Patent Publication Number: US-2021164595-A1

Title: Methods for decreasing stress in flange bolting

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims priority from U.S. Provisional Application Ser. No. 62/725,009; filed on Aug. 30, 2018, entitled “METHODS FOR DECREASING STRESS IN FLANGE BOLTING” the entire disclosure of which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to flanges and, more particularly, to systems and methods for decreasing stress in flange bolting. 
     BACKGROUND 
     Flanges are used in a wide variety of contexts, including, the field of subsea equipment. Traditionally, subsea flanges have been almost exclusively based on standardized geometry, defined by the American Petroleum Institute (API), which consists of a single huh face consisting of a small groove cut out for a metal sealing gasket. In recent years, the oil and gas industry has begun to push the limits of technology by drilling and producing subsea wells in high-pressure/high-temperature (HPHT) environments. Currently, API has only a limited selection of smaller-diameter flanges that are rated for these high-pressure and high-temperature environments. In development, of a new large diameter flange for subsea HPHT use, it has been discovered that the large thermal gradients subjected to subsea HPHT flanges produce new challenges that cannot be easily met by the traditional single hub face API style flanges. The contemporary approach adopted by HPHT equipment manufacturers has been to increase the thickness of the flange. Detailed analysis has shown that this approach alone may still not be sufficient for handling all HPHT loading unless the thickness is substantially increased over traditional API flange thicknesses. It is now recognized that flanges utilizing a compound hub face inside the bolt circle diameter provides increased rated capacities without the need of increasing the thickness of the flange. 
     In some applications, a flange is made up directly to an adjacent flange, with multiple bolts extending through the two flanges, and each having a pair of nuts (one on each side of the flange connection) to secure the flanges together. In other applications, particularly in certain subsea equipment configurations, a flange is made up directly to another piece of equipment using a stud configuration. That is, a bolt extends through the flange and into the adjacent part, and only one nut on the flange side is used to tighten the connection. In such instances, the bolts are screwed directly into tapped holes on the adjacent part, resulting in a shorter clamping length for the bolt. 
     Analysis has shown that increasing clamping length of a bolt through a flange connection results in decreased bending stresses in the bolts. It is desirable to minimize these bending stresses. To minimize these bending stresses, a commonly practiced approach has been to increase the thickness of the flange. Unfortunately, increasing the flange thickness results in additional stack height and weight for the connection. This increased stack height and weight is undesirable, particularly in subsea equipment configurations due to the already very large sizes of the flanges and equipment being used. It is now recognized that a more space-efficient and weight-efficient method is needed to reduce the bending stresses in flange bolting in assemblies where the flange is connected to another piece of equipment via stud connections. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and its features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a top view of a flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 2A  is a cross-sectional view of the flange connection of  FIG. 1  taken along lines A-A, in accordance with an embodiment of the present disclosure; 
         FIG. 2B  is a detailed view of the flange connection of  FIG. 2A  taken within the circle  2 B, in accordance with an embodiment of the present disclosure; 
         FIG. 3A  is a cross-sectional view of the flange connection of  FIG. 1  taken along lines A-A, in accordance with an embodiment of the present disclosure; 
         FIG. 3B  is a detailed view of the flange connection of  FIG. 3A  taken within the circle F, in accordance with an embodiment of the present disclosure; 
         FIG. 4  is a plot illustrating, bending stresses on a flange stud used in three different flange connections, in accordance with an embodiment of the present disclosure; 
         FIG. 5A  is a cross-sectional view of a compound hub flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 5B  is a detailed view of the compound hub flange connection of  FIG. 5A  taken within the circle C, in accordance with an embodiment of the present disclosure; 
         FIG. 6A  is a cross-sectional view of a compound huh flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 6B  is a cross-sectional view of a compound hub flange connection of  FIG. 6A  taken within the circle B, in accordance with an embodiment of the present disclosure; 
         FIG. 6C  is a plot illustrating preload and subsequent exposure to a thermal gradient on a compound hub flange connection of  FIGS. 6A and 6B , in accordance with an embodiment of the present disclosure; 
         FIG. 7A  is a cross-sectional view of a traditional single hub flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 7B  is a cross-sectional view of a thermal gradient of a traditional hub flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 7C  is a plot illustrating preload and subsequent exposure to a thermal gradient on a traditional single hub flange connection of  FIGS. 7A and 7B , in accordance with an embodiment of the present disclosure; 
         FIG. 8A  is a cross-sectional view of a compound hub flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 8B  is a cross-sectional view of a thermal gradient of a compound hub flange connection, in accordance with an embodiment of the present disclosure; 
         FIG. 9A  is a plot illustrating a pressure versus bending load capacity chart on a compound hub flange connection, in accordance with an embodiment of the present disclosure; and 
         FIG. 9B  is a plot illustrating a pressure versus bending load capacity chart on a traditional hub flange connection, in accordance with an embodiment of the present disclosure. 
