9 results
A dynamic model of ${\rm CO}_2$ storage in layered anticlines
- Patrick K. Mortimer, Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 979 / 25 January 2024
- Published online by Cambridge University Press:
- 18 January 2024, A39
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We explore ${\rm CO}_2$ injection into a layered permeable rock consisting of high permeability reservoir layers, separated by low permeability mudstone, and taking the shape of an anticline within a laterally extensive aquifer. We first show how the storage capacity of the formation depends on the capillary entry pressure of the inter-layer mudstone, so that ${\rm CO}_2$ cannot flow from one layer into the next. We then consider a formation composed of two layers, overlain by a cap rock. For injection into the lowest layer, we show that the injection rate, capillary entry pressure and buoyancy driven flux through the mudstone determine whether the lower or upper layer fills to the spill point first. We also show that at the end of the injection phase, ${\rm CO}_2$ may continue to flow from the lower to the upper layer. This implies that injection should be stopped once the injected volume matches the static capacity of the formation in order to prevent spilling after injection. We present a series of analogue experiments of a two layered system that illustrate some of the principles described by the model, and assess the implications of the results for field scale systems.
Experiments on fluid entrainment and slip in continuous bubble plumes
- Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 973 / 25 October 2023
- Published online by Cambridge University Press:
- 18 October 2023, A22
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A series of laboratory experiments are reported in which a continuous stream of bubbles rise from a small source at the base of a tank of water. Using different nozzles, bubble sizes $d$ ranging from 1.2 to 11.6 mm were produced for a number of gas volume fluxes, $Q_b$, ranging between 1.1 and $21.1\times 10^{-6}\ {\rm m}^3\ {\rm s}^{-1}$. Within a small distance from the source, the slip speed of these bubbles exceeds the speed of the equivalent single-phase plume with the same buoyancy flux, leading to formation of what we refer to as the ‘slip plume’ regime. Through a combination of high-speed photography, coupled with flow visualisation in the plume and the ambient fluid using dye, we find that the bubble speed and the fluid speed remain nearly constant with height, with the maximum fluid speed being of order $0.30\pm 0.03$ of the bubble speed. Using the filling box method, we also find that the net fluid volume flux in the slip plume increases linearly with distance from the source at a rate $Q_l = \lambda Bz/v_s^2$, where $B$ is the buoyancy flux of the gas, $v_s$ the rise speed of the gas bubbles, $z$ the distance above the source and $\lambda$ is a constant related to the dimensionless volume of fluid in the wake of each bubble. This slip-dominated flow regime can be understood in terms of kinetic energy imparted to the fluid as the bubbles rise and release potential energy. Further experiments with particle-laden plumes illustrate similar scalings for the volume flux in a particle-driven slip plume once the slip speed of the particles exceeds the bulk speed of the equivalent single-phase buoyant plume with the same buoyancy flux. Near the source the slip speed may be smaller than the plume speed, and the flow follows the classical model for a turbulent buoyant plume, with the transition to the slip regime occurring at a distance $z^*\approx (32\pm 5)\lambda ^{3/2} B/v_s^3$ from the source, where the dimensionless parameter $\lambda$ relates to the dimensionless volume of the fluid wake, which we find varies with the Reynolds number of the particles.
