Model output - Revision history

Klmos: /* Discussion of model concepts */ Revised chapter

2019-07-03T09:45:28Z

‎Discussion of model concepts: Revised chapter

Klmos: /* Recommendations for modeling flow and transport in fractured limestone aquifers */ Small text edits

2019-04-21T12:16:09Z

‎Recommendations for modeling flow and transport in fractured limestone aquifers: Small text edits

Klmos: Renamed headings, grouped models in "Discussion of model concepts"

2019-04-21T12:10:44Z

Renamed headings, grouped models in "Discussion of model concepts"

Klmos: /* Dual continuum model (DCM) */

2018-02-09T16:36:34Z

‎Dual continuum model (DCM)

Klmos at 16:14, 9 February 2018

2018-02-09T16:14:36Z

Klmos at 16:11, 9 February 2018

2018-02-09T16:11:20Z

Klmos at 15:58, 9 February 2018

2018-02-09T15:58:42Z

Klmos at 15:49, 9 February 2018

2018-02-09T15:49:35Z

Klmos: /* Equivalent porous medium (EPM) model */

2017-02-27T14:44:34Z

‎Equivalent porous medium (EPM) model

Klmos at 13:20, 15 February 2017

2017-02-15T13:20:02Z

@@ Line 18: / Line 18: @@
 Compared to the dual-continuum model or the discrete-fracture model, it has low computational costs.
 It is well-established for porous media systems without fractures.
-However, for fractured aquifers, it should only be used for a rough approximation, particularly for solute transport, and has to be used with care.
+However, for fractured aquifers, it should only be used for a rough approximation and with care, particularly for solute transport.
-It cannot reproduce the interactions between fractures and matrix (storage in matrix, diffusive mass exchange).
+It cannot reproduce the interactions between fractures and matrix (diffusive mass exchange, storage in matrix).
-That the EPM model fails in heavily fractured limestone aquifers becomes obvious when trying to simulate the tracer tests, which were performed at the Akacievej site.
+That the EPM model fails in fractured limestone aquifers becomes obvious when trying to simulate the tracer tests, which were performed at the Akacievej site.
-A homogeneous equivalent porous medium model could only be fitted to the fast arrival observed in the tracer tests by lowering the (effective) porosity to very low values (below 1 %, in the order of the fracture porosity).
+A homogeneous EPM model could only reproduce the fast arrival observed in the tracer tests by lowering the (effective) porosity to very low values (below 1 %, in the order of the fracture porosity).
-Then, the simulated peak concentrations were higher than the observed ones, because diffusion of tracer into the matrix is neglected by the model.
+Then, however, the simulated peak concentrations were higher than the observed ones, because diffusive exchange of tracer with the matrix is neglected by the model.
-The simulated tracer breakthrough concentration decreased early, and the tailing observed in the field tests could not be reproduced.
+Hence, the simulated tracer breakthrough concentration decreased early, and the tailing observed in the field tests could not be reproduced.
 It is possible to obtain a tailing in the simulated breakthrough curve if a heterogeneous parameter distribution in the porous medium is included (Figure 6.9), introducing very conductive structures and less conductive structures that are less penetrated by flow <ref>Pedretti et al. (2013), ''On the formation of breakthrough curves tailing during convergent flow tracer tests in three-dimensional heterogeneous aquifers'', Water Resources Research, 49, 4157-4173.</ref>.
-However, the variation of the hydraulic conductivity has to be of a similar order of magnitude to the contrast between fracture and matrix conductivity and have a similar connectivity of the highly conductive zones (fractures).
+However, the variation of the hydraulic conductivity has to be of a similar order of magnitude as the contrast between fracture and matrix conductivity and it has to have a similar connectivity of the highly conductive zones (fractures).
 Note that a different vertical placement of the screens for injection and extraction can also lead to a tailing in the breakthrough curves.
-The use of an EPM model for the simulation of the migration of a contaminant is not recommended, because exchange processes between fractures and matrix are generally neglected and model results may be misleading for risk assessment or remedial planning.
+The use of an EPM model for the simulation of the fate of a contaminant in a fractured limestone aquifer is not recommended, because exchange processes between fractures and matrix are generally neglected and model results may be misleading for risk assessment or remedial planning.
 For example, remediation times can be greatly underestimated because the effect of back-diffusion from the matrix cannot be reproduced.
-It is preferable from the point of view of the actual physics to include fractures in a model as discrete features.
