Patent Publication Number: US-2004055759-A1

Title: Apparatus and method to expand casing

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
     [0001] This application is a continuation of U.S. patent application Ser. No. 10/004,179, filed on Oct. 24, 2001, which issued as U.S. Pat. No. 6,622,799 on Sep. 23, 2003. That application is incorporated by reference in its entirety. 
    
    
     
       BACKGROUND OF INVENTION  
       [0002] 1. Field of the Invention  
       [0003] This invention relates generally to a device and method adapted for use with oilfield pipe (“tubulars”). More specifically, the invention relates to a device and method used to plastically radially expand downhole tubular members in a wellbore.  
       [0004] 2. Background Art  
       [0005] Casing joints, liners, and other oilfield tubulars are often used in drilling, completing, and producing a well. Casing joints, for example, may be emplaced in a wellbore to stabilize a formation, to protect a formation against elevated wellbore pressures (e.g., wellbore pressures that exceed a formation pressure), and the like. Casing joints may be coupled in an end-to-end manner by threaded connections, welded connections, and other connections known in the art. The connections may be designed so as to form a seal between an interior of the coupled casing joints and an annular space formed between exterior walls of the casing joints and walls of the wellbore. The seal may be, for example, an elastomer seal (e.g., an o-ring seal), a metal-to-metal seal formed proximate the connection, or similar seals known in the art.  
       [0006] In some well construction operations, it is advantageous to radially plastically expand threaded pipe or casing joints in a drilled (“open”) hole or inside a cased wellbore. In a cased wellbore, radially expandable casing can be used to reinforce worn or damaged casing so as to, for example, increase a burst rating of the old casing, thereby preventing premature abandonment of the hole. In open hole sections of the wellbore, the use of radially expandable casing may reduce a required diameter of a drilled hole for a desired final cased hole diameter, and may also reduce a required volume of cement required to fix the casing in wellbore.  
       [0007] In conventional oilfield drilling, casing strings are installed at regular intervals whereby the casing for the next interval is installed through the casing for the previous interval. This means that the outer diameter of a casing string is limited by the inner diameter of the previously installed casing string. Thus the casing strings in a conventional wellbore are nested relative to each other, with casing diameters decreasing in a downward direction.  
       [0008] Conventionally, an annular space is provided between each string of casing and the wellbore so that cement may be pumped into the annular space or annulus to seal between the casing and the wellbore.  
       [0009] Because of the nested arrangement of the casing strings in a conventional wellbore, and the annular space required around the casing strings for cement, the hole diameter required at the top of the wellbore is relatively large. This large initial wellbore diameter may lead to increased costs due to the expense of large diameter casing, the expense of drilling large diameter holes, and the added expense of cementing a large casing string.  
       [0010] In addition, the nested arrangement of the casing strings in a conventional wellbore can severely limit the inner diameter of the final casing string at the bottom of the wellbore, which restricts the potential production rate of the well.  
       [0011] It is desirable that a casing string can be radially expanded in situ after it has been run into the wellbore through the previous casing string, so as to minimize the reduction of inner diameter of the final casing string at the bottom of the wellbore. Radially expanding a casing string in the wellbore has the added benefit of reducing the annular space between the drilled wellbore and the casing string, which reduces the amount of cement required to effect a seal between the casing and the wellbore.  
       [0012] When a cold-forming expansion process is used (e.g., when a cold-forming expansion tool or “pig” is moved through a casing string so as to radially plastically expand the casing string), the casing string is usually run into the hole “box-down” (e.g., the “box” or female threaded connection is run into the hole facing downhole so that the expansion tool (“pig”) does not deform the “pin” nose or male threaded connection when the expansion tool is forced upward through the casing string). Note that tubular strings such as drill pipe, casing, or similar tubular members are normally run into the hole “pin-down” because it is easier to make up the threaded connections in the tubular string.  
       [0013] Various expandable casing techniques have already been developed. An expansion tool is typically used to plastically radially expand a string of casing or tubing disposed inside a wellbore from an initial condition (e.g., from an initial diameter) to an expanded condition (e.g., with a larger diameter). One common prior-art expansion process uses a conically tapered, cold-forming expansion tool (commonly referred to as a “pig”) to expand casing in a wellbore. The expansion tool is generally attached to a lower end of a casing string that is run into the wellbore. A leading mandrel of the expansion tool generally comprises a cylinder with an external diameter that is less than a “drift” diameter of the made-up casing or tubing that is to be radially expanded. The expansion tool includes a tapered section having a taper angle that is generally between 5 degrees and 45 degrees. The expansion tool is generally symmetric about a longitudinal axis thereof. The expansion tool also includes a cylindrical section having a diameter typically corresponding to a desired expanded inner diameter of a casing string. The cylindrical section is followed by a tapered section.  
       [0014] After the casing string is set in place in the hole, usually by hanging-off the casing string from a casing hanger, a working string of drillpipe or tubing is run into the wellbore and attached to the expansion tool (e.g., the working string is generally attached to the leading mandrel). The expansion tool may also comprise an axial bore therethrough (not shown) so that pressurized fluid (e.g., drilling fluid) may be pumped through the working string, through the expansion tool, and in to the wellbore so as to hydraulically pressurize the wellbore. Hydraulic pressure acts on a piston surface defined by a lower end of the expansion tool, and the hydraulic pressure is combined with an axial upward lifting force on the working string to force the expansion tool upward through the casing string so as to outwardly radial displace the casing string to a desired expanded diameter. In this expansion process, a rate of radial expansion is determined by, for example, a total plastic strain required to expand the casing string, the taper angle, and a rate of axial displacement of the expansion tool through the casing string. Consistency of the expansion process is controlled by transitions along the expansion tool and a cross-sectional area of, for example, lengths of casing that form the casing string, threaded connections that couple the length of casing, and the like.  