Dynamics of sediment-laden plumes in the ocean
- Nicola Mingotti, Andrew W. Woods
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- Journal:
- Flow: Applications of Fluid Mechanics / Volume 2 / 2022
- Published online by Cambridge University Press:
- 23 August 2022, E26
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We present a series of experiments to illustrate the dynamics of positively or negatively buoyant particle-laden plumes in a cross-flow, with relevance for the discharge of sediment into the ocean during deep-sea mining operations. In an unstratified ambient fluid, our experiments identify three different regimes, corresponding to (i) a dense particle-laden plume, host to relatively dense saline fluid, in which the particles separate from the descending plume as the flow speed falls below the particle settling speed; (ii) a dense particle-laden plume, host to buoyant fluid, in which the fluid gradually rises from the sinking plume of particles, to form a second rising plume of source fluid; and (iii) a buoyant particle-laden plume, host to buoyant fluid, which rises from the discharge pipe, and from which particles gradually sediment. Classical models of single-phase plumes describe the initial motion of the plumes in cases (i) and (iii), but as the flow speed falls below the particle fall speed, sedimentation leads to a change in the averaged buoyancy, and, hence, the plume speed. Our data also suggest that the sedimentation leads to a reduction in the rate of entrainment of ambient fluid, compared with the classical single-phase plumes. We also show that with a density stratified ambient fluid, the stratification may arrest the plume prior to significant particle sedimentation, and in this case, the plume tends to spread downstream at the level of neutral buoyancy where particle sedimentation proceeds. The bulk density of the residual plume fluid may then remain intermediate between the density of the upper and lower layer fluid, or may become less dense than the upper layer fluid, in which case, following sedimentation, the plume fluid rises through the upper layer. While the dynamics of deep-sea mining plumes in the ocean are more complex, for example, owing to background turbulence and mixing, the results of our new laboratory experiments highlight the range of flow processes which may influence the initial dispersion and sedimentation of particles in such plumes following release into the water, depending on the initial conditions, the ambient density and the particle fall speed. We also discuss the relevance of our work in the context of ash dispersal by volcanic plumes.
On particle separation from turbulent particle plumes in a cross-flow
- Cara B.G. James, Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 932 / 10 February 2022
- Published online by Cambridge University Press:
- 14 December 2021, A45
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We present new experiments of particle-driven turbulent plumes issuing from a constant source of dense particle-laden fluid, with buoyancy flux, $B$, in a uniform horizontal current, $u$. Experiments show that a turbulent, well-mixed plume develops, in which the downward vertical speed $w$ decreases with depth $z$ according to $w = 0.76 (B/uz)^{1/2}$ while the horizontal speed rapidly asymptotes to the current speed $u$, provided that the Stokes settling speed of the particles $v<0.92 w$. For $v > 0.92 w$, the particles separate from the plume fluid, and their depth $z$ increases according to the simple sedimentation trajectory $\textrm {d}z/{\textrm {d}\kern0.7pt x} = v/u$. As the particles sediment, they form clusters of particles, which lead to fluctuations in the particle load with position, but do not appear to change the time-average sedimentation speed. We explore the impact of these results for deep-sea mining, in which the fate of the plume water as well as the particles is key for assessing potential environmental impacts.
The mixing of airborne contaminants by the repeated passage of people along a corridor
- Nicola Mingotti, Richard Wood, Catherine Noakes, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 903 / 25 November 2020
- Published online by Cambridge University Press:
- 02 October 2020, A52
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We report a series of experiments in which a cylinder, with a vertical axis, is moved back and forth along a long narrow channel containing fresh water at Reynolds numbers $Re=3220\text {--}13\,102$. We examine the mixing of a cloud of dye along the channel by the oscillatory motion of the cylinder. Using light attenuation techniques to measure the time evolution of the concentration of dye along the channel, we find that at early times the concentration profile collapses to a Gaussian profile with dispersivity, $D=(2.4\pm 0.5) fdW$, where $f$ is the frequency of the cylinder oscillation, $d$ is the diameter of the cylinder and $W$ is the width of the channel, respectively. For times much longer than $L^2/D$, with $L$ being the length of the channel, the concentration becomes progressively more uniform over the whole length of the channel, and we show that the long-time non-uniform component decays with time dependence $\exp (- 4{\rm \pi} ^2 Dt / L^2)$. We consider the implications of these experiments for the dispersal of viral aerosols along poorly ventilated corridors, with implications for infection transmission in hospitals and public buildings.
