Collapse Analysis of Perforated Pipes Under External Pressure

This work is a study of collapse pressure of perforated pipes to evaluate the effect of lateral perforations on the radial resistance of pipes under external pressure.

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This work is a study of collapse pressure of perforated pipes to evaluate the effect of lateral perforations on the radial resistance of pipes under external pressure. These types of pipes represent a simple and economical technology widely used as sand-control meshes or perforated liners.


One of the most common challenges to high flow rates in mature fields is the migration of sand to the well. High rates of oil production together with maximum sand retention is the optimal result. In accomplishing this complex goal, perforated pipes play a vital role because they are a simple and inexpensive application, and they are widely used in the industry. Failures of such pipes are directly related to the collapse resistance of a pipe weakened by the perforations. Such failures can occur because of the plugging of holes or changes in differential pressure. This study might contribute to future prediction of collapse pressures of perforated pipes without resorting to costly full-scale experiments.

Methodology Development

Geometric Properties. This study involves four intact and eight perforated specimens as study bodies. All of them were obtained from four pipes designated as T3, T4, T5, and T6. A special nomenclature was defined to identify each one with a sequence of letters and numbers. An explanation of this nomenclature is shown in Fig. 1.

Fig. 1—Nomenclature of specimens.


The geometrical properties were obtained by means of a physical mapping, taking 10 measurements in the longitudinal direction and five in the circumferential direction to calculate the average thickness, average diameter, and initial imperfections (ovalization and eccentricity) of each specimen.

Material Properties. The mechanical properties were also determined for each specimen by means of traction tests on 18 proof bodies, including some in the longitudinal direction and others in the circumferential direction. After processing the results, the average curves and values for the mechanical properties for each tube were defined. Because of the remarkable differences in shape and behavior of the curves, an average curve was calculated also. The results of monotonic traction tests in the circumferential direction are shown in Table 4 of the complete paper, and the plots are shown in Figs. 3 and 4 of the complete paper.

Collapse Test in Full Scale. Initially, the tube to be tested was prepared by using a 10-mm-thick metal tape and a 1-mm‑thick rubber blanket to cover the entire tube. The tube is placed inside a hyperbaric chamber, which is filled with water at a rate of 200 psi/min until the space between the tube and the chamber wall is completely free of air; the interior of the tube, however, will remain full of air. The assembly is then finally pressurized to collapse, which is characterized by a distinctive noise followed by an abrupt drop in applied pressure.

Numerical Simulation. A tridimensional finite-element model was developed by use of commercial software. Typical meshes were used in the numerical models for intact tubes and tubes with holes. These meshes were determined following mesh sensitivity in the circumferential, axial, and radial directions. Also, a special mesh-­sensitivity analysis was evaluated in the region near the holes. The models were developed to simulate the results of the experimental tests, with the objective of verifying their capacity to reproduce the physical phenomena of collapse. The radial and axial symmetry of the tube were recognized, to save computational time. Thus, only half the length of the specimens was modeled (750 mm) and the circumferential superior half, obtaining only one-fourth of the tube. The ­finite-element mesh was developed with 3D solid elements, which have 20 nodes and three degrees of freedom per node. This element presents quadratic displacement functions, and it is appropriate for irregular meshes. Each model consisted of approximately 60,000 nodes and 9,000 elements.

Initial geometric imperfections were considered with the maximum measured ovalization in each tube and located in the center of the tube to simulate the real geometric conditions of each tube. The material was modeled in the elastic case with a linear isotropic behavior, with modulus of elasticity and Poisson’s coefficient obtained from the tensile tests. In the elastoplastic case, a law of potential flow was adopted and associated with the von Mises plasticity theory, with a nonlinear isotropic behavior. For the solution method of the modified algorithm of risk, where the load was evaluated at each increment of displacement, the collapse occurs when the load drops.

Analytical Approximations for Intact Pipes. American Petroleum Institute (API) Standards 5C2 and 5C3 can be used for different types of pipes: casings, drillpipes, line pipes, and tubings. According to the approximation therein, there are essentially four types of failure modes: yield strength, plastic collapse, transition collapse, and elastic collapse. To define which type of collapse formulation should be applied for a specific tube, five constants must be calculated and the intervals limiting the application of each one must be evaluated. The collapse pressure is obtained by replacing the values of each formulation. The Det Norske Veritas (DNV) equation considers that the collapse is a function of three properties: elastic capacity, plastic capacity, and ovalization. These functions are combined into a polynomial of the third degree that resolves the collapse pressure.

