Abstract:
Systems and methods for generating transfer functions associated with calculating local stresses on pipe elements by post processing forces and moments of a pipe model representing the piping system. The transfer functions are reusable and allow recalculation with different sets of user data without requiring regeneration of the transfer functions.

Description:
RELATED APPLICATION 
       [0001]    This application is a divisional application of U.S. patent application No. 12/772,289, filed May 3, 2010, which claims priority and benefit from, U.S. Provisional Patent Application Ser. No. 61/267,234, entitled “Design Method for Subsea Equipment Subject to Hydrogen Induced Stress Cracking”, filed on Dec. 7, 2009, the disclosure of which is incorporated here by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention relates generally to subsea equipment piping design and, more specifically, to designing subsea piping systems subject to Hydrogen Induced Stress Cracking (HISC). 
       BACKGROUND 
       [0003]    The world&#39;s use of fossil fuels has grown exponentially over the past several decades. With this growth, the oil and gas industry has broadened the search for new oil and gas reserves to meet the ever growing consumer demand. The search for new oil and gas reserves now includes areas previously unimaginable for exploration. The need to produce oil and gas from these new regions has presented a new set of problems related to the design and validation of equipment used in the production of the newly discovered oil and gas reserves. 
         [0004]    Some of the new areas which are producing substantial oil and gas reserves are located beneath the ocean. In the subsea environment, new problems associated with flow line and production equipment have produced a new class of equipment design problems which are sometimes referred to as “Hydrogen Induced Stress Cracking” (HISC). In general, HISC problems are created by two environmental factors, specifically the availability of ionic hydrogen at the surface of chromium alloyed steel constructed subsea equipment due to such equipments&#39; immersion in an aqueous solution. 
         [0005]    The result of such HISC related problems is manifested by a weakening of the alloyed steel components and structures. Subsequent component and/or structural failure can occur leading to safety issues, environmental damage by contamination to the surrounding subsea location and high repair costs based on equipment location. Analysis of failed subsea systems has indicated that consideration of HISC factors should be included in the overall design process associated with subsea systems which are made of certain materials (e.g. Duplex and Super Duplex Stainless Steel) used in the acquisition and recovery of subsea reserves of oil and gas. 
         [0006]    Current methods for analyzing and designing subsea oil and gas production systems, while capable of allowing for HISC considerations, require many hours of computer computational time to complete an analysis of one set of conditions. For example, in a first design/evaluation step, a one-dimensional frame model is developed with center lines representing the axis of the piping system. After the frame model is complete, the axial lines are replaced by finite pipe elements. The pipe elements are able to simulate all various types of operating and non-operating conditions and allow the assessment of ASME requirements (i.e. ASME B31.8). 
         [0007]    In a second step, the pipe elements are partially or fully replaced by shell elements. The number of elements replaced is dependent on the sections of the design under review. Like the pipe elements, the shell elements are able to simulate both operating and non-operating conditions. However a significant feature of shell elements in the design process is that the shell elements allow for the prediction of local stresses and therefore the assessment of linear HISC (i.e. DNV RP-F112). However the many sets of load conditions and the associated sets of computational runs associated with processing the shell elements in this second step can be prohibitively expensive both in terms of time and computing requirements. 
         [0008]    In a third step, elements identified as not compliant with required conditions based on the linear analysis of step two are replaced with three-dimensional sub-models. An analysis is performed with elasto-plastic material properties allowing the assessment of non-linear HISC conditions. The result of the three-dimensional sub-model analysis allows for the prediction of local strains on the analyzed elements. 
         [0009]    Accordingly, market pressure is demanding a method for designing subsea oil and gas equipment capable of withstanding the rigors of the subsea environment without the prohibitively expensive costs, in terms of analysis time and computational requirements, of existing techniques. 
       SUMMARY 
       [0010]    Exemplary embodiments relate to systems and methods for analyzing and designing subsea components and systems for oil and gas recovery capable of withstanding the subsea environment and the problems associated with HISC. The methodology includes the development of Transfer Functions (TF) for each type of pipe element. For example, transfer functions can be developed for bends, tees, couplings, welds and the like which are associated with subsea piping. 
         [0011]    According to an exemplary embodiment, the data collected from the first step of the current methodology is provided to the appropriate TF. The appropriate transfer function is based on the pipe element under investigation. The TF transforms the collected pipe data into local stresses associated with the pipe element for the user specified conditions of the analysis. However, it will be appreciated by those skilled in the art that such advantages are not to be construed as limitations of the present invention except to the extent that they are explicitly recited in one or more of the appended claims. 
