Patent Publication Number: US-2022229951-A1

Title: Stress analysis for plastic material lined tubular structures for boreholes

Description:
TECHNICAL FIELD 
     This application is directed, in general, to tubular structure design for boreholes and, more specifically, to using a plastic material lining for tubular structures. 
     BACKGROUND 
     When developing and drilling boreholes, it is important to be able to support the borehole against collapse, ensure borehole integrity, and protect equipment that is lowered into the borehole from fluid corrosion. In addition, the borehole may be exposed to varying temperatures, varying pressures, formation fluids, electromagnetic radiation, and varying types of mineralogy. These factors can adversely affect the equipment lowered into the borehole. Tubular structures, for example, casing, tubing, or drill string, can assist in protecting the equipment, as well as in some aspects of supporting the borehole against formation leakage and collapse. It would be beneficial to improve the efficiency of the borehole design, by more accurate stress analysis of the tubular structures used within the borehole when using plastic material lined tubular structures. The plastic material may cause a challenge for borehole tubular design since the thermal and mechanical properties of plastic material may be very different from those of carbon steels. 
     SUMMARY 
     In one aspect a method is disclosed. In one embodiment, the method includes (1) receiving input parameters for a tubular structure design of a plastic material lined tubular structure of a borehole, wherein the tubular structure design utilizes a thermal model and one or more strength models, (2) modifying one or more input parameters to generate modified input parameters, wherein an initial wall thickness of the tubular structure is modified to an adjusted wall thickness for each layer of the tubular structure using the input parameters, (3) applying the modified input parameters to the one or more strength models to generate a respective strength rating, (4) generating a pressure parameter and a temperature parameter using the input parameters and the thermal model, and (5) executing a stress analysis utilizing the modified input parameters, the respective strength rating, the pressure parameter, and the temperature parameter. 
     In a second aspect a tubular structure design system is disclosed. In one embodiment, the tubular structure design system includes (1) a parameter receiver, capable to receive input parameters, (2) a result transceiver, capable of communicating result parameters, and (3) a stress analyzer, capable of utilizing the input parameters to determine one or more load factors, one or more safety factors, or one or more design limit parameters to apply to a plastic material lined tubular structure for a tubular structure design for a borehole, and to generate the result parameters, wherein a thermal model and one or more strength models are utilized to generate the result parameters. 
     In a third aspect a computer program product having a series of operating instructions stored on a non-transitory computer-readable medium that directs a data processing apparatus when executed thereby to perform operations is disclosed. In one embodiment, the operations include (1) receiving input parameters for a tubular structure design of a plastic material lined tubular structure of a borehole, wherein the tubular structure design utilizes a thermal model and one or more strength models, (2) modifying one or more input parameters to generate modified input parameters, wherein an initial wall thickness of the tubular structure is modified to an adjusted wall thickness for each layer of the tubular structure using the input parameters, (3) applying the modified input parameters to the one or more strength models to generate a respective strength rating, (4) generating a pressure parameter and a temperature parameter using the input parameters and the thermal model, and (5) executing a stress analysis utilizing the modified input parameters, the respective strength rating, the pressure parameter, and the temperature parameter. 
    
    
     