       [0015] The expansion tool may be inserted into the casing string at either the bottom or the top, depending on the tool design and the application. Radial expansion may be performed at rates of, for example, 25 to 60 feet per minute. Other expansion processes, such as expansion under localized hydrostatic pressure, or “hydroforming,” are known in the art, but are generally not used as much as the aforementioned cold-forming expansion process.  
       [0016] U.S. Pat. No. 5,348,095, issued to Worrall et al, discloses a method of creating a wellbore in an underground formation. A borehole is drilled in the underground formation, whereafter a casing of a ductile material is lowered into the borehole. The casing is selected to have a smaller elastic radial deformation than the surrounding formation when the casing is radially expanded against the borehole wall by application of a radial force to the casing. The radial force is applied to the casing so as to radially expand the casing against the borehole wall thereby inducing a plastic radial deformation of the casing and an elastic radial deformation of the surrounding underground formation, whereafter the radial force is removed from the casing.  
       [0017] U.S. Pat. No. 5,667,011, issued to Gill et al, discloses a method of creating a casing in a borehole formed in an underground formation. The method comprises the steps of (a) installing a tubular liner in the borehole, the liner being radially expandable in the borehole whereby the liner in its radially expanded position has a plurality of openings which are overlapping in the longitudinal direction of the liner, (b) radially expanding the liner in the borehole, and (c) either before or after step (b), installing a body of hardenable fluidic sealing material in the borehole so that the sealing material fills the openings and thereby substantially closes the openings. The sealing material is selected so as to harden in the openings and thereby to increase the compressive strength of the liner.  
       [0018] U.S. Pat. No. 6,012,523, issued to Campbell et al, discloses a downhole apparatus for use in expanding liner or tubing. The apparatus comprises a body for connection to a string and an expansion portion on the body. The expansion portion includes a plurality of radially movable parts for defining an outer surface thereof. The parts are initially arranged in an axially and circumferentially offset first configuration in which the parts may assume a smaller diameter first configuration. The apparatus is then run into a borehole and through a length of expandable tubing. The parts are then moved radially outwardly and axially aligned such that the parts assume a larger diameter second configuration and define a substantially continuous outer circumference. The expansion portion is then pulled through the tubing to expand the tubing.  
       [0019] U.S. Pat. No. 6,021,850, issued to Wood et al, discloses a method and apparatus of expanding tubulars. In the preferred embodiment, a rounded tubular is inserted through a larger tubular while suspended on a mandrel. A stop device, such as a liner hanger, is attached to the larger tubular after delivery downhole on the mandrel. Upon engagement of the liner hanger or other stop device to the larger tubular, the mandrel is freely movable with respect to the stop device. The mandrel contains a deforming device such as a conically shaped wedge located below the tubular to be expanded. A force is applied from the surface to the mandrel, pulling the wedge into the tubular to be expanded. When the wedge clears through the tubular to be expanded, it releases the stop device so that the stop device can be retrieved with the mandrel to the surface. Thus, the stop device is supported by the larger tubing while the smaller tubing is expanded when the wedge is pulled through it. Should the tubular being expanded contract longitudinally while it is being expanded radially, it is free to move away from the stop device.  
       [0020] U.S. Pat. No. 6,029,748, issued to Forsyth et al, discloses an apparatus and method that allow for downhole expansion of long strings of rounded tubulars, using a technique that expands the tubular from the top to the bottom. The apparatus supports the tubular to be expanded by a set of protruding dogs which can be retracted if an emergency release is required. A conically shaped wedge is driven into the top of the tubing to be expanded. After some initial expansion, a seal behind the wedge contacts the expanded portion of the tubing. Further driving of the wedge into the tubing ultimately brings in a series of back-up seals which enter the expanded tubing and are disengaged from the driving mandrel at that point. Further applied pressure now makes use of a piston of enlarged cross-sectional area to continue the further expansion of the tubular. When the wedge has fully stroked through the tubular, it has by then expanded the tubular to an inside diameter larger than the protruding dogs which formerly supported it. At that point, the assembly can be removed from the wellbore. An emergency release, involving dropping a ball and shifting a sleeve, allows, through the use of applied pressure, the shifting of a sleeve which supports the dog which in turn supports the tubing to be expanded. Once the support sleeve for the dog has shifted, the dog can retract to allow removal of the tool, even if the tube to be expanded has not been fully expanded.  
       [0021] U.S. Pat. No. 6,085,838, issued to Vercaemer et al, discloses a method of cementing a well permitting a reduction in the degree of diameter reduction of casing or liners required, and not requiring excessively large initial conductor casing. The method is characterized by provision of an enlarged wellbore and a novel liner structure which is adapted for expansion of a reduced diameter section thereof downhole, providing, before expansion of the section, unimpeded flow of fluid from the enlarged wellbore during cementing and close fit of the expanded section with the casing or preceding liner, after cementing is completed and expansion of the section. A novel well liner structure and novel well liner expansion means are also disclosed.  
       SUMMARY OF THE INVENTION  
       [0022] In one aspect, the invention comprises a tool for radially plastically expanding a pipe having a threaded connection therein, that includes a first section. The first section has an increasing diameter and increasing cone angle along a direction of travel through the pipe. The first section includes a first outer surface adapted to contact an inner surface of the pipe at a plurality of selected contact patches on the first outer surface. The tool also includes a second section axially disposed behind the first section along the direction of travel. The second section has an increasing diameter and decreasing cone angle along the direction of travel. The second section includes a second outer surface adapted to contact an inner surface of the pipe at least one selected contact patch on the second outer surface.  
       [0023] In another aspect, the invention comprises a method of expanding casing comprising forcing a casing expansion tool through a casing segment. The casing segment has a smaller inside diameter than a largest outside diameter of the expansion tool. The expansion tool includes an outer surface, and a plurality of contact patches on the outer surface. The contact patches are adapted to contact a section of casing at a plurality of axial locations on the inside diameter of the casing.  
