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\begin{document}

\title{Numerical Study of the Impacts of Increased Ductility on Hydraulic
Fracturing in Organic-rich Shale}



\author[1]{Chang Huang}%
\author[1]{Shengli Chen}%
\affil[1]{Louisiana State University}%


\vspace{-1em}



  
  \date{June 18, 2024}


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\begin{abstract}
The research on increased ductility of organic-rich shale and its
impacts on hydraulic fracturing has received relatively little
attention. According to recent experimental studies, the popular
cohesive zone model that only features decreasing traction along with
crack separation may not adequately represent the crack behavior in
shale due to ample organic matter. This paper starts by proposing a
modified cohesive zone model that can represent various
traction-separation laws (TSL) within a unified formulation. Then a
fully coupled poroelastic XFEM framework to simulate hydraulic
fracturing in organic-rich shales was developed in Matlab and
comprehensively verified against the latest analytical solutions. The
influences of increased ductility in different forms were studied using
the modified cohesive zone model in the context of field-scale hydraulic
fracturing simulations. Three important conclusions were drawn. First,
the shape of TSL does affect the hydraulic fracturing given the same
cohesive crack energy and tensile strength. It suggests that ductility
is not only controlled by cohesive crack energy and tensile strength,
which further indicates the necessity of the newly proposed TSL. Second,
the tensile strength, controlling when the cohesive crack starts
propagating, has the greatest impact on the hydraulic fracturing, among
all TSL shape parameters. The impacts of TSL parameters become less
significant as the fracturing fluid viscosity increases. Lastly, Young's
modulus is the only one among four common poroelastic parameters that
significantly changes the ductility/brittleness of rock formation and
hydraulic fracture lengths. The increase in cohesive energy accompanied
by the decrease of Young's modulus will greatly reduce the induced
fracture length.%
\end{abstract}%



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