General Analytical Solution for Estimating the Elastic Deformation of an Open Borehole Wall

Research output: Research - peer-reviewPaper

External Organisational units

  • Universidade Estadual Paulista (UNESP)


Few analytical solutions have been published in the past decades for quantifying the ballooning volume caused by elastic deformation of an open borehole; nevertheless none of them takes into consideration the effects of permeability and thermoelasticity. This paper introduces new analytical solutions aiming at predicting a radial elastic displacement for any point along an open borehole wall. The presented analytical formulas here are general and taking into account the effective stresses, thermoelasticity and the poroelasticity effects. Two analytical formulas are derived, one for impermeable borehole, whereas the second is for permeable borehole. To utilize the proposed analytical solution for estimation the volumetric expansion and contraction of an open borehole, a recognized mathematical method has been adapted to be used for defining the areal elastic deformation of an open borehole at a given depth, which later can be used to quantify the volumetric change of an open borehole for specified depth interval. In order to validate the proposed formulas a finite element simulation was utilized. Several cases have been examined and compared, generally good results were observed with relative error less than 15%. Finally, results of a sensitivity study which was performed in order to assess the effects of different parameters on volumetric deformation of the open borehole are presented and discussed in details, the main finding of this study was that the deformation area of the borehole due to the elastic deformation is not significant and controlled mainly by the wellbore pressure.


Original languageEnglish
StatePublished - 11 Feb 2016