Numerical investigation of the fluid lag during hydraulic fracturing

Abstract

Purpose The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag evolution, the transition between different stages and their coupling with dynamic fracture propagation under common conditions. Design/methodology/approach A plane 2D model is developed to simulate the complex evolution of fluid lag during the propagation of a hydraulic fracture driven by an impressible Newtonian fluid. Based on the finite element method, a fully implicit solution scheme is proposed to solve the strongly coupled rock deformation, fluid flow and fracture propagation. Using the proposed model, comprehensive parametric studies are performed to examine the evolution of fluid lag in various geological and operational conditions. Findings The numerical simulations predict that the lag ratio is around 5% or even lower at the beginning stage of hydraulic fracture under practical geological conditions. With the fracture propagation, the lag ratio keeps decreasing and can be ignored in the late stage of hydraulic fracturing for typical parameter combinations. On the numerical aspect, whether the fluid lag can be ignored depends not only on the lag ratio but also on the minimum mesh size used for fluid flow. In addition, an overall mixed-mode fracture propagation factor is proposed to describe the relationship between diverse parameters and fracture curvature. Research limitations/implications In this study, relatively simple physical models such as linear elasticity for solid, Newtonian model for fluid and linear elasticity fracture mechanics for fracture are used. The current model does not account for such effects like leak off, poroelasticity and softening of rock formations, which may also visibly affect the fluid lag depending on specific reservoir conditions. Originality/value This study helps to understand the effect of fluid lag during hydraulic fracturing processes and provides numerical experience in dealing with the fluid lag with finite element simulation.

Coalescence of thermal fractures initiated at parallel cooling surfaces

“…The mixed-mode fracture propagation governed by the theory of linear elastic fracture mechanics is assumed to be quasi-static. According to the maximum tensile-stress criterion (Chen et al ., 2018; Erdogan and Sih, 1963), fracture propagation occurs when the following condition is satisfiedwhere KI and KII are the Mode I and Mode II stress intensity factors, respectively, and KIc is the rock toughness. The propagation direction θ is determined bywhere function sgn() returns 1, 0 and − 1 for positive, zero and negative input.…”

A Review of Hydraulic Fracturing Simulation

“…A significant difference from previous models is that the LEFM theory is used as the fracture propagation criterion. Chen et al [51] developed a unified FEM-based model to simulate the hydraulic fracturing with and without fluid lag. By transferring between two different boundary conditions for the case with and without fluid lag, the fluid front and fracture tip are tracked accurately and the complex evolution of fluid lag (decrease, increase, vanishment and initiation) is successfully simulated.…”

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

“…For the FEM analyses, rock deformation is governed by the linear elasticity theory and fracture propagation is governed by the LEFM. The stress intensity factor is computed according to the interaction energy integral method (Chen, Cen, et al, 2018;Menouillard & Belytschko, 2010). ], as used in Tarasovs and Ghassemi (2014).…”