         FIG. 10  is a cross-sectional view of flange connection having a compound flange connected to a piece of equipment, in accordance with an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Illustrative embodiments of the present disclosure are described in detail herein. In the interest of clarity, not all features of an actual implementation are described in this specification. it will of course be appreciated that in the development of any such actual embodiment, numerous implementation specific decisions must be made to achieve developers&#39; specific goalS, such as compliance with system related and business related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of the present disclosure. Furthermore, in no way should the following examples be read to limit, or define, the scope of the disclosure. 
     Certain embodiments according to the present disclosure are directed to systems and methods for decreasing bending stress in flange bolting for a flange connection between a flange and an adjacent piece of equipment. The flange connection includes a single flange with multiple bolts extending therethrough. The bolts are threaded into the adjacent piece of equipment at one end, and a nut is disposed at an opposite end of each bolt to provide a means for tightening and/or securing the flange connection. The equipment to which the flange is attached may include subsea well equipment with relatively large outer diameters. 
     The disclosed flange connection utilizes an initial region of a counterbored (or untapped) hole in the mating equipment piece just prior to the start of the thread formed through the equipment. That is, instead of the bolt being connected via threads to the equipment piece for the entire length that the bolt extends into the equipment, a first longitudinal segment of the bolt extending through the equipment will not be in threaded engagement with the equipment. This provides an increased clamp length for the bolt without increasing a thickness of the flange, thereby reducing resultant maximum bending stresses in the bolts. This is accomplished by distributing the stresses over the longer clamping length. 
     Detailed finite element analysis (FEA) of the disclosed flange connection shows that tier large diameter subsea sized flanges, a notable reduction of bending stress on bolts can be achieved using an unthreaded region formed through the adjacent piece of equipment. A ratio of the bending stress reduction on the bolt offered from increased flange thickness compared to that offered from a length of unthreaded region is approximately 1.5. As such, the flange thickness can be reduced by 1 inch for every 1.5 inches of untapped hole through the equipment piece to provide the same bending stress protection. 
     For purposes of this disclosure, the terms “bolts”, “studs”, and “screws” as used herein are intended to refer to a general class of generally cylindrical fasteners consisting of threads on some portion of the round face of the generally cylindrical body. As would be understood by one of ordinary skill in the art, in many situations, the fasteners within this class may be used interchangeably, with or without modifications to the mating components, and yield similar performance. Thus, it will be appreciated that the terms “bolts”, “studs”, and “screws”, may be used interchangeably herein without limiting the scope of the present disclosure. Additionally, other types of fasteners not listed may also be used to gain similar benefits in accordance with aspects of the present disclosure. 
     Turning now to the drawings,  FIG. 1  is a top view of a flange connection  100  in accordance with an embodiment of the present disclosure. The flange connection  100  may form a piece of subsea well equipment. In some embodiments, the flange connection  100  may be utilized to connect a first tubular to a second tubular for use in a subsea environment. The flange connection  100  generally includes a flange  102  connected to another piece of equipment (not visible). 
     The flange  102  may form part of an upper tubular  104  having a bore  106  formed therethrough. The piece of equipment connected to the flange  102  may include a lower tubular having a bore formed therethrough: The upper tubular  104  may be connected to the lower tubular (not shown) via the flange connection  100 . In such embodiments the flange connection  100  may include studs  110  that pass through the flange  102  (e.g., upper tubular  104 ) and the piece of equipment (e.g., lower tubular) and are threadedly connected to the piece of equipment. Although the flange connection  100  is illustrated herein as providing a connection of two tubular components, other embodiments of the flange connection  100  may include the flange  102  being used to connect other subsea components, such as connecting a block to a subsea tree or an actuator assembly to a blowout preventer. 
