From 428d4997f75b2b45cca9b4fdeeeec6945b578c45 Mon Sep 17 00:00:00 2001
From: Maziar Veyskarami <maziar.veyskarami@iws.uni-stuttgart.de>
Date: Fri, 19 Aug 2022 13:29:44 +0200
Subject: [PATCH] [examples][porenetwork_upscaling] update the example
description and figures, include missed header files, add references, minor
changes
---
CHANGELOG.md | 1 +
examples/porenetwork_upscaling/CMakeLists.txt | 14 +-
examples/porenetwork_upscaling/README.md | 41 ++-
examples/porenetwork_upscaling/doc/_intro.md | 41 ++-
examples/porenetwork_upscaling/doc/main.md | 36 ++-
.../porenetwork_upscaling/doc/main_intro.md | 2 +-
examples/porenetwork_upscaling/doc/problem.md | 46 ++-
.../doc/upscalinghelper.md | 276 +++++++++++++-----
.../doc/upscalinghelper_intro.md | 20 +-
...nverse_apppermeability_versus_rhovmu-1.png | Bin 0 -> 34731 bytes
...bility_ratio_versus_forchheimer_number.png | Bin 42823 -> 31909 bytes
examples/porenetwork_upscaling/main.cc | 13 +-
examples/porenetwork_upscaling/params.input | 9 +-
examples/porenetwork_upscaling/problem.hh | 15 +-
examples/porenetwork_upscaling/properties.hh | 12 +-
.../porenetwork_upscaling/spatialparams.hh | 4 +-
.../porenetwork_upscaling/upscalinghelper.hh | 11 +-
...ersePrmeabilityVsInertiaToViscousRatio.dat | 10 +
...r_PermeabilityratioVsForchheimerNumber.dat | 10 +
...noncreeping_flow_X_direction-reference.dat | 15 -
...noncreeping_flow_Y_direction-reference.dat | 15 -
...noncreeping_flow_Z_direction-reference.dat | 15 -
22 files changed, 394 insertions(+), 212 deletions(-)
create mode 100644 examples/porenetwork_upscaling/img/inverse_apppermeability_versus_rhovmu-1.png
create mode 100644 test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_InversePrmeabilityVsInertiaToViscousRatio.dat
create mode 100644 test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_PermeabilityratioVsForchheimerNumber.dat
delete mode 100644 test/references/example_porenetwork_upscaling_noncreeping_flow_X_direction-reference.dat
delete mode 100644 test/references/example_porenetwork_upscaling_noncreeping_flow_Y_direction-reference.dat
delete mode 100644 test/references/example_porenetwork_upscaling_noncreeping_flow_Z_direction-reference.dat
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 6a54811077..cb39e723b1 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,7 @@ that implement an empty cache (i.e. nothing is cached for the flux variables).
- __Pore-network model__: Pore-network model will no longer prevent non-wetting fluid flowing out by default. Throats blocking non-wetting fluid can be specified by setting runtime parameter `InvasionState.BlockNonwettingPhaseAtThroatLabel`.
+- __Examples__: Extend the porenetwork_upscaling example to include non-creeping flow simulation in pore network. The example is able now to provide not only upscaled Darcy permeability but also Forchheimer permeability and coefficient (employed in Forchheimer equation).
### Immediate interface changes not allowing/requiring a deprecation period:
diff --git a/examples/porenetwork_upscaling/CMakeLists.txt b/examples/porenetwork_upscaling/CMakeLists.txt
index efa1bbe485..da306ea845 100644
--- a/examples/porenetwork_upscaling/CMakeLists.txt
+++ b/examples/porenetwork_upscaling/CMakeLists.txt
@@ -6,16 +6,14 @@ dumux_add_test(NAME example_pnm1p_upscaling
CMAKE_GUARD HAVE_UMFPACK dune-foamgrid_FOUND
COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
CMD_ARGS --script fuzzyData --delimiter " "
- --files ${CMAKE_SOURCE_DIR}/test/references/example_porenetwork_upscaling_noncreeping_flow_X_direction-reference.dat
- ${CMAKE_CURRENT_BINARY_DIR}/X-dir.dat
- ${CMAKE_SOURCE_DIR}/test/references/example_porenetwork_upscaling_noncreeping_flow_Y_direction-reference.dat
- ${CMAKE_CURRENT_BINARY_DIR}/Y-dir.dat
- ${CMAKE_SOURCE_DIR}/test/references/example_porenetwork_upscaling_noncreeping_flow_Z_direction-reference.dat
- ${CMAKE_CURRENT_BINARY_DIR}/Z-dir.dat
- --command "${CMAKE_CURRENT_BINARY_DIR}/example_pnm1p_upscaling params.input -Problem.AssumeCreepingFlow false")
+ --files ${CMAKE_SOURCE_DIR}/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_PermeabilityratioVsForchheimerNumber.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/X-dir-PermeabilityratioVsForchheimerNumber.dat
+ ${CMAKE_SOURCE_DIR}/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_InversePrmeabilityVsInertiaToViscousRatio.dat
+ ${CMAKE_CURRENT_BINARY_DIR}/X-dir-InversePrmeabilityVsInertiaToViscousRatio.dat
+ --command "${CMAKE_CURRENT_BINARY_DIR}/example_pnm1p_upscaling params.input -Problem.AssumeCreepingFlow false -Problem.Directions 0")
dumux_add_test(NAME example_pnm1p_creeping_flow_upscaling
TARGET example_pnm1p_upscaling
CMAKE_GUARD HAVE_UMFPACK dune-foamgrid_FOUND
COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
- CMD_ARGS --command "${CMAKE_CURRENT_BINARY_DIR}/example_pnm1p_upscaling params.input -Problem.AssumeCreepingFlow true")
\ No newline at end of file
+ CMD_ARGS --command "${CMAKE_CURRENT_BINARY_DIR}/example_pnm1p_upscaling params.input -Problem.AssumeCreepingFlow true")
diff --git a/examples/porenetwork_upscaling/README.md b/examples/porenetwork_upscaling/README.md
index 117d570f5a..92b1b7c60a 100644
--- a/examples/porenetwork_upscaling/README.md
+++ b/examples/porenetwork_upscaling/README.md
@@ -6,15 +6,15 @@ __In this example, you will learn how to__
* simulate creeping/non-creeping flow on a pore network by applying a pressure gradient in a given direction
* perform an upscaling in order to determine the flow properties of the porous medium such as:
-the Darcy (interinsic) single-phase permeability $`\mathbf{K}`$ [m$`^2`$] using the creeping flow simulation, the Forchheimer permeability $`\mathbf{K}`$ [m$`^2`$] and the Forchheimer coefficient $`\mathbf{\beta}`$ [m$`^{-1}`$] using the non-creeping flow simulation.
+the Darcy (intrinsic) single-phase permeability $`\mathbf{K}`$ [m$`^2`$] using the creeping flow simulation, the Forchheimer permeability $`\mathbf{K}`$ [m$`^2`$] and the Forchheimer coefficient $`\mathbf{\beta}`$ [m$`^{-1}`$] using the non-creeping flow simulation.
__Result__.
-As a result of the creeping flow simulation of this example, you will get the Darcy (interinsic) single-phase permeabilities for each spatial direction $`K_{xx}`$, $`K_{yy}`$, $`K_{zz}`$ [m$`^2`$] as direct output on your terminal as following:
+As a result of the creeping flow simulation of this example, you will get the Darcy (intrinsic) single-phase permeabilities for each spatial direction requested by the user $`K_{xx}`$, $`K_{yy}`$, $`K_{zz}`$ [m$`^2`$] as a direct output on your terminal as the following example for the x-direction:
```
X-direction:
--- Darcy permeability = 3.326e-12 m^2
+-- Darcy (intrinsic) permeability = 3.326e-12 m^2
```
@@ -28,25 +28,34 @@ Figure 1 shows the pressure distribution within the pore network for the case of
</center>
</figure>
-The non-creeping flow simulation additionally gives you Forchheimer permeability and coefficient for each spatial direction as in the example below for the x-direction:
+The non-creeping flow simulation additionally gives you the Forchheimer permeability and coefficient for each spatial direction as in the example below for the x-direction:
```
X-direction:
--- Darcy permeability = 3.326e-12 m^2
--- Forchheimer permeability = 3.270e-12 m^2
--- Forchheimer coefficient = 8.666e+04 m^-1
+-- Darcy (intrinsic) permeability = 3.326e-12 m^2
+-- Forchheimer permeability = 3.196e-12 m^2
+-- Forchheimer coefficient = 8.553e+04 m^-1
```
-Furthermore, the ratio of apparent permeability to Darcy permeability is plotted versus the Forchheimer number for three spatial dimension as figure 2 shows.
+Furthermore, the ratio of apparent permeability to Darcy permeability is plotted versus the Forchheimer number for the spatial dimensions specified by the user, see Fig. 2.
<figure>
<center>
<img src="img/permeability_ratio_versus_forchheimer_number.png" alt="Permeability ratio vs. Forchheimer number" width="60%"/>
- <figcaption> <b> Fig.2 </b> - Variation of apparent to darcy permeability ratio versus Forchheimer number. </figcaption>
+ <figcaption> <b> Fig.2 </b> - Variation of apparent to Darcy permeability ratio versus Forchheimer number. </figcaption>
</center>
</figure>
-After building the executable, use the keyword `Problem.AssumeCreepingFlow` in params.input file to select the flow type to be simulated (i.e. set it true for creeping flow and false for non-creeping flow simulations). Then, run the simulation with `./example_pnm1p_upscaling`.
