Spontaneous counter-current imbibition outwards from a hemi-spherical depression

Spontaneous counter-current imbibition occurs when brine spontaneously displaces oil from a very strongly water-wet rock. Past experiments have been performed on cylindrical rock cores, with or without a cylindrical hole drilled through them, that have some or all of their faces open to imbibition. Changes in the area open to imbibition and the boundary conditions of the core plug can make large differences to the rate of imbibition. For example, linear imbibition into a core with one-end-open is significantly slower than imbibition into an all-faces-open core, and radial inwards imbibition goes faster than radial outwards imbibition. For linear imbibition, the volume imbibed with time varies as the square root of time as compared with almost linear variation with time for radial outwards imbibition. The reason for this behaviour during radial outwards imbibition is that most of the flow resistance is in the vicinity of the cylindrical hole, whereas most of the volume is near the closed outer boundary of the core. One would expect similar behaviour (i.e. imbibition volume linear with time) from spherical outwards imbibition. Experimentally, the situation can be realised by imbibition from an open hemi-spherical cavity on one face of a hemi-spherical block which is sealed on all other faces. In the present paper, a theory for spontaneous spherical outwards imbibition is developed assuming piston-like advance of a front from such a hemi-spherical cavity. Results are calculated and compared for various boundary conditions and the spherical outwards prediction is then tested by experimental results obtained for chalk blocks. The predictions and the experiments confirm that, for the spherical outwards boundary condition, the production curves can be almost linear with time.