1,720,985 research outputs found
Theoretical and experimental investigation of two-phase gas-non Newtonian fluid flows in pipes
No full textThe Impact of Pore-Scale Flow Regimes on Upscaling of Immiscible Two-Phase Flow in Porous Media
No full textEmpirical or theoretical extensions of Darcy's law for immiscible two-phase flow have shown significant limitations in properly modeling the flow at the continuum scale. We tackle this problem by proposing a set of upscaled equations based on pore-scale flow regimes, that is, the topology of flowing phases. The incompressible Navier-Stokes equation is upscaled by means of multiple-scale expansions and its closures derived from the mechanical energy balance for different flow regimes at the pore scale. We also derive the applicability conditions of the upscaled equations based on the order of magnitude of relevant dimensionless numbers, that is, Eotvos, Reynolds, capillary, Froude numbers, and the viscosity and density ratio of the system, as well as a set of closures valid for the basic flow regimes of low Eotvos number systems, that is, core-annular and plug and drop traffic flows. We provide analytical expressions for the relative permeability of the wetting and nonwetting phases in different flow regimes and demonstrate that the effect of the flowing-phases topology on the relative permeabilities is significant. Finally, we show that the classical two-phase Darcy law is recovered for a limited range of operative conditions, while specific terms accounting for interfacial and wall interactions should be incorporated to accurately model ganglia or drop traffic flow
Scaling of two-phase water-steam relative permeability and thermal fluxes in porous media
No full textTwo-phase water-steam flow conditions are frequently encountered in many engineering applications, including geothermal reservoirs. Although routine calculations are based on the multiphase Darcy's law, the role of the topology of the flowing phases at the pore-scale is usually neglected in the estimation of relative permeabilities. Instead, the latter are frequently computed using empirical models like the Corey correlation. In this work, we first apply the model for relative permeabilities based on pore-scale flow regimes developed by Picchi and Battiato (2019), Relative permeability scaling from pore-scale flow regimes, Water Resour. Res. 55, 3215–3233, to scenarios typical of geothermal reservoirs and then extend it by deriving the scaling laws for the transmissibilities and the thermal properties as a function of temperature. First, we discuss the scaling behavior of normalized relative permeabilities in terms of viscosity ratio and capillary number of water-steam systems and, then, we provide a validation of the model against experimental data available in the literature. The model captures well the data trends collected in real 3D porous media. These results suggest that water-steam relative permeabilities follow the same scaling behavior of gas-liquid systems where the non-wetting phase is much less viscous than the wetting phase. Finally, we investigate the impact that relative permeabilities have on heat transfer rates at two-phase flow conditions and the scaling of mass and energy transmissibility and thermal properties of the mixture. An estimation of the exergy carried by the two-phase water-steam mixture is also included
Relative Permeability Scaling From Pore-Scale Flow Regimes
No full textRelative permeability measurements are commonly fitted with the Corey and Brooks-Corey correlations. Despite such correlations fit experimental data generally well, they are mostly of an empirical nature. Here, we propose a semiempirical model to determine relative permeabilities of the wetting and the nonwetting phases in real 3-D porous media that accounts for pore-scale flow regimes. The starting point is the homogenization framework proposed by Picchi and Battiato (2018, https:// doi .org/10.1029/ 2018WR023172), where the upscaling is conducted for different spatial distributions of the flowing phases in the capillary tube setting. First, we extend the approach to realistic media by allowing pore-scale flow regimes to coexist in a complex geometry while accounting for capillary and viscous limits in the dynamics. Then, we discuss the scaling behavior of normalized relative permeabilities in terms of the phases viscosity ratio and identify three classes which govern their scaling. We also derive an analytical expression for the fractional flow. Finally, we provide a detailed validation of the proposed model for both relative permeabilities and fractional flow against data from numerical simulations and experiments available in the literature. The data set used for validation covers a wide range of systems, ranging from brine-CO2 to oil-water flows. The equations derived capture well the trend of both numerical and experimental data
Energy-based upscaling of immiscible two-phase flow in porous media: flow regimes and applicability conditions