       [0024] In another aspect, the invention comprises a downhole apparatus including a casing expansion tool comprising an outer surface and a plurality of contact patches on the outer surface. Two adjacent contact patches define two circumferential contact surfaces having two different diameters. The apparatus also includes a section of casing. An inside surface of the section of casing is in contact with a plurality of the circumferential contact surfaces of the casing expansion tool on at least two axial locations.  
       [0025] Other aspects and advantages of the invention will be apparent from the following description and the appended claims. 
     
    
    
     BRIEF DESCRIPTION OF DRAWINGS  
     [0026]FIG. 1 shows a partial cross section of a made-up prior art tubular threaded connection with wedge threads and a metal-to-metal internal seal.  
     [0027]FIG. 2 shows a sectional view of a typical prior art conical expansion tool, beginning to deform casing pipe with a made-up tubular threaded connection.  
     [0028]FIG. 3 shows a made-up tubular threaded connection with wedge threads during the expansion by a prior art frustoconical expansion tool.  
     [0029]FIG. 4 shows the made-up tubular threaded connection of FIG. 3 in the expanded state, that is, after the prior art expansion tool has passed completely through the connection.  
     [0030]FIG. 5 shows a cross-sectional view of an embodiment of the casing expansion tool of the current invention.  
     [0031]FIG. 5A shows a partial cross-sectional view of an embodiment of the casing expansion tool of the current invention.  
     [0032]FIG. 5B shows a cross section of another embodiment of the casing expansion tool of the current invention entering a casing pipe.  
     [0033]FIG. 6 shows a partial cross-sectional view of an embodiment of a five-segment expansion tool of the current invention.  
     [0034]FIG. 7 shows a partial cross-sectional view of another embodiment of the expansion tool of the current invention.  
     [0035]FIG. 8 shows a partial cross-sectional view of another embodiment of the expansion tool of the current invention.  
     [0036]FIG. 9 shows a partial cross-sectional view of another embodiment of the expansion tool of the current invention.  
     [0037]FIG. 10 shows a partial cross-sectional view of another embodiment of the expansion tool of the current invention.  
     [0038]FIG. 11 shows a partial cross-sectional view of another embodiment of the expansion tool of the current invention. 
    
    
     DETAILED DESCRIPTION  
     [0039] The radial plastic expansion of made-up threaded connections on oilfield and other tubular goods may exhibit structural sealing problems in the expanded threaded connections. Threaded connections that undergo radial expansion have a tendency to exhibit a non-uniform axial elongation and react differently to residual hoop stresses remaining after radial expansion. Specifically, male (pin) threaded members and female (box) threaded members deform differently during radial expansion. Depending on a direction of travel of the expansion tool (e.g., pin to box or box to pin), the second member to undergo radial expansion will generally move away from the first member. This differential displacement phenomenon results in a loss of preload in axially-engaged seals, making the use of conventional metal-to-metal seals (including, for example, shoulder seals) generally ineffective for plastically radially expanded casing and tubing.  
     [0040] When a joint of casing or tubing is radially plastically expanded, a wall thickness of the casing joint and an overall axial length of the casing joint are reduced by a process commonly referred to as “Poissoning,” and residual stresses are retained in the casing joint. At any given finite element proximate a middle of the casing joint, the casing joint will maintain a substantially uniform diameter and wall thickness because each finite element experiences support from adjoining finite elements.  
     [0041]FIG. 1 shows a cross section of made-up tubular threaded connection with wedge threads and a metal-to-metal internal seal of a type which is preferred for use on expandable casing. Wedge threads are generally dovetail shaped threads with converging thread crest width. Wedge threads are extensively disclosed in U.S. Pat. No. RE 30,647, U.S. Pat. No. RE 34,467, U.S. Pat. No. 4,703,954, and U.S. Pat. No. 5,454,605, all assigned to the assignee of the current invention. This made-up connection consists of female box connection  100 , and male pin connection  101 . The made-up connection has overall connection length  102  (or the quantity L1) from pin nose  103  to box nose  104 , and engaged thread length  105  (or the quantity L2) from the beginning of first engaged thread on the pin  106  to the end of last engaged thread on the pin  107 . Note that engaged thread length  105  cannot always be measured in the same axial plane as implied by FIG. 1, as the start of the first engaged thread will not always lie in the same axial plane as the end of the last engaged thread.  
     [0042] The wedge thread-form has stab flanks  108 , so called because they generally come into contact when the threaded connection is initially “stabbed” together to be made-up. The thread-form also has load flanks  109 , so called because they carry tensile load exerted on a made-up connection within a string of casing hanging in a wellbore. The thread-form on pin connection  101  has pin thread roots  110  and pin thread crests  111  with pin thread crest width  114 . The thread-form on box connection  100  has box thread roots  112  and box thread crests  113 .  
     [0043] Wedge threads are a suitable thread-form for expandable casing applications because (a) their generally dovetail-shaped thread-form resists radial forces during and after expansion which might tend to separate the pin connection from the box connection, and (b) because they may not make-up against a radial torque shoulder, but instead typically make-up by simultaneous contact of thread load flanks  109  and stab flanks  108 . During the expansion process, axial strains in the connection will often cause a radial torque shoulder to fail when the compressive stresses at the shoulder exceed the compressive yield strength of the casing material. Other types of tubular threaded connections can also be successfully used in expanded casing applications with a tool and method according to the invention.  
     [0044] The made-up connection of FIG. 1 has an internal metal-to-metal seal area  115 . This type of metal-to-metal seal is of a type taught by U.S. Pat. No. 5,423,579, issued to Blose et al. To achieve a metal-to-metal seal of this type, the two seal surfaces on the pin and box must come together to form a thin cylindrical or frustoconical contact patch (commonly achieved in the current art there must be a certain minimum contact stress at the seal contact patch to effect sealing against internal pressure inside the casing. Conventionally, this contact stress may be developed during make-up when the pin and box seal surfaces are axially forced together as the connection is threaded together (“made-up”) and the pin seal area is deflected slightly inwards. This slight deflection creates a residual bending stress in the pin nose which in turn creates the contact stress at the seal contact patch.  