         [0012]    According to another exemplary embodiment, a series of simulations can be performed on the subject pipe element using different conditions without developing a new transfer function for each set of conditions. The results of the series of simulations creates a profile of the local stresses, based on the different conditions, allowing a more accurate and reliable design of the associated pipe element. Any pipe element determined to be non-compliant with the linear HISC analysis provided by the TF can then be analyzed by the previously described third step of the existing HISC analysis. The elimination of the time and resource intensive second step of the existing HISC analysis provides for designing a subsea oil and gas system capable of withstanding the conditions of the subsea environment while providing an economical and timely analysis and design phase as demanded by current industry and market requirements. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The accompanying drawings illustrate exemplary embodiments, wherein: 
           [0014]      FIG. 1  depicts system models representing the three different simulations associated with the background art; 
           [0015]      FIG. 2  depicts a pipe with a ninety degree bend to illustrate the amount of FEM elements required in the three different types of simulations; 
           [0016]      FIG. 3  depicts a method of making a HISC assessment based on a pipe model, transfer functions and a three dimensional sub-model according to an exemplary embodiment; 
           [0017]      FIG. 4  depicts a method of generating transfer functions and making a HISC assessment based on a series of user defined conditions according to an exemplary embodiment; 
           [0018]      FIG. 5  depicts a general computing environment for performing the calculations associated with generating transfer functions and making a HISC assessment according to an exemplary embodiment; 
           [0019]      FIG. 6  depicts a transfer function component comprising a transfer function generator, a transfer function engine and transfer function storage according to an exemplary embodiment; 
           [0020]      FIG. 7  depicts a bend pipe element illustrating representative independent variables associated with deriving a transfer function according to an exemplary embodiment; 
           [0021]      FIG. 8  depicts a bend pipe element illustrating forces and moments acting on the bend pipe element according to an exemplary embodiment; and 
           [0022]      FIG. 9  depicts a bend pipe element illustrating predicted locations of maximum stress on the bend pipe element according to an exemplary embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0023]    The following detailed description of the exemplary embodiments refers to the accompanying drawings. The same reference numbers in different drawings identify the same or similar elements. Also, the following detailed description does not limit the invention. Instead, the scope of the invention is defined by the appended claims. 
         [0024]    To provide context for the subsequent discussion relating to transfer function generation and the use of the generated transfer functions in HISC assessment systems according to these exemplary embodiments,  FIG. 1  schematically illustrates piping models associated with the current method of system design. As discussed previously, the method uses three modeling systems illustrated by system  100  and is comprised of three steps. In a first step, a frame model of the piping system is constructed with piping lines  108  coinciding with the axis of the three-dimensional pipes. After constructing the frame model, the lines are replaced with pipe elements  104  representing the piping system and providing data (area, inertia, etc.) associated with the desired piping system. The result of the first step is the production of a pipe model  102 . 
         [0025]    Next, in a second step, the pipe model produced by the first step is fully or partially replaced by shell elements  110 . The resultant shell model  106  can simulate operating, incidental and stroke conditions allowing the assessment of linear HISC conditions. The driving force behind this model is the prediction of local stresses of the pipe elements. 
         [0026]    Proceeding to the third step, a determination is made for each pipe element to determine if the linear HISC assessment is compliant. If it is determined that a particular pipe element is non-compliant with the linear HISC assessment then a three-dimensional sub-model  112  is generated for the pipe element  114 . The three dimensional sub-model  112  is then run with elasto-plastic material properties, developing a non-liner HISC assessment. After running the three-dimensional sub-model  112 , a determination is made regarding the acceptability of the pipe element based on its current design. 
         [0027]    Looking now to  FIG. 2  and another exemplary embodiment  200  of the current method of piping system design, representations of a bend pipe element for the three different models depicts the relative complexity of the different models. The bend with a uni-axial element  202  is the model used for the first step  102  previously described. This model requires the least amount of input data and the least amount of computational time. For example, the representative bend uni-axial element  202  has twelve degrees of freedom, six for each element end. 
