Gravity Currents
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Recent papers in Gravity Currents
Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The... more
Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.
KEY POINTS: The present work aims to study the behavior of a dense fluid current in a rectangular (or in a circular) cross-section channel. The denser fluid propagates into a less dense ambient fluid, with linear stratification of... more
KEY POINTS: The present work aims to study the behavior of a dense fluid current in a rectangular (or in a circular) cross-section channel. The denser fluid propagates into a less dense ambient fluid, with linear stratification of density in the vertical A simplified model was used to compute the front speed of the gravity current. The theoretical speed was obtained by: a) imposing the continuity between the injected and the propagating fluid; b) by considering the jump condition and the energetic balance at the head of the current. Seventy-six experiments were performed. The results show a systematic overestimation of the experimental front speed. The discrepancy decreases significantly for increasing value of the parameter S (representative of the relation between the density stratification of the ambient fluid and the density of the intruding current) and is at a minimum for S 1 (i.e., density of the intruding current equal to the bottom density of the ambient fluid).
We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal impermeable boundary, driven by... more
We consider the motion of shallow two-dimensional gravity currents of a purely viscous and relatively
heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal
impermeable boundary, driven by the release from a point source of a volume of fluid increasing with
time like ta. The equation of motion for power-law fluids in porous media is a modified Darcy’s law taking
into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance
equation yields a nonlinear differential problem which admits a self-similar solution describing the shape
of the current, which spreads like t(a+n )/(2+n), generalizing earlier results for Newtonian fluids. For the particular
values a = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the
numerical scheme is tested against the analytical solutions. Two additional analytical approximations,
valid for any a, are presented. The space-time development of the gravity current is discussed for different
flow behavior indexes.
heavy power-law fluid of flow behavior index n in a uniform saturated porous layer above a horizontal
impermeable boundary, driven by the release from a point source of a volume of fluid increasing with
time like ta. The equation of motion for power-law fluids in porous media is a modified Darcy’s law taking
into account the nonlinearity of the rheological equation. Coupling the flow law with the mass balance
equation yields a nonlinear differential problem which admits a self-similar solution describing the shape
of the current, which spreads like t(a+n )/(2+n), generalizing earlier results for Newtonian fluids. For the particular
values a = 0 and 2, closed-form solutions are derived; else, a numerical integration is required; the
numerical scheme is tested against the analytical solutions. Two additional analytical approximations,
valid for any a, are presented. The space-time development of the gravity current is discussed for different
flow behavior indexes.
We study axisymmetric gravity currents consisting of a constant or time-dependent volume of a powerlaw viscous fluid propagating on a horizontal rigid plane below a fluid of lesser density. The intruding fluid is considered to have a pure... more
We study axisymmetric gravity currents consisting of a constant or time-dependent volume of a powerlaw
viscous fluid propagating on a horizontal rigid plane below a fluid of lesser density. The intruding
fluid is considered to have a pure Ostwald–DeWaele power-law constitutive equation. First, the conditions
for buoyancy–viscous balance are examined, and the current rate of spreading is derived with a
box-model. An existing self-similar solution to the nonlinear differential problem for the influx of a constant
or time-variable volume of fluid is then described. Results from a number of experiments conducted
in a 30 sector with shear thinning, Newtonian and shear thickening fluids, and with constant and
increasing release rate, are presented and interpreted with the theoretical solution, obtaining globally
a very satisfactory agreement. The rheological parameters of the fluid, derived with a best fit procedure,
are compared to those measured independently with conventional rheometry. Confidence intervals are
evaluated for both estimates of flow behavior and consistency indices. Results support the feasibility
of controlled constant flux laboratory experiments with gravity currents in axisymmetric geometry to
infer the rheology of power-law fluids, especially at very low shear rates and with shear thinning fluids.
viscous fluid propagating on a horizontal rigid plane below a fluid of lesser density. The intruding
fluid is considered to have a pure Ostwald–DeWaele power-law constitutive equation. First, the conditions
for buoyancy–viscous balance are examined, and the current rate of spreading is derived with a
box-model. An existing self-similar solution to the nonlinear differential problem for the influx of a constant
or time-variable volume of fluid is then described. Results from a number of experiments conducted
in a 30 sector with shear thinning, Newtonian and shear thickening fluids, and with constant and
increasing release rate, are presented and interpreted with the theoretical solution, obtaining globally
a very satisfactory agreement. The rheological parameters of the fluid, derived with a best fit procedure,
are compared to those measured independently with conventional rheometry. Confidence intervals are
evaluated for both estimates of flow behavior and consistency indices. Results support the feasibility
of controlled constant flux laboratory experiments with gravity currents in axisymmetric geometry to
infer the rheology of power-law fluids, especially at very low shear rates and with shear thinning fluids.
