Miscible transfer of solute in different model fractures: From random to multiscale wall roughness

Abstract

Miscible tracer dispersion measurements in transparent model fractures with different types of wall roughness are reported. The nature (Fickian or not) of dispersion is determined by studying variations of the mixing front as a function of the traveled distance but also as a function of the lateral scale over which the tracer concentration is averaged. The dominant convective dispersion mechanisms (velocity profile in the gap, velocity variations in the fracture plane) are established by comparing measurements using Newtonian and shear thinning fluids. For small monodisperse rugosities, front spreading is diffusive with a dominant geometrical dispersion (dispersion coefficient D ∝ Pe) at low Péclet numbers Pe; at higher Pe values one has either D ∝ Pe 2 (i.e. Taylor dispersion) for obstacles of height smaller than the gap or D ∝ Pe 1.35 for obstacles bridging the gap. For a self affine multiscale roughness like in actual rocks and a relative shear displacement δ of complementary walls, the aperture field is channelized in the direction perpendicular to δ. For a mean velocity U parallel to the channels, the global front geometry reflects the velocity contrast between them and is predicted from the aperture field. For U perpendicular to the channels, global front spreading is much reduced. Local spreading of the front thickness remains mostly controlled by Taylor dispersion except in the case of a very strong channelization parallel to U.

Numerical modeling of non-Newtonian fluid flow in fractures and porous media

“…This affects the effective permeability of the fracture to such fluids [16]. It also affects transport since the flow becomes more channelized [18,17,2,3]. In hydraulic fracturing models, power-law rheology has been routinely used to describe fracturing gels [33,27].…”

The effect of spatial aperture variations on the thermal performance of discretely fractured geothermal reservoirs

“…They further showed how the mean flow rate was either enhanced or inhibited, depending on the orientation of the applied pressure drop. Transport properties such as dispersion have also been studied in self-affine fractures (Plouraboué et al 1998;Drazer and Koplik 2002;McDermott et al 2009;Auradou et al 2010). Numerical studies exhibit non-Gaussian transit time distribution with long tails (Drazer and Koplik 2002) and experiments with Newtonian and shear thinning fluids showed that geometric/hydraulic dispersion is dominant at low Péclet numbers with the dispersion coefficient on the order of the Péclet number (Auradou et al 2010).…”

On the way to the exploitation of deep geothermal resources in naturally fractured environments

“…In this way, chemical tracings between wells should be an efficient tool for creating a database for all future modelling of the exploited geothermal system. Auradou et al (2010) show how tracers can be used in such complex geological systems to follow their progression and the mechanism of their dispersion in the reservoir. These points have to be well understood to make progress in the industrial use of the tracers' information.…”

“…Pour ce faire, les trac ¸ages inter-puits sont un outil essentiel dont l'interpre ´tation des re ´sultats constitue l'une des bases indispensables a `toute mode ´lisation. Auradou et al (2010) montrent que, lorsque des traceurs sont utilise ´s dans des milieux aussi complexes, leurs cheminements et donc les modalite ´s suivies par leur dispersion dans le re ´servoir e ´tudie ´exercent des influences complexes qu'il importera de prendre autant que possible en compte.…”