       BRIEF DESCRIPTION 
       Reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is an illustration of a diagram of an example drilling system; 
         FIG. 2  is an illustration of a diagram of an example wireline system; 
         FIG. 3  is an illustration of a diagram of an example offshore system; 
         FIG. 4  is an illustration of a diagram of an example hydraulic fracturing system; 
         FIG. 5  is an illustration of a diagram of an example cross-sectional view of a plastic material lined tubular structure; 
         FIG. 6A  is an illustration of a diagram of an example graph of a metal tubular structure; 
         FIG. 6B  is an illustration of a diagram of an example graph of a plastic material lined tubular structure; 
         FIG. 7  is an illustration of a flow diagram of an example method of a stress analysis of a tubular structure; 
         FIG. 8  is an illustration of a block diagram of an example tubular structure design system; and 
         FIG. 9  is an illustration of a block diagram of an example of a tubular structure design controller according to the principles of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     When designing borehole systems, one factor to be considered is the lifetime integrity of tubular structures to be used in the borehole. It is beneficial at the stage of tubular structure design to conduct detailed stress analyses, including the damage factors, such as corrosion and mechanical wear. First, tubular structures should be sufficiently strong to withstand the pressures and stresses associated with fluid flow between the formation and borehole surface during drilling, production, and stimulation operations. The safety factors, e.g., a ratio of resistance to load, of various load scenarios such as burst, collapse, tension, compression, and triaxial should be greater than the required design factor, e.g., a design factor of 1.0. To ensure the tubular structure meets the operational goal, such as satisfying the operational lifetime of the borehole or another specified time interval, the estimated total amount of material loss or corrosion, e.g., metal loss or other material loss, can be compared against the determined maximum allowable wear, or a maximum allowable material loss, as a safety check of the design. 
     Tubular structures can vary as to the material used and the thickness of the wall of the tubular structure. The type of tubular structure used at a particular depth can be different than the tubular structure used in another portion of the borehole. During the design phase, it is beneficial to select a tubular structure that can maximize the efficiency of the borehole operations at a particular location within the borehole. 
     Additional cost could be incurred in replacing a section of the tubular structure if that portion or section of the tubular structure wears out sooner than planned. Wear on the tubular structure can occur due to various factors, for example, physical or mechanical wearing due to trip in or trip out of tools such as a wireline tool or a drill string, physical or mechanical wearing due to rotation of a drill string, corrosion factors, pressure factors, temperature factors, mineralogy factors, and other factors. 
     Typically, users design the tubular structures against various load factors such as axial, triaxial, burst, compression, torsion, and collapse. Designing for the various load factors can involve modeling and simulating tubular structures under various conditions and factors. Conventionally, tubular structure loads, e.g., integrity or safety factors, can be calculated using industry accepted models. In some aspects, the conventional wear and strength models can miss estimate the load ratings of the tubular structure. As a result, the tubular structure could be over-designed in terms of the load factor, which is not cost effective for the borehole system. Tubular structures can be casing, pipes, drill strings, downhole tools, and other types of tubular structures. Tubular structures can be constructed of a metal layer of steel, carbon-steel, other metallic alloys, or other materials, as well as a plastic material layer attached to the metal layer. 
     Corrosion in borehole completions can lead to borehole integrity issues, leading to an increase in expense to repair or replace those sections of the tubular structure affected by the corrosion. Using corrosive resistant alloys for the tubular structures in boreholes subject to higher corrosive effects can increase the cost of the tubular structures. Using plastic material to line tubular structures can lower the cost for each section of the tubular structure while improving the corrosion resistance. For example, the plastic material can be a polymer, a glass fiber reinforced epoxy (GRE), or a carbon fiber plastic composite. The plastic material can exhibit thermal and mechanical characteristics that differ from the conventional tubular structure material. Conventional tubular structure design systems may not be able to utilize plastic material. Implementing a stress analysis for plastic material lined tubular structures can involve a time consuming three-dimensional finite element method. 
     This disclosure presents processes and methods to analyze a tubular structure design where the tubular structure incorporates a plastic material lined tubular structure, such as where the plastic material is attached to the internal diameter (ID) of the tubular structure using a grout, e.g., adhesive. The tubular structure design can utilize an approximate stress analysis of plastic material lined tubular structures. The equivalent density, the equivalent thermal conductivity, and the equivalent thermal capacity can be determined for the plastic material lined tubular structure and used in a simulation of the heat transfer. 
     These equivalent thermal conduction properties and heat transfer analysis can be utilized for a thermal flow analysis of various borehole operations, such as a production operation, an injection operation, a drilling operation, or other borehole operations. The thermal flow analysis can be used to generate pressure and temperature parameters, which can be used as inputs, along with tubular structure model data, to a stress analyzer. The stress analyzer can utilize the non-plastic material portion of the tubular structure for the tubular structure modeling, e.g., using the critical dimension, which can be a percentage of the initial wall thickness used in the calculations of the axial, triaxial, burst, collapse, torsion, and compression ratings. In some aspects, the stress analysis can utilize a strength factor contribution from the plastic material of zero, which can allow a more conservative strength calculation of the tubular structure design. In some aspects, the strength factor contribution from the plastic material can be specified. 
