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PRIORITY CLAIM 
     The present application claims priority on European Patent Application 03254300.1 filed Jul. 7, 2003. 
     1. Field of the Invention 
     The present invention relates to a method of expanding a tubular element having a first portion to be expanded to a first inner diameter and a second portion to be expanded to a second inner diameter larger than the first inner diameter. 
     2. Background of the Invention 
     Expandable tubular elements find increased application in the industry of wellbore construction, for example, in applications whereby the tubular element, after installation in the wellbore, is radially expanded to form a wellbore casing or liner. Typically the wellbore is drilled in sections, whereby after drilling each wellbore section a casing or liner is lowered in unexpanded state into the newly drilled wellbore section and subsequently radially expanded. Optionally the expanded casing/liner can be cemented in the wellbore by pumping a layer of cement between the casing/liner either before or after the expansion process. 
     Generally it will be required that subsequent casing or liner sections are interconnected in a manner that a fluid tight seal is obtained at the interconnection. This can be achieved, for example, by creating an overlap between subsequent sections of casing or liners such that an upper end portion of a lower casing section extends into a lower end portion of an upper casing section, either with or without a sleeve of deformable material there-between. Such overlap requires that the end portion of the tubular element into which the other tubular element extends, is expanded to a relatively large diameter. However, no reliable expansion method for achieving such result is available. 
     SUMMARY OF THE INVENTION 
     The present inventions include a method of expanding a tubular element having a first portion to be expanded to a first inner diameter and a second portion to be expanded to a second inner diameter larger than the first inner diameter, the method comprising:
     a) arranging an expandable sleeve of selected wall thickness in said second tubular element portion;   b) positioning an expander in the tubular element;   c) operating the expander so as to expand said first tubular element portion to the first inner diameter, and operating the expander so as to expand the sleeve to an inner diameter substantially equal to the second inner diameter minus double the wall thickness of the sleeve; and   d) retrieving the sleeve from the tubular element.   

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be explained hereinafter in more detail by way of example with reference to the accompanying drawings in which: 
         FIG. 1A  schematically shows a side view of an expander when in retracted mode, used in an embodiment of the method of the invention; 
         FIG. 1B  schematically shows the expander of  FIG. 1A  when in expanded mode; 
         FIG. 1C  schematically shows the expander of  FIG. 1A  in longitudinal section; 
         FIG. 2  schematically shows a first step in expansion of a tubular element; 
         FIG. 3A  schematically shows a side view of an expandable sleeve for use in the embodiment of the method of the invention; 
         FIG. 3B  schematically shows a side view of the sleeve of  FIG. 3A  after radial expansion thereof; 
         FIGS. 4-6  schematically show a sequence of steps in expansion of the tubular element of  FIG. 2 ; and 
         FIGS. 7A-B  schematically show a retrieval tool positioned in the tubular element of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the drawings, like reference numerals relate to like components. 
     Referring to  FIGS. 1A-C  there is shown an expander  1  including a steel tubular expander body  2  having a front cylindrical part  2   a , a rear cylindrical part  2   b , and a tapering part  2 c arranged between the cylindrical parts  2   a ,  2   b . A plurality of narrow longitudinal slots  6  are provided in the expander body  2 , which slots are regularly spaced along the circumference of the expander body  2 . Each slot  6  extends radially through the wall of tubular expander body  2 , and has opposite ends  7 ,  8  located at some distance from the respective ends of the expander body  2 . The slots  6  define a plurality of longitudinal body segments  10  spaced along the circumference of the expander body  2 , whereby each body segment  10  extends between a pair of adjacent slots  6  (and vice versa). By virtue of their elongate shape and elastic properties, the body segments  10  will elastically deform by bending radially outward upon application of a suitable radial load to the body segments  10 . Thus the expander  1  is expandable from a radially retracted mode ( FIG. 1A ) whereby each body segment  10  is in its rest position, to a radially expanded mode ( FIG. 1B ) whereby each body segment  10  is in its radially outward bent position upon application of said radial load to the body segment  10 . 
