A mathematical model considering complex fractures and fractal flow for pressure transient analysis of fractured horizontal wells in unconventional reservoirs

• Fractal permeability and porosity were introduced to represent formation heterogeneity.
• Fractal dual-continuum flow mechanism is taken into consideration in the model.
• Five main transient flow regimes are recognized for fractal-trilinear flow model.
• Type curve for fractal pressure transient behavior was thoroughly examined.

This article is the first investigation on the fracture network heterogeneity flow for multiple fractured horizontal wells in unconventional reservoirs. Currently, most modeling approaches for multiple fractured horizontal wells are based on flow in several distinct scales (matrix/fracture), in which the network of fractures is assumed to be connected and equivalent to a homogeneous medium of Euclidean geometry. To account for more detailed description of unconventional reservoir, fractal permeability and porosity relationship was introduced to represent reservoir heterogeneity. Fractal flow in a dual-continuum porous medium is taken into consideration to establish a model of hydraulically fractured horizontal wells. The coupled fractal-based tri-linear diffusivity equation helps illuminate the reservoir performance and improve the pressure transient analysis. A tri-linear flow mathematical model is used to represent the flow in hydraulic fractures, in the formation between the fractures, and in the formation away from the hydraulic fractures. To solve the equations at different regions, we prescribe the proper boundary conditions and use Laplace transformation and numerical inversion from the Laplace domain to the time domain. The new semi-analytical solutions were validated via numerical simulations.The type curve of fractal pressure transient behavior was thoroughly examined; which were found to be primarily dependent on the value of the fractal parameters chosen. The proposed model could be used to diagnose the flow regime and interpret the pressure response more accurately for shale/tight oil reservoirs.