     The flange  102  is connected to the piece of equipment via a plurality of studs  110  to form the flange connection  100 . Each stud  110  includes a bolt  112  having a nut  114  disposed thereon. In general, the nut  114  is threadedly coupled to the bolt  112 , and the bolt  112  extends in an axial direction through the flange  102  and the adjacent piece of equipment. 
       FIGS. 2A and 2B  provide cross-sectional views of an embodiment of the flange connection  100 , taken along lines A-A of  FIG. 1  and within circle  213  of  FIG. 2A , respectively,  FIG. 2A  shows the flange connection  100  being used to secure the flange  102 . (which is part of an upper tubular  104 ) to an adjacent piece of equipment  200  (which in  2 A and  2 B is a lower tubular  202 ). The lower tubular  202  has a bare  204  formed therethrough, similar to the bore  106  of the upper tubular  104 . As shown, multiple studs  110  extend through the flange  102  and the adjacent equipment  200  to secure the flange connection  100 . Each stud  110  may include a bolt  112  extending from a location above an upper surface of the flange  102  to a position within the equipment component  200 . The bolts  112 , as shown, each terminate within the equipment component  200 . The bolts  112  are each disposed through the flange  102  and then attached to the equipment component  200  via a threaded connection, which is described in greater detail below. The nuts  114  are threaded onto the top of the corresponding bolts  112  to complete the flange connection  100 . As illustrated, the flange  102  and equipment component  200  may be shaped such that the bolts  112  pass through a small gap  205  between a downward facing surface of the flange  102  and an upward facing surface of the equipment  200 . 
     As shown in  FIGS. 2A and 2B , the flange  102  may have multiple untapped or counterbored apertures  206  formed therethrough, one for receiving each of the bolts  112 . The term “untapped” or “counterbored” refers to the apertures  206  having relatively smooth (i.e., non-threaded) interior walls that are slightly larger than an outer diameter of the bolt  112  passing therethrough. The untapped apertures  206  basically function as passages through which the bolts  112  extend axially (along axes  208 ) through the flange  102 . The axis  208  of each aperture and/or bolt  112  through the flange connection  100  is parallel to and radially offset from a longitudinal axis  210  of the flange  102  and the corresponding equipment  200 . 
     The piece of equipment  200  to which the flange  102  is attached may have multiple apertures formed therethrough as well. These apertures may each have an untapped or counterbored section  212  extending a first axial distance  214  along axis  208 , and a tapped or threaded section  216  extending a second axial distance  218  along axis  208 . That is, a first portion ( 212 ) of each aperture through the piece of equipment  200  may have relatively smooth (i.e., non-threaded) interior walls that are slightly larger than an outer diameter of the bolt  112  to allow the bolt  112  to pass therethrough, while a second portion ( 216 ) of each aperture through the equipment  200  has threads formed in the interior walls to interface directly with threads on an external diameter of the bolts  112 . 
     The bolts  112  pass through the untapped apertures  206  of the flange  102  and the corresponding untapped portions  212  of the apertures through the equipment  200 , and then a lower portion of the length of each bolt  112  is threaded into engagement with the equipment  200  via the threaded sections  216  of the apertures through the equipment  200 . The nuts  114  are then threaded onto the upwardly extending portions of the bolts  112  to securely fasten the flange connection  100 . The additional untapped or counterbored sections  212  of the apertures formed through the equipment  200  provide an increased clamping length for the bolts  11 : 2  as compared to a similar system where the entire length of the apertures through the equipment are threaded. This increased clamping length reduces the bending stresses experienced by the bolts  112  during operation of the equipment without having to increase an, axial thickness of the flange  102 . 
       FIGS. 2A and 2B  illustrate an embodiment of the flange connection  100  where the length  214  of the untapped portions  212  of the apertures through the equipment  200  is approximately 1.5 inches in length. This provides roughly the same decrease in bending stresses on the bolts as a 1 inch increase in axial thickness of the flange. Thus, the disclosed flange connection  100  facilitates reduced bending stresses on the bolts  112  while also keeping the overall dimensions and weight of the flange connection  100  to a minimum, as no increase in flange thickness is required. 
