saltwater-freshwater transition zone modeling at a coastal aquifer

[haiya...@subsurfaceinsights.com]

Hello All,

I am trying to model the saltwater-freshwater transition at a coastal aquifer with PFLOTRAN. The initial and boundary conditions are shown in attached Figure 1. 

PFLOTRAN results are shown in Figure 2 which is the tracer at the end of the simulation. However, what I expect is something like Figure 3 shows, in that the saltwater is denser than the injected freshwater.

I also attached the PFLOTRAN input file for your reference.

Can anyone help me to find the mistake I made? Thanks.

Best regards,

Haiyan

[Hammond, Glenn E]

Haiyan,

 

You are injecting with a volumetric rate.  The volumetric rate source/sink computes water density internally based on the pressure within the injected cell.  Deeper cells will have higher pressure and thus higher density and thus more mass injected.  Try a mass rate instead of volumetric rate:

 

FLOW_CONDITION inj

  TYPE

    RATE mass_rate

  /

  RATE 100. kg/day

END

 

Also, you should be able to apply that single condition to all the cells at the left boundary at once.  Create a region:

 

REGION wells

  COORDINATES

    0.d0 0.d0 -1000.d0

    10.d0 1.d0 0.d0

  /

END

 

SOURCE_SINK wellsinj

  FLOW_CONDITION inj

  TRANSPORT_CONDITION initial

  REGION wells

END

 

We need to resolve this non-uniformity in injected mass first before we can further resolve the problem.  Let us know what happens either way.

 

Glenn

[haiya...@subsurfaceinsights.com]

Hi Glenn,

Thanks for pointing me out the problem.

The new region "wells" covers all the previous 100 wells which have a total injection rate of 10 m^3/day (0.1m^3/day * 100). So if I use this flow condition to all the cells on the left it should be

FLOW_CONDITION inj

  TYPE

    RATE scaled_mass_rate volume

  /

  RATE 10000. kg/day

END

Am I right?

By the way, what do you mean by "non-uniformity" in injected mass? It is freshwater that is injected into the domain which is initially saturated with saltwater.

I will let you know once the results are available.

Best,

Haiyan

[Hammond, Glenn E]

Haiyan,

 

I recommendation below is BOGUS.  Leave the source/sinks as volumetric.  FLOW_CONDITION initial needs to be set as HYDROSTATIC, not DIRICHLET.  Give that a try.  I was able to get a more realistic solution, though your injection rates push the water to the right, not matter what. 

 

Glenn

[Hammond, Glenn E]

Hi Glenn,

 

Thanks for pointing me out the problem.

 

The new region "wells" covers all the previous 100 wells which have a total injection rate of 10 m^3/day (0.1m^3/day * 100). So if I use this flow condition to all the cells on the left it should be

 

FLOW_CONDITION inj

  TYPE

    RATE scaled_mass_rate volume

  /

  RATE 10000. kg/day

END

Am I right?

 

You can do it either way.  10000 m^3/day with scaled_volumetric_rate or 10 m^3/day with volumetric_rate.  Do not use the mass_rate, I was COMPLETELY WRONG.  The volumetric rate will account for the hydrostatic equilibrium.  However, as the simulation proceeds, I have no idea what will happen as the left boundary is no flow.

 

By the way, what do you mean by "non-uniformity" in injected mass? It is freshwater that is injected into the domain which is initially saturated with saltwater.

 

Hydrostatic pressure gradients will result in greater density with depth and volumetric inputs account for this.  However, you need to ignore my comments about using mass_rate.!!!

 

Glenn

[Hammond, Glenn E]

Haiyan,

 

There is still another issue.  The hydrostatic boundary condition which calculates pressure along a 1D vertical column does not factor in the solute concentration in its density calculation.  This will have to be fixed to use the hydrostatic flow condition.  I can attempt to fix this sometime next week.

