400)(12)(0.052) = 3370 psi.
The 3370 psi collapse pressure is less than the 3392 psi collapse rating (derated for safety factor) on the 23 Ib/ft pipe so the pick of 5400 ft as max set depth is a good one. The bottom of the 23 Ib/ft string sets the top of the 26 lblft casing. The set points of the 26 Ib/ft are 7600 ft to 5400 ft. The lesser of the two will almost always be the difference of the pore pressure and the gas gradient. In special cases where high stimulation pressures must be handled, the stimulation pressure may be selected as the design criteria. Since the top of the 26 Ib/ft is above the neutral point, the burst design begins to govern. The 23 lblft will also be checked for burst to see how shallow it can be safely set. For a burst design, a surface pressure is needed. Use lesser of: Max pressure at surface = frac press at bottom - gas grad. P S m a = [(7600 ft)(0.77 psi/ft)-(7600)(0.1 psi/ft)] = (5852-760) = 5092 psi
or Max pressure at surface = pore pressure - gas gradient PSm, = [(7600 ft)(O.56 psi/ft)-(7600)(0.1 psilft)] = 3496 psi Since the 3496 psi is the highest likely pressure while running pipe (before cementing), it will be used for my design. There will be many cases where the pore pressure is not known. In these cases, use the mud weight to approximate the pore pressure.
Burst Design (The burst rating of 23 Ib/ft C-75 = 5940 psi) The shallowest that the 23 Ib/ft can be set is:
3496 - (594OD.25) Dx = (0.624 - 0.1 ) Since the value of from 5400 to 0.
- 3496 - 4752 < (0.524)
D, is less than zero, the 23 Ib/ft C-75 can be set to surface. The 23 Ib/ft C-75 runs
If the fracture breakdown pressure (with gas column) had been used,
2-25
Ps,,= 5092 psi, the top of the 23 Ib/ft C-75 would have been 649 ft and 23 Ib/ft C-95 would have needed to reach to surface. Notice that a higher grade pipe was used rather than a heavier wall pipe. This allows a packer to be run from surface that would set in the 23 Ib/ft pipe. For some close clearance packers, the packer for 23 Ib/ft may not be able to pass through even one joint of heavier wallpipe that was set at the top of the well. Tensile (uncorrected for buoyancy)
Design
0 - 5400 ft
23 Ib/ft C-75
5400 ft - 7600 ft
26 Ib/ft C-75
Notice that the tensile calculations on the bottom most string only extend to the neutral point. An intermediate string is slightly different from a single production string since it may experience the burst pressures from deeper zones. Collapse forces may be felt as well if there is zone communication between the interval below the intermediate string and any zone that contacts the outside of the intermediate string. This problem is more fully addressed in the section on liners. Depending on the job conditions and assumptions, a higher pore pressure in a lower zone may have to be used for burst calculations. It is reasonable in most intermediate casing designs to verify that the burst rating (with safety factor) is adequate for the mud from the lower zone. If the cement job extends along the full length of all strings, collapse or burst forces have much less effect.
-
-
Example 2.3 Casing Design Intermediate String
Given: 13-3/8" surface casing at 2500 ft 12-1/4" hole drilled to 9500 ft Mud weight = 12 Ib/gal Future depth = 12,000 ft, future mud weight = 14.5 Ib/gal Frac gradient @ 9500 ft, = 0.884 psi/ft Design a 9-5/8" Intermediate String An intermediate string is slightly different from a production string since it will experience the collapse and burst forces encountered during the next deeper segment. If it is fully cemented, it is much less likely to fail, regardless of the pressure of produced fluid or the mud. Depending on conditions, the job design may require the intermediate string to stand the pressures of the zone below, particularly the burst. Additionally, the mud weights inside and outside the string can be considered with the formulas. 1. Determine max BHP BHP = (pd (0.052)(03 = (14.5) (0.052) (12,000) = 9048 psi the 12,000 ft depth is used to give a worst case 2. Collapse resistance design and pressures a. max. collapse pressure generated by mud wt. outside the pipe
2-26
Pcx = Dx (0.052) po- Dx(0.052) pj + ( PO- P;) po pi PO Pi
= mud density outside
pi
= 0 since the csg is empty, PO= Pi since the top of the string is at the surface and csg
= mud density inside = external surf. press. = internal surf. press.
empty Pcx = D, (0.052) po = (9500) (0.052) (12) = 5928 psi b. Neutral point (point at which load goes from compression to tension). Note: this is only usable for casing collapse calculations. N.P. = D(1-
&)
= 9500( 1
- &) =
(9500) ( 1 -0.183) = 7756 ft
You can round the 7756 value to 7760 to make calculations easier. c. Casing selection, select lightest, lowest grade. Use safety factor of 1.125 for collapse. (1) Pick 47 Ib/ft S-95, collapse = 7100 psi, burst = 8150 psi, tension (joint) = 1,053,000 psi Collapse = 7100/1.125 = 6311 psi (derated) this satisfies Pcx (2) Pick next lower strength casing, 43-1/2 Ib/ft, col. = 5600, burst = 7510, tens. = 960,000 Collapse = 5600/1.125 = 4977 psi Now:
Calculate the maximum set depth for the 43-1/2 Ib/ft section. This depth sets the top of the 47 Ib/ft section.
PC
Dx = 0.052 ( 1 2 )
=:
4977 = 7975 ft 0.052 (12)
The 47 Ib/ft casing runs from 9500 ft to 7975 ft. Since 7975 is below the neutral point of 7760, no correction is needed. To determine the top of the 43-112 Ib/ft casing string, the base of the next string must be selected. Select 40 Ib/ft S-95 collapse = 4230 psi, burst = 6820 psi, tension = 858,000 psi. Derated collapse = 4230A.125 = 3760 psi, burst = 6820/1.125 = 6062 psi (both collapse and burst are derated by safety factor of 1.125. The maximum set depth is:
Dx = PC/0.052po
=
3760/ [ (0.052) (12) ]
=
6025
ft
Since this section will be above the neutral point, the effect of tension on collapse rating must be calculated
2-27
1. Derate the 6025 ft value slightly, use 5900 ft as a first guess.
2. Calculate a unit tensile stress.
S, = (7760-5900) (43.5)
80,910 lb
Note that the weight calculated is the 43-1/2 Ib/ft pipe, above the neutral point. This is the weight that the 40 Ib/ft pipe feels. 3.
80,910 ‘ R = tensile body strength here.]
-
80’ = 0.074 1, 088, 000
[Note that tensile body strength is used
4. The derating factor, from Figure 2.11, is 0.975. 5. The collapse, derated for tension, is Pc = (3760) (0.975) = 3666 psi.
Calculate collapse pressure at 5900 ft.
P,
=
DJO.052) (p,)
=
(5900) (0.059) (12)
=
3681 psi
The guess of 5900 ft was a little too deep, but 15 psi difference is not excessive so we will keep the 5900 ft depth. The 43-1/2 Ib/ft casing runs from 7975 ft to 5900 ft. 6. Since it is above the neutral point, the burst design will dominate the casing selection. To start the burst design, calculate a surface pressure that is the lesser of: a. Fracture gradient at the 9-5/8 in. casing shoe, less a gas gradient. b. Formation pressure in the future pay (at 12,000 ft), less a gas gradient. The maximum surface pressure, P,, that the frac gradient will support is:
P,
=
Dtfg- DtGg = (9500)(0.88)
- 9500 (0.1)
=
7448 psi
For a calculation of the formation (pore) pressure’s effect on the surface pressure, use the pressure on the zone at 12,000 ft. Since all that was given is the mud weight, we use that as the formation pressure gradient. To get maximum surface pressure, subtract the gas gradient (times depth):
Ps
D f ( p f ) (0.052)-Df(O.l)
(12,000)(14.5)(0.052)- (12,000)(0.1)
7848
if this maximum pressure at the surface ever occurred, what would be the pressure at the shoe ofthe 9-5/8 in. casing?
2-28
P(at 9500 ft)
=
D,(p,)
(0.052)
- [ (0,0,) Gg]
- [(12,000-9500)
=
[(12,000) (14.5) (0.052)]
=
8798 or a gradient o f 0.926 psi/ft
(O.l)]
Since the 8798 psi is above the pressure necessary to fracture the formation at the shoe of the 9518 in., the surface pressure of 7848 psi would never occur. To proceed with burst design, use the surface pressure of 7448 psi from the frac. gradient. The shallowest depth that a casing string can be set (limited by burst) comes from: Pbx= P, P O (0.052) (0x1 b ‘x
=
7448 + (0.1) (0,) - (12) (0.052) (0,)
Q,
+ GgDx-
7448 + Dx(0.1 - 0.624)
7448 - Pbx =
0.524
The shallowest depth that the 40 Iblft pipe can be set is:
D,
=
7448-6062 0.524
=
(6062 is the derated burst of the 40 lb/ft casing)
2645 ft
as a check, the collapse pressure is: (the derated collapse was 3760 for the 40 Ib/ft casing)
P, = (12) (0.052) (2645) = 1650 psi
The 40 lblft pipe runs from 5900 ft to 2645 ft. Since the 40 Ib/ft pipe cannot be run above 2645 ft, a stronger pipe is needed. Although 43-1/2Ib/ft pipe would handle the pressure, the smaller id would restrict the packer size that could be run below it, hence, a stronger grade of pipe (at 40 Ib/ft) is needed. Since the casing tables show that a 40 Ib/ft P11 O is unavailable, the lower string design must be changed to 43-1/2Ib/ft strings to allow a packer to pass any section of the string and still be set in the bottom section. Select 43-1/2Ib/ft P-110 for the upper section (collapse 4430 psi, burst 8700 psi, tension 1,106,000Ib). This practical overriding of the design theory is very common, especially when higher grades are more available or occasionally more economical. Burst = 8700/1.125= 7733 psi
D,
=
7448 - 7733 < 0.524
2-29
The 43-1/2 Ib/ft, P-110 can be run to surface. Check for tension design
Final Design
Interval 0-14/5
1475-2645 2645-5900 5900-7975 7975-9500
Grade
Wt 43.5 43.5 43.5 43.5 47
P-110
LI BC
S-95 S-95 S-95 S-95
LT&C LT&C LT&C LT&C
The string from 2645 ft to 5900 ft would have been the 40 Ib/ft except that upper sections had to be the heavier weight with smaller diameter to handle the burst load. For packer access, the id of the string must be at least as large at the top as it is in the sections below it. High Pressure Gas For purposes of simple calculations, the pressure exerted by the gas column is approximated by 0.1 psi/ft. As pressure rises, gas density increases. In high pressure cases, the hydrostatic column of
gas can be substantial. The following graph, from the Baker Calculations Handbook may be useful in more closely estimating pressure. More exact figures are available from computer programs that use PVT data. Additional Graphical Illustrations The method of graphical illustration of collapse and burst used in Figures 2.13 and 2.14, can be extended to analysis of tension, Figure 2.1 6, the stresses involved in overpull, Figure 2.1 7, and buoyancy 2.1 8. All these illustrations are from Hills and are the start of the X-diagram casing design process. Running The Casing Dynamic loads from running casing into the well can be estimated with the following formula from Vreeland.
Fm- W vc =
pC,A
2-30
(2.27)
1
.-. ---
Bottom-Hole Pressure for a Column of Gaseous Nitrogen -!-
700(
E a
500(
U) U)
2 a
3001 <
.
200(
1001
I
1000
2000
3000
4000
5000
6000
7000
Nitrogen Wellhead Pressure in PSI
I
Temperature of Nltrogen at Wellhead 70" Fahrenheit
I
I
I
2-31
Geothermal Gradient 1.6" Fahrenheit Increase Per 100 Feet of Depth
I I
where: V,
= critical velocity
F, W p
= the force required to yield the casing = weight of casing hanging below the slips = mass per unit volume
CO
= speed of sound in the material =
A
= cross-sectional area
€ For steel, pC, = &
= 150 lb-sec/h3
For example, the load increment produced when 7 in. diameter, 29 Ib/ft casing is being lowered at 3 ft/sec (12 seconds per 40 ft joint) and is stopped suddenly can be calculated by rearranging Eqns. 2 and 3 to solve for a force, 6 applied at any casing running velocity, V: F
=VpCd
F = (36 in./sec) (150Ib ~ e c / i n . ~(8.449 ) in.2) F = 46,000 Ib The force would be in addition to string tensile weights. Once a usable hole has been drilled, the casing string or liner is run to depth and cemented in place.
Actual running of the string involves several operations to properly place the pipe and to avoid damaging the well. Like any pipe or drill string run in the well, casing is susceptible to differential sticking. To minimize the problem, mud conditioning and centralizers are used. In the case of differential sticking, the pull required to free differentially stuck pipe is:’9
(2.28) where: F AP
= pulling force, Ib = differential pressure into the zone from the hole, psi
Ac = contact area of pipe and mud cake, in.2 = coefficient of friction (avg. of 0.25 is normal)* Cf As seen from the formula, differential sticking force (equal in magnitude to F) is dependent upon the contact area of the pipe and the mud cake and the mud weight. In a situation with 1.5 in. to 2 in. of diameter difference between pipe and hole, there is about 2 in. contact between the casing and the mud cake. When the mud cake is thick and spongy or when clearances are very tight, contact crosssectional area may double.
