In this paper we present an application of the recently developed control
volume function approximation (CVFA) method to the modeling and simulation
of 2D and 3D horizontal wells in petroleum reservoirs. The base grid for this
method is based on a Voronoi grid. One of the features of the CVFA is that
the flux at the interfaces of control volumes can be accurately computed via
function approximations. Also, it reduces grid orientation effects and applies
to any shape of elements. It is particularly suitable for hybrid grid reservoir
simulations. Through extensive numerical experiments and comparisons with the
finite difference method for benchmark flow problems, we show that this method
can effciently and accurately handle complex horizontal wells in any direction.