In this study, we investigate the motion of particulate gravity currents in a horizontal V-shaped channel. The particulate currents consisted of particles whose size varied between 0 and 100 μm but whose mean size increased. Particles... more
In this study, we investigate the motion of particulate gravity currents in a horizontal V-shaped channel. The particulate currents consisted of particles whose size varied between 0 and 100 μm but whose mean size increased. Particles were poorly sorted as the variance of the grain size distributions varied between 50 and 200. While the phases of propagation of homogeneous currents in such a geometry have been studied
in the literature, this study considers the effects of the grain size on the propagation. The distance of propagation and front velocity of full-depth high-Reynolds-number lock-release experiments and shallow-water equation simulations were analyzed as the mean grain size of the initial particle distributions, defined by mass, was increased from 19 to 58 μm. Similar to the homogeneous currents, three consecutive phases of
the front velocity could be identified but their characteristics and extent depend on the particle size. The initial phase, in particular, depends on a dimensionless settling number β that is defined as the ratio of two characteristic time scales, the propagation time x0/U, where U is the scale for the front speed and x0 the lock length, and the settling time h0/vs, where vs is the scale for the settling velocity and h0 the initial height of the current. For dimensionless settling numbers less than 0.001, the initial
phase is characterized by a constant velocity for over about 6-7 lock lengths that is alike the initial slumping phase of perfectly constant velocity of the homogeneous currents. For dimensionless settling numbers greater than 0.001 and less than 0.015, the initial phase is no longer characterized by a constant velocity but an almost constant velocity for over about a similar 6-7 lock lengths. For dimensionless settling
numbers greater than 0.015, however, as such, this phase is no longer seen. This initial phase is followed by a continuous decrease of the front advance, which results from the sedimentation of the particles. Unlike the homogeneous currents, this phase is a non-self-similar propagation. This phase is ended by a viscosity-dominated phase appearing to vary as ∼t1/7. The good agreement between the front advance of the experiments and shallow-water equation simulations demonstrates that the mean size by mass is a fairly good proxy of poorly sorted particles.
in the literature, this study considers the effects of the grain size on the propagation. The distance of propagation and front velocity of full-depth high-Reynolds-number lock-release experiments and shallow-water equation simulations were analyzed as the mean grain size of the initial particle distributions, defined by mass, was increased from 19 to 58 μm. Similar to the homogeneous currents, three consecutive phases of
the front velocity could be identified but their characteristics and extent depend on the particle size. The initial phase, in particular, depends on a dimensionless settling number β that is defined as the ratio of two characteristic time scales, the propagation time x0/U, where U is the scale for the front speed and x0 the lock length, and the settling time h0/vs, where vs is the scale for the settling velocity and h0 the initial height of the current. For dimensionless settling numbers less than 0.001, the initial
phase is characterized by a constant velocity for over about 6-7 lock lengths that is alike the initial slumping phase of perfectly constant velocity of the homogeneous currents. For dimensionless settling numbers greater than 0.001 and less than 0.015, the initial phase is no longer characterized by a constant velocity but an almost constant velocity for over about a similar 6-7 lock lengths. For dimensionless settling
numbers greater than 0.015, however, as such, this phase is no longer seen. This initial phase is followed by a continuous decrease of the front advance, which results from the sedimentation of the particles. Unlike the homogeneous currents, this phase is a non-self-similar propagation. This phase is ended by a viscosity-dominated phase appearing to vary as ∼t1/7. The good agreement between the front advance of the experiments and shallow-water equation simulations demonstrates that the mean size by mass is a fairly good proxy of poorly sorted particles.
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