     [0045]FIG. 2 is a sectional drawing of a typical prior art conical expansion tool  202  (or “expansion pig”), beginning to deform casing pipe  260  with a made-up tubular threaded connection  250  consisting of box connection  200  and pin connection  201 . The made-up tubular threaded connection  250  has overall connection length  209  and engaged thread length  208 .  
     [0046] The conical expansion tool  202  and the made-up tubular threaded connection  250  share a common center line  203 . In this figure, conical expansion tool  202  is forced through the casing  260  in expansion tool direction of travel  204 .  
     [0047] Conical expansion tool  202  has cylindrical surface  210 , frustoconical exit surface  211 , and frustoconical expansion surface  205  with cone angle  206  (labeled α) of approximately 10 degrees from axial, and an active length  207 . The intersection of cylindrical surface  210  and frustoconical expansion surface  205  forms inflection point  213 .  
     [0048] Most prior art expansion tools have a cone angle larger than 10 degrees. A shallow cone angle  206  is used in the example of the prior art shown in FIG. 2 to demonstrate that simply using a shallow cone angle  206  on a frustoconical expansion surface  205  may still present deficiencies of other prior art expansion tools having large cone angles when used to expand tubular threaded connections.  
     [0049] The active length  207  of the frustoconical expansion surface  205  is defined as the axial length of the expansion surface  205  from the intersection with the inside surface of the casing  212  to the inflection point  213  (the intersection of expansion surface  205  and cylindrical surface  210 ). The active length  207  is therefore the section of the frustoconical expansion surface  205  that bears on the inside surface of the casing  212  during the casing expansion process. It is characteristic of prior art expansion tools that the active length of the expansion surface is quite short, typically in order to minimize the friction between the expansion tool and the casing. Typically, the active length  207  of the expansion surface is shorter than engaged thread length  208  of the connection to be expanded.  
     [0050] In one embodiment of the invention, it has been discovered through experimentation and Finite Element Analysis that tubular threaded connections on expandable oilfield casing and the like which are mechanically expanded as with a frustoconical expansion tool must be axially supported during the expansion process, either by continuous support over the engaged thread length, or preferably at a number of points within the engaged thread length. Some possible consequences of using an expansion tool which is too short to properly support the threaded connection are illustrated in FIGS. 3 and 4.  
     [0051]FIG. 3 shows a made-up tubular threaded connection  350  with wedge threads consisting of box connection  300  and pin connection  301 , similar to the connection shown in FIG. 2, during the expansion by a prior art frustoconical expansion tool (not shown) with the threaded section of the connection over the active length of the expansion tool. As is common practice in the prior art, the expansion tool proceeds in expansion tool travel direction  302 , from pin connection  301  to box connection  300 , to avoid gross deformation of the pin nose  301 A. This requirement severely restricts the expansion operation, in that either the expansion tool (not shown) must travel down the well (if the string is run into the hole in the conventional manner, with the pin connection facing down) or the string must be run into the hole “box down” (which is generally much slower, and therefore more expensive) to allow the expansion tool (not shown) to travel up the well.  
     [0052] The box end  300 A of the made-up connection  350  has already passed inflection point  308 , which is the intersection of the frustoconical expansion surface  309  and cylindrical surface  310 . Note that the last engaged female thread  303  on the pin connection has “combed open” (so-called because the effect resembles the spreading of the teeth of a comb as it is bent backwards at its spine) and that the first engaged male thread  304  on the box connection has experienced severe plastic deformation in bending. Similar “combing” is beginning to occur at next female thread  305  on the pin connection, which is directly adjacent to inflection point  308  on the expansion tool, and a large clearance gap has formed at stab flank  306  of the second engaged male thread on the box. Note that a clearance gap at stab flank  307  has already begun to form, even though there is not yet evidence at this point in the connection of “combing.” 
     [0053]FIG. 4 shows made-up tubular threaded connection  450  of FIG. 3 in the expanded state, that is, after the expansion tool (not shown) has passed completely through the connection in expansion tool travel direction  402 . The made-up tubular threaded connection  450  consists of box connection  400  and pin connection  401 .  
     [0054] The last engaged female thread  403  of the pin connection  401  has experienced significant axial strain as a result of the “combing” induced by the expansion tool. The first engaged male thread  404  of the box connection  400  exhibits the plastic deformation in bending seen in FIG. 3. As a result, these threads have essentially no stab flank contact and greatly reduced load flank contact. The next engaged male thread  408  of the box connection  400  shows similar plastic deformation in bending, which contributes to a large clearance gap at the load flank  407 . The next engaged male thread  410  of the box connection  400  shows slightly less plastic deformation in bending, but still has a significant clearance gap at the corresponding load flank  409 .  
     [0055] Similarly, last engaged female thread  406  of the box connection  400  exhibits plastically enlarged thread width, while first engaged male thread  405  of the pin connection  401  exhibits plastic deformation in bending, resulting in a very large load flank clearance gap  411 .  
     [0056] In addition, pin nose  401 A will typically be slightly radially deformed inward, reducing the contact stress at metal-to-metal seal  412 . Expansion with a prior art expansion tool, particularly an expansion tool with a simple frustoconical expansion surface, usually causes the metal-to-metal seal to begin to leak during the expansion process. This can be a critical limitation for those expansion processes which rely on fluid pressure behind the expansion tool to help propel the tool. Using prior art expansion processes to expand a tubular threaded connection with a metal-to-metal seal, it is unlikely that the metal-to-metal seal will survive the expansion process intact.  
     [0057] A possible result of these deformations in a tubular threaded connection caused by prior art expansion methods is that (a) the efficiency of the connection (commonly defined as the ratio of a mechanical property of the pipe body, such as axial tension capacity, to the same mechanical property across the connection) may drop severely after casing expansion, despite the fact that the pipe body wall thickness is generally reduced during the expansion process, thus reducing the mechanical properties of the pipe body itself, and (b) metal-to-metal seals may not survive the expansion process.  
