scholarly journals Droplets in homogeneous shear turbulence

2019 ◽  
Vol 876 ◽  
pp. 962-984 ◽  
Author(s):  
Marco E. Rosti ◽  
Zhouyang Ge ◽  
Suhas S. Jain ◽  
Michael S. Dodd ◽  
Luca Brandt

We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

1985 ◽  
Vol 25 (01) ◽  
pp. 101-112 ◽  
Author(s):  
Stanley C. Jones

Jones, Stanley C., SPE, Marathon Oil Co. Abstract Displacements were conducted in Berea cores to gain insight into the mechanism of tertiary oil displacement and propagation by a micellar slug. Contrary to expectation, propagation by a micellar slug. Contrary to expectation, the first oil mobilized by micellar fluid was among the first oil (instead of the last oil) to be produced, giving the appearance of either viscous fingering or of unusually large dispersion. To eliminate the possibility of unfavorable mobility ratios caused by oil/water/surfactant interaction, we conducted several runs in which an injected hydrocarbon displaced another hydrocarbon, initially at residual saturation. In other experiments, water (the wetting phase) at irreducible saturation was displaced by a distinguishable injected aqueous phase. Injected hydrocarbon appeared in the produced fluids immediately after oil breakthrough, yielding behavior similar to the micellar-slug experiments. Even with a favorable viscosity ratio of less than 0.01, the apparent dispersion was huge. However, mixing zones in the wetting-phase displacements were quite normal and similar to those observed for single-phase flow. Nonwetting-phase fronts (injected hydrocarbon displacing resident hydrocarbon) are smeared much more than wetting-phase fronts because the entrance of hydrocarbon into smaller water-filled pore throats is delayed until the capillary entrance pressure is overcome by differences in the flowing oil and water pressure gradients. Oil might not be displaced from the smaller pores until long after oil breakthrough. Nonwetting-phase dispersion, which occurs in many EOR processes, can be expected to be one or two orders of magnitude greater than dispersion measured in single-phase-flow experiments. Entrance of the wetting phase, however, is not delayed; hence, wetting-phase Mixing zones are short. Introduction Experiments for this study were inspired by the question: How is residual oil, which has been mobilized by a micellar slug, transported? More specifically, does the first oil mobilized by a slug (near the injection end of a core) contact and mobilize oil downstream from it, which displaces more oil even farther downstream? If this were the case, the first oil to be produced would be the most-downstream oil (i.e., oil nearest the outlet). The last oil produced would be the first oil mobilized from the produced would be the first oil mobilized from the injection end of the core. This scheme is somewhat analogous to pushing a broom across a floor covered with a heavy layer of dust. The first dust encountered by the broom stays next to the broom. As the accumulated layer of dust in front of the broom becomes adequately compacted, it pushes dust ahead of it to from an ever-widening band or "dust bank" ahead of the broom. The dust farthest ahead of the broom is the first to be pushed into the dustpan, and the dust first encountered by the broom is the last to be pushed in. Or is this concept all wrong? Another model postulates that the oil first contacted by a micellar slug is mobilized and quickly travels away from the slug so that the downstream oil is contacted and mobilized by the slug, not by the first-mobilized oil. If this process were to proceed to its logical conclusion, the first-produced oil would proceed to its logical conclusion, the first-produced oil would be from the inlet end of the core, and the last-produced from the outlet end. Either of these two extremes would be modified by dispersion, which smears sharp fronts by mixing displaced and displacing fluids. Dispersion in porous media has been investigated extensively. Perkins and Johnston have reviewed several studies, mostly involving single-phase flow. The simultaneous injection of the water with light hydrocarbon solvents is a technique used to reduce solvent mobility and viscous fingering. Raimondi et al. performed steady-state experiments in which flowing performed steady-state experiments in which flowing water and oil were miscibly displaced by the simultaneous injection of water and solvent. They found that the longitudinal mixing coefficient for the hydrocarbon phase increased sharply with increasing water above the irreducible saturation. The displacement of the wetting phase was not greatly affected by the presence of the nonwetting phase. However, a large amount of oil that initially phase. However, a large amount of oil that initially seemed to be trapped by water was eventually recovered by continued solvent injection. Raimondi and Torcaso later found that some oil, particularly at high water-to-solvent injection ratios, was particularly at high water-to-solvent injection ratios, was trapped permanently, provided that injection rates, ratios, and pressure drops were unchanged in switching from water/oil to water/solvent injection. Fitzgerald and Nielsen also found that only part of the in-place crude was recovered by solvent injection. Moreover, solvent appeared in the effluent shortly after oil breakthrough. Oil recovery was further decreased when solvent and water were injected simultaneously. Thomas et al. reported slightly increased wetting-phase longitudinal mixing during simultaneous water/oil injection as the wetting-phase saturation decreased. Non-wetting-phase mixing increased substantially as the nonwetting-phase saturation decreased from 100%. SPEJ p. 101


1984 ◽  
Vol 106 (2) ◽  
pp. 193-200 ◽  
Author(s):  
V. Arp ◽  
J. M. Persichetti ◽  
Guo-bang Chen

