Pressure Responses of a Vertically Hydraulic Fractured Well in a Reservoir with Fractal Structure

TL;DR

This paper develops an analytical model for pressure transient analysis of a hydraulic fractured well in a fractal reservoir, incorporating reservoir heterogeneity via fractional calculus to better understand pressure behavior.

Contribution

It introduces a novel analytical solution that accounts for fractal reservoir heterogeneity using fractional derivatives, advancing pressure analysis methods.

Findings

Reservoir heterogeneity significantly affects pressure responses.

Fractional calculus effectively models memory effects in fractal reservoirs.

The model provides insights into pressure behavior under various parameters.

Abstract

We obtain an analytical solution for the pressure-transient behavior of a vertically hydraulic fractured well in a heterogeneous reservoir. The heterogeneity of the reservoir is modeled by using the concept of fractal geometry. Such reservoirs are called fractal reservoirs. According to the theory of fractional calculus, a temporal fractional derivative is applied to incorporate the memory properties of the fractal reservoir. The effect of different parameters on the computed wellbore pressure is fully investigated by various synthetic examples.