     Turning now to the figures,  FIG. 1  is an illustration of a diagram of an example drilling system  100 , for example, a logging while drilling (LWD) system, a measuring while drilling (MWD) system, a seismic while drilling (SWD) system, a telemetry while drilling (TWD) system, injection well system, extraction well system, and other borehole systems. Drilling system  100  includes a derrick  105 , a well site controller  107 , and a computing system  108 . Well site controller  107  includes a processor and a memory and is configured to direct operation of drilling system  100 . Derrick  105  is located at a surface  106 . 
     Extending below derrick  105  is a borehole  110  with downhole tools  120  at the end of a drill string  115 . Downhole tools  120  can include various downhole tools, such as a formation tester or a bottom hole assembly (BHA). At the bottom of downhole tools  120  is a drilling bit  122 . Other components of downhole tools  120  can be present, such as a local power supply (e.g., generators, batteries, or capacitors), telemetry systems, sensors, transceivers, and control systems. Borehole  110  is surrounded by subterranean formation  150 . 
     Well site controller  107  or computing system  108  which can be communicatively coupled to well site controller  107 , can be utilized to communicate with downhole tools  120 , such as sending and receiving telemetry, data, instructions, subterranean formation measurements, and other information. Computing system  108  can be proximate well site controller  107  or be a distance away, such as in a cloud environment, a data center, a lab, or a corporate office. Computing system  108  can be a laptop, smartphone, PDA, server, desktop computer, cloud computing system, other computing systems, or a combination thereof, that are operable to perform the processes described herein. Well site operators, engineers, and other personnel can send and receive data, instructions, measurements, and other information by various conventional means, now known or later developed, with computing system  108  or well site controller  107 . Well site controller  107  or computing system  108  can communicate with downhole tools  120  using conventional means, now known or later developed, to direct operations of downhole tools  120 . 
     Casing  130  can act as barrier between subterranean formation  150  and the fluids and material internal to borehole  110 , as well as drill string  115 . In some aspects, as drill string  115  rotates within borehole  110  or during trip in or trip out operations, there can be wear of casing  130 . In some aspects, as fluid passes through borehole  110 , corrosion can effect casing  130 , for example, when the fluid is acidic. Casing  130  should be designed to account for this wear or corrosion for an operational time interval, such as the operational lifetime of borehole  110 . Replacing casing sections of casing  130  can be scheduled though it can be more cost effective to design casing  130  prior to placement to avoid replacement during the operational time interval. 
       FIG. 2  is an illustration of a diagram of an example wireline system  200 . Wireline system  200  depicts a wireline well system and includes a derrick  205 , a well site controller  207 , and a computing system  208 . Well site controller  207  includes a processor and a memory and is operable to direct operation of wireline system  200 . Derrick  205  is located at a surface  206 . Computing system  208  can be proximate well site controller  207  or be a distance away, such as in a cloud environment, a data center, a lab, or a corporate office. Computing system  208  can be a laptop, smartphone, PDA, server, desktop computer, cloud computing system, and other computing systems. 
     Extending below derrick  205  is a borehole  210 , with a cased section  215   a , a cased section  215   b , and one uncased section  216 . Wireline  220  is inserted in borehole  210  to hold a downhole tool  225 . Borehole  210  is surrounded by a subterranean formation  235  which includes a hydrocarbon reservoir. In some aspects, cased section  215   a  and cased section  215   b  can be designed to withstand subterranean formation  235 . In some aspects, cased section  215   a  and cased section  215   b  can be designed to withstand the operations of downhole tool  225 . In some aspects, cased section  215   a  and cased section  215   b  can be designed to withstand corrosion from fluid flowing through borehole  210 . The design parameters of cased section  215   a  can vary from the design parameters of cased section  215   b . It is beneficial for cased section  215   a  and cased section  215   b  to be designed for a desired operational time interval or an operational lifetime of borehole  210  to minimize the cost of replacing a section of casing. 
       FIG. 3  is an illustration of a diagram of an example offshore system  300  with an electric submersible pump (ESP) assembly  320 . ESP assembly  320  is placed downhole in a borehole  310  below a body of water  340 , such as an ocean or sea. Borehole  310 , protected by casing, screens, or other structures, is surrounded by subterranean formation  345 . ESP assembly  320  can be used for onshore operations. ESP assembly  320  includes a well controller  307  (for example, to act as a speed and communications controller of ESP assembly  320 ), an ESP motor  314 , and an ESP pump  324 . 
     Well controller  307  is placed in a cabinet  306  inside a control room  304  on an offshore platform  305 , such as an oil rig, above water surface  344 . Well controller  307  is configured to adjust the operations of ESP motor  314  to improve well productivity. In the illustrated aspect, ESP motor  314  is a two-pole, three-phase squirrel cage induction motor that operates to turn ESP pump  324 . ESP motor  314  is located near the bottom of ESP assembly  320 , just above downhole sensors within borehole  310 . A power/communication cable  330  extends from well controller  307  to ESP motor  314 . A fluid pipe  332  fluidly couples equipment located on offshore platform  305  and ESP pump  324 . 
