Abstract:
A method and apparatus for multilateral completion comprises providing a casing string having a casing, a branching sub connected to the casing, and a locating profile. An expanding tool positionable in the branching sub is adapted to mate with the locating profile to fix a position of the expanding tool, such as to rotationally orient the expanding tool, fix a radial position of the expanding tool, and/or fix an axial position of the expanding tool. The branching sub has a non-expanded state, and the expanding tool is adapted to expand the branching sub.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 09/518,365, filed Mar. 3, 2000, which is a continuation of Application Ser. No. 08/898,700, filed Jul. 24, 1997 (now U.S. Pat. No. 6,056,059, which is a continuation-in-part of application Ser. No. 08/798,591, filed Feb. 11,1997 (now U.S. Pat. No. 5,944,107, which claimed priority from Provisional Application No. 60/013,227 filed Mar. 11, 1996 and Provisional Application No. 60/025,033 filed Aug. 27, 1996. The &#39;700 Application claimed further priority from Provisional Application No. 60/022,781, filed Jul. 30, 1996, the contents of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates generally to the field of wells, particularly to the field of establishing branch wells from a parent hydrocarbon well. More particularly the invention relates to establishing multiple branch wells from a common depth point, called a node, deep in the well. 
     2.Description of the Related Art 
     Multiple wells have been drilled from a common location, particularly while drilling from an offshore platform where multiple wells must be drilled to cover the great expenses of offshore drilling. As illustrated in FIGS. 1A and 1B, such wells are drilled through a common conductor pipe, and each well includes surface casino liners, intermediate casino and parent casing as is well known in the field of offshore drilling of hydrocarbon wells. U.S. Pat. No. 5,458,199 describes apparatus and methods for drilling multiple wells from a common wellbore at or near the surface of the earth. U.S. Pat. No. 4,573,541 describes a downhole take-off assembly for a parent well which includes multiple take-off tubes which communicate with branched wells from a common point. 
     Branch wells are also known in the art of well drilling which branch from multiple points in the parent well as illustrated in FIG.  2 . Branch wells are created from the parent well, but necessarily the parent well extends below the branching point of the primary well. As a result, the branching well is typically of a smaller diameter than that of the primary well which extends below the branching point. Furthermore, difficult sealing problems have faced the art for establishing communication between the branch well and the primary well. 
     For example, U.S. Pat. No. 5,388,648 describes methods relating to well juncture sealing with various sets of embodiments to accomplish such sealing. The disclosure of the &gt;648 patent proposes solutions to several serious sealing problems which are encountered when establishing branches in a well. Such sealing problems relate to the requirement of ensuring the connectivity of the branch casing liner with the parent casing and to maintaining hydraulic isolation of the juncture under differential pressure. 
     A fundamental problem exists in establishing branch wells at a depth in a primary well in that apparatus for establishing such branch wells must be run on parent casing which must fit within intermediate casing of the well. Accordingly, any such apparatus for establishing branch wells must have an outer diameter which is essentially no greater than that of the parent casing. Furthermore, it is desirable that when branch wells are established, they have as large a diameter as possible. Still further, it is desirable that such branch wells be lined with casing which may be established and sealed with the branching equipment with conventional casing hangers. 
     An important object of this invention is to provide an apparatus and method by which multiple branches connect to a primary well at a single depth in the well where the branch wells are controlled and sealed with respect to the primary well with conventional liner-to-casing connections. 
     Another important object of this invention is to provide a multiple outlet branching sub having an outer diameter such that it may be run in a well to a deployment location via primary casing. 
     Another object of this invention is to provide a multiple outlet branching sub in which multiple outlets are fabricated in a retracted state and are expanded while downhole at a branching deployment location to produce maximum branch well diameters rounded to provide conventional liner-to-casing connections. 
     Another object of this invention is to provide apparatus for downhole expansion of retracted outlet members in order to direct each outlet into an arcuate path outwardly from the axis of the primary well and to expand the outlets into an essentially round shape such that after a branch well is drilled through an outlet, conventional liner-to-casing connections can be made to such outlet members. 
     SUMMARY OF THE INVENTION 
     These objects and other advantages and features are provided in a method and apparatus for establishing multiple branch wells from a parent well. A multiple branching sub is provided for deployment in a borehole by means of a parent casing through a parent well. The branching sub includes a branching chamber which has an open first end of cylindrical shape. The branching chamber has a second end to which branching outlet members are connected. The first end is connected to the parent well casing in a conventional manner, such as by threading, for deployment to a branching location in the parent well. 
     Multiple branching outlet members, each of which is integrally connected to the second end of the branching chamber, provide fluid communication with the branching chamber. Each of the outlet members is prefabricated such that such members are in a retracted position for insertion of the sub into and down through the parent well to a deployment location deep in the well. Each of the multiple outlets is substantially totally within an imaginary cylinder which is coaxial with and of substantially the same radius as the first end of the branching chamber. The prefabrication of the outlet members causes each outlet member to be transformed in cross-sectional shape from a round or circular shape to an oblong or other suitable shape such that its outer profile fits within the imaginary cylinder. The outer profile of each outlet member cooperates with the outer profiles of other outlet members to substantially fill the area of a cross-section of the imaginary cylinder. As a result, a substantially greater cross-sectional area of the multiple outlet members is achieved within a cross-section of the imaginary cylinder as compared with a corresponding number of tubular multiple outlet members of circular cross-section. 
     The multiple outlet members are constructed of a material which may be plastically deformed by cold forming. A forming tool is used, after the multiple branching sub is deployed in the parent well, to expand at least one of the multiple branching outlet members outwardly from the connection to the branching chamber. Preferably all of the outlet members are expanded simultaneously. Simultaneously with the outward expansion, the multiple outlets are expanded into a substantially circular radial cross-sectional shape along their axial extent. 
     After the multiple outlet members which branch from the branching chamber are expanded, each of the multiple branching outlets are plugged. Next, a borehole is drilled through a selected one of the multiple branching outlets. A substantially round liner is provided through the selected branching outlet and into the branch well. The liner of circular cross-section is sealed to the selected branching outlet circular cross-section by means of a conventional casing hanger. A borehole and liner is established for a plurality of the multiple branching outlets. A downhole manifold is installed in the branching chamber. Next multiple branch wells are completed. The production of each branch well to the parent well is controlled with the manifold. 
     The apparatus for expanding an outlet of the multiple branching sub includes an uphole power and control unit and a downhole operational unit. An electrical wireline connects the uphole power and control unit and the downhole operational unit. The wireline provides a physical connection for lowering the downhole operational unit to the branching sub and provides an electrical path for transmission of power and bidirectional control and status signals. 
     The downhole operational unit includes a forming mechanism arranged and designed for insertion in at least one retracted branching outlet member of the sub (and preferably into all of the outlet members at the same time) and for expanding the outlet member outwardly from its imaginary cylinder at deployment. Preferably each outlet member is expanded outwardly and expanded to a circular radial cross-section simultaneously. The downhole operational unit includes latching and orientation mechanisms which cooperate with corresponding mechanisms of the sub. Such cooperating mechanisms allow the forming mechanism to be radially oriented within the multiple branching sub so that it is aligned with a selected outlet of the sub and preferably with all of the outlets of the sub. The downhole operational unit includes a hydraulic pump and a head having hydraulic fluid lines connected to the hydraulic pump. The forming mechanism includes a hydraulically powered forming pad. A telescopic link between each forming pad and head provides pressurized hydraulic fluid to the forming pads as they move downwardly while expanding the outlet members. 
