Journal of Petroleum Science and Engineering 133 (2015) 328–334 Contents lists available at ScienceDirect Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol Worn pipes collapse strength: Experimental and numerical study N.M. Moreira Junior a,b, A.A. Carrasquila b, A. Figueiredo c, C.E. da Fonseca a,n a b c Petrobras, Brazil North Fluminense State University, Brazil Vallourec do Brasil, Brazil art ic l e i nf o a b s t r a c t Article history: Received 13 March 2015 Received in revised form 17 June 2015 Accepted 22 June 2015 Available online 23 June 2015 After drilling an oil or gas well the open well-bore is usually cased with steel pipes, which must be properly designed to support all predicted loads (pressures) along its service life. Such casing can be subject to material loss after deployed. One of the reasons for material loss comes from that the well-bore is drilled deeper with rotating drill pipes after casing installation. The interaction between the rotating drill-pipes and casing inner wall leads to the casing wear, which can significantly reduce the wall thickness at particular regions. Casing designers usually assume evenly distributed inner casing wear. Under this assumption the remaining wall is constant and the predictive burst and collapse strength equations presented by standards are applied, but resulting in much lower strength values than the real case. Few authors studied the pipe remaining strength under more realistic wear assumptions. Kuryama et al. presented an analytical formulation based on pipes with circular cross-section and an equivalent wall thickness eccentricity to simulate material loss over an angular section. Sakakibara et al. presented a model for collapse strength prediction of worn pipes with initial geometric imperfection (cross-section ovalization) and constant pipe wall loss within a given angular section. None of them combined real initial (ovalization and eccentricity) and produced (casing wear) geometric imperfections. This paper presents the full scale experimental set up and results for thin and thick walled intact and worn pipes under applied external hydrostatic pressure. The test procedure included pipes’ geometry mapping and wear production to match real conditions. The specimens were collapsed and numerical analysis based on finite element analysis and an analytical model were carried out to simulate physical conditions. The numerical results were then extended to a broad range of pipes with different geometries and steel grades representative of drilling well applications. As expected, one developed model developed predicts really well thin walled pipes, but not for thicker ones. & 2015 Elsevier B.V. All rights reserved. Keywords: Worn pipes Collapse Experimental Numerical 1. Introduction After drilling an oil or gas well the open well-bore is usually cased with steel pipes, which can have from hundreds to thousands meters of length. The pipes are installed together through threaded connections and are subject to a harsh downhole environment. A proper casing design has to address possible chemical reactions or mechanical interactions leading to pipe wall material loss (as corrosion and erosion), and the remaining pipe wall thickness must support all predicted loads (pressures) along the well life. If the material is properly designed, corrosion rate can be neglected. Usually the well-bore is drilled deeper with rotating drill pipes inside steel casing after it is installed. The interaction between the n Corresponding author. E-mail address: [email protected] (C.E. da Fonseca). http://dx.doi.org/10.1016/j.petrol.2015.06.024 0920-4105/& 2015 Elsevier B.V. All rights reserved. rotating drill-pipes and casing inner wall can lead to the so-called casing wear, which can significantly reduce the wall thickness at particular regions. Assessing properly the strength of the worn pipe can be the key to achieve a feasible technical and economical well design. Casing designers usually assume evenly distributed inner casing wear. Under this assumption the remaining wall thickness is constant and equal to minimum remaining wall. Predictive burst and collapse strength equations presented by API 5C3 (API BULL, 1994) or ISO TR 10400 (ISO TR, 2007) are applied. Assuming the remaining wall thickness as the lowermost possible results in the lowermost strength values. Few authors studied the pipe remaining strength under more realistic wear assumptions. Some authors developed analytical models to account the wear at inner wall to evaluate the burst strength (Wu and Zhang, 2005; Shen and Beck, 2012), or to evaluate the stress concentration of plain dents due to mechanical damages in steel pipes subjected to internal pressure (Pinheiro, 2006). Regarding to the remaining collapse strength for worn N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334 329 Fig. 1. Sketches of wear mechanism and casing cross-sectional worn geometry: (a) rotating drill-string connection (tool joint) causing a wear groove located only at one side of inner wall; (b) pipe circular cross-section with outer radius ro and inner radius ri . The circle representing the inner wall presents an offset t w , which is chosen to match an equivalent geometry of the worn area (modified from Kuriyama et al., 1992). Dashed line represents the real casing wear and (c) constant wear geometry of thickness tmin for a given circular sector (modified from Sakakibara et al., 2008). pipes, Kuriyama et al. (1992) presented an analytical formulation based on pipes with perfectly circular cross-section and an equivalent wall thickness eccentricity to simulate material loss over an angular section (Fig. 1(b)). Sakakibara et al. (2008) presented a model for collapse strength prediction of worn pipes with initial geometric imperfection (cross-section ovalization) and constant pipe wall loss within a given angular (1-(c)). Though the latter presents good match with experimental results, the produced wear does not match the geometry usually produced by rotary pipes inside casings. To accurately predict collapse strength of worn pipes, the initial (cross section ovalization and wall thickness eccentricity) and resulting (casing wear) geometrical imperfections must be included in any analysis. This paper presents the full scale experimental set up and results for thin and thick walled, intact and worn pipes, under applied external hydrostatic pressure. The test procedure included pipe geometry mapping, before and after producing wear, to account both initial and produced (wear) geometrical imperfections. Casing wear was produced to match real conditions. The specimens were collapsed and numerical analysis based on finite element analysis and model developed by Sakakibara et al. (2008) were carried out to simulate physical conditions. The numerical results were then extended to a broad range of pipes with different geometries and steel grades representative of drilling well applications. Table 2 Typical material properties for both pipes (which are different steel grades). The values inside parentheses are in psi. Specimen series E - MPa (psi) 7 3 10 (207,532) 3 107 (207,532) 80 90 so - MPa (psi) ν 1070 (155,215) 1002 (145,455) 0.29 0.29 effect of material loss and collapse mechanism (elastic versus “plastic” collapse). With full-scale geometry it was possible to build a representative damage at the inner pipe wall. The samples prepared from pipe type 1 were called series 80, and from pipe type 2 series 90 respectively. Samples were prepared long enough to avoid end effects during collapse tests.1 Samples geometry (do, t ) were gathered before and after machining (to produce worn pipes). The geometrical data were gathered from measurements over 12 equally spaced cross sections spanned by 200 mm, called sections A till L, depicted at Fig. 2. Typical values are presented in Tables 3 and 4 before machining, and Table 5 for intact (non-machined) samples. These data are representative of the collapsed cross sections during tests. The initial ovalization was evaluated by Eq. (1) below, where ⎛ ⎞ ⎛ ⎞ D = max ⎜do ⎟ and d = min ⎜do ⎟ represent the maximum and minido ∈ : ⎝ ⎠ do ∈ : ⎝ ⎠ mum measured outside diameter at a given cross-section : {:≔A , B… , L}: D−d × 100% D+d 2. Material and methods ▵= 2.1. Full scale samples preparation It is important to remember that geometry mapping was done before and after machined (see Fig. 3). Herein the pipes’ types 1 and 2 were sampled and labeled according machined (label 83 and 93 respectively) or non-machined (84 and 94 respectively). The machined samples from pipe type 1 (namely 83-1, 83-2, and 83-3) were prepared in order to present maximum wall thickness reduction of 20%. The machined samples from pipe type 2 (namely The full scale physical tests were addressed to collapse specimens prepared from two-representative pipe configurations: (i) representing thick pipes (with do/t = 13.5, herein called type 1), and (ii) representing thin pipes (with do/t = 20.3, type 2). Both configurations are usual for oil and gas industry (Table 1). Intact and worn samples were prepared making possible to compare the Table 1 Nominal geometry of chosen pipes to evaluate hydrostatic collapse loads (measures in parentheses are in inches). Pipe type/specimen series do -mm (in.) t-mm (in.) do/t 1-80 273 (103/4 ) 245 (95/8) 20.24 (0.797) 13.5 11.99 (0.472) 20.3 2-90 (1) 1 The samples dimensions criteria to collapse tests were followed as recommended by ISO 10400 (ISO TR, 2007). According to these recommendations, the samples prepared for tests shall have a minimum length in relation to the outer diameter of the sample. For pipes with outer diameter lower or equal than 95/8 in., the sample shall have a length of at least 8 times its diameter. For pipes with outside diameter of 103/4 in. or larger, the ratio is at least 7 times the outer diameter. These limits are established for the purpose of eliminating the influence of the ends in the collapse strength. Small samples present higher stiffness and therefore are not representative of collapse strength values. From Fig. 2 it is possible to see that the length is at least 10 times the outside diameter. 