     In some aspects, ESP pump  324  can be a horizontal surface pump, a progressive cavity pump, a subsurface compressor system, or an electric submersible progressive cavity pump. A motor seal section and intake section may extend between ESP motor  314  and ESP pump  324 . A riser  315  separates ESP assembly  320  from water  340  until sub-surface  342  is encountered, and a casing  316  can separate borehole  310  from subterranean formation  345  at and below sub-surface  342 . Perforations in casing  316  can allow the fluid of interest from subterranean formation  345  to enter borehole  310 . In some aspects, the design of casing  316  should be sufficient to maintain integrity of borehole  310  for an operational time interval or for the lifetime of operations of borehole  310 . 
       FIG. 4  is an illustration of a diagram of an example hydraulic fracturing (HF) well system  400 , which can be a well site where HF operations are occurring through the implementation of a HF treatment stage plan. HF well system  400  demonstrates a nearly horizontal wellbore undergoing a fracturing operation. 
     HF well system  400  includes surface well equipment  405  located at a surface  404 , a well site controller  407 , a surface HF pump system  406 , and a computing system  408 . In some aspects, well site controller  407  is communicatively connected to separate computing system  408 , for example, a separate server, data center, cloud service, tablet, laptop, smartphone, or other types of computing systems capable of executing the processes and methods described herein. Computing system  408  can be located proximate to well site controller  407  or located a distance from well site controller  407 . 
     Extending below surface  404  from surface well equipment  405  is a borehole  410 . Borehole  410  can have zero or more cased sections, such as a cased section  450  and cased section  452 , and a bottom section that is uncased. Inserted into borehole  410  is a fluid pipe  420 . The bottom portion of fluid pipe  420  has the capability of releasing downhole material  430 , such as carrier fluid with diverter material, from fluid pipe  420  to subterranean formations  435  containing fractures  440 . The release of downhole material  430  can be by perforations in fluid pipe  420 , by valves placed along fluid pipe  420 , or by other release means. At the end of fluid pipe  420  is an end of pipe assembly  425 , which can be one or more downhole tools or an end cap assembly. Cased section  450  and cased section  452  can utilize differing tubular structure designs, such as a plastic material lined tubular structure. 
     As described in  FIGS. 1-3 , cased section  450  and cased section  452  can be designed to withstand subterranean formation  435 , resist corrosion from downhole material  430 , and operations internal of borehole  410  so as to reduce the incidence that the respective cased sections would need to be replaced during an operational time interval or the operational lifetime of borehole  410 . The design of cased section  450  and cased section  452  can be optimized to minimize cost while satisfying the operational goal. 
       FIGS. 1, 2, and 4  depict onshore operations. Those skilled in the art will understand that the disclosure is equally well suited for use in offshore operations, such as shown in  FIG. 3 .  FIGS. 1-4  depict specific borehole configurations, those skilled in the art will understand that the disclosure is equally well suited for use in boreholes having other orientations including vertical boreholes, horizontal boreholes, slanted boreholes, multilateral boreholes, and other borehole types. 
       FIG. 5  is an illustration of a diagram of an example cross-sectional view  500  of a plastic material lined tubular structure  505 . Tubular structure  505  can be of various types of tubular structures, such as casing, fluid pipes, downhole tool casings, or drill strings. Metal layer  510  forms the outer layer of tubular structure  505 . Metal layer  510  can be carbon-steel, steel, metal alloys, or other combinations of materials used for conventional tubular structures. A grout layer  515  is a layer between metal layer  510  and a plastic material layer  520 . Grout layer  515  can be one or more of various types of adhesives that are capable of adhering plastic material layer  520  to metal layer  510 . In this example, plastic material layer  520  is the innermost layer of tubular structure  505 , so as corrosive fluids flow through tubular structure  505 , plastic material layer  520  can protect the other portions of tubular structure  505 . The combined layers of tubular structure  505  can be more difficult to analyze for design purposes than conventional tubular structures because each respective layer can exhibit differing characteristics, for example, the thermal and mechanical properties can be different. 
     When performing an analysis of the tubular structure design of tubular structure  505 , the wall thickness of each layer can be used. In aspects where metal layer  510  is used, the wall thickness of metal layer  510  can be used in the analysis. As corrosion occurs, the respective wall thicknesses can decrease. In some aspects, various radii of tubular structure  505  can be utilized to determine the respective wall thicknesses. A radius r 1   530  is a radius from the center of tubular structure  505  to the ID of plastic material layer  520 . A radius r 2   535  is a radius from the center of tubular structure  505  to the outer diameter (OD) of plastic material layer  520 , which is the ID of grout layer  515 . A radius r 3   540  is a radius from the center of tubular structure  505  to the OD of grout layer  515 , which is the ID of metal layer  510 . A radius r 4   545  is a radius from the center of tubular structure  505  to the OD of metal layer  510 . 
       FIG. 6A  is an illustration of a diagram of an example graph  600  of a metal tubular structure. Graph  600  utilizes sample data executed through a stress analysis with the results plotted on graph  600 . Graph  600  utilizes, as the demonstration sample, C-75 carbon steel as the metal tubular structure, with an OD of 3.5 inches and an ID of 2.75 inches. Graph  600  includes an x-axis  605  indicating the equivalent axial load, in pounds per foot. A y-axis  606  indicates the differential pressure in pounds per square inch. 
     In plot area of graph  600 , a limit box  620  roughly approximates a combination of the various stress factors, such as an axial burst factor, a triaxial and torsion stress factors, a tension factor, a compression factor, and a collapse rating factor. A safety factor  630 , shown as an oval, approximates the design safety of the metal tubular structure. Line  640  is the initial state of the metal tubular structure. Line  640  is within the bounds of safety factor  630  which indicates a satisfactory design at the initial stage. Line  645  is the steady state production effects on the metal tubular structure. Line  645  is within the bounds of safety factor  630  which indicates a satisfactory design during the production stages of the borehole. 