The force involved in differential sticking is illustrated in the following example. For a casing string run across a series of permeable zones with a total zone thickness of 100 ft, the mud overbalance is 4000 psi at a depth of 8000 ft with a mud weight of 11 Ib/gal against a pore pressure of 10.0 Ib/gal. AP
= (8000)(11-10) (0.052) = 416 psi
A, F
= (100x12~2)= 2400 in.* = (416 psi) (2400) (0.25) = 249,600 Ib
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Increased mud weight and increased contact area can significantly increase the differential sticking force. The differential sticking force can be considerably lessened by the use of centralizers. Although centralizers cause an increase in drag in the casing and are often difficult to run in the well near the surface, Bowman and Sherer20*23estimate that the increase in drag from running centralizers will be less than the weight of the casing over the zone where differential sticking is a problem. In the case of the previous example, the air weight of a 100 ft section of the 8-5/8 in. casing (40 Ib/ft) is 4000 Ib. Thus, if the drag caused by centralizers over a 100 ft section were equal to the weight of the casing, the increase in drag would be 4000 Ib or 1.6% of the differential sticking force. Such an analysis and an associated estimate of cost savings is dependent on the zone of differential sticking being located near the bottom of the well. This would mean that only the section of casing to be landed across the zone would need to be centralized. In reality, the simple example provides a very low estimate of centralizer drag since centralizers need to be run over the entire string and more densely on casing that passes intervals prone to differential sticking. Centralizers, however, are a necessary design item on most strings and every effort should be made to run them. It is nearly impossible to differentially stick a casing string with centralizers on every joint2’ but field experience is that it may be difficult to run that many in a hole with 2 in. or less clearance. Centralizers aid in getting the pipe to bottom, being able to move the pipe and to improve chances of a successful primary cement job. The number of centralizers needed depends upon pipe and mud weight, hole deviation and hole condition. Calculation programs are available for centralizer spacing. The number of centralizers per joint depends upon the lateral forces exerted by the weight of casing and casing It is this weight that forces the casing into the side of the hole. Obviously, the lateral force increases with casing weight, hole deviation angle, and weight differential between cement and mud while the cement is in the annulus. Occurrence of doglegs and other hole problems also influence the force on casing. The use of centralizers in soft or unconsolidated formations is very difficult since the centralizer blades or springs will tend to imbed in the formation. The number of centralizers must be sufficient to offset the lateral force and position the casing near the middle of the hole. For the lowest possible drag while running pipe, it is important that the right number and type of centralizers be run. Slim hole centralizers should be used in close-clearance holes. The strongest centralizers are full bodied types described in the chapter on Cementing. Necessary support equipment includes stop devices to keep the centralizers in place and avoid bunching them on the pipe by free sliding along the pipe at a bend or a point of close-clearance. Casing collars are usually used for stop devices when only one centralizer per joint is needed. When more than one centralizer per joint is required or where a flush joint liner is used, stop devices must be added to position the centralizers. With the use of very hard grades of flush joint liners such as V-150,slip on stop devices, even those with set screws or slips may not work. Centralizers should not hinder the ability to move pipe during cementing: rather the centralizers prevent the sticking that hinders pipe movement. The inability to rotate some liners is often caused by insufficient starting torque or increased torque as cement travels up the annulus.21The following example of starting torque for a liner is taken directly from Lindsey.21 “For example, assume a liner joint has a maximum allowable torque rating of 5500 ft-lb, and rotating drill pipe and liner before hanging requires a torque of 3500 ft-lb. After hanging the liner and releasing the setting tool, torque required to rotate only the drill pipe is 1000 ft-lb, and rotating drill pipe and liner totals 4200 ft-lb. To calculate maximum allowable surface torque, the torque required to rotate drill pipe only and the torque to overcome bearing friction must be added to the maximum permissible liner joint torque of 5500 ft-lb. In this case, it takes 700 ft-lb (4200-3500) to overcome bearing friction, plus 1000 ft-lb to rotate only the drill string. All 1700 ft-lb of torque is above the top liner joint and must be added to the maximum permis-
2-33
sible liner joint torque of 5500 ft-lb. Therefore, maximum allowable surface torque to initiate rotation, and for the duration of the job, is 7200 ft-lb - not 5500 ft-lb.” The torque to start rotation may approach the maximum but should reduce to a lesser value as the string is rotated.20121 The second torque factor increase, that of cement movement up the annulus will steadily increase rotating torque. The torque limit for the string being run should be known before the job. Torque is read from a torque indicator or estimated by the number of pipe turns to initiate downhole rotation.21 The most successful methods of rotation are power swivels, rotary tables, and casing power tongs. The power swivels and rotary tables are the most reliable; casing power tongs are normally only used for joint makeup. Drilling a usable hole is vital to the use of centralizers. It is a high risk operation to run centralizers in a hole drilled without stabilizers. Bowman and Sherer20give four reasons why liners (and other casing strings) do not make it all the way to bottom: 1. a usable hole was not drilled (the drift diameter is not equal to the bit diameter),
2. differential sticking occurs because centralizers were not used,
3. the wrong type centralizers and support equipment were used, and 4. a dirty hole was drilled (one full of bridges or fill).
Speed of running the string is a critical factor in formation damage since the casing is like a piston in a cylinder with mud as the pressure seal. The pressures created by running casing can be easily enough to fracture the formation and force mud into pay zones. Loss of mud in this manner will also reduce hydrostatic load and can cause a blowout. Safe running speeds on wells with normal clearances and low viscosity mud are 40 to 60 seconds per joint (equal or less than 1 ft/sec). Close clearance strings or heavily gelled muds require longer run times. A procedure for actual running of a casing string is advanced by API Bulletin D-17, and was reported by Bowman and Sherer.23
Prior to running the casing, the hole should be cleaned by mud circulation with the bit on bottom and a conditioned mud with low solids content and low viscosity should be circulated into the hole. After the casing is run, circulation of mud “bottoms up” at least twice is recommended. The mud circulation with the casing in the well is necessary since velocity of the mud in the close-clearance annulus of the casing and hole will be much higher than with the drill string in the hole and more cuttings will be moved. If these cuttings are not removed, they may form bridges in the annulus, blocking or restricting cement flow.
-
Casing String Design Deviated Wells The basic difference in casing design for a deviated well is the magnitude of the loads encountered in the deviated or angle build section. This requires bending and torque considerations. Greenip offers three major points for consideration: 1. Axial and torque loads can be estimated by analyzing separate sections. 2. Relationships can be developed for various parameters in casing string design.
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3. The pickup, set down, and neutral states produce sufficiently different loads and magnitudes to analyze each separately.
First, divide the string into three segments, (1) the extension or reach interval, (2) the build interval (containing the deviation) and (3) the vertical interval, Figure 2.20. As with conventional casing design, the casing in a horizontal well is designed from the bottom up. Interval (2),the build interval, is simplified by assuming the angle is constant. Interval ( l ) , the extension or reach portion is assumed to be a constant inclination. An example of the magnitude of the forces at pickup, neutral and set down are shown in Figure 2.21.
-r
Point 3 -surface
-
Vertical interval
-
Point 2 KOP Build interval Point 1
\
TD
1
(Greenip (Hydril) P.E.I. Dec. 1989)
Figure2.20: On a deviated well, divide the well into three areas: vertical, kickoff or build interval, and extended reach interval. Compression, 1.OOO Ib -10
-5
I
0 .
Tension, 1,000 Ib
5
10
15
20
25 I
30
TD = 6,400 MD = 0.35 Build angle = 20"/100 n Reach length = 2.000 R Reach angle = 80'
(Greenip (Hydril) P.E.I. Dec. 1989)
Figure 2.21: The stress in the casing is most in the build section. Conditions are shown for set down, neutral and pickup.
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Liner Design A liner is a casing string that does not extend back to surface. Liners may be permanent or temporary and run for a variety of reason^:^*^^^ 1. Wear protection of the permanent casing string from rotating drill pipe or frequent tubing move-
ment, especially in a deviated section. 2. Correction of hole difficulty such as doglegs, Key seats, or ledges. 3. Zone isolation of a high pressure zone or a lost circulation zone. 4. As an economical alternative to a full casing string.
5. To allow adequate room above the liner top for a large diameter pump. 6. To reduce casing tension loads in deep wells or to allow use of an available, low strength connection. 7 . For repair of leaks or buckled casing.
8. For casing strengthening in earth shift zones.
Most reasons for liner design incorporate the cost reduction factor of not running casing back to surface. Liners have drawbacks as well, including several problems related to liner cementing. From a design standpoint, perhaps the biggest concern is that the intermediate string or the last full string becomes the top part of the liner and must handle the burst force generated by the zones crossed by the liner. Before a decision is made on use of a liner, the strength of the top part of the last full string must be checked against the new maximum expected surface pressure. Unless proven otherwise by cement bond evaluation tools, the upper pipe strength alone (no assistance from the cement sheath) must be capable of withstanding the pressure. If the upper section will not withstand the forces, it should be protected by running a full string, or, the string should be run before perforating the well. The first approach liner design is the same as for full casing strings. The collapse, burst, and tension safety factors and design equations are the same. The basic differences between liner and casing design come to light in the design of liners for deep wells, hot environments, and very high pressure zones.
