A hybrid model for the combined impact of non-Darcy flow, stimulated matrix permeability, and anomalous diffusion flow in the unconventional reservoirs

A hybrid model for unconventional gas reservoirs that couples three different parameters is presented in this paper. The first is the anomalous diffusion in a fractal porous media. The second is the stimulated or induced matrix permeability in the stimulated reservoir volume (SRV). The third is the non-Darcy flow permeability in the hydraulic fractures. This model is generated from the multi-linear flow model for fractal reservoirs controlled by diffusive flow mechanism with adjustment for fluid flux through hydraulic fracture face considering minimum fracture relative permeability (k_mr) and non-Darcy flow Number (F_ND).

Pressure distributions, flow regimes, and reservoir performances have been investigated for three types of unconventional reservoirs. The first is formations with homogenous matrix permeability where petrophysical properties of stimulated and un-stimulated reservoir volume are the same. The second is fractal reservoirs with different petrophysical properties in the two volumes without considering normal or classic diffusion mechanism. The third is the fractal reservoirs where anomalous diffusive flow mechanism dominates fluid flow. A set of comparisons has been generated between the three types for better understand the impact of non-Darcy flow permeability and stimulated matrix permeability on reservoir performance under normal and anomalous diffusion flow mechanisms.

The outcomes of this study are: (1) Generating a new analytical model that describes pressure distribution in fractal unconventional reservoirs and couples non-Darcy flow, stimulated or induced matrix permeability with the anomalous diffusion in porous media. (2) Understanding the impact of these different parameters on reservoir performance. (3) Developing different models for all types of flow regimes that are expected to be observed during the entire production life. (4) Comparing the productivity index of reservoirs: having homogeneous matrix permeability, fractal with normal diffusion, and fractal with anomalous diffusion. The most interesting points in this study are: (1) Minimum fracture relative permeability (k_mr) significantly enhances the productivity index by eliminating the impact of non-Darcy flow while non-Darcy flow number (F_ND) works conversely (2) Increasing stimulated matrix permeability enhances reservoir performance (3) The impact of non-Darcy flow permeability of hydraulic fractures is seen at early and intermediate production time where transient flow is dominant. (4) Two different trends are recognized for the impact of anomalous diffusion flow: the first is a positive impact on the transient flow period and the second is negative in the pseudo-steady state flow.