Commit 08d50e5e authored by Katharina Heck's avatar Katharina Heck

Merge branch 'update-EFM2Exercises2019' into 'master'

Update efm2 exercises2019

See merge request !79
parents dae97a08 82b7bcbc
......@@ -48,25 +48,25 @@
{\Large
\begin{center}
{\bfseries Environmental Fluid Mechanics
% Multiphase Flow and Transport in Porous Media\\
{\bfseries Environmental Fluid Mechanics
% Multiphase Flow and Transport in Porous Media\\
- Computer Exercises -\\
\vspace{\baselineskip}
Advection, Diffusion, Dissolution -- A Time Scale Evaluation}\\
\vspace{\baselineskip}
Advection, Diffusion, Dissolution -- A Time Scale Evaluation}\\
\end{center}
}
%*************************************
\section{Purpose}
\label{purpose}
The aim of this exercise is to get a better feeling about the time scales on which the different flow processes (advection, diffusion, dissolution) occur.
The aim of this exercise is to get a better feeling about the time scales on which the different flow processes (advection, diffusion, dissolution) occur.
The exercise consists of three parts, which are to be solved by different groups.
\begin{enumerate}
\item one-phase--two-component flow
\item two-phase flow
\item two-phase--two-component flow
\item one-phase--two-component flow
\item two-phase flow
\item two-phase--two-component flow
\end{enumerate}
%Based on the experience gained from the model simulations, appropriate remediation methods
......@@ -99,7 +99,7 @@ Figure \ref{boundarycond_fig} shows a sketch of the problem. The domain is initi
%\end{table}
\input{timescale}
%\input{timescale_solution}
% \input{timescale_solution}
\end{document}
......@@ -15,6 +15,7 @@ There is one parameter file (exercise3.input) for all groups. The Brooks-Corey p
\lstset{numbers=left, breaklines=true, morecomment=[l]{\#}, commentstyle=\color{blue}\tiny, breakindent=28em}
\lstinputlisting{../exercise3.input}
}
Reduce the value of parameter ``EpisodeLength'' to 5.0e4 s. For the cases with a pressure gradient, you may need to reduce it (and the parameter ``TEnd'' even more.
\paragraph{Remark} Sometimes it is very important to rescale the output to a reasonable (not min/max) color scale to visualize the interesting parts of the processes properly.
......@@ -23,34 +24,33 @@ There is one parameter file (exercise3.input) for all groups. The Brooks-Corey p
Simulate a one-phase--two-component flow system with a pressure gradient of $10^4$ Pa/m and without any pressure gradient.
\begin{enumerate}
\item Monitor the characteristic flow behaviour. Which processes (advection, diffusion, dispersion, dissolution) can you observe?
\item What are the driving forces?
\item Note the breakthrough time at the lower boundary.
\item How does a change of permeability or porosity affect the breakthrough time?
\item On what time scale do the processes occur?
\item Monitor the characteristic flow behaviour. Which processes (advection, diffusion, dissolution) can you observe?
\item What are the driving forces?
\item When does the nitrogen reach the lower boundary?
\item How does a change of permeability or porosity affect the breakthrough time?
\item On what time scale do the processes occur?
\end{enumerate}
\subsection{Two-Phase Flow}
Simulate a two-phase flow system with a pressure gradient of $10^4$ Pa/m and without any pressure gradient.
\begin{enumerate}
\item Monitor the characteristic flow behaviour. Which processes (advection, diffusion, dispersion, dissolution) can you observe?
\item What are the driving forces?
\item When does the gas phase reach the lower boundary?
\item How does a change of permeability or porosity affect the breakthrough time?
\item On what time scale do the processes occur?
\item Monitor the characteristic flow behaviour. Which processes (advection, diffusion, dissolution) can you observe?
\item What are the driving forces?
\item When does the gas phase reach the lower boundary?
\item How does a change of permeability, porosity, residual saturation or the Brooks-Corey parameters affect the breakthrough time?
\item On what time scale do the processes occur?
\end{enumerate}
\subsection{Two-Phase--Two-Component Flow}
Simulate a two-phase--two-component flow system with a pressure gradient of $10^4$ Pa/m and without any pressure gradient.
\begin{enumerate}
\item Monitor the characteristic flow behaviour. Which processes (advection, diffusion, dispersion, dissolution) can you observe?
\item What are the driving forces?
\item When does the gas phase reach the lower boundary?
\item When does the nitrogen reach the lower boundary?
\item How does a change of permeability, porosity, residual saturation or the Brooks-Corey parameters affect the breakthrough time?
