An Analytical Solution for Pressure-Induced Deformation of Anisotropic Multilayered Subsurface

Joonsang Park,Tore Ingvald Bjørnarå,Bahman Bohloli

doi:10.3390/geosciences11040180

Joonsang Park, Tore Ingvald Bjørnarå + Show 1 more

Open Access

https://doi.org/10.3390/geosciences11040180

Copy DOI

Journal: Geosciences	Publication Date: Apr 18, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Norwegian Geotechnical Institute

Abstract

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.

Highlights

We have presented a generalized Geertsma solution that can consider any number of layers in the subsurface whose properties and thicknesses can be different from layer to layer
The generalized Geertsma solution is applied to a linear superposition framework via square-cuboid-shaped grids so that we can calculate arbitrarily-distributed pressure anomaly cases, the simple case of a constant pressure anomaly of cylinder shape
We have defined the condition that the lateral length of a square-cuboid should be shorter than the overburden thickness (i.e., Lre /Hob ≤ 1.0) in order to guarantee the accurate displacement calculation at the top surface for a square-cuboid shape pressure via the equivalent cylinder shape pressure. The performance of this linear superposition approach is tested by solving a realistic synthetic model based on the In Salah CO2 storage site, simplified by removing the vertical fault in Well KB502

Summary

Analytical Solution for Anisotropic Layered Subsurface

We present an analytical solution for displacement field for an anisotropic layered subsurface subjected to fluid-induced pore pressure disturbance in a reservoir layer. To derive the analytical solution for the VTI medium shown, we apply the following axis-symmetric governing equation in cylindrical coordinate (r, z) and Hankel transforms with k being the transform parameter (or wavenumber). It is important to remember that the solution derived above is valid only for VTI layers, not for an exact isotropic layer (i.e., Vp = Vpt ), because the linear independence among the four unknown coefficients are not valid for the exact isotropic case For the latter, we need to use the corresponding solution for the isotropic medium, which is presented by Mehrabian and Abousleiman [16]. Following the same Hankel transform procedure, we can calculate the displacement field for an isotropic layered subsurface subjected to the same type of axis-symmetric pore pressure disturbance of finite radius and thickness

Validation

Representation of Arbitrarily-Distributed Pressure Anomaly

Synthetic Model Study Inspired by in Salah CO2 Storage Dataset

Findings

Conclusions