+In addition, in Fig. 3, the inverse of the apparent permeability versus $`\varrho v /\mu`$ is plotted to compare the data from the pore-network model simulation and the data obtained by applying the Forchheimer equation using the Forchheimer permeability and coefficient. As evident in the figure, the Forchheimer equation is not able to accurately predict the flow behavior in the low-velocity regime.
+<figure>
+ <center>
+ <img src="img/inverse_apppermeability_versus_rhovmu-1.png" alt="Inverse of apparent permeability vs. rhovmu-1" width="60%"/>
+ <figcaption> <b> Fig.3 </b> - Inverse of apparent permeability versus ρv / μ.
+ </figcaption>
+ </center>
+</figure>
+
+After building the executable, use the parameter `Problem.AssumeCreepingFlow` in the `params.input` file to select the flow regime to be simulated (i.e. set it to `true` for creeping flow and to `false` for non-creeping flow simulations). Then, run the simulation with `./example_pnm1p_upscaling`.
__Table of contents__. This description is structured as follows:
@@ -57,17 +66,17 @@ __Table of contents__. This description is structured as follows:
We consider a single-phase problem within a randomly generated pore network of 20x20x20 pores cubed from which some of the pore throats were [deleted randomly](https://doi.org/10.1029/2010WR010180).
The inscribed pore body radii follow a truncated log-normal distribution.
-To calculate the upscaled properties, $`15`$ pressure differences in the range of $`1`$ to $`10^{10}`$ Pa are applied sequentially in every direction, while all lateral sides are closed.
-The resulting mass flow rates are then used to determine upscaled properties as described [later](upscalinghelper.md).
+To calculate the upscaled properties, $`10`$ pressure differences in the range of $`10`$ to $`10^{10}`$ Pa/m are applied sequentially in directions specified by the user by setting the parameter `Problem.Directions` in the `params.input` file, while all lateral sides are closed.
+The resulting mass flow rates are then used to determine upscaled properties as described [later](upscalinghelper.md).
## Mathematical and numerical model
-In this example we are using the single-phase pore-network model of DuMu<sup>x</sup>. We require mass conservation at each pore body $`i`$:
+In this example, we are using the single-phase pore-network model of DuMu<sup>x</sup>. We require mass conservation at each pore body $`i`$:
```math
\sum_j Q_{ij} = 0,
```
-where $`Q_{ij}`$ is the discrete volume flow rate in a throat connecting pore bodies $`i`$ and $`j`$. In case of creeping flow, the pore network model considers a Hagen-Poiseuille-type law to relate the volume flow from on pore body to another to discrete pressure drops $`\Delta p = p_i - p_j`$ between the pore bodies usig throat conductance, $`g_{ij}`$.
+where $`Q_{ij}`$ is the discrete volume flow rate in a throat connecting pore bodies $`i`$ and $`j`$. In case of creeping flow, the pore network model considers a Hagen-Poiseuille-type law to relate the volume flow from on pore body to another to discrete pressure drops $`\Delta p = p_i - p_j`$ between the pore bodies using throat conductance, $`g_{ij}`$.
```math
Q_{ij} = g_{ij} (p_i - p_j),
@@ -78,13 +87,13 @@ or
(p_i - p_j) = Q_{ij} / g_{ij} .
```
-In the simulation of non-creeping flow, to capture inertial effects in fluid flow, an extension of the Hagen-Poiseuille-type law which includes expansion and contraction of flow moving from a throat to a pore and vice versa is used.
+In the simulation of non-creeping flow, to capture inertial effects in fluid flow, an extension of the Hagen-Poiseuille-type law which includes the expansion and contraction of the pore space when moving from a throat to a pore and vice versa.
```math
(p_i - p_j) = Q_{ij} / g_{ij} + (C_{exp} + C_{cont})Q^2,
```
-where $`C_{exp}`$ and $`C_{cont}`$ are expansion and contraction coefficients.
+where $`C_{exp}`$ and $`C_{cont}`$ are the expansion and the contraction coefficient, respectively.
# Implementation & Post processing
diff --git a/examples/porenetwork_upscaling/doc/_intro.md b/examples/porenetwork_upscaling/doc/_intro.md
index 6e75ab181a..12706ab582 100644
--- a/examples/porenetwork_upscaling/doc/_intro.md
+++ b/examples/porenetwork_upscaling/doc/_intro.md
@@ -4,15 +4,15 @@ __In this example, you will learn how to__
* simulate creeping/non-creeping flow on a pore network by applying a pressure gradient in a given direction
* perform an upscaling in order to determine the flow properties of the porous medium such as:
-the Darcy (interinsic) single-phase permeability $`\mathbf{K}`$ [m$`^2`$] using the creeping flow simulation, the Forchheimer permeability $`\mathbf{K}`$ [m$`^2`$] and the Forchheimer coefficient $`\mathbf{\beta}`$ [m$`^{-1}`$] using the non-creeping flow simulation.
+the Darcy (intrinsic) single-phase permeability $`\mathbf{K}`$ [m$`^2`$] using the creeping flow simulation, the Forchheimer permeability $`\mathbf{K}`$ [m$`^2`$] and the Forchheimer coefficient $`\mathbf{\beta}`$ [m$`^{-1}`$] using the non-creeping flow simulation.
__Result__.
-As a result of the creeping flow simulation of this example, you will get the Darcy (interinsic) single-phase permeabilities for each spatial direction $`K_{xx}`$, $`K_{yy}`$, $`K_{zz}`$ [m$`^2`$] as direct output on your terminal as following:
+As a result of the creeping flow simulation of this example, you will get the Darcy (intrinsic) single-phase permeabilities for each spatial direction requested by the user $`K_{xx}`$, $`K_{yy}`$, $`K_{zz}`$ [m$`^2`$] as a direct output on your terminal as the following example for the x-direction:
```
X-direction:
--- Darcy permeability = 3.326e-12 m^2
+-- Darcy (intrinsic) permeability = 3.326e-12 m^2
```
@@ -26,25 +26,34 @@ Figure 1 shows the pressure distribution within the pore network for the case of
</center>
</figure>
-The non-creeping flow simulation additionally gives you Forchheimer permeability and coefficient for each spatial direction as in the example below for the x-direction:
+The non-creeping flow simulation additionally gives you the Forchheimer permeability and coefficient for each spatial direction as in the example below for the x-direction:
```
X-direction:
--- Darcy permeability = 3.326e-12 m^2
--- Forchheimer permeability = 3.270e-12 m^2
--- Forchheimer coefficient = 8.666e+04 m^-1
+-- Darcy (intrinsic) permeability = 3.326e-12 m^2
+-- Forchheimer permeability = 3.196e-12 m^2
+-- Forchheimer coefficient = 8.553e+04 m^-1
```
-Furthermore, the ratio of apparent permeability to Darcy permeability is plotted versus the Forchheimer number for three spatial dimension as figure 2 shows.
+Furthermore, the ratio of apparent permeability to Darcy permeability is plotted versus the Forchheimer number for the spatial dimensions specified by the user, see Fig. 2.
<figure>
<center>
<img src="img/permeability_ratio_versus_forchheimer_number.png" alt="Permeability ratio vs. Forchheimer number" width="60%"/>
- <figcaption> <b> Fig.2 </b> - Variation of apparent to darcy permeability ratio versus Forchheimer number. </figcaption>
+ <figcaption> <b> Fig.2 </b> - Variation of apparent to Darcy permeability ratio versus Forchheimer number. </figcaption>
</center>
</figure>
-After building the executable, use the keyword `Problem.AssumeCreepingFlow` in params.input file to select the flow type to be simulated (i.e. set it true for creeping flow and false for non-creeping flow simulations). Then, run the simulation with `./example_pnm1p_upscaling`.
+In addition, in Fig. 3, the inverse of the apparent permeability versus $`\varrho v /\mu`$ is plotted to compare the data from the pore-network model simulation and the data obtained by applying the Forchheimer equation using the Forchheimer permeability and coefficient. As evident in the figure, the Forchheimer equation is not able to accurately predict the flow behavior in the low-velocity regime.
+<figure>
+ <center>
+ <img src="img/inverse_apppermeability_versus_rhovmu-1.png" alt="Inverse of apparent permeability vs. rhovmu-1" width="60%"/>
+ <figcaption> <b> Fig.3 </b> - Inverse of apparent permeability versus ρv / μ.
+ </figcaption>
+ </center>
+</figure>
+
+After building the executable, use the parameter `Problem.AssumeCreepingFlow` in the `params.input` file to select the flow regime to be simulated (i.e. set it to `true` for creeping flow and to `false` for non-creeping flow simulations). Then, run the simulation with `./example_pnm1p_upscaling`.
__Table of contents__. This description is structured as follows:
@@ -55,17 +64,17 @@ __Table of contents__. This description is structured as follows:
We consider a single-phase problem within a randomly generated pore network of 20x20x20 pores cubed from which some of the pore throats were [deleted randomly](https://doi.org/10.1029/2010WR010180).
The inscribed pore body radii follow a truncated log-normal distribution.
-To calculate the upscaled properties, $`15`$ pressure differences in the range of $`1`$ to $`10^{10}`$ Pa are applied sequentially in every direction, while all lateral sides are closed.
-The resulting mass flow rates are then used to determine upscaled properties as described [later](upscalinghelper.md).