\item On what time scale do the processes occur?
\item Monitor the characteristic flow behaviour. Which processes (advection, diffusion, dissolution) can you observe?
\item What are the driving forces?
\item When does the gas phase reach the lower boundary?
\item When does the nitrogen reach the lower boundary?
\item How does a change of permeability, porosity, residual saturation or the Brooks-Corey parameters affect the breakthrough time?
\item On what time scale do the processes occur?
\end{enumerate}
......@@ -74,7 +74,7 @@ active. Activate by clicking somewhere in the window.\\
On the command line in window 1 type\\
{\em cd /EFM2-2014/ex3}\\
{\em cd /temp/efm2019/ex3}\\
\vspace{0.1cm}
{\bfseries ... set the model parameters:}\\
......@@ -92,9 +92,9 @@ Change the necessary parameters and save the file before you leave the editor.\\
On the command line (window 1), type\\
\noindent
{\em ./lens1p2cexercise3 -ParameterFile exercise3.input} for group one\\
{\em ./lens2pexercise3 -ParameterFile exercise3.input} for group two \\
{\em ./lens2p2cexercise3 -ParameterFile exercise3.input} for group three.
{\em ./lens1p2cexercise3 exercise3.input} for group one\\
{\em ./lens2pexercise3 exercise3.input} for group two \\
{\em ./lens2p2cexercise3 exercise3.input} for group three.
\vspace{0.1cm}
The simulation will start with the given time step size (e. g. 10) and run until the simulation time (use e. g. 1000) is reached.
......@@ -121,4 +121,7 @@ You can look at the saturations and the capillary pressure and for the component
To show the saturation or the pressure more clearly it might be necessary to
adjust the visualisation scale. You may do this by clicking on the button 'rescale to data range'. You find it on the upper left side of the paraview window next to where you choose your variable currently visualized with a double arrow on it.
{\bfseries ...view the code (if you want):}\\
In case you already finished the exercise and want to have a look at the code:\\
{\em cd /temp/efm2019/DUMUX/dumux-lecture/lecture/efm/1p2c\_2p\_2p2c}\\
\clearpage
......@@ -28,3 +28,4 @@ UpperPressure = 4.0e5 # Dirichlet pressure value for the b
[Problem]
EnableGravity = false
Name = exercise3
......@@ -18,17 +18,17 @@ in saturated porous media in general:
and for the two-dimensional system:
\begin{equation}
\label{onephase_transp_gen}
\frac{\partial (c \phi)}{\partial t} =
-\frac{\partial}{\partial x}\left [ \phi \left (cv_x - \left ( D_m + D_t\right ) \frac {\partial c}{\partial x} \right ) \right ]
\frac{\partial (c \phi)}{\partial t} =
-\frac{\partial}{\partial x}\left [ \phi \left (cv_x - \left ( D_m + D_t\right ) \frac {\partial c}{\partial x} \right ) \right ]
-\frac{\partial}{\partial z}\left [ \phi \left (cv_z - \left ( D_m + D_l\right ) \frac {\partial c}{\partial z} \right ) \right ]
+ r\phi
\end{equation}
In case of flow only in a vertical direction ($v_x = 0$), shown in figure \ref{fig_tr_eq}, we can simplify (\ref{onephase_transp_gen}) to
\begin{equation}
\label{onephase_transp}
\frac{\partial (c \phi)}{\partial t} =
\frac{\partial}{\partial x}\left ( \phi \left ( D_m + D_t\right ) \frac {\partial c}{\partial x} \right )
- \frac{\partial}{\partial z} \left [ \phi \left (cv_z - ( D_m + D_l) \frac {\partial c}{\partial z} \right) \right]
\frac{\partial (c \phi)}{\partial t} =
\frac{\partial}{\partial x}\left ( \phi \left ( D_m + D_t\right ) \frac {\partial c}{\partial x} \right )
- \frac{\partial}{\partial z} \left [ \phi \left (cv_z - ( D_m + D_l) \frac {\partial c}{\partial z} \right) \right]
+ r\phi
\end{equation}
\begin{equation}
......@@ -39,10 +39,10 @@ D_l = \alpha _l v_z \qquad \qquad D_t = \alpha _t v_z
\label{darcy}
v_z = \frac{- k}{\mu \phi} \cdot \frac{\partial p}{\partial z}
\end{equation}
With these assumptions and an incompressible fluid (\ref{conti}) reduces to
With these assumptions and an incompressible fluid (\ref{conti}) reduces to
\begin{equation}
\label{conti_red}
\frac{\partial^2 p}{\partial z^2} =0.0
\frac{\partial^2 p}{\partial z^2} =0.0
\end{equation}
The unknowns $p(x,z)$, $c(x,z)$ in equations (\ref{conti_red}),(\ref{onephase_transp}) lead to a closed system.
