SWELLING OF SHALE AROUND A CYLINDRICAL WELLBORE

A modified form of Biot's linear theory of poroelasticity is applied t o shale swelling in contact with an aqueous electrolyte. The shale is assumed to behave as an isotropic, perfect ion exclusion membrane, and in this limit swelling depends only upon the total stress and on the chemical potential of water within the pores of the rock. An axisymmet ric, plane-strain analysis of swelling around a wellbore is first pres ented, and this is subsequently extended to include swelling of a cyli ndrical hole in a finite, cylindrical shale sample. It is predicted th at swelling is prevented if the chemical potential of water within the shale equals that within the wellbore. The predictions of the analysi s are compared with experimental results obtained when drained outcrop shale swelled in contact with aqueous solutions of KCl or NaCl. The e xperimental swelling did indeed vary with water chemical potential, an d could be prevented if the salt concentration within the wellbore flu id was sufficiently high. However, post-mortem chemical analysis of th e shale showed that ion-exchange had taken place, with consequent modi fication of the shale's mechanical and chemical properties. Ion exclus ion was therefore imperfect, and an analysis that incorporates the che mical potentials of components other than water is necessary.