Analytical Approximations for Perforated Pipes. The mechanism of the four-hinge method was proposed more than 30 years ago and assumes that, during the collapse, four sections are formed that allow the collapse to occur. In general terms, this method consists of obtaining the collapse pressure by verifying the cross plots of elastic ovalization and plastic collapse. A modification was proposed for this model later to determine the analytical collapse pressure of tubes with holes, including a geometric parameter related to the diameter of the hole and the spacing between holes.


Collapse-Pressure Experimental Test and Numeric Simulations. Figs. 2 and 3 show real pipe collapsed after the testing. Generally, the perforated pipes show values of collapse pressure 10% lower than those of intact pipes, but this difference could increase or decrease as a function of other variables, such as material data, geometric hole distribution, and initial imperfections.

Fig. 2—Real collapsed pipe (Pipe 1).


Fig. 3—Real collapsed pipe (Pipe 2).


The collapse values obtained from the Group A material data (using the material plot obtained for each pipe) show a difference of between 1 and 20% between the experimental and the numerical pressures. This variation could explain the differences in the material behavior between pipes, where material properties obtained in some test bodies could represent in a better way the structure behavior, whereas other bodies have important differences and cannot represent as well. To avoid this variation, the most-divergent curves were disregarded. The authors then determined an average curve and simulated the collapse pressure again for all the pipes. This second group of results was called Group B.

Analytical Collapse Results and Correlations. Tables 8 and 9 of the complete paper show the calculated values for the analytical pressure and the differences compared with the experimental values. The results show that the best correlations stem from the DNV equation, with differences of 11% or less. The four-hinge method yields results with representative differences of between 4 and 15%. On the other hand, the API equation provides the worst correlation, showing pronounced differences close to 30% or more. The results for perforated pipes using the four-hinge mechanism indicate that it could be an effective method of obtaining an approximation for the collapse pressure, although the high differences between 17 and 32% suggest that using this tool could provide results with bad approximations.


The mechanical material properties presented a wide variation in the behavior of the stain/stress curve between test bodies from the same tube, as well as between the average curves for each tube. One reason for these variations may be the existence of residual stresses in the tubes from which the test bodies were removed. This variation also demonstrated the importance of having various specimens from the same tube, to improve repeatability and reliability of material results. The results of the circumferential traction tests presented similar behaviors for T5 and T6. Anisotropy also showed similar values and behaviors.

The numerical model proved to be a good tool to predict the values of collapse pressure of perforated pipes for a vast range of geometries. The use of a pattern curve of material data (Group B) shows results with differences of between 8 and 12%, improving on the results obtained for Group A. On the other hand, the intact tubes had better adjustments when compared with the perforated pipes. Group A shows differences of between 0.18 and -7%; in the case of Group B, these were between 0.02 and 0.5%.

The differences between the experimental-collapse-­pressure values and the analytical approximations considered in this work are considerable even in the case of intact tubes. The API equation presented quite conservative results. The fact that it incorporates safety factors causes the sensitivity of the results to be lost somewhat. The four-hinge model presented reasonable results, and the DNV equation showed an excellent fit (the safety factor was not considered in the calculations there).

For pipes with holes, the four-hinge mechanism seems a weak tool for approximating collapse pressure. In other words, for this approximation, no results close to the experimental values are obtainable. One reason could be the calculated geometric parameter that considers only the longitudinal spacing between holes and the diameter of the hole, disregarding other effects (for example, circumferential spacing). A readjustment of the geometric parameter could be considered in future research.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 184946, “Collapse Analysis of Perforated Pipes Under External Pressure,” by K. Beltrán and T. Netto, Federal University of Rio de Janeiro, prepared for the 2017 SPE Latin American and Caribbean Mature Fields Symposium, Salvador, Bahia, Brazil, 15–16 March. The paper has not been peer reviewed.