Experimental verification of power-law non-Newtonian axisymmetric porous gravity currents

Longo, Sandro; Federico, Vittorio Di; Chiapponi, L.; Archetti, Renata

doi:10.1017/jfm.2013.389

Cited by 38 publications

(23 citation statements)

References 19 publications

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“…Various self-similar solutions exist to describe the spreading of gravity currents of constant or variable volume in cases similar to our problem where κ = 0, n = 1 (e.g., King & Woods 2003;Lyle et al 2005), and where κ = 0 (Pascal & Pascal 1993;Longo et al 2013bLongo et al , 2015bCiriello et al 2016). For the current study where both yield stress and shear thinning/thickening effects are present, a generalized form of such solutions is not available since the presence of yield stress breaks self-similarity.…”

Section: Self-similar Solutionmentioning

confidence: 84%

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Gravity-driven flow of Herschel–Bulkley fluid in a fracture and in a 2D porous medium

et al. 2017

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New analytical models are introduced to describe the motion of a Herschel–Bulkley fluid slumping under gravity in a narrow fracture and in a porous medium. A useful self-similar solution can be derived for a fluid injection rate that scales as time $t$; an expansion technique is adopted for a generic injection rate that is power law in time. Experiments in a Hele-Shaw cell and in a narrow channel filled with glass ballotini confirm the theoretical model within the experimental uncertainty.

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Section: Self-similar Solutionmentioning

confidence: 84%

“…Gravity currents of a power-law fluid in porous media have recently been analysed with a combination of analytical, numerical, and experimental techniques (e.g., Longo et al 2013b;Di Federico et al 2014;Longo et al 2015a;Ciriello et al 2016).…”

Section: Introductionmentioning

confidence: 99%

Gravity-driven flow of Herschel–Bulkley fluid in a fracture and in a 2D porous medium

et al. 2017

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“…The propagation of such currents was analysed by Pascal & Pascal (1993) for constant injected volume and plane geometry, and by Bataller (2008) for assigned depth or flux at the origin and radial geometry. General solutions for a time-variable current volume were derived in a two-dimensional (Di Federico, Archetti & Longo 2012a) and axisymmetric geometry (Di Federico, Archetti & Longo 2012b); the results obtained in the latter paper were confirmed by the experiments of Longo et al (2013b).…”

mentioning

confidence: 75%

A dipole solution for power-law gravity currents in porous formations

2015

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A theoretical and experimental analysis of non-Newtonian gravity currents in porous media with variable properties is presented. A mound of a power-law fluid of flow behaviour index n is released into a semi-infinite saturated porous medium above a horizontal bed, and can drain freely out of the formation at the origin. The porous medium permeability varies along the vertical as z (ω−1) , porosity varies along the vertical as z (γ −1) , z being the vertical coordinate and ω and γ constant numerical coefficients. A self-similar solution describing the space-time evolution of the resulting gravity current is derived for shear-thinning fluids with n < 1, generalizing earlier results for Newtonian fluids. The solution conserves a generalized dipole moment of the mound. The spreading of the current front is proportional to t γ n/(2+ω(n+1)) . Expressions for the time evolution of the outgoing flux at the origin and of the current volume are derived in closed form. The Hele-Shaw analogue is derived for flow of a power-law fluid in a porous medium with vertically variable properties. Results from laboratory experiments conducted in two Hele-Shaw cells confirm the constancy of the dipole moment, and compare well with the theoretical formulation.

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“…for which an analytical solution can be written as: (15) or equivalently function of the flow rate Q,…”

Section: Flow Between Two Parallel Platesmentioning

confidence: 99%

“…The rate of advancement of the pressure front, as a function of the model parameters is also discussed in details. In [15] a validation of the theoretical prediction for the gravity currents of power-law fluids, intruding into a saturated porous medium, is provided. In addition, non-Newtonian power-law fluid has been adopted to numerically investigate the flow in rough-walled fractures [16,17], and an extension to a radial flow is proposed in [18].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

et al. 2017

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Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by simulation of the 3D micro-CT images using a Finite Volume Method (FVM). The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive mesh generation technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM). Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration in agreement with a derived theoretical model, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a master curve is derived when normalizing the mobility for both the carbonate and the sandstone.

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Experimental verification of power-law non-Newtonian axisymmetric porous gravity currents

Cited by 38 publications

References 19 publications

Gravity-driven flow of Herschel–Bulkley fluid in a fracture and in a 2D porous medium

Gravity-driven flow of Herschel–Bulkley fluid in a fracture and in a 2D porous medium

A dipole solution for power-law gravity currents in porous formations

The Effect of Heat Transfer and Polymer Concentration on Non-Newtonian Fluid from Pore-Scale Simulation of Rock X-ray Micro-CT

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