A Semianalytical Formulation for Estimating Induced Surface Subsidence of a Poroelastic Reservoir

Abstract

Summary Monitoring and controlling surface subsidence are important to the safety of production operations as well as to the compliance of environmental regulations. Quantitively predicting surface subsidence caused by subsurface pressure change due to well production or injection would be very useful for operators. However, running a 3D geomechanics simulation for such a purpose is technically demanding and computationally expensive. Currently, a quick and easy alternative to get accurate results to fulfill such a task is lacking. In this work, we propose a semianalytical formulation to efficiently calculate the surface subsidence of a reservoir during the primary and enhanced recovery processes. Our method is based on the Green’s function solution of the Navier-Beltrami-Michell equation of poroelastic rocks. It takes the pressure field from a reservoir simulator or an analytical solution as the input and calculates the surface displacement along the vertical direction. We benchmarked the proposed formulation with numerical methods on a refined grid as well as with a semianalytical solution to ensure its accuracy. We applied the developed formulation to optimize the injection well position and vertical injection zone for pressure management. Compared to the previous analytical formulations that are based on the average pressure decline of the reservoir, our method explicitly considers the spatial distribution of the pressure field and is therefore more accurate. Compared with numerical methods, our method avoids the discretization of the caprock region and is thus faster by several orders of magnitude.