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 distance travelled but also as a function of the lateral scale over which the tracer concentration is averaged. The dominant hydrodynamic 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 or constant dispersivity l d = D / U ) at low Péclet numbers Pe ; at higher Pe values, one has either l d ∝ Pe (i.e. Taylor dispersion) for obstacles of height smaller than the gap, or l d ∝ Pe 0.35 for obstacles bridging the gap. For a self-affine multiscale roughness like in actual rocks and a relative shear displacement <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>δ</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> of complementary walls, the aperture field is channelized in the direction perpendicular to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>δ</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> . For a mean velocity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>U</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> parallel to the channels, the global front geometry reflects the velocity contrast between them and is predicted from the aperture field. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>U</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mi>U</mml:mi> <mml:mo>→</mml:mo> </mml:mover> </mml:math> .