330 N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334 Table 4 Typical geometric values for samples series 90 (prior machining), in mm, with ⎛⎞ ⎛⎞ max ⎜⎟ and min ⎜⎟ representing the maximum and minimum outside diameter and ()∈ : ⎝⎠ ()∈ : ⎝⎠ wall thickness at section : . The sections presented are the ones where the collapse occurred. Fig. 2. Pipe geometry mapping sketch. In the left cross-sections labeled from A to L spanned by 200 mm where diameter and wall-thickness measurements were gathered. In the right the cross-section locations from where outside diameter and wall thickness were measured, with shaded area representing the worn region. Table 3 Typical geometric values for samples series 80 (prior machining), in mm, with ⎛⎞ ⎛⎞ max ⎜⎟ and min ⎜⎟ representing the maximum and minimum outside diameter and ()∈ : ⎝⎠ ()∈ : ⎝⎠ wall thickness at section : . The sections presented are the ones where the collapse occurred. Sample 83-1 F G H ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 275.0 275.44 275.14 ⎛ ⎞ min ⎜do ⎟ do∈ : ⎝ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 274.49 274.44 274.412 0.093 21.99 0.182 21.40 0.186 21.39 ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ 20.29 20.26 20.57 Sample 83-2 G H I ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 275.4 274.9 275.4 ⎛ ⎞ min ⎜do ⎟ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 274.2 274.1 274.6 0.218 20.99 0.146 20.96 0.145 21.14 20.56 20.69 20.31 Sample 93-1 H I J ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 246.93 246.52 246.77 ⎛ ⎞ min ⎜do ⎟ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 246.07 246.11 246.04 0.17 13.26 0.08 13.40 0.15 13.38 ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ 11.84 11.79 11.89 Sample 93-2 F G H ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 246.14 246.53 246.46 ⎛ ⎞ min ⎜do ⎟ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 245.94 245.81 245.93 0.049 12.77 0.146 12.93 0.108 13.05 12.14 12.30 12.30 do∈ : ⎝ do∈ : ⎝ ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ 93-1, 93-2, and 93-3) were prepared to present maximum wall thickness reduction of 30% . The worn geometry was mapped to guarantee the maximum wall thickness in accordance with the plan. inside a cap attached to the chamber body by bolts, as shown in Fig. 5. It is possible to see that the pipe ends located inside the caps were free to rotate under applied external pressure, but not for applied internal pressure. Rubber and metal seal rings are inserted over the pipe end which is outside the chamber. A ring is screwed behind the rings completing the sealing mechanism. Inner pipe side is subject to atmospheric pressure at all times. The collapse test consisted of slowly pressure increase to avoid pressure waves inside the chamber. The tests’ sequence was to test first two intact and then two machined samples. If the results presented great difference, a third sample could be prepared and tested. The pipe collapse is defined as the sudden change of its cross sectional shape. After the pipe collapse, the shape change results in volume increase between the pipe specimen and the pressure chamber, which leads to a sharp system pressure drop. The collapse pressure is then defined as the maximum pressure during the test, which occurs exactly before the pressure drop. 2.2. Steel grade properties 2.4. Numerical model The nominal yield strength so (according to Iso, 2011) of pipes type 1 and 2 are 965 MPa (140 ksi) and 861 MPa (125 ksi) respectively. But tensile tests for both pipes were conducted based on ASTM (2007) procedures, and values for Young Modulus E, yield strength so and Poisson ratio ν, and plastic deformation were obtained once numerical analysis using finite element method were done using isotropic hardening. Typical values for elastic properties are presented in Table 2 and characteristic stress–strain curve is presented in Fig. 4. Yield stress was obtained following specifications of Iso (2011). Numerical models were built using the commercial software Abaqus v.6.1014 based on the finite element analysis. The geometry was sketched based on the geometric mapping of the samples, considering actual external diameter, wall thickness, and constant initial ovalization overall length. Initial ovalization was taken as geometric average of ovalization values presented in Tables 3–5. For each tested sample one model was built representing its geometric and material properties. The worn geometry assumption was based on one inner mandrel with 5.5 in. intersecting the original pipe along the full sample length. This consideration leads to