Approximate model for productivity of nonconventional wells in heterogeneous reservoirs

A semianalytical method is presented for the approximate modeling of the pr oductivity of nonconventional wells in heterogeneous reservoirs. The approa ch is based on Green's functions and represents an extension of a previous model applicable for homogeneous systems. The new method, referred to as th e s-k* approach, models permeability heterogeneity in terms of an effective skin s that varies along the well trajectory and a constant background per meability k*. The skin is computed through local, weighted integrations of the permeability in the near-well region and is then incorporated into the semianalytical solution method. The overall method, which can also model ef fects due to wellbore hydraulics, is quite efficient in comparison to detai led finite-difference calculations. Results for the performance of nonconventional wells in three-dimensional h eterogeneous reservoirs are computed using the s-k* approach and compared t o finite-difference calculations resolved on the geostatistical fine grid. The new method is shown to provide an accurate estimate of wellbore pressur e and production rate, as a function of position along the wellbore, for va rious well configurations and heterogeneous permeability fields. The possib le use of the overall approach in a simulation while drilling (SWD) tool, i n which the well path and trajectory are "optimized" using real-time data, is also discussed.