Commit 76843d61 authored by Johannes Hommel's avatar Johannes Hommel Committed by Katharina Heck

[EFM][Exercise1] updated descriptions, highlighted 2p-parameters in input file

parent dae97a08
......@@ -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}
......@@ -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
......@@ -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, 2019}}
\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}
......@@ -120,9 +120,16 @@ 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.
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.\\
\vspace{0.1cm}
{\bfseries ... start the simulation:}\\
......@@ -131,7 +138,7 @@ 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 +148,17 @@ 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 +188,13 @@ 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}\\
\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]
......
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