     [0058]FIG. 5 shows a cross-section of an embodiment of a casing expansion tool  500  of the current invention. Expansion tool  500  is axi-symmetric about center-line  501 , has first chamfer  502  with chamfer angle  502 A, and last chamfer  503 , overall length  504 , length-less-chamfers  505 , and expansion tool direction of travel  510 . Length-less-chamfers  505  is divided into four sections: first expansion section  506 , second expansion section  507 , cylindrical section  508 , and tail section  509 .  
     [0059] First expansion section  506  in this embodiment is further divided into four substantially equal-length frustoconical expansion segments  506 A through  506 D, each with a different cone angle, and separated by radius intervals  511 A through  511 C.  
     [0060] Expansion segment  506 A has included angle  513 A of approximately 177.5 degrees from cylindrical plane  515 , equivalent to a cone angle β  515 A of 2.5 degrees. The cone angle β  515 A is the angle formed by the intersection of cylindrical plane  515  and the outer surface  550  of expansion segment  506 A. The included angles  513 B through  513 D between adjacent expansion segments  506 A through  506 D are also approximately 177.5 degrees in this embodiment of the current invention. That is, the cone angle for expansion segment  506 B is approximately 5.0 degrees (the angle formed by the intersection of cylindrical plane  515  and the outer surface  551  of expansion segment  506 B), the cone angle for expansion segment  506 C is approximately 7.5 degrees (the angle formed by the intersection of cylindrical plane  515  and the outer surface  552  of expansion segment  506 C), and the cone angle for expansion segment  506 D is approximately 10.0 degrees (the angle formed by the intersection of cylindrical plane  515  and the outer surface  553  of expansion segment  506 D). In the first expansion section  506  of this embodiment, each segment has a cone angle that is 2.5 degrees greater than the previous segment.  
     [0061] Second expansion section  507  is further divided into three substantially equal-length frustoconical expansion segments  507 A through  507 C, each with a different cone angle, and separated by radius intervals  511 E and  511 F. In the second expansion section  507  of this embodiment, each segment has a cone angle that is 2.5 degrees less than the previous segment.  
     [0062] First expansion section  506  and second expansion section  507  are separated by inflection plane  516  which lies at the midpoint of radius interval  511 D. The included angle  514 A between expansion segments  506 D (the last expansion segment in first expansion section  506 ) and expansion segment  507 A (the first expansion segment of second expansion section  507 ) is approximately 182.5 degrees in this embodiment. The cone angle of expansion segment  507 A is therefore approximately 7.5 degrees.  
     [0063] The included angles  514 B and  514 C between adjacent expansion segments  507 A through  507 C, and included angle  514 D between expansion segment  507 C and cylindrical segment  508 A, are also all approximately 182.5 degrees in this embodiment of the current invention. That is, the cone angle for expansion segment  507 B is approximately 5.0 degrees, and the cone angle for expansion segment  507 C is approximately 2.5 degrees.  
     [0064] Generally, expansion segments  506 A through  506 D within first expansion section  506  form a “concave” surface, that is, each frustoconical expansion segment in first expansion section  506  has a larger cone angle than the preceding segment. Generally, expansion segments  507 A through  507 C within second expansion section  507  form a “convex” surface, that is, each frustoconical expansion segment in second expansion section  507  has a smaller cone angle than the preceding segment.  
     [0065] In one embodiment, it has been determined from modeling and experimentation that the cone angle β  515 A of first expansion segment  506 A of the first expansion section  506  should be between about 2 degrees and about 6 degrees, and that the included angle between adjacent expansion segments should be between about (180°−β) and (180°+β).  
     [0066] Radius intervals  511 A through  511 C may be included to provide a radiused transition from one expansion segment to the next, following conventional machining practice. See FIG. 5A, which shows a partial cross section of expansion tool  500  shown in FIG. 5, and expanded views of radius interval  511 A (between expansion segments  506 A and  506 B) and of radius interval  511 D, between expansion segments  506 D and  507 A. In this embodiment of the current invention, radius intervals  511 A through  511 C have concave radii of curvature of about 2 inches, which yields a smooth transition from one expansion segment to the next, but which has an axial length which is less than one tenth of the axial length of the neighboring expansion segments. By contrast, radius intervals  511 D through  511 G have convex radii of curvature of about 2 inches.  
     [0067]FIG. 5B shows a cross section of an embodiment of the expansion tool  500  of the current invention entering a casing or pipe  517  to be expanded. In this embodiment, first chamfer  502  has chamfer angle  502 A which matches the chamfer angle on pipe chamfer  517 A, and the axial length of first chamfer  502  is longer than the first chamfer shown in FIG. 5 and FIG. 5A. These modifications ensure that the tool  500  will pilot inside the casing  517  when starting the expansion process.  
     [0068] In addition, first expansion segment  506 A of first expansion section  506  is about twice the length of each of the other expansion segments  506 B through  506 D and  507 A through  507 C. The first diameter  518  of expansion segment  506 A is determined so that the nominal ID of casing  517  will contact the surface of expansion segment  506 A at first contact plane  519 , which is located approximately halfway along the surface of expansion segment  506 A. That is, the length of segment  506 A after contact plane  519  is approximately the same as the length of the other expansion segments. These features ensure that expansion segment  506 A can be stabbed deeply into the casing  517  to be expanded, but that allowance has been made for variation in pipe ID from its nominal ID.  
