@@ -7,7 +7,7 @@ Diffusive forces are to be neglected in this part.

\item What are the driving forces that should be considered?

\item Guess how long the different parts of the process will take.

\item Which equation(s) do you need to describe the problem? Which assumptions do you make?

\item How much DNAPL would be necessary, so that it enters the groundwater system? Is that a realistic amount? Use the parameters given in section \ref{prop_paramI}.

\item How much DNAPL would be necessary, so that it enters the groundwater system? Is that a realistic amount given the leaky car engine setup? Use the parameters given in section \ref{prop_paramI}.

\end{enumerate}

\section{Numerical Simulation}

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@@ -20,7 +20,10 @@ Diffusive forces are to be neglected in this part.

\end{enumerate}

\subsection{Exercise}

Simulate the given problem.

Simulate the given problem.\\

Open a terminal and type {\em cd /temp/efm2019/ex2}\\

Run the simulation: {\em ./lens2pexercise}\\

\begin{enumerate}

\item Find out how long the different parts of the process will take.

\item Try different soil properties and see how they affect the simulation.

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@@ -28,7 +31,7 @@ Simulate the given problem.

\end{enumerate}

\clearpage

\subsection{Properties and parameters - exercise3.input}

\subsection{Properties and parameters - lens2pexercise2.input}

{\em It is assumed, that the DNAPL cannot infiltrate the less permeable layer by diffusion, but nevertheless it is distributed in the domain equally, i.e. (\ref{volume}) holds at any time. The equations do not account for saturation, i.e. it is assumed that the DNAPL pool only consists of DNAPL ($S_n=1.0$).}

\item How much DNAPL would be necessary, so that it enters the groundwater system? Is that a realistic amount? \\

{\em Equation (\ref{pd}) gives a height of 0.277m to overcome the entry pressure of 1250 Pa. That leads to an amount of 2494$l$ oil in the 3m by 3m domain. If a large limousine with a total engine oil of ca. 8$l$ is assumed, that is not realistic. Assuming still a constant distribution in the x-y--plane and a radial spreading, the plume must not spread more than 0.096m ($r=\sqrt{V \,/(\pi h)}$) to generate a pressure large enough to make the DNAPL enter the less permeable layer.}

\item How much DNAPL would be necessary, so that it enters the groundwater system? Is that a realistic amount given the leaky car engine setup? \\

{\em Equation (\ref{pd}) gives a height of 0.11m to overcome the entry pressure of 500 Pa. with a 1D assumption, that leads to an amount of 399l oil in the 3m by 3m domain. However, on the other extreme, assuming that the oil spreads radially in every direction in the form of a half sphere, the maximum volume is much smaller. In this case, only 1.1l are needed to reach the entry pressure.}

\end{enumerate}

\clearpage

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@@ -111,7 +111,7 @@ $q_w$ & mass source/sink rate for non-wetting phase & [kg/(m$^3$s)]

\item What simplifications can you you use to get a reduction of computational time?\\

{\em Reduce the dimension of the domain to the necessary size, i.e. adapt the length/width/height, choose a 2D domain or a radial symmetric ``cake'' domain.}

{\em Reduce the dimension of the domain to the necessary size, i.e. adapt the length/width/height, choose a 1D or 2D domain or a radial symmetric ``cake'' domain.}

\item Which boundary conditions would you use?\\

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@@ -138,6 +138,6 @@ It is not at all easy to guess in an analytical approach the result for a more c

@@ -57,7 +57,7 @@ A Lens Problem - Two-Phase Flow with Capillary Pressure}\\

%*************************************

\section{Purpose}

\label{purpose}

The aim of this exercise is to get a better feeling about capillary pressure and permeabilities in two-phase systems. Therefore an oil contamination scenario is presented, where a car has a leaky engine and looses oil while parking. The oil enters the soil without problems. The main question is, if the groundwater will be polluted.

The aim of this exercise is to get a better feeling about capillary pressure and permeabilities in two-phase systems. Therefore, an oil contamination scenario is presented, where a car has a leaky engine and looses oil while parking. The oil enters the soil without problems. The main question is, if the groundwater will be polluted.

To address this question, the exercise consists of two parts:

\begin{enumerate}

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@@ -76,12 +76,12 @@ To address this question, the exercise consists of two parts:

\label{boundarycond_fig}

\end{figure}

Figure \ref{boundarycond_fig} shows the problem in three dimensions with the given parameters. It is assumed that the maximum area of contamination is three by three meter. It consists of two different soils, a higher permeable, coarse sand on the top and a less permeable clay in the middle under which the groundwater flows. For the reason of simplicity the system is initially fully saturated with water, but the groundwater of interest is below the less permeabl layer. In the middle of the top side, there is an oil contamination source, i.e. the DNAPL enters the soil.

Figure \ref{boundarycond_fig} shows the problem in three dimensions with the given parameters. It is assumed that the maximum area of contamination is three by three meter. It consists of two different soils, a higher permeable, coarse sand on the top and a less permeable clay in the middle under which the groundwater flows. For the reason of simplicity, the system is initially fully saturated with water, but the groundwater of interest is below the less permeable layer. In the middle of the top side, there is an oil contamination source, i.e. the DNAPL enters the soil.