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Modeling reactive solute transport coupled with flow in Cathy : preparatory work.

Laura Gatel (Irstea Lyon, France)

23 septembre 2015

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Context

Flow and solute pathways in agricultural hillsopes are complex to precisly caracterize, particularly for what concerns surface/subsurface exchanges and lateral transfers. Modelisation can help, and in order to obtain accurate results on those kind of domains, the use of a physically-based model is required.

Study site at the Morcille catchment (Beaujolais)

First work centered on vagatative buffer strip zones :

Those areas are a way to limit solute transfers from the field to aquatic environments and particularly activ for what concerns water infiltration.

→ About the influence of soil heterogeneity on surface and subsurface flow

Example of 3 saturated conductivity statistical fields

Generation of statistical fields with variable characteristics (correlation, enforcement with measured conductivity values, ... )

Comparison of the runoff and subsurface patways with field data on three events

→ Results are very sensitive to the conductivity dictributions→ Generated hydrodynamic parameters with enforcement are quite close to data→ Need to take into account microtopography

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Objectives

3-years PhD objectives :

● To develop a coupled surface / surbsurface flow and solute reactive transport model in 3D based on the Cathy model.

● Validate the model at the hillslope scale with a global sensitivity analysis and the comparison with field data (large database from Irstea Lyon on two hillslopes of the Morcille catchment, Beaujolais, France)

● Upscaling from hillslope to catchment

INRS summer 2015 session obectives :

● Merge a calculation flow model and a reactive transport model● Compare the results of this new model with two litterature examples and control the mass

balance.

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Existing tools

Cathy flow

Coupled subsurface flow (FLOW3D) and surface routing (SURF_ROUTE) model

Variably saturated flow

3D

subsurface calculation : finite elements (FLOW3D)

Tran3d

Solute transport model with decay and linear sorption

Variably saturated flow

3D

Advection, sorption and decay resolved with finite elements

BUT no flow calculation → steady state cases only

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Context

Flow and solute pathways in agricultural hillsopes are complex to precisly caracterize, particularly for what concerns surface/subsurface exchanges and lateral transfers. Modelisation can help, and in order to obtain accurate results on those kind of domains, the use of a physically-based model is required.

Study site at the Morcille catchment (Beaujolais)

First work centered on vagatative buffer strip zones :

Those areas are a way to limit solute transfers from the field to aquatic environments and particularly activ for what concerns water infiltration.

→ About the influence of soil heterogeneity on surface and subsurface flow

Example of 3 saturated conductivity statistical fields

Generation of statistical fields with variable characteristics (correlation, enforcement with measured conductivity values, ... )

Comparison of the runoff and subsurface patways with field data on three events

→ Results are very sensitive to the conductivity dictributions→ Generated hydrodynamic parameters with enforcement are quite close to data→ Need to take into account microtopography

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Method

- Two study cases from the literature (Gureghian 1983 and Huyakorn et al. 1985)

Merging of the two models

Validation

Application to a real hillslope (Beaujolais, France)

Mas

s ba

lanc

e ca

l cul

ati o

n

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Merging of the two model

Merged model

- Initialisation of surface and flow calculation- Initialisation of reactive transport calculation

Beginning of the time loop

- Surface flow calculation- Subsurface flow calculationBackstepping if necessary

- Reactive transport calculation (only one resolution for advection, sorption and decay)End of the time loop

Tran3d :- Initialisation of reactive transport calculation- Integration of steady-state resultsBeginning of the time loop

- Reactive transport calculation (only one resolution for advection, sorption and decay)End of the time loop

Cathy flow :- Initialisation of surface and flow calculationBeginning of the time loop

- Surface flow calculation- Subsurface flow calculationEnd of the time loop

At each time step, reactive transport calculation is based on the flow calculation results : the merging allows the study of no-steady state cases

● At each step, flow and transport are calcultated with the same Δt (if necessary, backsteping occurs after subsurface flow and before transport)

● Surface transport isn't take into account.

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ValidationTest case 1 (Huyakorn et al. 1985) : case descriptionTransport of non-conservative solute in a unsaturated soil.

3D mesh as modelised in the merged model (surface of 10 cm * 15 cm and 10 cm deep) with steady-state pressure in the domain.

Boundary conditions used for the test case.

2D mesh (15 cm wide and 10 cm deep).

