50th U.S. Rock Mechanics/Geomechanics Symposium,
2016. American Rock Mechanics Association
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The geomechanical problem of a hole closing in a creeping formation is interesting for different industries (oil, mining, tunneling). Analytical solutions have been derived in the case where far field pressure boundary conditions are applied (Barker et al., 1994, Liu et al., 2011). Using a power law creep model, we study the effect of applying additional shear stresses at infinity.
We start by deriving an analytical solution for the case of far field isotropic stresses to define a characteristic viscosity and velocity. We show that the solution reproduces Liu et al., 2011 without referring to Perzyna viscoplasticity. Compared to Barker et al., 1994 the closing velocities of our solution are substantially slower, which we attribute to their solution not fulfilling the incompressibility condition.
Using a finite element code, we investigate how far field shear stresses affect the viscosities and velocities in the vicinity of the hole. New characteristic viscosities and velocities are proposed based on the ones derived for pressure loads. These characteristic values reduce the problem to study the effects of β, the ratio of deviatoric to hydrostatic stress at infinity, and n, the stress exponent of the constitutive law. A numerically verified proxy shows that the effect of shear can be modelled as increasing the closure velocity by a factor equal to (1+nβ)n. The bigger the stress exponent the bigger the shear enhancement. This result can be used in the industry to quickly estimate the amount of creep due to general stress conditions.
Wellbores going through creeping formations experience time dependent closure which might translate into drilling problems (Dusseault et al., 2004). In the oil industry, a commonly encountered rock that exhibits creep is salt. From the Gulf of Mexico to Iran or offshore Brazil, massive salt bodies have to be safely drilled through to reach reservoirs. To address this challenge, a number of guidelines have been developed to efficiently deal with stuck pipes related with time dependent borehole closure. These guidelines are based both on field experience (e.g. Yearwood et al., 1988 or Holt and Johnson, 1986) and on numerical simulations (e.g. Moghadam, 2013, Xie and Tao, 2013 or Poiate et al., 2006). Both field and numerical studies show the influence of the wellbore pressure on formation creep and the goal is then to determine which mud weight to use to prevent borehole closure.
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