A Semi-Analytical Model to Simulate Fluid Flow in Fractured Reservoirs

Abstract

A semi-analytical simulator has been developed to describe single-phase gas flow in hydraulically fractured wells hosted by naturally fractured rock. The governing formulation embeds Streltsova’s unsteady-state matrix-transfer function to fracture directly in a dual-porosity finite difference framework and advances the solution with an implicit–explicit scheme. This strategy preserves the analytical description of transient exchange, while avoiding the convolution integrals and tight time-step controls that burden fully numerical unsteady-state models. Both pseudo steady-state and unsteady-state transfer functions can be invoked with different shape factor and we use the logarithmic spaced, local grid refinement methodology to consider the hydraulic fracturing effects that occur near well at minimal computational cost. The simulator was tested on homogeneous, discretely segmented, and fully heterogeneous synthetic reservoirs under constant rate and constant pressure production. In every case, the unsteady-state option reproduced the characteristic early-time pressure transients and matrix-fracture flow that the classical Warren–Root’s model with the pseudo-transitory transfer function may not capture. Compared with a published hybrid numerical–analytical workflow for same shape factor, the new implementation is faster than twelve times, while presenting good pressure behavior and maintaining numerical precision. Because the transfer function remains analytical, computational effort scales only with fracture count and not with matrix grid density, making the approach well suited to large, heterogeneous unconventional plays as well as geothermal and subsurface storage applications. The tests confirm that the method achieves the desired balance between physical fidelity and computational efficiency, providing a robust tool for transient flow analysis and production-strategy optimization in fractured reservoirs.

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