......@@ -91,20 +91,23 @@ On the top a pressure Dirichlet value is given as well as a homogenous Dirichlet
The time stepping of the numerical solver is adaptive. {\em MaxTimeStepSize} determines the maximum time step. Adapting this value can be usefull if processes occur very fast and cannot be seen anymore if the time step gets too large.
\begin{table}[ht!]
\label{transp_equation_param2}
\begin{tabular}[t]{lll}
$D_m=$ & $1.0 \cdot 10^{-9}$ & [m$^2$/s] \\
$\alpha_l=$ & $1.0 \cdot 10^{-5}$ & [m] \\
$\alpha_t=$ & $1.0 \cdot 10^{-6}$ & [m] \\
$t_0$ & injection starts after the first time step & \\
\end{tabular}
\end{table}
%%We currently do not consider dispersion in the example!
% \begin{table}[ht!]
% \label{transp_equation_param2}
% \begin{tabular}[t]{lll}
% $D_m=$ & $1.0 \cdot 10^{-9}$ & [m$^2$/s] \\
% $\alpha_l=$ & $1.0 \cdot 10^{-5}$ & [m] \\
% $\alpha_t=$ & $1.0 \cdot 10^{-6}$ & [m] \\
% $t_0$ & injection starts after the first time step & \\
% \end{tabular}
% \end{table}
\paragraph{Remark}
The diffusion and dispersion coefficients are fixed values for this exercise.
A very strong diffusion in flow direction can be seen, which is caused by
numerical diffusion due to the used
The diffusion coefficient is
% and dispersion coefficients are
fixed values for this exercise and we do not consider dispersion in this exercise ($\alpha _l=\alpha _t=0$).
A very strong diffusion in flow direction can be seen, which is caused by
numerical diffusion due to the used
model and the spatial and temporal resolution (grid resolution and time step sizes).
\subsection{How to...}
......@@ -118,7 +121,7 @@ Download the handout of the exercise from the ILIAS system.\\
{\bfseries ... open a window:}\\
In the tool bar at the bottom of the screen, click the symbol with a window
In the tool bar at the bottom of the screen, click the symbol with a window
and a shell. We will call this window ``window 1''. Only one window at the time is
active. Activate by clicking somewhere in the window.\\
\vspace{0.1cm}
......@@ -127,7 +130,7 @@ active. Activate by clicking somewhere in the window.\\
On the command line in window 1 type\\
{\em cd /temp/EFM2-2015/ex1 }\\
{\em cd /temp/efm2019/ex1 }\\
\vspace{0.1cm}
{\bfseries ... set the model parameters:}\\
......@@ -135,18 +138,25 @@ On the command line in window 1 type\\
The parameters used by the program are listed in the file ``exercise1.input''.
To open the file, type (in window 1)\\
{\em gedit exercise1.input \&}\\
{\em kate exercise1.input \&}\\
Change the necessary parameters and save the file before you leave the editor.\\
You can change parameter values used by the simulation in this input file.
For a start, change the parameters
``MaxTimeStepSize'' to ``5.0e2'',
``TEnd'' to ``1.0e4'',
``EpisodeLength'' to ``5.0e2'',
``Name'' to ``lens1p2c'',
``InfiltrationEndTime'' to ``5000'',
and save the file before you leave the editor.\\
\vspace{0.1cm}
{\bfseries ... start the simulation:}\\
On the command line (window 1), type\\
{\em ./lens1p2cexercise1 -{}-parameterFile=exercise1.input}\\
{\em ./lens1p2cexercise1 -{}-parameterFile exercise1.input}\\
The simulation will start with the given time step size dtInitial (e. g. 100) and run until the simulation time tEnd (use e. g. 2500) is reached.
The simulation will start with the given time step size DtInitial (e. g. 10) and run until the simulation time tEnd (use e. g. $10\,000$) is reached.