     According to a second, alternative embodiment of the invention , a branching sub is provided which allows multiple branches from a parent casing without the need for sealing joints and which allows the use of conventional well controlled liner packers and casing joints. The geometry of the housing of the branching sub allows the housing to achieve maximum pressure rating considering the size of the branch outlet with regard to the size of the parent casing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The objects, advantages and features of the invention will become more apparent by reference to the drawings which are appended hereto and wherein an illustrative embodiment of the invention is shown, of which: 
     FIGS. 1A and 1B illustrate a prior art triple liner packed in a conductor casing termination in which the outlet members are round during installation and are packed to fit within the conductor casing; 
     FIG. 2 illustrates a prior art parent or vertical well and lateral branch wells which extend therefrom; 
     FIGS. 3A,  3 B, and  3 C illustrate a three outlet branching sub according to a first embodiment of the invention where FIG. 3A is a radial cross-section through the branching outlets of the sub, with one outlet completely in a retracted position, with another outlet in a position between its retracted position and its fully expanded position, and the third outlet being in a fully expanded position, and where FIG. 3B is a radial cross-section through the branching outlets of the sub with each of the outlets fully expanded after deployment in a parent well, and FIG. 3C is an axial cross-section of the branching sub showing two of the branching outlets fully expanded to a round shape in which casing has been run into a branch well and sealed with respect to the branching outlets by means of conventional liner hanging packers. 
     FIG. 4 is a perspective view of a three symmetrical outlet branching sub of a first embodiment of the invention with the outlet branches expanded. 
     FIGS. 5A,  5 B,  5 C, and  5 D illustrate configurations of the first embodiment of the invention with asymmetrical branching outlets with at least one outlet having larger internal dimensions than the other two, with FIG. 5A being a radial cross-section through the branching outlets along line  5 A— 5 A in a retracted position, with FIG. 5B being an axial cross-section through the lines  5 B— 5 B of FIG. 5A, with FIG. 5C being a radial cross-section along lines  5 C— 5 C of FIG. 5D with the branching outlets in an expanded position, and with FIG. 5D being an axial cross-section along lines  5 D— 5 D of FIG. 5C with the branching outlets in an expanded position; 
     FIGS.  6 A— 6 E illustrate radial cross-sections of several examples of branching outlet configurations of the branching sub according to the first embodiment of the invention, with all outlet branches fully expanded from their retracted state during deployment in a parent well, with FIG. 6A illustrating two equal diameter outlet branches, FIG. 6B illustrating three equal diameter outlet branches, FIG. 6C, like FIG. 5C, illustrating three outlet branches with one branch characterized by a larger diameter than the other two, with FIG. 6D illustrating four equal diameter outlet branches, and with FIG. 6E illustrating five outlet branches with the center branch being of smaller diameter than the other four; 
     FIGS. 7A-7E illustrate stages of expanding the outlet members of an expandable branching sub according to the invention, with FIG. 7A illustrating an axial cross-section of the sub showing multiple branching outlets with one such outlet in a retracted position and the other such outlet being expanded starting with its connection to the branching head and continuing expansion downwardly toward the lower opening of the branching outlets, with FIG. 7B illustrating a radial cross-section at axial position B of FIG.  7 A and assuming that each of three symmetrical branching outlets are being expanded simultaneously, and with FIGS. 7C through 7E showing various stages of expansion as a function of axial distance along the branching outlets; 
     FIGS. 8A and 8B illustrate respectively in axial cross-section and a radial cross-section along lines  8 B— 8 B, latching and orientation profiles of a branching chamber of the branching sub, and FIG. 8A further illustrates an extension leg and supporting shoe for deployment in a parent well and for providing stability to the branching sub while expanding the branching outlets from their retracted position; 
     FIG. 9 schematically illustrates uphole and downhole apparatus for expanding the branching outlets of the branching sub; 
     FIG. 10 illustrates steps of the process of expanding and forming the branching outlets with a pressure forming pad of the apparatus of FIG. 9; 
     FIGS. 11A-11H illustrate steps of an installation sequence for a nodal branching sub and for creating branch wells from a parent well; 
     FIG. 12 illustrates a branching sub deployed in a parent well and further illustrates branch well liners hung from branching outlets and still further illustrates production apparatus deployed in the branching sub for controlling production from branch wells into the parent well; 
     FIGS. 13A and 13B geometrically illustrate the increase in branch well size achievable for this invention as compared with prior art conventional axial branch wells from liners packed at the end of parent casing; 
     FIGS. 14A-14D are illustrative sketches of nodal branching according to the invention where FIG. 14A illustrates establishing a node in a parent well and establishing branch wells at a common depth point in the parent well, all of which communicate with a parent well at the node of the parent well; with FIG. 14B illustrating an expanded branching sub which has had its branching outlets expanded beyond the diameter of the parent casing and formed to be substantially round; with FIG. 14C illustrating using a primary node and secondary nodes to produce hydrocarbons from a single strata; and with FIG. 14D illustrating using an expanded branching sub from a primary node to reach multiple subterranean targets; 
     FIG. 15A illustrates a two outlet version of a branching sub according to the first embodiment of the invention, with FIGS. 15B,  15 B′,  15 C, and  15 D illustrating cross-sectional profiles of such two outlet version of a branching sub with an alternative post-forming tool at various depth locations in the outlet members; 
     FIG. 16 illustrates a two arm alternative version of a post-forming tool; 
     FIGS. 17A-17D illustrate the operation of such alternative post-forming tool; 
     FIGS. 18A-18E illustrate a branching sub according to the first embodiment of the invention with concave deformation of the branching outlets; 
     FIGS. 19A-19C illustrate an alternative actuating apparatus according to the invention. 
     FIGS. 20A and 20B illustrate a second embodiment of the invention where FIG. 20A is an exterior view of a branching sub with a main pipe and a lateral branching outlet and FIG. 20B is an axial section view of such branching sub; 
     FIGS. 21A and 21B are axial and radial section views of the branching sub of FIGS. 20A and 20B but in a retracted state, and 
     FIGS. 21C and 21D are axial and radial section views of the branching sub of FIGS. 20A and 20B in an expanded state; 
     FIG. 22 is a graph which shows that the yield strength of the housing material of the branching sub increases with the rate of deformation during expansion; 
     FIG. 23 is a schematic illustration of the branching sub according to a second embodiment of the invention where lateral or branch holes are created from the main body of the sub or subs to reach distinct formations from one main borehole; 
     FIG. 23A shows a portion of the branching sub of FIG. 23; 
     FIG. 24 illustrates the use of a deflecting tool which may be inserted within the main pipe of the branching sub whereby a drilling tool which enters from the top of the sub may be directed into the lateral outlet; 
     FIG. 25 illustrates two branching subs connected in tandem with the tandem connection placed in a series of casing links of a casing string; and 
     FIGS. 26A and 26B illustrate a cap which may be welded across the branching outlet in order to close it off for certain well operations. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As described above, FIGS. 1A and 1B illustrate the problems with prior art apparatus and methods for establishing branch wells from a parent well. FIGS. 1A and 1B show radial and axial cross-sections of multiple outlet liners  12  hung and sealed from a large diameter conductor pipe  10 . The outlets are round in order to facilitate use of conventional lining hanger packers  14  to seal the outlet liners  12  for communication with the conductor pipe  10 . The arrangement of FIGS. 1A and 1B requires that multiple round outlets of diameter Do fit within the diameter Ds 1  of the conductor pipe  10 . In many cases, especially where the conductor pipe must be deployed at a depth in the well, rather than at the surface of the well, it is not feasible to provide a borehole of sufficient outer diameter to allow branch well outlets of sufficient diameter to be installed. 
