Mathematical Modeling of Hydraulic Fracture Formation and Cleaning Processes

Abstract

The effectiveness of the hydraulic fracturing procedure is crucially dependent on the stage of fracture planning and design. Forecasting fracture behavior in rock formations characterized by non-uniform toughness is a serious challenge. In the present paper, a planar-3D model considering the rock’s non-uniform fracture toughness has been developed for the uneven propagation of a hydraulic fracture. The series of numerical experiments were designed to study the effect of inhomogenous fracture toughness. The results show that the fracture toughness contract significantly controls the overall direction of fracture propagation, and a combination of toughness contrast and the proportion between the pay zone and barrier zone determine the fracture profile: from almost circular with or without a pair of narrow wedges when the proportion is small to almost rectangular otherwise. This paper also discusses the process of cleaning a fracture from hydraulic fracturing fluid by oil. Using numerical modeling on the basis of the constructed mathematical model, a relationship is established between the quality of hydraulic fracture cleaning and the geometrical parameters of the fracture and the region filled with the hydraulic fracturing fluid. The results of numerical experiments show that while fracturing fluid is more viscous than oil, the length of the fracture has a greater influence on the cleaning process than the viscosity of the fracturing fluid.

A Planar-3D Mathematical Model for Studying the Effect of Heterogeneity of Rock Fracture Toughness on Hydraulic Fracture Propagation: Early-Time Solution including the Stage before Propagation

“…Generally, there are two different injection modes in experiments or practices: the constant volumetric velocity of injection and the constant fluid pressure at the wellbore. In this model we chose the first mode, namely, Q(t) = Q 0 as a constant, so the boundary condition at the wellbore was formulated as [52]:…”

“…The study of stress intensity factors for branching cracks in three-dimensional space was performed [49][50][51]. In addition, the formation and cleaning of hydraulically driven fractures in 3-D space was discussed in some studies [52,53].…”