Numerical Simulation of An In-situ Fluid Injection Experiment into a Fault Using Coupled X-FEM Analysis

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ORIGINAL PAPER

Numerical Simulation of An In‑situ Fluid Injection Experiment into a Fault Using Coupled X‑FEM Analysis Adam K. Schwartzkopff1   · Atsushi Sainoki1 · Derek Elsworth2  Received: 1 April 2020 / Accepted: 31 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020

Abstract Fluid injection into a rock mass from industrial processes can cause perceivable seismic events that may raise public concern and affect the mechanical and physical properties of the rock mass. One such notable source of seismicity is from the additional fluid pressure added to the rock mass causing slip on faults. The aim is to provide a method to predict efficiently the fault mechanics due to anthropogenic fluid injection. This was achieved by extending a two-dimensional fully coupled fluid and mechanical loading extended finite element method (X-FEM) formulation via development of a standalone code in Matlab. This code considers fluid flow along the fault as well as into the rock mass and uses a directly proportional equivalent injected flow rate into the fault as the input. This model was validated by comparing the resultant pressure, normal and tangential displacements at the center of the fault to a previously published in-situ experiment. The main results were that the mechanics of the fault could be simulated with sufficient accuracy using this approach given appropriate assumptions, measurements, and simplifications of the fault and rock properties. The main conclusion is that this coupled X-FEM approach may provide an efficient and accurate method to assist in predicting the fault mechanics due to fluid injection. These results are important, since it shows the applicability of X-FEM in predicting the mechanics of the fault and hence the applicability of this method to predict seismicity due to fluid injection. Keywords  Fault mechanics · Simulation · Coupled X-FEM · Induced seismicity Abbreviations DDM Displacement discontinuity method DEM Distinct element method DOF Degrees of freedom FEM Finite element method FLAC Fast Lagrangian analysis of continua software NoF Number of fractures traversing the borehole section used for fluid injection PEST Parameter estimation software suite SIMFIP Step-rate injection method for fracture in-situ properties Tough A multiphase flow simulator

* Adam K. Schwartzkopff aschwartzkopff@kumamoto‑u.ac.jp 1



International Research Organization for Advanced Science and Technology, Kumamoto University, Kumamoto, Kumamoto Prefecture 860‑8555, Japan



Department of Energy and Mineral Engineering, G3 Centre and Energy Institute, The Pennsylvania State University, University park, PA 16802, USA

2

UDEC Universal distinct element code X-FEM Extended finite element method List of symbols 2h Hydraulic aperture (m) 2h0 Initial hydraulic aperture (m) 2hm Normal mechanical displacement (m) 𝐚j (t) Enriched nodal DOF associated with the Heaviside function at node j a Empirical coefficient that controls the magnitude of the velocity frictional response 𝐛 Body force ve