An Analytical Solution of Pressure and Displacement Induced by Recovery of Poroelastic Reservoirs and Its Applications

An analytical solution of induced pressure and displacement fields during reservoir production enables rapid yet accurate prediction, as well as optimization of reservoir performance. Traditionally, such solutions are primarily obtained for infinite or semi-infinite domains using Green's function method, which requires time-consuming numerical integral operations. In this work, we have developed a series solution of transient pressure and displacement fields of a finite -size reservoir using the eigenfunction expansion method. The solution is derived based on the stress formulation of geomechanical governing equations. We have validated the developed solution and applied it to a series of case studies, including the stress concentration effect induced by neighboring horizontal wells and subsidence induced by production. The results demonstrate that, compared to Green's function method, the series solution is more convenient in implementation and more flexible in handling boundary effects.