         [0028]    The bend pipe element  204  with a shell elements  206  is a more complex model with each shell element  206  having twenty-four degrees of freedom. The shell elements  206  are pieced together to represent the surface of the bend pipe element  204  and require many more calculations per shell element  206  in addition to the many shell elements  206  required to represent the surface of the bend pipe element  204 . The three-dimensional sub-model  208  with solid elements  210  is the most complex model because it models the entire structure of the bend. The solid elements  210  and the shell elements  206  have similar degrees of freedom and therefore computational complexities but the three-dimensional sub-model  208  requires many more solid elements to define the structure. Accordingly, the computational times required for a solid element modeled bend is much greater than the computational time required for a shell element modeled bend. However, in the current design method the second step  106  shell modeling is conducted over the entire piping system whereas the third step  112  three-dimensional sub-modeling is applied to only pipe elements viewed as linear HISC non-compliant based on the shell model analysis. 
         [0029]    Referring now to  FIG. 3 , a method  300  of making a HISC assessment based on a pipe model, transfer functions and three-dimensional sub-model according to an exemplary embodiment is illustrated. Beginning at step  302 , a pipe model is generated representing the piping system. A frame model is first constructed of lines representing the axis of the pipes in the system. Next, the frame lines are replaced by their corresponding pipe elements. Each pipe element provides the associated real data such as area, inertia and the like representing the actual piping system configuration. 
         [0030]    Next at step  304 , the pipe model results for each pipe element are collected and presented to the transfer function associated with the pipe element. The transfer function calculates predictions for the local stresses of the elements by post-processing forces and moments of the pipe model. The manner in which such transfer functions can be determined according to exemplary embodiments is described below. Next at step  306 , the calculated local stress values are evaluated for linear HISC compliance. Compliance is determined by comparing the calculated local stress values to standard engineering tolerances. In particular, the linear compliance is assessed by listing, for each component: 1) the maximum membrane stress in the principal directions, 2) the maximum membrane plus bending stresses in the principal directions and 3) Von Mises [eqv.] with just membrane plus bending stresses. 
         [0031]    Continuing to step  308 , a determination is made of whether the pipe element is linear stress compliant. If the pipe element is not linear stress compliant then the method  300  proceeds to step  310 . At step  310  the method simulates the pipe element with a three-dimensional sub-model. The three-dimensional sub-model performs a non-linear HISC assessment by predicting local strains on the pipe element. If the pipe element is non-compliant with the non-linear HISC assessment then a redesign of the pipe element is required. If the pipe element is compliant with the non-linear HISC assessment then the method  300  continues to step  312  and a determination is made as to whether any other pipe elements require evaluation. If additional pipe elements require evaluation then the method  300  returns to step  306  and repeats with the next pipe element. For example, the non-linear HISC compliance is assessed in a course and, if required, fine evaluation. According to an exemplary embodiment, the previously described evaluation is performed just for those pipe elements for which predicted strains are not sufficiently below HISC limits. The method according to this exemplary embodiment provides results inside and outside of five percent of wall thickness and generates strain plots versus wall thickness, however those skilled in the art will appreciate that other limits may be used. The plots are automatically generated for any sections where stress concentrates. In another aspect of this exemplary embodiment, plots are also generated at regularly spaced sections from the bend end section. 
         [0032]    Looking now to  FIG. 4 , a method  400  of generating transfer functions and using the transfer functions for repetitive calculations using different user defined conditions without generating new transfer functions according to an exemplary embodiment is illustrated. Beginning at step  402 , the method generates transfer functions by running a set of combinations of the pipe element dimensions for each type of load applicable to the pipe element. Next, at step  404 , user defined conditions are provided to the transfer function as inputs. Continuing to step  406 , the transfer functions are exercised and the local pipe element stresses calculated by the transfer functions are collected. 
         [0033]    Next at step  408 , a determination is made regarding additional calculations with a different set of user defined conditions. If additional transformations are required using another set of user defined conditions then the method returns to step  404  and repeats the transformation without generating new transfer functions based on the updated user defined conditions. It should be noted that an optimization point of the method according to this exemplary embodiment is the ability to calculate local pipe element stresses for different user defined conditions without the need to generate new transfer functions based on the new user defined conditions. 
         [0034]    Referring now to  FIG. 5 , illustrated therein is an example of a suitable computing system environment  500  in which the claimed subject matter can be implemented. It should be noted that the computing system environment  500  is only one example of a suitable computing environment for a mobile device and is not intended to suggest any limitation as to the scope of use or functionality of the claimed subject matter. Further, the computing environment  500  is not intended to suggest any dependency or requirement relating to the claimed subject matter with respect to any one, or any combination, of the components illustrated in the exemplary operating environment  500 . 
