Conventional IPR models are used in coupled wellbore-reservoir transient simulations, even if bottomhole pressure conditions are assumed to be constant on the derivation of such IPR models. The dynamic IPR model proposed in this paper not only captures the relevant reservoir dynamics from the well perspective, but is also computationally more efficient than discretized models using hundreds of gridblocks to simulate the near wellbore region.
Any well-behaved function can be decomposed in a combination of sinusoidal functions. Hence, a sinusoidal bottomhole flowing pressure with a frequency varying from a given value down to zero is assumed as a boundary condition to the hydraulic diffusivity equation. The zero frequency corresponds exactly to the conventional IPR model since it is the steady-state condition. The analytical solution that calculates the flow rate for the sinusoidal pressures for each one of the frequencies is presented. Finally, the Dynamic IPR is defined as the low-order, linear ordinary differential equation that best approximates this solution.
It is a well known fact that the reservoir dynamics is relevant to the calculation of the flow rate in certain conditions, such as drawdown and pressure buildup well tests. A comparison between the Dynamic IPR function, the conventional IPR models, and the analytical solution is presented for these cases. The conventional IPR model gives unrealistic results, since it allows the flow rate to change instantaneously to the next equilibrium condition, as opposed to the Dynamic IPR which can capture the fully transient response. The Dynamic IPR showed excellent agreement with the true solution. Two different examples are presented in this paper showing the application of the Dynamic IPR: a reservoir well testing and a severe slugging well. With a given measured bottomhole flowing pressure, a comparison between the Dynamic IPR, conventional IPR and a reservoir simulation is presented. Once again, the conventional IPR model provides unsatisfactory results when compared to the Dynamic IPR. These results showed that neglecting reservoir dynamics in transient simulations might result in inadequate production forecasts, inefficient designs and eventually unsafe operations while using conventional IPR models.
This work points out some limitations in one of the common practices in the industry, which is the use of steady state IPR for coupled wellbore-reservoir transient simulations. The alternative Dynamic IPR herein proposed is computationally inexpensive when compared to discretized reservoir models while still being able to capture the transient well behavior and the steady-state solution.