Correlation of porosity and permeability of reservoirs with well oscillations induced by earth tides

Summary. Periodic gravity perturbations, known as earth tides, produce minute expansions and contractions of subsurface geologic formations. The motions induce water level oscillations in wells connected to the deep reservoirs, and a measurable phase lag occurs between the maximum gravity and the maximum water level. The amplitude of the water level oscillations induced by the small harmonic gravity variations of the earth tides and the phase lag relative to the tide are related to the reservoir porosity and permeability. The motions of an elastic subsurface reservoir are analysed by considering an axially symmetric system of finite volume which is activated by oscillations of a rigid rock mass overlying the reservoir. The geometric parameters involved are the thickness of the reservoir, radial extent, depth and fluid level in the well. The physical parameters for which data are available or satisfactory estimates can be made are the fluid viscosity, densities, temperature, compressibilities and shear modulus. These properties refer to in situ conditions at large overburden pressure. Permeability and porosity at in situ conditions are not directly measurable, and methods of indirect estimation are of practical interest. This analysis correlates these two parameters with the amplitude and phase lag of the induced well fluid oscillation. For the very small strains and fluid volume fraction changes induced by the tides, slow flow of a viscous fluid through an isotropic porous matrix is assumed. An axially‐symmetric analysis for a uniform permeable layer perturbed by the oscillations of the rigid overburden rock yields explicit expressions for the oscillation amplitude and phase in the well. Selected results from numerical solutions having a wide range of realistic parameter values are presented. The results clearly show the dependence of amplitude and phase lag on the dimensionless permeability, and the near proportionality of the amplitude on the reciprocal of the porosity (porosity has no other significant influence). Finally, it is shown how asymptotic approximations of the direct solution allow an inversion which determines the permeability and porosity in terms of the amplitude and phase lag, given the other reservoir properties.