     [0069] Referring again to FIG. 1, when expansion tool  500  is forced through casing, one would expect that the casing ID will be expanded to a new diameter which is the same as the largest diameter of expansion tool  500 , namely the diameter of cylindrical section  508 . However, in practice, frustoconical-type expansion tools are typically moved through solid casing or expanded metal screens as quickly as possible, with the result that the casing ID usually expands to a diameter larger than the largest diameter of the expansion tool used. This additional amount of expansion is conventionally called “surplus” expansion. This surplus expansion may be caused by differential stresses created by the expansion process. The amount of surplus expansion seems to depend on the design of the expansion tool, the coefficient of friction between the tool and the casing, and the rate of application of the tool to the casing. At the current state of the art, the amount of surplus expansion is most economically determined in an empirical fashion, by testing particular combinations of expansion tools and tubular goods at different rates of expansion tool travel.  
     [0070] Expansion tool  500  is designed for a particular application by first establishing the following variables:  
     [0071] nominal ID of the unexpanded casing pipe  
     [0072] expanded ID of the expanded casing pipe  
     [0073] diametrical surplus expansion expected  
     [0074] L2=engaged thread length  105  (in FIG. 1) of the tubular threaded connection  
     [0075] Diameter of the expansion tool of this embodiment of the current invention at first contact plane  519  in FIG. 5B is designed to be equal to the nominal ID of the unexpanded casing pipe  517 .  
     [0076] The diameter of the cylindrical section  508  in FIG. 5B is designed to be equal to the expanded ID of the expanded casing, less the diametrical surplus expansion.  
     [0077] The difference between the diameter of the first contact plane  519  in FIG  5 B and the diameter of the cylindrical section  508  in FIG  5 B is the required diametrical change in the expansion tool  500 .  
     [0078] In one embodiment, the axial length of each expansion segment within first expansion section  506  and second expansion section  507  has been determined by experiment to be between about L2 (engaged thread length  105  in FIG. 1), and about 0.1 L2 (or, one-tenth of the engaged thread length). In another embodiment, the axial length of each expansion segment within first expansion section  506  and second expansion section  507  has been determined by experiment to be between about 0.8 L2, and about 0.2 L2. In another embodiment, the axial length of each expansion segment within first expansion section  506  and second expansion section  507  has been determined by experiment to be between about 0.5 L2, and about 0.25 L2.  
     [0079] In one embodiment, the combined length of the first expansion section  506  and second expansion section  507  must be at least about L2 (engaged thread length  105  in FIG. 1).  
     [0080] In one embodiment, all of the expansion segments are of equal axial length. In another embodiment, all of the expansion segments are of equal axial length with the exception of the first expansion segment  506 A of the first expansion section  506 , which can be made longer to facilitate stabbing the expansion tool into the casing, as shown in FIG. 5B. Longer axial length of the expansion segments may increase the friction between the expansion tool and the casing, and may result in a smaller surplus expansion. Shorter axial length of the expansion segments may reduce the friction between the expansion tool and the casing during the expansion process, but may result in a larger surplus expansion.  
     [0081] In another embodiment, each expansion segment may have a different axial length in order to make the contact patches have a uniform length. Generally, as the cone angle increases, the length of the contact patch increase. In order to equalize the length of the contact patches, the segments with a higher cone angle would have a shorter axial length, while the segments with a lower cone angle would have a longer axial length.  
     [0082] A “step-angle” between about 2 degrees and about 6 degrees may be selected. This step angle will be the cone angle of the first expansion segment  506 A and the absolute value of the change in angle between contiguous expansion segments. For example, the included angle between the expansion segments in first expansion section  506  in FIG. 2 is 177.5 degrees, so that the step angle is 2.5 degrees, or the absolute value of 180 degrees minus the included angle. It has been found by Finite Element Analysis that the step angle for moderate casing expansions, typically between 10-15%, may be from about 2 to about 2.5 degrees.  
     [0083] A total number of expansion segments is selected, which may be an odd integer. In most cases of casing expansion, it has been found that about 7 or about 9 expansion segments may be practical, although it is possible to design a serviceable tool with more or fewer segments.  
     [0084] The following equations relate the expansion segment length, the step angle, and the total number of segments to the required diametrical change in the expansion tool. For each segment:  
       H=L  tan β 
     [0085] where:  
     [0086] H=radial height of segment  
     [0087] L=axial length of segment  
     [0088] β=step angle  
     [0089] For an expansion tool with seven expansion segments, this yields  
       H 1= L tanβ+ L tan2β+ L tan3β+ L tan4β 
       H 2= L tanβ+ L tan2β+ L tan3β 
     [0090] and  
     HTOTAL= H 1+ H 2  
     [0091] where  
     [0092] H1=radial height of First Expansion Section  
     [0093] H2=radial height of Second Expansion Section  
     [0094] HTOTAL=total radial height of the expansion tool  
     [0095] Which yields  
     HTOTAL= L tanβ+ L tan2β+ L tan3β+ L tan4β+ L tan β+ L tan 2β+ L tan3β 
     HTOTAL=2L (tanβ+tan2β+tan3β+½ tan4β)  
     DTOTAL=4L (tanβ+tan2β+tan3β+½ tan4β)  
     [0096] where  
     [0097] HTOTAL=total radial height of expansion tool  
     [0098] DTOTAL=total diametrical change in expansion tool  
     [0099] For example, if it is desired to expand a 7⅝ inch OD oilfield casing pipe with a nominal ID of 6.875 inches, to an expanded ID of at least 8.005 inches (an expansion of 16%), an expansion tool according to the embodiment of the current invention shown in FIG. 2 could be designed as follows:  
     [0100] The first contact plane  519  in FIG. 5B should be 6.875 inches, the ID of the unexpanded 7⅝ inch, 29.70 pound per foot casing.  
     [0101] Assuming a surplus expansion (established empirically by experimentation) of about 1%, the diameter of the cylindrical section  508  in FIG. 2 should be 8.005 inches less 1%, or 7.925 inches.  
     [0102] The total diametrical change required in the expansion tool is therefore 1.050 inches.  