-
Example 2.4 Liner Design
A well is being drilled through the formations and pressures shown in Figure 2.22. A conventional design for the primary 9-518in. casing with safety factors of 1.125 for collapse, 1.125 for burst, and 1.8 for tension is:
P
=
D x ( 0 . 0 5 2 ) p 0 - D x ( 0 . 0 5 2 ) p ~ +(PO- Pi)
PO = Pi, pi
=
8.3 lb/galmd p o = 18.5 lb/gal
(Note pi is normally assumed equal to 0 for a conservative design; however, in this case, the high pressure zone will be isolated by casing and liner during production so a fresh water weight can be used in calculations.)
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(13250) (0.052) (18.5)
P,,
P,,
NP,
=
=
k)=
D(1-
65.4
- (13250) (0.052) (8.3)
6821 psi
-)
13250( 1 - 18.2 65.4
=
9563 ft
The casing pick for lowest part of full string: Collapse minimum = (6821) (1.125) = 7674 psi satisfied by 53.5 Ib/ft P-110 (Note: standard casing design can be used to design the full string to surface, although it will not be done here.) The first liner will be 6 4 8 in. Mud weight is 9.2 Ib/gal
P,,
=
14800 (0.052) (9.2)
collapse minimum
=
=
7080 psi
(7080) (1.125)
=
7965 psi
satisfied by 28 Ib/ft N-80
NP,
=
14800 1-
(
-
12718 ft (above liner top)
=
The second liner will be 3-1/2 in. Mud weight is 15 Ib/gal.
Pcx = 15900 (0.052) ( 15) collapse minimum
=
=
12402 psi
(12402) (1.125)
=
13952 psi
satisfied by a 9.2 Ib/gal P-110 (NE)
63
NP2 = 15900 1- -
(
=
12253 ft (above liner top)
Burst failure of liners is usually caused by kicks while drilling below a liner,39p40pressure when fracture stimulating, or a tubing leak while producing a deep, high pressure zone. All these factors are made worse by a poor cement job. Since filling the casing/openhole annulus with cement significantly strengthens and supports the pipe, a good cement job over high pressure or earth movement zones is a requirement in any deep well. An illustration of the complications caused by a poor cement job 39*40 is illustrated in Figure 2.22. After a primary cement job on the 9-5/8 in. string, the 6-518 in. liner is run and a circulation cement job is initiated. The low pressure zone at 13,800 breaks down while cementing, returns are lost and the cement top peaks at 13,400 (Figure 2.23a). A top squeeze with cement seals the top of the liner but leaves an uncemented zone from 13,120 ft to 13,400 ft (Figure 2.23b). While drilling near TD to test a deep structure, the temperature of the mud goes from 270" (temp. of the zone at 15,400 ft) to the bot-
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tomhole temperature (at 18,500 ft) of 345°F. Since both ends of the liner are cemented, stress will be induced by the temperature rise.
12800 f t
13100 f t
13800 f t
14400 f t 14800 f t
14-6 1bfgaL (0.759 p i f E t ) 1yx,f t
TD 1 8 x 0 f t
Figure 2.22:
An example of two liner design for a deep well. The high pressure zone is isolated by the primary casing string and the first liner covers the lost circulation zone at 13800 ft. The last liner is designed as the production zone completion string. Cementing provides pressure integrity and support.
The amount of stress in fixed end casing is CJ =
Ea(AT)
=
200T
where:
o a E AT
= stress, psi
= coefficient of thermal expansion, 6.9 x 10-6 in./in./OF, for steel = Young's modulus, 30 x 1O6 psi, for steel = increase in temperature, OF
The stress is compressional axial load that can cause pipe splitting or deformation, Figure 2.23~. Repair of the collapse may be made by running the 3-1/2 in. liner from above the first liner to TD, Figure 2.24.
Liner Tie-Backs Although the liner completion described in Figure 2.22 may be used only as a liner, there are some conditions when the liner may be run back to surface. This liner tie-back may be temporary, to protect
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B
A 9-5/8",
6-5/8" 20 Ib/ft N-80
53.5 Ib/ft, P-110
l b / p l (0.946 pi/ft)
13120'
b/gal (0.468 psi/ft)
I Figure 2.23: The problem of an incomplete cement job on a deep liner below a high pressure zone A. The initial primary circulation of cement on the liner breaks down the zone at 13800 ft and the final top of the cement is measured by a temperature log as 13400 ft. B. Top squeeze job seals the liner top but leaves a void from 13120 to 13400 ft behind the 6-5/8'1iner. C. The shoe of the 9-518l casing leaks, allowing the high pressure zone at 13100 ft to pressure up outside of the 6-5/8". Deeper drilling increases mud temperature and results in higher compressive stresses in the 6-518" liner. Combination of outside pressure and temperature induced stress causes collapse and split of the 6-518".
permanent casing strings from wear during drilling4' or permanently, with cement, to strengthen the casing string through a high pressure zone or isolate and stop a casing leak38or a leaking liner top.42 To allow a tie-back, most liners are equipped with a liner tie-back receptacle. The receptacle is an internally polished receiver that will accept the seal assembly of the tie-back liner. The tie-back liner usually incorporates some type of cement port or sliding sleeve and seat that will allow cement to be circulated through to the annulus and up the annulus to surface. The seat, float equipment andlor plugs used in the cementing operation are of drillable material.
Cementing Cementing a liner in place requires very closely controlled application of existing technology4s46 and a fair amount of risk. Three cementing methods are generally accepted for liners.47 Calculating the volume of cement to be used in a liner cementing job is extremely difficult and requires more information than available from a simple caliper run. For maximum caliper information, a four arm device capable of determining elliptical holes should be utilized for hole volume. Cement excesses of between 20% and 100% have been used on a number of liner jobs with larger excesses being responsible for better bonding and less channels. There is also a direct correlation with absence of channels and pipe movement. In liners of 500 ft or less, Bowman and Sherer4s46 recommend 100% excess over the calculated annular volume and on liners of 3000 ft or more at least a 30% excess is recommended. A single-stage cementing job in which cement is circulated to the top of a liner; much like a
2-39
9-5/8", 53.5 lb/ft, P-110
6-5/8",
28 W f t , N-80
3-1/2", 9.2 lb/ft, P-110
Figure 2.24
.
Collapsed area repaired by running a 3-112" liner and cementing.
primary cement job and may include pipe movement during cementing. A planned squeeze program in which the lower part of the liner is cemented and the top part of the liner is squeezed later. This technique does not have good middle support and should not be used to isolate high pressure zones. The procedure is more widely followed in worldwide operations because of perceived problems of disengaging the liner running assembly from the liner and of flash setting of cement. Disengaging from the liner before cementing eliminates the ability to move the liner and almost universally results in poor cement jobs. A third procedure commonly reserved for short liners is to fill part of the hole with cement and then slowly run the casing string into the cement, forcing the cement to flow up around the pipe. While this method can be accomplished with the minimum amount of pumping, the lack of circulation can result in poor removal of drilling mud. The technique is called a puddle job.
Most liner jobs do not include plans to move the liner during the primary ~ e m e n t i n g .The ~ ~ ?reasons ~~ for this include: 1. Detaching the drill pipe from the liner before cementing minimizes the risk of being unable to
detach from the liner once the cement is in place. 2. It may be necessary to change to a higher strength drillstring to allow pipe movement. 3. Movement may cause the liner hanger to become tangled with the centralizers near the top of
the string. 4. Swab or surge pressures may be created during liner movement, especially in close tolerance
wellbores.
2-40
5. Movement of the liner during cementing may knock off debris from the borehole wall. The debris
may cause bridges and reduce the possibility of circulating cement.
