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Andrew W Woods - One of the best experts on this subject based on the ideXlab platform.
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topographic viscous fingering Fluid Fluid displacement in a channel of non uniform gap width
Philosophical Transactions of the Royal Society A, 2016Co-Authors: Andrew W Woods, Nicola MingottiAbstract:We consider the displacement of one Fluid by a second immiscible Fluid through a long, thin permeable channel whose thickness and permeability decrease away from the axis of the channel. We build a model that illustrates how the shape of the Fluid–Fluid interface evolves in time. We find that if the Injected Fluid is of the same viscosity as the original Fluid, then the cross-channel variations in permeability and thickness tend to focus the flow along the centre of the channel. If the viscosity of the Injected Fluid is smaller than the original Fluid, then this flow focusing intensifies, leading to very poor sweep of the original Fluid in the system, with the Injected Fluid bypassing much of the channel. We also show that if the viscosity ratio of the Injected Fluid to the original Fluid is sufficiently large, then a blunt nose may develop at the leading edge of the Injected Fluid, whereas the remainder of the Fluid–Fluid interface becomes stretched out along the edges of the channel. This leads to a much more efficient sweep of the original Fluid from the channel. We generalize the model to illustrate how buoyancy forces and capillary pressure affect the evolution of the system and compare our model predictions with some simple laboratory experiments. This partial stabilization of a Fluid interface in a channel of non-uniform width represents a generalization of the classical Saffman–Taylor instability, and our nonlinear solutions for the evolution of the interface highlight the importance of cross-channel variations in permeability and thickness in modelling flow in channelled reservoirs. This article is part of the themed issue ‘Energy and the subsurface’.
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early time periodic injection and extraction in an inclined confined aquifer
Journal of Fluid Mechanics, 2015Co-Authors: Peter Dudfield, Andrew W WoodsAbstract:We consider the periodic injection and extraction of Fluid from a horizontal line well in an inclined saturated aquifer of finite thickness, , as part of an aquifer thermal energy storage system. We focus on the case in which the Injected Fluid is dense relative to the original Fluid in the aquifer and hence tends to run off downslope, so that during the extraction cycle a mixture of original aquifer Fluid and Injected Fluid is produced. We study the controls on the composition of the extracted Fluid, distinguishing between the cases where there is an open boundary downslope or upslope of the source, with the other boundary being sealed. We find that initially the fraction of original aquifer Fluid recovered during an extracted cycle decreases from cycle to cycle, and at long times this fraction asymptotes to a value, , that depends on and , where is the time period of injection, is the porosity of the aquifer, is the injection rate, is the speed of the buoyancy driven flow and is the angle of inclination to the horizontal. At long times the flow asymptotes to a quasi-steady exchange flow solution that develops in an inclined saturated porous layer of thickness in contact with a stratified Fluid reservoir, filled to thickness with relatively dense Fluid. This enables us to calculate the average composition of the extracted Fluid, which is of concern if the original aquifer Fluid contains contaminants. Since the produced aquifer Fluid is driven by this quasi-steady exchange flow, we show that contaminants downslope of the well will be produced after a finite time, whereas contaminants upslope of the well typically remain in the aquifer, irrespective of the far-field boundary conditions. We successfully test the models with a series of analogue experiments of both the injection extraction flow and the exchange flow using a Hele-Shaw cell.