+To calculate the upscaled properties, $`10`$ pressure differences in the range of $`10`$ to $`10^{10}`$ Pa/m are applied sequentially in directions specified by the user by setting the parameter `Problem.Directions` in the `params.input` file, while all lateral sides are closed.
+The resulting mass flow rates are then used to determine upscaled properties as described [later](upscalinghelper.md).
## Mathematical and numerical model
-In this example we are using the single-phase pore-network model of DuMu<sup>x</sup>. We require mass conservation at each pore body $`i`$:
+In this example, we are using the single-phase pore-network model of DuMu<sup>x</sup>. We require mass conservation at each pore body $`i`$:
```math
\sum_j Q_{ij} = 0,
```
-where $`Q_{ij}`$ is the discrete volume flow rate in a throat connecting pore bodies $`i`$ and $`j`$. In case of creeping flow, the pore network model considers a Hagen-Poiseuille-type law to relate the volume flow from on pore body to another to discrete pressure drops $`\Delta p = p_i - p_j`$ between the pore bodies usig throat conductance, $`g_{ij}`$.
+where $`Q_{ij}`$ is the discrete volume flow rate in a throat connecting pore bodies $`i`$ and $`j`$. In case of creeping flow, the pore network model considers a Hagen-Poiseuille-type law to relate the volume flow from on pore body to another to discrete pressure drops $`\Delta p = p_i - p_j`$ between the pore bodies using throat conductance, $`g_{ij}`$.
```math
Q_{ij} = g_{ij} (p_i - p_j),
@@ -76,13 +85,13 @@ or
(p_i - p_j) = Q_{ij} / g_{ij} .
```
-In the simulation of non-creeping flow, to capture inertial effects in fluid flow, an extension of the Hagen-Poiseuille-type law which includes expansion and contraction of flow moving from a throat to a pore and vice versa is used.
+In the simulation of non-creeping flow, to capture inertial effects in fluid flow, an extension of the Hagen-Poiseuille-type law which includes the expansion and contraction of the pore space when moving from a throat to a pore and vice versa.
```math
(p_i - p_j) = Q_{ij} / g_{ij} + (C_{exp} + C_{cont})Q^2,
```
-where $`C_{exp}`$ and $`C_{cont}`$ are expansion and contraction coefficients.
+where $`C_{exp}`$ and $`C_{cont}`$ are the expansion and the contraction coefficient, respectively.
# Implementation & Post processing
diff --git a/examples/porenetwork_upscaling/doc/main.md b/examples/porenetwork_upscaling/doc/main.md
index af18166c72..d484fe132d 100644
--- a/examples/porenetwork_upscaling/doc/main.md
+++ b/examples/porenetwork_upscaling/doc/main.md
@@ -7,7 +7,7 @@
# Part 2: Main program flow
The main program flow is implemented in file `main.cc` described below.
-For each spatial direction x, y and z, flow through the network is simulated using several pressure gradients and the resulting mass flow rate
+For each spatial direction x, y and z, flow through the network is simulated using several pressure gradients and the resulting mass flow rates
are used to determine the upscaled properties.
The code documentation is structured as follows:
@@ -30,7 +30,10 @@ Pore-Network-Model to evaluate the upscaled Darcy permeability of a given networ
#include <iostream>
+#include <algorithm>
+
#include <dune/common/float_cmp.hh> // for floating point comparison
+#include <dune/common/exceptions.hh>
#include <dumux/common/properties.hh> // for GetPropType
#include <dumux/common/parameters.hh> // for getParam
@@ -56,8 +59,8 @@ Pore-Network-Model to evaluate the upscaled Darcy permeability of a given networ
### The driver function
-It depends on the template argument `TypeTag` if we run the example assuming
-a creeping flow regime or not. This is decided with the parameter
+The template argument `TypeTag` determines if we run the example assuming
+a creeping flow regime or not. Which regime is selected is set with the parameter
`Problem.AssumeCreepingFlow` in the input file.
```cpp
@@ -131,9 +134,9 @@ specify the field type explicitly since it may not be possible
to deduce this from the vector size in a pore network
```cpp
- vtkWriter.addField(gridGeometry->poreVolume(), "poreVolume", VtkWriter::FieldType::vertex);
- vtkWriter.addField(gridGeometry->throatShapeFactor(), "throatShapeFactor", VtkWriter::FieldType::element);
- vtkWriter.addField(gridGeometry->throatCrossSectionalArea(), "throatCrossSectionalArea", VtkWriter::FieldType::element);
+ vtkWriter.addField(gridGeometry->poreVolume(), "poreVolume", Vtk::FieldType::vertex);
+ vtkWriter.addField(gridGeometry->throatShapeFactor(), "throatShapeFactor", Vtk::FieldType::element);
+ vtkWriter.addField(gridGeometry->throatCrossSectionalArea(), "throatCrossSectionalArea", Vtk::FieldType::element);
```
### Prepare the upscaling procedure.
@@ -170,10 +173,15 @@ determine it automatically based on the network's bounding box.
problem->setSideLengths(sideLengths);
```
-Get the maximum pressure gradient and the population of sample points specified in the input file
+Get the maximum and minimum pressure gradient and the population of sample points specified in the input file
```cpp
- const Scalar maxPressureGradient = getParam<Scalar>("Problem.MaximumPressureGradient");
+ const Scalar minPressureGradient = getParam<Scalar>("Problem.MinimumPressureGradient", 1e1);
+ const Scalar maxPressureGradient = getParam<Scalar>("Problem.MaximumPressureGradient", 1e10);
+
+ if (!(minPressureGradient < maxPressureGradient))
+ DUNE_THROW(Dune::InvalidStateException, "Maximum pressure gradient must be greater than minimum pressure gradient");
+
const int numberOfSamples = getParam<int>("Problem.NumberOfPressureGradients", 1);
```
@@ -181,7 +189,8 @@ Iterate over all directions specified before, apply several pressure gradient, c
and finally determine the the upscaled properties.
```cpp
- const auto directions = getParam<std::vector<int>>("Problem.Directions", std::vector<int>{0, 1, 2});
+ const auto directions = getParam<std::vector<std::size_t>>("Problem.Directions", std::vector<std::size_t>{0, 1, 2});
+ upscalingHelper.setDirections(directions);
for (int dimIdx : directions)
{
// set the direction in which the pressure gradient will be applied
@@ -193,7 +202,10 @@ and finally determine the the upscaled properties.
x = 0;
// set the pressure gradient to be applied
- Scalar pressureGradient = maxPressureGradient*std::exp(i+1 - numberOfSamples);
+ Scalar pressureGradient = maxPressureGradient * std::exp(i + 1 - numberOfSamples);
+ if (i == 0)
+ pressureGradient = std::min(minPressureGradient, pressureGradient);
+
problem->setPressureGradient(pressureGradient);
// solve problem
@@ -201,7 +213,7 @@ and finally determine the the upscaled properties.
// set the sample points
const Scalar totalFluidMassFlux = boundaryFlux.getFlux(std::vector<int>{ problem->outletPoreLabel() })[0];
- upscalingHelper.setSamplePoints(*problem, totalFluidMassFlux);
+ upscalingHelper.setDataPoints(*problem, totalFluidMassFlux);
}
// write a vtu file for the given direction for the last sample
@@ -210,7 +222,7 @@ and finally determine the the upscaled properties.
// calculate and report the upscaled properties
constexpr bool isCreepingFlow = std::is_same_v<TypeTag, Properties::TTag::PNMUpscalingCreepingFlow>;
- upscalingHelper.calculateUpscaledProperties(isCreepingFlow);
+ upscalingHelper.calculateUpscaledProperties(*problem, isCreepingFlow);
upscalingHelper.report(isCreepingFlow);
// compare the Darcy permeability with reference data if provided in input file and report in case of inconsistency
diff --git a/examples/porenetwork_upscaling/doc/main_intro.md b/examples/porenetwork_upscaling/doc/main_intro.md
index 4e105b6d0f..bb5d5dfd27 100644
--- a/examples/porenetwork_upscaling/doc/main_intro.md
+++ b/examples/porenetwork_upscaling/doc/main_intro.md
@@ -1,7 +1,7 @@
# Part 2: Main program flow
The main program flow is implemented in file `main.cc` described below.
-For each spatial direction x, y and z, flow through the network is simulated using several pressure gradients and the resulting mass flow rate
+For each spatial direction x, y and z, flow through the network is simulated using several pressure gradients and the resulting mass flow rates
are used to determine the upscaled properties.
The code documentation is structured as follows:
diff --git a/examples/porenetwork_upscaling/doc/problem.md b/examples/porenetwork_upscaling/doc/problem.md
index 09635e6eeb..778c5e350e 100644
--- a/examples/porenetwork_upscaling/doc/problem.md
+++ b/examples/porenetwork_upscaling/doc/problem.md
@@ -35,6 +35,19 @@ type tag, which we want to modify or for which no meaningful default can be set.
#include <dumux/porenetwork/1p/model.hh>// for `TTag::PNMOneP`
```
+The class that contains a collection of single-phase flow throat transmissibilities
+among them the transmisibility model to be used can be specified in AdvectionType class
+
+```cpp
+#include <dumux/material/fluidmatrixinteractions/porenetwork/throat/transmissibility1p.hh>
+```
+
+The class that provides specializations for both creeping and non-creeping advection types.
+
+```cpp
+#include <dumux/flux/porenetwork/advection.hh>
+```
+
The local residual for incompressible flow is included.
