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\title{Rock Physics simulations using core data to estimate the stiffness   tensor in Vaca Muerta organic-rich mudrock}

\subtitle{SEG International Meeting, Houston, August 29  2023} 
\author{{\bf Juan E. Santos},}%${^\dag}$ }
\institute{% 
Universidad de Buenos Aires (UBA),  Argentina, Hohai University, Nanjing, China and Purdue University, Indiana, USA.\\
 {\color{blue} In collaboration Sanchez Camus (Solaer Ingemier\'\i a, UNLP),  P. M. Gauzellino (UNLP)  G. B. Savioli (UBA) and 
 J. Ba (Hohai  University) } 
} 

%\author{Pepe}
%\institute{% 
%UBA. }
\AtBeginSubsection[]
{
  \begin{frame}<beamer>
    \frametitle{Sketch of the talk}
    \tableofcontents[currentsection,currentsubsection]
  \end{frame}
}



\begin{document}


\begin{frame}
  \titlepage
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small characterization of ultra-low permeability,
organic-rich mudrock reservoirs. I}}
{\small
\begin{itemize}



\item This work presents   a methodology to characterize and analyze 
 the lower section of the Vaca
   Muerta Formation (VMF) in the Neuqu\'en Basin, Argentina.
   
\item A core sample extracted at depth 3100 m  was dried under
laboratory conditions.

\item Ultrasonic phase velocity measurements  conducted at a frequency
of 1 MHz,  exhibited a clear {\color{blue} vertical transverse anisotropy (VTI)} behavior in the formation.

\item VMF has a  stratified microstructure, with clay platelets and {\color{magenta} organic matter 
(mostly kerogen)}  parallel  or sub-parallel to bedding.





\end{itemize} 
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Well in the VMF from where the core sample was extracted }}
\vskip -.3cm
\begin{figure}
\label{fig1}
{
%\centering
\begin{center}
%\includegraphics[scale=0.29,angle=0]{Fig1_comprimido.eps}
\includegraphics[scale=0.33,angle=0]{Fig1_comprimido.eps}
\end{center}

 {{\tiny   Minerals and its proportions in the VMF  well.
 The core interval is indicated by red dots.} }

}
\end{figure}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Characterization of ultra-low permeability,
organic-rich mudrock reservoirs. II}}
{\small 
\begin{itemize}
\item  VMF is assumed to consist of a periodic 
sequence of very thin horizontal layers where  {\color{blue}  Biot’s theory in the diffusive frequency range} is applicable.


\item To characterize the VTI stiffness coefficients p$_{ij}$ of the equivalent 
VTI medium, numerical harmonic simulations—both compressional and shear—were performed on a representative synthetic rock model. 

\item 
The {\color{blue} model consists of a periodic sequence of  two porous materials}, both of 6 percent porosity
 and permeability  2.75 10$^{-18}$ m$^2$.

\end{itemize} 
}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Characterization of ultra-low permeability,
organic-rich mudrock reservoirs. III}}
{\small 
\begin{itemize}


\item Material 1 is a complex, multimineral assemblage composed of
seven solid phases, including 23 percent of kerogen, which is treated as a solid mineral constituent.

\item After estimating the bulk and shear moduli  of the indvidual solid phases  using 
a {\color{blue} generalized Krief's model},  and taking into account their volume fractions, {\color{magenta}  for Material 1
  we get a frame bulk modulus of  29.19 GPa 
  and  a shear modulus of  17.78 GPa}, values that lie withing the Hashin–Shtrikman bounds.

\item Material 2  is composed entirely of pure kerogen with grain
modulus 7 GPa,  density  1400 kg/m$^3$,  frame modulus  1.29 GPa and shear modulus  0.36 GPa.


