Patent Publication Number: US-8973654-B2

Title: System and method for anchoring an expandable tubular to a borehole wall

Description:
PRIORITY CLAIM 
     The present application claims priority to PCT Application EP2008/062445, filed 26 Aug. 2010, which claims priority to U.S. Patent Application Ser. No. 61/237,819, filed 28 Aug. 2009. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to an expandable assembly for use in a wellbore formed in an earth formation, the assembly comprising a mechanism for increased radial expansion upon expansion. More particularly, the invention relates to a radially expandable device that mechanically engages a borehole wall so as to form an anchor. 
     BACKGROUND OF THE INVENTION 
     In the drilling of oil and gas wells, a wellbore is formed using a drill bit that is urged downwardly at a lower end of a drill string. After drilling a predetermined depth, the drill string and bit are removed, and the wellbore is typically lined with a string of steel pipe called casing. The casing provides support to the wellbore and facilitates the isolation of certain areas of the wellbore, for instance adjacent hydrocarbon bearing formations. The casing typically extends down the wellbore from the surface of the well to a designated depth. An annular area is thus defined between the outside of the casing and the earth formation. This annular area is filled with cement to permanently set the casing in the wellbore and to facilitate the isolation of production zones and fluids at different depths within the wellbore. 
     Expandable tubular elements are finding increasing application in the context of hydrocarbon drilling and production. A main advantage of expandable tubular elements in wellbores relates to the increased available internal diameter downhole for fluid production or for the passage of tools, compared to conventional wellbores with a more traditional nested casing scheme. Generally, an expandable tubular element is installed by lowering the unexpanded tubular element into the wellbore, whereafter an expansion device is pushed, pumped or pulled through the tubular element. The expansion ratio, being the ratio of the diameter after expansion to the diameter before expansion, is determined by the effective diameter of the expander. 
     When an expandable tubular is run into a wellbore, it must be anchored within the wellbore at the desired depth to prevent movement of the expandable tubular during the expansion process. Anchoring the expandable tubular within the wellbore allows expansion of the length of the expandable tubular into the wellbore by an expander tool. The anchor must provide adequate engagement between the expandable tubular and the inner diameter of the wellbore to stabilize the expandable tubular against rotational and longitudinal axial movement within the wellbore during the expansion process. 
     The expandable tubular is often run into the wellbore after previous strings of casing are already set within the wellbore. The expandable tubular must be run through the inner diameter of the previous strings of casing to reach the portion of the open hole wellbore slated for isolation, which is located below the previously set strings of casing. Accordingly, the outer diameter of the anchor and the expandable tubular must be smaller than all previous casing strings lining the wellbore in order to run through the liner to the depth at which the open hole wellbore exists. 
     Additionally, once the expandable tubular reaches the open hole portion of the wellbore below the previous casing or liner, the inner diameter of the open hole portion of the wellbore is often larger than the inner diameter of the previous casing. To hold the expandable tubular in place within the open hole portion of the wellbore, the anchor must have a large enough outer diameter to sufficiently fix the expandable tubular at a position within the open hole wellbore before continuing with the expansion process. 
     U.S. Pat. No. 7,104,322 discloses a method and apparatus for anchoring an expandable tubular within a wellbore. The apparatus includes a deployment system comprising an inflatable packing element. The packing is arranged inside the liner and is supported on the drill string. When inflated, the packing radially expands an anchoring portion of the expandable tubular. The outside of the anchoring portion engages the wellbore wall and forms an anchor. The remainder of the expandable tubular can subsequently be expanded using an expander tool. The holding power and shape of the anchoring portion may be manipulated by altering the characteristics of the packer such as the shape and wall thickness of the packer. 
     However, engagement of the tubular with the formation, as disclosed in U.S. Pat. No. 7,104,322, is limited by the amount of expansion of the tubular element, which is typically constrained by the mechanical limits of the expansion device. For instance in cases where the annulus between the unexpanded tubular and the borehole wall is relatively large, the amount of available mechanical expansion may not be sufficient to cause the expanded tubular to engage the borehole wall. 
     In addition, although the friction between the outside of the tubular and the wellbore wall that keeps the expandable tubular in position may withstand the reactive forces induced on the expandable tubular by a rotational expansion tool, the friction may be insufficient to withstand the reactive force when pulling an expander cone through the expandable tubular. If the friction is insufficient, the expansion tool may move the expandable element in axial direction during expansion, and the unexpanded tubular may obstruct the previous casing. The unexpanded element must then be removed, at considerable costs, or the obstruction may render the wellbore useless, at even greater expense. 
     Thus, it remains desirable to provide a device that will mechanically engage the borehole wall upon expansion of a tubular, even in instances where the expanded tubular does not itself engage the borehole wall. 
