A wellbore is drilled first vertically to the point h of depth D, and then exten

Question

A wellbore is drilled first vertically to the point h of depth D, and then extends in the horizontal direction (parallel to the y-axis) at constant level of that depth. The rock formation is fully isotropic and homogeneous everywhere with specific weight of Prg = 1 psi/ft and Poisson's ratio v = 0.3. The rock has an unconfined compressive strength of 21,000 psi (shear failure or collapse) while the tensile strength (fracture) is almost negligible. However, the horizontal in situ stresses in the x-y plane are equal. At depth D1 = 5,000 ft while drilling (section 1-1 in xy plane), calculate the concentrated stresses at points A and B; At the same depth of 5,000 ft, draw roughly the tangential stress distributions along x direction, i.e., sigma yy in xy plane, from point A to a distance of 10 times radius (as shown in the figure); If D = 9000 ft, calculate the stress concentrations at section 3-3 in the x-z plane, at points E and F; Draw roughly the tangential stress distributions along x direction, i.e., sigma xx in xz plane, from point F to a distance of 10 times radius, at the depth of D = 9,000 ft (as shown in the figure); Determine the minimum mud pressure pw and mud density pw [Pw = Pw/(0.052D)] required to keep the horizontal wellbore (D = 9000 ft) stable from collapse; What will be the minimum mud pressure pw and mud density pw required to fracture the horizontal wellbore at depth D = 9,000 ft, and show the potential fracture direction; Determine the maximum depth Dmax that the vertical wellbore can be drilled under stable condition without considering the use of mud weight.

Explanation / Answer

refer to this link........www.spe.org/dl/docs/2012/osisanya.pdf

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