Semi-analytical solution for unsteady fluid flow to a partially penetrating well

An analytical solution of the problem of unsteady fluid flow to a partially penetrating well flowing at constant rate in an anisotropic reservoir with the impermeable top and bottom boundaries has been obtained. The problem reduces to a system of integral equations in the Laplace transform domain that connects the pressure drop and flux distribution along the open interval. The arbitrary number and position of the opening intervals relative to the top and bottom boundaries have been taken into account, as well as the wellbore storage effect and non-uniform skin effect. By using the superposition method, the solution for unsteady fluid flow to a partially penetrating well after its shut down has been obtained. Simulations have showed that the fluid overflow takes place through the opening intervals after a well is shut down at the bottomhole.