     The technique of providing branch wells according to the prior art arrangement depicted in FIG. 2 creates branch wells  22 ,  24  from a primary well  20 . Special sealing arrangements  26 , unlike conventional casing hangers, must be provided to seal a lined branch well  22 ,  24  to the primary well  20 . 
     Description of Branching Sub According to a First Embodiment of the Invention 
     FIGS. 3A,  3 B, and  3 C illustrate a branching sub  30  according to the invention. The branching sub includes a branching chamber  32 , (which may be connected to and carried by parent well casing (See parent casing  604  of FIG.  12 ), and multiple outlet members, for example three outlet members  34 ,  36 ,  38  illustrated in FIGS. 3A,  3 B, and  3 C. FIG. 3A is a radial cross-section view through the branching chamber  32  which illustrates one outlet member  34  in a retracted state, a second outlet member  36  in the state of being expanded outwardly, and a third outlet member  38  which has been fully expanded outwardly. (FIG. 3A is presented for illustrative purposes, because according to the invention it is preferred to expand and circularize each of the outlets simultaneously.) In the retracted state, each cutlet is deformed as shown particularly for outlet member  34 . A round tube is deformed such that its cross-sectional interior area remains essentially the same as that of a circular or round tube, but its exterior shape is such that it fits cooperatively with the deformed shape of the other outlet members, all within an imaginary cylinder having a diameter essentially the same as that of the branching chamber  32 . In that way the branching chamber  32  and its retracted outlet members have an effective outer diameter which allows it to be run in a parent well to a deployment location while attached to a parent casing. Outlet member  34  in its retracted state is illustrated in an oblong shape, but other retracted shapes may also prove to have advantageous characteristics. For example, a concave central area of deformation in the outer side of a retracted outlet member may be advantageous to provide a stiffer outlet member. Such deformation is progressively greater and deeper starting from the top to the bottom of the outlet member. 
     FIG. 3A shows outlet member  36  in a state of being expanded in an arcuate path outwardly from the branching chamber  32  while simultaneously being rounded by a downhole forming-expanding tool that is described below. The arrows labeled F represent forces being applied from the interior of the outlet member  36  in order to expand that outlet member both outwardly in an arcuate path away from branching chamber  32  and to circularize it from its retracted state (as is the condition of outlet member  34 ) to its expanded or fully deployed state like outlet member  38 . 
     FIG. 3B is a radial cross-section as viewed by lines  3 B— 3 B of FIG.  3 C through the branching sub  30  at the level of outlet members  36 ,  38 . FIG. 3C illustrates conventional casing liners  42 ,  44  which have been installed through branching chamber  32  and into respective outlet members  36 ,  38 . Conventional liner hanging packers  46 ,  48  seal casing liners  42 ,  44  to outlet members  36 ,  38 . As illustrated in FIGS. 3B and 3C, if the diameter Ds 2  of the branching chamber  32  is the same as the diameter Ds 1  of the conductor pipe of prior art FIG. 1B, then the outlet diameter Dc of FIG. 3C is 1.35 times as great as the outer diameter Do of FIG.  1 B. The liner cross-sectional area Sc of the sub of FIG. 3C is 1.82 times as great as the liner cross-sectional area S 0  of FIG.  1 A. When fully expanded, the effective diameter of the expanded outlet members  34 ,  36 ,  38  exceeds that of the branching chamber  32 . 
     Experiments have been conducted to prove the feasibility of manufacturing branching sub  30  with outlets in a retracted state, and later operationally expanding outwardly and rounding the outlets. 
     Experiment Phase 1 
     Two casing sizes were selected: a first one, one meter long was 7 inch diameter casing with a wall thickness of 4.5 mm; the second was one meter long and was 7 inch diameter casing with a wall thickness of 8 mm. A hydraulic jack was designed for placement in a casing for expanding it. Each casing was successfully preformed into an elliptical shape, e.g., to simulate the shape of outlet member  34  in FIG.  3 A and reformed into circular shape while using a circularizing forming head with the jack. Circularity, like that of outlet member  38  of FIG. 3A was achieved with plus or minus difference from perfect circularity of 2 mm. 
     Experiment Phase 2 
     Two, one meter long, 7 inch diameter, 23 pound casings were machined axially at an angle of 2.5 degrees. The two casings were joined together at their machined surfaces by electron beam (EB) welding. The joined casings were deformed to fit inside an 11 inch diameter. The welding at the junction of the two casinos and the casings themselves had no visible cracks. The maximum diameter was 10.7 inches; the minimum diameter was 10.5 inches. 
     a) Machinery 
     Before milling each casing at an angle of 2.5 degrees, a spacer was temporarily welded at its end to avoid possible deformation during machining. Next each casing was machined roughly and then finished to assure that each machined surface was coplanar with the other. The spacer welded at the end of the casing was machined at the same time. 
     b) Welding 
     The two machined casings were assembled together with a jig, pressed together and carefully positioned to maintain alignment of the machined surfaces. The assembly was then fixed by several tungsten inert gas (TIG) spot welds and the jig was removed. In an EB welding chamber, the two machined casings were spot welded alternately on both sides to avoid possible deformation which could open a gap between the two surfaces . Next, about 500 mm were EB welded on one side; the combination was turned over and EB welded on the other side. Finally the bottom of the combination was EB welded and turned over again to complete the welding. The result was satisfactory; the weld fillet was continuous without any loss of material. As a result, the two machined surfaces of the casings were joined with no gap. 
     c) Deformation 
     Deformation was done with a special jig of two portions of half cylinders pushed against each other by a jack with a force of 30 metric tons (66,000 pounds). The half cylinders had an inside diameter which was slightly smaller than 11 inches. Accordingly, the final diameter of the deformed assembly was less than 11 inches when the junction was deformed. Pliers were placed inside the junction to aid deformation of the outlet where it is critical: at the end of the tube where the deformation is maximal. 
     A large wedge with a 5 degree angle was installed between the two outlets to facilitate flattening them when deforming. The deformation started at the outlets. Force was applied on the pliers and simultaneously on the jack. A force of about one ton was continuously applied to the pliers; the outside jig was moved down in steps of 125 mm; at each step a force of 15 metric tons (33,000 pounds) was applied. The operation was repeated with a force of 20 metric tons (44,000 pounds), and the end of the outlets started to flatten on the wedge. The process was completed at a force of 30 metric tons (66,000 pounds). The resulting deformed product was satisfactory. 
     It is preferred to modify the shape of the pliers in such a way that the pliers deform the outlet with a smooth angle and to weld the wedge after deformation, rather than before, and to weld it by using two large wedges on each side of it to avoid a Anegative≅ deformation of this area. 
     Experiment Phase 2 was conducted a second time, but with a steel sheet metal stiffener welded along the EB welds of both sides of the junction of the two casings. The junction was deformed as in Experiment Phase 2 to fit within an 11 inch diameter. A jack with a force of 30 metric tons (66,000 pounds) was used. Pliers, as for the first junction, were not used. A large wedge was used for the first junction with a 5 degree angle cut in two and installed on each side of the welded wedge between the two outlets to facilitate flattening of the outlets when deforming. The deformation started at the outlets and continued toward the junction. This operation was repeated with a force of 30 metric tons. The end of the outlets started to flatten on the wedge. The portion most difficult to deform was around the junction of the casings where the outlets are complete inside but welded together, where the welded surface is between the top of the inside ellipse and the top of the outside ellipse. As a result of this experiment, a higher capacity jack of 50 metric tons force was provided. 
