Abstract
Summary The network of induced fractures and their properties control pressure propagation and fluid flow in hydraulically fractured shale reservoirs. We present a novel fully fractal model in which both the spacing and the porosity/permeability of induced fractures are distributed according to fractal dimensions (i.e., fractal decay of fracture density and the associated porosity/permeability away from the main induced fracture). The fractal fracture distribution is general, and handles exponential, linear, power, and uniform distributions. We also developed a new fully fractal diffusivity equation (FDE) using the fractal distribution of fractures and their properties. We then used, for the first time, the semianalytic Bessel spline scheme to solve the developed diffusivity equation. Our proposed model is general and can capture any form of induced-fracture distribution for better analysis of pressure response and production rates at transient- and pseudosteady-state conditions. We compared the unsteady-state and pseudosteady-state pressure responses calculated by our fully fractal model with former models of limited cases: uniform fracture spacing and uniform porosity/permeability [conventional diffusivity equation (CDE)]; variable fracture spacing and uniform porosity/permeability [modified CDE (MCDE)]; and uniform fracture spacing and fractal porosity/permeability distribution (FPPD). We used these models to match and predict the production data of a multifractured horizontal gas well in the Barnett Shale. Our results showed that the fractal distribution of fracture networks and their associated properties better matches the field data. Uniform distribution of induced-fracture networks underestimates production rate, especially at early time.
Published Version
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