Paper on Geertsma solution published in Geosciences

The paper is authored by Joonsang Park, Tore Ingvald Bjørnarå and Bahman Bohloli from NGI – Norwegian Geotechnical Institute.

The paper is an open access article published in Geosciences and can be read here.


We present a generalized Geertsma solution that can consider any number of finite-thickness layers in the subsurface whose mechanical properties are different from layer to layer. In addition, each layer can be assumed either isotropic or anisotropic. The accuracy of the generalized solution is validated against a numerical reference solution. The generalized Geertsma solution is further extended by a linear superposition framework that enables a response simulation due to an arbitrarily-distributed non-uniform pressure anomaly. The linear superposition approach is tested and validated by solving a realistic synthetic model based on the In Salah CO2 storage model and compared with a full 3D finite element solution. Finally, by means of a simple inversion exercise (based on the linear superposition approach), we learn that the stiffnesses of cap rock and reservoir are the most influencing parameter on the inversion result for a given layering geometry, suggesting that it is very important to estimate high-confidence mechanical properties of both cap rock and reservoir.

Featured image/figure text: VTI anisotropic subsurface model consisting of N layers and subjected to fluid-induced constant pore pressure p(r, z) (darker-shaded) of radius R in an n-th layer. Note ρ, Vs, Vst, Vp, Vpt, and h are mass density, radial/horizontal and vertical S-wave velocities, radial/horizontal and vertical P-wave velocities, and layer thickness, respectively. Axis-symmetric coordinates (r, z) are used and z-positive is upwards.