The Gru¨neisen parameter has long been used in equations of state for solids to relate thermodynamic properties to lattice vibrational spectra [1]. A few papers have extended the concept to studies of liquid structure. Knopoff and Shapiro [2] have evaluated a Gru¨neisen parameter for water and for mercury, attempting to relate its temperature dependence in a limited range to atomic clustering within the liquid. Sharma [3], in a series of papers, has evaluated a pseudo-Gru¨neisen parameter in mercury and liquefied gases and related it to internal pressures, a solubility parameter, and clustering phenomena. In this paper we evaluate the Gru¨neisen parameter for a variety of fluids, and show how it occurs in many problems in compressible fluid hydrodynamics, without reference to concepts of liquid structure. The work extends that reported in an earlier paper for the special case of steady state, single phase flow [4].


Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 300
Author(s):  
Taoufik Wassar ◽  
Matthew A. Franchek ◽  
Hamdi Mnasri ◽  
Yingjie Tang

Due to the complex nonlinearity characteristics, analytical modeling of compressible flow in inclined transmission lines remains a challenge. This paper proposes an analytical model for one-dimensional flow of a two-phase gas-liquid fluid in inclined transmission lines. The proposed model is comprised of a steady-state two-phase flow mechanistic model in-series with a dynamic single-phase flow model. The two-phase mechanistic model captures the steady-state pressure drop and liquid holdup properties of the gas-liquid fluid. The developed dynamic single-phase flow model is an analytical model comprised of rational polynomial transfer functions that are explicitly functions of fluid properties, line geometry, and inclination angle. The accuracy of the fluid resonant frequencies predicted by the transient flow model is precise and not a function of transmission line spatial discretization. Therefore, model complexity is solely a function of the number of desired modes. The dynamic single-phase model is applicable for under-damped and over-damped systems, laminar, and turbulent flow conditions. The accuracy of the overall two-phase flow model is investigated using the commercial multiphase flow dynamic code OLGA. The mean absolute error between the two models in step response overshoot and settling time is less than 8% and 2 s, respectively.


1964 ◽  
Vol 47 (1) ◽  
pp. 165-176 ◽  
Author(s):  
R. De Hertogh ◽  
J. J. Hoet ◽  
F. Materazzi ◽  
E. Ekka

ABSTRACT 1,2-3H cortexolone was injected into normal subjects and the disappearance curve of the radioactive hormone in the plasma was determined. This follows a biexponential function, according to a digital computer analysis. The half-life values calculated for the first and the second components of the experimental curves are 4 and 24 min respectively. On the basis of a two compartment open system, in which the second compartment is assumed to be metabolically inactive, cortexolone spreads rapidly into an apparent volume of 19 l and more slowly into a total volume of 37 l. Endogenous production rate of cortexolone was estimated from the isotope dilution of the injected hormone as determined by measurement of the specific activity of urinary tetrahydrocortexolone. The mean production rate for 4 normal subjects was calculated to be 1100 μg per day. From these data the size of the endogenous pool of cortexolone was calculated. This averages 9.3 and 9.2 μg for the first and second compartments respectively. The experiments are discussed with regard to a possible disturbance in the steady state by the amount of cortexolone injected.


1985 ◽  
Vol 25 (04) ◽  
pp. 573-579 ◽  
Author(s):  
Jamal H. Abou-Kassem ◽  
Khalid Aziz

