A NEW FRACTAL TEMPORAL CONDUCTIVITY MODEL FOR PROPPED FRACTURE AND ITS APPLICATION IN TIGHT RESERVOIRS

Abstract

Current hydraulic fracture conductivity evolution models fail to incorporate the fractures microscopic petrophysical properties, and notable discrepancies consequently exist between predictions and observations. We present a new conductivity model considering the irregular fracture undulation and channel roughness in propped fractures. The propped fracture networks are treated as bundles of tortuous capillaries with a fractal distribution of sizes with the size of a single capillary calculated using a constitutive model representing contacting rock surfaces under normal cyclic loading. The capillaries tortuosity is described by the effective inclination angle, and the fracture closure is calculated by the history of the in situ stress distribution and rock property changes. The fracture surface roughness, number of capillaries per unit width of the hydraulic fracture, and total cross-sectional area are obtained using fractal theory. The proposed model is validated by comparison with experimental data and other analytical solutions. The results indicate that the apparent permeability and conductivity of the fracture significantly decrease to 58.0% and 48.2% within 2 years of production, respectively, and then remain steady for the remainder of the well life. Compared with fixed fracture conductivity, the temporal variability in conductivity leads to a lower formation pressure drop and reduction in final production. Furthermore, the influences of the effective inclination angle, relative roughness of micro-channel, fracture porosity, and microchannel fractal dimension on the conductivity are investigated and the conductivity proves to be largely controlled by the fracture porosity, while the influence of the relative roughness ratio on the conductivity is least significant.