The flexible control-volume finite-element (CVFE) method is used to co
nstruct hybrid grids. The method involves use of a local cylindrical o
r elliptical grid to represent near-well flow accurately while honorin
g complex reservoir boundaries. The grid transition is smooth without
any special discretization approximation, which eliminates the grid tr
ansition problem experienced with Cartesian local grid refinement and
hybrid Cartesian gridding techniques.