       FIGS. 3A and 3B  illustrate a similar embodiment of the flange connection  100  described above, but where a length.  300  of the untapped portions  212  of the apertures through the equipment  200  is approximately 3 inches in length. This provides roughly the same decrease in bending stresses on the bolts as a 2 inch increase in axial thickness of the flange. Thus, the disclosed flange connection  100  facilitates reduced bending stresses on the bolts  112  while also keeping the overall dimensions and weight of the flange connection  100  to a minimum, as no increase in flange thickness is required. 
       FIG. 4  is a plot  400  comparing bending stresses in flange studs  110  for flange connections having different relative constructions. The plot  400  shows a normalized moment  402  (from bending stress) experienced within the bolt  112  of a stud  110 , taken with respect to a distance  404  along the bolt  112  measured from the nut  114 . Three trend lines  406 A,  406 B, and  406 C are shown, each corresponding to a different clamp length  408 A,  408 B, and  408 C, respectively. “Clamp length” refers to a distance along the bolt axis ( 208  of  FIGS. 2A-3B ) from the nut  114  to where the threaded portion ( 216  of  FIGS. 2A-3B ) starts within the equipment ( 200  of  FIGS. 2A-3B ). A flange connection with a longer untapped section of the aperture through the piece of equipment will have a longer clamp length  408 . 
     In  FIG. 4 , the trend line  406 A corresponds to the bending moment on a bolt connecting a flange to a piece of equipment that does not have any untapped section ( 216 ) of the apertures formed therethrough. This represents a “normalized” bending moment for a typical flange connection. The clamp length  408 A is a “normalized” clamp length. The trend line  406 B corresponds to the bending moment on a bolt connecting a flange to a piece of equipment that has a 1.5 inches long untapped section ( 216 ) of the apertures formed therethrough. This specifically corresponds to the embodiment of the flange connection  100  shown in  FIGS. 2A and 2B . The clamp length  408 B is equal to the “normalized” clamp length+1.5 inches. The trend line  406 C corresponds to the bending moment on a bolt connecting a flange to a piece of equipment that has a 3 inches long untapped section ( 216 ) of the apertures formed therethrough. This specifically corresponds to the embodiment of the flange connection  100  shown in  FIGS. 3A and 3B . The clamp length  408 C is equal to the “normalized” clamp length+3 inches. 
     As can be observed from the plot  400 , the highest bending moments on the two trend lines  406 B and  406 C are both less than the highest bending moment on the trend line  406 A. According to the analysis results of plot  400 , the presently disclosed flange connection  100  (which has at least some untapped or counterbored portion of the apertures formed through the piece of equipment) decreases the bending stresses on the bolts  112  compared to flange connections that do not have such untapped/counterbored portions. 
       FIGS. 5A and 5B  provide cross-sectional views of a compound hub flange connection  500  in accordance with another aspect of the present invention. A compound bob flange connection  500  may reduce the bending and tensile stresses on bolts  112  without having to increase the axial thickness of a compound flange  502  or the size of the bolts  112 . Compound hub flange connection  500  may be used to connect a first tubular to a second tubular, tor example, the upper tubular  104  and the lower tubular  202  of  FIG. 2A . 
     Ha  5 A shows the compound hub flange connection  500  being used to secure an upper compound hub flange  502   a  (which is part of upper tubular  104 ) to a lower compound hob flange  502   b  (which is part of lower tubular  202 ). The compound hub flange connection  500  can secure compound flanges  502   a  and  502   b  using one or more studs lit) extending through the compound flanges  502   a  and  502   b . Each stud  110  may comprise a bolt  112  extending from an upper surface of an upper flange  102   a  to a lower surface of a lower flange  102   b . Nuts  114   a  and  114   b  may be threaded on both ends of bolt.  112  to secure the flanges  502   a  and  502   b  in compression. As shown, compound flanges  502   a  and  502   b  may be shaped such that bolt  112  passes through a gap between a downward facing surface of upper compound flange  502   a  and an upward facing surface of lower compound flange  502   b.    
