A novel model for predicting the productivity index of horizontal/vertical wells based on Darcy's law, drainage radius, and flow convergence

Abstract

The Productivity Index (PI) of oil wells is essential to developing a field's production plan, and previous studies report different models for predicting the PI of horizontal or vertical wells. However, predicting the PI of horizontal and vertical wells using a single cost-effective model remains unaccomplished. The models only predict results for either box-shaped or circular reservoirs. Thus, this study reports a new model for predicting the PI of horizontal and vertical wells in any reservoir type. The model incorporates the length of the horizontal section and formation thickness to Darcy's equation, and forms empirically the external drainage radius using vertical and horizontal radii. It includes both geometric pseudoskin (accounting for fluid convergence) and empirically determined correction parameters. The derived PI is validated using data from box-shaped and circular reservoirs, and the results showed that changes in permeability, well length, or well radius affect the PI for both reservoir types. In addition, the drainage radius of the horizontal well increased non-linearly with the PI. Sensitivity analyses of 20,000 runs and 20,000 trials, carried out with the Crystal Ball software, showed that the viscosity and formation volume factor were the most important variables that affected the PI, for both reservoir types.