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Synthetic experimentsfor understanding and upscaling flow and transport processes in heterogeneous mediaJean-Raynald de Dreuzy, Tanguy Le Borgne
Classical modeling protocol
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Example of numerical experimenation Investigation of transport processes in heterogeneous mediaMacro-dispersion, Mixing and Reactivity
Upscaling solute transport processes (heterogeneous media)
▪ Purposes
▪ Effect of heterogeneity on inert and reactive solute processes
▪ Enhancement of dispersion and mixing induced by permeability heterogeneity
▪ Determine effective, upscale laws: Multiple scales in the same simulations
▪ Conceptual model (Assumptions)
▪ Stochasticly well-defined heterogeneity fields with evolving levels of complexity
▪ Simplification of boundary and initial conditions to focus on the processes
▪ Stochastic simulations
▪ Mathematical model
▪ Advection-diffusion-dispersion equations
Physical model
lengthncorrelatio
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varlog:
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Transport model
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Periodic boundary conditions
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Reflecting boundary conditions
c=0
Adsorbing boundary conditions
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Initial conditionsc(x,t=0)=0
Numerical methods
▪ Multi-scale stochastic simulations
▪ requires parallel computation
▪ Flow equation
▪ finite volume discretization
▪ algebraic multigrid linear solver
▪ Transport equation
▪ Lagrangian method: random walks
▪ Numerical strategy
▪ Macrodispersion: stochastic simulations with limited number of particles
▪ Mixing: few simulations with large number of particles
Beaudoin, A., J. R. de Dreuzy, and J. Erhel (2007), An efficient parallel tracker for advection-diffusion simulations in heterogeneous porous media, paper presented at Europar, Rennes, France, 28-31 August 2007, Lecture Notes in
Computer Science 4641 705-714 Springer-Verlag, Berlin, Heidelberg
Some examples of software for porous and fractured media▪ Classical hydrogeological models
▪ MODFLOW
▪ FEEFLOW
▪ HYDROGEOSPHERE
▪ Specialized modelling plateforms
▪ Tough, Berkeley, reactive transport
▪ DUMUX, DUNE, Stutgart, Multiphase flow, Multiphysics
▪ GEOSYS, UFZ, THMC
▪ PROOST, Barcelona
▪ H20lab, Rennes, heterogeneity (porous,fracture) and transport
▪ Multiphysics models
▪ COMSOL
▪ ABACUS
▪ Fluid mechanics models
▪ Open foam
Permeability variance 0.25 < y2 < 9
Domain size Nx = 16384, Ny =Nz = 128
500 Monte Carlo simulations
10 000 particles
Extensive parameter study :
Cluster = 64 nodes of 2 processors Intel Quad Core x5472. Each processor is composed of 4 cores (Harpertown 3GHz) and 4GB of memory per core.
permeability generation = 20 stime for flow = 213stime for transport = 1605s
Example of CPU times :
Performances
Temporal evolution of the dimensionless longitudinal effective dispersivity L(t) for various values of y²
Validation against analytical predictions sY2<1
Predictions
2D and 3D longitudinal macro dispersivities LA as function of y²
3D transverse macro dispersivity TA for various values of y²
A. Beaudoin and J.R. de Dreuzy, Numerical assessment of 3D macro dispersion in heterogeneous porous media, Water Resources Research, Vol. 43, 2013
A. Beaudoin and J.R. de Dreuzy, Numerical assessment of 3D macro dispersion in heterogeneous porous media, Water Resources Research, Vol. 43, 2013
Presentation of results
Low heterogeneitysY
2=1
High heterogeneitysY
2=6.25
Simulation and analysis of concentration distributions
Probability distribution of concentrations
macrodispersion model
Simulations at different times
Definition and validation of a new effective mixing model
Lamella representation
Villermaux, Cargèse summer school 2010
Quantification of fluid deformation processes
Map of fluid deformation Distribution of elongations
Le Borgne et al., JFM 2015
Definition and validation of a new effective mixing model
t1
t2
𝒑 (𝒄 ,𝒕 )
t2 t3
Fluid deformation Concentrations
𝒑 (𝒄∨𝝆)
Lamella representation Concentration PDF
Le Borgne et al. PRL 2013
macrodispersion model
Scope: develop simulation projects in interaction with lecturers (on a voluntary basis)
▪ Projects linked to practical courses
▪ Simulation of saltwater/freshwater interface
▪ Simulation of heat transport and potential fiber optic signal
▪ Direct modelling of geophysical signals (Resistivity, Spontaneaous Potential…)
▪ Projects linked to lectures
▪ Transport in heterogeneous media
▪ Reactive transport, colloid transport
▪ Multiphase or Non-Newtonian flows..
▪ Hydro-mechanics
▪ Projects linked to students PhD topics
Tool: COMSOL multiphysics
▪ Advantages
▪ Easy to learn in a week (friendly interface)
▪ Handles a large spectrum of coupled flow and transport processes
▪ Disadvantages
▪ Commercial licence
▪ Limited in terms of simulation size
▪ Free alternatives
▪ OpenFoam
▪ FreeFem
▪ …