Establishment and Application of the Flowing Material Balance(FMB) Equation for Water-Drive Gas Reservoirs

Conventional flowing material balance methods are based on the assumption of closed gas reservoirs and do not account for the impact of water influx on reservoir performance. Consequently, when applied to water-drive gas reservoirs, these methods struggle to accurately identify and quantitatively evaluate the extent of water influx, which limits the depth of dynamic information that can be extracted from production data. To address this issue, the water invasion sweep efficiency coefficient was introduced to characterize the alteration of flow characteristics caused by water influx, and the deliverability equation for gas wells in the form of pseudo-pressure was modified. By jointly solving the Al-Hussainy pseudo-pressure expression, the modified deliverability equation, and the material balance equation for water-drive gas reservoirs, a flowing material balance equation suitable for water-drive gas reservoirs was established. The research results indicate that: The new equation reveals that for gas wells in water-drive reservoirs experiencing different stages of water influx, a strict linear relationship always exists between the normalized pseudo-pressure and the normalized gas production rate. This provides a theoretical basis for the dynamic diagnosis of water influx. Based on this linear relationship, by utilizing the daily production data of gas wells and fitting the data points to approach the theoretical straight line through trial calculations, the dynamic reserves of the gas well, the water invasion sweep efficiency coefficient, and the cumulative water influx can be determined simultaneously. Furthermore, the coefficient of the Darcy flow term in the pseudo-pressure deliverability equation can be dynamically corrected, enabling a quantitative evaluation of water influx. The application to example gas wells in the Sichuan Basin verifies the reliability of the new equation, with actual data points falling well onto the theoretical straight line. It is concluded that the newly established flowing material balance equation provides a dynamic analysis tool for water-drive gas reservoirs that integrates real-time water influx diagnosis with quantitative evaluation. This method effectively enhances the utilization value and mining depth of production data. It holds significant theoretical guidance and strong potential for practical application in the development performance evaluation of piston-like water-drive gas reservoirs. Developing a flowing material balance method for complex, heterogeneous water invasion will be a key focus of future research.