If you want to stop the simulation earlier, activate the window from where you started the simulation and press ``Ctrl C'' (or ``Strg C'').\\
\vspace{0.1cm}
......@@ -156,17 +166,17 @@ In window 1, type\\
{\em paraview\&}\\
In paraview you can open your result files (lens-1p2c.pvd, if you finished a simulation or lens-1p2c-*.vtu, if you have not finished your simulation). \\
In paraview you can open your result files (lens1p2c.pvd). \\
\vspace{0.1cm}
{\bfseries ...choose the variable to visualize:}\\
You can either look at the water pressure or at the contaminant concentration. You can choose the variable currently visualized at a small menue at the upper left side of the paraview window. \\
You can either look at the water pressure or at the contaminant mass or mole fraction. You can choose the variable currently visualized at a small menue at the upper left side of the paraview window. \\
\vspace{0.1cm}
{\bfseries ...adapt the color scale:}\\
To show the contaminant concentration or the water pressure more clearly it might be necessary to
To show the contaminant mass or mole fraction or the water pressure more clearly it might be necessary to
adjust the visualisation scale. You may do this by clicking on the button 'rescale to data range'. You find it on the upper left side of the paraview window next to where you choose your variable currently visualized with a double arrow on it.
If you want to rescale to the minimum/maximum of the entire simulated time, you can find the button \emph{``rescale to temporal range''} in the ``display tab'' in the ``object inspector'' by editing the color map.
......@@ -177,14 +187,19 @@ Please answer the following questions:
\begin{enumerate}
\item What are the driving forces for the movement of the contaminant?
\item What other physical processes or parameters influence the transport?
\item What parameters do you have to change and how in order to make it more
\item What parameters do you have to change and how in order to make it more
difficult for the contaminant to enter $\Omega _2$?
Use the model to answer the question. In
section \ref{prop_paramI}, the current values
of properties and parameters of the model of the one-phase system are
Use the model to answer the question. In
section \ref{prop_paramI}, the current values
of properties and parameters of the model of the one-phase system are
listed.
\item In general, what remediation techniques would you suggest to remove a
dissolved contaminant? What advantages / disadvantages does the proposed
method have?
\item In general, what remediation techniques would you suggest to remove a
dissolved contaminant? What advantages / disadvantages do the proposed
methods have?
\end{enumerate}
Hint: If you want to compare different parameter combinations, it might be good to each time run the simulation with a different name, e.g. ``lens1p2c-highPerm'' for a case with higher permeability.
You can do this either by changing the parameter ``Name'' in the file ``exercise1.input'' or by starting the simulation with: \\
{\em ./lens1p2cexercise1 -{}-parameterFile exercise1.input -{}-Problem.Name lens1p2c-highPerm}\\
\clearpage
......@@ -2,36 +2,36 @@
\begin{enumerate}
\item What are the driving forces for the movement of the contaminant?\\[1ex]
{\em The piezometric head gradient induces flow from high to low potential.}
\item What other physical processes or parameters influence the transport?\\[1ex]
{\em The Darcy velocity q is determined by the permeability k and the dynamic
viscosity $\mu$. A high permeability and a low viscosity lead to high velocities.
However, the velocity that determines the advective transport of the contaminant is the seepage velocity $v= q / \phi$.\\
Dispersion and diffusion cause a smoothing of the concentration
front, depending on the concentration gradient and the seepage velocity.}
\item What parameters do you have to change and how in order to make it more difficult
for the contaminant to enter $\Omega _2$?
Use the model to answer the question. In section \ref{prop_paramI} the current values of properties and parameters of the model of the one-phase system are listed.\\[1ex]
{\em By reducing the permeability $k_2$, the advective transport
into the lense gets weaker. However, there is still a certain amount of the contaminant entering the lense.
into the lense gets weaker. However, there is still a certain amount of the contaminant entering the lense.
If one would reduce additionally the dispersivity $\alpha$ and the diffusion coefficient $D_m$, even less contaminant would be transported into the lense.
For the unrealistically small values $k_2 \approx 10^{-25} [m^2]$,
If one would reduce additionally the dispersivity $\alpha$ and the diffusion coefficient $D_m$, even less contaminant would be transported into the lense.
For the unrealistically small values $k_2 \approx 10^{-25} [m^2]$,
$\alpha _l \approx 10^{-6} [m]$, $\alpha _t \approx 10^{-7} [m]$ and
$D_m \approx 10^{-20} [m]$, contaminant is still entering the lense. Here also the numerical diffusion comes into play again, i.e., if there is a $v_z \neq 0$ the numerical diffusion transports contaminant into the lense.}
\item What remediation techniques would you suggest to remove the dissolved
\item What remediation techniques would you suggest to remove the dissolved
contaminant? What advantages / disadvantages does the proposed method have?\\[1ex]
{\em A "pump and treat" technique is suggested. This method is feasible if
the advective transport is the determining transport mechanism. An
advantage is that it is relatively simple. The disadvantage is that the
{\em A "pump and treat" technique is suggested. This method is feasible if
the advective transport is the determining transport mechanism. An
advantage is that it is relatively simple. The disadvantage is that the
total remediation time might be very long (due to the low permeability lense)
before all contaminant is removed.