     The expander further includes cylindrical end closures  12 ,  14  arranged to close the respective ends of the expander body  2 , each end closure  12 ,  14  being fixedly connected to the expander body  2 , for example by suitable bolts (not shown). End closure  12  is provided with a through-opening  15 . 
     An inflatable member in the form of elastomeric bladder  16  is arranged within the tubular expander body  2 . The bladder  16  has a cylindrical wall  18  resting against the inner surface of the tubular expander body  2 , and opposite end walls  20 ,  22  resting against the respective end closures  12 ,  14 , thereby defining a fluid chamber  23  formed within the bladder  16 . The end wall  20  is sealed to the end closure  12  and has a through-opening aligned with, and in fluid communication with, through-opening  15  of end closure  12 . A fluid conduit  26  is at one end thereof in fluid communication with the fluid chamber  23  via through-opening  15 . The fluid conduit  26  is at the other end thereof in fluid communication with a fluid control system (not shown) for controlling inflow of fluid to, and outflow of fluid from, the fluid chamber  23 . 
     Reference is further made to  FIG. 2  showing the expander  1  arranged at the lower end  30  of a tubular casing  32  which extends into a wellbore  34  formed in an earth formation  35 . The expander  1  is suspended from surface by a conduit  26 . An expandable tubular sleeve  36  is arranged in a lower portion  38  of the casing  32  and temporarily fixed to the lower end  30  of the casing  32  by tack-welds  39  which should be strong enough to carry the weight of the sleeve  36  and to allow initial expansion of the sleeve  36  and lower casing portion  38 . Hereinafter the lower casing portion  38  is referred to as the bell portion  38  of the casing, and the remainder of the casing  32  is referred to as the remainder casing portion  41 . The front cylindrical part  2   a  of expander  1  extends into the sleeve  36 . 
     The sleeve  36  is shown in more detail in  FIGS. 3A and 3B , whereby  FIG. 3A  shows the sleeve  36  before radial expansion thereof, and  FIG. 3B  shows the sleeve  36  after radial expansion thereof. The wall of the sleeve  36  is provided with a plurality of through-openings in the form of slots  40  extending in axial direction. The slots  40  are arranged in rows of axially aligned slots, whereby adjacent rows are arranged staggered relative to each other so as to form a plurality of axially overlapping slots  40 . Each slot  40  is at each end thereof provided with a circular hole  42 . Plastic hinges  43  are formed by the wall portions of the sleeve  36  between each slot  40  and the respective adjacent holes  42 . In  FIG. 3A  the width of each plastic hinge  43  is indicated by symbol H. 
     The resistance to bending of the hinges  43  is governed by their wall thickness and width H. 
     In  FIG. 4 , the expander  1  is located in the sleeve  36  whereby part of the sleeve  36  and part of the casing  32  have been radially expanded. 
     In  FIG. 5 , the expander  1  is located upwardly from the bell portion  38  whereby the sleeve  36 , the bell portion  38  and part of the remainder casing portion  41  have been radially expanded. 
     In  FIG. 6 , the expander  1  is located further upwardly from the bell portion  38  whereby the sleeve  36 , the bell portion  38  and a further part of the remainder casing portion  41  have been radially expanded. 
     Referring to  FIG. 7A  there is shown a retrieval tool  46  suspended from surface on a running string  48  extending into the casing  32 . The retrieval tool  46  is provided with a number of radially extending spring-loaded pins  50  biased into corresponding openings  52  formed in the wall of the sleeve  36  so as to latch the retrieval tool  46  to the sleeve  36 . 
     Referring to  FIG. 7B  there is shown the retrieval tool  46  latched to the sleeve  36  whereby the sleeve has been pulled upwardly a short distance through the casing  32 . 
