This study presents an integrated approach to evaluate the efficiency of fracturing stimulation and predict well production performance. As the pressure disturbance propagates throughout the reservoir during long-time transient flow regimes, it will shape an expanding drainage volume. A macroscopic “compressible tank model (CTM)” using weak (integral) form of mass balance equation is derived to relate dynamic drainage volume (DDV) and average reservoir pressure to production history in extremely shale reservoirs. Fluids and rock compressibility, desorption parameters (for shale or coal gas), and production rates control the speed at which the boundaries advance. After the changes of average reservoir pressure within the expanding drainage volume are obtained, a new empirical inflow performance relationship (transient IPR) correlation is proposed to describe well performance during long transient flow periods in shale reservoirs. This new empirical correlation shows better match performance with field data than that of conventional Vogel-type IPR curves. The integrated approach of both CTM model and transient IPR correlation is used to determine and predict the optimal fracturing spacing and the size of horizontal section for few wells from one of shale oil plays in U.S. The results suggest the existence of optimal fracture spacing and horizontal well length for multistage fractured horizontal wells in shale oil reservoirs. In practice, this paper not only provides an insight in understanding the long transient flow production characteristics of shale reservoirs using concept of expanding drainage volume. Neither methods require comprehensive inputs for the strong form (differential) nor any prior knowledge about the sophisticated shale reservoir features (shape, size, etc.), the ultimate drainage volume, the ultimate recovery, optimal fracture spacing, and the length of horizontal section for each well can also be easily obtained by this new integrated analytical method.

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