a reduced wall thickness section in the cross sectional plane equal to approximately 36°. So the geometry were sketched applying material loss within 36° in the cross sectional using a cosine law. Considering the two symmetry planes of this problem (x – y and x – z as depicted in Fig. 6), it was possible to reduce the model size by one quarter of original sample dimensions. The worn area was thus constructed do∈ : ⎝ ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ 2.3. Pressure test procedure The samples were collapsed under hydrostatic pressure in pressure chambers as depicted in Fig. 5. The pipe specimen free span subject to hydrostatic external pressure was a little bit smaller than the total specimen length. Pipe ends were located N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334 331 Table 5 ⎛⎞ ⎛⎞ Data from intact pipes in mm, with max ⎜⎟ and min ⎜⎟ representing the maximum ()∈ : ⎝⎠ ()∈ : ⎝⎠ and minimum outside diameter and wall thickness at section : : (a) pipe type 1; (b) and (c) pipe type 2. The sections presented are the ones where the collapse occurred. (a) Sample 84-1 G H I ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 275.26 275.21 275.17 ⎛ ⎞ min ⎜do ⎟ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 274.46 273.45 274.45 0.146 21.55 0.321 21.80 0.129 21.62 20.22 20.07 20.44 E F G ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 246.17 246.29 246.27 ⎛ ⎞ min ⎜do ⎟ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 246.10 246.15 245.93 0.028 13.33 0.077 13.15 0.069 13.28 11.73 11.85 11.88 E F G ⎛ ⎞ max ⎜do ⎟ do∈ : ⎝ ⎠ 246.33 246.29 246.76 ⎛ ⎞ min ⎜do ⎟ ⎠ ▵ (%) ⎛ ⎞ max ⎜t ⎟ t∈ : ⎝ ⎠ 246.12 246.06 245.17 0.042 13.03 0.046 13.18 0.119 12.87 11.97 12.02 12.43 do∈ : ⎝ ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ (b) Sample 94-1 do∈ : ⎝ ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ (c) Sample 94-2 do∈ : ⎝ ⎛ ⎞ min ⎜t ⎟ t∈ : ⎝ ⎠ Fig. 3. Worn sample after machining. as 18° only, being located at the x – z plane. Also the x – z plane ⎛ ⎞ contains the maximum measured outside diameter (D = max ⎜do ⎟), do ∈ : ⎝ ⎠ ⎛ ⎞ while the x – y plane contains the minimum one (d = min ⎜do ⎟) of do ∈ : ⎝ ⎠ each sample, as presented in Tables 3–5. The pipe ends boundary conditions were set to be rotation free. The samples ends outside the pressure chamber were not simulated. A three dimensional quadrilateral element was used to build Fig. 4. Stress–strain characteristic curve. The yield stress so is very close to ultimate stress su, being possible to use an elastic-perfect plastic material to represent it. the mesh. This quadrilateral element has eight nodes, with linear interpolation function and reduced integration (C3D8R). Mesh with two, three, four, and five elements at the wall thickness were built. In the longitudinal direction, 160 were always used (remember that only half length was simulated). In circumferential direction, 40 and 50 elements were tested. After some simulations, the minimum requested number of elements along wall thickness 332 N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334 Fig. 5. On top: sketch of pressure chamber with pipe specimen. On bottom: pictures from seal mechanism. Pipe specimen free span subject to hydrostatic pressure is a little bit smaller than the total specimen length. Pipe ends are located inside a cap attached to the chamber body by bolts. The ends located inside the cap are free to rotate under applied external pressure, but not for applied internal pressure. Seal rings are located between the chamber body and the cap. Fig. 6. Worn pipe model. On the top left the two symmetry planes defining the model and in the right the central cross-section meshing with worn area. In the bottom left and right, inelastic stress for model A-II and model H-V respectively. Applied pressure is lower than collapse pressure in both cases. (radial axis), circumference (hoop axis), and z-axis were 3, 40 and 160 respectively. Numerical results with only two elements in wall thickness were considerable higher then others. These results also presented good correlation to test results (and are presented in the next section). The collapse pressure was achieved under static analysis arc-length methodology (Riks, 1979) to assess the bifurcation point under static load. Besides the overall collapsed pipe geometry was closely recovered, the post-buckling behavior was not the focus of this study. After choosing external diameter, wall thickness, initial ovalization, and logarithmic stress–strain inelastic curve for both materials, one simple computational code in Python1.6 was written to build the model for all simulations. One example of the final model in the x – y plane view is presented in Fig. 6, including principal axis and worn area. 3. Results and discussions 3.1. Full scale tests and numerical simulation All the samples were subjected to hydrostatic external pressure and the collapse pressures are presented