Approximate model for productivity of nonconventional wells in heterogeneous reservoirs

A semianalytical method is presented for the approximate modeling of the productivity of nonconventional wells in heterogeneous reservoirs. The approach is based on Green's functions and represents an extension of a previous model applicable for homogeneous systems. The new method, referred to as the s-k* approach, models permeability heterogeneity in terms of an effective skin s that varies along the well trajectory and a constant background permeability 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 effects due to wellbore hydraulics, is quite efficient in comparison to detailed finite-difference calculations. Results for the performance of nonconventional wells in three-dimensional heterogeneous reservoirs are computed using the s-k* approach and compared to finite-difference calculations resolved on the geostatistical fine grid. The new method is shown to provide an accurate estimate of wellbore pressure and production rate, as a function of position along the wellbore, for various well configurations and heterogeneous permeability fields. The possible use of the overall approach in a simulation while drilling (SWD) tool, in which the well path and trajectory are "optimized" using real-time data, is also discussed.