Productivity equations for oil wells in anisotropic reservoirs.

摘要

Well productivity is one of primary concerns in field development and provides the basis for field development strategy. Well productivity is often evaluated using the productivity index, which is defined as the production rate per unit pressure drawdown. We often relate the productivity evaluation to the long-time performance behavior of a well, that is, the behavior during pseudo-steady state or steady state flow.; This study examines the production performance of oil wells with constant flow rates in different shapes of anisotropic reservoirs, a library of new solutions to productivity equations is provided.; Well responses in a variety of reservoir models (circular, rectangular, sector, channel, etc.) are investigated. Wells may be located arbitrarily in an anisotropic reservoir, several combinations of closed and/or constant-pressure boundary conditions are considered at vertical and lateral reservoir boundaries.; The effects of permeability anisotropy on well performance are discussed. Convenient algorithms to calculate shape factor and pseudo skin factor due to partial penetration are provided. Comparison of different drive mechanisms is presented.; Steady state and pseudo-steady state productivity equations for multiple vertical wells system in a homogeneous, anisotropic reservoir are provided. Multiwell productivity index (MPI) is obtained by solving a square matrix equation of dimension n, where n is the number of wells. The proposed equations which relate the production rate vector to the pressure drawdown vector provide simple, accurate and fast analytical tools to evaluate well performance without dividing the cluster into single well drainage areas.