A New Analytical Method for Calculating Subsidence Resulting by Fluid Withdrawal from Disk-Shaped Confined Aquifers

Abstract

This work presents the derivation of analytical solutions concerning the radial subsidence distribution ensuing from fluid extraction from a disk-shaped confined aquifer in homogeneous formations. The study draws upon methodologies developed in petroleum geomechanics of deep reservoirs to estimate surface uplift due to CO2 injection using Hankel-transformed thin plate theory. These methods yield simplified expressions as compared to previous results derived using the superposition principle on surface uplift from a uniform pressure field. Hence, closed-form formulas for the subsidence at the well location are re-derived, while the formulas for the subsidence field are deducted by both methods and the mathematical relation between the two methodologies is discussed. Additionally, innovative closed-form asymptotic solutions for radial subsidence distribution are deduced for scenarios involving deep aquifers. These solutions demonstrate exceptional accuracy when aquifer depth exceeds aquifer diameter, exhibiting independence from formation permeability and fluid viscosity. The study explores the influence of physical parameters on the subsidence field.