A Semi-Analytical Approach for Calculating Productivity Index in Vertical Flowing Well: High Gas-Oil Ratio Field Data as a Case Study

The concurrent transport of hydrocarbon, water, and most times solids ensues all through the production system concerned in transporting multiphase fluid from the producing reservoir zone to the wellbore and then to surface. The flow capacity of a well can be estimated through the inflow performance relationship (IPR) that essentially depends on productivity index (PI). Productivity index is a vital and indispensable oil and gas industry tool for forecasting the deliverability and helps in economic feasibility studies of the well. The lack of a correct model for bottom-hole flowing pressure calculation has always been a challenge and results in erroneous estimate of productivity index of a production well. Numerous models on bottom-hole flowing pressure in wells have been recounted in different literatures over the years. Many of the earlier works were based on steady-state flow assumption, likewise not all the constituent terms that practically influence flow behavior of fluid in pipe were considered in derivation of the past models. In the present work, an enhanced semi-analytical model for determining well bottom-hole flowing pressure is offered where all the constituent terms practically influence flow behavior of fluid in pipe and employed in building the new model for estimating productivity index in a vertical well. This article builds a semi-analytical model for predicting flowing pressure at every flow transition period evidencing the water hammer pressure fluctuations often experienced at the start-up operation. Subsequently, the time-dependent flowing pressure obtained from the newly derived model was used to estimate the productivity index using high gas-oil ratio surface data from Niger Delta field. The result of productivity index obtained at steady-state period shows that the average prediction percentage error of the current approach is reduced to 3.78% compared to previously derived steady-state-based model by Guo et al. (2007, “A Rigorous Composite-IPR Model for Multilateral Wells,” Society of Petroleum Engineers, SPE 100923, San Antonio, TX, p. 11), Guo (2001, “Use of Wellhead-Pressure Data to Establish Well-Inflow Performance Relationship,” SPE Eastern Regional Meeting, Canton, OH, Oct., SPE 72372, p. 7), and Adesina et al. (2018, “A Realistic Model for Estimating Productivity Index of Vertical Well Using Wellhead Data,” Society of Petroleum Engineers, SPE-193506-MS) that, respectively, report as 18.59%, 5.23%, and 3.96%. The factors that influence the magnitude of water hammer pressure fluctuation at the start-up period have been identified through the derivation. The semi-analytical model improves the prediction accuracy and aids the reliability of design to avoid incidence of pipe burst due to pressure peak and serves as a tool to analyze the well performance.