Reactive transport :Dispersion α

L = 1 cm α

T = 0

Diffusion 0,01 cm²/dSorption Rd = 2Decay 0,001 d-1

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ValidationTr

an3d

Me r

ged

mo

de l

0,053 d (1 h 15 min)0,165 d (4 h) 0,508 d (12 h)

Test case 1 (Huyakorn et al. 1985) : resultsConcentration contours

Mass balance :For each time step of this run, mass balance error stayed between 0,01 % and 1 %

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Validation

Vertical concentration profiles at x = 3 cm and three different times

Horizontal concentration profiles at z = 10 cm and three different times

t = 0,053 d

t = 0,165 d

T = 0,508 d

Tran3dMerged model

Test case 1 (Huyakorn et al. 1985) : resultsRelative concentration

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ValidationTest case 2 (Gureghian 1983) : case descriptionFlow and transport in a ditch-drained aquifer with incident steady rainfall and infiltration of solute

3D mesh as modelised in the merged model (surface of 10 cm * 15 cm and 10 cm deep) with steady-state pressure in the domain.→ 176 nodes for the plan (XZ)

Boundary conditions used for the test case.

2D mesh ( 100 cm wide and 50 cm deep). → 176 nodes

The mesh is not exactly reproduced, because Cathy flow does not allow unregular mesh.

Reactive transport :Dispersion αL = 0,5 cm αT = 0,1 cmDiffusion 1e-5 cm²/dSorption -Decay -

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ValidationTest case 2 (Gureghian 1983) : resultsConcentration contours

Tran3dCombined model

15 days

45 days

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ValidationTest case 2 (Gureghian 1983) : resultsConcentration contours

Tran3dMerged model

→ Little differences observed between tran3d and merged model results in the shape of the non-zero concentration zone.In this case, the slightly different used mesh could explain this variations.

90 days

120 days

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ValidationTest case 2 (Gureghian 1983) : resultsMass balance

Inside mass

Entering mass

Exiting mass

d = 15Solute infiltartion stops

d ~ 70Solute shape reaches

seepage faces

If we continue the run until 600 d ...

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Discussion

Even if there is little unexplained differences in the results of case 1, and inconsistent mass balance for seepage faces, the coupled model gives good results on those two simple examples.

But in other situations, when concentration evolutions are less « smooth » (less or no dispersion or diffusion for example), the model becomes unstable and the user have to carrefully choose the time stepping to avoid concentration explosions.

→ It will not be enough stable to modelise complex hillslopes caracterized by important heterogeneity (with no string conditions on mesh or time steps)

Solution : separate advection and reaction parts and calculate advection as finite volumes (see S. Weill et al. 2011).

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Perspectives

Short-term objective :From the last version of Cathy with non-reactive transport (probably Carlotta's version with velocity fields reconstruction), integrate sorption and decay equations.

Construction scheme of the last version of transport on Cathy :

InitialisationBeginning of the time loop

Surface flowSurface transportSubsurface flowSubsurface transport

- advective part → finite volume- reactive part (for now, only dffusion and dispersion) → finite elements

End of the time loopAddition of linear sorption and first order decay

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Perspectives

Mid-term objective :

● Validation :1- Apply the new model to a hillslope (Morcille's

catchment, Beaujolais). The site is instrumented since more than a decade → a large database to compare with the model.

2- Global sensitivity analysis

• Upscaling :Apply the model to the entire Morcille catchment and compare results with actual data (all in all 3 sites instrumented sites on the catchment).

Rabiet et al. (2015)

Bo

ivin

(2

007)

St-Joseph site on the Morcille Catchment

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Thank you for your attention !

References :

Camporese M., Paniconi C., Putti M., and Orlandini S. (2010). Surface and subsurface flow modeling with path-based runoff routing, boundary condition-based coupling, and assimilation of multisource observation data. Water Resources Research, 46(2).

Gambolati G., Pini G., Putti M. and Paniconi C. (1994). Finite element modeling of the transport of reactive contaminants in variably saturated soils with LAE and non LEA sorption. Environmental Modeling vol. 2, ch. 7, pp. 173-212.

Paniconi C., Wood E. (1983). A detailed model for simulation of catchment scale subsurface hydrologic processes. Water resources Research, 29(6):1601-1620.

Weill S., Mazzia A., Putti., Paniconi C. (2011). Coupling water flow and solute transport into a physically-based surface-subsurface hydrological model. Advances in Water Resources vol 34, pp 128-136.