Glenn

 

From: pflotra...@googlegroups.com [mailto:pflotra...@googlegroups.com] On Behalf Of Hammond, Glenn E

Sent: Friday, March 24, 2017 4:11 PM
To: pflotra...@googlegroups.com

[haiya...@subsurfaceinsights.com]

Hi Glenn,

Thanks. It would be great if you can fix this problem.

 

I tested HYDROSTATIC and as you said it pushed all freshwater to right instead of forming a wedge-shape transition zone. The model-setting requires the initial head of 0 m over the domain, which is the reason why I selected DIRICHLET.

Can the wells on the left serve as boundary condition since injection happens throughout the simulation period?

Best,

Haiyan

[zhouhai...@gmail.com]

Hi Glenn,

I am wondering if you have fixed the following issue in hydrostatic flow condition? Thanks,

Haiyan

[Hammond, Glenn E]

I have not.  It is still on my TODO list, but I cannot estimate when it will get fixed as I have a lot going on.

 

Glenn

[haiya...@subsurfaceinsights.com]

Hi Glenn,

It has been a while since we had the problem. I wonder if there is any progress in fixing this issue?

Thanks,

Haiyan

[Hammond, Glenn E]

No progress.  I have no immediate need for this capability on any of my projects and it would require substantial time to implement properly.

[haiya...@subsurfaceinsights.com]

OK. Thanks for letting me know.

Haiyan

[Richard Peralta]

Hello All, Is PFLOTRAN currently able to simulate the saltwater-freshwater transition zone at a coastal aquifer? or to simulate density-dependent flow at a brine injection site?

The flow is affected by the different concentrations of salts within the different types of water (which thus have different densities), but somewhat readily mix with each other. This is not a multi-phase flow situation.

For example, In a coastal aquifer,  fresh groundwater water discharges from the land mass toward the ocean where it meets salty groundwater. The more dense salt water from the ocean forms a wedge under the less dense freshwater. The interface where the salt water and fresh water meet is not sharp in reality because the two waters mix in a transition zone. Mixing results from tides, other changes in boundary conditions, advection, hydrodynamic dispersion, and chemical diffusion due to concentration gradients.)

I look forward to hearing from you, and thank you in advance. Richard 

 

[Hammond, Glenn E]

Richard,

 

PFLOTRAN can calculate salinity from the solute transport side of the code and factor the salinity into the density dependent flow problem.  Our short course exercise

https://bitbucket.org/pflotran/pflotran/src/master/shortcourse/exercises/density_dependent_flow/density_dependent_flow.in

demonstrates this capability.  This functionality is not well-documented and more a research capability.  Bear in mind that since flow and transport are sequentially coupled, there is splitting error introduced that is proportional to time step size.

 

The biggest challenge with using this capability on realistic problems is that concentrations must be uniform across the boundary and initial condition regions.  There is currently no way to prescribe a gradient, though one could overwrite species concentrations in our HDF5 formatted checkpoint file (using a some Python) and use that for an initial condition through the RESTART keyword.  However, on the boundary, the is no way to prescribe a concentration gradient over a region using a single TRANSPORT_CONDITION.

 

Regards,

 

Glenn

 

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[Richard Peralta]

Hello Glenn, 

Thank you very much for your answer. I did not precisely know how to interpret the caveat you mentioned. So here I describe a 2D cross-sectional modeling setting (X and Z directions), and ask different questions. 

First, analytical solutions exist that represent the coastal freshwater and saltwater interface as a sharp divide (see below picture): 

But in reality, depending upon the site, the interface is more like this:

For either of the above images, assume:

-   Lateral boundary conditions: 

- - on the left side should be specified fresh water head in some simulations, and specified entering fresh water flow rate in other simulations. 

- -On the right side the salt water head would be specified, but in some simulations, specified inputs would vary with time to represent tides and storms.  

- - Because we would not want the incoming fresh water to flush out all salt on the right side of the interface, we will have to have some specified ocean salt concentration boundary on the right side.