Despite the quoted disadvantages of staying attached during the cementing operation, Bowman and Sherer4346 site several serious disadvantages with releasing the liner before cementing. 1. If the liner is hung off, the small bypass area around the liner offers a greater restriction to flow
and causes more lost circulation because of the backpressure on the flowing cement. 2. If a downhole rotating liner hanger is used (rotation only), additional torque is required to initiate rotation to overcome bearing friction. Pipe often rotates easier when it is being raised or lowered. The difference in torque required is often substantial.
3. The potential for sloughing shale and annulus bridging is lessened when the operator can alternate between rotation and reciprocation. 4. Premature shearing of the pins in the liner-wiper plug is less likely because there is no relative
movement between the liner and the setting tool (these two pieces of equipment move together).49 5. If cement channels and there is a large hydrostatic pressure difference between inside and outside of the running tools, the cups or seals can give way before cementing of the liner is complete. 6. The displacement efficiency of cement around the tubulars when pipe is not moved is lessened.
When liners are close clearance, then the density differences between mud and cement should be as close as possible. This negates the advantages of hole cleaning by higher density cement. Reciprocation4’ of the string is helpful because it produces lateral pipe movement that causes the pipe to change sides in the wellbore while it is alternately compressed and stretched (slacked off and picked up).43 R o t a t i ~ helps n ~ by ~ ~mixing ~ ~ the ~ ~cement into wellbore irregularities and displacing mud due to drag forces produced by the flowing cement.43 Although liner movement should be a goal in any liner operation, well conditions may prevent any type of movement. In many cases, however, liner movement can be achieved in a well conditioned hole. Two clear cases where liner should not be moved are:43 1. When a short or small liner (3-1/2 in. or smaller) is run in a deep well, the liner should be hung off
first since it may be impossible to tell from the weight indicator whether the liner had been released from the drill pipe. 2. In cases of hole deviation over 35O, reciprocation may be difficult due to high drag forces. Many of the problems in liner running can be lessened by drilling a usable hole. Problems with keyseats, ledges, washouts, and other nongauge problems intensify when close tolerance liners are to be run. For additional information on problems involved in drilling a usable hole, refer to the chapter on Drilling The Pay. When cement is circulated from the liner bottom to over the liner top, the cement must remain fluid long enough to detach from the liner and to circulate the cement from the well or to pull up above the top of the cement with the drillstring. Ifthe cement flash sets, then the drillstring will become cemented in place and the hole most likely will be lost. Cement may prematurely set, thicken, or cement circulation may be lost for a number of reasons.
2-41
1. Improper thickening or pump times caused by a poor design, ineffective field operations, or bad test results. 2. Poor density control on the cement or poor mixing of the cement at the surface.
,
3. Bridging in the annulus caused by a buildup of cuttings. This is caused typically by the increased number of particles picked up by higher annular velocities with a liner in the hole (due to its larger ID) than around the drillstring. 4. Plugging from dehydration of cement caused by excessive water loss in openhole sections below the overlap. 5. Increased hole cleaning of the cement as compared to4he drilling mud.
One of the most troublesome problems in cementing design is inadequate hole cleaning prior to cementing. This is especially true when light weight, low viscosity muds are used and little attention is paid to cuttings removal. Heaving shales are also a problem in hole fill and may cause washouts. Under no circumstances should circulation be halted with the liner in the hole before all of the cement has been displaced. Due to the small clearances and the yield point of cement, it may be very difficult to start circulation again.
Problems 1. For a 16,000 ft string of 5-1/2 in., 20 Iblft, C-75, calculate the final hook load at the end of the
cement job when 16 Ib/gal cement is in the annulus to surface and a 10.5 Ib/gal mud is inside the casing. Surface pressure on the mud in the casing will be 500 psi. 2. A 5000 ft, 4-1/2 in., 10.5 Ib/ft, K-55 liner is run on 3-1/2 in., 13. Ib/ft drill pipe. The liner top is at 12,500 ft. Calculate maximum hook load in a 15 Ib/gal mud if the drill pipe and liner are filled with mud. 3. Calculate the weight of mud that will just balance the weight (float) of a 5000 ft string of 103/4 in., 40.5 Ib/ft, K-55 casing string if the string is run empty (neglect wt. of air).
References 1. Buzarde, L. L., Jr., Kastor, R. L., Bell, W. T., DePriester, C. L.: “Production Operations Course 1. - Well Completions,” SPE, 1972. 2. Oil & Gas Journal Tables.
3. Bollfrass, C. A.: “Sealing Tubular Connections,” J. Pet. Tech., (June 1985), pp. 955-965. 4. Goins, W. C., Jr., Collings, B. J., O’Brien, T. B.: “A New Approach to Tubular String Design, Part 1,” World Oil, (Nov. 1965). 5. Goins, W. C., Jr., Collings, B. J., O’Brien, T. B.: “A New Approach to Tubular String Design, Part 2,”World Oil, (Dec. 1965), pp. 83-88.
6. Klementich, E. F., Jellison, M. J.: “A Service Life Model for Casing Strings,” SPE Drilling Engineering, (April 1986), pp. 141-152. 7. Rike, E. A., Bryant, G. A., Williams, S.D.: “Success in Prevention of Casing Failures Opposite Salts, Little Knife Field, North Dakota,” SPE Drilling Engineering, (April 1986), pp. 131-140.
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8. Greer, J. B., Holland, W. E.: “High-Strength Heavy-Wall Casing for Deep, Sour Gas Wells,” J. Pet. Tech. (Dec. 1981), pp. 2389-2398. 9. Wooley, G. R., Prachner, W.: “Reservoir Compaction Loads on Casing and Liners,” SPE Production Engineering, (Feb. 1988), pp. 96-102. 10. Holliday, G. H.: “Calculation of Allowable Maximum Casing Temperature to Prevent Tension Failures in Thermal Wells,” ASME 69-Pet-10, Tulsa, Sept. 21-25, 1969. 11. Pattillo, P. D., Huang, N. C.: “The Effect of Axial Load on Casing Collapse,” J. Pet. Tech., (Jan.
1982), pp. 159-164. 12. Durham, K. S.: “How to Prevent Deep Well Liner Failure, Part 2,”World Oil, Nov. 1987. 13. Lubinski, A., Althouse, W. S., Logan, J. L.: “Helical Buckling of Tubing Sealed in Packers,”Trans. AIME, June 1962, p. 655. 14. Rabia, H.: Fundamentals of Casing Design, Graham 8t Trotman, 1987, Boston.
15. API Bulletin 5C3:“Formulas and Calculations for Casing, Tubing, Drillpipe, and Line-Pipe Properties,” American Petroleum Institute, (1983). 16. API Specification 5A: “Specifications for Casing, Tubing and Drillpipe,” American Petroleum Institute, (1982). 17. Halliburton Modern Well Completion Course.
18. Woodlan, B., Powell, G. E.: “Graphical Method Speeds Deviated Well Design,” World Oil, (Feb. 1, 1975) pp. 40-43. 19. Wojtanowics, A. K., Maidla, E. E.: “Minimum Cost Casing Design for Vertical and Directional Wells,” J. Pet. Tech. (Oct. 1987), pp. 1269-1282. 20. Bowman, G. R., Sherer, B.: “How to Run and Cement Liners, Pt. 3,” World Oil, (May 1988), pp. 58-66. 21. Lindsey, H. E., Jr., “Rotate Liners for a Successful Cement Job,’’ World Oil, (Oct. 1986), pp. 3943. 22. API Bulletin 5C-1. 23. Bowman, G. R., Sherer, B.: “How to Run and Cement Liners, Pt. 4,” World Oil, (July 88), pp. 8488. 24. Lee, H. K., Smith, R. C., Tighe, R. E.: “Optimal Spacing for Casing Centralizers, SPE Drilling Engineering, (April 1986), pp. 122-130. 25. “API Specification for Casing Centralizers,” API Specification IOD, second edition, API, Dallas (1973). 26. Myers, G. M., Sutko, A. A.: “The Development and Application of a Method for Calculating the Forces on Casing Centralizer,” paper 851-42-H, presented at the 1968 API Spring Meeting of the Mid-Continent Dist., Amarillo, TX, April 3-5, 1968.