     SUMMARY OF THE INVENTION 
     The present invention provides a tubing-mounted device that will mechanically engage a borehole wall upon expansion of a tubular, even in instances where the expanded tubular does not itself engage the borehole wall. 
     A system for anchoring an expandable tubular to a borehole wall according to the present invention comprises: a ramping member having an anchor ramp face on one side and a support ramp face on the opposite side, said ramping member being fixed relative to the outside of the tubular; an anchor member having a first anchor end fixed relative to the outside of the tubular and a second anchor end extending toward the anchor ramp face of the ramping member, said second anchor end being movable relative to the outside of the tubular; a support member having a first support end fixed relative to the outside of the tubular and a second support end extending toward the support ramp face of the ramping member, wherein said second support end surface is axially spaced apart from said first support end by a distance L B  and wherein said support member includes a brace extending between said first support end and said second support end, said brace and said second support end being movable relative to the outside of the tubular; said first anchor end and said first support end defining an initial axial device length L 1  therebetween; wherein expansion of the portion of the expandable tubular between the first anchor end and the ramping member causes the axial device length to shorten sufficiently to cause the second anchor end to move radially outward and engage the borehole wall as a result of engagement with said anchor ramp face, and wherein expansion of the portion of the expandable tubular between the ramping member and the first support end causes the axial device length to shorten further to cause the second support end to move radially outward and engage the second anchor end as a result of engagement with said support ramp face, unless the borehole wall prevents shortening, whereupon the expandable tubular will be prevented from shortening further by the brace. 
     The anchoring device of the invention enables the tubular and brace to be designed so that expansion of the portion of the expandable tubular between the ramp surface and the first support end causes the axial device length to shorten further unless the borehole wall prevents shortening, whereupon the expandable tubular will be prevented from shortening further by the brace. The radial force exerted on the tubular wall can thus be limited to a predetermined maximum radial force, so that collapse of the tubular wall during expansion can be prevented. Besides, the brace that can slide onto the support ramp side and under the anchor extends the radial reach of the anchor away from the tubular and toward or into the formation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention is better understood by reading the following description of non-limitative embodiments with reference to the attached drawings, wherein like parts of each of the figures are identified by the same reference characters, and which are briefly described as follows: 
         FIG. 1  is a schematic cross-section of a first embodiment of the invention positioned in a borehole before being expanded; 
         FIG. 2  is a cross-sectional view of the device of  FIG. 1  in an intermediate level of expansion; 
         FIG. 3  is a cross-sectional view of the device of  FIG. 1  fully expanded within the borehole; 
         FIG. 4  is a cross-sectional view of a first alternate embodiment of the present device in an intermediate level of expansion; 
         FIG. 5  is a cross-sectional view of the device of  FIG. 4  fully expanded within the borehole; 
         FIG. 6  is an enlarged view of an anchor suitable for use in the system of  FIG. 4 ; 
         FIGS. 7-11  are enlarged views of alternative anchor configurations suitable for use in the present invention; 
         FIG. 12  is an enlarged perspective view of an embodiment of the invention after being expanded; 
         FIG. 13  is an enlarged perspective view of the device of  FIG. 10  after being expanded; 
         FIG. 14  is an enlarged perspective view of the device of  FIG. 11  after being expanded; 
         FIG. 15  is a schematic cross-section of another embodiment of the invention in an intermediate level of expansion; 
         FIG. 16  is a perspective view of the device of  FIG. 15   
         FIGS. 17A-F  are sequential cross-sectional illustrations showing operation of the device of  FIG. 15 ; 
         FIG. 18  is a schematic cross-section of still another embodiment of the invention in an intermediate level of expansion; 
         FIG. 19  is a perspective view of the device of  FIG. 18 ; and 
         FIGS. 20A-F  are sequential cross-sectional illustrations showing operation of the device of  FIG. 18 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  shows an expandable anchoring device  10  for anchoring an expandable tubular  20  to a borehole wall  11  constructed in accordance with a first embodiment of the present invention. The anchoring device  10  comprises an anchor  12  and a wedging member  16  both mounted on the outside of an expandable tubular  20  and separated by a first distance L 1 . The expandable tubular  20  may include a single tubular element, or any number of interconnected tubular elements. The tubular elements can be interconnected using threaded connections known in the art (not shown). Anchor  12  includes a fixed end  14  that is preferably affixed to tubular  20  by welding or other means that prevents relative movement between fixed end  14  and tubular  20 . The other end of anchor  12  extends toward wedging member  16  but is not affixed to the outside of tubular  20 , so that all of anchor  12  except fixed end  14  is free to move relative to tubular  20 . Anchor  12  may be constructed such that its inner diameter is the same as or, more preferably, greater than the unexpanded outside diameter of tubular  20 . 
     It will be understood that anchor  12  and fixed end  14  can be formed as a single, integral component, constructed from separate pieces that have been joined, or comprise separate pieces that are not mechanically joined. It is preferred that at least fixed end  14  be affixed to tubular  20 , preferably but not necessarily by welding. 