This implicates high operating costs.
A possibility to enhance the remediation process could be to stimulate
A possibility to enhance the remediation process could be to stimulate
the biodegradation of the contaminant.}
\end{enumerate}
\subsection{Conclusion}
......@@ -42,12 +42,12 @@
\item The porosity, in contrast to the permeability, does not has such a big influence, mainly because the difference can be at maximum one whereas the permeabilities can differ by orders of magnitude.
\end{itemize}
\begin{figure}\centering
\includegraphics[width=0.6\linewidth]{pics/result1.png}
\caption{K$_{\mathrm{fine}}$=0.3e-12 m$^2$, K$_{\mathrm{coarse}}$=5.89912e-11 m$^2$, $\Phi=0.5$, $\Delta p= 0.1$ bar, infiltration rate=0.5 kg/(m$^2$s), infiltration end time=30000 s, time=64684 s}
\includegraphics[width=0.6\linewidth]{pics/result_original.png}
\caption{Simulation result for N$_2$ molefractions for original parameter: K$_{\mathrm{fine}}$=3.1e-11 m$^2$, K$_{\mathrm{coarse}}$=3.1e-10 m$^2$, $\Phi_{\mathrm{fine}}=0.1$, $\Phi_{\mathrm{coarse}}=0.2$, $\Delta p= 0.01$ bar, infiltration rate=0.4 kg/(m$^2$s), infiltration end time=5000 s, time=4055 s}
\end{figure}
\begin{figure}\centering
\includegraphics[width=0.6\linewidth]{pics/result2.png}
\caption{K$_{\mathrm{fine}}$=0.3e-11 m$^2$, K$_{\mathrm{coarse}}$=5.89912e-11 m$^2$, $\Phi_1=0.5$, $\Phi_2=0.4$, $\Delta p= 0.1$ bar, infiltration~rate=0.5~kg/(m$^2$s), infiltration end time=20000 s, time=31984 s}
\includegraphics[width=0.6\linewidth]{pics/result_100LessPerm.png}
\caption{Simulation result for N$_2$ molefractions for decreased fine lens permeability: K$_{\mathrm{fine}}$=3.1e-13 m$^2$, K$_{\mathrm{coarse}}$=3.1e-10 m$^2$, $\Phi_{\mathrm{fine}}=0.1$, $\Phi_{\mathrm{coarse}}=0.2$, $\Delta p= 0.01$ bar, infiltration rate=0.4 kg/(m$^2$s), infiltration end time=5000 s, time=4055 s}
\end{figure}
\clearpage
......@@ -33,7 +33,7 @@
%---- pagestyle ---- start -------------------------------------
\lhead[\fancyplain{}{\thepage}] %Header links, gerade Seitenzahl
% {\fancyplain{}{EGW Short Course, March 2002}}
{\fancyplain{}{EFM Exercise, 2015}}
{\fancyplain{}{EFM Exercise 1}}
\rhead[\fancyplain{}{Environmental Fluid Mechanics}]
%\rhead[\fancyplain{}{Multiphase Flow and Transport in Porous Media}]
{\fancyplain{}{\thepage}} %Header rechts, ungerade Seitenzahl
......@@ -47,16 +47,16 @@
{\Large
\begin{center}
{\bfseries Environmental Fluid Mechanics\\
% Multiphase Flow and Transport in Porous Media\\
- Computer Exercises -}\\
{\bfseries Environmental Fluid Mechanics\\
% Multiphase Flow and Transport in Porous Media\\
- Computer Exercises -}\\
\end{center}
}
%*************************************
\section{Purpose}
\label{purpose}
The aim of this exercise is to get a better understanding for contaminant--flow in
The aim of this exercise is to get a better understanding for contaminant--flow in
one-phase as well as in immiscible two-phase systems and to make clear what the physical differences
are.
......@@ -79,8 +79,8 @@ A model will be set up and used for application of two different cases:
\end{figure}
Figure \ref{boundarycond_fig} shows a section of an experimental
set-up used for investigation of contaminant-transport in porous media.
The bottom-side is open (atmospheric pressure) and along the top-side there is a
set-up used for investigation of contaminant-transport in porous media.
