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\title{\large{EOSC252}\\ \Large{Lab2: Porosity Measurement (part 2)}}\date{}


\begin{document}
\maketitle

\section{Introduction}

In this lab you will determine the porosity of your rock sample using
the helium porosimeter shown on page~4. This device contains two
cells, the sample cell and the expansion cell. Three valves, V1, V2
and V3 control the gas flow throughout the system:
\begin{itemize}
 \item V1 connects the sample cell to the helium tank
 \item V2 allows gas out of the system
 \item V3 controls the flow between the sample cell and the expansion cell
\end{itemize}

A pressure sensor provides measurements of the gas pressure inside the
sample cell. The pressure readings are displayed on a multimeter connected
to the sensor (in units of Volts).

To find the porosity using the helium porosimeter, we will
apply Boyle's law. This law states that, under conditions
of fixed gas quantity and constant temperature, the product of the
pressure and volume stay constant. Boyle's law is expressed as follows:

$$P_1V_1=P_2V_2.$$

\section{Experimental Procedure}

Be sure to record exactly what you do, what readings you take, and what
valves you open or close at various stages in this experiment. THINK
ABOUT WHAT PARTS OF THE SYSTEM ARE CONNECTED AT ALL TIMES.

\textbf{****DANGER!!!! NEVER OPEN THE SYSTEM WITHOUT FIRST LETTING OUT
    THE GAS SO THE PRESSURE DROPS TO ZERO.****}

  \newpage
  
\begin{enumerate}

\item Measure the length and the diameter of your sample. Repeat this 5
  times, taking measurements at different points around your sample.

  \begin{tabular}{|l|p{0.6in}|p{0.6in}|p{0.6in}|p{0.6in}|p{0.6in}|p{0.6in}|}
    \hline
    &1&2&3&4&5&Average\\
    \hline
    Diameter (\underline{\hspace{0.25in}})&&&&&&\\
    \underline{$\pm$ \hspace{1in}}&&&&&&\\
    \hline
    Length (\underline{\hspace{0.25in}})&&&&&&\\
    \underline{$\pm$ \hspace{1in}}&&&&&&\\
    \hline
  \end{tabular}

\item Determine the volume of the sample cell, $V_{cell}$, and
  expansion cell, $V_{exp}$, of the porosimeter

  \begin{enumerate}

  \item Ensure V1 is closed tightly. Open V2 and V3. Wait until the
    reading on the multimeter is stable. Record the voltage
    corresponding to the atmospheric pressure.

  \item Ensure V2 and V3 are closed tightly. Open V1 to let gas
    flow into sample cell only. When the reading on multimeter stabilizes,
    close V1. Record the reading.

  \item Ensure V1 and V2 are closed tightly. Open V3 to let the gas
    flow into the expansion cell. Record the reading.

  \item Open V2 to release the gas from the system. Make sure V3 is
    open as well. Close V3 after the gas after gas is completely released from
    the system.

  \item Measure the diameter of the calibration sphere using the
    caliper. Take 5 measurements at different points around the sphere.
    
    \hspace{-0.26in}{
    \begin{tabular}{|l|p{0.6in}|p{0.6in}|p{0.6in}|p{0.6in}|p{0.6in}|p{0.6in}|}
      \hline
      &1&2&3&4&5&Average\\
      \hline
      Diameter (\underline{\hspace{0.25in}})&&&&&&\\
      \underline{$\pm$ \hspace{1in}}&&&&&&\\
      \hline
    \end{tabular}}

  \item Ensure that V1 is shut tightly and that no gas is left in the
    system. Open the sample cell by unscrewing the lid and place the
    calibration sphere inside. Close the lid carefully (in particular, be
    careful not to cross-thread the lid).

  \item Repeat the steps (b) through (d) with the calibration sphere in the cell.
    
  \end{enumerate}

\item Calculate the volume of the sample cell, $V_{cell}$, and of the
  expansion cell, $V_{exp}$. Make sure you have a clean account of
  your calculations. Don't forget to correct for the atmospheric
  pressure. If you set the problem right, you should end up with
  2~equations and 2~unknowns that are $V_{cell}$ and $V_{exp}$. Make
  sure that your solution is an expression of a volume by looking at
  the units and verify that the order of magnitude is consistent with
  the size of the components of the porosimeter (e.g. a volume of
  $1\,\mathrm{km}^3$ would be excessive).

\item Determine the porosity of your rock sample

  \begin{enumerate}
    
  \item Ensure that V1 is shut tightly and that no gas is left in the
    system. Open the sample cell by unscrewing the lid and place your
    sample inside. Close the lid properly.

  \item Ensure V2 and V3 are closed tightly. Open V1 to let gas
    flow into the sample cell only. When the reading on multimeter stabilizes,
    close V1. Record the reading.
    
  \item Ensure V1 and V2 are closed tightly. Open V3 to let the gas
    flow into the expansion cell. Record the reading.

  \item Open V2 to release the gas from the system. Make sure V3 is
    open. Close V3 after the gas has been completely released from
    the system.

  \end{enumerate}

\item Calculate the effective volume of your sample (i.e. the volume
  that is not filled with helium) using $V_{cell}$ and $V_{exp}$. Now
  use this value to find the its porosity. Before you do your
  calculations, think about which volume you are measuring. Are all
  the pores filled with helium? What is the difference between water
  and helium? Is the maximum saturation different when using helium
  instead of water? Please comment on that in your discussion.

 \end{enumerate}

\section{Results}

\begin{tabular}{|l|p{2in}|}
  \hline
  &Pressure (\underline{\hspace{0.25in}})\\
  &\underline{$\pm$ \hspace{1in}}\\
  \hline
  $P_0$ empty no gas&\\
  \hline
  $P_{1Empty}$ $V_{cell}$ empty&\\
  \hline
  $P_{2Empty}$ $V_{cell}$ empty + $V_{exp}$&\\
  \hline
  $P_{1Sphere}$ Sphere in $V_{cell}$&\\
  \hline
  $P_{2Sphere}$ Sphere in $V_{cell}$+$V_{exp}$&\\
  \hline
  $P_{1Sample}$ Sample in $V_{cell}$&\\
  \hline
  $P_{2Sample}$ Sample in $V_{cell}+V_{exp}$&\\
  \hline
\end{tabular}

\section{Discussion}

As part of your discussion please answer the following questions:

\begin{itemize}

\item Is the porosity measured using the helium porosimeter different
  from the value obtained in lab~1? If so, why are the two
  techniques not leading to comparable results? What are the assumptions
  you have made in lab~1 that could lead to such discrepancy?

\item Is helium porosimetry an accurate means of determining the
  volume of a rock sample that will be filled with water, when
  saturated in the subsurface? Explain your answer.

\end{itemize}

\begin{figure}[htb]
  \vspace{-0.5in}
    \center{\includegraphics[width=1.0\textwidth]{setup.png}}
  \label{fig:Porosimeter}
  %\caption{Helium porosimeter}
\end{figure}

\end{document}