     [0103] For an expansion tool with seven expansion stages and a step angle of 2 degrees (β=2 degrees) the segment length is calculated as follows:  
     DTOTAL=4L (tanβ+tan2β+tan3β+½ tan4β)  
     1.050=4 L  (tan 28+tan 48+tan 68 +½ tan 88)  
     1.050=4L (0.280)  
       L= 1.050/1.120=0.937 inches  
     [0104] For a threaded connection with an engaged thread length (L2) of 3 inches, a segment length of 0.937 inches represents 0.312 L2, within the range for expansion segment length of 0.25 L2 to 0.5 L2.  
     [0105]FIG. 6 shows a cross-sectional view of a five-segment expansion tool which is another embodiment of the current invention. In this embodiment, the cone angles and the changes in cone angles between segments are much larger than the equivalent angles of the embodiments shown in FIGS. 5, 5A, and  5 B. This means that the included angles between expansion segments  605 A through  605 C are much smaller, and included angles between expansion segments  605 C,  606 A and  606 B are much larger, than the equivalent angles of the embodiments shown in FIGS. 5, 5A, and  5 B. These angles are exaggerated in the view of FIG. 6 primarily for the purposes of clarity.  
     [0106] Expansion tool  600  has center-line  601 , first chamfer  602 , last chamfer  603 , and expansion tool travel direction  604 . Total  600  also has first expansion section  605 , second expansion section  606 , cylindrical section  607 , and tail section  608 .  
     [0107] First expansion section  605  is divided into three expansion segments  605 A through  605 C, each with a different cone angle. For purposes of clarity, no radius intervals are shown between the expansion segments. Second expansion section  606  is divided into two segments  606 A and  606 B.  
     [0108] Expansion segment  605 A has a cone angle  608 A of 12 degrees from cylindrical plane  609 . Expansion segment  605 B has cone angle  608 B of 24 degrees, and expansion segment  605 C has a cone angle  608 C of 36 degrees. In the second expansion section  606 , expansion segment  606 A has cone angle  611 A of 24 degrees, and expansion segment  606 B has cone angle  611 B of 12 degrees. First expansion section  605  and second expansion section  606  are separated by inflection plane  610 .  
     [0109] Casing  612  is shown during the process of expansion. As the expansion tool passes through the casing pipe, the casing pipe shows the characteristic surplus expansion  613 , which is the difference between the ID of the expanded casing pipe and the largest OD of the expansion tool, namely the diameter of cylindrical section  607 .  
     [0110] Expansion segments  605 B,  605 C,  606 A, and  606 B are all approximately the same axial length, while expansion segment  605 A is approximately twice as long as the other expansions, as in the embodiment of the current invention shown in FIG. 5B, in order to ease entry into the casing pipe. Alternatively, expansion segments  605 B,  605 C,  606 A, and  606 B may have varying lengths in order to equalize the length of the contact patches  614 A through  614 E as discussed above.  
     [0111] The large cone angles of the expansion segments on the expansion tool shown in FIG. 6 allow one to clearly see the contact patches  614 A through  614 E between casing pipe  612  and expansion tool  600 . Note that the contact patches  615 A through  615 C in first expansion section  605  occur near the middle of their respective expansion segments, while contact patches  614 D and  614 E in second expansion section  606  occur at the inflection planes between the segments. Contact patch  614 C, which occurs immediately before inflection plane  610  is characteristically axially longer than the other contact patches, and clearance gap  615 C, immediately after inflection plane  610 , is axially longer than the other contact patches.  
     [0112]FIG. 6 shows many of the important elements of the current invention. A plurality of contact patches provide support under the threaded tubular connection during the expansion process. In one embodiment, there are at least two contact patches. In another embodiment, there are at least three contact patches. In another embodiment, there are at least four contact patches. Relatively small included angles between the expansion stages limit the strain rate imposed on the casing pipe. The expansion tool has two distinct sections of expansion stages: the first section is nominally “concave”, that is, the included angle between stages within the first section is less than 180 degrees. The second section is nominally “convex”, that is, the included angle between stages within the second section is greater than 180 degrees. Clearance gaps between the contact patches both reduce friction between the expansion tool and the expanding pipe, and it is believed, allow the stresses in the expanding casing to equalize or equilibrate through the entire thickness of the pipe body and the tubular threaded connection during expansion.  
     [0113] Design of prior art expansion tools has followed the intuitive principle that the profile of the expansion tool should be in contact with the expanding casing pipe as long as possible, consistent with limiting the friction between the expansion tool and the casing pipe to control the expansion force required. It has been discovered through Finite Element Analysis and experimentation, however, that an uninterrupted expansion tool profile may result in large differences between residual stresses at the OD of the pipe and residual stresses at the ID of the pipe. These differential residual stresses are generally not deleterious in the pipe body, but may inevitably cause the failure of threaded tubular connections at the end of a pipe joint, where the residual stresses can not be relieved by a neighboring pipe-body element, but must be relieved through the threaded tubular connection. It has been demonstrated that even the best available wedge thread connection may not tolerate moderate radial plastic expansion (on the order of 10 per cent or greater) by a full-contact expansion tool of the prior art without failure of the connection and/or the metal-to metal seal.  
     [0114]FIG. 7 shows a cross-section of another embodiment of the expansion tool of the current invention. Expansion tool  700  has expansion surface profile  703 , cylindrical section  706 , first expansion section  701  with expansion segment  701 A through  701 C, and second expansion section  702  with expansion segments  702 A and  702 B. First expansion section  701  and second expansion section  702  are separated by inflection plane  705 . Each expansion segment has a frustoconical contact plane  704 A through  704 C and  706 A and  706 B. The nominal contact planes are tangential to the contact patch on the surface of each expansion segment. The expansion surface profile  703  is radially relieved (or “cut-back”) between the contact patches to form radial relief grooves  707 A through  707 D. In this embodiment, the relief grooves form an acute angle at their roots.  
     [0115] For example, contact plane  704 A has a cone angle  707  of 6 degrees, and intersects contact plane  704 B, which has a cone angle of 12 degrees, at plane  708  separating expansion elements  701 A and  701 B. In turn, contact plane  704 C has a cone angle of 18 degrees, contact plane  706 A has a cone angle of 12 degrees, and contact plane  706 B has a cone angle of 6 degrees.  
