This paper adopts an empirical-analytical hybrid model of dynamic drainage volume (DDV) into a novel workflow of integrated production analysis to evaluate and predicate the performance of multi-stage fractured horizontal well (MFHW). A weak (integral) form of macroscopic mass balance model with moving boundary is developed for the expanding productive region (drainage volume) during long-term transient-flow regimes in non-static shale reservoirs saturated with compressible fluids. An analytical-empirical formulation of DDV is derived using concept of impulse response and multi-variable regression method, which includes the effects of different diffusivity within both stimulated-reservoir volume (SRV) and unstimulated matrix, fracture half-length, and fracture spacing etc. The effects of stress-dependent reservoir and pressure-dependent fluid properties on production analysis are incorporated by a pressure-dependent correction factor. To verify the accuracy of our integrated analysis, firstly, we start with a synthetic simulation example with known parameters. In the next stages, several field examples are examined with our integrated analysis approach to evaluate and predicate the performance of MFHW.
The size of DDV and associated average reservoir pressure, recovery factor (RF) and phase saturation (oil/gas/water) are achieved. The half-length of primary fracture and diffusivity within SRV are also evaluated by coupled with a correction factor, and the ultimate drainage volume (estimated as ultimate recovery, EUR) is also predicated at abandonment condition, which indicates the maximum size of system affected by single-well production for us to optimize well spacing. Moreover, the contributions of both unstimulated-reservoir matrix and stimulated-reservoir volume (SRV) are quantified with changing time, respectively.
The proposed approach has the following novel contributions: (1) capability to ascertain DDV and associated average reservoir pressure throughout different transient-flow regimes; (2) coupled the non-static, fluid compressibility, multi-phase flow and moving flow boundary effects into production history analysis; and 3) simplicity and efficiency; does not require comprehensive inputs as opposed to sophisticated numerical simulations, but could obtain almost all of the necessary parameters for evaluation and predication.