     Similarly, wedging member  16  is preferably affixed to tubular  20  by welding or other means that prevents relative movement therebetween. Wedging member  20  includes a ramp member  18  that extends toward anchor  12 . Ramp  18  may be constructed with any desired surface angle. 
     The thicknesses of wedging member  16  and anchor  12  are a matter of design, but are limited by the maximum allowable diameter of the system prior to expansion, which is smaller than the inner diameter of the previous casing string. 
     Anchor  12  and wedging member  16  can each have either an annular or segmented construction. In a segmented construction, anchor  12  and/or wedging member  16  may comprise longitudinal strips, rods, or plates. For example, eight strips, each extending around 45 degrees or less of the outer circumference of tubular  20  could be used. Alternatively, anchor  12  and/or wedging member  16  may include both an annular portion and a segmented portion. In the latter case, it is preferred that the annular portion lie outside of the separation distance L 1 . 
     It is further preferred that any fixed end and/or annular portion be made from a ductile material and have sufficient thickness and length that it can be expanded without requiring undue force. A suitable ductile material is for instance carbon steel A333. The material has for instance a modulus of elasticity with respect to tension in the order of 30 or more and with respect to torsion in the order of 11 or more. 
     Expandable anchoring device  10  is intended for use in conjunction with an expandable tubular  20 , which in turn is expanded by an expansion device  30 . As illustrated, expansion device  30  may comprise a cone having a frustoconical expansion surface  32  that increases the inside diameter of tubular  20  as expansion device  30  is pushed or pulled through tubular  20 , but it will be understood that expansion device  30  can comprise any suitable mechanism for applying a radial expansion force to the inside of tubular  20 . 
     Referring to  FIGS. 2 and 3 , it can be seen that as expansion device  30  moves through tubular  20 , tubular  20  shortens. Thus, as expansion device  30  moves from one end of L 1  to the other; the distance between wedging member  16  and fixed end  14  of anchor  12  decreases. The final distance between wedging member  16  and fixed end  14  of anchor  12  is reached once expansion device  30  has moved past wedging member  16 , and is defined as L 2 . Because anchor  12  is not affixed to tubular  20  apart from fixed end  14 , the shortening of tubular  20  has virtually no effect on the length of anchor  12 . 
     For a given tubular and expansion ratio, the amount of shortening that will occur if the tubular is not constrained during expansion can be predicted. In a preferred embodiment, the distance L 1  is selected such that the amount of shortening, which can be expressed as the difference between L 1  and L 2 , is sufficient to cause the anchor  12  to overlap wedging member  16  by a desired longitudinal distance. The difference between L 1  and L 2  is a function of the expansion ratio, the expansion mode and, less so, of the original tubing wall thickness and can be predicted on the basis of those parameters. 
     As used herein, “expansion mode” distinguishes between so-called expansion in tension and expansion in compression, which in turn are used to describe stress states experienced by the tubular during expansion. During expansion in tension, the expansion device moves away from a location where the expandable tubular is fixed, which is for instance the position of an anchor. During expansion in compression the expansion device moves towards the location where the expandable tubular is fixed. The expandable tubular shortens approximately two times more during expansion in compression, than during expansion in tension. Shortening herein indicates the difference in length of (a section of) the tubular before and after expansion. During expansion of the tubular, the mode of expansion may change. In addition, the weight of the expandable tubular may introduce a second order effect. However, in general the mode of expansion is known, as is described in more detail below. Thus, it is possible and desirable to calculate and use a predetermined spacing L 1  that will result in a desired overlap and outward movement of anchor  12 . 
     During expansion of the expandable tubular element according to the present invention, the section of the tubular that is provided with the anchor of the invention is preferably expanded in a first step. During this first step, gripping means hold the unexpanded tubular element in a predetermined position until the anchor engages the wellbore wall. Suitable gripping means that operate in conjunction with an expansion device are for instance disclosed in US-2009/0014172-A1, which is in this respect incorporated herein by reference. In a first expansion step, the gripping means engage the wall of the tubular. Than, an actuator, including for instance a hydraulic actuator, pulls the expansion device through the tubular until the anchor is activated. In a subsequent step, once the anchor has engaged the borehole wall, the remainder of the tubular element can be expanded by pulling the expansion device toward the surface. Expansion by pulling the expander toward the surface is relatively fast compared to other ways of expansion. Expansion using the gripper system can be nominated expansion in compression, wherein pulling the expander to the surface when the anchor is activated is called expansion in tension. Thus, the mode of expansion may change when the anchor is activated and engages the borehole wall. 