     Compound hub flange connection  500  depicted in  FIGS. 5A and 5B  may be used in combination with the flange  102  and lower equipment  200  described in  FIGS. 2A and 2B , and similarly in  FIGS. 3A and 3B . Such a combination of these components is illustrated in  FIG. 10 . The system of  FIG. 10  includes, for example, the upper compound hub flange  502   a  fraying an aperture extending therethrough, an inner hub face  512   a , an outer hub face  514   a , and a groove  520  that is formed between the inner hub face  512   a  and the outer hub face  514   a . The system of  FIG. 10  also includes the piece of equipment  200  adjacent the compound flange  502   a  and having an aperture extending therethrough and aligned with the aperture of the compound flange  502   a . The bolt  112  extends through the compound flange  502   a  and is threaded into the piece of equipment  200  to connect the compound flange  502   a  to the piece of equipment  200 . 
     The compound hub flange connection  500  of  FIG. 10  may benefit from the untapped or counterbored section  212  and the tripped or threaded section  216  of the aperture  206 , as described above, to reduce the bending stress on bolts  112 . Thus, a compound hub flange connection  500  as described in more detail below (and in combination with the untapped or counterbored section  212  and the tapped or threaded section  216  of the aperture  206 ) may′ provide an even greater reduction in the bending stress on bolts  112  than the embodiments described with respect to  FIGS. 2A, 2B, 3A, and 3B . Compound hub flange  500  may also be used in accordance with flange connections comprising fully threaded apertures. The compound hub flanges described herein may also be used with other types of mechanical couplings of similar geometric proportions to a flange. These types of couplings may include, but are not limited to, couplings using clamps or external threaded rings in substitution or addition to the threaded fasteners. 
     A compound huh flange  502  of compound hub flange connection  500  may comprise an inner hub face  512  and an outer hub face  514 . For example, an upper compound hub flange  502   a  may comprise an inner hub face  512   a  and an outer hub face  514   a . A lower compound hub flange  502   b  may similarly comprise an inner hub face  512   b  and an outer hub face  514   b . The inner hub faces  512   a  and  512   b  of the hub flange  502  are located closer (along a radial direction) to a longitudinal axis  550  of the hub flange  502 . When upper compound hub flange  502   a  is connected to lower compound hub flange  502   b , inner hub faces  512   a  and  512   b  may contact one another via a radially inner hub  513  and outer hub faces  514   a  and  514   b  may contact one another via a radially outer hub  515 . In this manner, a groove  520  may be formed. Groove  520  may be hexagonal in shape when viewed as a circumferential cross section, as depicted in  FIGS. 5A and 5B , or groove  520  may be circular or substantially rounded or any similar shape. Groove  520  provides reduced stiffness between the inner and outer hub faces. Groove  520  is not intended to provide a sealing surface and is approximately an order of magnitude larger in volume than grooves traditionally used to house gaskets. The reduced stiffness allows for increased stability of hub face preloads when subjected to external and thermal loads by allowing for flexibility within the body of the flange. This flexibility and increased stability of the hub preloads reduces the load transferred to the highest loaded bolt by more evenly distributing the load between bolts  112 . Additionally, when the flange  502  is subjected to external bending, the outer huh  515  reduces the load on the bolts  112  that are on the tension side of bending by imparting an opposing three on the compressive side of bending, thereby coupling the external moment with a compressive reaction point, on outer hub  515 , that is located further from the neutral axis of bending. 
       FIGS. 6A and 6B  illustrate a similar embodiment of the compound hub flange connection  500  described above, but with a small gap  605  between outer hubs  514   a  and  514   b  compound hub flanges  502   a  and  502   b , respectively. As illustrated, such a gap may not be present between inner hubs  512   a  and  512   b  of the compound hub flanges  502   b  and  502   b , respectively. As bolt  112  is fastened to compound flanges  502   a  and  502   b , gap  605  closes to improve the seal integrity between inner hub  513  and gasket  505  by storing a preload in the inner hub  513 . As a result, the gap  605  may be useful for mitigating separation between inner hub faces  512   a  and  512   b . Mitigation of hub face separation is beneficial for minimizing relative sliding on interfacing surfaces between the flange  500  and the metal gasket  505 . Minimizing sliding between the gasket  505  and flange  500  increases the life of the gasket  505  by reducing wear between the metallic surfaces. 