       FIG. 6B  is an illustration of a diagram of an example graph  650  of a plastic material lined tubular structure. Graph  650  is similar to graph  600  though using a different tubular structure, a plastic material lined tubular structure. Graph  650  utilizes, as the demonstration sample, C-75 carbon steel with a plastic material layer attached to the ID of the C-75 carbon steel. The overall dimensions of the tubular structure is the same as used in graph  600 , with some of the C-75 carbon steel replaced with a grout layer and a plastic material layer. The sample data was processed using the processes and methods as disclosed herein. Graph  650  includes an x-axis  655  indicating the equivalent axial load, in pounds per foot. A y-axis  656  indicates the differential pressure in pounds per square inch. 
     In plot area of graph  650 , a limit box  670  roughly approximates a combination of the various stress factors, such as an axial burst factor, a triaxial and torsion stress factors, a tension factor, a compression factor, and a collapse rating factor. A safety factor  680 , shown as an oval, approximates the design safety of the plastic material lined tubular structure. Line  690  is the initial state of the plastic material lined tubular structure. Line  690  is partially outside of the bounds of safety factor  680 , as shown by line portion  691 , which indicates an unsatisfactory design at the initial stage. Line  695  is the steady state production effects on the plastic material lined tubular structure. Line  695  is partially outside of the bounds of safety factor  680 , as shown by line portion  696 , which indicates an unsatisfactory design during the production stages of the borehole. This indicates that the wall thickness of the metal portion of plastic material lined tubular structure should be increased to improve the various stress analysis factors, thereby increasing the size of safety factor  680 . 
       FIG. 7  is an illustration of a flow diagram of example method  700  of a stress analysis of a plastic material lined tubular structure. Method  700  can be performed on a computing system, such as a well site controller, a server, a laptop, a mobile device, a cloud computing system, or other computing system capable of receiving the input parameters and outputting results. Other computing systems can be a smartphone, a mobile phone, a PDA, a laptop computer, a desktop computer, a server, a data center, a cloud environment, or other computing system. The computing system can be located proximate a borehole or can be located in a data center, a cloud environment, a lab, a corporate office, or other distance locations. Method  700  can be encapsulated in software code or in hardware, for example, an application, a code library, a dynamic link library, a module, a function, a RAM, a ROM, and other software and hardware implementations. The software can be stored in a file, database, or other computing system storage mechanism. Method  700  can be partially implemented in software and partially in hardware. 
     Method  700  starts at a step  705  and proceeds to a step  710  where input parameters are received. In some aspects the input parameters include the wall thickness or radius parameters of the plastic material lined tubular structure, which can include parameters for each layer of the tubular structure, such as the wall thickness or radius parameters of the metal layer, of the grout layer, and of the plastic material layer. In some aspects the input parameters can include the anticipated downhole conditions, for example, mineralogy factors, temperature factors, pressure factors, measured depth, true vertical depth, fluid exposure factors, electromagnetic exposure factors, and other downhole conditions. In some aspects the input parameters can include a tolerance factors or tolerance thresholds and a selected strength model to be used for each stress analysis factor, for example, an axial strength model, a triaxial strength model, a tension strength model, a torsion strength model, a compression strength model, and a collapse strength model. 
     In some aspects, default parameters can be utilized in place of receiving one or more of the input parameters. In some aspects, a machine learning algorithm can be used in place of some of the input parameters, for example, the downhole condition factors can be determined using an output from the machine learning algorithm to improve the efficiency of the method results. 
     Proceeding from step  710 , method  700  can proceed to a step  720  or a step  740 . Step  720  and its subsequent steps through a step  730 , and step  740  its subsequent steps through step  755  can be performed serially, in parallel, partially overlapping, or various combinations thereof. In step  720  the tubular wall thickness can be calculated using the input parameters. For example, if the input parameters include an ID or OD radius for each layer of the tubular structure, the step can convert the input parameters to a wall thickness parameter. 
     Proceeding to a step  725 , the critical dimensions, including the wall thickness can be modified using the output of step  720  and the input parameters to generate an adjusted wall thickness. This modification can take into account the wall thickness of the grout layer and the plastic material layer. In aspects where the grout layer and the plastic material layer are not incorporated into the stress analysis, these portions of the wall thickness can be removed from the critical dimensions and other input parameters, such as reducing the wall thickness by a percentage or a measured value to represent the metal layer. 
     In step  730 , the modified input parameters, such as the critical dimensions and wall thickness parameters, can be applied to one or more strength models, such as a standard strength model, a hybrid strength model, or other models to generate a respective strength rating for the utilized strength models. 
     Proceeding from step  710 , in step  740 , the equivalent thermal properties can be determined of the plastic material lined tubular structure. The thermal properties can be the density, the thermal conductivity, and the thermal capacity. The equivalent density can be determined, for example, using Equation 1. 
     Equation 1: Example Equivalent Density Calculation 
     