     As an alternative to the gripping system, the string of expandable tubular elements  20  can be closed at its downhole (not shown), forming a closed fluid pressure chamber between the closed end and the expansion device  30 . I.e., the downhole end is closed at surface, before introducing the expandable tubular including the closed end and the expansion device in the wellbore. The expansion device  30  will be provided with a fluid passage connecting the top and bottom end thereof. For instance tubing of a hollow pipe string is connected to the top end of the fluid passage, to pass fluid under pressure from surface and through the expansion device into the fluid pressure chamber, wherein the resulting pressure in the fluid chamber pushes the expansion device through the expandable tubular. Expansion using a pressure chamber under the expansion device is called expansion in tension. 
     Referring now to  FIGS. 4 ,  5 , and  6 , an alternative embodiment includes an anchor  42  having a fixed end  44 , a first portion  46  having cutting end  47 , a second portion  48 , and a hinge  45  disposed between first and second portions  46 ,  48 . Hinge  45  is provided so that anchor  42  will deform plastically during the expansion process. As wedging member  16  begins to slide under anchor  42 , cutting end  47  will be pushed radially outward. Hinge  45  will provide a point of rotation for first portion  46  with respect to second portion  48 , allowing cutting end  47  to rotate toward the formation. 
     In an embodiment, once hinge  45  has reached the limit of its rotation and/or wedging member  16  reaches hinge  45  and slides under second portion  48  of anchor  42 , second portion  48  will begin to rotate radially outward, thereby increasing the angle at which cutting end  47  engages the formation. 
     In  FIGS. 4 and 6 , hinge  45  is shown as a groove or slot in the outside of anchor  42 . In  FIG. 5 , the groove has closed as a result of the bending of anchor  42 . 
       FIGS. 7-10  show alternative embodiments of the anchor. In  FIG. 7 , an anchor  52  has a tapered first portion  53 . In  FIG. 8 , an anchor  54  has a first portion  55  with a reduced thickness. In  FIG. 9 , anchor  56  has a hinge comprising a rectilinear notch  57 . 
     In  FIG. 10 , anchor  58  has a first portion  59  having a reduced thickness and an enhanced cutting end  60  that includes a wedge- or blade-shaped tip that is thicker than the rest of first portion  59 . Two or more of said tips may be arranged successively. 
     It will be understood that the foregoing are merely illustrative embodiments and that a two-part anchor could have any of an infinite variety of shapes. In each instance, an increase in thickness and therefore in bending force that occurs at the junction between the first portion and the second portion defines a hinge that in turn defines the extent of bending and plastic deformation. Thus, the position of the hinge and the relative length of the first portion determine the reach of the anchor into the formation. 
       FIG. 12  shows an anchor  12  having a substantially constant thickness, which after expansion slid onto the wedging member  16 . The end of the anchor is provided with the enhanced cutting end  60  that includes a wedge- or blade-shaped tip that is thicker than the rest of the anchor. The cutting end  60  is pushed toward and partly into the formation  72  to anchor the liner in the formation. Penetration depth is schematically indicated with L 3 . The angle of the ramp member  18  with respect to the axis of the tubular and the contact lengths are designed so as to avoid excessive loading of the liner during pulling of the expansion device through the liner. 
     The expansion process of the expandable liner  20  actuates the anchoring device of the present invention. Due to the shortening of the liner as the expansion device moves from one end of L 1  to the other, the anchor  12  slides onto the ramp  18  of the wedging member  16 . In the absence of hinges, the free end of the anchor may overlap the wedging member  16  by a desired longitudinal distance L 4  ( FIG. 12 ). The length L 4  of the overlap is preferably minimized, in order to limit the increase in expansion force. 
     The cutting end or tip  60  focuses the radial force that the anchor exerts on the formation during expansion of the liner  20  on the surface of the end of the tip. Thus, the radial force that will be exerted per area of the formation increases. The local resistance or strength of the formation may be expressed as a resistive force per area (e.g. in units psi or Pa). The formation resistance within the wellbore may range between 500 psi up to 16000 psi, and can for instance be measured or estimated. This allows the contact area between the formation and the tip, as well as the corresponding maximum radial force on the tip to be designed such that the tip will penetrate over a predetermined minimum penetration depth L 3  into the formation during expansion of the tubular element ( FIG. 12 ). 
     Improved embodiments of the anchor lock themselves in the formation when they are subjected to an external force. In other words, the design of the anchor imposes that the tip end of the anchor tries to penetrate further into the formation when subjected to such force, as opposed to for instance chafing against the wellbore wall. This is referred to as a self-locking effect. The external force includes for instance the upward force that the expansion device  30  transmits to the tubular  20  during expansion thereof when the expander is beyond the position of the anchoring device  10 . 
       FIG. 13  shows an anchor  12 , which is provided with the first portion  59  having a reduced thickness after being expanded and subjected to an additional external load. The tip end of the anchor has curled radially outward with respect to the tubular  20  and into the formation when subjected to force. 