       FIG. 6C  depicts the contact forces for the inner huh  513  of the hub flange connection  500  of  FIGS. 6A and 6B , represented by inner hub curve  613 .  FIG. 6C  also depicts the contact forces for the outer hub  515 , represented by outer hub curve  615 . Inner hub curve  613  and outer hub curve  615  are shown relative to a sum of the bolt loads  614 , specifically for a compound hub flange with an initial gap  605  at the external hub face as depicted in  FIGS. 6A and 6B . The left half  616  of this plot shows the relationship between these forces as the flange body is joined with its mating part by increasing the bolt forces. For explanation purposes of the left half  616  of  FIG. 6C , the preloading of the bolt may be represented by two phases of increasing bolt load. A first phase  617  begins at the origin  618  of the plot. In this phase, the bolt load  614  is approximately equal to the inner huh load  613 . In this phase, the bolt load  614  and inner hub load  613  increase in equal magnitude until contact is first made on the outer hub, which ends the first phase  617  and starts the second phase  620 . This is indicated on this plot at vertical line  619 , which represents a point of first contact. The point of first contact on the outer hub begins the second phase  620  of bolt preload. In this stage, the remaining bat preload primarily reacts against the outer huh. The second phase  620  ends at vertical line  621 . This represents the end of the initial mating of the flange and the end of the second phase of bolt preload. For this representative embodiment, the outer hub resists approximately 60% of the initial bolt preload and the inner hub resists approximately 40% of the initial bolt preload, as shown in  FIG. 6C . 
     The right half  622  of the plot shows how these threes change when subjected to a thermal gradient consisting of a hot bore  710  and a cold exterior  720 , shown in  FIGS. 7A and 7B , as is commonly experienced by flanges that are installed subsea after initial makeup. As can be seen in the right half  622  of  FIG. 6C , the inner hub curve  613  increases in load, to approximately 105% of the bolt load, due to thermal expansion at the inner hub  513 . The outer hub curve  615  decreases in load, to approximately 5%, due to thermal contraction at the hub  515  and the increase in load on the inner hub  513 . The net increase in the load on the bolts is approximately 10%. The magnitudes of the load values represented in  FIG. 6C  are representative of a single embodiment of flange  600 . These values may be systematically changed by variation of the overall size of the flange, the size and shape of groove  520 , the magnitude of gap  605 , and the outer diameter of hub  515 . It should also be noted that similar thermal benefits of a compound hub flange would be experienced without the initial gap  605 . This would likely yield an even lower change in the resultant bolt stress after the thermal gradient is applied, but would sacrifice some performance regarding the life of the metal gasket. Other embodiments of this design may include a series of stepped hub faces, which would yield similar benefits, but at the cost of increased manufacturing difficulty. As will be demonstrated in a subsequent figure, the increase in bolt load due to thermal expansion on a compound hub flange is far less than the increase in bolt load experience by a single hub flange of similar size. 
       FIGS. 7A and 7B  provide cross-sectional views of a traditional hub flange connection  700 , where  FIG. 7A  shows a traditional hub flange connection  700  under ambient conditions without effect of a thermal gradient, and  FIG. 7B  depicts a traditional hub flange connection  700  under high temperature conditions causing a thermal gradient, for example, at a downhole location. A traditional hub flange connection  700  may be used to connect a flange  102   a  to a flange  102   b . Flange  102   a  and flange  102   b  may be similar to flange  102  and equipment component  200  as described with  FIGS. 2A and 2B . 
     As used herein, the term “ambient temperature” refers to the general temperature of a flange and its surrounding environment (including other equipment) prior to installation in a subsea environment. “Ambient temperature” may mean that the flange and its surrounding environment are in a state of substantially uniform temperature distribution with a negligible temperature or thermal gradient, relative to the extreme temperature or thermal gradients possible after subsea installation. As shown in  FIG. 7A , a traditional hub flange connection  700  may have 100% of the initial bolt preload on a traditional hub  730  with no thermal gradient. In a subsea environment, thermal gradients are formed due to the contrast of high temperatures within a hot bore  710 , which may be a composite of bores  106  and  204 , and the low temperatures of the exterior of a bore, for example, a cold exterior  720 . For example, in subsea conditions, the temperature of the hot bore  710  may be 350° F., and the temperature of the cold exterior  720  may be 35″ F. 
