A wellbore/reservoir flow coupling model is developed. It can be applied to a parallelepiped drainage domain consisting of any number of wells with any number of laterals of arbitrary configurations. Reservoir inflow for entire time period (from early transient to late pseudo-steady 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 includes those caused by wall friction, gravity, and acceleration due 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 which lead to several important and interesting observations. The coupling model may be applied to determine well productivity, well index, wellbore pressure profile, wellbore inflow or outflow distribution for any time in the well's production/injection life.