     The tip curls outward, when the force moment acting on the tip end of the anchor is greater than the bending moment M h  of the weakest part of the anchor. In the embodiment of  FIG. 13 , this is the first portion  59 . Typically, the force moment is a function of distance L 5  between the wall of the tubular and the formation  72 , the external force F e , and the resulting reaction force F r  ( FIG. 13 ). Herein, F r  also depends on the formation hardness and the penetration depth L 3 , as the formation will crumble or otherwise granulate when the required force F r  per area exceeds the strength (expressed in psi or Pa) of the formation. The above values however may differ on a local scale. Approximately, the anchor will provide a self-locking effect when M h &lt;L 5 *F r . 
     In another embodiment, the anchor includes one or more hinges  57 ,  62 ,  66  ( FIGS. 11 ,  14 ). Now, the bending resistance or strength of the anchor is the lowest at the location of the hinges. Similar to the embodiment described above, the tip end  60  of the anchor will curl or bend radially outward and into the formation when subjected to a force that provides a moment that exceeds the bending moment of one or more of the hinges. 
     Referring to  FIGS. 11 and 14 , when subjected to force, the anchor  12  will for instance bend first at the point of hinge  62 , so that tip  60  starts to curl toward the formation and away from the tubular  20 . When the hinge  62  closes, the anchor will bend at the point of hinge  66 , so that the tip  60  and section  64  will curl toward the formation and away from the tubular  20 . When the hinge  66  closes, the anchor will bend at the point of hinge  57 , so that the tip  60 , section  64 , and section  68  will curl toward the formation and away from the tubular  20 . When hinge  57  closes, the anchor will reach the state shown in  FIG. 14 . 
     In embodiments where the hinge is provided as a groove or notch ( FIGS. 6 ,  9 ), the groove or notch may close after some amount of deformation, thus ceasing to operate as a hinge and restricting further deformation ( FIG. 14 ). This is also referred to as self-locking and may be desirable in some instances. 
     The maximum anchoring force is for instance determined by one or more of the force needed to fold the bending zones  59  or the hinges, the strength of the formation in conjunction with the contact area between the anchors and the formation perpendicular to the axis of the tubular, the penetration depth, the number of anchors disposed around the circumference of the tubular element, etc. 
     In still other embodiments, more than one hinge may be provided, so that the deformed anchor has a shape such as is illustrated in  FIGS. 11 and 14 . The length L 6 , L 7  of respective sections between adjacent hinges determines the reach of the anchor in the radial direction. The thicker section in between the hinges prevents the anchor from folding ( FIG. 14 ), thus setting the reach of the anchor into or towards the formation. The maximum anchoring force increases with penetration depth, as the anchoring force depends on the contact area between the anchor and the formation. 
     Referring to  FIG. 14 , in embodiments that include one or more hinges, the relatively thicker parts  64 ,  68 ,  58  adjacent to the respective hinges will limit this curling movement. The anchor will curl at the position of the hinge, but this curling movement will end when the thicker parts bordering the respective hinge come into contact, as shown in  FIG. 14 . The lengths L 6 , L 7  of thicker parts  68 ,  64  thus determine the final shape of the anchor. In the embodiment shown in  FIG. 14 , for instance, the length L 6  determines how far the end of the anchor will extend away from the liner, as adjacent hinges  57 ,  66  will close and further folding of the anchor can only occur when a greater force is applied thereto. Thus, the length L 6  enables the setting of a penetration depth L 3 , and/or a minimal anchoring force. The penetration depth L 3  of the anchor  12  in the formation  72  depends in part on the strength or hardness of the formation. 
     In another embodiment, shown in  FIGS. 15 to 17 , the anchoring device of the invention aims to provide a maximum upward anchoring force to prevent movement of the liner, and at the same time limit the radial inward force on the liner, which could result in collapse of the liner wall. The part of the anchor  12  that overlaps the wedging member engages and pushes into the formation, and the wall of the liner must be capable of providing a reaction force. 
     Referring to  FIG. 15 , an anchoring device  110  constructed in accordance with a second embodiment of the present invention comprises an anchor  112  and a wedging member  116  both mounted on the outside of an expandable tubular  20  and separated by a first distance L 1 . Anchor  112  includes a fixed end  114  that is preferably affixed to tubular  20  by welding or other means that prevents relative movement between fixed end  114  and tubular  20 . The free other end of anchor  112  extends toward wedging member  116  but is not affixed to the outside of tubular  20 , so that all of anchor  112  except fixed end  114  is free to move relative to tubular  20 . The anchor  112  may be constructed such that its inner diameter is the same as or greater than the unexpanded outside diameter of tubular  20 . 