The bottom-side is open (atmospheric pressure) and along the top-side there is a
constant higher pressure. The left- and the right-hand sides are impermeable. Over a certain
length of the top-side, a contaminant is been infiltrated during a defined period of time.
The two domains $\Omega _1$ and $\Omega _2$ contain a coarse and a fine sand, respectively.
......
......@@ -16,7 +16,7 @@ For the non-wetting phase (gas or NAPL):
\begin{equation}
\phi \varrho_{n} \frac{\partial ( S_{n})}{\partial t} - \nabla
\cdot \left( \varrho_{n} \underbrace{\frac{k_{rn}}{\mu_n} \mathbf{K} \cdot
(\nabla p_{w} + \nabla p_c - \varrho_{n} \mathbf{g})}_{v_n} \right) -
(\nabla p_{w} + \nabla p_c - \varrho_{n} \mathbf{g})}_{v_n} \right) -
q_{n} = 0 \; .
\label{DGLn}
\end{equation}
......@@ -103,7 +103,7 @@ Download the handout of the exercise.\\
{\bfseries ... open a window:}\\
In the tool bar at the bottom of the screen, click the symbol with a window
In the tool bar at the bottom of the screen, click the symbol with a window
and a shell. We will call this window ``window 1''. Only one window at the time is
active. Activate by clicking somewhere in the window.\\
\vspace{0.1cm}
......@@ -112,7 +112,7 @@ active. Activate by clicking somewhere in the window.\\
On the command line in window 1 type\\
{\em cd /temp/EFM2-2015/ex1}\\
{\em cd /temp/efm2019/ex1 }\\
\vspace{0.1cm}
{\bfseries ... set the model parameters:}\\
......@@ -120,9 +120,17 @@ On the command line in window 1 type\\
The parameters used by the program are listed in the file ``exercise1.input''.
To open the file, type (in window 1)\\
{\em gedit exercise1.input \&}\\
Change the necessary parameters and save the file before you leave the editor.\\
{\em kate exercise1.input \&}\\
You can change parameter values used by the simulation in this input file.
Change the parameters
``MaxTimeStepSize'' to ``5.0e2'',
``TEnd'' to ``1.0e4'',
``EpisodeLength'' to ``5.0e2'',
``Name'' to ``lens2p'',
``InfiltrationEndTime'' to ``5000'',
and save the file before you leave the editor.\\
If you do not change the parameter ``Name'', your previous simulation results of the 1p2c part of the excercise will be overwritten!
\vspace{0.1cm}
{\bfseries ... start the simulation:}\\
......@@ -131,7 +139,7 @@ On the command line (window 1), type\\
{\em ./lens2pexercise1 -{}-parameterFile=exercise1.input}\\
The simulation will start with the given time step size dtInitial (e. g. 100) and run until the simulation time tEnd (use e. g. 2500) is reached.
The simulation will start with the given time step size DtInitial (e. g. 10) and run until the simulation time tEnd (use e. g. $10\,000$) is reached.
If you want to stop the simulation earlier, activate the window from where you started the simulation and press ``Ctrl C'' (or ``Strg C'').\\
\vspace{0.1cm}
......@@ -141,17 +149,17 @@ In window 1, type\\
{\em paraview \&}\\
In paraview you can open your result files (lens-2p.pvd, if you finished a simulation or lens-2p-*.vtu, if you have not finished your simulation). \\
In paraview you can open your result files (lens2p.pvd). \\
\vspace{0.1cm}
{\bfseries ...choose the variable to visualize:}\\
You can either look at the phase pressures or at the saturations. You can choose the variable currently visualized at a small menue at the upper left side of the paraview window. \\
\vspace{0.1cm}
{\bfseries ...adapt the color scale:}\\
To show the saturation or the pressure more clearly it might be necessary to
To show the saturation or the pressure more clearly it might be necessary to
adjust the visualisation scale. You may do this by clicking on the button 'rescale to data range'. You find it on the upper left side of the paraview window next to where you choose your variable currently visualized with a double arrow on it.
\subsection{Questions}
......@@ -181,8 +189,15 @@ Please answer the following questions:
account for?
\end{enumerate}
Hint: If you want to compare different parameter combinations, it might be good to each time run the simulation with a different name, e.g. ``lens2p-highPEntry'' for a case with higher entry pressure in the fine lense.