         [0035]    With reference to  FIG. 5 , an example of a remote device for implementing the various aspects described herein includes a general purpose computing device in the form of a computer  510 . Components of computer  510  can include, but are not limited to, a processing unit  520 , a system memory  530 , and a system bus  521  that couples various system components including the system memory  530  to the processing unit  520 . The system bus  521  can be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. 
         [0036]    Computer  510  can include a variety of computer readable media. Computer readable media can be any available media that can be accessed by computer  510 . By way of example, and not limitation, computer readable media can comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile as well as removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CDROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by computer  510 . Communication media can embody computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and can include any suitable information delivery media. 
         [0037]    The system memory  530  can include computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) and/or random access memory (RAM). A basic input/output system (BIOS), containing the basic routines that help to transfer information between elements within computer  510 , such as during start-up, can be stored in memory  530 . Memory  530  can also contain data and/or program modules that are immediately accessible to and/or presently being operated on by processing unit  520 . By way of non-limiting example, memory  530  can also include an operating system, application programs, other program modules, and program data. 
         [0038]    The computer  510  can also include other removable/non-removable, volatile/nonvolatile computer storage media. For example, computer  510  can include a hard disk drive that reads from or writes to non-removable, nonvolatile magnetic media, a magnetic disk drive that reads from or writes to a removable, nonvolatile magnetic disk, and/or an optical disk drive that reads from or writes to a removable, nonvolatile optical disk, such as a CD-ROM or other optical media. Other removable/non-removable, volatile/nonvolatile computer storage media that can be used in the exemplary operating environment include, but are not limited to, magnetic tape cassettes, flash memory cards, digital versatile disks, digital video tape, solid state RAM, solid state ROM and the like. A hard disk drive can be connected to the system bus  521  through a non-removable memory interface such as an interface, and a magnetic disk drive or optical disk drive can be connected to the system bus  521  by a removable memory interface, such as an interface. 
         [0039]    A user can enter commands and information into the computer  510  through input devices such as a keyboard or a pointing device such as a mouse, trackball, touch pad, and/or other pointing device. Other input devices can include a microphone, joystick, game pad, satellite dish, scanner, or the like. These and/or other input devices can be connected to the processing unit  520  through user input  540  and associated interface(s) that are coupled to the system bus  521 , but can be connected by other interface and bus structures, such as a parallel port, game port or a universal serial bus (USB). A graphics subsystem can also be connected to the system bus  521 . In addition, a monitor or other type of display device can be connected to the system bus  521  via an interface, such as output interface  550 , which can in turn communicate with video memory. In addition to a monitor, computers can also include other peripheral output devices, such as speakers and/or a printer, which can also be connected through output interface  550 . 
         [0040]    The computer  510  can operate in a networked or distributed environment using logical connections to one or more other remote computers, such as remote server  570 , which can in turn have media capabilities different from device  510 . The remote server  570  can be a personal computer, a server, a router, a network PC, a peer device or other common network node, and/or any other remote media consumption or transmission device, and can include any or all of the elements described above relative to the computer  510 . The logical connections depicted in  FIG. 5  include a network  571 , such local area network (LAN) or a wide area network (WAN), but can also include other networks/buses. Such networking environments are commonplace in homes, offices, enterprise-wide computer networks, intranets and the Internet. 
         [0041]    When used in a LAN networking environment, the computer  510  is connected to the LAN  571  through a network interface or adapter. When used in a WAN networking environment, the computer  510  can include a communications component, such as a modem, or other means for establishing communications over the WAN, such as the Internet. A communications component, such as a modem, which can be internal or external, can be connected to the system bus  521  via the user input interface at input  540  and/or other appropriate mechanism. In a networked environment, program modules depicted relative to the computer  510 , or portions thereof, can be stored in a remote memory storage device. It should be appreciated that the network connections shown and described are exemplary and other means of establishing a communications link between the computers can be used. 