Multiphase plumes in a stratified ambient
- Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 869 / 25 June 2019
- Published online by Cambridge University Press:
- 23 April 2019, pp. 292-312
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We report on experiments of turbulent particle-laden plumes descending through a stratified environment. We show that provided the characteristic plume speed $(B_{0}N)^{1/4}$ exceeds the particle fall speed, where the plume buoyancy flux is $B_{0}$ and the Brunt–Väisälä frequency is $N$, then the plume is arrested by the stratification and initially intrudes at the neutral height associated with a single-phase plume of the same buoyancy flux. If the original fluid phase in the plume has density equal to that of the ambient fluid at the source, then as the particles sediment from the intruding fluid, the fluid finds itself buoyant and rises, ultimately intruding at a height of about $0.58\pm 0.03$ of the original plume height, consistent with new predictions we present based on classical plume theory. We generalise this result, and show that if the buoyancy flux at the source is composed of a fraction $F_{s}$ associated with the buoyancy of the source fluid, and a fraction $1-F_{s}$ from the particles, then following the sedimentation of the particles, the plume fluid intrudes at a height $(0.58+0.22F_{s}\pm 0.03)H_{t}$, where $H_{t}$ is the maximum plume height. This is key for predictions of the environmental impact of any material dissolved in the plume water which may originate from the particle load. We also show that the particles sediment at their fall speed through the fluid below the maximum depth of the plume as a cylindrical column whose area scales as the ratio of the particle flux at the source to the fall speed and concentration of particles in the plume at the maximum depth of the plume before it is arrested by the stratification. We demonstrate that there is negligible vertical transport of fluid in this cylindrical column, but a series of layers of high and low particle concentration develop in the column with a vertical spacing which is given by the ratio of the buoyancy of the particle load and the background buoyancy gradient. Small fluid intrusions develop at the side of the column associated with these layers, as dense parcels of particle-laden fluid convect downwards and then outward once the particles have sedimented from the fluid, with a lateral return flow drawing in ambient fluid. As a result, the pattern of particle-rich and particle-poor layers in the column gradually migrates upwards owing to the convective transport of particles between the particle-rich layers superposed on the background sedimentation. We consider the implications of the results for mixing by bubble plumes, for submarine blowouts of oil and gas and for the fate of plumes of waste particles discharged at the ocean surface during deep-sea mining.
On turbulent particle fountains
- Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 793 / 25 April 2016
- Published online by Cambridge University Press:
- 23 March 2016, R1
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We describe new experiments in which particle-laden turbulent fountains with source Froude numbers $20>Fr_{0}>6$ are produced when particle-laden fresh water is injected upwards into a reservoir filled with fresh water. We find that the ratio $U$ of the particle fall speed to the characteristic speed of the fountain determines whether the flow is analogous to a single-phase fountain ($U\ll 1$) or becomes a fully separated flow ($U\geqslant 1$). In the single-phase limit, a fountain with momentum flux $M$ and buoyancy flux $B$ oscillates about the mean height, $h_{m}=(1.56\pm 0.04)M^{3/4}B^{-1/2}$, as fluid periodically cascades from the maximum height, $h_{t}=h_{m}+{\rm\Delta}h$, to the base of the tank. Experimental measurements of the speed $u$ and radius $r$ of the fountain at the mean height $h_{m}$, combined with the conservation of buoyancy, suggest that $Fr(h_{m})=u(g^{\prime }r)^{-1/2}\approx 1$. Using these values, we find that the classical scaling for the frequency of the oscillations, ${\it\omega}\sim BM^{-1}$, is equivalent to the scaling $u(h_{m})/r(h_{m})$ for a fountain supplied at $z=h_{m}$ with $Fr=1$ (Burridge & Hunt, J. Fluid Mech., vol. 728, 2013, pp. 91–119). This suggests that the oscillations are controlled in the upper part of the fountain where $Fr\leqslant 1$, and that they may be understood in terms of a balance between the upward supply of a growing dense particle cloud, at the height where $Fr=1$, and the downward flow of this cloud. In contrast, in the separated flow regime, we find that particles do not reach the height at which $Fr=1$: instead, they are transported to the level at which the upward speed of the fountain fluid equals their fall speed. The particles then continuously sediment while the particle-free fountain fluid continues to rise slowly above the height of particle fallout, carried by its momentum.
