\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}



\usepackage{float}








\begin{document}

\title{Are natural fractures pervasive?}



\author[1]{Weiwei Zhu}%
\author[2]{Gang Lei}%
\author[3]{Xupeng He}%
\author[4]{Yafan Yang}%
\author[5]{Ryan Kurniawan Santoso}%
\author[1]{Moran Wang}%
\affil[1]{Tsinghua University}%
\affil[2]{China University of Geosciences}%
\affil[3]{Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC)}%
\affil[4]{China University of Mining and Technology}%
\affil[5]{RWTH Aachen University}%


\vspace{-1em}



  
  \date{May 27, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Fractures and their connectivity are essential for fluid flow in low
perme-ability formations. Abundant outcrops can only provide
two-dimensional (2D) information, but subsurface fractures are
three-dimensional (3D). The percola-tion status of 3D fracture networks
and their 2D cross-section maps are rarely investigated simultaneously.
In this work, we construct 3D fracture networks with their geometries
characterized by different stochastic distributions. Then, we take
cross-section maps to mimic real outcrops and label clusters to check
the percolation status of 3D fracture networks and their 2D
cross-section maps. The properties, reflecting the connectivity of two
essential phases, are summarized and analyzed. We find that clustering
effects impact local intersections significantly but have negligible
impacts on fracture intensities of 3D fracture networks. The number of
intersections per fracture is not a proper percolation parameter for
complex 2D and 3D fracture networks. Fracture intensities are
scale-dependent and usually decrease with increasing scales. The real
fracture networks in the subsurface should be geometrically
well-connected and pervasive if their outcrop maps are well connected.
In particular, the fracture intensity of the real fracture network can
be several times (at least 3.6 times) larger than the intensity at
percolation. However, if outcrop maps are not well-connected, but their
intensities are large enough (at least 0.43 times as large as the
intensity at percolation), corresponding 3D fracture networks can also
form a spanning cluster and show good connectivity with a high
possibility.%
\end{abstract}%



\sloppy




\selectlanguage{english}
\FloatBarrier
\end{document}

