MN - Modèles Numériques

Lattice Boltzmann for complex flow and transport in heterogeneous porous media – LaboCothep

Submission summary

Governing equations classically used to model flow and transport in multi-scale heterogeneous porous media strongly depend on the scale distribution itself. The aim of the present work is to develop a stable, robust and efficient Lattice-Boltzmann equation scheme that allows for the investigation of two processes relevant for which the multi-scale structure of the porous media cannot be neglected: dispersion and non-Newtonian flows. In the case of dispersion it is known that heterogeneities may lead to strong deviation from the standard advection dispersion equations. Indeed, in multi-scale porous media, a major part of the transport takes place in high velocity zones situated in large pores or fractures. However, low porosity zones can strongly increase residence times leading to asymmetric breakthrough curves. Non-Newtonian transport in heterogeneous porous media strongly depends on the scale distribution of the porous media itself and on the rheology of the fluid. A strong coupling between pore structure and constitutive equation determines the flow distribution in the geometry. For example, the mobilisation of a yield stress fluid in the smallest pore of the medium drastically depends on the flow characteristics (flow rate, shear rate distribution…).
In the last two decades, thanks to their exact verification of the conservation relations, straightforward implementation of complex structures and possibility of parallelisation, Lattice Boltzmann (LB) methods have become very popular to solve flow and transport in porous media. However, a careful analysis shows that some LB method (particularly the broadly used BGK scheme) may display strong and critical numerical errors at boundaries and interfaces. In principle, better grid refinement could cope with this problem. However, in complex structures, a large enough domain is necessary in order to investigate a statistical representative sample, one cannot refine at the smallest scale because of numerical restrictions. Developing more accurate schemes allows one to overcome these difficulties.
The objective of the present work is twofold:
1) To construct an ensemble of Lattice Boltzmann schemes necessary for modelling Newtonian/non-Newtonian flows and associated transport at different scales in heterogeneous porous media. This new set of numerical schemes will then be assessed by comparing with well referenced configurations found in the literature using other complementary numerical calculations and with experiments using several techniques (NMR, PIV, Breakthrough curve…).
2) This set of LBE schemes will then be used to solve effective flow and transport equations at higher scales (so called “upscaled” equations). Improved comprehension and modelling of scale heterogeneities will be achieved. For that purpose, we will perform also experimental measurements on synthetic model and real rock/soil samples.
Three scales as well as the corresponding upscaling will be considered: micro scale (characterized by Stokes flow in homogeneous porous media), meso scale (represented by Darcy -Brinkman flow in heterogeneous porous media characterized by two distinct porosity scales) and macro scale (reservoir scale, laboratory column…).
In the case of dispersion we only investigate the meso and macro scale as dispersion on the micro scale is already well known. In contrast, non-newtonian flows are still not well understood even at the micro scale, where confinement due to the porous structure plays an important role. Experimental measurements will therefore also be performed at the micro scale.

Project coordination

Laurent TALON (Fluides, Automatique et Sytemes Thermiques) –

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.


FAST Fluides, Automatique et Sytemes Thermiques
IFPEN IFP Energies nouvelles
Cemagref/Irstea Cemagref/Irstea
LOF Laboratoire du Futur

Help of the ANR 546,979 euros
Beginning and duration of the scientific project: September 2012 - 36 Months

Useful links

Explorez notre base de projets financés



ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter