Pseudotransient Linear Flow in Naturally Fractured Reservoirs

Abstract

Abstract Most unconventional reservoirs are characterized by an ultra-tight matrix and commercial production requires existence of a pervasive fracture network surrounding hydraulically fractured horizontal wells. Production behavior of fractured horizontal wells in these reservoirs is usually associated with natural-fracture dominated linear flow, which is diagnosed by a ½-slope straight line on log-log coordinates. This paper shows that additional pseudotransient linear flow regimes are possible at late-intermediate times with the same conventional diagnostic features of linear flow. These flow regimes correspond to the physical conditions (i) where the flow in the matrix is pseudosteady while the natural fractures have transient flow or (ii) where the natural fractures experience boundary dominated flow concurrent with transient flow in the matrix. An analytical solution is provided with a suite of tools to analyze transient and pseudotransient linear flows. The solution is based on the trilinear model with a stimulated reservoir volume (SRV) idealized by the transient, dual-porosity slab assumption. The model is a proxy for some tight-oil plays, such as the Eagle Ford, Bakken, and Niobrara, where thin layers of fractured carbonates providing the flow capacity are interbedded by layers of tight shale or marl, which act as the storage medium. Asymptotic solutions are derived for linear and bilinear flow regimes and conditions for their existence and start and end times are provided. Simulated examples indicate that confusing pseudotransient linear flow with the conventional linear flow creates up to three orders of magnitude differences in the estimates of permeability, fracture half-lengths, or the size of the SRV. Application of the analysis is also demonstrated on real data from an unconventional well.