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Numerical investigation of the fluid lag during hydraulic fracturing

Bin Chen (Energy Safety Research Institute and Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea, UK)
Song Cen (Department of Engineering Mechanics and Key Laboratory of Applied Mechanics, Tsinghua University, Beijing, China)
Andrew R. Barron (Energy Safety Research Institute, College of Engineering, Swansea University, Swansea, UK and Department of Chemistry and Department of Materials Science and Nanoengineering, Rice University, Houston, USA)
D.R.J. Owen (School of Engineering, University of Swansea, Swansea, UK)
Chenfeng Li (Energy Safety Research Institute and Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 24 August 2018

Issue publication date: 5 September 2018




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.


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.


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.


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.



Chen, B., Cen, S., Barron, A.R., Owen, D.R.J. and Li, C. (2018), "Numerical investigation of the fluid lag during hydraulic fracturing", Engineering Computations, Vol. 35 No. 5, pp. 2050-2077.



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