     Experiment Phase 3 
     A full length prototype with two 7 inch casings connected to a 9⅝ inch casing was manufactured and pressure tested. Testing stopped at 27 bar because deformation was occurring without pressure variation. 
     a) Machining 
     Machining was performed in the same way as for the two previous junctions except that the length of the casings was 1.25 meters instead of 1 meter, and a groove was machined around the elliptical profile to enhance the EB welding process. Additionally, a blind hole was machined on the plane of the cut of each casing to install a pin between the two casings to provide better positioning. The upper adapter was machined out of a solid bar of steel on a numerically controlled milling machine to provide a continuous profile between the 7 inch casings, with a 2.5 degree angle, and the 9⅝ inch casing. The adapter was machined to accept a plug. The inner diameter of the lower end of the 7 inch casings was machined to accept the expanding plugs. 
     b) Welding 
     The two machined casings were assembled together with a jig and pressed together. The assembly was then fixed together by several spot TIG welds and the jig was removed. In an EB chamber, the two parts were EB spot welded alternately on both sides to avoid possible deformation. Then the two casings were EB welded on one side; the assembly was turned over and EB welded on the other side. The assembled casings were joined satisfactorily. An adapter was then TIG welded on the assembled casings as well as a wedge in between the 7 inch casings. 
     c) Pressure Testing 
     Deformation during pressure testing was measured using two linear potentiometers placed on the EB weld. The pressure was increased by steps of 5 bar, and the value of the potentiometer was recorded at atmospheric pressure, at the given pressure, and when returned to atmospheric pressure. As a result of such pressure testing, it was determined that the total plastic deformation of the casings near their junction was 4.7 mm and outwardly of their junction was 3.7 mm. 
     Experiment Phase 3 showed that the deformation at 27 bar was too high. Nevertheless, the deformation was localized in a small area. The upper adapter and the large casing welding act as stiffeners. It was determined to add a stiffener in the plane of welding which can be Aanchored≅ in the area of low deformation. 
     Experiment Phase 4 
     A full length prototype with two 7 inch casings (9 mm thickness) connected to a 9 ⅝ inch casing was deformed to fit inside a 10.6 inch cylinder. This deformation was performed using the same jig used for Experiment Phase 3, but with a jack with 50 metric tons capacity instead of 30 metric tons. 
     a) Deformation Jig 
     The deformation jig was modified to accept a higher deforming force and the bar which supports the fixed half shell was reinforced. The jig was bolted on a frame and a crane was included in the frame to lift the junction and displace it during the deformation process. 
     b) Deforming Process 
     The change of dimension of the joined casing during deformation was measured using a sliding gauge. Such change of dimension was measured before applying the pressure, under pressure and after releasing the pressure. Deformation started at the middle of the junction where it is stiffest and continued toward the ends of the outlets because the deformation must be larger at the outlets. The deformation on the bottom of the junction was too high on the first run and reached nearly 10 inches. At the middle of the junction, the deformation was about 10.6 inches. Except for the bottom end which was deformed too much with negative curvature around the wedge, the remainder of the junction stayed around 10.6 inches. The maximum pressure applied was 670 bar which required a force of 48 metric tons. For joining and deforming casings of thicker tubes, the jig must be rebuilt to accept large deforming forces. 
     c) Conclusion 
     The deformation of the prototype of Experiment Phase 4 was conducted easily with the new jig. The casings were reopened to the original shape. 
     FIG. 4 is a perspective view of the branching sub  30  of FIGS. 3A,  3 B,  3 C where the branching sub is shown after expansion. Threads  31  are provided at the top end of branching chamber  32 . Threads  31  enable branching sub  30  to be connected to a parent casing for deployment at a subterranean location. Outlet members  34 ,  36 ,  38  are shown expanded as they would look downhole at the end of a parent well. 
     FIGS. 5A-5D illustrate an alternative three outlet branching sub  301  according to the invention. FIGS. 5A and 5B illustrate in radial and axial cross-section views the sub  301  in its retracted position. Outlet members  341 ,  361  and  381  are illustrated with outlet member  361  being about equal to the combined radial cross-sectional area of outlet members  341  and  381  combined. Each of the outlet members are deformed inwardly from a round tubular shape to the shapes as illustrated in FIG. 5A whereby the combined deformed areas of outlet members  341 ,  361  and  381  substantially fill the circular area of branching chamber  321 . Other deformation shapes may be advantageous as mentioned above. Each deformed shape of outlet members  341 ,  361  and  381  of FIG. 5A is characterized by (for example, of the outlet member  341 ) a circular outer section  342  and one or more connecting, non-circular sections  343 ,  345 . Such non-circular sections  343 ,  345  are cooperatively shaped with section  362  of outlet member  361  and  382  of outlet member  381  so as to maximize the internal radial cross-sectional areas of outlet members  341 ,  361  and  381 . 
     FIGS. 5C and 5D illustrate the branching sub  301  of FIGS. 5A and 5B after its outlet members have been fully expanded after deployment in a parent well. Outlet members  361  and  381  are illustrated as having been simultaneously expanded in a gently curving path outwardly from the axis of branching chamber  321  and expanded radially to form circular tubular shapes from the deformed retracted state of FIGS. 5A and 5B. 
     FIGS. 6A-6E show in schematic form the size of expanded outlet members as compared to that of the branching chamber. FIG. 6A shows two outlet members  241 ,  242  which have been expanded from a deformed retracted state. The diameters of outlet members  241  and  242  are substantially greater in an expanded state as compared to their circular diameters if they could not be expanded. FIG. 6B repeats the case of FIG.  3 B. FIG. 6C repeats the uneven triple outlet configuration as shown in FIGS. 5A-5D. FIG. 6D illustrates four expandable outlet members from a branching chamber  422 . Each of the outlet members  441 ,  442 ,  443 ,  445  are of the same diameter. FIG. 6E illustrates five outlet members, where outlet member  545  is smaller than the other four outlet members  541 ,  542 ,  543 ,  544 . Outlet member  545  may or may not be deformed in the retracted state of the branching sub. 
     Description of Method for Expanding a Deformed Retracted Outlet Member FIGS. 7A-7E illustrate downhole forming heads  122 ,  124 ,  126  operating at various depths in outlet members  38 ,  34 ,  36 . As shown on the right hand side of FIG. 7A, a generalized forming head  122  is shown as it enters a deformed retracted outlet member, for example outlet member  38 , at location B. Each of the forming heads  122 ,  124 ,  126  has not yet reached an outlet member, but the heads have already begun to expand the outlet wall of branching chamber  32  outwardly as illustrated in FIG.  7 B. The forming heads  122 ,  124 ,  126  continue to expand the outlet members outwardly as shown at location C. FIG. 7C shows the forming heads  122 ,  124 ,  126  expanding the outlet members outwardly while simultaneously circularizing them. Forming pads  123 ,  125 ,  127  are forced outwardly by a piston in each of the forming heads  122 ,  124 ,  126 . The forming heads simultaneously bear against central wall region  150  which acts as a reaction body so as to simultaneously expand and form the outlet members  38 ,  34 ,  36  while balancing reactive forces while expanding. FIGS. 7D and 7E illustrate the forming step at locations D and E of FIG.  7 A. 
     FIGS. 8A and 8B illustrate an axially extending slot  160  in the branching chamber  32  of branching sub  30 . Such slot  160  cooperates with an orienting and latching sub of a downhole forming tool for radial positioning of such orienting and latching sub for forming and expanding the multiple outlet members downhole. A notch  162  in branching chamber  32  is used to latch the downhole forming tool at a predetermined axial position. 