         [0042]    Looking now to  FIG. 6 , a transfer function component  602  according to an exemplary embodiment comprises a transfer function generator  604 , a transfer function engine  606  and transfer function storage  608 . It should be noted that the transfer function component is, in this exemplary embodiment, stored in the system memory  530  of the computing environment  510  and executed by the processing unit  520  of the computing environment  510 . The transfer function generator provides for the creation of transfer functions associated with pipe elements that correlate local stresses on a pipe element with loads applied to the pipe element. A second order transfer function equation for a unitary load in a specific location (node), would appear as: 
         [0000]        S   Fi   =c+ ( a   1   *Ro )+( a   2   *Ri )+( a   3   *Rb )+( a   4   *Ab )+( a   5   *Ro*Ri )+( a   7   *Ro*Rb )+( a   8   *Ro*Ab )+( a   9   *Ri*Rb )+. . . +( a   a+1   *Ro 2)+( a   n+2   *Rb   2 )+. . . +( a   n+5   *Ab   2 )  eq.1
 
         [0043]    where S Fi =Stress (S) generated by a specific force or moment (F, M) in a direction (i); 
         [0044]    c=constant; a 1  . . . a n =coefficients, Ro=outer radius; Ri=inner radius; Ab=bend angle; and 
         [0045]    Rb=bend radius, see also the variables  700  as illustrated in  FIG. 7 . Based on the fact that stress distribution is linearly dependent on the load, transfer functions are generated for non-unitary loads as the product of the non-unitary load at the node and the stress at the node (S Fi@node =Li*S Fi@node ) as evaluated by eq. 1. For example, transfer functions are created for each stress component (e.g. radial stress, axial stress, hoop stress, etc.) and for each type of load with the total component stress evaluated as 
         [0000]      Sradial@node= L 1*S F1     —     radial@node   +L 2 *S   F2     —     radial@node   +L 4i*S M1     —     radial@node . . .    +L 6 *S   M3     —     radial@node    
         [0000]    where S=stress; L=load; F=force and M=moment, see forces/moments  800  as illustrated in  FIG. 8 . It should be noted that similar equations are derived for hoop stress axial stress etc. It should also be noted that according to exemplary embodiments, a transfer function is generated for each load type and, therefore, the total local stress is calculated by summing the stress values for each load type. The summation is valid because the stresses are component stresses such as hoop stress, radial stress, etc. 
         [0046]    According to one exemplary embodiment, transfer functions are generated only for nodes where stress concentrates. For example, in a bend, stress concentrates at one of the three stress locations  900  in a system under design as indicated in  FIG. 9 . In  FIG. 9 , the illustrated sections indicate the typical locations where stresses concentrate. Based on the load combination, one section will develop more stress than the others. For example, pressure stresses the ½ of ANG section while out of plane movement stresses the ⅓ of ANG section. Further, the angular position can vary based on the load combination. For the elaborated reasons, transfer functions are generated at twenty-four different angular locations. The maximum may fall between any two consecutive locations therefore a final evaluation is performed by interpolation. In total, analysis of the bend in this exemplary embodiment employs four hundred thirty-two transfer functions based on locations, force components and force types. 
         [0047]    The transfer function engine  606  provides for executing the appropriate transfer function with the data necessary from the previously constructed pipe model to transform the structural input data into local pipe element stress values. In another exemplary embodiment, the transfer function engine  606  can loop through a series of input data collections and transform the input data to a corresponding series of pipe element local stress values. Alternatively, the local transfer function engine  606  can transmit the data collected from the pipe model to a remote transfer function engine  606 , located on another computer communicatively connected to the local transfer engine function  606 , for processing the input data into the pipe element local stress values. In this manner, the data processing can be accomplished on either (or both) the local computer and a remote computer. 
         [0048]    The transfer function storage component  608  provides for storing generated transfer functions so that the transfer functions can be reused to run another simulation at a later time. In one non-limiting example, new user defined conditions can appear as a result of a change in the piping configuration and the applicable transfer functions can be recalled without the need for generating a new set of transfer functions. In another non-limiting example, the stored transfer functions can be transmitted to another computer system and stored or executed at the remote location. 
         [0049]    As used in this application, terms such as “component”, “display”, “interface” and the like are intended to refer to a computer-related entity, either hardware, a combination of hardware and software, software, or software in execution as applied to a system for verification of subsea equipment subject to HISC. For example, a component may be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program and a computer. By way of illustration, both an application running on a server and the server can be components. One or more components may reside within a process and/or thread of execution and a component may be localized on one computer and/or distributed between two or more computers, industrial controllers, and/or modules communicating therewith. Additionally, it is noted that as used in this application, terms such as “system user”, “user”, “operator” and the like are intended to refer to the person operating the computer-related entity referenced above. 
         [0050]    The above-described exemplary embodiments are intended to be illustrative in all respects, rather than restrictive, of the present invention. Thus the present invention is capable of many variations in detailed implementation that can be derived from the description contained herein by a person skilled in the art. All such variations and modifications are considered to be within the scope and spirit of the present invention as defined by the following claims. No element, act, or instruction used in the description of the present application should be construed as critical or essential to the invention unless explicitly described as such. Also, as used herein, the article “a” is intended to include one or more items.