The one-phase flow model (included above) uses a default implementation of the
local residual for single-phase flow. However, in this example we are using an
@@ -64,7 +77,8 @@ The classes that define the problem and parameters used in this simulation
### `TypeTag` definition
Two `TypeTag` for our simulation are defined, one for creeping flow and another for non-creeping flow,
-which inherit properties from the single-phase pore network model.
+which inherit properties from the single-phase pore network model. The non-creeping flow inherits
+all properties from the creeping flow simulation but sets an own property for the `AdvectionType`.
```cpp
namespace Dumux::Properties {
@@ -110,7 +124,7 @@ public:
using type = PoreNetwork::CreepingFlow<Scalar, TransmissibilityLaw>;
};
-//! The advection type for non-creeping flow (includes model for intertia effects)
+//! The advection type for non-creeping flow (includes model for inertia effects)
template<class TypeTag>
struct AdvectionType<TypeTag, TTag::PNMUpscalingNonCreepingFlow>
{
@@ -217,19 +231,18 @@ Fluid properties that depend on temperature will be calculated with this value.
```cpp
Scalar temperature() const
{ return 283.15; }
- // [[codeblock]]
+```
- // #### Pressure gradient
- // Set the pressure gradient to be applied to the network
- // [[codeblock]]
+Set the pressure gradient to be applied to the network
+
+```cpp
void setPressureGradient(Scalar pressureGradient)
{ pressureGradient_ = pressureGradient; }
```
#### Boundary conditions
This function is used to define the __type of boundary conditions__ used depending on the location.
-Here, we use Dirichlet boundary conditions (fixed pressures) at the inlet and outlet and Neumann
-boundary conditions at all remaining boundaries. Note that the PNM does not support Neumann boundaries.
+Here, we use Dirichlet boundary conditions (fixed pressures) at the inlet and outlet. Note that the PNM does not support Neumann boundaries.
To specify a certain mass flux on a boundary, we would have to use a source term on the boundary pores (which is not done in this example).
```cpp
@@ -302,16 +315,23 @@ and the length of the domain at the inlet.
// Return the applied pressure gradient.
Scalar pressureGradient() const
{ return pressureGradient_; }
+```
+
+</details>
+Return the label of inlet pores assuming a previously set direction.
- // Return the label of inlet pores assuming a previously set direction.
+```cpp
int inletPoreLabel() const
{
static constexpr std::array<int, 3> label = {1, 3, 5};
return label[direction_];
}
+```
+
+Return the label of outlet pores assuming a previously set direction.
- // Return the label of outlet pores assuming a previously set direction.
+```cpp
int outletPoreLabel() const
{
static constexpr std::array<int, 3> label = {2, 4, 6};
@@ -335,8 +355,11 @@ private:
else
return scv.dofPosition()[direction_] > this->gridGeometry().bBoxMax()[direction_] - eps_;
}
+```
+
+private data members
- // private data members
+```cpp
Scalar eps_;
Scalar pressureGradient_;
int direction_;
@@ -347,7 +370,6 @@ private:
} // end namespace Dumux
```
-</details>
</details>
diff --git a/examples/porenetwork_upscaling/doc/upscalinghelper.md b/examples/porenetwork_upscaling/doc/upscalinghelper.md
index b6e3011633..7b671b301a 100644
--- a/examples/porenetwork_upscaling/doc/upscalinghelper.md
+++ b/examples/porenetwork_upscaling/doc/upscalinghelper.md
@@ -4,7 +4,7 @@
| [:arrow_left: Back to the main documentation](../README.md) | [:arrow_left: Go back to part 2](main.md) |
|---|---:|
-The upscaling helper evaluates the pore-network simulation results for each direction $`i`$ and calculates the upscaled properties in this direction. Firstly, it evaluates the the Apparent velocity as:
+The upscaling helper evaluates the pore-network simulation results for each direction $`i`$ and calculates the upscaled properties in this direction. Firstly, it evaluates the apparent velocity as:
```math
v_{\mathrm{Apparent},i} = \frac{q_{\mathrm{mass,tot},i} / \varrho}{A_{\mathrm{tot},i}}
@@ -14,18 +14,29 @@ where $`q_{\mathrm{mass,tot},i}`$ is the total mass flow leaving the network ove
$`A_{\mathrm{tot},i}`$ in $`i`$-direction. $`\varrho `$ is the fluid mass density. Then, we calculate upscaled permeability as:
```math
- K_i = v_{\mathrm{Apparent},i} / \nabla p_i ~ \mu.
+ K_D = v_{\mathrm{Apparent},i} ~ \mu / \nabla p_i.
```
-$`\nabla p_i`$ is a given pressure gradient in $`i`$-direction and $`\mu`$ the fluid dynamic viscosity. In creeping flow simulation, calculated permeability, $`K_i`$, is Darcy (intrinsic) permeability, $`K_D`$ of the system.
+$`\nabla p_i`$ is a given pressure gradient in $`i`$-direction and $`\mu`$ the fluid dynamic viscosity. In the creeping flow simulation, the calculated permeability, $`K_D`$, is the Darcy (intrinsic) permeability of the system.
To simulate non-creeping flow, we use Forchheimer's equation to upscale the properties.
```math
\nabla p_i = \frac{\mu}{K_f} v_{\mathrm{Apparent},i} + \varrho \beta v_{\mathrm{Apparent},i}^2,
```
-where $`K_f`$ is Forchheimer permeability and $`\beta`$ is Forchheimer coefficient. Although some researchers for the sake of simplicity assumes that $`K_f = K_i`$, they are not exactly the same properties. As the velocity increases, the flow regime in a porous medium shifts from Darcy to Forchheimer regime. This change in the flow regime causes that the pressure drop ,which in Darcy flow just includes the viscous dissipation, becomes a combination of both viscous dissipation (the first term in the Forchheimer equation) and the inertial term (the second term in Forchheimer equation). Considering the shift in flow regime, a porous medium having a Forchheimer flow regime shows a different viscous dissipation than when the same porous medium experiences a Darcy fllow. In other words, moving from Darcy to Forchheimr regime establishes a new velocity field in the porous medium which needs a new viscous dissipation and also an inertial term. Furthermore, the first and second terms in Forchheimer equation have strong influence on each other. For more detail, We refer to the study conducted by [Dukhan and Minjeur (2010)](https://link.springer.com/article/10.1007/s10934-010-9393-1). To calculate upscaled properties, we rearrange Forchehimer's equation and find the linear regression line of $`\nabla p_i v_{\mathrm{Apparent},i}/\mu `$ versus $`\varrho v_{\mathrm{Apparent},i}/\mu `$. Using the intercept and the slope of the regreesion line, we can respectively calculate Forchheimr permeability and coefficient. It should be noted that the calculation of the Forchheimer permeability is highly affected by the pressure range applied to the porous medium as well as the number of sample points that are used in the regression process. We compute Darcy (intrinsic) permeability as the maximum permeability of the sample of data of the system which happens when pressure gradient is small enough such that inertial effects are negligible. To ensure such a small pressure gradient, it is recommended to use more than 10 pressure smaple points which can be set in the input file. As mentioned before, considering a slight difference between Darcy (intrinsic) permeability and Forchheimer permeability, in many applications they can be used interchangeabely. Here, however, we distinguish between them, calculate and report them separately.
+where $`K_f`$ is the Forchheimer permeability and $`\beta`$ is the Forchheimer coefficient.
+
+Although it is sometimes assumed for the sake of simplicity that $`K_f = K_D`$, they are not exactly the same properties. As the velocity increases, the flow regime in a porous medium shifts from the Darcy to the Forchheimer regime. This change in the flow regime means that in addition to viscous dissipation (the first term in the Forchheimer equation), we also need to consider inertia effects (the second term in the Forchheimer equation). Moreover, the shift in the flow regime, means a different viscous dissipation than what the same porous medium experiences a Darcy flow. In other words, moving from the Darcy to the Forchheimer regime establishes a new velocity field in the porous medium which causes the difference in viscous dissipation in addition to inertia effects. The first and second terms in the Forchheimer equation are correlated. For more detail, we refer to the study conducted by [Dukhan and Minjeur (2010)](http://dx.doi.org/10.1007/s10934-010-9393-1).
+
+In this example the end of the creeping flow (Darcy regime) is defined as the moment when the pressure drop calculated by the Dracy (intrinsic) permeability $`\Delta p_i = v_{\mathrm{Apparent},i} \mu l/ K_D`$ becomes less than 99% of the total pressure drop [Muljadi et al.](https://doi.org/10.1016/j.advwatres.2015.05.019).
+To calculate upscaled properties, we rearrange Forchehimer's equation as:
+
+```math
+ \frac{\nabla p_i v_{\mathrm{Apparent},i}}{\mu} = \frac{1}{K_f} + \frac{\varrho v_{\mathrm{Apparent},i}}{\mu} \beta .
+```
+Finding the linear regression line of $`\nabla p_i v_{\mathrm{Apparent},i}/\mu `$ versus $`\varrho v_{\mathrm{Apparent},i}/\mu `$ and using the intercept and the slope of the regression line, we can respectively calculate the Forchheimer permeability and coefficient. It should be noted that the calculation of the Forchheimer permeability can be affected by the pressure range applied to the porous medium as well as the number of sample points that are used in the regression process. We compute the Darcy (intrinsic) permeability as the maximum permeability of the sample of data of the system which happens when the pressure gradient is small enough such that inertial effects are negligible. To ensure such a small pressure gradient, we set the first pressure gradient to be applied as $'10 Pa/m'$. However, this value can be adapted using the keyword `Problem.MinimumPressureGradient` in params.input. it is recommended to use more than 10 pressure sample points which can be set in the input file. As mentioned before, considering a slight difference between Darcy (intrinsic) permeability and Forchheimer permeability, in many applications they can be used interchangeabely. Here, however, we distinguish between them, calculate and report them separately.