     An extension leg  170  projects downwardly from the central wall region  150  of branching sub  30 . A foot  172  is carried at the end of extension leg  170 . In operation, foot  172  is lowered to the bottom of the borehole at the deployment location. It provides support to branching sub  30  during forming tool expanding and other operations. 
     Description of Forming Tool 
     a) Description of Embodiment of FIGS. 9,  10 FIGS. 9 and 10 illustrate the forming tool used to expand multiple outlet members, for example outlet members  34 ,  36 ,  38  of FIGS. 3A,  3 B, and  3 C and FIGS. 7B,  7 C,  7 D and  7 E. The forming tool includes uphole apparatus  100  arid downhole apparatus  200 . The uphole apparatus  100  includes a conventional computer  102  programmed to control telemetry and power supply unit  104  and to receive commands from and display information to a human operator. An uphole winch unit  106  has an electrical wireline  110  spooled thereon for lowering downhole apparatus  200  through a parent well casing and into the branching chamber  32  of a branching sub  30  which is connected to and carried at the end of the parent casing. 
     The downhole apparatus  200  includes a conventional cable head  202  which provides a strength/electrical connection to wireline  110 . A telemetry, power supplies and controls module  204  includes conventional telemetry, power supply and control circuits which function to communicate with uphole computer  102  via wireline  110  and to provide power and control signals to downhole modules. Hydraulic power unit  206  includes a conventional electrically powered hydraulic pump for producing downhole pressurized hydraulic fluid. An orienting and latching sub  208  includes a latching device  210  (schematically illustrated) for fitting within notch  162  of branching chamber  32  of FIG.  8 A and an orienting device  212  (schematically illustrated) for cooperating with slot  160  of branching chamber  32 . When the downhole apparatus  200  is lowered into branching sub  30 , orienting device  212  enters the slot  160  and the downhole apparatus  200  is further lowered until the latching device  210  enters and latches within notch  162 . 
     Fixed traveling head  213  provides hydraulic fluid communication between hydraulic power unit  206  and the traveling forming heads  122 ,  124 ,  126 , for example. Telescopic links  180  provide pressurized hydraulic fluid to traveling forming heads  122 ,  124 ,  126  as the heads  122 ,  124 ,  126  move downwardly within the multiple outlet members, for example outlet members  34 ,  36 ,  38  of FIGS. 7B-7E. Monitoring heads  182 ,  184 ,  186  are provided to determine the radial distance moved while radially forming an outlet member. 
     FIG. 10 illustrates traveling forming heads  126 ,  124 ,  122  in different stages of forming an outlet member of branching sub  30 . Forming head  126  is shown in outlet member  36 , which is illustrated by a heavy line before radial forming in the retracted outlet member  36 . The outlet member is shown in light lines  36 ′,  36 ″, where the outlet member is depicted as  36 ′ in an intermediate stage of forming and as  36 ″ in its final formed stage. 
     The forming head  124  is shown as it is radially forming retracted outlet member  34  (in light line) to an intermediate stage  34 ′. A final stage is illustrated as circularized outlet member  34 ″. The forming head  124 , like the other two forming heads  126 ,  122 , includes a piston  151  on which forming pad  125  is mounted. Piston  151  is forced outwardly by hydraulic fluid applied to opening hydraulic line  152  and is forced inwardly by hydraulic fluid applied to closing hydraulic line  154 . A caliper sensor  184  is provided to determine the amount of radial travel of piston  151  and forming pad  125 , for example. Suitable seals are provided between the piston  151  and the forming head  124 . 
     The forming head  122  and forming pad  123  are illustrated in FIG. 10 to indicate that under certain circumstances the shape of the outlet member  38  may be Aover expanded≅ to create a slightly oblong shaped outlet, such that when radial forming force from forming pad  123  and forming head  122  is removed, the outlet will spring back into a circular shape due to residual elasticity of the steel outlet member. 
     At the level of the branching chamber  32 , forming heads  122 ,  124 ,  126 , balance each other against the reaction forces while forcing the walls of the chamber outwardly. Accordingly the forming heads  122 ,  124 ,  126  are operated simultaneously, for example at level B of FIG. 7A, while forcing the lower end of the wall of the branching chamber  32  outwardly. When a forming head  122  enters an outlet member  38  for example, the pad reaction forces are evenly supported by the central wall region  150  of the branching chamber  32 . The telescopic links  180  may be rotated a small amount so that the forming pads  127 ,  125 ,  123  can apply pressure to the right or left from the normal axis and thereby improve the roundness or circularity of the outlet members. After a forming sequence is performed, for example at location D in FIG. 7A, the pressure is released from piston  151 , and the telescopic links  180  lower the forming heads  122 , for example, down by one step. Then the pressure is raised again for forming the outlet members and so forth. 
     The composition of the materials of which the branching sub  30  is constructed is preferably of an alloy steel with austenitic structure, such as manganese steel, or nickel alloys such as AMonel≅ and AInconel≅ series. Such materials provide substantial plastic deformation with cold forming thereby providing strengthening. 
     b) Description of Alternative Embodiment of FIGS. 15A-15D,  16  and  17 A- 17 D 
     An alternative post-forming tool is illustrated in FIGS. 15A,  15 B,  15 BN,  15 C,  15 D,  16 , and  17 A- 17 D. The post-forming tool  1500  is supported by common downhole components of FIG. 9 including a cable head  202 , telemetry, power supplies and controls module  204 , hydraulic power unit  206  and an orienting and latching sub  208 . FIG. 16 illustrates that post-forming tool  1500  includes a travel actuator  1510 . A piston  1512  of travel actuator  1510  moves from an upper retracted position as shown in FIG. 17A to a lower extended position as shown in FIGS. 17C and 17D. FIG. 17B shows the piston  1512  in an intermediate position. Piston  1512  moves to intermediate positions depending on the desired travel positions of forming heads in the outlet members. 
     FIGS. 16 and 17D illustrate a two forming head embodiment of the post-forming tool  1500  where two outlet members (e.g., see outlet members  1560  and  1562  of FIGS. 15A-15D) are illustrated. Three or more outlet members may be provided with a corresponding number of forming heads and actuators provided. Links  1514  connect the piston  1512  to actuator cylinders  1516 . Accordingly, actuator cylinders  1516  are forced downwardly into outlet members  1560 ,  1562  as piston  1512  moves downwardly. 
     Actuator cylinders  1516  each include a hydraulically driven piston  1518  which receives pressurized hydraulic fluid from hydraulic power unit  206  (FIG. 9) via travel actuator  1510  and links  1514 . The piston  1518  is in an upper position as illustrated in FIGS. 17A and 17C and in a lower position as illustrated in FIGS. 17B and 17D. 
     The actuator cylinders  1516  are pivotally linked via links  1524  to forming pads  1520 . The pistons  1518  are linked via rods  1526  to expanding rollers  1522 . As shown in FIGS.  17 A and  15 BN, the forming pads  1520  enter an opening of two retracted outlet members as illustrated in FIG.  15 B. The expanding rollers  1522  and forming pads  1520  are in a retracted position within retracted outlet members  1560 ,  1562 . 