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27. Lubinski, A.: “Maximum Permissible Dog-Legs in Rotary Boreholes,” J. Pet. Tech. (Feb. 1961), pp. 175-194. 28. Lubinski, A.: “How to Spot Dog-Legs Easily,” Oil and Gas J., (Feb. 4, 1957), 129-133. 29. Hammerlindl, D. J.: “Basic Fluid and Pressure Forces on Oilwell Tubulars,” J.P.T., (Jan. 1980), pp 153-159. 30. Love, A. E. H.: A Treatise on the Mathematical Theory of Elasticity, 4th ed., Dover Publications, NY (1944), p. 144. 31. Klinkenberg, A.: “The Neutral Zones in Drill Pipe and Casing and Their Significance in Relation to Buckling and Collapse. 32. Lubinski, A., Althouse, W. S., Logan, J. L.: “Helical Buckling of Tubing Sealed in Packers,” J. Pet. Tech. (June 1962), pp. 655-670. 33. Hammerlindl, D. J.: “Movement, Forces and Stresses Associated with Combination Tubing Strings Sealed in Packers,” J. Pet. Tech. (Feb. 1977), pp. 195-208. 34. Woods, H. B.: “Discussion of The Neutral Zones in Drill Pipe and Casing by Klinkenberg,” API (1951), pp 65-76. 35. Hills, J.O.: “A Review of Casing String Design Principles and Practice,” API Production Practices, 1951.
36. Greenip, J. F., Jr.: “How to Design Casing Strings for Horizontal Wells,” Pet. Eng. Intl., (Dec 1989), pp. 34-38. 37. World Oil Tubing Tables. 38. Linsey, H. E., Jr.; “Techniques for Liner Te-Back Cementing,” Production Operations, 1979, pp. 37-39. 39. Durham, K. S.; “How to Prevent Deep-Well Liner Failure,” World Oil, (October 1987), pp. 46-50. 40. Durham, K. S.; “How to Prevent Deep-Well Liner Failure,” World Oil, (November 1987), pp. 4749. 41. Manley, D. D.; “Installation of Retrievable Liners,” SPE 17523, Rocky Mountain Regional, Casper, May 11-13, 1988. 42. Agnen, J. W., Klein, R. S.; “The Leaking Liner Top,” SPE 12614, SPE Deep Drilling and Production Symposium, Amarillo, April 1-3, 1984. 43. Bowman, G. R., Sherer, B.; “How to Run and Cement Liners, Part 1,” World Oil, (March 1988), pp. 38-45. 44. Bowman, G. R., Sherer, B.; “How to Run and Cement Liners, Part 2,” World Oil, (May 1988), pp. 58-66. 45. Bowman, G. R., Sherer, B.; “How to Run and Cement Liners, Part 3,” World Oil (June 1988), pp. 55-58.
2-44
46. Bowman, G. R., Sherer, B.; “How to Run and Cement Liners, Part 4,” World Oil, (July 1988), pp. 84-88. 47. Linsey, H. E.; “New Tools Make Liner Rotation During Cementing Practical,” World Oil, (October 1981). 48. Linsey, H. E., Jr.; “Rotate Liners for a Successful Cement Job,” World Oil, (October 1986), pp. 39-43. 49. Howell, F. R.; “Liner Reciprocation While Cementing,” Drilling-DCW, July 1979. 50. Arceneaux, M. A., Smith, R. L.; “Liner Rotation While Cementing: An Operators Experience in South Texas,” SPE/IADC 13448, New Orleans, March 6-8, 1985.
51. Lindsey, H. E., Durham, K. S.; “Field Results of Liner Rotation During Cementing,” SPE 13047, Houston, Sept. 16-19, 1984.
52. Garcia, J. A.; “Rotating Liner Hangers Helps Solve Cementing Problems,” Petroleum Engineer International, (Sept. 19851, pp. 38-48.
Other References 1. Arceneaux, M. A.; “Liner Operations Made Easy,” Pet. Eng. Intl. (Sept. 1966). 2. Goins, W. C.; “Better Understanding Prevents Tubular Buckling Problems,” World Oil, (Feb. 1980). 3. Short, J. A.; “Drilling and Casing Operations,” Penn Well Publishing Co., 1982. 4. Haut, R. C., Crook, R. J.; “Primary Cementing: The Mud Displacement Process,” SPE 8253, Las Vegas, Sept. 23-26, 1979. 5. Clark, C. R., Carter, L. G.; “Mud Displacement with Cement Slurries,” J. Pet. Tech., (July 1973), p. 775-783.
2-45
Appendix 2.A In the following explanation of buoyancy and neutral point, the explanation of Hammerlind129 is used here almost in its entirety as he explains the concepts and formulas advanced by Lubinski13 and Hammerlindl.29 A tube hanging free in a well exerts its full weight at the surface slips. If the hole is partially or completely filled with liquid, there will be less weight for the same string since the liquid will exert a buoyant force on the pipe. In Figure 2.8a (from Hammerlindl, 1980), the tube is supported only at the surface (no liquid in the hole) and the stress distribution in the absence of liquid is shown in Figure 20.20b. Since the only support is at the surface, the neutral point is at the bottom of the string. Without fluid, the axial stress, oatmay be calculated at any point “x” above the bottom of the tube by:
where W, is the average wt (in air) per unit length and A, is the cross sectional area of tubing wall. The 0, curve in Figure 2.8b connects the peak tensile surface load produced by the weight of the tube with the “ 0 dividing line separating surface compression and tension forces, The radial stress, CJ,, in the tube at any point is:32
where: pressure inside tube at desired depth, psi
pi
=
Pe
= pressure outside tube at desired depth, psi
ri
= internal radius of tube, in
re
= external radius of tube, in
rd
= radial distance to point under consideration, in
In the case of the tube hanging free, there is no liquid inside or outside the tube, so the radial stress is zero. The tangential stress, at any point, is: For the case of no liquid, the tangential stress is also zero. In the previous formulas, a negative value indicates a tensile force while a positive value shows compression. The direction of the stresses and their position on the pipe is shown in Figure 2.9. According to the Archimedes principle, a body submerged in fluid exerts and upward force, Fb, equal to the weight of the volume, V; of fluid of density p displaced by the body or Fb = p V. If the tube has a constant cross section, then the volume may be replaced by immersed tube length, L, and the tube cross section A,
2.A-46
since density (expressed as a gradient) times length is pressure, p, the equation becomes:
where p i s the upward pressure exerted on the end of the pipe. This pressure is a compressive force and shifts the loads in the stress distribution diagram to a positive shown by Figure 2.8~. The fluid in which the tube is suspended, creates a stress at every point equal to the corresponding pressure at that point. This assumes the fluid inside and outside the tube is the same. The axial stress equation is then modified to include buoyancy:
At this point, the liquid is inside and outside the tube and radial and tangential stresses become important. These stresses are equal to a pressure p’ and p’ = p/-p;. At a distance x above the bottom of a tube of length L,
P = P,+p(L-X) where P, is the surface pressure (if any). Hammerlindl points out that by substituting Pfor Pi for P,’ in the equations for radial and tangential stress, or= at = P (some works use a -P depending on direction of force or pressure). This shows that stress is equal to the pressure at the point of interest. The difference in stress distribution with and without fluid is seen in Figures 2.8b and 2.8~.The differences (from Hammerlindl) are: 1. The lower end of the tube is now in compression.