- Initial conditions:

--slight fresh water salinity concentration on the left side of an assumed sharp interface, 

--high salt water salinity concentration on the right side as shown below. 

1. Assuming the above BCs, can PFLOTRAN simulate and develop the shape and approximate concentrations of the interface (less dense freshwater  overlying a wedge of dense saltwater). If specified freshwater inflow from the left (or if specified freshwater head at the decreases) , the salt water wedge should move to the left. 

2. Although involving inexact physics, for steady hydraulic and concentration boundary conditions, can PFLOTRAN compute a resulting steady state concentration gradient for the above specified boundary conditions?  (or does PFLOTRAN have to do a transient simulation to reach an equilibrium concentration gradient)? 

3. Do you think PFLOTRAN will be able to simulate the transient concentration changes resulting from specified boundary heads that change with time during a day or longer period? 

To view this discussion on the web visit https://groups.google.com/d/msgid/pflotran-users/CO6PR09MB8600DE4598BB18BC6BF647229A599%40CO6PR09MB8600.namprd09.prod.outlook.com.

--

Richard C. Peralta, PhD, PE, F.ASCE, Professor,

Civil and Environmental Engineering Dept.

Utah State University

4110 Old Main Hill,

Logan, UT 84322-4110

preferred email:   peral...@gmail.com  preferred mobile  4358814947

USU phone         4357972786   USU email     richard...@usu.edu

[Hammond, Glenn E]

See my comments below in red.  Glenn

 

From: pflotra...@googlegroups.com <pflotra...@googlegroups.com> On Behalf Of Richard Peralta
Sent: Wednesday, May 5, 2021 5:14 PM
To: pflotra...@googlegroups.com
Cc: Richard Peralta <richard...@usu.edu>; richard peralta <peral...@gmail.com>
Subject: Re: [EXTERNAL] [pflotran-users: 6287] saltwater-freshwater transition zone modeling at a coastal aquifer

Hello Glenn, 

Thank you very much for your answer. I did not precisely know how to interpret the caveat you mentioned. So here I describe a 2D cross-sectional modeling setting (X and Z directions), and ask different questions. 

First, analytical solutions exist that represent the coastal freshwater and saltwater interface as a sharp divide (see below picture): 

But in reality, depending upon the site, the interface is more like this:

For either of the above images, assume:

-   Lateral boundary conditions: 

- - on the left side should be specified fresh water head in some simulations, and specified entering fresh water flow rate in other simulations. 

- -On the right side the salt water head would be specified, but in some simulations, specified inputs would vary with time to represent tides and storms.  

- - Because we would not want the incoming fresh water to flush out all salt on the right side of the interface, we will have to have some specified ocean salt concentration boundary on the right side.

- Initial conditions:

--slight fresh water salinity concentration on the left side of an assumed sharp interface, 

--high salt water salinity concentration on the right side as shown below. 

 

1. Assuming the above BCs, can PFLOTRAN simulate and develop the shape and approximate concentrations of the interface (less dense freshwater  overlying a wedge of dense saltwater). If specified freshwater inflow from the left (or if specified freshwater head at the decreases) , the salt water wedge should move to the left. 

 

Yes.  I believe that the attached input deck demonstrates the capability.

 

2. Although involving inexact physics, for steady hydraulic and concentration boundary conditions, can PFLOTRAN compute a resulting steady state concentration gradient for the above specified boundary conditions?  (or does PFLOTRAN have to do a transient simulation to reach an equilibrium concentration gradient)? 

 

PFLOTRAN has to pseudo step to steady-state.  It cannot calculate the steady state solution since the flow and transport are sequentially coupled.

 

3. Do you think PFLOTRAN will be able to simulate the transient concentration changes resulting from specified boundary heads that change with time during a day or longer period? 

 

Yes.

To view this discussion on the web visit https://groups.google.com/d/msgid/pflotran-users/CAGTjFuiOCAKRi8rc43ABWtzjHYStRpxFVCMMC2t0X6u-Sv83Eg%40mail.gmail.com.