Bratli et al. (1983) and Risnes et al. (1982) derived equations for the near-wellbore stresses (axial, tangential, radial...) around a pressurized hole in a porous, permeable "poroelastic" medium. Their expressions includes Biot's constant, A which in turn contains the Biot poroelastic coefficient, α.
Should at α = 1.0 those expressions give the same answer as when using the standard near-wellbore stress equations for linearly elastic media (the Kirsch solutions on pages 170 and 174 in Zoback, 2010)? I was of the impression that the answer will be "yes" but the math seems to prove me wrong.
Dear Andreas,
it will be helpful if you provide your math which does not add up.
Sergey
Hello Sergei,
I am sorry for the late reply. I was referring to the poroleastic near-wellbore stress solutions shown here (Risnes +, '82) as Eq. 1-3:
https://www.onepetro.org/journal-paper/SPE-9650-PA
He uses β for Biot's coefficient. Usually we define Biot's coefficient as, A = (1-2v)β/(1-v). I thought that at β = 1.0 those equations will simplify to the Kirsch solutions as Equations 1-2 in:
https://petrowiki.org/Elastic_wellbore_stress_concentration
which does not seem to be the case.
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