Mud weight design for horizontal wells in shallow loose sand reservoir with the finite element method
5.6 NUMERICAL RESULTS WITH FINITE ELEMENT MODELING
This section describes the results of model simulations in which the mud weight and friction angle are varied. As expected, as the mud weight and friction angle are increased, the plastic yield zone decreases in size, as does the deformation. Boundary effects are evident at the edge of the models, and the most representative cross section of the model is in the center.
With respect to wellbore stability, it is a rule of thumb to avoid mud weights that will result in the entire wellbore being surrounded by failed material. Based on this design criterion, the minimum mud weight should be 12330.1 Pa/m (10.5 ppg). Note that the figures that illustrate total displacement do not take creep processes into account. Because the Tambaredjo wells are drilled very fast, creep is not expected to play as significant a role in deformation as would be the case in wellbores that remain in the openhole state for extended periods of time.
Figure 5.6 through Figure 5.12 show the numerical results at 587.2 Pa/m (0.5 ppg) incre-ments, from 11155.8 Pa/m (9.5 ppg) (Figure 5.6) to 14091.5 Pa/m (12 ppg) (Figure 5.12). The internal friction angle for all of these results is held constant at 21.88°.
Figure 5.13 through Figure 5.18 show the model results at 587.2 Pa/m (0.5 ppg) incre-ments, from 11155.8 Pa/m (9.5 ppg) (Figure 5.13) to 13504.4 Pa/m (11.5 ppg) (Figure 5.18).
The friction angle for these results is held constant at 25°.
Elasto-plastic modeling based upon rock strength parameters from Horsrud’s correlations (Sikaneta and Shen 2009) yield shear failure gradients that are relatively reasonable for shale formations. However, the Horsrud correlations fail to capture the cohesionless nature of the sands; analytical elastoplastic models also fail to capture the essential features of sand geo-mechanics. A FEM was developed to better assess the feasibility of drilling horizontal wells at approximately 305 m. TVD. Based on the finite element and analytical models, a minimum mud weight of 10.5 ppg is recommended for drilling a horizontal well at 305 m. The relatively low pressure in the shallow Tambaredjo reservoirs should help to mitigate the risk of dif-ferential sticking. The fracture gradient at 305 m is approximately 17027.3 Pa/m (14.5 ppg).
The recommended mud window for drilling is between 12330.1 to 17027.3 Pa/m (10.5 and 14.5 ppg) for the horizontal section and at the end of build sections.
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Figure 5.7. The resultant active plastic zone distribution around the wellbore at PMW = 11155.8 Pa/m (9.5 ppg), Φ = 21.88°.
Figure 5.8. The resultant active plastic zone distribution around the wellbore at PMW = 11743 Pa/m (10 ppg), Φ = 21.88°.
Figure 5.9. The resultant active plastic zone distribution around the wellbore at PMW = 12330 Pa/m (10.5 ppg), Φ = 21.88°.
Figure 5.6. The resultant active plastic zone distribution around the wellbore at PMW = 10568 Pa/m (9 ppg), Φ = 21.88°.
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Figure 5.10. The resultant active plastic zone distribution around the wellbore at PMW = 12917.2 Pa/m (11 ppg), Φ = 21.88°.
Figure 5.11. The resultant active plastic zone distribution around the wellbore at PMW = 13504.4 Pa/m (11.5 ppg), Φ = 21.88°.
Figure 5.12. The resultant active plastic zone distribution around the wellbore at PMW = 14091.5 Pa/m (12 ppg), Φ = 21.88°.
Figure 5.13. The resultant active plastic zone distribution around the wellbore at PMW = 10568.7 Pa/m (9 ppg), Φ = 25°.
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Figure 5.14. The resultant active plastic zone distribution around the wellbore at PMW = 11155.8 Pa/m (9.5 ppg), Φ = 25°.
Figure 5.15. The resultant active plastic zone distribution around the wellbore at PMW = 11743 Pa/m (10 ppg), Φ = 25°.
Figure 5.16. The resultant active plastic zone distribution around the wellbore at PMW = 12330.1 Pa/m (10.5 ppg), Φ = 25°.
Figure 5.17. The resultant active plastic zone distribution around the wellbore at PMW = 12917.2 Pa/m (11 ppg), Φ = 25°.
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Based on an analytical model of the effect of water cut on cohesive strength, there is little likelihood of production-induced saturation changes causing problematic weakening of unconsolidated sand.
5.7 CONCLUSIONS
With the mean-stress dependent model for Young’s modulus and Poisson’s ratio, 3D numeri-cal analysis has been performed with FEM software for a section of horizontal wellbore within a loose sand reservoir. Experimental values of cohesive strength parameters at the target depth have been presented. Geomechanical parameters and pore pressure were pre-dicted with 1D analytical software by using logging data, which provided a sound basis for numerical analysis.
The results of minimum safe mud weight values predicted here were successfully used in a field development plan for the Tambaredjo NW field in Suriname. This case study provides a good example of the integrated use of 2D prediction software with 3D FEM numerical software.
ACKNOWLEDGEMENTS
The authors would like to thank Alejandro Arboleda, project manager from Halliburton Consulting—Geomechanics Practice Group, for his management over the project related to this chapter, as well as Franklin Sanchez and Jose Luis Ortiz Volcan, Halliburton regional managers, and Lilian Mwakipesile-Arnon of Staatsolie for their assistance with the works related to this chapter.
NOMENCLATURE
A = Model parameter B = Model parameter c = Cohesive strength, Pa
di = Diameters of grain size fraction, fi, m Deff = Effective grain size, m
σh
eff = Minimum horizontal effective vertical stress, Pa σv
eff = Vertical effective vertical stress, Pa Kh = Effective stress ratio
Tf = Tectonic factor
Figure 5.18. The resultant active plastic zone distribution around the wellbore at PMW = 13504.4 Pa/m (11.5 ppg), Φ = 25°.
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σv = Effective vertical stress gradient, Pa
σH = Maximum horizontal effective vertical stress, Pa φ = Internal friction angle, °
ρ = Density, kg/m3 CS = Cohesive strength DT = Sonic data
EMW = Mud weight equivalent, Pa/m (ppg) FEM = Finite Element method
MW = Mud weight, Pa/m (ppg) RHOB = Bulk density kg/m3 TVD = True vertical depth, m (ft)
UCS = Unconfined compressive strength, Pa
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