A Semi-Analytical Model for Studying the Transient Flow Behavior of Nonuniform-Width Fractures in a Three-Dimensional Domain

In the fracture propagation model, the assumption that hydraulic fractures with non-uniform widths have been successfully utilized to predict fracture propagation for decades. However, when one conducts post-fracture analysis, the hydraulic fracture is commonly simplified with a uniform width, which is contradictory to the real fracture models. One of the reasons for over-simplifying the fracture geometry in the post-fracture analysis can be ascribed to the fact that we are still lacking a model to characterize the pressure transient behavior of the nonuniform-width fractures which can induce three-dimensional flow around the fractures. In this work, on the basis of the Green function and Newman product method, the authors derived a semi-analytical model to account for the effect of non-uniform width distribution of the hydraulic fractures in a three-dimensional domain. In addition, the effect of the fracturing strategies on the well performance is investigated based on the developed semi-analytical model. The calculated results from the developed model show that the vertical flow in the vicinity of the fracture cannot be neglected if the fracture height is sufficiently small (e.g., h f = 10 m), and one can observe vertical elliptical flow and vertical pseudo-radial flow during the production. A nonuniform-width fracture can penetrate further into the reservoir with a lower injection rate (e.g., q i = 1.44 × 10 3 md). For the scenarios of high fracture permeability (i.e., k f = 1 × 10 5 md), a smaller fracture height, lower injection rate, and larger Young’s modulus can be more favorable for enhancing the well productivity. Compared to the influence of fracture height, the influences of injection rate and Young’s modulus on the well performance are less pronounced.