     Similarly, wedging member  116  includes a fixed end  117  that is preferably affixed to tubular  20  by welding or other means that prevents relative movement between fixed end  117  and tubular  20 . The free other end of the wedging member  116  extends toward the anchor  112  and defines a brace  115  having a length L B . Brace  115  is not affixed to the outside of tubular  20  and is free to move relative to the tubular  20 . At the free end, wedging member  116  includes a ramp member  118  that extends toward the anchor  112 . The ramp  118  may be constructed with any desired surface angle and may be integral with or a separate piece from brace  115 . 
     The thicknesses of wedging member  116  and anchor  112  are a matter of design, but are limited by the maximum allowable diameter of the system prior to expansion, which is smaller than the inner diameter of the previous casing string. 
     Anchor  112  and wedging member  116  can each have either an annular and/or a segmented construction. In a segmented construction, anchor  112  and/or wedging member  116  may comprise longitudinal strips, rods, or plates. As shown in  FIG. 16 , the anchor  112  and the wedging member  116  each comprise for instance eight strips  122 ,  124  respectively. The eight strips  122 ,  124  extend around the outer circumference of the tubular  20 . Optionally, the strips of the anchor  112  and/or the wedging member  116  include a segmented section, comprising strips or fingers  126  which have a smaller width than the strips  122 . The anchor and the wedging member may include any number of strips  122  and/or corresponding fingers  126  that is suitable with respect to the size of the tubular  20 . 
     Expandable anchoring device  110  is intended for use in conjunction with an expandable tubular  20 , which in turn is expanded by an expansion device  30  as illustrated generally in  FIGS. 1 to 3 . During expansion, the expansion device moves in the direction of arrow  128 . 
     Referring to  FIGS. 17A to 17F , it can be seen that as the expansion device (the position of which is indicated by arrow  30 ) moves through tubular  20 , tubular  20  shortens. Initially, the free end of the anchor  112  touches the ramp member  118  ( FIG. 17A ). Until the expansion device reaches the ramp member, the result of the shortening is that the distance between ramp member  118  and fixed end  114  of the anchor  112  decreases. The free end of the anchor will slide onto the ramp member and toward to borehole wall  11 , overlapping the ramp member and extending away from the tubular  20 . Preferably, the length of the anchor  112  is chosen such that the free end thereof engages the borehole wall  11  by the time that the expansion device passes ramp  118  ( FIG. 17B ). 
     The expansion device subsequently progresses beyond the ramp member, and the tubular  20  continues to expand and shorten at the position of the expander. Due to the shortening, fixed end  117  of wedging member  116  moves toward anchor  112 , and as a result ramp member  118  is pushed against anchor  112  ( FIG. 17C ). If the radial force on the free end of anchor  112 , which is induced by shortening of the tubular element  20  due to expansion thereof, is greater than the local resistance or strength of the formation, the tip  60  at the free end will penetrate further into the formation ( FIG. 17D ). 
     However, if said radial force is smaller than or equal to the local resistance or strength of the formation, the tip  60  of the anchor will be unable to penetrate further into the formation. In that case, anchor  112  will be held in place by the formation and ramp member  118  will in turn be held in place by anchor  112 . With the brace  115  of wedging member  116  unable to slide further along the outside of tubular  20 , no further shortening can occur. The final distance between fixed end  117  of wedging member  116  and fixed end  114  of anchor  112  is reached once the expansion device has moved past the fixed end  117  of the wedging member  116 , and is defined as L 8  ( FIG. 17D ). Because the tubular is prevented from shortening during a portion of the expansion process, the final overall device length L 8  for this embodiment may not be as small as L 2  for a device constructed in accordance with the embodiment of  FIG. 1  and having the same L 1 . The difference is a result of the fact that tubular may have been prevented from shortening as it traverses at least some portion of the length L B  of brace  115 . 
     When the free end of the wedging member  116 , which comprises the ramp member  118 , is held in place by the anchor, the maximum load that is applied to the wall of the liner  20  is about equal to the so-called fixed-fixed load. The fixed-fixed load is the local load that is applied to the liner wall when the expander moves between two points at which the liner is fixed, such that the liner cannot shorten between the two points. As the fixed-fixed load can be determined beforehand, for instance during lab tests, the anchoring device  10  of the invention can be designed such that the radial force exerted on the formation does not exceed the maximum radial load of the wall of the tubular  20 . Thus, the anchoring device of the present invention ensures that the tubular wall can be sufficiently strong to withstand the maximum radial force during expansion, so that the wall will remain substantially cylindrical, i.e. circular, when the anchor engages the formation. 
     The embodiment shown in  FIGS. 15 to 17  allows the expandable tubular to be designed so as to avoid collapse, even in the event that the formation is too hard to receive anchor  112 , as the maximum load on the tubular wall will not exceed the fixed-fixed load, which can be calculated or at least determined empirically. This will prevent collapse, rupture, or similar damage to the tubular wall during expansion. As indicated above, if the expandable element were damaged, the entire downhole section could be rendered useless and would then have to be removed, at considerable costs. The expandable tubular arrangement of the present invention thus greatly improves reliability in this respect. 