     The piston  1512  is stroked downwardly a small amount to move actuator cylinders  1516  downwardly a small amount. Next, pistons  1518  are stroked downwardly causing expanding rollers  1522  to move along the inclined interior face of forming pads  1520  causing the pads to push outwardly against the interior walls of retracted outlet members  1560 ,  1562  until the outlet members achieve a circular shape at that level. Simultaneously, the outlet members are forced outwardly from the axis of the multiple outlet sub  1550 . Next, the pistons  1518  are stroked upwardly, thereby returning the expanding rollers  1522  to the positions as shown in FIG.  15 C. The piston  1512  is stroked another small distance downwardly thereby moving the forming pads  1520  further down into the outlet members  1560 ,  1562 . Again, the pistons  1518  are stroked downwardly to further expand the outlet members  1560 ,  1562  outwardly and to circularize the outlets. The process is continued until the positions of FIGS. 15D and 17D are reached which illustrate the position of the forming pads  1520  and actuator cylinders  1516  at the distal end of the multiple outlet members  1560 ,  1562 . 
     Description of Method for Providing Branch Wells 
     FIGS. 11A-11H and FIG. 12 describe the process for establishing branch wells from a branching sub  30  in a well. The branching sub  30  is illustrated as having three outlet members  34 ,  36 ,  38  (per the example of FIGS. 3A,  3 B,  3 C and FIGS. 7A-7E) but any number of outlets may also be used as illustrated in FIGS. 6A-6E. Only the outlets  38 ,  36  are illustrated from the axial cross-sectional views presented, but of course a third outlet  34  exists for a three outlet example, but it is not visible in the views of FIGS. 11A-11H or FIG.  12 . 
     FIG. 11A shows that the branching sub  30  is first connected to the lower end of a parent casing  604  which is conveyed through intermediate casing  602  (if present). Intermediate casing  602  lines the wellbore and is typically run through surface casing  600 . Surface casing  600  and intermediate casing  602  are typically provided to line the wellbore. The parent casing  604  may be hung from intermediate casing  602  or from the wellhead at the surface of the earth or on a production platform. 
     The outlet members  36 ,  38  ( 34  not shown) are in the retracted position. Slot  160  and notch  162  are provided in branching chamber  32  of branching sub  30  (see FIG. 12) to cooperate with orienting device  212  and latching device  210  of orienting and latching sub  208  of downhole apparatus  200  (See FIG.  9 ). When the parent casing  604  is set downhole, the branching sub  30  may be oriented by rotating the parent casing  604  or by rotating only the branching sub  30  where a swivel joint is installed (not illustrated) at the connection of the branching sub  30  with the parent well casing  604 . The orienting process may be monitored and controlled by gyroscopic or inclinometer survey methods. 
     Description of Alternative Embodiment of FIGS. 18A-18F and  19 A- 19 C FIGS. 18A-18F illustrate concave deformation of outlet members in a retracted state of a branching sub according to an alternative embodiment of the invention. The outlets are shaped similar to that of a ruled surface shell. Concave deformation of retracted outlet members, under certain circumstances, provides advantages for particular outlet arrangements, especially for three or more outlet nodal junctions. 
     FIG. 18A illustrates, in a radial cross section through lines  18 A of the branching chamber  1821 , of the branching sub  1850  of FIG.  18 EB, that the outlets have a concave shape. Stiffening structure  1800  is provided at the juncture of each outlet member  1881 ,  1842 ,  1861  with its neighbor. As a result, the area that is capable of plastic deformation is reduced as the number of outlets increases. Providing the retracted shape of the outlet members, as in FIGS. 18A and 18B, allows minimization of the area to be deformed, and simultaneously respects the principle of deformation of a ruled surface shell that allows expansion by post-forming with a minimum of energy required. FIG. 18A illustrates an envelope  1810  of the overall diameter of the branching sub  1850  when the outlet members  1881 ,  1842 ,  1861  are retracted. The arrow  1806  points to a circled area of structural reinforcement. Arrow  1804  points to an area of concave deformation of the outlets in branching chamber  1821 . 
     FIG. 18C illustrates the branching sub  1850  at a longitudinal position at the junction of the outlet members with a radial cross section through lines  18 C of FIG.  18 B. Arrow  1810  points to the outer envelope of the branching sub in its retracted state. FIG. 18D illustrates the branching sub  1850  near the end of the outlets while in a retracted state. Arrow  1810  points to the outer envelope of branching sub  1850  in the retracted state, while arrows  1881 N,  1842 N and  1861 N point to dashed line outlines of the outlet members  1881 ,  1842  and  1861 , respectively, after expansion. 
     FIGS. 18E and 18F illustrate the branching sub  1850  in an expanded state where FIG. 18E is a radial cross section of through the outlet members at the end of the outlet. Arrow  1810  points to the outer envelope of the branching sub  1850  when in a retracted state; arrow  1810 N points to the outer envelope when the outlet members  1881 N,  1842 N and  1861 N have been expanded. 
     A preferred way of placing the outlet members  1881 ,  1842 ,  1861  into the retracted state of FIGS. 18A-18D is to construct the sub with the geometry of FIG.  18 E and apply concave pliers along the vertical plan of axis symmetry of the junction. The deformation is progressively greater and deeper starting from the top of the outlet members (FIG. 18A) to the bottom of the outlet members. The entire junction of outlet members  1881 ,  1842 ,  1861  to branching chamber  1821  preferably includes welding of super plastic materials such as nickel-based alloys (Monel or Inconel, for example) in the deformed areas and materials of higher yield strength in the non-deformed part of the branching sub. Electron beam welding is a preferred method of welding the composite shell of the branching sub, because electron beam welding minimizes welding induced stresses and allows joining of sections of different compositions and thick walls with minimum loss of strength. 
     FIGS. 19A,  19 B and  19 C illustrate a post-forming tool  1926  similar to the post-forming tool of FIGS.  15 BN- 15 D and  16  described above. An actuator sonde (not shown) supports the post-forming tool  1926  including actuator  1910 , push rod  1927 , and forming rollers  1929 . FIG. 19A shows an axial section schematic of the post-forming tool  1926  operating in one outlet member  1881  of branching sub  1850  when it begins to expand such outlet member. FIG. 19B illustrates a similar axial section where actuator  1910  has been stroked outwardly to force push rod  1927  and traveling forming head  1928  downward, with forming rollers  1929  expanding outlet member  1881  outwardly while simultaneously rounding it. FIG. 19C shows a vertical cross section through the branching sub  1850  with a traveling forming head  1928  in each of the three outlet members  1881 ,  1842 ,  1861 . Forming rollers  1929  force the concave portion of outlet members  1881 ,  1842  and  1861  outwardly while support rollers  1931  are supported against stiffening structure  1800 . Push beams  1933  provide a frame for rotationally supporting forming rollers  1929  and support rollers  1931 . Springs and linkages (not illustrated) are provided among push beams  1933 , forming rollers  1929 , and support rollers  1931  to insure that all moving parts retract to a top position so that the overall tool diameter collapses to the diameter of the branching chamber  1821  (FIG. 18B) of the branching sub  1850 . 
     In operation, the traveling forming head  1928  of FIGS. 19A-19C follows a sequence of steps similar to that described above with respect to FIGS. 17A-17D. The post-forming tool  1926  is conveyed by means of a wireline and its associated sonde with cable head, telemetry power supplies and controls sub, hydraulic power unit, and orienting and latching sub, and is set so that the actuator  1910  seats above the top of the junction of stiffening structure  1800 . The traveling forming head  1928 , comprising push beams  1933  carrying forming rollers  1929  and support rollers  1931 , is pushed downwardly by powering actuator  1910  so that the expansion of each outlet member (e.g.,  1881 ,  1842 ,  1861 ) begins at its top end where it exits from the branching chamber  1821  and continues to the lower end of each outlet member. This sequence is repeated until the proper circular shape is achieved. 