The code documentation is structured as follows:
+
## Upscaling helper struct (`upscalinghelper.hh`)
This file contains the __upscaling helper struct__ which considers the volume flux leaving
@@ -52,42 +63,46 @@ class UpscalingHelper
public:
```
-### Set sample points to calculate intrinsic permeability and Forchheimer coefficient
+### Set data points to calculate intrinsic permeability and Forchheimer coefficient
This function first evaluates the mass flux leaving the network in the direction of the applied pressure gradient.
-Afterwards, the mass flux is converted into an area specify volume flux which with its corresponding pressure gradient are stored as
-sample points to be used in regression operation to find intrinsic permeability and Forchheimer coefficient
+Afterwards, the mass flux is converted into an volume flux which is used to calculate the apparent velocity.
+Then apparent permeability of the network is computed and stored for furthure calculations.
```cpp
- template<class Problem>
- void setSamplePoints(const Problem& problem, const Scalar totalMassFlux)
+ template <class Problem>
+ void setDataPoints(const Problem &problem, const Scalar totalMassFlux)
{
// get the domain side lengths from the problem
auto sideLengths = problem.sideLengths();
+
+ // get the applied pressure gradient
+ const auto pressureGradient = problem.pressureGradient();
+ const auto pressureDrop = pressureGradient * sideLengths[problem.direction()];
+
+ // get the fluid properties
+ const auto liquidDensity = problem.liquidDensity();
+ const auto liquidDynamicViscosity = problem.liquidDynamicViscosity();
+
// convert mass to volume flux
- const auto volumeFlux = totalMassFlux / problem.liquidDensity();;
+ const auto volumeFlux = totalMassFlux / liquidDensity;
+ ;
// calculate apparent velocity
sideLengths[problem.direction()] = 1.0;
const auto outflowArea = std::accumulate(sideLengths.begin(), sideLengths.end(), 1.0, std::multiplies<Scalar>());
- const auto vApparent= volumeFlux / outflowArea;
-
- // set sample point for permability calculation
- const auto samplePointY = problem.pressureGradient() / problem.liquidDynamicViscosity() / vApparent;
- const auto samplePointX = problem.liquidDensity() * vApparent / problem.liquidDynamicViscosity();
-
- samplePointsX_[problem.direction()].push_back(samplePointX);
- samplePointsY_[problem.direction()].push_back(samplePointY);
+ const auto vApparent = volumeFlux / outflowArea;
// compute apparent permeability
- const auto K = vApparent / problem.pressureGradient() * problem.liquidDynamicViscosity();
-
- // calculate Forchheimer number (Forchheimer coefficient will be included later)
- const auto forchheimerNumber = problem.liquidDensity() * vApparent / problem.liquidDynamicViscosity();
-
- // store apparent permeability and corresponding Forchheimer number
- apparentPermeability_[problem.direction()].push_back(K);
- forchheimerNumber_[problem.direction()].push_back(forchheimerNumber);
+ const auto KApparent = vApparent / pressureGradient * liquidDynamicViscosity;
+ // calculate rho v / mu, called inertia to viscous ratio in the rest of the code
+ const auto inertiaToViscousRatio = liquidDensity * vApparent / liquidDynamicViscosity;
+
+ // store the required data for further calculations
+ totalPressureDrop_[problem.direction()].push_back(pressureDrop);
+ apparentVelocity_[problem.direction()].push_back(vApparent);
+ apparentPermeability_[problem.direction()].push_back(KApparent);
+ inertiaToViscousRatio_[problem.direction()].push_back(inertiaToViscousRatio);
}
```
@@ -97,14 +112,34 @@ and reports them. It also plot the apparent permeability of the porous medium ve
simulation.
```cpp
- void calculateUpscaledProperties(bool isCreepingFlow)
+ template <class Problem>
+ void calculateUpscaledProperties(const Problem &problem, bool isCreepingFlow)
{
- for (int dirIdx = 0; dirIdx < 3; dirIdx++)
+ const auto sideLengths = problem.sideLengths();
+ const auto liquidDynamicViscosity = problem.liquidDynamicViscosity();
+
+ for (const auto dirIdx : directions_)
{
// determine Darcy permeability as the maximum permeability of the domain
darcyPermeability_[dirIdx] = *max_element(apparentPermeability_[dirIdx].begin(), apparentPermeability_[dirIdx].end());
if (!isCreepingFlow)
{
+ for (int i = 0; i < totalPressureDrop_[dirIdx].size(); i++)
+ {
+ // calculate the Darcy pressure drop.
+ const Scalar darcyPressureDrop = liquidDynamicViscosity * apparentVelocity_[dirIdx][i] * sideLengths[dirIdx] / darcyPermeability_[dirIdx];
+
+ // calculate the ratio of Dracy to total pressure drop
+ const Scalar pressureDropRatio = darcyPressureDrop / totalPressureDrop_[dirIdx][i];
+
+ // set sample points for upscaling of Forchheimer parameters.
+ // first, check the permability ratio to see if the flow regime is Forchheimer.
+ if (pressureDropRatio < 0.99)
+ {
+ samplePointsX_[dirIdx].push_back(inertiaToViscousRatio_[dirIdx][i]);
+ samplePointsY_[dirIdx].push_back(1 / apparentPermeability_[dirIdx][i]);
+ }
+ }
// determine regression line and accordingly the Forchheimer permeability and the Forchheimer coefficient
const auto [intercept, slope] = linearRegression(samplePointsX_[dirIdx], samplePointsY_[dirIdx]);
forchheimerPermeability_[dirIdx] = 1.0 / intercept;
@@ -140,27 +175,11 @@ We determine the domain side length by using the bounding box of the network
```cpp
void plot()
{
- // using gnuplot interface
- Dumux::GnuplotInterface<Scalar> gnuplot(true);
- gnuplot.setOpenPlotWindow(true);
- std::string title{}, option{};
- for (int dirIdx = 0; dirIdx < 3; dirIdx++)
- {
- // add the data in each direction for plot
- gnuplot.addFileToPlot(dirName_[dirIdx] + "-dir.dat");
- // set the properties of lines to be plotted
- option += Fmt::format("set linetype {0} linecolor {0} linewidth 7\n", dirIdx+1);
- // report the darcy permeability in each direction as the title of the plot
- title += Fmt::format("{}-permeability= {:.3e} m^2 ", dirName_[dirIdx], darcyPermeability_[dirIdx]);
- }
- option +="set title \"" + title + "\"\n";
- option += "set logscale x""\n";
- option += "set format x '10^{%L}'""\n";
-
- gnuplot.setXlabel("Forchheimer Number [-]");
- gnuplot.setYlabel("Apparent permeability / Darcy permeability [-]");
- gnuplot.setOption(option);
- gnuplot.plot("permeability_ratio_versus_forchheimer_number");
+ // plot permeability ratio vs. Forchheimer number
+ plotPermeabilityratioVsForchheimerNumber_();
+
+ // plot inverse of apparent permability vs. rho v / mu
+ plotInversePrmeabilityVsInertiaToViscousRatio_();
}
```
@@ -170,21 +189,11 @@ We determine the domain side length by using the bounding box of the network
```cpp
void writePlotDataToFile(std::size_t dirIdx)
{
- // Open a logfile
- std::ofstream logfile(dirName_[dirIdx]+"-dir.dat");
+ // write permeability ratio vs. Forchheimer number
+ writePermeabilityratioVsForchheimerNumber_(dirIdx);
- // Save the data needed to be plotted in logfile
- for (int i = 0; i < apparentPermeability_[dirIdx].size(); i++)
- {
- // Include characteristics length, sqrt(permeability) to Reynolds number calculation
- const Scalar forchheimerNumber
- = darcyPermeability_[dirIdx] * forchheimerCoefficient_[dirIdx] * forchheimerNumber_[dirIdx][i];
- // Ratio between apparrent permeability and darcy permeability
- const Scalar permeabilityRatio
- = apparentPermeability_[dirIdx][i] / darcyPermeability_[dirIdx];
-
- logfile << forchheimerNumber<< " " << permeabilityRatio << std::endl;
- }
+ // write inverse of apparent permability vs. rho v / mu
+ writeInversePrmeabilityVsInertiaToViscousRatio_(dirIdx);
}
```
@@ -195,7 +204,7 @@ We determine the domain side length by using the bounding box of the network
void report(bool isCreepingFlow)
{
// Report the results for each direction
- for (int dirIdx = 0; dirIdx < 3; dirIdx++)
+ for (const auto dirIdx : directions_)