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on the periodic injection of Fluid into and its extraction from a confined aquifer
Journal of Fluid Mechanics, 2014Co-Authors: Peter Dudfield, Andrew W WoodsAbstract:We consider the periodic injection and extraction of Fluid from a line well in a horizontal saturated aquifer of finite thickness as part of an aquifer thermal energy storage system. We focus on the case in which the Injected Fluid is dense relative to the original Fluid in the aquifer and we explore the competition between the driving pressure and buoyancy force in controlling the dispersal of the Injected Fluid through the aquifer. We show that, after each cycle, a progressively larger fraction of the Injected Fluid is extracted, while the remainder of the Injected Fluid gradually migrates away from the well such that, after time t, the position of the leading edge of the Injected Fluid, xnose.t/, scales as xnose.t/ xnose./ p t= , where is the period of injection. If the Fluid is extracted from the base of the layer, then, near the well, the thickness of the Injected Fluid at the end of the extraction cycle tends to a constant value, which decreases with injection rate. We also show that there is a class of self-similar exchange-flow solutions that develop when a saturated porous layer of thickness H is in contact with a stratified Fluid reservoir, filled to thickness F0H< H with relatively dense Fluid, and with original reservoir Fluid above this level. We show that these solutions coincide exactly with the far-field flow produced by the injection‐extraction cycles. We successfully test the models with a series of analogue experiments of both the injection‐extraction flow and the exchange flow using a Hele-Shaw cell. In the case that the Fluid is Injected and extracted from the top of the aquifer, the value F0 tends to unity in all cases, although the convergence time depends on the rate and period of injection, the buoyancy speed and the vertical extent and the porosity of the aquifer. We use the model to explore how the concentration of reservoir Fluid in the produced Fluid varies as the system evolves from cycle to cycle, and we also examine the time required to transport a localised but distant contaminant to the production well through the far-field exchange flow. Finally, we consider the analogous axisymmetric injection‐extraction flow problem, and show, through both numerical solution of the governing equations and experiment, that, although there is no simple class of similarity solutions, the fraction of Injected Fluid that is extracted progressively increases in each cycle.
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on the flow of buoyant Fluid Injected into an aquifer with a background flow
Journal of Fluid Mechanics, 2012Co-Authors: Iain A D Gunn, Andrew W WoodsAbstract:We study the dispersal of a plume of incompressible buoyant Fluid Injected into a confined inclined aquifer in which there is a background flow. We assume that, to prevent pressure buildup in the system, there is an outflow from the aquifer, with flux equal to the injection flux, through a producing well. Using the method of characteristics, we identify that the trajectory of the plume of Injected Fluid depends on the magnitudes of both the injection flux and the background aquifer flux relative to the buoyancy-driven exchange flow of Injected and original Fluid within the aquifer , on the direction of the background aquifer flow, and on whether the producing well lies upslope or downslope from the injecting well. We find the values of the controlling parameters and for which all Injected Fluid flows up-dip, for which the Injected Fluid partitions into a component moving up-dip and a component moving down-dip, and for which all Injected Fluid flows down-dip. A key learning from the analysis is that there may be very different plume trajectories when a buoyant Fluid is Injected into a confined, inclined aquifer, and prediction of the trajectory depends on knowledge of the background flow as well as the injection rate and location of the producing wells. In the process of sequestration, this range of initial plume geometries can inform analysis of longer-term geological storage and assessment of the risk of activating different possible leakage pathways to the surface.
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on the flow of buoyant Fluid Injected into a confined inclined aquifer
Journal of Fluid Mechanics, 2011Co-Authors: Iain A D Gunn, Andrew W WoodsAbstract:We study the dispersal of a plume of incompressible buoyant Fluid Injected into a confined sloping aquifer which has an outflow at a single fault which may be up-dip (up-slope) or down-dip (down-slope) from the point of injection. We develop a long-time asymptotic solution for the motion of the Injected Fluid. We show that for the case in which the outflow fault is up-dip from the point of injection, there is a critical injection rate above which the Injected Fluid floods the full depth of the aquifer, and we show that for the case in which the outflow fault is down-dip from the point of injection, there is a critical injection rate below which all Injected Fluid initially flows up-dip. Our analysis leads to expressions for the lateral extent of the Injected Fluid as a function of time, and we consider the implications of the model for the dispersal of supercritical carbon dioxide Injected into deep saline aquifers. The work also indicates that the geometry of the system may have a significant effect on (i) the total volume of carbon dioxide which it is possible to sequester in a faulted aquifer and (ii) the interpretation of the dispersed position of any Injected tracers.
Eric H Oelkers - One of the best experts on this subject based on the ideXlab platform.
