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The objective of this work is to present a new IPR model for transient well simulations that gives precise results without the high computational costs of the reservoir finite difference simulation. The limitations of using conventional IPR models for transient well simulations, specifically for oscillatory wells experiencing severe slugging or casing heading phenomena, are evidenced. The flow rate calculated with the IPR might significantly differ from the results obtained with the reservoir finite differences model for periodic bottom-hole pressures. Analytical solutions of a radial homogeneous reservoir were developed (both in time and Laplace domain) and they were used to generate its frequency response. A low order transfer function that approximated this frequency response was generated, which was named "Dynamic IPR". Adequate boundary conditions are essential to obtain a precise result for transient well simulations. The conventional IPR models are frequently employed as the bottom-hole boundary conditions to represent the reservoir response even in transient simulations. Another possibility is to couple the reservoir finite difference model with the well and solve them simultaneously, when the IPR transient response is known to be inaccurate. A new alternative approach, the Dynamic IPR, is presented as a low order system of ordinary differential equations that can be applied for oscillatory wells and supposedly for any transient simulation without complex reservoir behavior such as coning for example. The Dynamic IPR was compared with the two analytical solutions (the deconvolution of the Laplace domain solution was performed with the Iseger algorithm) and the conventional IPR. A sinusoidal bottom-hole flowing pressure was assumed and the corresponding liquid flow rates were calculated. The liquid flow rates determined from the transfer function were almost identical to the exact results and the computational costs incredibly lower than performing finite differences in cases in which the conventional IPR presented poor results. This work emphasizes that there are some situations for which the IPR are inadequate and presents simple procedures to determine when that is the case. Most importantly, the proposed Dynamic IPR can be easily included in any transient simulation and greatly improve the results. |