+It is preferable to include fractures in a model as discrete features in order to better reproduce the actual physics.
 <br clear=all>
@@ Line 40: / Line 41: @@
 The dual-continuum model matches the observed tracer breakthrough curves from the Akacievej tracer tests better than the EPM model.
 The fractures and the matrix are each represented as a continuum and the coupling of the two continua allows for an exchange of substances between fractures and matrix.
-With this model, the breakthrough behavior can be reproduced by fitting the fracture and matrix porosities and conductivities, and the parameters controlling the exchange between fractures and matrix (Dpm, α, a).
+With a DCM, the breakthrough behavior can be reproduced by choosing appropriate fracture and matrix porosities and conductivities, and by fitting the parameters controlling the exchange between fractures and matrix (Dpm, α, a).
 However, this concept has many degrees of freedom, and it is not clear how to determine the required parameters governing the fracture-matrix exchange experimentally.
-It is also reported in the literature to be a “black-box” model  <ref name="Riley" />.
+The DFM is also reported in the literature to be a “black-box” model  <ref name="Riley" />.
 The computational effort required to run this model type is usually moderate.
-It has been reported in the literature that the dual-continuum  model has to be recalibrated, when is used to different flow conditions or to different scales.
+It has been reported in the literature that the dual-continuum  model has to be recalibrated, when it is used with different flow conditions or at different scales.
 <br clear=all>
 === Discrete-fracture model (DFM) ===
 [[File:DFM.png|Discrete-fracture approach.|x180px|frameless|right|Discrete-fracture approach.]]
-The discrete-fracture model aims at representing the actual physics and yields the best results.
+The discrete-fracture model aims at representing the actual physics in a fractured limestone aquifer and yields the best results.
-Drawbacks are the often-limited knowledge of the fracture geometry and parameters and the large computational costs.
+Drawbacks are the often limited knowledge of the fracture parameters and geometry, the complexity of the model and the high computational costs.
-The inclusion of fractures requires a very high grid resolution next to them, and the computational effort does usually not permit to include all fractures in a model.
+The inclusion of fractures requires a very high grid resolution next to them to correctly resolve concentration gradients, and the computational effort usually limits the number of fractures that can be included in a model.
-When setting up the model for the tracer tests in Geo18s, Geo19d and Geo5, it was sufficient to include just a few horizontal fractures to provide preferential flow paths for the tracer.
+When setting up the model for the tracer tests at the Akacievej site, it was sufficient to include major horizontal fractures to provide preferential flow paths for the tracer transport to obtain a fast tracer arrival and the tailing caused by the matrix diffusion.
-The fractures were located to match high-flow zones that were observed on flow logs in the boreholes.
+However, this has to be based on the observed fracture pattern.
-The real medium is likely to have many more fractures on different scales, providing a bigger specific surface area for the exchange between fractures and matrix.
+The horizontal fractures were placed at locations where high-flow zones were seen on flow logs in the boreholes (indicating horizontal fractures), see Chapter [[Data acquisition]] for more information.
-This can be accounted for by adjusting the matrix diffusivity, which controls the exchange between fractures and matrix.
-In the simulations presented here, it had to be increased by a factor of 100 to 1000 in order to fit the observed breakthrough behavior.
+However, at the Akacievej site, the limestone is likely to have many more fractures at different scales, providing a bigger specific surface area for the exchange between fractures and matrix and leading to more matrix diffusion.
 <br clear=all>

@@ Line 92: / Line 92: @@
 * In general, it is a good idea to start with a simple model and to increase complexity. If the results look strange, try to simplify the system.
 * Always be critical with modeling results.
-* When a discrete-fracture model is used, the grid resolution has to be high in the vicinity of the fractures, in order to approximate the gradients of primary variables properly there.
+* When a discrete-fracture model is used, the mesh resolution has to be high in the vicinity of the fractures in order to properly approximate the gradients of primary variables there.
 * A too coarse grid resolution can lead to oscillations in the solution and a bad convergence behavior.
 {{Return}}
 |}
 [[Category:Modeling]]