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reaction path modelling of in situ mineralisation of co2 at the carbfix site at hellisheidi sw iceland
Geochimica et Cosmochimica Acta, 2018Co-Authors: Sandra O Snaebjornsdottir, Sigurdur R Gislason, Iwona Galeczka, Eric H OelkersAbstract:Abstract Results from injection of 175 tonnes of CO2 into the basaltic subsurface rocks at the CarbFix site in SW-Iceland in 2012 show almost complete mineralisation of the Injected carbon in less than two years (Matter et al., 2016; Snaebjornsdottir et al., 2017). Reaction path modelling was performed to illuminate the rate and extent of CO2-water-rock reactions during and after the injection. The modelling calculations were constrained by the compositions of Fluids sampled prior to, during, and after the injection, as reported by Alfredsson et al. (2013) and Snaebjornsdottir et al. (2017). The pH of the Injected Fluid, prior to CO2 dissolution was ∼9.5, whereas the pH of the background waters in the first monitoring well prior to the injections was ∼9.4. The pH of the sampled Fluids used in the modelling ranged from ∼3.7 at the injection well to as high as 8.2 in the first monitoring well. Modelling results suggest that CO2-rich water-basalt interaction is dominated by crystalline basalt dissolution along a faster, high permeability flow path, but by basaltic glass dissolution along a slower, pervasive flow path through which the bulk of the Injected Fluid flows. Dissolution of pre-existing calcite at the onset of the injection does not have a net effect on the carbonation, but does contribute to a rapid early pH rise during the injection, and influences which carbonate minerals precipitate. At low pH, Mg, and Fe are preferentially released from crystalline basalts due to the higher dissolution rates of olivine, and to lesser extent pyroxene, compared to plagioclase and glass (Gudbrandsson et al., 2011). This favours the formation of siderite and Fe-Mg carbonates over calcite during early mineralisation. The model suggests the formation of the following carbonate mineral sequences: siderite at pH 5, and calcite at higher pH. Other minerals forming with the carbonates are Al- and Fe-hydroxides and chalcedony, and zeolites and smectites at elevated pH. The most efficient carbonate formation is when the pH is high enough for formation of carbonates, but not so high that zeolites and smectites start to form, which compete with carbonates over both cations and pore space. The results of reaction path modelling at the CarbFix site in SW-Iceland indicate that this “sweet spot” for mineralisation of CO2 is at pH from ∼5.2 to 6.5 in basalts at low temperature (20–50 °C).
Howard A Stone - One of the best experts on this subject based on the ideXlab platform.
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axisymmetric flows from Fluid injection into a confined porous medium
Physics of Fluids, 2016Co-Authors: O Guo, Zhong Zheng, Michael A Celia, Howard A StoneAbstract:We study the axisymmetric flows generated from Fluid injection into a horizontal confined porous medium that is originally saturated with another Fluid of different density and viscosity. Neglecting the effects of surface tension and Fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp Fluid-Fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced Fluid relative to Injected Fluid, and Γ, which measures the relative importance of buoyancy and Fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the Injected Fluid being more viscous tha...
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flow regimes for Fluid injection into a confined porous medium
Journal of Fluid Mechanics, 2015Co-Authors: Zhong Zheng, O Guo, Michael A Celia, Iva C Christov, Howard A StoneAbstract:We report theoretical and numerical studies of the flow behaviour when a Fluid is Injected into a confined porous medium saturated with another Fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the Fluid–Fluid interface. In the early time period, the Fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the Fluid flow is mainly driven by the injection, and the governing equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the Injected Fluid is more viscous than the displaced Fluid, whereas a rarefaction wave solution is found when the Injected Fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an Injected Fluid with a viscosity higher than or equal to that of the displaced Fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutionsmore » are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less
Michael A Celia - One of the best experts on this subject based on the ideXlab platform.