     FIG. 11B illustrates the forming step described above with forming heads  122 ,  126  shown forming outlet members  38 ,  36  with hydraulic fluid being provided by telescopic links  180  from hydraulic power unit  206  and fixed traveling head  213 . The outlet members  36 ,  38  are rounded to maximize the diameter of the branch wells and to cooperate by fitting with liner hangers or packers in the steps described below. The forming step of FIG. 11B also strengthens the outlet members  36 ,  38  by their being cold formed. As described above, the preferred material of the outlet members  36 ,  38  of the branching sub is alloyed steel with an austenitic structure, such as manganese steel, which provides substantial plastic deformation combined with high strengthening. Cold forming (plastic deformation) of a nickel alloy steel, such as AInconel≅ , thus increases the yield strength of the base material at the bottom end of the branching chamber  32  and in the outlet members  36 ,  38 . The outlet members are formed into a final substantially circular radial cross-section by plastic deformation. 
     As described above, it is preferred under most conditions to convey and control the downhole forming apparatus  200  by means of wireline  110 , but under certain conditions, e.g., under-balanced wellbore conditions, (or in a highly deviated or horizontal well) a coiled tubing equipped with a wireline may replace the wireline alone. As illustrated in FIG.  1 B and described above, the downhole forming apparatus  200  is oriented, set and locked into the branching sub  30 . Latching device  210  snaps into notch  162  as shown in FIG. 11B (see also FIG.  12 ). Hydraulic pressure generated by hydraulic power unit  206  is applied to pistons in forming heads  122 ,  126  that are supported by telescopic links  180 . After a forming sequence has been performed, the pressure is released from the pistons, and the telescopic links  180  lower the forming pads down by one step. Then the pressure is raised again and so on until the forming step is completed with the outlet members circularized. After the outlet members are expanded, the downhole forming apparatus  200  is removed from the parent casing  604 . 
     FIGS. 11C and 11D illustrate the cementing steps for connecting the parent casing  604  and the branching sub  30  into the well. Plugs or packers  800  are installed into the outlet members  36 ,  38 . The preferred way to set the packers  800  is with a multiple head stinger  802  conveyed either by cementing string  804  or a coiled tubing (not illustrated). A multiple head stinger includes multiple heads each equipped with a cementing flow shoe. The stinger  802  is latched and oriented in the branching chamber  32  of branching sub  30  in a manner similar to that described above with respect to FIG.  11 B. As illustrated in FIG. 11D, cement  900  is injected via the cementing string  804  into the packers  800 , and after inflating the packers  800  flows through conventional check valves (not shown) into the annulus outside parent casing  604 , including the bottom branching section  1000 . Next, the cementing string  804  is pulled out of the hole after disconnecting and leaving packers  800  in place as shown in FIG.  11 E. 
     As shown in FIG. 11F, individual branch wells (e.g.  801 ) are selectively drilled using any suitable drilling technique. After a branch well has been drilled, a liner  805  is installed, connected, and sealed in the outlet member,  36  for example, with a conventional casing hanger  806  at the outlet of the branching sub  30  (See FIGS.  11 G and  11 H). The liner may be cemented (as illustrated in FIG. 11G) or it may be retrievable depending on the production or injection parameters, and a second branch well  808  may be drilled as illustrated in FIG.  11 H. 
     FIG. 12 illustrates completion of branch wells from a branching sub at a node of a parent well having parent casing  604  run through intermediate casing  602  and surface casing  600  from wellhead  610 . As mentioned above, parent casing  604  may be hung from intermediate casing  602  rather than from wellhead  610  as illustrated. The preferred method of completing the well is to connect the branch wells  801 ,  808  to a downhole manifold  612  set in the branching chamber  32  above the junction of the branch wells  801 ,  808 . The downhole manifold  612  is oriented and latched in branching chamber  32  in a manner similar to that of the downhole forming tool as illustrated in FIGS. 8A,  8 B and  11 B. The downhole manifold  612  allows for control of the production of each respective branch well and provides for selective re-entry of the branch wells  801 ,  808  with testing or maintenance equipment which may be conveyed through production tubing  820  from the surface. 
     In case of remedial work in the parent casing  604 , the downhole manifold  612  can isolate the parent well from the branch wells  801 ,  808  by plugging the outlet of the downhole manifold  612 . This is done by conveying a packer through production tubing  820 , and setting it in the outlet of downhole manifold  612  before disconnecting and removing the production tubing  820 . Valves controllable from the surface and testing equipment can also be placed in the downhole equipment. The downhole manifold  612  can also be connected to multiple completion tubing such that each branch well  801 ,  808  can be independently connected to the surface wellhead. 
     The use of a branching sub for branch well formation, as described above, for a triple branch well configuration, allows the use of dramatically smaller parent casing as compared to that required in the prior art arrangement of FIGS. 1A and 1B. The relationships between the branching sub diameter Ds, the maximum expanded outlet diameter Do, and the maximum diameter of a conventional axial branch Dc for a two outlet case is shown in FIG. 13A, and for a three outlet case in FIG.  13 B. The same kind of analysis applies for other multiple outlet arrangements. In comparison to an equivalent axial branching that could be made of liners packed at the end of the parent casing, the branching well methods and apparatus of the present invention allow a gain in branch cross-sectional area ranging from 20 to 80 percent. 
     FIGS. 14A-14D illustrate various uses of two node branch well configurations according to the invention. FIGS. 14A and 14B illustrate a branching sub at a node according to the invention. FIG. 14C illustrates how branch wells may be used to drain a single strata or reservoir  1100 , while FIG. 14D illustrates the use of a single node by which multiple branch wells are directed to different target zones  1120 ,  1140 ,  1160 . Any branch well may be treated as a single well for any intervention, plugging, or abandonment, separate from the other wells. 
     Description of Alternative Embodiment of a Branching Sub According, to the Invention 
     1) Description of Alternative Branching Sub 
     FIGS. 20A and 20B show an alternative embodiment  3000  of the invention of a branching sub. FIG. 20A shows an exterior view of the branching sub  3000  including a housing  3002  having threaded ends  3004 ,  3006 . The branching sub  3000  of FIGS. 20A,  20 B is illustrated in an expanded or post-formed state. The branching sub  3000  includes a main pipe  3010  which defines a feed through channel  3011  (see FIG. 20B) and at least one lateral branching outlet  3012  which defines a lateral channel  3013  (see FIG.  20 B). A branching chamber  3008  is defined between the top channel  3007  and the feed through channel  3011  and lateral channel  3013 . A bottom hole assembly (BHA) deflecting area  3015  separates main pipe  3010  from lateral branching outlet  3012 . 
     In a retracted state, the branching sub  3000  may be placed in series with sections of well casing and positioned in a borehole with the running of the casing string into the borehole. After placement in the borehole, the housing of the branching sub  3000  is post-formed so that both the feed through channel  3011  and the lateral channel  3013  (or multiple branching outlets) are shaped to a final geometry which increases resistance to pressure and which maximizes the drift diameter of the lateral channel  3013  and the feed through channel  3011 . Longitudinal ribs  3018  provide strength to the housing  3002  of the branching sub  3000 . Longitudinal rib  3018  extends the entire axial length of the branching sub  3000  and is integral with the BHA deflecting area  3015  for a distance from the bottom threaded end  3006  of the branching sub  3000  to the branching chamber  3008 . 