     During normal operation, the casing  32  is lowered into the wellbore  34  whereby the sleeve  34  and the expander  1  are arranged relative the casing. 32  in the position shown in  FIG. 2  whereby a moderate pulling force is exerted from surface to the expander  1  via conduit  26 . Subsequently the casing  32  is radially expanded in a plurality of expansion cycles whereby each cycle includes a first stage and a second stage, as explained below. 
     In the first stage of the expansion cycle the fluid control system is operated to pump pressurised fluid, for example drilling fluid, via the conduit  26  into the fluid chamber  23  of the bladder  16 . As a result the bladder  16  is inflated and thereby exerts a radially outward pressure against the body segments  10  which thereby. become elastically deformed by radially outward bending. 
     The volume of fluid pumped into the bladder  16  is selected such that any deformation of the body segment  10  remains within the elastic domain. 
     In order to promote uniform outward bending of the segments  10 , the front part  2   a  of the expander body  2  is optionally provided with a ring or a sleeve (not shown) which limits outward bending of the segments  10 . 
     Thus the body segments  10  revert to their initial positions after release of the fluid pressure in the bladder  16 . Thus the expander  1  is expanded upon pumping of fluid into the bladder  16  from the radially retracted mode to the radially expanded mode thereof. As a result a short initial section of the casing  32  becomes plastically expanded. 
     In the second stage of the expansion cycle the fluid control system is operated to release the fluid pressure in the bladder  16  by allowing outflow of fluid from the bladder  16  back to the control system. The bladder  16  thereby deflates and the body segments  10  move back to their initial undeformed shape so that the expander  1  moves back to the radially unexpanded mode thereof. Optionally, the fluid pressure in the bladder is reduced to below the hydrostatic head, causing the segments to bend inwards. As a result the expander  1  is pulled by conduit  26  a short distance further into the sleeve  36 . 
     Subsequently the above expansion cycle is repeated as many times as needed to expand successively the bell portion  38  of the casing and the remainder casing portion  41  or a desired length thereof. 
     During expansion of the bell portion  38  of the casing, the sleeve  36  is expanded simultaneously with the bell portion  38 . Upon expansion of the sleeve  36 , the plastic hinges  43  deform plastically. The wall sections between the respective hinges  43  rotate thereby opening-up the slots  40  ( FIG. 3B ). Such rotation causes the sleeve  36  to shorten, and the diameter increase of the sleeve  36  is accommodated by deformation of the hinges  43 . 
     By virtue of opening-up of the slots  40 , the expansion force required to expand the sleeve  36  is significantly lower than the force required to expand the casing  32 . Therefore, simultaneous expansion of the sleeve  36  and the bell portion  38  of the casing  32  requires only a slightly higher force than the force required to expand the casing  32  only. It will be understood that the inner surface of the sleeve  36  and the inner surface of the remainder casing portion  41  are expanded to the same diameter. This implies that the inner surface of the bell portion  38  of the casing is expanded to a larger diameter than the inner surface of the remainder casing portion  41 . The difference between the inner diameter of the bell portion  38  and the inner diameter of the remainder casing portion  41  after the expansion process, is substantially equal to twice the wall thickness of the sleeve  36 . The wall thickness of the sleeve  36  does not change during expansion because the deformation is concentrated in the plastic hinges  43 . 
     Furthermore, the sleeve  36  has a relatively large tendency to spring back after expansion because elastic relaxation of the sleeve is governed by elastic reverse bending of the hinges  43  rather than elastic contraction in circumferential direction as occurs in the casing  32 . 
     The tack-welds  39  are sheared-off during expansion of the bell portion  38  due to differential axial shortening of the sleeve  36  and the bell portion  38  as a result of the expansion process. 
     Subsequent stages of the expansion process are shown in  FIGS. 4-6  indicating gradual progression of the expander  1  through the casing  32 . 