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axisymmetric flows from Fluid injection into a confined porous medium
Physics of Fluids, 2016Co-Authors: O Guo, Zhong Zheng, Michael A Celia, Howard A StoneAbstract:We study the axisymmetric flows generated from Fluid injection into a horizontal confined porous medium that is originally saturated with another Fluid of different density and viscosity. Neglecting the effects of surface tension and Fluid mixing, we use the lubrication approximation to obtain a nonlinear advection-diffusion equation that describes the time evolution of the sharp Fluid-Fluid interface. The flow behaviors are controlled by two dimensionless groups: M, the viscosity ratio of displaced Fluid relative to Injected Fluid, and Γ, which measures the relative importance of buoyancy and Fluid injection. For this axisymmetric geometry, the similarity solution involving R2/T (where R is the dimensionless radial coordinate and T is the dimensionless time) is an exact solution to the nonlinear governing equation for all times. Four analytical expressions are identified as asymptotic approximations (two of which are new solutions): (i) injection-driven flow with the Injected Fluid being more viscous tha...
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flow regimes for Fluid injection into a confined porous medium
Journal of Fluid Mechanics, 2015Co-Authors: Zhong Zheng, O Guo, Michael A Celia, Iva C Christov, Howard A StoneAbstract:We report theoretical and numerical studies of the flow behaviour when a Fluid is Injected into a confined porous medium saturated with another Fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the Fluid–Fluid interface. In the early time period, the Fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the Fluid flow is mainly driven by the injection, and the governing equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the Injected Fluid is more viscous than the displaced Fluid, whereas a rarefaction wave solution is found when the Injected Fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an Injected Fluid with a viscosity higher than or equal to that of the displaced Fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutionsmore » are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less
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similarity solutions for Fluid injection into confined aquifers
Journal of Fluid Mechanics, 2006Co-Authors: Ja M Nordbotte, Michael A CeliaAbstract:Fluid injection into the deep subsurface, such as injection of carbon dioxide (CO $_2$ ) into deep saline aquifers, often involves two-Fluid flow in confined geological formations. Similarity solutions may be derived for these problems by assuming that a sharp interface separates the two Fluids, by imposing a suitable no-flow condition along both the top and bottom boundaries, and by including an explicit solution for the pressure distribution in both Fluids. When the Injected Fluid is less dense and less viscous than the resident Fluid, as is the case for CO $_{2}$ injection into a resident brine, gravity override produces a Fluid flow system that is captured well by the similarity solutions. The similarity solutions may be extended to include slight miscibility between the two Fluids, as well as compressibility in both of the Fluid phases. The solutions provide the location of the interface between the two Fluids, as well as drying fronts that develop within the Injected Fluid. Applications to cases of supercritical CO $_{2}$ injection into deep saline aquifers demonstrate the utility of the solutions, and comparisons to solutions from full numerical simulations show the ability to predict the system behaviour.
Erfan Mohammadian - One of the best experts on this subject based on the ideXlab platform.
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experimental investigation of interfacial tension measurement and oil recovery by carbonated water injection a case study using core samples from an iranian carbonate oil reservoir
Energy & Fuels, 2017Co-Authors: Bizhan Honarvar, Ali Rahimi, Amin Azdarpour, Mohammad Karimi, Mohammad Afkhami Karaei, Hossein Hamidi, James Ing, Erfan MohammadianAbstract:Low volumetric sweep efficiency, early breakthrough of Injected Fluid, and high risk of gas leakage from the reservoir are the major technical challenges associated with direct gas and water injection into oil reservoirs. Injection of carbonated water (CW) into oil reservoirs is a carbon dioxide-augmented water injection technique, which results in improved oil recovery and possible CO2 storage in the reservoir. In this paper, the potential of carbonated water injection (CWI) into an Iranian carbonate reservoir for the purpose of improving oil recovery was investigated. In addition, the interfacial tension (IFT) of crude oil and two different carbonated brines (carbonated formation brine and carbonated seawater) as well as CO2 solubility in these two carbonated brines was determined. Experimental results showed that CO2 solubility in both brines increases with pressure and decreases with temperature. However, CO2 solubility was more promising in seawater compared to formation brine because of the lower sa...