     As a result, a temperature gradient may be formed between the hot bore  710  and cold exterior  720 . For example, zones  712 ,  714 , and  716  representing different ranges of temperatures may be formed through the traditional hub flange connection  700 . A first zone  712  may have a temperature range of 350° F. to 250° F., a second zone  714  may have a temperature range from 250° F. to 100° F., and a third zone  716  may have a temperature range from 100° F. to 35° F. The exposure of high temperatures of the thermal gradient on flange connection  700  causes thermal expansion of flanges  102   a  and  102   b . Since hub  730  is located in these higher temperature zones, the metal expands at this interface. On the contrary, the bolts  110  are located in lower temperature zones, which results in the unstressed-state of the bolts reducing in overall length. This contradictory metal expansion between hub  730  and bolts  110  results in increased stresses in the bolts. For large diameter subsea flanges subjected to large thermal gradients, FBA has shown that the increase of stress in bolts  112  may be 35% or greater. Such an increase of tensile stress on bolt  112  is undesirable and can be mitigated without increasing the thickness of the flange  102  using the compound huh flange connection  500  of  FIGS. 5A, 5B, 6A, and 6B  described below. 
       FIG. 7C  depicts the contact forces for a single hub curve  713  relative to the sum of the bolt loads  714 , specifically for a traditional hub flange of similar size to the compound hub flange represented in  FIG. 6C . The left half  716  of this plot shows the relationship between these forces as the flange body is joined with its mating part by increasing the bolt forces (preloading). For explanation purposes of figure  FIG. 7C , more specifically the left half  716 , the preloading of the bolt only needs to be represented in a single phase since there is not an outer hub with an initial gap. For the typical single hub flange the sum of forces in the bolts are equivalent in magnitude to the forces in the single huh  730  at the end of flange make-up. The right hall  717  shows how these forces change when subjected to a thermal gradient consisting of a hot bore  710  and a cold exterior  720 , as is commonly experienced by flanges that are installed subsea after initial makeup. As can be seen in the right half  717  of  FIG. 7C , both the hub load  713  and bolt load  714  increase by approximately 35%, from 100% to 135%. This is a result of thermal gradient and thermal expansion/contraction causing the unstressed-state of the hub  730  to expand and unstressed-state of the bolts  112  to contract. Additionally, due to additional stiffness resulting from the lack of groove  520 , this effect is further amplified, resulting in bolt stresses that are near the limit of industry regulations on the allowable stress levels for bolting. This phenomenon, as proven by detailed FBA, leaves traditional single hub flanges with little remaining stress capacity in the bolts for carrying the external loads subjected to subsea flanges. An alternative option to combat the negative thermal effects subjected to bolting in subsea flanges is to reduce the initial bolt preload, but this is unfavorable due to the inverse relationship between bolt preload and fatigue life. 
     For purposes of this disclosure, thermal expansion and thermal contraction refers to the general physics and engineering, definition of this phenomenon. This phenomenon may be thought of as the property of a metal (and most other materials shrink or expand in an unloaded or unstressed state when subjected to a change in temperature. For clarification purposes, thermal expansion and/or thermal contraction as used herein is referring to this properly and related phenomena, and not necessarily the explicit expansion or contraction of material. For example, fasteners on flanges subjected to the temperature gradients described herein (i.e., higher internal bore temperatures relative to the adjacent exterior temperatures) are explained to thermally contract due to the reduction in temperature. Although the effect of the lower local temperature at a fastener experiencing thermal contraction is to reduce the length and/or volume of the fastener, external forces and/or displacements or deformations of surrounding material (including the effects of thermal expansion and/or thermal contraction outside of the fasters) may result in the overall lengthening or expansion of the fastener. 
       FIGS. 8A and 8B  provide cross-sectional views of a compound hub flange connection  500 , where  FIG. 8A  shows a compound hub flange  500  under ambient conditions without the effect of a thermal gradient, and  FIG. 8B  depicts a compound huh flange  500  under high temperature conditions causing a thermal gradient, for example, at a subsea location. As shown in  FIG. 8A , a compound hub flange connection  500  may have a higher percentage preload on outer hub  515  and a lower percentage preload on inner hub  513 . For example, at ambient temperatures, outer hub  515  may have a 70% preload and inner hub  513  may have a 30% preload. 