in Table 6. During tests one sample did not collapse and the test was canceled because the applied pressure was close to chamber limits. Also in Table 6 results from numerical simulation and comparison with real collapse pressures are presented. As can be noticed that the numerical simulation is capable of evaluating really well the collapse pressure once the geometry and material properties are fully mapped. But during fabrication both pipe geometry and material properties present variation. For oil and gas upstream activities the tolerances described by API (2005) are widely accepted. To develop models for pipes in which the geometry and material behavior were not N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334 Table 6 Collapse pressure test and numerical results. Values in parenthesis are in psi. Sample Test - MPa (psi) Model - MPa (psi) error (%) 84-1 83-1 83-2 94-1 94-2 93-1 93-2 151.1 (21,929) 121.8 (17,666) 123.9 (17,970) 64.7 (9384) 64.1 (9296) 42.0 (6092) 39.9 (5800) 151.5 (21,982) 115.8 (16,795) 123.7 (17,949) 63.5 (9207) 64.7 (9390) 43.5 (6313) 40.9 (5930) 0.24 4.93 0.11 1.88 1.01 3.62 2.24 gathered, some assumptions based on API (2005) were adopted. The experimental tests were used to choose a geometry approach and minimal mesh to accurately represent the problem, and these approaches were used as basis to build geometry and mesh for a broad number of pipes. The geometry and material properties for all samples presented values above minimal limit values established by API (2005). It is worth to notice the well behavior for the yield stress in all tested samples. Other properties as Poisson's ratio and elastic modulus are very consistent with general steel knowledge. The adopted values from now on are 0.29 and 207.5 GPa. 3.2. Parametric study The models to perform the parametric study were built for a wide range for do/t ratio, based on real pipes usually applied in the industry with well established geometric and materials properties. Table 7 presents main geometrical and material properties chosen to build these models. Ovalization was established as 0.18%, as per data used in series 90 tests. The models were named with capital letter (A to H). For each geometric and material combination five models were built varying the final wall thickness, simulating different worn pipe conditions. The models representing the new pipe were labeled as A-I, B-I, etc. The most critical models were built with 40% of maximum wall thickness loss, and were named as A-V, B-V, etc. The other three models per chosen pipe presented 10%, 20%, and 30% of maximum wall thickness loss, totalizing 45 numerical results for collapse pressure of new and worn pipe for three different steel grades and do/t ratio. Table 8 summarizes the collapse pressures results for each combination (models A to I) based on the maximum wall thickness loss (0% up to 40%) and yield strength. The easiest analysis is to compare the residual collapse strength for each model based on the original collapse strength for a new pipe (without any worn or defect). Such analysis can be seen in Fig. 7, where the results from Table 8 were plotted together and in the Y-axis a normalization result was applied, presenting the remaining collapse pressure normalized by the original collapse pressure of the intact respectively pipe. For higher steel grades (higher yield stress represented by models from A to G) just one model presented a different behavior for de-rated collapse Table 7 Model main properties for parametric study. Model so (MPa) do/t Δo A B C D E F G H I 1002 1070 1002 1070 1002 1002 1070 517 517 11.19 13.49 13.49 16.00 16.00 17.66 20.39 11.19 20.39 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 333 Table 8 Numerical collapse pressure for different models (values in MPa). Model I - 0% wear II - 10% wear III - 20% wear IV - 30% wear V - 40% wear A B C D E F G H I 145.1 114.4 109.2 75.8 81.3 57.2 40.6 97.8 33.9 124.1 92.7 88.7 65.9 63.6 48.6 35.3 88.3 29.6 108.1 79.8 76.8 54.2 51.8 42.3 29.1 79.0 25.6 190.9 151.5 141.2 98.8 97.2 75.3 52.2 133.2 48.5 168.5 130.6 122.3 88.1 91.8 68.9 46.1 107.9 39.9 strength (model A) and all others suggest a linear relationship between de-rated collapse pressure and remaining wall thickness of the pipes. For the lowest steel grades (models H and I) the answers seem to be slightly different from the linear pattern presented by high steel grades models. It can be justified by the larger inelastic deformation observed prior to the external applied pressure reach the collapse pressure, once the material has lower yield stress. This is true especially for model I, which also presents larger do/t ratio. Also in Fig. 7 is possible to see an exponential defining a lower boundary (dashed line). Fig. 6 shows inelastic deformation for models A and H (bottom left and right), with 10% and 40% wall thickness reduction respectively. Models with larger wall thickness loss