{
std::cout << Fmt::format("\n{:#>{}}\n\n", "", 40)
<< Fmt::format("{}-direction:\n", dirName_[dirIdx])
@@ -219,7 +228,7 @@ We determine the domain side length by using the bounding box of the network
```cpp
void compareWithReference(std::vector<Scalar> referenceData)
{
- for (int dirIdx = 0; dirIdx < 3; dirIdx++)
+ for (const auto dirIdx : directions_)
{
const auto K = darcyPermeability_[dirIdx];
static const Scalar eps = getParam<Scalar>("Problem.TestEpsilon", 1e-3);
@@ -234,16 +243,151 @@ We determine the domain side length by using the bounding box of the network
```
+### Set the directions that need to be considered
+
+
```cpp
+ void setDirections(std::vector<std::size_t> directions)
+ {
+ directions_ = directions;
+ }
+ // [[codeblock]]
+
private:
+ // ### Save the relevant data for plot of permeability ratio vs. Forchheimer number
+ // [[codeblock]]
+ void writePermeabilityratioVsForchheimerNumber_(std::size_t dirIdx)
+ {
+ // open a logfile
+ std::ofstream logfile(dirName_[dirIdx] + "-dir-PermeabilityratioVsForchheimerNumber.dat");
+
+ // save the data needed to be plotted in logfile
+ for (int i = 0; i < apparentPermeability_[dirIdx].size(); i++)
+ {
+ // compute the Forchheimer number
+ const Scalar forchheimerNumber = darcyPermeability_[dirIdx] * forchheimerCoefficient_[dirIdx] * inertiaToViscousRatio_[dirIdx][i];
+ // ratio between apparrent permeability and darcy permeability
+ const Scalar permeabilityRatio = apparentPermeability_[dirIdx][i] / darcyPermeability_[dirIdx];
+
+ logfile << forchheimerNumber << " " << permeabilityRatio << std::endl;
+ }
+ }
+```
+
+### Save the relevant data for plot of inverse of apparent permability vs. rho v / mu
+
+```cpp
+ void writeInversePrmeabilityVsInertiaToViscousRatio_(std::size_t dirIdx)
+ {
+ // open a logfile and write inverese of apparent permeability given by the model vs. inertial to viscous ratio (rho v / mu)
+ std::ofstream logfile(dirName_[dirIdx] + "-dir-InversePrmeabilityVsInertiaToViscousRatio.dat");
+
+ // save the data needed to be plotted in logfile
+ for (int i = 0; i < apparentPermeability_[dirIdx].size(); i++)
+ {
+ const Scalar inertiaToViscousRatio = inertiaToViscousRatio_[dirIdx][i];
+ const Scalar inverseAppPermeability = 1 / apparentPermeability_[dirIdx][i];
+
+ // compute inverse of apparent permeability using the Forchheimer permeability and coefficient
+ const Scalar inverseAppPermeabilityForchheimer = 1 / forchheimerPermeability_[dirIdx] + inertiaToViscousRatio * forchheimerCoefficient_[dirIdx];
+
+ logfile << inertiaToViscousRatio << " " << 1e-12 * inverseAppPermeability << " " << 1e-12 * inverseAppPermeabilityForchheimer << std::endl;
+ }
+ }
+```
+
+
+### Plot permeability ratio vs. Forchheimer number using Gnuplot
+
+
+```cpp
+ void plotPermeabilityratioVsForchheimerNumber_()
+ {
+ // using gnuplot interface
+ Dumux::GnuplotInterface<Scalar> gnuplot(true);
+ gnuplot.setOpenPlotWindow(true);
+
+ for (const auto dirIdx : directions_)
+ {
+ gnuplot.resetAll();
+ std::string title{}, option{};
+
+ // add the data in each direction for plot
+ gnuplot.addFileToPlot(dirName_[dirIdx] + "-dir-PermeabilityratioVsForchheimerNumber.dat", "notitle with lines");
+ // set the properties of lines to be plotted
+ option += "set linetype 1 linecolor 1 linewidth 7\n";
+ // report the darcy permeability in each direction as the title of the plot
+ title += Fmt::format("{}-direction, Darcy permeability= {:.3e} m^2 ", dirName_[dirIdx], darcyPermeability_[dirIdx]);
+
+ option += "set title \"" + title + "\"\n";
+ option += "set logscale x""\n";
+ option += "set format x '10^{%L}'""\n";
+
+ gnuplot.setXlabel("Forchheimer Number [-]");
+ gnuplot.setYlabel("Apparent permeability / Darcy permeability [-]");
+ gnuplot.setOption(option);
+ gnuplot.plot("permeability_ratio_versus_forchheimer_number");
+ }
+ }
+```
+
+
+### Plot inverse of apparent permability vs. rho v / mu using Gnuplot
+
+
+```cpp
+ void plotInversePrmeabilityVsInertiaToViscousRatio_()
+ {
+ // using gnuplot interface
+ Dumux::GnuplotInterface<Scalar> gnuplot(true);
+ gnuplot.setOpenPlotWindow(true);
+
+ for (const auto dirIdx : directions_)
+ {
+ gnuplot.resetAll();
+ std::string title{}, option{};
+ std::string legend0 = "u 1:2 title \"Network model\" with lines";
+ // add the data in each direction for plot, first set of data
+ gnuplot.addFileToPlot(dirName_[dirIdx] + "-dir-InversePrmeabilityVsInertiaToViscousRatio.dat", legend0);
+
+ // set the properties of lines to be plotted
+ option += "set linetype 1 linecolor 1 linewidth 5\n";
+
+ std::string legend1 = "u 1:3 title \"Forchheimer equation\" with lines";
+ // add the data in each direction for plot, second set of data
+ gnuplot.addFileToPlot(dirName_[dirIdx] + "-dir-InversePrmeabilityVsInertiaToViscousRatio.dat", legend1);
+
+ // set the properties of lines to be plotted
+ option += "set linetype 2 linecolor 2 linewidth 5\n";
+
+ // report the darcy permeability in each direction as the title of the plot
+ title += Fmt::format("{}-direction, Darcy permeability= {:.3e} m^2 ", dirName_[dirIdx], darcyPermeability_[dirIdx]);
+
+ option += "set title \"" + title + "\"\n";
+ option += "set logscale x""\n";
+ option += "set format x '10^{%L}'""\n";
+
+ gnuplot.setXlabel("{/Symbol r} v / {/Symbol m} [1/m]");
+ gnuplot.setYlabel("1/ Apparent permeability [1/m^2] x 1e12");
+ gnuplot.setOption(option);
+ gnuplot.plot("inverse_apppermeability_versus_rhovmu-1");
+ }
+ }
+```
+
+
+```cpp
std::array<std::vector<Scalar>, 3> samplePointsX_;
std::array<std::vector<Scalar>, 3> samplePointsY_;
+ std::array<std::vector<Scalar>, 3>totalPressureDrop_;
+ std::array<std::vector<Scalar>, 3> apparentVelocity_;
std::array<std::vector<Scalar>, 3> apparentPermeability_;
- std::array<std::vector<Scalar>, 3> forchheimerNumber_;
+ std::array<std::vector<Scalar>, 3> inertiaToViscousRatio_;
std::array<Scalar, 3> darcyPermeability_;
std::array<Scalar, 3> forchheimerPermeability_;
std::array<Scalar, 3> forchheimerCoefficient_;
const std::array<std::string, 3> dirName_ = {"X", "Y", "Z"};
+ std::vector<std::size_t> directions_;
};
} // end namespace Dumux
diff --git a/examples/porenetwork_upscaling/doc/upscalinghelper_intro.md b/examples/porenetwork_upscaling/doc/upscalinghelper_intro.md
index 55d485f057..76c143622b 100644
--- a/examples/porenetwork_upscaling/doc/upscalinghelper_intro.md
+++ b/examples/porenetwork_upscaling/doc/upscalinghelper_intro.md
@@ -1,4 +1,4 @@
-The upscaling helper evaluates the pore-network simulation results for each direction $`i`$ and calculates the upscaled properties in this direction. Firstly, it evaluates the the Apparent velocity as:
+The upscaling helper evaluates the pore-network simulation results for each direction $`i`$ and calculates the upscaled properties in this direction. Firstly, it evaluates the apparent velocity as:
```math
v_{\mathrm{Apparent},i} = \frac{q_{\mathrm{mass,tot},i} / \varrho}{A_{\mathrm{tot},i}}
@@ -8,14 +8,24 @@ where $`q_{\mathrm{mass,tot},i}`$ is the total mass flow leaving the network ove
$`A_{\mathrm{tot},i}`$ in $`i`$-direction. $`\varrho `$ is the fluid mass density. Then, we calculate upscaled permeability as:
```math
- K_i = v_{\mathrm{Apparent},i} / \nabla p_i ~ \mu.
+ K_D = v_{\mathrm{Apparent},i} ~ \mu / \nabla p_i.
```
-$`\nabla p_i`$ is a given pressure gradient in $`i`$-direction and $`\mu`$ the fluid dynamic viscosity. In creeping flow simulation, calculated permeability, $`K_i`$, is Darcy (intrinsic) permeability, $`K_D`$ of the system.
+$`\nabla p_i`$ is a given pressure gradient in $`i`$-direction and $`\mu`$ the fluid dynamic viscosity. In the creeping flow simulation, the calculated permeability, $`K_D`$, is the Darcy (intrinsic) permeability of the system.
To simulate non-creeping flow, we use Forchheimer's equation to upscale the properties.