     The radial load during expansion on the liner and on the formation depends for instance on one or more of the surface angle of the ramp  118 , the friction between the wedging member  116  and the liner  20 , the friction between the wedging member and the anchor  112 , the formation hardness, the distance between the tubular wall and the formation during expansion, etc. The surface angle of the ramp is preferably designed such that a maximum radial force is applied, whereas at the same time the radial load remains within the radial collapse load of the liner. 
     As the radial and axial load on the wall of the tubular is limited, the embodiment of  FIGS. 15 to 17  is suitable for relatively hard formations, such as those, for example, having a strength or hardness of for instance 3000 (20 MPa) to 4000 psi (28 MPa) or more. In addition, the radial load on the tubular wall can be limited by limiting the overlap between the anchor and the wedging member, and/or by limiting the contact area between the anchor and the formation. The contact area between the anchor and formation perpendicular to the radius of the tubular is minimized to reduce the radial loading on the liner. In a practical embodiment, the surface angle of the ramp  118  is in the range of 30 to 60 degrees, for instance about 45 degrees. 
     Referring to  FIG. 18 , an anchoring device  210  constructed in accordance with still another embodiment of the present invention comprises an anchor  212  and a wedging member  216  both mounted on the outside of an expandable tubular  20 . The anchor  212  includes a fixed end  214  that is preferably affixed to tubular  20  by welding or other means that prevents relative movement between fixed end  214  and tubular  20 . The free other end of the anchor  212  extends toward wedging member  216  and is not affixed to the outside of tubular  20 , so that all of anchor  212  except fixed end  214  is free to move relative to tubular  20 . The anchor  112  may be constructed such that its inner diameter is the same as or greater than the unexpanded outside diameter of tubular  20 . 
     Likewise, the wedging member  216  includes a fixed end  217  that is preferably affixed to tubular  20  by welding or other means that prevents relative movement between fixed end  217  and tubular  20 . The free other end of the wedging member  216  extends toward anchor  112  and is not affixed to the outside of tubular  20 , so that all of wedging member  216  except fixed end  217  is free to move relative to tubular  20 . The wedging member  216  may be constructed such that its inner diameter is the same as or greater than the unexpanded outside diameter of tubular  20 . 
     A ramping member  218  is disposed between the free ends of anchor  212  and wedging member  216 . Ramping member  218  includes an anchor ramp face  219   a , which tapers in the direction of anchor  216 , and a wedging ramp face  219   b , which tapers in the direction of wedging member  216 . Ramping member  218  is preferably affixed to the outside of tubular  20  so as to prevent relative movement therebetween. 
     The free end of anchor  212  may be provided with a tip  60 , having a slanted side  280  facing tubular  20 . Slanted side  280  cooperates with anchor ramp face  219   a . The free end of wedging member  216  may be provided with a thickened end  282 , having a slanted top surface  284  and a slanted bottom surface  286 . Slanted surface  284  cooperates with anchor  218  as shown in  FIG. 18 . The slated bottom surface cooperates with wedging ramp face  219   b.    
     Anchor  212  and wedging member  216  can each have either an annular and/or a segmented construction. In a segmented construction, anchor  212  and/or wedging member  216  may comprise longitudinal strips, rods, or plates. As shown in  FIG. 19 , the anchor  212  and the wedging member  216  each comprise for instance eight strips  222 ,  224  respectively. The eight strips  122 ,  124  extend around the outer circumference of the tubular  20 . Optionally, the strips of the anchor  212  and/or the wedging member  216  include a segmented section, comprising strips or fingers  225 ,  226  which have a smaller width than the strips  122 . The anchor and the wedging member may include any number of strips  222  and/or corresponding fingers  226  that is suitable with respect to the size of the tubular  20 . 
     Referring to  FIGS. 20A to 20F , it can be seen that as the expansion device (the position of which is indicated by arrow  30 ) moves through tubular  20 , tubular  20  shortens. Initially, the free end of the anchor  212  touches the ramp surface  219   a  ( FIG. 20A ). Until the expansion device reaches the ramp member, the result of the shortening is that the distance between ramp member  218  and fixed end  214  of the anchor  212  decreases. The free end of the anchor will slide onto the ramp surface  219   a  of the ramp member and toward to formation, overlapping the ramp member and extending away from the tubular  20 . Preferably, the length of the anchor  212  is chosen such that the free end thereof touches or extends into the formation ( FIG. 17B ). 
