A 3D numerical model is presented to analyze the gas flow behavior in hydraulically fractured horizontal wells in anisotropic heterogeneous naturally fractured reservoirs with triple porosity (organic and inorganic matrix, and a fracture network). This model generalizes the models proposed previously in the technical literature because it integrates the effects of fractality, present in the stimulated reservoir volume (SRV), triple-porosity, slip and viscous flow, Knudsen diffusion, kerogen adsorption/desorption from the organic pore walls, geomechanics effects, anisotropy, and anomalous diffusion.

An SRV with improved petrophysical properties of the original natural microfracture network, represented by anisotropic and heterogeneous fractal distributions around each of the hydraulic fractures, is considered, and a consistent matrix shape factor distribution is proposed. The model also includes the presence of anomalous diffusion both in the natural fracture network and in the organic and inorganic matrices through the application of the Caputo fractional derivative, geomechanical effects of production on petrophysical properties, correction in apparent permeability with slip and viscous flow, Knudsen diffusion, the adsorption-desorption process of kerogen from organic pore walls, and high velocity flow in hydraulic fractures.

The accuracy of the model is verified using approximate analytical solutions, previously presented in the literature, and asymptotic cases by means of a commercial simulator. The different periods of flow are identified in the determined numerical solutions.

The results indicate that the shape of the rate and pressure decay curves are causally related to the anisotropic fractal exponents and the order of the fractional derivatives, which represent the density and connectivity of natural fractures within the SRV and the degree of anomalous diffusion, respectively.

At long producing times, the decrease in gas pressure produces an improvement in the apparent permeability due to the sliding effect in both the organic and inorganic matrices. The desorption of gas from the organic walls also contributes to the production.

The proposed model presents for the first time the production behavior which considers the anisotropic permeability behavior of the SRV using the fractal geometry, with associated distributions of porosity and matrix shape factor, and combines these petrophysical properties with the effects of triple-porosity, different scale-dependent transport mechanisms, geomechanics, and anisotropic anomalous diffusion.

The practicality of using all these characteristics together for reservoir simulation is demonstrated and evaluated in relation to the benefits of obtaining more realistic production scenarios.

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