Abstract The computation of flowing-well bottomhole pressure from the pressure of the block containing the well or of well now rate when the flowing bottomhole pressure is specified are important considerations in reservoir simulation. While this problem has been addressed by several authors, some important aspects of the problem are not treated adequately in the literature. We present an analytical method for computing the wellblock factors (constants of the PI) for a well located anywhere in a square or rectangular block (aspect ratio between 1/2 and 2). Equations for well geometric factors and well fraction constants are given for gridblocks of various types, containing a single well, encountered in reservoir simulation studies. The equations given in this paper can be used for both block-centered and paper can be used for both block-centered and point-distributed grids in five- and nine-point two-dimensional point-distributed grids in five- and nine-point two-dimensional (2D), finite-difference formulations. The radial flow assumption used in deriving the equations in this paper is not always strictly valid; however, for most practical situations it provides an adequate approximation for near-well flow. Introduction Handling of wells in reservoir simulators presents several difficulties that require special considerations. These difficulties generally can be divided into two classes.Problems arise because the block size usually is large compared to the size of the well, and hence the pressure of the block computed by the reservoir simulator is not a good approximation for the well pressure.Problems can be caused by the complex interaction (coupling) between the reservoir and the wellbore in both injection and production wells. Some aspects of this second problem are discussed by Settari and Aziz and Williamson and Chappelear, and other important aspects remain unresolved. This paper, however, deals with only the first problem-the problem of relating well-block pressure in the finite-difference model to the well pressure. The discussion is further restricted to single-phase 2D areal models, without any direct consideration of three-dimensional (3D) and cross-sectional flow problems. In die absence of more accurate model, well factors derived from single-phase flow considerations may be used even when two- or three-phase flow exists near the well. Well-Block Equations Peaceman has defined an equivalent well-block radius, Peaceman has defined an equivalent well-block radius, ro, as the radius at which the steady-state flowing pressure in the reservoir is equal to the numerically pressure in the reservoir is equal to the numerically calculated pressure, po, of the block containing the well This definition of ro can be used to relate the well pressure, pw, to the flow rate, q, through po: pressure, pw, to the flow rate, q, through po:Peaceman has obtained an approximate value of ro for Peaceman has obtained an approximate value of ro for an interior well in a uniform square grid by assuming radial steady-state flow between the well block and the blocks adjacent to this block:where i=1, 2, 3, 4 for the four surrounding blocks in the five-point finite-difference scheme. Combining this equation with the steady-state difference equation for the well block,Peaceman obtained the value Peaceman obtained the valuewhich is close to the more precise numerically computed value of 0. 1982 ( – 0.2). Peaceman obtained this more precise value by use of the difference in pressure between precise value by use of the difference in pressure between injection and production wells in a repeated five-spot as derived by Muskat, who used potential theory. Peaceman applied this solution to the difference in Peaceman applied this solution to the difference in pressure between the injection and production blocks and pressure between the injection and production blocks and obtainedwhere Delta pm is the numerically computed pressure difference between injection and production blocks for an M × M grid. The right side of Eq. 5 approaches an approximately correct value of 0.194 for M=3. This implies that the assumption of radial flow used to obtain Eq. 4 is reasonable even for a very coarse 3 ⨯ 3 grid. SPEJ P. 573


1998 ◽  
Vol 22 (4A) ◽  
pp. 325-339
Author(s):  
R. Balachandar ◽  
M.F. Tachie

The size-velocity characteristics of a droplet-laden air jet impinging on a normal wall is investigated using a phase-Doppler anemometer. The results of measurements conducted for two jet-exit-to-impingement-wall distances are presented. Experimental data are obtained across the jet at several axial stations covering the first ten jet-exit diameters. The radial variation of droplet mean velocity, rms velocity and skewness coefficient indicates that similarity is not achieved. The rate of spreading of the jet is higher than that noticed in both single-phase flow and previous two-phase flow studies. The presence of the impingement wall does not have a significant effect on the mean velocity distributions for Z/Zi < 0.8. There is an increase in droplet size with increasing distance from the nozzle for Z/D > 4.0. In the early regions of the jet, the water droplet size and velocity are strongly correlated, especially in the core regions. With increasing Z/D, there is no association between size and velocity.


2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Xiaoyan Meng ◽  
Daoyong Yang

Over the past few decades, due to the special features (i.e., easily produced, large-surface-area-to-volume ratio, and engineered particles with designed surface properties), nanoparticles have not only attracted great attentions from the oil and gas industry but also had various applications from drilling and completion, reservoir characterization, to enhanced oil recovery (EOR). As sensors or EOR agents, thus, fate and behavior of nanoparticles in porous media are essential and need to be investigated thoroughly. Nevertheless, most of the published review papers focus on particle transport in saturated porous media, and all of them are about steady-state flow conditions. So far, no attempts have been extended to systematically review current knowledge about nanoparticle transport in porous media with single-phase and two-phase flow systems under both steady-state and unsteady-state conditions. Accordingly, this review will discuss nanoparticle transport phenomena in porous media with its focus on the filtration mechanisms, the underlying interaction forces, and factors dominating nanoparticle transport behavior in porous media. Finally, mathematical models used to describe nanoparticle transport in porous media for both single-phase flow and two-phase flow under steady-state and transient flow conditions will be summarized, respectively.


2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Tat Thang Nguyen ◽  
Hiroshige Kikura ◽  
Ngoc Hai Duong ◽  
Hideki Murakawa ◽  
Nobuyoshi Tsuzuki

Ultrasonic Velocity Profile (UVP) method for measurement of single-phase and two-phase flow in a vertical pipe has recently been developed in the Laboratory for industrial and Environmental Fluid Dynamics, Institute of Mechanics, VAST. The signal processings of the UVP method include the ultrasonic pulse Doppler method (UDM)and the ultrasonic time-domain cross-correlation (UTDC) method. For two-phase flow, simultaneous measurements of both liquid and gas are enabled by using a multi-wave ultrasonic transducer (multi-wave TDX). The multi-wave TDX is able to emit and receive ultrasound of two different center frequencies of 2 MHz and 8 MHz at the same time and position. 2 MHz frequency with beam diameter 10 mm is exploited for measurement of gas. 8 MHz one with beam diameter 3 mm is used for liquid. Measurements have been carried out for laminar and turbulent single-phase flows and bubbly counter-current two-phase flows in two flow loops using two vertical pipes of 26 mm inner diameter (I.D.) and 50 mm I.D. respectively. Based on the measured results, assessment of each method is clarified. Applicability of each method for different conditions of pipe flow has been tested. Suggestions for application of the two methods have been recommended.


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