A Virtual Node Method for Treatment of Wells in Modeling Multiphase Flow in Reservoirs

How to treat well boundary conditions is a difficult issue when formulating and coding a multiphase numerical reservoir simulator. The difficulty arises because the partial differential equations governing multiphase subsurface flow are of a mixed parabolic-hyperbolic type. Maximum changes in primary variables and mass/heat fluxes occur only at boundaries or well nodes. Consequently, these well nodes tend to be singular, leading to computational convergence problems. The conventional method of well treatment in geothermal or oil reservoir simulators is to use a sink/source term approach and distributes flow rates by a potential or mobility allocation scheme for a multilayered well. However, this traditional method cannot rigorously handle a backflow problem, which may occur in a multilayered well in heterogeneous formations. Any potential backflowing layer has its flow set to zero by the standard method, which may lead to a physically incorrect solution for well flow. This paper presents a “virtual node” method for treating well boundary conditions. This method handles a wellbore either as a single node or several computational nodes that are screened and connected to many neighboring nodes for a multilayered well. The wellbore can be vertical, inclined, or horizontal, and the well borehole node is treated in the same way as any other nonwell node for flow calculations. Pumping/injection conditions are accounted for using sink or source terms to the well node only. The solution at the well is then obtained by solving mass-balance equations for the well node. It will be shown that the new method provides a natural, physically consistent, and numerically efficient approach to handling well flow problems. In addition, implementation of this new method for a three-phase flow reservoir simulator will be discussed, and an application example will be provided.