     Referring now to  FIG. 8B , as discussed above with respect to  FIG. 7B , large temperature differences between a hot bore  710  and cold exterior  720  may result in thermal gradients  712 ,  714 , and  716 . High temperatures from these thermal gradients May cause compound hub flanges  502   a  and  502   b  to expand, and thus produce increased bending stress on bolts  112 . However, the configuration of compound hub flange connection  500  results in less of an increase in bending stress of the bolt three. Taking the example above, where the inner hub  513  had a 40% preload and the outer hub  515  had a 60% preload under ambient conditions,  FIG. 8B  (and  FIG. 6C ) shows the resulting changes in hub and bolt loads when the compound hub flanges  502   a  and  502   b  are subjected to thermal expansion at inner hub  513  and thermal contraction at outer hub  515 . 
     Inner hub  513  is subjected to the highest temperature zone  712  of the thermal gradient, and thus experiences an increase in hub force from 40% to 105%, compared to the original preloaded condition. As a result of the thermal expansion of inner hub  513  and thermal contraction of outer hub  515 , the preload on outer hub  515  decreases from 60% to 5%, compared to the original preloaded condition. The net effect of this is a net increase of 10% load on bolt  112 , compared to the 35% increase on bolt  112  in a traditional huh flange shown in  FIG. 7B . Thus, compound hub flanges reduce the load of bolts  112  compared to traditional hub flanges when subjected to high thermal gradients typical for subsea flanges. These high thermal gradients typical for subsea flanges are typical because of the difference in temperature between the cold water surrounding (radially external to) the subsea flange and hot production fluid transported internally through (radially internal to) a flowbore of the subsea flange. This reduction in bolt stresses induced by the thermal gradient allows for additional external loading capability before the allowable stress limit of the bolt is reached. 
       FIGS. 9A and 9B  are plots comparing the combined loading capabilities in a traditional hub flange connection versus a compound bub flange connection. These charts are often provided by manufacturers to end-users so that they may assess the whether a flange, or other mechanical joint, is sufficiently strong to meet the intended load combination. The load combinations that are typically shown on these charts include combinations of internal pressure versus external bending moment. For subsea flanges, the strength of the flange joint is typically limited by the stress in the bolts. Lines  910  and  912  in  FIG. 9A  represent the limits of the combined loads that may be applied to the compound hub flange before exceeding the rated capability of the flange. For example, all combinations of bending and internal pressure that fall to the left of line  910  are within the rated capability of the compound hub flange without thermal gradient. Any combination of external bending and internal pressure that falls to the right of line  910  is undesirable, as it exceeds the rated capability of the flange. Similarly, external load combinations that fall to the left of line  912  are within the rated capability of the compound hub flange when additionally subjected to a high temperature gradient. The two horizontal leftward pointing arrows indicates the change in the rated capability of the compound hub flange when subjected to a thermal gradient. Similarly, line  920  and  922  in  FIG. 9B  show the rated capabilities of the traditional single hub flange for both the “without thermal gradient” and “with thermal gradient” conditions, respectively. 
     By comparing  FIG. 9A  to  FIG. 9B , it can be realized that the thermal gradient reduces the rated capabilities of both flanges, but the percent and magnitude of reduction of rated capability is significantly lower with the compound hub flange versus the single hub flange. This a result of thermally contracting external hub  515  counteracting the thermally expanding inner hub  513  as previously described. It can also be realized that the compound hub flange has greater rated capability in all relative scenarios. This is a result of the increased flange body flexibility, from groove  520 , more evenly distributing the load across all bolts and external bending moment reaction point on external hub lace  514 . Thus, the compound hub flange  500  provides a rated capability under ambient conditions, and also provides, less of a decrease in the rated capability under high temperature conditions as compared to the traditional hub flange. 
     Accordingly, the present disclosure provides a flange connection that reduces stresses on the bolts used to form the connection while minimizing an overall size and weight of the flange connection. This is particularly useful in the field of subsea equipment, where components with very large diameters are routinely connected and it is important to keep the stack height and weight of this subsea equipment as low as possible. 
     Although the present disclosure and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the disclosure as defined by the following claims.