```math
\nabla p_i = \frac{\mu}{K_f} v_{\mathrm{Apparent},i} + \varrho \beta v_{\mathrm{Apparent},i}^2,
```
-where $`K_f`$ is Forchheimer permeability and $`\beta`$ is Forchheimer coefficient. Although some researchers for the sake of simplicity assumes that $`K_f = K_i`$, they are not exactly the same properties. As the velocity increases, the flow regime in a porous medium shifts from Darcy to Forchheimer regime. This change in the flow regime causes that the pressure drop ,which in Darcy flow just includes the viscous dissipation, becomes a combination of both viscous dissipation (the first term in the Forchheimer equation) and the inertial term (the second term in Forchheimer equation). Considering the shift in flow regime, a porous medium having a Forchheimer flow regime shows a different viscous dissipation than when the same porous medium experiences a Darcy fllow. In other words, moving from Darcy to Forchheimr regime establishes a new velocity field in the porous medium which needs a new viscous dissipation and also an inertial term. Furthermore, the first and second terms in Forchheimer equation have strong influence on each other. For more detail, We refer to the study conducted by [Dukhan and Minjeur (2010)](https://link.springer.com/article/10.1007/s10934-010-9393-1). To calculate upscaled properties, we rearrange Forchehimer's equation and find the linear regression line of $`\nabla p_i v_{\mathrm{Apparent},i}/\mu `$ versus $`\varrho v_{\mathrm{Apparent},i}/\mu `$. Using the intercept and the slope of the regreesion line, we can respectively calculate Forchheimr permeability and coefficient. It should be noted that the calculation of the Forchheimer permeability is highly affected by the pressure range applied to the porous medium as well as the number of sample points that are used in the regression process. We compute Darcy (intrinsic) permeability as the maximum permeability of the sample of data of the system which happens when pressure gradient is small enough such that inertial effects are negligible. To ensure such a small pressure gradient, it is recommended to use more than 10 pressure smaple points which can be set in the input file. As mentioned before, considering a slight difference between Darcy (intrinsic) permeability and Forchheimer permeability, in many applications they can be used interchangeabely. Here, however, we distinguish between them, calculate and report them separately.
+where $`K_f`$ is the Forchheimer permeability and $`\beta`$ is the Forchheimer coefficient.
-The code documentation is structured as follows:
\ No newline at end of file
+Although it is sometimes assumed for the sake of simplicity that $`K_f = K_D`$, they are not exactly the same properties. As the velocity increases, the flow regime in a porous medium shifts from the Darcy to the Forchheimer regime. This change in the flow regime means that in addition to viscous dissipation (the first term in the Forchheimer equation), we also need to consider inertia effects (the second term in the Forchheimer equation). Moreover, the shift in the flow regime, means a different viscous dissipation than what the same porous medium experiences a Darcy flow. In other words, moving from the Darcy to the Forchheimer regime establishes a new velocity field in the porous medium which causes the difference in viscous dissipation in addition to inertia effects. The first and second terms in the Forchheimer equation are correlated. For more detail, we refer to the study conducted by [Dukhan and Minjeur (2010)](http://dx.doi.org/10.1007/s10934-010-9393-1).
+
+In this example the end of the creeping flow (Darcy regime) is defined as the moment when the pressure drop calculated by the Dracy (intrinsic) permeability $`\Delta p_i = v_{\mathrm{Apparent},i} \mu l/ K_D`$ becomes less than 99% of the total pressure drop [Muljadi et al.](https://doi.org/10.1016/j.advwatres.2015.05.019).
+To calculate upscaled properties, we rearrange Forchehimer's equation as:
+
+```math
+ \frac{\nabla p_i v_{\mathrm{Apparent},i}}{\mu} = \frac{1}{K_f} + \frac{\varrho v_{\mathrm{Apparent},i}}{\mu} \beta .
+```
+Finding the linear regression line of $`\nabla p_i v_{\mathrm{Apparent},i}/\mu `$ versus $`\varrho v_{\mathrm{Apparent},i}/\mu `$ and using the intercept and the slope of the regression line, we can respectively calculate the Forchheimer permeability and coefficient. It should be noted that the calculation of the Forchheimer permeability can be affected by the pressure range applied to the porous medium as well as the number of sample points that are used in the regression process. We compute the Darcy (intrinsic) permeability as the maximum permeability of the sample of data of the system which happens when the pressure gradient is small enough such that inertial effects are negligible. To ensure such a small pressure gradient, we set the first pressure gradient to be applied as $'10 Pa/m'$. However, this value can be adapted using the keyword `Problem.MinimumPressureGradient` in params.input. it is recommended to use more than 10 pressure sample points which can be set in the input file. As mentioned before, considering a slight difference between Darcy (intrinsic) permeability and Forchheimer permeability, in many applications they can be used interchangeabely. Here, however, we distinguish between them, calculate and report them separately.
+
+The code documentation is structured as follows:
diff --git a/examples/porenetwork_upscaling/img/inverse_apppermeability_versus_rhovmu-1.png b/examples/porenetwork_upscaling/img/inverse_apppermeability_versus_rhovmu-1.png
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diff --git a/examples/porenetwork_upscaling/img/permeability_ratio_versus_forchheimer_number.png b/examples/porenetwork_upscaling/img/permeability_ratio_versus_forchheimer_number.png
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diff --git a/examples/porenetwork_upscaling/main.cc b/examples/porenetwork_upscaling/main.cc
index 91e25974e8..540109b475 100644
--- a/examples/porenetwork_upscaling/main.cc
+++ b/examples/porenetwork_upscaling/main.cc
@@ -30,6 +30,7 @@
#include <algorithm>
#include <dune/common/float_cmp.hh> // for floating point comparison
+#include <dune/common/exceptions.hh>
#include <dumux/common/properties.hh> // for GetPropType
#include <dumux/common/parameters.hh> // for getParam
@@ -54,8 +55,8 @@
//
// ### The driver function
//
-// It depends on the template argument `TypeTag` if we run the example assuming
-// a creeping flow regime or not. This is decided with the parameter
+// The template argument `TypeTag` determines if we run the example assuming
+// a creeping flow regime or not. Which regime is selected is set with the parameter
// `Problem.AssumeCreepingFlow` in the input file.
namespace Dumux {
@@ -116,9 +117,9 @@ void runExample()
VtkOutputFields::initOutputModule(vtkWriter);
// specify the field type explicitly since it may not be possible
// to deduce this from the vector size in a pore network
- vtkWriter.addField(gridGeometry->poreVolume(), "poreVolume", VtkWriter::FieldType::vertex);
- vtkWriter.addField(gridGeometry->throatShapeFactor(), "throatShapeFactor", VtkWriter::FieldType::element);
- vtkWriter.addField(gridGeometry->throatCrossSectionalArea(), "throatCrossSectionalArea", VtkWriter::FieldType::element);
+ vtkWriter.addField(gridGeometry->poreVolume(), "poreVolume", Vtk::FieldType::vertex);
+ vtkWriter.addField(gridGeometry->throatShapeFactor(), "throatShapeFactor", Vtk::FieldType::element);
+ vtkWriter.addField(gridGeometry->throatCrossSectionalArea(), "throatCrossSectionalArea", Vtk::FieldType::element);
// ### Prepare the upscaling procedure.
// Set up a helper class to determine the total mass flux leaving the network
@@ -155,7 +156,7 @@ void runExample()
const Scalar maxPressureGradient = getParam<Scalar>("Problem.MaximumPressureGradient", 1e10);
if (!(minPressureGradient < maxPressureGradient))
- throw std::runtime_error("maximum pressure gradient must be greater than minimum pressure gradient");
+ DUNE_THROW(Dune::InvalidStateException, "Maximum pressure gradient must be greater than minimum pressure gradient");
const int numberOfSamples = getParam<int>("Problem.NumberOfPressureGradients", 1);
// [[/codeblock]]
diff --git a/examples/porenetwork_upscaling/params.input b/examples/porenetwork_upscaling/params.input
index 19cdb8e5eb..12261739b5 100644
--- a/examples/porenetwork_upscaling/params.input
+++ b/examples/porenetwork_upscaling/params.input
@@ -1,11 +1,10 @@
[Problem]
EnableGravity = 0 # disable gravity
Name = upscaling_pnm
-MinimumPressureGradient = 1e5
-MaximumPressureGradient = 1e10
-NumberOfPressureGradients = 5 # the number of sample points for regression process
-Directions = 0 # the directions to be plotet 0 1 2
-Epsilon = 1e-3
+MaximumPressureGradient = 1e10 #Pa/m
+NumberOfPressureGradients = 10 # the number of sample points for regression process
+Directions = 0 # the directions to be plotted 0 1 2
+Epsilon = 1e-13
AssumeCreepingFlow = false
ReferencePermeability = 3.326e-12 1.394e-12 7.449e-13
diff --git a/examples/porenetwork_upscaling/problem.hh b/examples/porenetwork_upscaling/problem.hh
index f1e55f1b01..2b028111c5 100644
--- a/examples/porenetwork_upscaling/problem.hh
+++ b/examples/porenetwork_upscaling/problem.hh
@@ -78,19 +78,15 @@ public:
// [[codeblock]]
Scalar temperature() const
{ return 283.15; }
- // [[codeblock]]
+ // [[/codeblock]]
- // #### Pressure gradient
// Set the pressure gradient to be applied to the network
- // [[codeblock]]
void setPressureGradient(Scalar pressureGradient)
{ pressureGradient_ = pressureGradient; }
- // [[codeblock]]
// #### Boundary conditions
// This function is used to define the __type of boundary conditions__ used depending on the location.
- // Here, we use Dirichlet boundary conditions (fixed pressures) at the inlet and outlet and Neumann
- // boundary conditions at all remaining boundaries. Note that the PNM does not support Neumann boundaries.
+ // Here, we use Dirichlet boundary conditions (fixed pressures) at the inlet and outlet. Note that the PNM does not support Neumann boundaries.
// To specify a certain mass flux on a boundary, we would have to use a source term on the boundary pores (which is not done in this example).
// [[codeblock]]
BoundaryTypes boundaryTypes(const Element &element, const SubControlVolume& scv) const
@@ -161,8 +157,9 @@ public:
// Return the applied pressure gradient.