     FIGS. 21A-21D schematically illustrate the branching sub  3000  in its retracted state (see FIGS. 21A,  21 B) and in its expanded state (see FIGS. 21C,  21 D). In the retracted state shown in FIGS. 21A,  21 B, the main pipe  3010  and the branching outlet  3012  have been prefabricated so that the maximum outer diameter D of the branching sub  3000  is not greater than the top threaded end  3004  or bottom threaded end  3006 . FIG. 21B, taken along section line  21 B of FIG. 21A, illustrates the oblong shape of the feed through channel  3011  of main pipe  3010  and of the lateral channel  3013  of lateral branching outlet  3012 . In the retracted state, branching sub  3000  can be placed between sections of borehole casing and run into an open borehole to a selected depth. 
     FIGS. 21C and 21D schematically illustrate the branching sub  3000  after it has had its feed through channel  3011  expanded and its lateral channel  3013  expanded. The maximum diameter in the expanded state, performed downhole, at section line  21 D is DN as compared to the diameter D of the top and bottom threaded ends  3004 ,  3006  of the branching sub  3000 . FIG. 21D illustrates that the main pipe  3010  and the lateral branching outlet  3012  not only have been expanded outwardly from their retracted state of FIGS. 21A,  21 B, but that they have been substantially circularized. Thus, in FIG. 21D, feed through channel  3011  and lateral channel  3013  are characterized by substantially circular internal diameters. 
     The downhole post-forming method and apparatus illustrated and described above by reference to FIGS. 7A-7E,  8 A,  8 B,  9  and  10  are used to expand the feed through channel  3011  and the lateral channel  3013 . 
     The construction of branching sub  3000  is based on the combination of material and geometrical properties of the BHA deflecting area  3015 . The material is specifically selected and treated to allow a large rate of deformation without cracks. The geometry of the wall is such that both its combined thickness and shape ensure a continuous and progressive rate of deformation during the expansion. The plastic deformation increases the yield strength by cold work effect and hence gives the joint an acceptable strength that is required to support the pressure and liner hanging forces. FIG. 22 shows that the yield strength after expansion increases with the rate of deformation of the outlets. A preferred material for use in the post-forming areas is a fine grain normalized carbon steel or an austenitic manganese alloyed steel that reacts favorably to cold working. A preferred construction method is to manufacture different specific components in order to optimize the material and forming process of each particular part. In a final stage, the components are welded together so that the housing  3002  becomes one single continuous structural shell. 
     2) Description of Use of Alternative Branching Sub 
     FIG. 23 schematically illustrates the use of the alternative branching sub  3000  as described above. A preferred use of the branching sub  3000  is for providing multiple branches in a parent well. Such multiple branches may improve the drainage of a subterranean formation. 
     Before the invention of the branching sub  3000  of FIGS. 20A,  20 B and  21 A- 21 D, connection of a lateral branch to a parent well has generally made use of an arrangement of several parts with sealing of the branch well to the parent well with rubber, resin or cement. Such joints require a complex method of installation and present a risk of hydraulic isolation failure after several pressure cycles in the well. 
     The branching sub  3000  according to the invention allows for providing multiple branches from a parent casing with no sealing joint, but with conventional liner hanging packers and casing joints. The geometry of the housing  3002  of the branching sub  3000  allows the pressure rating of the sub and the size of the branch to be maximized with regard to the parent casing size. FIG. 23 shows an example of the use of a branching sub  3000  where, after expansion downhole, branch wells  3014  are provided to separate parts of the earth&#39;s crust by means of lateral channels  3013 . The branch wells  3014  can be used for extraction, storage or injection of various fluids such as mono or poly-phasic fluids of hydrocarbon products, steam or water. 
     c) Description of Deflection Apparatus and Procedures 
     FIG. 24 illustrates how a drilling tool  3030  can be guided or deflected from main pipe  3010  into lateral branching outlet  3012  after the branching sub  3000  has been expanded downhole. A deflecting tool  3036  is set in main pipe  3010  by means of elements which cooperate with the positioning groove  3040  and orienting cam and slot  3042  illustrated schematically. 
     Several lateral branching subs can be stacked in tandem at a location in the well or at several places along the casing string in order to provide optimal communication with various formations from the parent well. FIG. 25 illustrates two branching subs  3000  according to the alternative embodiment of the invention which are connected in tandem in a casing string  3300 . Where two or more branching subs  3000  are connected in a casing string  3300 , each sub can be oriented with the same or a different face angle for the lateral branches. As a consequence, different angular orientations from the parent well may be provided to reach a large volume of subterranean formations with different lateral branches. The casing string  3300  may be oriented vertically or horizontally, or it may be tilted; but the lateral branches may in any case extend laterally from the parent casing. Although departing at a narrow angle from the casing string  3300 , lateral boreholes from the lateral outlets of branching subs  3000  can be directionally drilled to a vertical, deviated or horizontal orientation. 
     FIGS. 26A and 26B illustrate a drillable cap  3400  welded about the opening of lateral branching outlet  3012  in its retracted and expanded conditions, respectively. When conveying the casing string into the borehole, the cap  3400  isolates the lateral channel  3013  from the borehole and maintains a differential pressure across the casing wall which may be required to control the borehole pressure when casing is conveyed downhole. When the lateral branch is to be drilled, a drilling tool bores through cap  3400  and into a formation to form a lateral branch. 
     d) Description of Advantages and Features of Alternative Branching Sub 
     As mentioned above, a single branching sub  3000  can be provided with more than one lateral outlet. Such multiple outlets can be coplanar with each other or non-coplanar. A single branching sub  3000  can be connected in tandem with one or more other branching subs  3000  either at its top end or its bottom end. A branching sub  3000  can be provided with a foot at its lower end in a similar manner to foot  172  of FIG.  8 A. 
     A lateral branching outlet  3012  of FIG. 20B may support a liner hanging packer which holds a liner connected to the housing  3002  in order to isolate the branching chamber  3008  from the borehole. Appropriate grooves at the top of the lateral branching outlet  3012  may be provided to secure the liner hanger and prevent the liner from accidentally moving out of the outlet during the liner setting operation or later. Alternatively, the interior wall of the lateral branching outlet  3012  can be provided without grooves. 
     The lateral branching outlet  3012  can be terminated with a ramp that guides the drilling bit when starting the drilling of the lateral borehole. Such ramp can prevent the drilling bit from accidentally drilling back toward the main pipe  3010 . 
     Other structures may be provided inside the branching chamber  3008  such as a guidance ramp, secondary positioning groove, or the like to validate conveying equipment through the feed through channel  3011  or toward a specific lateral channel  3013 . The branching chamber  3008 , or the lateral branching outlet  3012 , or the main pipe  3010 , can be provided with temporary or permanent flow control devices such as valves, chokes, or temporary or permanent recording equipment with temperature, pressure or seismic sensors, for example. The branching chamber  3008  can also be provided with a production tubing interface with a flow connector, or a flow diverter, or an isolating packer. A lateral branching outlet  3012  can also be provided with an artificial lifting device such as a pump, gas influx injectors, and the like. 
     As an alternative to the apparatus and techniques of FIGS. 7-10 for expanding the main pipe  3010  and the lateral branching outlet  3012 , an inflatable packer may be placed on the inside wall of the main pipe  3010  or the lateral branching outlet  3012  whereby the expansion force of the packer is used to expand the pipes by plastic deformation. 
     Various modifications and alterations in the described methods and apparatus will be apparent to those skilled in the art of the foregoing description which do not depart from the spirit of the invention. For this reason, such changes are desired to be included within the scope of the appended claims which include the only limitations to the present invention. The descriptive manner which is employed for setting forth the embodiments should be interpreted as illustrative but not limitative.