The dominate flow regime for multistage fractured wells in unconventional shale reservoirs is transient flow regime. Understanding the interplay between flow rates and the flowing pressures for different fracturing schemes and completions is critical knowledge required for production optimization. The well production can be optimized by adjusting the flowing bottom-hole pressure. The Inflow Performance Relationships (IPR) are based on the premise of pseudo-steady state flow regime that is inherently not applicable to transient flow; thus, this paper introduces a new empirical IPR model obtained by integrating a series of piece-wised pseudo-steady state flow regimes that occur as the drainage volume expands. The average reservoir pressure calculated within the dynamical drainage volume (DDV) at any given time is used to derive an IPR model.

A computer code is developed to evaluate the evolution of DDV using the macroscopic material balance equation. Fluid and rock compressibilities are the only production mechanism. The computer code is used for ten wells in the Niobrara shale oil play. The size of the DDV, associated average reservoir pressure, and transient productivity index are calculated. This newly derived empirical IPR is capable of predicting production performance

In practice, this paper provides an insight to understand the long-term transient flow regime and its impact on productivity of wells in shale plays. The method does not require comprehensive inputs, and can be used to optimize the design of multistage fractured wells.

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