     After the casing  32  has been expanded, the expander  1  is removed from the casing and the retrieval tool  46  is lowered on running string  48  through the casing  32 . Upon arrival of the retrieval tool  46  at the sleeve  36 , lowering is slowly continued until the retrieval tool latches to the sleeve  36  by virtue of latching of the spring-loaded pins  50  into the openings  52  of the sleeve  36 . The retrieval tool  46  is then pulled upwardly on running string  48 . 
     As shown in  FIG. 7B , the sleeve  36  is thereby radially compressed as it moves upwardly into the remainder casing portion  41 . Compression of the sleeve  36  does not require a high compression force since such compression is accomplished by closing of the slots  50  of the sleeve  36 . Furthermore, the tendency of the sleeve to spring back elastically, and the pulling force exerted to the sleeve by the retrieval tool, enable easy removal of the sleeve  36  from the casing  32 . The sleeve  36  is finally removed from the casing  32  at the upper end thereof. 
     In this manner it is achieved that the lower portion of the casing  32  is expanded to a larger diameter than the remainder of the casing so that a subsequent casing (not shown) can be installed and expanded below the casing  32  whereby an upper end portion of the subsequent casing extends into the bell portion  38  of the casing  32 . 
     Thereby an overlap is created between the casing  32  and the subsequent casing, which enables fixing and sealing of the casings to each other. 
     The resistance to expansion of the sleeve can be reduced further by reducing the width H of the hinges and/or by reducing the wall thickness of the sleeve at the hinges and/or by increasing the length of the slots. 
     Instead of fixing the sleeve to the casing by welding, the sleeve can be fixed to the casing by a layer of adhesive which fails upon differential movement between the sleeve and the casing during expansion. It is thereby ensured that the sleeve is secured in place until the entire sleeve has been expanded. Also the body segments can be spot-welded to the tubular element at their respective mid portions. 
     Instead of using the expander described above, a conventional expander cone can be used, for example an expander cone which is pulled, pumped or pushed through the casing. 
     Instead of using the retrieval tool described above, a retrieval tool can be used which is connected to the expander and therefore moves simultaneously with the expander through the casing. In such application the sleeve is removed from the casing simultaneously with expansion of the remainder casing portion. 
     Instead of the expander body being provided with slots having opposite ends near the respective ends of the expander body, the expander body can be provided with slots which extend only along a portion of the length of the expander body and which are arranged in a longitudinally overlapping arrangement. Such arrangement can be, for example, similar to the arrangement of the slots of the sleeve shown in  FIGS. 3A ,  3 B. 
     In addition to operating the fluid control system so as to pump pressurised fluid via the conduit into the bladder, the fluid control system can be operated to exert suction to the bladder so as to extract fluid from the bladder causing inward bending of the segments of the expander body. In this manner the expansion ratio of the expander can be increased. 
     Instead of applying a sleeve with hinges which deform plastically, a sleeve can be applied with hinges which deform purely elastically, such as, for example, a sleeve made of shape memory metal. 
     Another example of a suitable sleeve is a sleeve provided with slots defining a pattern of bi-stable cells, each cell being capable of assuming a first stable configuration and a second stable configuration, whereby the sleeve has a larger inner diameter when the cells are in their respective second stable configurations than when the cells are in their respective first stable configurations. An example embodiment of such sleeve is the tube formed of bi-stable cells disclosed in GB-A-2368082.

Summary:
A method of expanding a tubular element is provided, the tubular element having a first portion to be expanded to a first inner diameter and a second portion to be expanded to a second inner diameter larger than the first inner diameter. The method comprising:
   a) arranging an expandable sleeve of selected wall thickness in said second tubular element portion;   b) positioning an expander in the tubular element;   c) operating the expander so as to expand said first tubular element portion to the first inner diameter, and operating the expander so as to expand the sleeve to an inner diameter substantially equal to the second inner diameter minus double the wall thickness of the sleeve; and   d) retrieving the sleeve from the tubular element.