During oilfield drilling operations, the rock originally in the volume occupied by the wellbore is replaced by drilling fluid that exerts pressure on the borehole wall. This leads to a redistribution of stress in the vicinity of the wellbore, and may lead to yield of rock close to the borehole. This results in a decrease in stress near the borehole wall. This redistribution in stress is studied in this paper for a vertical well using a computational model that accounts for rock deformation and plastic strain in the near-wellbore region. The stress changes around the borehole lead to changes in elastic wave velocities that may be used to monitor the changes in stress that occur. The change in elastic wave velocities are sensitive to the mechanical properties of the rock, and may therefore be used to calibrate mechanical earth models used to predict rock failure due to production.
The production of hydrocarbons leads to changes in rock stress that may result in damage or failure of the rock. Knowledge of the geomechanical properties of the reservoir is necessary, therefore, to optimize production. Current methods for determining rock strength include laboratory measurements of geomechanical properties, and the use of correlations between properties derived from logs such as dynamic elastic moduli, porosity, clay content, etc., and rock mechanical properties such as unconfined compressive strength, friction angle, etc. However, the drilling of a well can be considered as a rock mechanical test, since the stress acting in the vicinity of the wellbore is perturbed by the replacement of the rock originally in the volume occupied by the borehole by the drilling fluid, which exerts a pressure on the borehole wall.
The redistribution in stress shown in figure 1 may cause the rock to yield. Yield of the rock leads to further changes in the velocity of compressional and shear waves in the vicinity of the wellbore that vary with position relative to the borehole. Recent developments in sonic logging allow such changes in wave velocity to be monitored by making it possible to map the 3D variation in elastic wave velocities around the borehole (Pistre et al., 2005). Determination of the variation in velocity as a function of azimuth and radial distance from the wellbore therefore has the potential of allowing the strength characteristics of the formation to be determined. In this paper, the effect of the stress redistribution resulting from rock yield on the velocity of vertically propagating elastic waves is investigated
Key to the determination of the mechanical properties from the variation in velocity in the vicinity of the borehole is the ability to calculate wave velocities as a function of stress. Elastic wave velocities in sandstones vary with changes in effective stress due to the presence of stress sensitive grain boundaries within the rock. Sayers and Kachanov (1995) show that the elastic compliance tensor Sijkl of a sandstone may be written in the form