No full textModeling of core-annular and plug flows of Newtonian/non-Newtonian shear-thinning fluids in pipes and capillary tubes
No full textSolutions for concentric core-annular laminar flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined pipes are presented. The solution is computed for the general case of a Carreau non-Newtonian fluid proposing an iterative method based on Chebyshev collocation points. The effect of the rheology of the shear-thinning liquid on two-phase flow characteristics is investigated both for gas/liquid and liquid/liquid systems. Concurrent and counter-current flows in horizontal and inclined pipes were studied, while referring to practical two-phase flow aspects, such as the in-situ hold-up, lubrication effects and Ledinegg instability. The main characteristic of such systems is that even though the liquid has a complex rheology (Carreau fluid), the two-phase annular flow can exhibit a Newtonian/Newtonian behavior for a wide range of operational conditions. The identification of those conditions is a key aspect in the modeling activity, as to avoid unphysical predictions by the widely used power-law model. Particular attention is given to the core-annular flow characteristics in capillaries, where we propose also a model for the plug flow regime. Predictions of film thickness and plug propagation velocity are tested by comparison with experimental data, showing promising results and offering new insights on plug flow characteristics in capillaries, in particular for liquid-liquid plug flow. (C) 2018 Elsevier Ltd. All rights reserved
Forced convection in two-phase core-annular flows
Get PDFPredicting the temperature distribution in laminar two-phase flows is essential in a wide range of engineering applications, like heat dissipation of electronic equipment and thermal design of biological reactors. Motivated by this, we extend the classical Graetz problem, studying the heat transfer between two flowing phases in a core-annular flow configuration. Using a rigorous two-scale asymptotic analysis, we derived two coupled one-dimensional advection–diffusion heat-transfer equations (one for each phase) embedding the effects of advection, diffusion (both axial and transverse) and viscous dissipation. Specifically, the heat-transfer mechanisms are described through effective velocity and effective diffusion coefficients, while the interaction between the phases is accounted for via ad hoc coupling and source terms, respectively. The dynamics of the problem is controlled by seven dimensionless groups: the Péclet and Brinkman numbers, the heat flux, the viscosity, thermal diffusivity and thermal conductivity ratios, and the volume fraction. Our analysis reveals the existence of two main regimes, depending on the disparity in thermal conductivity between the phases. When the conductivity ratio is of order one, the problem is strongly coupled; otherwise, the phases are thermally decoupled. Interestingly, we investigate the evolution of the heat-transfer coefficient in the thin-film limit, shedding light on the most common assumptions underlying extensively used models in the context of film flows. Finally, we derived closed-form scaling laws for the Nusselt number clarifying the impact of the phases topology on heat-transfer dynamics. Since our model has been derived by first principles, we hope that it will improve the understanding of two-phase forced convection
Taylor drop in a closed vertical pipe
No full textIn this work, we study the ascent dynamics of a liquid Taylor drop formed from a lock-exchange configuration in a closed vertical pipe. We focus on the buoyancy-driven motion of an elongated drop surrounded by a denser fluid when viscous forces dominate over inertial and surface tension effects. While gaseous Taylor bubbles have been studied extensively, a liquid Taylor drop moving in a closed pipe is less well understood. We formulate an analytical model for estimating the ascent speed and drop thickness from first principles. First, we use a lubrication approximation to solve for the velocity profiles in the two fluids. Then, we analyse the mechanical energy balance of the whole system, including the effect of viscous dissipation, to understand how the ascent speed and drop thickness scale with the viscosity ratio. We show that a drop with density ratio reaches a stationary state with a uniform dimensionless thickness of in the absence of dissipation and in the dissipative regime. Through a comparison with existing experimental data, we demonstrate that our model correctly predicts the ascent speed of a Taylor drop if the material properties of the fluids and the geometry of the conduit are known. Our theoretical framework can be generalized to an isolated Taylor drop rising in a vertical pipe
Stability of stratified two-phase channel flows of Newtonian/non-Newtonian shear-thinning fluids
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