     The expansion device subsequently progresses beyond the ramp member  218 , and the tubular  20  continues to expand and shorten at the position of the expander. Due to the shortening, fixed end  217  of wedging member  216  moves toward ramp member  218 , and as a result the bottom surface  286  slides onto the ramp surface  219   b , wherein the top surface  284  is pushed against anchor  212  ( FIGS. 20D ,  20 E). If the radial force, which is induced by shortening of the tubular  20  due to expansion thereof, on the free end of anchor  212  exceeds the local resistance or strength of the formation, the free end will penetrate further into the formation ( FIG. 20D ). However, if said radial force at the free end of anchor  212  is smaller than or equal to the local resistance or strength of the formation, the tip  60  of the anchor will be unable to penetrate the formation. In that case, anchor  212  will be held in place by the formation and the free end of wedging member  216  will in turn be fixated against the anchor  212 . With the free end of ramp member  218  unable to slide further along the outside of tubular  20 , no further shortening can occur. The final distance between fixed end  217  of wedging member  216  and fixed end  214  of anchor  212  is reached once the expansion device has moved past the fixed end  217  of the wedging member  216 , and is defined as L 9  ( FIG. 20D ). Because the tubular is prevented from shortening during a portion of the expansion process, L 9  is not as small as L 2  for a given L 1 . 
     When the free end of wedging member  216  is held in place by the anchor, the maximum load that is applied to the wall of the liner  20  is about equal to the so-called fixed-fixed load. The fixed-fixed load is the local load that is applied to the liner wall when the expander moves between two locations at which the liner is fixed, such that the liner cannot shorten between the two positions. As the fixed-fixed load can be determined beforehand, for instance during lab tests, the liner wall can be designed to be sufficiently strong to withstand the load during expansion, so that collapse of the wall of the expandable tubular can be prevented. Consequently, the device of  FIGS. 18-20  is suitable for both soft and hard formation. The anchor  212  can however extend further away from the tubular wall and into the formation than the anchors  12 ,  112 , as the wedging member  216  can push the anchor toward and into the formation. The anchor  212  can extend for instance about two to three times further into the formation. 
     In a practical embodiment, the expandable tubular element may be expanded such that its radius increases up to about 30%, for instance about 10 to 15%. The length of the tubular may shorten for instance 5 to 10%. 
     For a tubular element having an external diameter of 9⅝ inch, the anchor and/or wedging members may have a thickness in the range of 0.3 to 1 inch (1 to 2.5 cm), for instance about 0.5 inch (1.2 cm). The ramp may typically have an angle with respect to the axis of the tubular element in the order of 30 to 60 degrees, for instance about 45 degrees. The overlap L 4  is for instance 0.5 to 2 inch (1 to 5 cm). The length of the anchor may be in the range of 3 to 16 inch (7.5 to 40 cm). The length of the brace L B  may be in the range of 4 to 20 inch (10 to 50 cm). The minimum penetration depth L 3  may be in the range of 0.2 to 1 inch (5 to 25 mm). The length L 5  may be in the range of 1 to 4 inch (2 to 10 cm). The length L 6  may be in the range of 1 to 8 inch (2 to 20 cm). 
     A single anchoring device provided around the circumference of the tubular can provide an anchoring force up to for instance 3 to 4 MN, for instance about 2 MN. The tubular may be provided with any number of consecutive anchoring devices, to increase the maximum anchoring force. The anchoring device of the invention can be scaled up or down to match any size of expandable tubular element that is commonly used when drilling for hydrocarbons. The force that is required to expand the expandable tubular element may increase locally for instance about 5% to 50% along the length of the anchoring member of the invention. The expansion force increases for instance about 10% to 20% at the position of the welds  14 ,  17 . At the position of the ramp member, the expansion force may increase about 20% to 40% when the tip  60  engages the formation. During fixed-fixed expansion, as described with respect to the  FIGS. 17 and 20 , the expansion force may increase in the range of about 5 to 20%, for instance about 10%. 
     In a practical embodiment of the device shown in  FIGS. 18-20 , the angle of anchor ramp face  219   a  with respect to the tubular axis may be in the range of 40 to 50 degrees, for instance about 45 degrees. The angle of wedging ramp face  219   b  with respect to the tubular axis is for instance in the range of 25 to 40 degrees, for instance about 30 degrees. 
     The angle of the slanted top surface  284  with respect to the tubular axis is in the range of 30 to 45 degrees, for instance about 38 degrees. This angle is chosen to create a sufficiently large area between the anchor  212  and the wedging member  216  to avoid yielding and stimulate relative sliding of the two components. The angle of the slanted bottom surface  286  with respect to the tubular axis is about equal to the angle of wedging ramp face  219   b  (for instance about 45 degrees) to ensure sufficient contact between the two components during expansion. 
     All exemplary sizes and shapes provided above could be scaled and adapted to the external diameter of any expandable tubular element that is typically used for the exploration and production of hydrocarbons. 
     The present invention is not limited to the above-described embodiments thereof, wherein many modifications are conceivable within the scope of the appended claims. Features of respective embodiments can for instance be combined.