- Using equations of stresses around a cylindrical cavity, calculate near-wellbore effective radial
and hoop
stresses for a vertical well 8 in diameter in the directions of (4,500 psi – acting E-W) and (6,000 psi) up to 3 ft of distance considering that = 320 0psi and
- = 3,200 psi
- = 4,000 psi

- Effect of overpressure:
Consider the problem solved in class (Wellbore: vertical; Site: onshore, 7,000 ft of depth, = 7,000 psi, = 4,300 psi, = 6,300 psi; Rock properties: = 3,500 psi, , = 800 psi).
- Calculate wellbore pressure and corresponding mud weight for (i) , (ii) ( ), and (iii) for inducing tensile fractures () for and . Compare with solved in class. How does the drilling mud window change with varying pore pressure?
- Assume horizontal stress directions near Dallas-Forth Worth region. What would the azimuth of breakouts and drilling induced fractures be?
`https://www.nature.com/articles/s41467-020-15841-5/figures/1`

- Effect of stress anisotropy (differential stress)
:
Consider the following problem, Wellbore: vertical; Site: onshore, 2 km of depth,
MPa/km,
,
; Rock properties: = 7 MPa, , = 2 MPa. Calculate wellbore pressure and corresponding mud weight for (i)
, (ii)
, and (iii) for inducing tensile fractures for
- How does the drilling mud window change with ?

- Offshore:
Consider an offshore vertical wellbore being drilled at 2 km of total vertical depth, with 500 m of water, hydrostatic pore pressure,
,
. The rock properties are = 7 MPa, , = 2 MPa. Calculate wellbore pressure and corresponding mud weight for (i)
, (ii)
, and (iii) for inducing tensile fractures.
- Horizontal wells:
Evaluate wellbore stability for horizontal wells that you will need to exploit in a gas reservoir subjected to a strike-slip stress environment.
- Consider two wellbores: one drilled parallel to and another drilled parallel to . Draw cross-sections of these two wells, identify involved stresses, and clearly mark expected positions of tensile fractures and wellbore breakouts.
- The horizontal wells lie at about 8,000 ft depth where it is estimated that = 50 MPa, = 70 MPa, psi/ft and . The unconfined compressive strength of the rock is 8,500 psi, the rock internal friction coefficient is , and tensile strength is about psi given the large density of natural fractures. Determine the mechanical stability limits on wellbore pressure for both horizontal well directions considered. Assume a safe breakout angle to calculate the lower bound for the mud window.
- Determine mud density window appropriate for these wells (keep in mind potential lost circulation).
- Which one appears to have a wider mud window? Justify