Unexpected matrix diffusion and inlet artifact in fracture–matrix reactive transport (GIRT mode)

[Leo]

Dear all,

I am currently working on a 2D fracture–matrix reactive transport model (with dissolution/precipitation processes unabled, as this test focuses on the diffusion in the matrix) using PFLOTRAN (SUBSURFACE, RICHARDS + GIRT mode), and I am encountering issues related to diffusion and potential numerical artifacts near the inlet.

Model description

• Geometry: rectangular domain (mm scale), with a horizontal narrow fracture (1.6e-6m of aperture) located at the bottom and a porous matrix (low porosity: 0.068 and permeability : 1e-18 m^2) above.

• Flow is imposed via a constant Neumann LIQUID_FLUW boundary condition at the inlet (west face) in the fracture. While the flow rate being low (0.1 mL/h), the narrow aperture of the fracture makes the actual flow speed in the fracture at a much higher scale (1.93e-3 m/s).

• Outlet is defined using a pressure boundary condition on the fracture and on the matrix on the east face.

Transport setup

• Molecular diffusion coefficient: 1e-9m^2/s

• Matrix effective diffusion is expected to be on the order of 10e-13m^2/s, through a low tortuosity (1.47e-3), controlled by a tortuosity power of 1.5

• No dispersivity in the matrix

Observed issues

• Near the inlet, an unexpected speed on the z axis is seen, even though no flow is expected in the matrix.

• This effect has an influence on the penetration of the elements into the matrix, and is more and more important with time.

Relevant points

• The issue is not occurring for a larger fracture, or a lower flow rate. However, those parameters cannot be changed, and an even higher flow rate (60mL/h) will also have to be simulated.

Questions

• Could the observed upstream enhancement of matrix penetration be caused by numerical dispersion or inlet-related artifacts?

• Is imposing a uniform LIQUID_FLUX boundary condition known to create such effects in fracture–matrix configurations?

• Are there recommended best practices for accurately representing diffusion-dominated transport in the matrix when strong advection occurs in the fracture?

Any insight or references would be greatly appreciated.

Thank you in advance for your help. The input file, a few results and my database are attached to this message.

Best regards,
Chapuis Léo

[Hammond, Glenn E]

Chapuis,

Thank you for reaching out.  Please consider the following:

A) Your conceptual model appears to be correctly set up for flow, with the Neumann condition applied at the fracture inlet and Dirichlet pressure at the outlet. Regarding transport, I recommend switching the inlet_chem condition from DIRICHLET_ZERO_GRADIENT to ZERO_GRADIENT at the inlet, although I do not believe this is the primary issue.

Based on your description, it seems likely that the time step size is too large for your discretization, which can lead to a high CFL number and subsequent numerical errors. To address this, try adding 'CFL_GOVERNOR 1' to the flow timestepper block as follows:

NUMERICAL_METHODS FLOW

...

TIMESTEPPER

CFL_GOVERNOR 1.

/

...

END

B) You should remove the GRAVITY card from your configuration unless your goal is to reverse the direction of gravity. If you do intend to reverse gravity, ensure that you input the numbers without any commas between them.

C) If achieving symmetry at the matrix's west and east boundaries is important for your model, consider adding a west boundary condition to the matrix. However, based on my assessment, I do not think this adjustment is central to resolving the issue at hand.

D) You may want to increase the fracture permeability to 1.d-9. By doing so, you'll help decrease the pressure gradient within the fracture, which can have a significant impact on the flow behavior, particularly in the Z-direction as it moves into the matrix (perhaps numerical dispersion).

Please let me know if these adjustments help remedy the issue.

Glenn

From: pflotra...@googlegroups.com <pflotra...@googlegroups.com> on behalf of Leo <leo.ch...@gmail.com>
Date: Friday, April 3, 2026 at 7:40 AM
To: pflotran-users <pflotra...@googlegroups.com>
Subject: [pflotran-users: 8737] Unexpected matrix diffusion and inlet artifact in fracture–matrix reactive transport (GIRT mode)

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[Leo]

Dear Glenn,

Thank you very much for your answer My problem has indeed been solved by following your advice.

I wish you a nice day and a happy Easter.

Best regards

Léo