Effect of Transient Surge Pressure on Stress Distribution around Directional Wellbores
Authors: Zamanipour Z. , Miska S. Z. , Hariharan P. R. 
Published: January 2016

Abstract
Fluid displacement due to pipe movement in and out of the wellbore generates surge/swab pressure. Surge/swab pressure could result in formation fracturing, lost circulation, kicks, and even blowouts. Transient surge pressure depends on tripping velocity, mud viscosity, fluid compressibility, wellbore expansion, and elasticity of the drillpipe. Considering wellbore stability, sudden pressurization of the wellbore causes rapid change in stress distribution in the zone near the wellbore that may result in wellbore instability. This makes it necessary to have an estimation of transient surge pressure and stresses for safe and effective tripping operations.
In this work, for the first time, stress distribution and the stability around the wellbore are being investigated when transient surge pressure is generated in the wellbore. Firstly, a transient surge pressure model is developed to calculate the pressure along the wellbore during the tripping-in operation. The model is based on transient wave propagation due to fluid compressibility and wellbore expansion. Then, the following steps are taken to obtain stresses around the wellbore: 1- Stress distribution around directional wellbore is calculated based on poroelasticity concept. 2- Induced pressure and stresses due to constant borehole pressure change are calculated. 3- The model is modified to include the effect of time dependency of surge pressure using Duhamel's theorem (superposition principle). 4- Induced stresses are calculated and added to existing stresses around the wellbore using the superposition principle.
The model is implemented for tripping into a directional wellbore with trapezoidal and parabolic velocity profiles. The induced pressure, radial and hoop stresses versus radius are calculated at different times. Results indicate that these induced effects almost vanish at a distance of about five times the wellbore radius. Induced pressure increases with time until it reaches its maximum which is the maximum of surge pressure and then dissipates with time. Its peak propagates into the formation and dissipates with time. Induced radial stress shows similar trend as induced pressure. However, its peak is always at the wellbore wall. Induced hoop stress is tensile with a maximum value of about 35% of induced radial stress before it decays and dissipates in both cases of tripping velocities. Total radial stress peaks about 30% for the case of trapezoidal velocity and 35% for the case of parabolic velocity compared to base value. However, same comparison for total tangential stress shows a reduction of 7% decrease for the case of trapezoidal velocity and 11% for the case of parabolic velocity which is due to the induced tensile stress. Comparing results for both velocity profiles show no difference in the trend of induced pressure and stresses. However, the magnitude of induced pressure and stresses depends on surge pressure which is different in case of trapezoidal and parabolic velocity profiles. A failure criterion can be applied to analyze the stability of the wellbore. It is noted that surge pressure changes as a function of time and dynamic rock strength must be taken into account in wellbore strength management.
The developed model presents an effective tool for wellbore stability analysis in tripping operations. The tool can be applied for optimization of tripping operations in vertical and directional wellbores.