       
         
           
             
               Equivalent 
               ⁢ 
               
                   
               
               ⁢ 
               density 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         
                           metal 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           weight 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           per 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           foot 
                         
                         + 
                       
                     
                   
                   
                     
                       
                         plastic 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         weight 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         per 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         foot 
                       
                     
                   
                 
                 ) 
               
               
                 volume 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 per 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 foot 
               
             
           
         
       
     
     The equivalent conductivity can be determined, for example, by using Equations 2-4. 
     Equation 2: Example Heat Transfer Using Heat Loss Principles 
     
       
         
           
             
               1 
               
                 Q 
                 total 
               
             
             = 
             
               
                 1 
                 
                   Q 
                   metal 
                 
               
               + 
               
                 1 
                 
                   Q 
                   grout 
                 
               
               + 
               
                 1 
                 
                   Q 
                   
                     plastic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     material 
                   
                 
               
             
           
         
       
     
     where Q total  is the total heat loss in watts, 
     Q metal  is the heat loss of the metal in watts, 
     Q grout  is the heat loss of the grout in watts, and 
     Q plastic material  is the heat loss of the plastic material in watts. 
     Equation 3: Example Conductivity Transfer Using Thermal Conductivity Principles 
     
       
         
           
             
               1 
               
                 Q 
                 total 
               
             
             = 
             
               
                 1 
                 
                   2 
                   ⁢ 
                   π 
                 
               
               [ 
               
                 
                   ( 
                   
                     
                       ln 
                       ⁡ 
                       
                         ( 
                         
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                         ) 
                       
                     
                     
                       K 
                       metal 
                     
                   
                   ) 
                 
                 + 
                 
                   ( 
                   
                     
                       ln 
                       ⁡ 
                       
                         ( 
                         
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ) 
                       
                     
                     
                       K 
                       grout 
                     
                   
                   ) 
                 
                 + 
                 
                   ( 
                   
                     
                       ln 
                       ⁡ 
                       
                         ( 
                         
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           
                             r 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ) 
                       
                     
                     
                       K 
                       
                         plastic 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         material 
                       
                     
                   
                   ) 
                 
               
               ] 
             
           
         
       
     
     where K metal  is the thermal conductivity of the metal in watts per meter-Celsius, 
     K grout  is the thermal conductivity of the grout watts per meter-Celsius, 
     K plastic material  is the thermal conductivity of the plastic material watts per meter-Celsius, 
     r 1  is the radius from the center of the tubular structure to the ID of the plastic material layer, 
     r 2  is the radius from the center of the tubular structure to the ID of the grout layer, 
     r 3  is the radius from the center of the tubular structure to the ID of the metal layer, and 
     r 4  is the radius from the center of the tubular structure to the OD of the metal layer. 
     Equation 4: Example Equivalent Thermal Conductivity Calculation 
     
       
         
           
             
               K 
               total 
             
             = 
             
               ( 
               
                 
                   Q 
                   total 
                 
                 * 
                 
                   
                     ln 
                     ⁡ 
                     
                       ( 
                       
                         
                           r 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           4 
                         
                         
                           r 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                       
                       ) 
                     
                   
                   
                     2 
                     ⁢ 
                     π 
                   
                 
               
               ) 
             
           
         
       
     
     where K total  is the equivalent thermal conductivity in watts per meter-Celsius. 
     The equivalent heat capacity can be determined, for example, by using Equation 5. 
     Equation 5: Example Equivalent Heat Capacity Calculation 
     
       
         
           
             
               Cp 
               total 
             
             = 
             
               ( 
               
                 
                   ( 
                   
                     
                       
                         M 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       MT 
                     
                     ⁢ 
                     
                       Cp 
                       metal 
                     
                   
                   ) 
                 
                 + 
                 
                   ( 
                   
                     
                       
                         M 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       MT 
                     
                     ⁢ 
                     
                       Cp 
                       grout 
                     
                   
                   ) 
                 
                 + 
                 
                   ( 
                   
                     
                       
                         M 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                       MT 
                     
                     ⁢ 
                     
                       Cp 
                       
                         plastic 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         material 
                       
                     
                   
                   ) 
                 
               
               ) 
             
           
         