Scalar pressureGradient() const
{ return pressureGradient_; }
-
-
+ // [[/codeblock]]
+ // [[/details]]
+ //
// Return the label of inlet pores assuming a previously set direction.
int inletPoreLabel() const
{
@@ -204,7 +201,5 @@ private:
};
} // end namespace Dumux
-// [[/codeblock]]
-// [[/details]]
// [[/content]]
#endif
diff --git a/examples/porenetwork_upscaling/properties.hh b/examples/porenetwork_upscaling/properties.hh
index d33fdb985b..0aa7ad8fe1 100644
--- a/examples/porenetwork_upscaling/properties.hh
+++ b/examples/porenetwork_upscaling/properties.hh
@@ -34,6 +34,13 @@
// type tag, which we want to modify or for which no meaningful default can be set.
#include <dumux/porenetwork/1p/model.hh>// for `TTag::PNMOneP`
+// The class that contains a collection of single-phase flow throat transmissibilities
+// among them the transmisibility model to be used can be specified in AdvectionType class
+#include <dumux/material/fluidmatrixinteractions/porenetwork/throat/transmissibility1p.hh>
+
+// The class that provides specializations for both creeping and non-creeping advection types.
+#include <dumux/flux/porenetwork/advection.hh>
+
// The local residual for incompressible flow is included.
// The one-phase flow model (included above) uses a default implementation of the
// local residual for single-phase flow. However, in this example we are using an
@@ -53,7 +60,8 @@
//
// ### `TypeTag` definition
// Two `TypeTag` for our simulation are defined, one for creeping flow and another for non-creeping flow,
-// which inherit properties from the single-phase pore network model.
+// which inherit properties from the single-phase pore network model. The non-creeping flow inherits
+// all properties from the creeping flow simulation but sets an own property for the `AdvectionType`.
namespace Dumux::Properties {
namespace TTag {
struct PNMUpscalingCreepingFlow { using InheritsFrom = std::tuple<PNMOneP>; };
@@ -95,7 +103,7 @@ public:
using type = PoreNetwork::CreepingFlow<Scalar, TransmissibilityLaw>;
};
-//! The advection type for non-creeping flow (includes model for intertia effects)
+//! The advection type for non-creeping flow (includes model for inertia effects)
template<class TypeTag>
struct AdvectionType<TypeTag, TTag::PNMUpscalingNonCreepingFlow>
{
diff --git a/examples/porenetwork_upscaling/spatialparams.hh b/examples/porenetwork_upscaling/spatialparams.hh
index d4c6c7c256..4faa56f345 100644
--- a/examples/porenetwork_upscaling/spatialparams.hh
+++ b/examples/porenetwork_upscaling/spatialparams.hh
@@ -102,14 +102,14 @@ public:
return M_PI * r * r;
}
- // dimensionless kinetic-energy coeffiecient which for non-creeping flow
+ // dimensionless kinetic-energy coefficient which for non-creeping flow
template<class ElementSolutionVector>
Scalar kineticEnergyCoefficient(const Element& element,
const SubControlVolume& scv,
const ElementSolutionVector& elemSol) const
{ return 1.0; }
- // dimensionless momentum coeffiecient which for non-creeping flow
+ // dimensionless momentum coefficient which for non-creeping flow
template<class ElementSolutionVector>
Scalar momentumCoefficient(const Element& element,
const SubControlVolume& scv,
diff --git a/examples/porenetwork_upscaling/upscalinghelper.hh b/examples/porenetwork_upscaling/upscalinghelper.hh
index 1e4a1c069e..b5beebae82 100644
--- a/examples/porenetwork_upscaling/upscalinghelper.hh
+++ b/examples/porenetwork_upscaling/upscalinghelper.hh
@@ -103,12 +103,9 @@ public:
// calculate the Darcy pressure drop.
const Scalar darcyPressureDrop = liquidDynamicViscosity * apparentVelocity_[dirIdx][i] * sideLengths[dirIdx] / darcyPermeability_[dirIdx];
- // claculate the ratio of Dracy to total pressure drop
-
+ // calculate the ratio of Dracy to total pressure drop
const Scalar pressureDropRatio = darcyPressureDrop / totalPressureDrop_[dirIdx][i];
- std::cout<<std::endl<<" the ratio "<<pressureDropRatio<<std::endl;
-
// set sample points for upscaling of Forchheimer parameters.
// first, check the permability ratio to see if the flow regime is Forchheimer.
if (pressureDropRatio < 0.99)
@@ -285,6 +282,7 @@ private:
option += "set title \"" + title + "\"\n";
option += "set logscale x""\n";
+ option += "set format x '10^{%L}'""\n";
gnuplot.setXlabel("Forchheimer Number [-]");
gnuplot.setYlabel("Apparent permeability / Darcy permeability [-]");
@@ -326,11 +324,12 @@ private:
option += "set title \"" + title + "\"\n";
option += "set logscale x""\n";
+ option += "set format x '10^{%L}'""\n";
- gnuplot.setXlabel("{/Symbol r} u / {/Symbol m} [1/m]");
+ gnuplot.setXlabel("{/Symbol r} v / {/Symbol m} [1/m]");
gnuplot.setYlabel("1/ Apparent permeability [1/m^2] x 1e12");
gnuplot.setOption(option);
- gnuplot.plot("inverse_apppermeability_versus_rhoumu");
+ gnuplot.plot("inverse_apppermeability_versus_rhovmu-1");
}
}
// [[/codeblock]]
diff --git a/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_InversePrmeabilityVsInertiaToViscousRatio.dat b/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_InversePrmeabilityVsInertiaToViscousRatio.dat
new file mode 100644
index 0000000000..b4d27680fa
--- /dev/null
+++ b/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_InversePrmeabilityVsInertiaToViscousRatio.dat
@@ -0,0 +1,10 @@
+0.0332584 0.300676 0.31292
+11107 0.302029 0.31387
+29965.6 0.30431 0.315483
+79894.3 0.310254 0.319753
+207384 0.324902 0.330657
+512009 0.357721 0.356711
+1.17636e+06 0.423229 0.413531
+2.49648e+06 0.542104 0.526439
+4.93037e+06 0.74615 0.734604
+9.19349e+06 1.08773 1.09922
diff --git a/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_PermeabilityratioVsForchheimerNumber.dat b/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_PermeabilityratioVsForchheimerNumber.dat
new file mode 100644
index 0000000000..e071f632ec
--- /dev/null
+++ b/test/references/example_porenetwork_upscaling_noncreeping_flow_X-dir_PermeabilityratioVsForchheimerNumber.dat
@@ -0,0 +1,10 @@
+9.46045e-09 1
+0.00315941 0.995519
+0.00852378 0.988056
+0.0227261 0.969127
+0.0589909 0.925434
+0.145642 0.84053
+0.334619 0.710432
+0.710131 0.554645
+1.40246 0.402969
+2.61511 0.276426
diff --git a/test/references/example_porenetwork_upscaling_noncreeping_flow_X_direction-reference.dat b/test/references/example_porenetwork_upscaling_noncreeping_flow_X_direction-reference.dat
deleted file mode 100644
index 344a5d2d0b..0000000000
--- a/test/references/example_porenetwork_upscaling_noncreeping_flow_X_direction-reference.dat
+++ /dev/null
@@ -1,15 +0,0 @@
-7.97017e-06 1
-2.16647e-05 0.999981
-5.88878e-05 0.999928
-0.000160051 0.999786
-0.000434895 0.999399
-0.00118093 0.99835
-0.00320102 0.99553
-0.00863605 0.988068
-0.0230255 0.969138
-0.0597679 0.925444
-0.147561 0.84054
-0.339027 0.71044
-0.719485 0.554652
-1.42093 0.402974
-2.64956 0.276429
diff --git a/test/references/example_porenetwork_upscaling_noncreeping_flow_Y_direction-reference.dat b/test/references/example_porenetwork_upscaling_noncreeping_flow_Y_direction-reference.dat
deleted file mode 100644
index 82e0d47e0c..0000000000
--- a/test/references/example_porenetwork_upscaling_noncreeping_flow_Y_direction-reference.dat
+++ /dev/null
@@ -1,15 +0,0 @@
-4.20828e-06 1
-1.14392e-05 0.999989
-3.1094e-05 0.999961
-8.45157e-05 0.999882
-0.000229688 0.999669
-0.000623997 0.999091
-0.00169355 0.99753
-0.00458429 0.993359
-0.0123253 0.982509
-0.0326009 0.956037
-0.0833465 0.899161
-0.201292 0.798881
-0.451368 0.65901
-0.936519 0.503018
-1.81435 0.358504
diff --git a/test/references/example_porenetwork_upscaling_noncreeping_flow_Z_direction-reference.dat b/test/references/example_porenetwork_upscaling_noncreeping_flow_Z_direction-reference.dat
deleted file mode 100644
index 6429c3f700..0000000000
--- a/test/references/example_porenetwork_upscaling_noncreeping_flow_Z_direction-reference.dat
+++ /dev/null
@@ -1,15 +0,0 @@
-2.41283e-06 1
-6.55871e-06 0.999995
-1.78282e-05 0.99998
-4.846e-05 0.99994
-0.000131714 0.999832
-0.00035793 0.999538
-0.00097218 0.998743
-0.00263698 0.996597
-0.00712702 0.990892
-0.0190865 0.976227
-0.0500292 0.941354
-0.12565 0.869755
-0.295092 0.751446
-0.639109 0.598716
-1.28049 0.441295
--
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