## Analytical Review Of Exploratory Riser Systems

Analyses for exploratory riser design must include a large number of variables. The combined stress in the riser is due to both axial and hoop or circumferential stress. Hoop stress is caused by internal pressure of the mud column and pressure with kicks. External forces on the riser result from hydrostatic pressure which is calculated for the given water depth.

The total axis stress is due to the tensioner load, riser buoyancy, riser weight, mud weight, current forces, and wave forces. With large surge or sway of the vessel the dynamic forces on the riser string must also be considered. A schematic of these stresses is shown in figure 2-18.

Various procedures are used for analysis of the riser, depending upon the required objective. Simple catenary equations can be used to get a ballpark type of solution with results that maybe off several hundred percent. This would be adequate for making rough comparisons of the effects of different water depths and diameters or wall thicknesses of the riser string.

For more accurate correlations, finite difference procedures

Tensioner

Tensioner

Fig, 2-18 Forces on the riser string

are used to solve differential equations. The finite difference approach gives excellent results for a very simple type of riser. However, a separate differential equation is required for each change in cross section and the joints of different cross sections are tied together mathematically by compatibility conditions. The problem with the finite difference approach is that the procedure becomes totally unwieldy and impractical for analyzing a design with many variations in riser diameter, wall thickness, floatation material on the riser, or any other variables.

Conversely, the finite element approach for design and analysis finds considerable favor since this approach is virtually unencumbered by limitations or conditions. For example, the digital programming and computer usage is essentially the same for any number of variables, such as riser wall thickness, added buoyancy, etc. With the finite element approach, other variables can also be considered that cannot be done on a practical basis by any other method.

This means that any current distribution can be considered {Figure 2-19), hydrodynamic drag effects of the riser couplings and the choke and kill lines can be accounted for, loads due to any wave height can be considered, the influence of the telescoping joint can be fully analyzed, etc.

Fisher and Ludwig2 have given generalized results that are very helpful for obtaining ballpark type answers. The value of their work is that the approximate response of any design can be quickly determined using their charts (Figures 2-20, 2-21).

g MWL

Uniform

Triangulor

Tropozord

Uniform

Triangulor

Tropozord

Parabolic Stopped Reversed

Fig. 2-19 Common design current profiles.

Parabolic Stopped Reversed

### Fig. 2-19 Common design current profiles.

However, detailed and accurate analyses such as with a nonlinear finite element routine must be used for either deep water conditions or severe environmental conditions.

The digital computer riser program, ETA/FLEXRIS, is a nonlinear finite element program. Nonlinear means that the equations for displacement are second order rather than first. (Second order displacement functions are required because of the large displacements and relatively low stiffness of the riser cross section.) The nonlinear ETAyFLEXRIS program has all of the versatility of finite element programs. With ordinary standards of programming, the linear programs can be off by as much as 100%. The nonlinear programs give solutions with an accuracy of about 1%.

### CONCLUSIONS

The technology of riser design and operations for 200-800 ft. water depths is well established. Special considerations are required for water depths greater than 800-1,500 ft. Innovative designs are needed for 1,500-3,000 ft. water depths to reduce riser running time and to decrease the possibility of environmental damage due to extreme winds, waves, and vortex shedding.

1. Because of the possibility of fracture of the geological formation with excessive mud pressure, radically different designs and procedures may be required for 3,000-6,000 ft. water depths.
2. Nonlinear finite element computer programs seem to be the best and most universal method for general design and analysis.
3. Computer simulated operations with various sets of wave and current forces and vessel motions can be used to set more realistic limits for drilling and hang-on conditions thereby decreasing weather related downtime.

### REFERENCES

1. Butler, H. L., Delfosse, C,, Galef, A., and Thorn, B, J., "Numerical Analysis of a Beam Under Tension,"/. Struct. Div., ASCE, Oct. 1967, pp. 165-174,
2. Fisher, W.r and Ludwig, M., "Design of Floating Vessel Drilling Riser,"/. Petr. Tech., March 1966, pp. 272-280.
3. Harris, L. M., Deep writer Floating Drilling Operations, Tulsa: Petroleum Publishing Co., 1972.
4. Kennedy, J. L., "High-Angle Holes, Supply Hurdles Complicate North Sea Drilling Work," OGJ, June 24, 1974, p. 132.
5. Morgan, G.W., "Riser Design Criteria and Considerations," Petr. Engr,, Nov. 1974, pp. 68-74.
6. Morgan, G. W. "General Aspects of Riser Design and Analysis Procedures,"
7. Engr., Oct. 1974, pp. 36-48. 7. Wilson, R. O., and Martin, M, R., "Deepwater Pipelay for Central North Sea," OTC Paper 1855, 1973.