       
     
     where Cp total  is the equivalent heat capacity, 
     Cp metal  is the heat capacity of the metal layer, 
     Cp grout  is the heat capacity of the grout layer, 
     Cp plastic material  is the heat capacity of the plastic material layer, 
     M 1  is the mass of the metal layer is grams per foot, 
     M 2  is the mass of the grout layer in grams per foot, 
     M 3  is the mass of the plastic material layer in grams per foot, and 
     MT is the total mass of the tubular structure in grams per foot. 
     Proceeding from step  740  to a step  745 , the equivalent thermal properties determined in step  740  can be used as input to simulate heat transfer of the plastic material lined tubular structure. In a step  750 , a thermal flow analysis can be performed using the output of step  745  and the input parameters. In a step  755 , a pressure parameter and a temperature parameter can be generated using the output of step  750  and the input parameters. 
     Proceeding from step  730  and step  755 , is step  760 . In step  760 , a stress analysis is executed using the outputs of step  730  and step  755  as well as the input parameters. The stress analysis can generate updated loads, updated safety factors, and updated design limit parameters, such as an axial rating, a burst rating, a collapse strength rating, a tension rating, a torsion rating, a compression rating, and a triaxial rating. In a step  770 , one or more of the input parameters, the modified input parameters, the updated loads, the updated safety factors, the updated design limit parameters, and other result parameters can be output, e.g., communicated, to another system for further analysis or processing, for example, a user, a borehole planning system, or another computing system. Method  700  ends at a step  795 . 
       FIG. 8  is an illustration of a block diagram of an example tubular structure design system  800 , which can be implemented using one or more computing systems, for example, a well site controller, a reservoir controller, a data center, a cloud environment, a server, a laptop, a smartphone, a mobile phone, a tablet, and other computing systems. The computing system can be located proximate the well site, or a distance from the well site, such as in a data center, cloud environment, corporate location, a lab environment, or another location. The computing system can be a distributed system having a portion located proximate the borehole and a portion located remotely from the well site. 
     Tubular structure design system  800 , or a portion thereof, can be implemented as an application, a code library, a dynamic link library, a function, a module, other software implementation, or combinations thereof. In some aspects, tubular structure design system  800  can be implemented in hardware, such as a ROM, a graphics processing unit, or other hardware implementation. In some aspects, tubular structure design system  800  can be implemented partially as a software application and partially as a hardware implementation. In some aspects, tubular structure design system  800  can be implemented using a tubular structure design controller  900  of  FIG. 9 . 
     Tubular structure design system  800  has a tubular structure modeler  810  that includes a parameter receiver  820 , a stress analyzer  830 , a thermal modeler  832 , a strength modeler  834 , and a result transceiver  840 . The results and outputs from tubular structure modeler  810  can be communicated to another system, such as one or more of a well site controller, a computing system, or a user. In some aspects, the communicated results can be used as inputs to a design operation for the borehole to identify appropriate casing to be utilized. In some aspects, the communicated results can be used as inputs into a borehole well planning system. A memory or data storage of tubular structure modeler  810  can be configured to store the processes and algorithms for directing the operations thereof. 
     Parameter receiver  820  can receive input parameters to direct further operations. The input parameters can be parameters, instructions, directions, data, and other information to enable or direct the remaining processing of tubular structure design system  800 . In some aspects, the input parameters include the wall thickness or radius parameters of the selected tubular structure, which can include parameters for each layer of the tubular structure, such as the wall thickness or radius parameters of the metal layer, of the grout layer, and of the plastic material layer. In some aspects, the input parameters can include the anticipated downhole conditions, for example, mineralogy factors, temperature factors, pressure factors, measured depth, true vertical depth, fluid exposure factors, electromagnetic exposure factors, and other downhole conditions. In some aspects, the input parameters can include a tolerance factors or tolerance thresholds, and a selected strength model to be used for each stress analysis factor, for example, an axial strength model for axial factors, a triaxial strength model for triaxial factors, a tension strength model for tension factors, a torsion strength model for torsion stress factors, a compression strength model for compression factors, and a collapse strength model for collapse factors. 
     In some aspects, default parameters can be specified by tubular structure modeler  810 , where those parameters can be utilized in place of receiving one or more of the input parameters. In some aspects, tubular structure modeler  810  can utilize a machine learning algorithm to generate one or more of the input parameters, for example, the downhole condition factors can be determined using an output from the machine learning algorithm to improve the efficiency of the method results. 
     Stress analyzer  830  can implement the processes and methods as described herein utilizing the input parameters. Stress analyzer  830  can use one or more algorithms to determine the result parameters, such as the load parameters, the safety factor parameters, and the design limit parameters. Stress analyzer  830  can direct operation of the thermal modeler  832  and the strength modeler  834 . Thermal modeler  832  can perform operations to determine equivalent thermal properties, simulate heat transfer, perform thermal flow analysis, and to generate pressure parameters and temperature parameters. Strength modeler  834  can perform operations to calculate tubular structure wall thicknesses, and modify the input parameters per the calculated wall thicknesses, and to apply the modified input parameters to one or more strength models. Stress analyzer  830  can perform operations to execute one or more stress analysis processes combining the outputs of the strength models and the thermal models. 
