A General Single-Phase Wellbore/Reservoir Coupling Model for Multilateral Wells

Abstract

Summary A general single-phase flow model that rigorously couples flow in the reservoir with flow in the wellbore is presented. The model can be applied to a parallelepiped drainage domain consisting of any number of wells containing any number of laterals of arbitrary configurations. The fluid is assumed to be slightly compressible, and gravity head is included. Reservoir inflow for the entire time period (from early transient to late pseudosteady state) is handled in the coupling model by integrating the instantaneous point source/sink solution over both time and space. Pressure drop along any lateral in the well system is the sum of three components: wall friction, gravity, and acceleration owing to wall inflow or outflow. Effects of wall mass transfer on wall friction and kinetic energy change are taken into account. A computer package has been developed and used to perform a series of sensitivity studies that lead to several important and interesting observations. The coupling model may be applied to determine well productivity, well index for multiphase flow simulation, wellbore pressure profile, and wellbore inflow or outflow distribution for any time in the well's production/injection life.