@@ Line 12: / Line 12: @@
 {| class="body1"
+|
-== Equivalent porous medium (EPM) model ==
+== Discussion of model concepts ==
 [[File:EPM_square.png|x200px|Equivalent porous medium approach.|frameless|right|Equivalent porous medium approach.]]
 The EPM model is the simplest of the considered models and is widely used in practice.
@@ Line 35: / Line 36: @@
 <br clear=all>
-== Dual continuum model (DCM) ==
+=== Dual-continuum model (DCM) ===
 [[File:DualContinuumSchematics.png|x180px|Dual continuum approach.|frameless|right|Dual continuum modeling approach.]]
 The dual-continuum model matches the observed tracer breakthrough curves from the Akacievej tracer tests better than the EPM model.
@@ Line 46: / Line 47: @@
 <br clear=all>
-== Discrete fracture model (DFM) ==
+=== Discrete-fracture model (DFM) ===
 [[File:DFM.png|Discrete-fracture approach.|x180px|frameless|right|Discrete-fracture approach.]]
 The discrete-fracture model aims at representing the actual physics and yields the best results.
@@ Line 61: / Line 62: @@
 <br clear=all>
-== Discussion and comparison ==
+== Comparison ==
 [[File:HeadsAroundGeo17.png|Head distribution around a pumped well. First figure: no pumping. Second figure: simulated heads while pumping and using a DFM Third picture: heads simulated with an EPM model that does not include fractures. Clear differences of the hydraulic head distributions can be observed for the two different models.|frameless|right|Dual continuum modeling approach.]]
 The tracer tests and model applications have clearly shown that a crucial aspect of the transport of a substance in fractured limestone cannot be reproduced with a simple equivalent porous medium model: the diffusion and back-diffusion of a substance between fractures with strong flow and low-conductive matrix.
@@ Line 74: / Line 75: @@
 The use of a discrete-fracture model comes with the cost of being the most complex and numerically demanding model described here.
-However, it represents the actual physics best and can, depending on the knowledge of the fracture system, lead to the best results.
+However, it represents the actual physics best and can, depending on the knowledge of the fracture system, yields the best results.
-Usually, only few details about the fracture network are available.
+Usually, only few details about the fracture network are available, which restricts the setup of a detailed model.
 In this study, the information provided by flow logs could successfully be used to setup a representative network containing the major horizontal flow paths.
 But such a model does not contain smaller fractures and to compensate for that the diffusion coefficient governing the exchange between fractures and matrix had to be greatly increased.
@@ Line 81: / Line 82: @@
 The tracer test in Geo18s before pumping clearly shows that the discrete-fracture model best reproduced the observed data.
-Since matrix and fractures are both included in the model and the exchange between the two happens naturally (continuity of fluxes, concentrations and heads at the fracture-matrix interface), the discrete-fracture model is the recommended approach in cases were fractures dominate the transport behavior.
+Since matrix and fractures are both included in the model and the exchange between the two happens naturally (continuity of fluxes, concentrations and heads at the fracture-matrix interface), the discrete-fracture model is the recommended approach in cases where fractures dominate the transport behavior and matrix diffusion occur.
 Even a simple analytical tool (such as Chambon et al. 2011 <ref name="Chambon">Chambon et al. (2011), ''A risk assessment tool for contaminated sites in low-permeability fractured media'', Journal of Contaminant Hydrology, 124, 82-98.</ref>) or a dual-continuum model should be preferred to an equivalent porous medium model, which completely neglects the influence of the fractures.

@@ Line 38: / Line 38: @@
 [[File:DualContinuumSchematics.png|x180px|Dual continuum approach.|frameless|right|Dual continuum modeling approach.]]
 The dual-continuum model matches the observed tracer breakthrough curves from the Akacievej tracer tests better than the EPM model.
-The second continuum represents the matrix and the coupling of the two continua allows an exchange of tracer between fractures and matrix.
+The fractures and the matrix are each represented as a continuum and the coupling of the two continua allows for an exchange of substances between fractures and matrix.
-With this model, the breakthrough behavior can be reproduced by fitting the fracture and matrix porosities and conductivities and the parameters governing the exchange behavior between fractures and matrix (Dpm, α, a).
+With this model, the breakthrough behavior can be reproduced by fitting the fracture and matrix porosities and conductivities, and the parameters controlling the exchange between fractures and matrix (Dpm, α, a).
 However, this concept has many degrees of freedom, and it is not clear how to determine the required parameters governing the fracture-matrix exchange experimentally.
 It is also reported in the literature to be a “black-box” model  <ref name="Riley" />.
 The computational effort required to run this model type is usually moderate.
-It is not known whether the model is capable of consistently simulating contaminant plume behavior at both small (site) and larger (catchment) scales.
+It has been reported in the literature that the dual-continuum  model has to be recalibrated, when is used to different flow conditions or to different scales.
 <br clear=all>

