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Triaxial-Load-Capacity Diagrams Provide a New Approach to Casing Provide a New Approach to Casing and Tubing Design Analysis
Summary. A computer program has been developed that generates a two-dimensional (2D) graphic representation to display the effect of anticipated service conditions on specific casing and tubing. The triaxial-load-capacity diagram permits a visual determination of string design adequacy by both API and equivalent-triaxial-stress design factors. The program is useful in the design and analysis of any casing or tubing string.
Historically, there has been wide variation in minimum acceptable "design factors" of oil-country tubular goods. This situation has been complicated recently by the increasing acceptance of triaxial-stress analysis. Consequently, difficulties exist for engineers and managers in evaluating string designs of both in-house and outside-operated wells. The anticipated service loads along the length of the string can be plotted computer-generated triaxial-load-capacity diagrams. In addition, plotted computer-generated triaxial-load-capacity diagrams. In addition, the specified API-load-capacity design factors for pressure (burst and collapse) and tension can be graphically represented. A direct visual comparison can be made between the anticipated service loads and the API-load-capacity and triaxial-stress-intensity design factors. An absolute method for evaluating the performance of casing and tubing string designs does not exist. Currently, this evaluation is based on various minimum API-load-capacity and equivalent-triaxial-stress design factors. The triaxial-load-capacity diagram is a representation of the von Mises equivalent (VME) triaxial-stress intensity in relation to axial force and either internal or external pressure. Because triaxial stress is defined by these three independent variables, a normalization operation is required to create a 2D representation. The normalization procedure used here and discussed in the Appendix uses the planes where external pressure equals 0 psi [0 MPa] in three dimensions as the top half or burst region of the diagram. The plane where internal pressure is 0 psi [0 MPa] corresponds to the collapse region of the diagram. For burst loads, the normalized internal pressure generating the same triaxial stress with the same axial force as the combined load, but at 0-psi [0-MPa] external pressure, is calculated and plotted on the diagram. An analogous procedure pressure, is calculated and plotted on the diagram. An analogous procedure is used to obtain a normalized external pressure under collapse loading. The program is useful in the design and analysis of any casing or tubing string. Furthermore, because all the anticipated service loads for the life of the string can be plotted, both a service-life envelope and a load path can be determined from the diagram. The load path is useful in developing test loads for connection performance tests and load application sequences for elastic/plastic finite-element modeling of connections. Examples of the use of load-capacity diagrams in the design of drilling and production casing are presented.
A number of parameters useful in understanding a triaxial-load-capacity diagram are defined as follows. The API operating window is the area enclosed by the API pressure and tension capacity of the pipe adjusted by suitable design factors. The biaxial effect of tension on collapse resistance is included. The VME stress curve defines the stress level in the pipe in terms of internal or external pressure and axial force. The VME design factor is simply the yield strength of the material divided by the triaxial stress. A load path shows the variation in service loads of a casing or tubing string over time. The service life envelope outlines the extreme limits of the anticipated service conditions for the string under consideration. The API specifies manufacturing tolerances fore the OD and wall thickness of tubulars - 1 API minimum pipe is defined as having the dimensions that produce the maximum triaxial stress at the ID surface of the pipe body and corresponds to the maximum de/h ratio. Fig. 1 is a load-capacity diagram for P-110, long threads and coupling (LT and C) casing of 7 in. [17.8 cm) and 38 Ibm/ft [56.6 kg/m]. Two VME curves are plotted for API minimum pipe. The solid VME curve corresponds to a triaxial stress of I 10,000 psi 1758 MPa). A VME design factor of 1.25 is represented by the dashed curve. The load capacity of the casing as determined by API formulas is also shown in the diagram API-load-capacity design factors of 1.0 in burst, collapse, and tension are displayed. Note that the connection is leak-resistance limited.
Conventional casing design is based on single-string analysis which ignores annulus fluid heat-up loads and composite cemented string effects. This paper presents the design of a 7' production casing and 10-3/4" x 9-5/8" protective casing under high burst/collapse conditions. Uniaxial and triaxial safety factors are computed and compared for single-string versus multi-string analysis with and without temperature loads. In the multi-string analysis, casing stresses are calculated for the radially composite structure assuming the elastic properties of casing, cement, and formation. Results demonstrate a significant increase in burst safety factor for cemented casing and show that burst/collapse tendency for HPHT wells is strongly dependent on multi-string top-of-cement locations. For this HPHT application, reliable triaxial design is achieved with multi-string analysis using standard weights and grades of casing, which otherwise is not possible with single-string uniaxial analysis.