On the transport of heavy particles through a downward displacement-ventilated space
- Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 774 / 10 July 2015
- Published online by Cambridge University Press:
- 08 June 2015, pp. 192-223
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We investigate the transport of relatively heavy, small particles through a downward displacement-ventilated space. A flux of particles is supplied to the space from a localised source at a high level and forms a turbulent particle-laden plume which descends through the space. A constant flow of ambient fluid which does not contain particles is supplied to the space at a high level, while an equal amount of fluid is vented from the space at a low level. As a result of the entrainment of ambient fluid into the particle plume, a return flow is produced in the ambient fluid surrounding the plume in the lower part of the space. At steady state, particles are suspended by this return flow. An interface is formed which separates the ambient fluid in the lower part of the space, which contains particles, from the particle-free ambient fluid in the upper part of the space. New laboratory experiments show that the concentration of particles in the ambient fluid below the interface is larger than the average concentration of particles in the plume fluid at the level of the interface. Hence, as the plume fluid crosses the interface and descends through the particle-laden fluid underneath, it becomes relatively buoyant and forms a momentum-driven fountain. If the fountain fluid impinges on the floor, it then spreads radially over the surface until lifting off. We develop a quantitative model which can predict the height of the interface, the concentration of particles in the lower layer, and the partitioning of the particle flux between the fraction which sediments over the floor and that which is ventilated out of the space. We generalise the model to show that when particles and negatively buoyant fluid are supplied at the top of the space, a three-layer stratification develops in the space at steady state: the upper layer contains relatively low-density ambient fluid in which no particles are suspended; the central layer contains a mixture of ambient and plume fluid in which no particles are suspended; and the lower layer contains a suspension of particles in the same mixture of ambient and plume fluid. We quantify the heights of the two interfaces which separate the three layers in the space and the concentration of particles in suspension in the ambient fluid in the lower layer. We then discuss the relevance of the results for the control of airborne infections in buildings. Our experiments show that the three-layer stratification is subject to intermittent large-scale instabilities when the concentration of particles in the plume at the source is sufficiently small, or the rate of ventilation of the space is sufficiently large: we describe the transient concentration of particles in the space during one of these instabilities.
On the transport of heavy particles through an upward displacement-ventilated space
- Nicola Mingotti, Andrew W. Woods
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- Journal:
- Journal of Fluid Mechanics / Volume 772 / 10 June 2015
- Published online by Cambridge University Press:
- 07 May 2015, pp. 478-507
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We explore the transport of heavy particles through an upward displacement-ventilated space. The space incorporates a localised source of buoyancy which generates a turbulent buoyant plume. The plume fluid is contaminated with a small concentration of particles, which are subject to gravitational settling. A constant flow of uncontaminated fluid is supplied at a low level into the space, while an equal amount of fluid is vented from the space at a high level. At steady state, a two-layer density stratification develops associated with the source of buoyancy. New laboratory experiments are conducted to explore how particles are transported by this flow. The experiments identify that the upper layer may either become well-mixed in particles or it may develop a vertical stratification in particle concentration, with the particle concentration decreasing with height. We develop a quantitative model which identifies that such stratification develops for larger particle setting speeds, or smaller ventilation rates. In accord with our experiments, the model predicts that the number of particles extracted from the space through the high-level vent is controlled by the magnitude of the particle stratification in the upper layer, and this in turn depends on the particle settling speed relative to the ventilation speed and also the cross-sectional area and height of the space. We compare the predictions of the model with measurements of the flux of particles vented from the space for a range of operating conditions. We explore the relevance of the model for the removal of airborne contaminants by displacement ventilation in hospital rooms, and we discuss how contamination is propagated in the room as a result of lateral mixing of pathogens in the upper layer.