@@ Line 41: / Line 41: @@
 With this model, the breakthrough behavior can be reproduced by fitting the fracture and matrix porosities and conductivities and the parameters governing the exchange behavior between fractures and matrix (Dpm, α, a).
 However, this concept has many degrees of freedom, and it is not clear how to determine the required parameters governing the fracture-matrix exchange experimentally.
-It is also reported in the literature to be a “black-box” model (Riley et al. 2001).
+It is also reported in the literature to be a “black-box” model  <ref name="Riley" />.
 The computational effort required to run this model type is usually moderate.
 It is not known whether the model is capable of consistently simulating contaminant plume behavior at both small (site) and larger (catchment) scales.
@@ Line 52: / Line 52: @@
 The inclusion of fractures requires a very high grid resolution next to them, and the computational effort does usually not permit to include all fractures in a model.
 Neglected smaller fractures can be accounted for by increasing the effective diffusion coefficient.
-The effective diffusion coefficient must be augmented to account for neglected fractures, stagnant flow zones and channeling within the fissures, increasing the diffusive exchange between fractures and matrix <ref>Riley et al. (2001), ''Converging flow tracer tests in fissured limestone'', Quarterly Journal of Engineering Geology and Hydrogeology, 34, 283-297.</ref> <ref>DeDreuzy et al.(2013), ''Multi-Rate Mass Transfer (MRMT) models for general diffusive porosity structures'', Advances in Water Resources, 76, 146-156.</ref>.
+The effective diffusion coefficient must be augmented to account for neglected fractures, stagnant flow zones and channeling within the fissures, increasing the diffusive exchange between fractures and matrix <ref name="Riley">Riley et al. (2001), ''Converging flow tracer tests in fissured limestone'', Quarterly Journal of Engineering Geology and Hydrogeology, 34, 283-297.</ref> <ref>DeDreuzy et al.(2013), ''Multi-Rate Mass Transfer (MRMT) models for general diffusive porosity structures'', Advances in Water Resources, 76, 146-156.</ref>.
 When setting up the model for the tracer tests in Geo18s, Geo19d and Geo5, it was sufficient to include just a few horizontal fractures to provide preferential flow paths for the tracer.
@@ Line 82: / Line 82: @@
 Since matrix and fractures are both included in the model and the exchange between the two happens naturally (continuity of fluxes, concentrations and heads at the fracture-matrix interface), the discrete-fracture model is the recommended approach in cases were fractures dominate the transport behavior.
-Even a simple analytical tool (such as Chambon et al. 2011 <ref>Chambon et al. (2011), ''A risk assessment tool for contaminated sites in low-permeability fractured media'', Journal of Contaminant Hydrology, 124, 82-98.</ref>) or a dual-continuum model should be preferred to an equivalent porous medium model, which completely neglects the influence of the fractures.
+Even a simple analytical tool (such as Chambon et al. 2011 <ref name="Chambon">Chambon et al. (2011), ''A risk assessment tool for contaminated sites in low-permeability fractured media'', Journal of Contaminant Hydrology, 124, 82-98.</ref>) or a dual-continuum model should be preferred to an equivalent porous medium model, which completely neglects the influence of the fractures.
 == Recommendations for modeling flow and transport in fractured limestone aquifers ==
@@ Line 88: / Line 88: @@
 * Modeling should be included at an early stage of a project based on the available data. This can be used to plan further measurements and investigations.
 * Traditional contaminant transport models fail at reproducing important processes in fractured aquifers (diffusion into matrix and back, slowing down of plume migration speed with time, extent of capture zones) and are not recommended for for fractured limestone geologies similar to the Akacievej site.
-* It is better to use a simple analytical model (as f.e. presented in Chambon, 2011) for the modeling than to use an equivalent porous medium model, which neglects the presence of fractures.
+* It is better to use a simple analytical model (as f.e. presented in Chambon, 2011<ref name="Chambon" />) for the modeling than to use an equivalent porous medium model, which neglects the presence of fractures.
 * In general, it is a good idea to start with a simple model and to increase complexity. If the results look strange, try to simplify the system.
 * Always be critical with modeling results.