2. The radial and tangential stresses equal the fluid hydrostatic pressure. 3. The tensile stress at the top is reduced by an amount equal to the fluid exerted stress at the bottom.
Static fluids exert a force only in a direction normal to a surface. For the case of a constant diameter vertical tube, the upward force of buoyancy is exerted only at the bottom. This is a concentrated force. If a compressive or tensile force, F; is applied at the lower end of the tube, (same fluid inside and out) the axial stress distribution is changed and
The new stress distribution is illustrated by Figures 2.8d and 2.8e (with fluid). Note that the neutral point is the intersection of the
2.A-41
line separating compressive and tensile loads.33This is true because 0 8 = of= 0; at the neutral point and thus o, must equal the full hydrostatic load. This can only occur at the bottom of the tube. The bottom end of the oa line is displaced from the “ 0 line, first by the magnitude of the pressure (this sets the end of the o,,ofline and then by the applied force to set the end of the 0, line. The direction of displacement is consistent with the sign of the pressure or force. In the absence of liquid in the hole, the neutral point is the point of zero axial stress. Since at the neutral point 6, = o r = og the only point where they may equal zero is the bottom of the tube. In the cases where there is an applied force, F; the neutral point may be shifted up the hole as shown in Figures 2.8d and 2.8e. A comparison of the neutral point location shows a considerable difference in location of the neutral point caused by the fluid. With fluid in the hole, the radial, ob and tangential, og stresses are no longer zero. They reach a maximum at the bottom and decrease toward a minimum at the top of the fluid column. Since the three stresses are equal at the neutral point, the neutral point is shifted up the hole. This is not due to buoyancy but due to the effect of fluid pressure on stability. The neutral point is located by
When fluid of different densities are inside and outside the tubing, the neutral point is described by?
and the neutral point is
2.A-48
-
Appendix 2.B API Casing Design Example Determine the collapse resistance of a casing string when 1. the casing has no tension applied (oa = 0)
2. the casing has an axial load of 215,000 Ib. Given: Casing 10-3/4,51 Ib/ft, C-75 id = 9.850 in., YP (body) = 1,092,000 Ib, For oa = 0, Ypa= 0 Converting YPin Ib into psi: YP(body) = l,092,0OO/((d4)(1 0.7s2 - 9.850)2))= 74,993 psi Diameter over thickness (wall) is: D/t = 10.75/(0.9/2) = 23.9 Since the casing is under no load, the mode of failure may be obtained from Figure 2.12. The Dltratio of 23.9 falls in the range of Figure 2.9b, transition collapse. This means that the collapse resistance equation is:
P,
=
(&-G)YP
When calculating values of A and B for calculation of Fand G, use the YP expressed in psi. From the calculations A B
= 3.00 = 0.064
3 B/A 2 + BIA F
G
=
0.0317
= 1.99 = 0.042
If tabulated ranges for Dltare not available, the Dlt range equations from Figure 2.12 may be solved to specify the proper equation to use. In this case
P,
=
(1.99 - 0.042 23.9
74,933
=
3094 psi
The 3094 psi value compares to the book collapse resistance of 31 00 psi. For part b, with an axial load of 21 5,000 psi:
2.B-49
Oa
axial load
Cross sect. area
-
215,000 psi ( d 4 ) ( 10.752- 9.8502)
Ypa = ( ( 1 - 0.75 (14,765/74,993) 2,
1’2
=
14,765 psi
- 0.4 (14,765 psi/74,993) ) 74,993
Ypa = 66,512 psi The values A to G are calculated using the reduced yield strength. A B
= 2.99 = 0.059 F =
1.96
3B’A
2 + BIA F
G
=
0.0293
= 1.96 = 0.039
and
pt=
(23.9lSg6 0.039)66,512
=
2861 psi
The reduction in collapse strength by 233 psi (7.5% of initial) may be significant in some projects where collapse forces are near the maximum of an unstressed casing.
2.B-50
Appendix 2.C The lateral load on a centralizer, from API Specification 1O06p7 is:
-
Wsjsinej+ wsi+,sinej+
+ 27sir16~
C0Sbi
’‘I
and the tensile force of pipe hanging below the centralizer is:
Tj
=
COS^
Tj- 1
sisin 8
+ w s p s e + w-
2
(tantji- tan?ji-
1
where:
Ni
= Incremental lateral load or force on a centralizer Ibf/in.
W
= Casing weight, Ib/ft
Si Oi
=
T
Incremental centralizer spacing or casing length between centralizers, inch = Incremental hole inclination at centralizer, degrees = Tension of pipe hanging below centralizer, Ib = One-half of the change in angle between centralizers
at 6, Ni = W, sin@+ 2 q sinbi and Ti= Tkl + W, cosOi If the borehole changes angle rapidly, the hole has a “dogleg.” The incidence of doglegs significantly increase the load. The term “dogleg” refers to a change in hole angle and hole direction; this is a 3-D curve. Hole curvature is determined by:
26
=
[ (y-)+ sin(
2 arc sin sin2
y ) s i n e i . sinei-
1
L ~ b i n s k ireferred ~ ~ i ~ ~the hole curvature to a standard 100 ft length to define dogleg severity. Total hole angle 26 and the radius of the hole curvature rare interrelated by the following equation. LetAL= r - 2 6 Then
2.C-5 1
26 (100) AL
~ D L S=
and
where: ljDLS
= the dogleg severity in the half angle 6
AL
= the length between survey points
The 3-D effect of the borehole curvature increases the lateral load on the centralizers. If the effect is ignored, too few centralizers will be used. With the 3-D effect, an effective load is calculated. The effective load, N, is defined as the root mean square of gravitational, hole-curvature, and axial-load forces.
We = ( Fb) ( W,> (s) sine and
T,
=
2Tsin6
The maximum deflection, ymm, or the sag of the casing between the centralizers is at the m i d p ~ i n t . ~
L
and
where: s
= centralizer spacing in.
2.C-52
J
E I
= Young’s modulus, 3 0 ~ 1 0 psi~ = moment of inertia for the casing string, in.4
With the preceding equations, it is possible to calculate centralizer load and the centralizer spacing at any point along the string as long as sufficient hole deviation survey information exists for the task. Because of the many values involved, most spacing calculations are done by computer program.