\end{itemize} 
}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

\begin{frame}
\frametitle{{\small Fluid and minerals properties}}
{\tiny {Tables 1 and 2 display the fluid and mineral physical properties 
used in the harmonic simulations.}
\begin{center}
{\bf Table 1. Fluid properties.}
\end{center}
\[
%\begin{tabular}{cccccc}
\begin{tabular}{lccccc}
\hline
 fluid &  Bulk modulus (Pa) & Density (kg/m$^3$) & Viscosity (Pa . s)  \\
\hline 
Air  &  1.01325d5  & 1.225d0            &  1.805d-5  \\
%
Water  &   2.25d9   & 1000   &  0.001  \\
Oil  & 0.57d9    & 700   &  0.01   \\
Gas  & 0.022d9    & 78  &  0.000015  
\end{tabular}
\]

\vskip1cm

\begin{center}
{\bf Table 2. Mineralogical properties obtained from X-ray diffraction (XRD) analysis of core sample,
used for Material 1 at an effective pressure of 17.23 MPa }
\end{center}
\[
%\begin{tabular}{cccccc}
\begin{tabular}{lccccc}
\hline
mineral  & Bulk modulus (GPa) & shear modulus (GPa) & Density (kg/m$^3$) & Proportions (\%) \\
\hline 
kerogen  &     7.0   & 2.         &  1400  & 23  \\
Clay     &     25    & 9          &  2700  & 0.3727 \\
Quartz   &     45    & 55         &  2700  & 0.1461\\
Calcite  &     80    & 40         &  2800  & 0.1068\\
Plagioclase&   80    & 40         & 2800   & 0.0257 \\
Dolomite  &   100    & 50         & 2900   & 0.0237 \\
Pyrite   &    170    & 110        & 5000   &0.035 \\
\end{tabular}
\]

}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Computed VTI velocities using dry-core data}}
{\tiny 


The harmonic simulations were performed on a dry, square sample with a side length of 2 mm,
consisting of four repetitions of a {\color{blue} periodic sequence composed of 49 layers of Material 1 and one layer of Material 2 per period}. Each layer has a uniform thickness 
  10$^{-5}$ m. The computational domain was discretized using a 200$\times$200 mesh.
 
 \vskip1cm
 Table 3 summarizes the results of the VTI analysis, showing a good agreement between the
simulated and laboratory-measured phase velocities, with relative errors remaining below 10 per-
cent. 
  
\begin{center}
{\bf Table 3. Phase velocities computed, measured and error  percentage.}
\end{center}
\[
\begin{tabular}{lccccc}
\hline
Phase velocity vp (m/s)& Computed  & Measured& Percentage error \\
\hline 
v11  & 4644.378    & 4331       &  7.2  \% \\ \\
v33  & 3804.510    & 4217.47    &  9.8 \% \\ \\
v55  & 1974.760    & 2193.61    &  9.9   \% \\ \\
v66  & 2742.641    & 2581 &     6.2 \%   \\
\end{tabular}
\]
\vskip1cm
Figures 2 and 3 present polar plots of the phase and energy velocities, respectively, for the qP,
qSV, and SH waves in the dry sample, computed using the FE method at a frequency of 1 MHz.

}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Polar representation of qP, qSV and SH phase velocities. Dry sample. }}
\vskip -.4cm
\begin{figure}
\label{fig3}
{
%\centering
\begin{center}
\includegraphics[scale=0.33,angle=-90]{phase_velocity_qP_qSV_SH_1MHz_2mm_sample.eps}
\end{center}

 {{\tiny Polar representation  of  phase  velocities of qP,
qSV  and SH waves  computed using the FE method. Frequency is 1 MHz. 0 and 90 degrees indicate
waves traveling parallel and normal to the bedding, respectively.  Strong VTI behavior is observed.  } }

}
\end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small  Polar representation of qP, qSV and SH  energy  velocities. Dry sample. }}
\vskip -.3cm
\begin{figure}
\label{fig4}
{
%\centering
\begin{center}
\includegraphics[scale=0.33,angle=-90]{energy_velocity_qP_qSV_SH_1MHz_2mm_sample.eps}
\end{center}

 {{\tiny Polar representation  of energy  velocities of qP,
qSV  and SH waves  computed using the FE method. Frequency is 1 MHz. A 
notable triplication in the qSV-wave
energy velocity pattern can be  seen. } }

}
\end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Analysis of fluid saturated VMF. }}
{\small
\begin{itemize}



\item Four fluid saturation scenarios are analyzed : 100 percent oil, 100 percent gas, 10 percent gas plus 90 percent oil 
 and a ternary fluid mixture consisting of 40 percent gas, 52 percent oil, and 8 percent water,  
 obtained from the well’s fluid saturation log.
 