     Tubular structure design system  800  demonstrates a functional view of the disclosure, and the described functions can be implemented in one or more functional units, for example, parameter receiver  820  or result transceiver  840  can be incorporated into stress analyzer  830 . In some aspects, the thermal modeler  832  and the strength modeler  834  can be implemented in the same modeler. In some aspects, thermal modeler  832  or strength modeler  834  can be incorporated into stress analyzer  830 . 
     Result transceiver  840  can communicate one or more generated outputs and results, such as one or more load parameters, one or more a safety factors, or one or more design limit parameters, to one or more other systems, such as a well site controller, a computing system, a user, or other borehole related systems. Parameter receiver  820  and result transceiver  840  can be, or can include, conventional interfaces configured for transmitting and receiving data. 
       FIG. 9  is an illustration of a block diagram of an example of tubular structure design controller  900  according to the principles of the disclosure. Tubular structure design controller  900  can be stored on a single computer or on multiple computers. The various components of tubular structure design controller  900  can communicate via wireless or wired conventional connections. A portion of tubular structure design controller  900  can be located downhole at one or more locations and other portions of tubular structure design controller  900  can be located on a computing device or devices located at the surface or a distant location. In some aspects, tubular structure design controller  900  can be wholly located at a surface or distant location. In some aspects, tubular structure design controller  900  is part of a borehole planner system or a wellsite job planner system, and can be integrated in a single device. 
     Tubular structure design controller  900  can be configured to perform the various functions disclosed herein including receiving input parameters and generating results from an execution of a stress analysis using a hybrid modeler, such as a thermal modeler and a strength modeler. Tubular structure design controller  900  includes a communications interface  910 , a memory  920 , and a processor  930 . 
     Communications interface  910  is configured to transmit and receive data. For example, communications interface  910  can receive input parameters regarding the tubular structure and the anticipated conditions that will be experienced downhole a borehole. Communications interface  910  can transmit the results and other generated parameters, such as the calculated safety factors over time at various borehole depths. In some aspects, communications interface  910  can transmit a status, such as a success or failure indicator of tubular structure design controller  900  regarding receiving the input parameters, transmitting the results, or generating the results. In some aspects, communications interface  910  can receive input parameters from a machine learning system, such as borehole conditions that could be experienced downhole during the time interval of the analysis. Communications interface  910  can communicate via communication systems used in the industry. For example, wireless or wired protocols can be used. Communication interface  910  is capable of performing the operations as described for parameter receiver  820  and result transceiver  840 . 
     Memory  920  can be configured to store a series of operating instructions that direct the operation of processor  930  when initiated, including the code representing the algorithms for determining the safety factors for a plastic material lined tubular structure. Memory  920  is a non-transitory computer readable medium. Multiple types of memory can be used for data storage and memory  920  can be distributed. 
     Processor  930  can be configured to determine results and statuses utilizing the received input parameters, and, if provided, the machine learning system inputs. For example, processor  930  can perform a stress analysis on the plastic material lined tubular structure by applying the anticipated downhole conditions. Processor  930  can be configured to direct the operation of the tubular structure design controller  900 . Processor  930  includes the logic to communicate with communications interface  910  and memory  920 , and perform the functions described herein to determine the results and statuses. Processor  930  is capable of performing or directing the operations as described by stress analyzer  830 , thermal modeler  832 , and strength modeler  834 . 
     A portion of the above-described apparatus, systems or methods may be embodied in or performed by various analog or digital data processors, wherein the processors are programmed or store executable programs of sequences of software instructions to perform one or more of the steps of the methods. A processor may be, for example, a programmable logic device such as a programmable array logic (PAL), a generic array logic (GAL), a field programmable gate arrays (FPGA), or another type of computer processing device (CPD). The software instructions of such programs may represent algorithms and be encoded in machine-executable form on non-transitory digital data storage media, e.g., magnetic or optical disks, random-access memory (RAM), magnetic hard disks, flash memories, and/or read-only memory (ROM), to enable various types of digital data processors or computers to perform one, multiple or all of the steps of one or more of the above-described methods, or functions, systems or apparatuses described herein. 
     Portions of disclosed examples or embodiments may relate to computer storage products with a non-transitory computer-readable medium that have program code thereon for performing various computer-implemented operations that embody a part of an apparatus, device or carry out the steps of a method set forth herein. Non-transitory used herein refers to all computer-readable media except for transitory, propagating signals. Examples of non-transitory computer-readable media include, but are not limited to: magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROM disks; magneto-optical media such as floppy disks; and hardware devices that are specially configured to store and execute program code, such as ROM and RAM devices. Examples of program code include both machine code, such as produced by a compiler, and files containing higher level code that may be executed by the computer using an interpreter. 
     In interpreting the disclosure, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. 
     Those skilled in the art to which this application relates will appreciate that other and further additions, deletions, substitutions and modifications may be made to the described embodiments. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, because the scope of the present disclosure will be limited only by the claims. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present disclosure, a limited number of the exemplary methods and materials are described herein.