In HPHT wells with subsea completions, temperatures can be critical to casing design, not only for heat-up due to production, but also for stimulation cooling and for beat-up during deeper drilling [1, 2, 3]. Additionally, these temperatures can magnify conventional loads associated with tubing leak, gas kick, and evacuation.
To determine casing temperatures and stresses, the WELLCAT tubular design system was used in this study. It consists of the five computer programs: WT-DRILL, WT-CIRC, WT-PROD, WS-CASING, and WS-TUBE. The first three codes predict temperature and pressure loads for planned operations [41, and the two stress codes provide uniaxial and triaxial analysis for casing and tubing. The codes are integrated so that predicted temperatures are automatically linked into the stress codes.
A schematic of the HPHT well is presented in Figure 1. The 7" production string consists of section 1 from 0-9000 ft (49.5#, C-90) and section 2 from 9000-18250 ft (38#, Q-125). For the protective string, the 10-3/4" section (109#, T-95) is from 09000 ft and the 9-5/8" section (53.5", Q-125) is from 900016300 ft. Cementing practice by the operator is to fully cement these strings, but we have assumed cement short-falls to investigate possibility of collapse from annulus heatup loads. Cement top outside the 7" is 3000 ft and outside the 10-3/4" x 9-5/8" is 2500 ft. The well is a subsea completion in 413 ft of water.
The analysis proceeded in four steps. First, conventional single- string analysis with standard loads (no temperatures) was performed with WS-CASING. Then, the same set of load conditions was run with multi-string analysis.
A closed form Triaxial Design procedure has been developed based upon the von Mises' criteria using the Lame' equations. This contrasts with the conventional biaxial procedure using Barlow's equation. The results of using the new procedure are compared which demonstrate the importance of incorporating the radial stress.
It is concluded the Triaxial Design procedure should be used when surface procedure should be used when surface pressures exceed +/-12,000 psi. This is based pressures exceed +/-12,000 psi. This is based on comparing a series of designs for surface pressures ranging from 3,300 to 21,000 psi. By first designing these strings using the Biaxial/Barlow approximation and then checking them with the Triaxial/Lame' procedure, it is noted that the Biaxial/Barlow design is in considerable error above +/-12,000 psi and may be unsafe above +/-15,000 psi.
It is also concluded that equivalent safety requires different values of Design Factor for Biaxial VS. Triaxial procedures. procedures. I. HISTORICAL BURST DESIGN
Historically Casing burst design has been based on a uniaxial assessment of the hoop stress due to the design pressure or a biaxial assessment of pressure or a biaxial assessment of the interaction of the hoop and axial stresses in accordance with some failure criteria. The usual failure criteria used is the von Mises, better known as the Ellipse of Plasticity.
Since the von Mises failure criteria predicts an enhancement of allowed predicts an enhancement of allowed hoop stress with increasing positive axial stress as shown in Figure 1 in quadrant I, the uniaxial assessment is conservative to the biaxial. It is known that both are approximations. However, calculations indicated the error to be small if the design pressure is below about 12,000 psi (82,740 Kpa).
However, above that pressure, it is anticipated the magnitude of the error might become so large that it would be undesirable to continue to use the biaxial procedures.
In essence the biaxial burst design procedure involves assessing the procedure involves assessing the axial load at a given point in the casing string and based upon the resulting axial stress calculating the corresponding allowed hoop stress based upon von Mises biaxial criteria. Then the resulting burst design pressure is calculated from Barlow's formula using the allowed hoop stress.
The Petroleum Industry is now encountering wells with shut in surface pressure approaching 20,000 psi (137,900 Kpa). This is significantly above the upper level of safe values of burst pressure for using the biaxial criteria. Therefore, procedures have been developed and are procedures have been developed and are presented in Appendix A to perform a presented in Appendix A to perform a true triaxial design by incorporating the radial stress.