2.C-53
Appendix 2.D Casing Horizontal Wells Reach Interval In the highly deviated section, weight does not play the same role as in a vertical well. The act of pushing the casing in this section generates a friction force that is in the opposite direction of pipe movement. This force is
dF
=
( w ) (BF) (cose) f (p) (W) (BF) (sine)
where: W = nominal pipe weight/ft BF = buoyancy factor 0 = inclination angle p = coefficient of friction dF = incremental tension At the top of the constant inclination reach section, the tension is:
where: L = reach interval length f1 = tension at the top of the interval While running the string in (setting down on the string), the friction acts to reduce the overall tension:
For a 4000 ft (measured depth) kickoff point (KOP), Figure 2.20, with a build angle of 20°/100 ft, an inclination in the reach section of 80°,a reach length of 2000 ft, pipe size of 5-1/2 in. (17 Ib/ft), coefficient of friction of 0.35 and a mud weight of 9 Ib/gal:
B F = 1 - (9 lb/gal) x (7.48 gal/ft3) (489.5 lb/ft3)
Fl
=
2000 [ (17) (0.86) (cos80)
=
0.86
- (0.35) (17) (0.86) (sin80) ]
=
5001 lb
Since the sign is negative, a 5000 Ib compressive force must be applied at the top of the reach interval to push the pipe to the full 2000 ft. The force required would start at 0 and increase to the full 5000 Ib as the pipe reached the end of the run. The string is usually picked-up after reaching bottom. This action reverses the friction direction. The total tension is:
2.D-54
F,
=
2000 [ (17) (0.86) (COS80)
- (0.35) (17) (0.86) (sin80) ]
=
15,156 lb
The load would be felt at the top of the section with the full column of pipe in the reach section. Put another way, it requires 5000 Ib of force to push the pipe and 15,156 Ib to pull the pipe. At any load between these two figures, the pipe does not move. In this wide range of loads where there is no pipe movement, there may still be a tension at the top of the section. At the balance point; friction is zero (no tendency toward movement) and the tension is:
F,
=
2000 [ (17) (0.86) (COS8O) ]
=
5077 lb
Rotation and Torque If rotation is used during placement or cementing, the torque should be estimated. The torque is a function of the normal force between pipe and open hole, the coefficient of friction and the pipe radius. Using pipe body outside diameter, OD, the incremental torque is
dM
=
(p) (W) (BF) (sine) ( 0 0 ) / 2
In the constant inclination reach section, the rate of torque increase rises with length. The torque, M,, at the top of the section is:
M,
=
(p)(w) (BF) (sine) ( L ) (OD)/24ft-lb
for the full 2000 ft of casing:
M,
=
(0.35) (17) (0.86) (sin80) (2000) (5.5)/24
=
2310 ft-lb
A lower torque may rotate the string if it were being simultaneously picked up or lowered.
The Build interval Unlike the reach interval, loads in the build interval do not change linearly with measured depth. The incremental tension, dFf, is a function of the normal force, which is a function of the tension, the inclination and the build angle.
dFf = (w) (BF) (Cose) f (p) (Fn) and, Fn, the normal force, is:
Fn
=
([(Ff) (da) (sine)l2+ (Ff) (do)-
where: Ff
= tension
2.D-55
[(w>
(BF) (sine)]2}0.5
= incremental change in a azimuth &I= incremental change in inclination angle
da
If the change in azimuth is zero: Fn is simplified to:
Fn
=
[ (Ff)(do) - (W) (5171 (sine)]
The effect of pickup and set down on tension in the build section has the same force effect as it did in the reach section, it opposes the moving force. Because simultaneous equations are solved for Ff, the program is usually handled on a computer. In the example here, the tension at the KOP in Figure 2.1 9, can be calculated. For pickup where Fl = 15,156 Ib (at the top of reach section), F2 = 28,100 ft (in 400 ft). This is a 32 Ib/ft average rate of increase and considerable higher than the 14.6 Ib/ft buoyed weight and gives an indication of the drag in this section. The rate of increase is not constant, but increases as the KOPpoint is neared. At the KOF the rate of tension increase is 50 Ib/ft in this example. For the compression at Point 1 of -5000 Ib (F1= -5000 Ib), the set down load is F2 = -4800 Ib. In Figure 2.20, Greenip illustrates the magnitude of tension and compression forces in the build and reach intervals. Note that the maximum compressional force occurs at about midpoint in the build interval. In this example, the maximum compressional force is about 5800 Ib. While not excessive, this force does show that intermediate calculations are needed. For the condition of Fl= 5100 Ib (neutral range), the load at point 2 is F2 = 9200 Ib (from Figure 2.19). Since the torque at point 2 is also a function of the changing normal force in the build interval, its calculation is also done on the computer. Maximum torque would occur when there is no axial movement (in and out). This could occur during cementing with rotation but no reciprocation. For the neutral state, using a value of 2310 ft-lb at point 1 (Ml= 2310 ft-lb), M2 = 2800 ft-lb. Setting down on the pipe (during wash downs) may increase torque load. In the vertical section of the hole, the torque is usually ignored and M3 z M 2 . The program calculations assume that rotation and axial drag are independent of each other. In the real case, rotation will reduce axial drag and make pipe movement easier either running in or out of the hole. Since the program ignores the effect, the calculations are conservative. Bending Stress
The bending stress occurs only at locations within the casing string where there is a change in bore hole angle. The maximum bending stresses occur in the build section of the hole. These stresses may dominate the design, especially where the build angle is high. For a given build angle BA, the bending stress, Sb, in the pipe body is given by:
Sb
=
k(211) (00) ( B A ) psi
Since the bending stress occurs only where there is a change in hole angle, there is no current bending stress in the constant inclination reach section. The pipe in the reach section must be designed for bending stress since it must pass through the build angle. In passing through a deviated section, a tensile force on one side of the pipe body and a compressive load on the other (Figure 2.1 0) is created. For design, bending stress is converted into tensile and compressive loads, Fb. This is accomplished by:
2.D-56
Fb
=
(Sb) (Ap)
The axial force, Fb, either positive or negative, is matched to the stress, Sb, in a pipe body OD using a pipe body area of Ap. In this example:
Sb
=
f (211)(5.5) (20) = f23,200 psi
and
Fb
=
f(23,200)(4.962) = f115,OOOlb
The axial load of the casing as it passes through the build interval has an additional, simultaneous load of 115,000 Ib from the bending force. Summing forces at the kick off point, the net tension load, F2b, is the total of the axial force at point 2, F2,plus the force, Fb, caused by bending. During string pickup,
F2b = 28,100f 115,100 = 143,200lb and -87,000lb During string set down,
F2b =
- 4800 +. 115,000
c
124,300lb and -105,900lb
For neutral state,
F2b
9200 f 115,100 == 124,300lb and -105,900lb
During pipe movement with a full string in the hole, the loads experienced at the KOPcould be from 143,200 Ib compression to 120,000 Ib tension. In this example in a medium radius build hole, the load caused by bending is over 75% of the total load.
Vertical Interval Once the load at point 2 has been determined, the tension at the surface (point 3) can be calculated by: For pickup
F3 = F2 + (KOP) ( W) (BF)
=
28,100+ (4000)(17)(0.86) = 86,600lb
For set down
2.D-57
F3 = - 4800 + 58,500
53,700 lb
=
For neutral state
F3 = 9200+58,500
=
67,7001b
Remember, the 14,000 Ib window for starting pipe movement (between the neutral point and set down) is the result of friction in the build section and the reach sections. Application For a 5-1/2 in., 17 Ib/ft L-30 casing and using a safety factor of 1.33 (Joint efficiency of 75%), the joint strength, Pj, is
Pi
=
(0.75) (4.962) (95,000)
=
354,000 lb
Since the tension loads are highest on pickup, the safety factor at surface is:
354,000/86,600
=
4.09
354,000/143,200
=
2.47
At the KOe safety factor is:
For a safety factor of 1.1 8 on the compression efficiency of the connection (85%), the compressive yield strength, Pjc, is
PiC
=
(0.85) (4.962) (80,000)
=
337,000 lb
Since the highest compressional loads are produced when setting down the string, the minimum safety factor occurs in the first joint below the KOR
337,000/119,900
=
2.81
For the compression calculation, the load, Fib, at the bottom of the build interval is:
337,000/120,100
=
2.81
When running the string, it will be necessary to apply compression frequently at the top of the reach interval to run the pipe into the hole.
2.D-58
