A COUPLED WELLBORE-RESERVOIR FLOW MODEL FOR NUMERICAL PRESSURE TRANSIENT ANALYSIS IN VERTICALLY HETEROGENEOUS RESERVOIRS

Pressure transient analysis in vertically heterogeneous reservoirs is examined. The inclusion of a separate model for the free fluid flow in the wellbore is essential to allow for hydraulic communication and mixing of the fluid issuing from different reservoir layers. A two-dimensional model coupling Darcy flow in the reservoir with Navier-Stokes flow in the wellbore is developed and solved by the finite element technique. The coupled wellbore-reservoir flow model is used to analyze a layered reservoir with an abrupt change in permeability and a thick formation showing a gradual change in permeability with depth. Contrary to conventional reservoir models, this new model is able to capture the wellbore storage effect directly and can handle wells with partial or complete perforations. The results obtained show that the coupled wellbore-reservoir model enables the development of numerical well test procedures capable of predicting the extent of vertical heterogeneity in both isotropic and anisotropic formations.