Burst and Collapse of a Sealed Multilateral Junction: Numerical Simulations
Authors: Bayfield Matt , Fisher S.L. , Ring L.M. 
Published: December 2007

Summary
Multilateral well technology progressed during the 1990's. Much effort is now concentrated on the development of multilateral systems where both a mechanical and a pressure seal are provided throughout by the well casing itself. Such a system would extend the application of multilaterals to a number of new environments (including higher pressure applications) and could also supersede many existing multilateral systems.
In this article we describe a finite element analysis undertaken to assess the effects of internal and external pressure on a sealed multilateral junction. The studies consider a junction formed between a 9.625-in. mainbore and a 7-in. lateral. Results suggest that an unreinforced junction with lateral inclined at 2.5° to the mainbore would burst at 8 to 16% of the mainbore casing strength and collapse at 8 to 28%. Increasing the angle between the mainbore and lateral to 5° gives only a limited increase in strength.
Subsequent finite element simulations were then performed to suggest alternative methods for improving burst and collapse strengths. The findings indicate that values can approach standard oilfield tubular strengths if steel reinforcement is provided at the junction. A significant increase in burst strength is also predicted if the junction can be firmly cemented. The extent of this increase is highly dependent on both the quality of the cementing and the cement's material properties. The benefits of cement under external pressure are generally limited due to failure of the cement.

Introduction
Drilling multilateral wells can be a technically and economically efficient method of developing a reservoir.1 A range of completion options is now commercially available, enabling multilateral technology to be exploited in a variety of environments.
The critical area of a multilateral completion is the junction: the interface between the mainbore and the lateral. Depending on the method of construction, the junction can offer either, or both, mechanical integrity (e.g., prevention of sand influx) and hydraulic integrity (a barrier between formation and wellbore pressures). The ultimate goal is a junction with full mechanical and hydraulic integrity provided by the casing itself, without the aid of cement. According to the Technology Advancement Multi-Laterals (TAML) classification system,2 such a design is termed a "level 6" junction.
In this article we present the results of numerical simulations investigating stress conditions, structural integrity, and burst and collapse strengths of a level 6 multilateral junction. The objectives were toevaluate the burst and collapse strengths of an unreinforced level 6 junction;investigate the effect of varying the angle between the mainbore and lateral;estimate the upper limits of burst and collapse strength that could be obtained if the junction were reinforced inside a solid steel cylinder;evaluate the effect of cementing the junction in the borehole.
All numerical modeling was performed using finite element (FE) techniques. No physical modeling was undertaken.

Description of Models
Five finite element models were constructed during the course of the simulations. These are subsequently referred to asbase case junction;five degree junction;solid steel cylinder junction;cemented junction A;cemented junction B.
All junctions have a single plane of symmetry. By applying appropriate boundary conditions, it was sufficient to model only half of each structure. Clamped boundary conditions (zero displacement) were applied at the ends of all tubulars. This condition would be representative of actual field application.

Base Case Junction.
The base case level 6 junction was modeled as a "y joint" formed by two intersecting steel tubulars. The dimensions of the tubulars are given in Table 1. The mainbore is representative of 47-lbm/ft, 9.625-in. casing and the lateral is 29-lbm/ft, 7-in. casing. The angle between the mainbore and lateral (the "junction angle") is 2.5°. The total length of the model is 440 in. Fig. 1 shows this geometry in true scale. Fig. 2 shows the finite element model of the same structure.
Steel was treated as an elastoplastic material using the von Mises criterion and a yield stress of 89,700 psi (i.e., a C-90 steel). The Young's modulus was taken as 30×106 and the Poisson ratio as 0.3. The stress-strain curve used is given in Fig. 3.

Five Degree Junction.
This junction is constructed from tubulars with the same dimensions and the same material properties as the base case junction. The only difference from the base case junction is that the angle between the mainbore and lateral is 5°.

Solid Steel Cylinder Junction.
This junction simulates heavy steel reinforcement by enclosing the base case junction in a solid steel cylinder 16.625 in. in diameter (Fig. 4). The minimum wall thickness is equal to 0.408 in., as for 29-lbm/ft, 7-in. casing.

Cemented Junction A.
This junction is created by setting a 22-in. cement cylinder around the base case steel junction and simulates the effect of a perfectly cemented borehole (Fig. 5). The cement was modeled as an elastoplastic isotropic material with a Young's modulus of 1,200×103 and a Poisson ratio of 0.2. The shear strength was described by the Mohr-Coulomb criterion, assuming a cohesion of 1,800 psi, a friction angle of 30°, and a dilatancy of 15°. These parameters give an unconfined compressive strength of the cement of around 6,300 psi. The tensile strength was taken as 700 psi. All values were taken from laboratory tests on a class G cement sample.