@@ Line 25: / Line 25: @@
 The simulated tracer breakthrough concentration decreased early, and the tailing observed in the field tests could not be reproduced.
-It is possible to obtain a tailing in the simulated breakthrough curve if a heterogeneous parameter distribution in the porous medium is included (Figure 6.9), introducing very conductive structures and less conductive structures that are less penetrated by flow (Pedretti et al. 2013).
+It is possible to obtain a tailing in the simulated breakthrough curve if a heterogeneous parameter distribution in the porous medium is included (Figure 6.9), introducing very conductive structures and less conductive structures that are less penetrated by flow (<ref>Pedretti et al. (2013), ''On the formation of breakthrough curves tailing during convergent flow tracer tests in three-dimensional heterogeneous aquifers'', Water Resources Research, 49, 4157-4173</ref>).
 However, the variation of the hydraulic conductivity has to be of a similar order of magnitude to the contrast between fracture and matrix conductivity and have a similar connectivity of the highly conductive zones (fractures).
 Note that a different vertical placement of the screens for injection and extraction can also lead to a tailing in the breakthrough curves.
@@ Line 85: / Line 85: @@
 Since matrix and fractures are both included in the model and the exchange between the two happens naturally (continuity of fluxes, concentrations and heads at the fracture-matrix interface), the discrete-fracture model is the recommended approach in cases were fractures dominate the transport behavior.
-Even a simple analytical tool (such as Chambon et al. 2011) or a dual-continuum model should be preferred to an equivalent porous medium model, which completely neglects the influence of the fractures.
+Even a simple analytical tool (such as Chambon et al. 2011 <ref>Chambon et al. (2011), ''A risk assessment tool for contaminated sites in low-permeability fractured media'', Journal of Contaminant Hydrology 124, 82-98</ref>) or a dual-continuum model should be preferred to an equivalent porous medium model, which completely neglects the influence of the fractures.
 == Recommendations for modeling flow and transport in fractured limestone aquifers ==

@@ Line 4: / Line 4: @@
+|
 * Flow and advective transport mainly in fractures
-* Mapping of well capture zones difficult
+* Standard equivalent porous medium model neglects interplay between fractures and matrix
 * Plume migration in fractured limestone slows down with time due to matrix diffusion
 * Predictions of different model types differ considerably
 |}
@@ Line 17: / Line 17: @@
 Compared to the dual-continuum model or the discrete-fracture model, it has low computational costs.
 It is well-established for porous media systems without fractures.
-However, for fractured aquifers, it can be used for a rough approximation of the transport behavior of a substance, but must be used with care.
+However, for fractured aquifers, it should only be used for a rough approximation, particularly for solute transport, and has to be used with care.
-It does not account for the interactions between fractures and matrix (like diffusive mass exchange).
+It cannot reproduce the interactions between fractures and matrix (storage in matrix, diffusive mass exchange).
-That the EPM model fails in heavily fractured aquifers becomes obvious when trying to simulate the tracer tests, which were performed at the Akacievej site.
+That the EPM model fails in heavily fractured limestone aquifers becomes obvious when trying to simulate the tracer tests, which were performed at the Akacievej site.
-The homogeneous equivalent porous medium model could only be fitted to the fast arrival observed in the tracer tests by lowering the (effective) porosity.
+A homogeneous equivalent porous medium model could only be fitted to the fast arrival observed in the tracer tests by lowering the (effective) porosity to very low values (below 1 %, in the order of the fracture porosity).
-Very low porosity values (below 1 %, in the order of the fracture porosity) had to be chosen to fit the fast tracer arrival.
+Then, the simulated peak concentrations were higher than the observed ones, because diffusion of tracer into the matrix is neglected by the model.
-Then, the peak concentrations were higher than those observed, because diffusion of tracer into the matrix is neglected by the model.
+The simulated tracer breakthrough concentration decreased early, and the tailing observed in the field tests could not be reproduced.
 It is possible to obtain a tailing in the simulated breakthrough curve if a heterogeneous parameter distribution in the porous medium is included (Figure 6.9), introducing very conductive structures and less conductive structures that are less penetrated by flow (Pedretti et al. 2013).
-However, the variation of the hydraulic conductivity must be of a similar order of magnitude to the contrast between fracture and matrix conductivity and have a similar connectivity of the highly conductive zones (fractures).
+However, the variation of the hydraulic conductivity has to be of a similar order of magnitude to the contrast between fracture and matrix conductivity and have a similar connectivity of the highly conductive zones (fractures).
 Note that a different vertical placement of the screens for injection and extraction can also lead to a tailing in the breakthrough curves.
 However, this does not account for fracture-matrix interaction and the storage effect of the matrix.
 The use of an EPM model for the simulation of the migration of a contaminant is not recommended, because exchange processes between fractures and matrix are generally neglected and model results may be misleading for risk assessment or remedial planning.
 For example, remediation times can be greatly underestimated because the effect of back-diffusion from the matrix cannot be reproduced.
 <br clear=all>

@@ Line 3: / Line 3: @@
 |-
+|
-try it out
+* Flow and advective transport mainly in fractures
 |}