You can do this either by changing the parameter ``Name'' in the file ``exercise1.input'' or by starting the simulation with: \\
{\em ./lens2pexercise1 -{}-parameterFile exercise1.input -{}-Problem.Name lens2p-highPEntry}\\
Additionally, in case you finished the exercise and want to have a look at the code at:\\
{\em cd /temp/efm2019/DUMUX/dumux-lecture/lecture/efm/1p2cvs2p }\\
\clearpage
%%% Local Variables:
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "handouts-1"
%%% End:
%%% End:
......@@ -16,6 +16,9 @@ FinePermeability = 3.1e-11 # intrinsic permeability of the fine
CoarsePermeability = 3.1e-10 # intrinsic permeability of the coarse porous medium [m^2]
FinePorosity = 0.1 # porosity of the fine porous medium [-]
CoarsePorosity = 0.2 # porosity of the coarse porous medium [-]
########
Parameters only relevant for two-phase simulations:
########
FineBrooksCoreyLambda = 3.5 # pore size distribution parameter for the Brooks-Corey capillary pressure - saturation relationship in the fine soil [-]
FineBrooksCoreyEntryPressure = 400 # entry pressure for the Brooks-Corey capillary pressure - saturation relationship in the fine soil [Pa]
CoarseBrooksCoreyLambda = 2.0 # pore size distribution parameter for the Brooks-Corey capillary pressure - saturation relationship in the coarse soil [-]
......@@ -24,6 +27,7 @@ FineResidualSaturationWetting = 0.05 # residual saturation of the wetting
FineResidualSaturationNonWetting = 0.3 # residual saturation of the non-wetting phase in the fine soil [-]
CoarseResidualSaturationWetting = 0.05 # residual saturation of the wetting phase in the coarse soil [-]
CoarseResidualSaturationNonWetting = 0.1 # residual saturation of the non-wetting phase in the coarse soil [-]
########
[Boundary]
LowerPressure = 1.0e5 # Dirichlet pressure value for the boundary condition at the lower boundary [Pa]
......
......@@ -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}
......@@ -20,7 +20,8 @@ Diffusive forces are to be neglected in this part.
\end{enumerate}
\subsection{Exercise}
Simulate the given problem.
Simulate the given problem.\\
\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.
......@@ -28,7 +29,7 @@ Simulate the given problem.
\end{enumerate}
\clearpage
\subsection{Properties and parameters - exercise3.input}
\subsection{Properties and parameters - lens2pexercise2.input}
\label{prop_paramI}
{\scriptsize
\lstset{numbers=left, breaklines=true, morecomment=[l]{\#}, commentstyle=\color{blue}\tiny, breakindent=28em}
......@@ -39,8 +40,8 @@ Simulate the given problem.
\begin{tabular}[t]{llll}
$\rho_n=$ & non-wetting phase density & $1.46 \cdot 10^{3}$ & [kg/m$^3$] \\
$\rho_w=$ & wetting phase density & $1.0 \cdot 10^{3}$ & [kg/m$^3$] \\
%$\Phi_1=$ & porosity in area one & $0.4$ & [-] \\
%$\Phi_2=$ & porosity in area two & $0.38$ & [-] \\
$\Phi_1=$ & porosity in area one & $0.4$ & [-] \\
$\Phi_2=$ & porosity in area two & $0.38$ & [-] \\
%$\mathbf{K}_1=$ & permeability in area one& $1.0 \cdot 10^{-10} \cdot \mathbf{I}$ & [m$^2$] \\
%$\mathbf{K}_2=$ & permeability in area two & $1.0 \cdot 10^{-13} \cdot \mathbf{I}$ & [m$^2$] \\
$\mathrm{g}=$ & gravitational acceleration & $9.806$ & [m/s$^2$] \\
......@@ -49,67 +50,69 @@ $\mathrm{g}=$ & gravitational acceleration & $9.806$ & [m/s$^2$] \\
\end{table}
% \subsection{How to simulate without ViPLab}
% \label{how_toII}
% \vspace{0.1cm}
%
% {\bfseries ... get the exercise stuff:}\\
%
% Download the handout of the exercise and the simulation tool from the ILIAS system and save everything in home/MSM/exercise2\\
% \vspace{0.1cm}
%
% {\bfseries ... open a window:}\\
%
% In the tool bar at the bottom of the screen, click the symbol with a window
% and a shell. We will call this window ''window 1''. Only one window at the time is
% active. Activate by clicking somewhere in the window.\\
% \vspace{0.1cm}
%
% {\bfseries ... change to the right directory:}\\
%
% On the command line in window 1 type\\
%
% {\em cd MSM/exercise2}\\
% \vspace{0.1cm}
%
% {\bfseries ... set the model parameters:}\\
%
% The parameters used by the program are listed in the file ``lens2pexercise2.input''.
