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Analysis of stress concentration around wellbore for different wellbore inclination and accounting for the effect of time for a new well drilled after production from an old well which affect far field stresses due to influence of stress path.

The pressure transient analytical solution using interference well is used to evaluate pore pressure at different times, using horizontal poison’s ratio values. The resulting pore pressure values are used to calculate new far-field stresses using concept of stress path. The new far-field stresses are applied to a new wellbore for different wellbore inclinations after performing coordinate transformation and applying Kirsch Solutions for plane strain assumptions in cylindrical coordinate system. The principal stresses at the bore-hole wall are evaluated and is assessed based on Griffith criteria for tensile fracture and Mohr-Coulomb criteria for shear failure. The study inspects the effect of time and wellbore inclination on stress concentration for cases of reservoir depletion. Also, further investigation has been done for cases of tripping in drill string. The reservoir formation is assumed to have majorly unconsolidated sand.

• MATLAB
• Latex

For isotropic far field stresses, the upper limit of mud-weight to prevent tensile fracture is found to decrease with increasing wellbore inclination because of change in orientation of far-field stress and overburden stress with respect to wellbore surface from inclination angle 0 to 90 degrees. The lower limit of mud-weight increases with increasing wellbore inclination due to the same reason. Since tectonic forces are not considered, the far-field stresses are only a small fraction (Poison’s ratio) of the overburden stress. For Isotropic far field stresses the upper limit of mud-weight increases with time because with pressure depletion due to production, the load support due to pore fluid drops and the far-field stresses thus increase; the stress required to fracture the wellbore, thus, increases. The same applies for lower limit, the rationale being that the increasing far-field stress causing higher stress concentration at the well bore wall, resulting in more sensitive wellbore with increasing time. For anisotropic far field stress, the behavior is similar to the isotropic case, except that since the weaker plane tends to be normal to the lower horizontal far field stress, the effect of time and inclination is seen to be more pronounced. The difference between the allowable limits are found to increase with time due to decreased load bearing by fluid due to production, causing higher far-field stress. The effect of depleting pore pressure can be seen in the calculated maximum and minimum horizontal stresses over time, which is found to increase. During tripping operations, like for well logging, the pore pressure can increase for a given instant of time. This can cause borehole failure as well.

The wellbore stability analysis for tight shale formation for orthotropic poison ratio stress distributions could yield better insights into the mechanics of shale formation fracking.