and lower yield stress presented larger inelastic deformation, always concentrated in the worn area. The inelastic deformation can be cause of reduced remaining collapse strength. Analyzing these results in logarithmic scale for remaining collapse pressure we can say that roughly speaking results are converging for a single curve and it is possible to assess one curve that can satisfy all models with safety. Thus it is possible to establish one simple model to evaluate collapse pressure for worn pipes under external pressure, where the remaining collapse pressure Pcw depicted in Fig. 7 can be expressed in terms of the intact and remaining wall thickness of the pipe, to and tr, and the original collapse pressure strength Pco as follows: ⎡ ⎛ tr − to ⎞ ⎤ Pcw = 0.9782 exp ⎢1.58 ⎜ ⎟⎥ o Pc ⎝ to ⎠ ⎦ ⎣ (2) Comparing the results from this study developed by Kuriyama et al. (1992) one can see that it does not fit very well for thick walled pipes (see Fig. 8), underestimating collapse pressure reduction compared to numerical analysis. For thin walled pipes it fits well as expected. 4. Conclusions and remarks The collapse strength de-ration as a function of increasing wall thickness wear was studied and some analytical and numerical models were analyzed. Among the few models developed to study such problem, the two most suitable in our opinion are Kuriyama et al. (1992) and Sakakibara et al. (2008). Both presented mechanical models to predict the remaining collapse pressure for worn pipes. In the first case, pipes with circular were considered, what can result in a much higher collapse pressure. The latter represents really well collapse pressure for thin walled pipes with worn area. But for thick walled pipes, where material non-linearity appears due to plastic deformation, none of the models can represent well the remaining collapse pressure. Full-scale tests were successfully performed and made possible to evaluate the effects of worn casing. Numerical models based on 334 N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334 Fig. 7. Comparative results among models (A to I). loss). For larger do/t ratios and lower wall thickness loss these results are very accurate. Analyzing all models as the remaining collapse pressure based on original collapse rate showed one consistent reduction in the collapse pressure for a typical value of initial ovalization (0.18%). These behaviors were well approximated by an exponential regression accounting with original (or nominal) wall thickness, remaining wall thickness, and original collapse pressure rate. The behavior seems to be compatible for all models despite the do/t ratio and elasto-plastic properties (but we also have to recognize the material elasto-plastic consistent behavior). The final equation does not account for initial pipe ovalization and future studies must be carried out to couple the geometric ovalization with worn wall of pipes developed at different angular sections. Fig. 8. Comparison between numerical results from this study and from Kuriyama et al. (1992) (lines are results from present study). finite element method were built considering an approximated worn shape constant through full sample length. Initial ovalization was applied in the middle of the model with the maximum observed value measured from each sample. The circumferential affected area was kept constant as 10% of inner pipe area, corresponding to cross-sectional angle of 36°, based on drilling operations assumptions. With few elements with linear interpolation were possible to have good prediction of collapse pressure. Also it was possible to notice plastic deformation across the inner face of the pipe in the worn area even before the pipe collapse, as shown in Fig. 6. Using an external script developed in python, the models building and simulation times were very attractive, making possible to simulate as many cases as planned, in order to perform the parametric study. The results from numerical model were compared to full scale hydrostatic pressure collapse tests for new and worn tubular with different do/t ratios and material properties. The results were pretty accurate and then the pattern adopted to build these models was applied to analyze several models with different do/t ratios, elastic-plastic materials, and remaining wall thickness after an abrasive effect. A parametric studied was carried out and compared to Kuriyama et al. (1992), showing the latter overestimates the remaining collapse pressure for pipes with do/t < 16, especially for lower remaining wall thickness (larger material References API BULL, 1994. 5C3 - Bulletin on Formulas and Calculations for Casing, Tubing, Drill Pipe, and Line Pipe Properties, 6th edition. API, 2005. Specification 5—Specification for Casing and Tubing. ASTM, 2007. A-370—Standard Test Methods and Definitions for Mechanical Testing of Steel Products. 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