% To open the file, type (in window 1)\\
%
% {\em gedit lens2pexercise2.input}\\
%
% Change the necessary parameters and save the file before you leave the editor.\\
% \vspace{0.1cm}
%
% {\bfseries ... start the simulation:}\\
%
% On the command line (window 1), type\\
%
% {\em ./lens2pexercise2 -parameterFile lens2pexercise2.input }\\
%
% The simulation will start with the given time step size (e. g. 100) and run until the simulation time (use e. g. 10000) is reached.
% If you want to stop the simulation earlier, activate the window from where you started the simulation and press
% \mbox{''Ctrl C''} (or \mbox{''Strg C''}).\\
% \vspace{0.1cm}
%
% {\bfseries ... look at the results:}\\
%
% In window 1, type\\
%
% {\em paraview \&}\\
%
% In paraview you can open your result lens-2p.pvd, if you finished a simulation (or lens-2p-*.vtu, if you have not finished your simulation). \\
% \vspace{0.1cm}
%
% {\bfseries ...choose the variable to visualize:}\\
%
% You can either look at the phase pressures, the capillary pressure (rescale the legend to a small range around the entry pressure of the higher permeable layer) or at the saturations. You can choose the variable currently visualized at a small menue at the upper left side of the paraview window. \\
% \vspace{0.1cm}
\subsection{How to ...}
\label{how_toII}
\vspace{0.1cm}
%
% {\bfseries ...adapt the color scale:}\\
%
% To show the saturation or the pressure more clearly it might be necessary to
% adjust the visualisation scale. You may do this by clicking on the button 'rescale to data range'. You find it on the upper left side of the paraview window next to where you choose your variable currently visualized with a double arrow on it.
{\bfseries ... open a window:}\\
In the tool bar at the bottom of the screen, click the symbol with a window
and a shell. We will call this window ''window 1''. Only one window at the time is
active. Activate by clicking somewhere in the window.\\
\vspace{0.1cm}
{\bfseries ... change to the right directory:}\\
On the command line in window 1 type\\
{\em cd /temp/efm2019/ex2}\\
\vspace{0.1cm}
{\bfseries ... set the model parameters:}\\
The parameters used by the program are listed in the file ``lens2pexercise2.input''.
To open the file, type (in window 1)\\
{\em kate lens2pexercise2.input}\\
Change the necessary parameters and save the file before you leave the editor.\\
\vspace{0.1cm}
{\bfseries ... start the simulation:}\\
On the command line (window 1), type\\
{\em ./lens2pexercise2 lens2pexercise2.input }\\
The simulation will start with the given time step size (e. g. 100) and run until the simulation time (use e. g. 10000) is reached.
If you want to stop the simulation earlier, activate the window from where you started the simulation and press
\mbox{''Ctrl C''} (or \mbox{''Strg C''}).\\
\vspace{0.1cm}
{\bfseries ... look at the results:}\\
In window 1, type\\
{\em paraview \&}\\
In paraview you can open your result lens-2p.pvd. \\
\vspace{0.1cm}
{\bfseries ...choose the variable to visualize:}\\
You can either look at the phase pressures, the capillary pressure (rescale the legend to a small range around the entry pressure of the higher permeable layer) or at the saturations. You can choose the variable currently visualized at a small menue at the upper left side of the paraview window. \\
\vspace{0.1cm}
{\bfseries ...adapt the color scale:}\\
To show the saturation or the pressure more clearly it might be necessary to
adjust the visualisation scale. You may do this by clicking on the button 'rescale to data range'. You find it on the upper left side of the paraview window next to where you choose your variable currently visualized with a double arrow on it.
\vspace{0.1cm}
{\bfseries ...view the code (if you want):}\\
In case you already finished the exercise and want to have a look at the code:\\
{\em cd /temp/efm2019/DUMUX/dumux-lecture/lecture/efm/2p }\\
\clearpage
......@@ -35,17 +35,17 @@ p_D=p_n -p_w = h \mathrm{g} (\rho_n-\rho_w)
\begin{equation}
\label{volume}
V = 3 \cdot 3\cdot h \qquad \mathrm{m}^3
V_\mathrm{1D} = \Phi_1 \cdot 3 \cdot 3\cdot h \qquad \mathrm{m}^3
V_\mathrm{half-sphere} = \Phi_1 \cdot \frac{2}{3} \cdot \pi \cdot h^3 \qquad \mathrm{m}^3
\end{equation}