     [0116] Essentially, the contact planes are “ghost” tangential surfaces which describe an embodiment of the current invention in which the expansion elements are a series of contiguous frustoconical surfaces. The embodiment shown in FIG. 7 can in fact be created by machining-away the expansion surface profile described by the contact planes until the shape of contact surface profile  703  is achieved, preserving the contact patches intact, but radially relieving the clearance gaps.  
     [0117]FIG. 8 shows another embodiment of the current invention similar to that shown in FIG. 7. Expansion tool  800  has expansion segments  801 A through  801 C, and  802 A and  802 B, and contact planes  803 A through  803 C, and  804 A and  804 B. Cone angles for the contact planes in this embodiment are the same as for the embodiment shown in FIG. 7. However, in this embodiment, radial relief grooves  805 A through  805 D are smooth troughs.  
     [0118]FIG. 9 shows another embodiment of the expansion tool of the current invention. This is a multi-part expansion tool which consists of a central shaft  900  about which are positioned a series of disks of varying profiles. Expansion die disks  901 A through  901 D have contact patches tangential to contact planes  902 A through  902 D. In one embodiment, the expansion die disks may be made from a very hard and durable material with a low coefficient of friction when used in cold-forming steel, for example a microgram tungsten carbide, or a ceramic material. Spacer spools  903 A through  903 E serve to axially position and support the expansion die disks on the central shaft. The disks may be secured on the shaft by any conventional means, including threaded end caps or shear pins, for example. This embodiment has the advantage that a relatively small inventory of die disks and spacer spools can be used to assemble a large range of expansion tools, that certain variables (such as the surplus expansion ratio) can be field-adjusted, and that individual die disks can be replaced or repaired rather than repairing an entire tool.  
     [0119]FIG. 10 shows another embodiment in which the surfaces of ball-bearings are used to provide contact patches along the length of an expansion tool. Expansion tool  1000  is divided into first expansion section  1001 , second expansion section  1002 , and cylindrical section  1003 . First expansion section  1001  has expansion segments  1001 A through  1001 C. Second expansion section  1002  has expansion segments  1002 A and  1002 B. Ball bearings  1005  are mounted in expansion tool body  1000  such that the surface of the ball bearing is tangential to the contact planes. This embodiment has the advantage that friction between the expansion tool and the casing pipe during the expansion process can be greatly reduced, and that the tool may be easily rotated as it is advanced. Depending on the helix angle described by a ball bearing as the expansion tool is rotated and advanced through the casing pipe at the same time, rotating the tool can yield a much lower effective cone angle than straight axial advancement of the expansion tool. In one embodiment, if the helix angle is known with some precision, that is, if the rate of axial travel and rate of rotation are both known, the ball bearings can be helically staggered around the circumference such that the circumferential gap between the balls is minimized. In another embodiment, the ball bearings can be circumferentially located around the tool.  
     [0120]FIG. 11 shows another embodiment which uses expansion rollers  1102 A through  1102 D mounted in expansion tool  1100  such that the radial surface of the rollers follows the contact planes  101 A through  101 E. Expansion tool  1000  has first expanding section  1103  and second expansion section  1104 . The expansion rollers are located axially such that they form the contact patches of the expansion tool. Expansion rollers  1102 A and  1102 B, in first expansion section, are located near the middle of an expansion segment, and have simple frustoconical profiles with cone angles equal to the cone angles of their associated contact planes. Expansion rollers  1102 C and  1102 D, in second expansion second, are located between expansion segments, and have compound frustoconical profiles with an obtuse included angle.  
     [0121] In one embodiment, the tool of this invention is lowered into a borehole and then pulled and/or forced up the borehole by fluid pressure in order to expand the casing. Pulling and/or forcing a tool up a borehole to expand casing is known in the art.  
     [0122] In another embodiment, the tool of this invention is pushed and/or forced down the borehole by fluid pressure in order to expand the casing, and then retrieved or abandoned. Pushing and/or forcing a tool down a borehole to expand casing is known in the art.  
     [0123] In one embodiment, the tool of this invention is a static single piece of material, for example steel, that has been machined and/or formed to achieve the desired shape to expand casing.  
     [0124] In another embodiment, the tool of this invention is made up a plurality of radially movable parts for defining an outer surface thereof as disclosed in U.S. Pat. No. 6,012,523, issued to Campbell et al. The plurality of radially movable parts would be formed so as to form a plurality of contact patches, for example 2, 3, 4, 5, 6, or 7, as discussed above.  
     [0125] In another embodiment, the tool of this invention includes a hydraulic mechanism that can serve to expand and/or contract the tool. The tool could be expanded before being used to expand casing, and the tool could be contracted before being run through casing in an unexpanded state. In another embodiment, the tool of this invention includes a mechanical mechanism and/or an electromechanical mechanism that can serve to expand and/or contract the tool.  
     [0126] In another embodiment, the tool is made up of a number of pieces that can be collapsed and/or disassembled in order to allow the tool to fit through shall diameter orifices. In addition, the pieces can be expanded and/or reassembled prior to being used to expand casing.  
     [0127] It will be apparent to those skilled in the art that the expansion tool of the current invention can assume many different shapes other than a monolithic “pig” with frustoconical segments.  
     [0128] Advantages of the invention may include one or more of the following:  
     [0129] A mechanical expansion technique that is reliable and/or relatively inexpensive;  
     [0130] An expansion tool having the ability to radially deform tubular threaded connections, which are conventionally used to join together segments (“joints”) of casing pipe into a long string, without significantly weakening the load-carrying capacity of the threaded connection, and/or without destroying the metal-to-metal seals commonly required in such threaded connections; and  
     [0131] An expansion tool that generates relatively low friction forces between the tool and the casing during the expansion process.  
     [0132] While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.