 
 
\item  the next Figures display phase velocities and attenuation factor 1000/Q, with Q denoting the quality factor. We consider waves traveling normaly to the layering plane ('33' waves).  

\item  For brevity, waves traveling parallel to the layering plane are not shown.

\item While  phase velocities allows to analyze velocity dispersion for the four saturation scenarios,  the attenuation figure allows to study the WIFF.


\end{itemize} 
}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small  Phase velocity of '33' waves.}}

\begin{figure}
\label{fig5}
{
%\centering
\begin{center}
\includegraphics[scale=0.33,angle=0]{vp33_100oil_100gas_10gas_90oil_52gas_40oil_8water.eps}
\end{center}

 {{\tiny  '33'  waves phase velocity as function of frequency.  } }

}
\end{figure}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Attenuation factor of '33' waves'. }}

\begin{figure}
\label{fig6}
{
%\centering
\begin{center}
\includegraphics[scale=0.33,angle=0]{33_aten_100oil_100gas_10gas_90oil_52gas_40_oil_8_water.eps}
\end{center}

 {{\tiny  '33'  waves phase attenuation factor  as function of frequency.  } }

}
\end{figure}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Patchy saturation }}
{\small

The von Karman self-similar correlation function was used to 
generate patchy saturation patterns, 

\begin{figure}
\label{fig7}
{
%\centering
\begin{center}
%\includegraphics[scale=0.5,angle=0]{matnum_patchy_gnu.dat_10_gas_grey_200x200.eps}
\includegraphics[width= 6.5cm,height=5.5cm,angle=0]{matnum_patchy_gnu.dat_10_gas_grey_200x200.eps}
\end{center}

 {{\tiny  White zones correspond to full gas saturation and black regions to full oil saturation. Overall gas saturation is 10 percent. } }

}
\end{figure}

 
}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Phase velocity   of '33' waves for uniform and patchy saturation.}}

\begin{figure}
\label{fig8}
{
%\centering
\begin{center}
\includegraphics[scale=0.33,angle=0]{vp33_uniform_nuevo_patchy.eps}
\end{center}

 {{\tiny  '33'  phase velocity  for uniform and patchy saturation as function of frequency.  } }

}
\end{figure}
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Attenuation factor  of '33' waves for uniform and patchy saturation.}}

\begin{figure}
\label{fig9}
{
%\centering
\begin{center}
\includegraphics[scale=0.33,angle=0]{33_aten_uniform_nuevo_patchy.eps}
\end{center}

 {{\tiny  '33' waves  attenuation factor for uniform and patchy saturation as function of frequency.  } }

}
\end{figure}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  slide %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small Fluid pressure   of '33' waves for uniform and patchy saturation.}}

\begin{figure}
\label{fig10}
{
%\centering
\begin{center}
\includegraphics[width=4.5cm,angle=0]{fluid_pressure_eff_fluid_uniform_100Hz.eps}
\includegraphics[width=4.5cm,angle=0]{fluid_pressure_patchy_100Hz.eps}
\end{center}

 {{\tiny  Fluid pressure  for the case of 10 \% gas, 90 \% oil  and uniform (left) and patchy (right)  saturation. Frequency is 100 Hz  } }

}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{{\small CONCLUSIONS}}
{\small 
\begin{itemize}
\item  This study presented a physically grounded, non-phenomenological methodology 
for estimating the effective anisotropic behavior of the organic-rich mudrock reservoirs.


\item The simulations were performed on a  finely layered synthetic medium representative
of a core sample from the Vaca Muerta Formation.

\item The computed  stiffness tensors  showed very good agreement with laboratory-measured phase
velocities  and well-log data, capturing the strong VTI anisotropy of the formation.


\item The inclusion of both patchy and uniformly mixed fluid saturation
scenarios  emphasized the critical influence of mesoscale fluid heterogeneities on seismic wave dispersion and attenuation.

\end{itemize} 
}
\end{frame}
 

\end{document}


