Viscous Instability Research Articles

Quantitative In Situ Enhanced Oil Recovery Monitoring Using Nuclear Magnetic Resonance

Quantitative in situ monitoring of oil recovery from sedimentary rock is demonstrated for the first time using advanced two-dimensional (2D) nuclear magnetic resonance (NMR) correlation measurements on a low field spectrometer. The laboratory-scale NMR system was chosen to provide a common physics of measurement with NMR well-logging tools. The NMR protocols are used to monitor recovery of a heavy Middle East crude oil from high permeability sandstone plugs using a brine (water) flood followed by chemical enhanced oil recovery agents: polymer and alkaline–surfactant–polymer solutions. 2D correlations between relaxation time (T 1, T 2) and apparent self-diffusion coefficient D app are used to obtain simultaneously a volumetric determination of the oil and aqueous fluid-phase saturations present in the porous material. The T 1 − T 2 and D app − T 2 correlations are bulk measurements of the entire rock core-plug; excellent agreement is shown between the measures of remaining oil (from NMR) and recovered oil (from gravimetric assay of the effluent). Furthermore, we introduce the capability to measure spatially resolved T 2 distributions on a low field spectrometer using a rapid frequency-encoded y − T 2 map. A non-uniform distribution of remaining oil is observed due to viscous instabilities in the flowing liquids; the final oil saturation ranges from $${S_{\rm o}^{\rm{(final)}} \approx 0}$$ to 20 % along the direction of flow. These results highlight the quantitative nature of the NMR data obtainable in low field NMR core analysis and also the importance of spatially resolved measurements when studying short core-plugs.

The influence of salinity on the viscous instability in viscous-modified low-interfacial tension flow during surfactant–polymer flooding in heavy oil reservoirs

In this study, the effect of viscous instability at varying salinities of the displacing non-wetting phase (i.e., surfactant–polymer solution) in surfactant–polymer flooding of heavy oil reservoirs– which is a viscous-modified low-interfacial tension (IFT) flow through an initially preferential oil-wet porous medium– is quantified in the presence of the adverse mobility ratio. The dynamic mean pore-scale capillary number values are determined using two different approaches. The first approach is a Pore network approach (PNA) that excludes the viscous instability effects. The second approach is using the Viscous instability model (VIM) proposed by Peters and Flock [49] in which the concept of the wavelength of the viscous fingers is introduced. Afterwards, these two dynamic mean pore-scale capillary number values are compared to each other to highlight the effects of viscous instability at different salinity levels of the surfactant–polymer solution. The results show that including the viscous instability effects in the qualitative and quantitative evaluations of the viscous-modified low-IFT flow is vital. In particular, the viscous instability effects become more complex near the breakthrough of the displacing non-wetting phase. Furthermore, the effects of the salinity on the dynamic mean pore-scale capillary number (by excluding/excluding the viscous instability effects, i.e., from PNA and VIM, respectively), IFT, dynamic viscosity, contact angle, displacement front configuration, wavelength of the viscous fingers, dynamic values of the desaturated displaced wetting phase, breakthrough time, and the time of infinite injected pore volume is discussed in the surfactant–polymer flooding of an initially preferential oil-wet porous medium containing heavy oil.

Interacting viscous instabilities in microfluidic systems

We discuss the formation, evolution, and stability of microfluidic flows involving two or more miscible fluids that have different viscosities. When two liquids that have widely different viscosities are injected into a rigid microfluidic device, their flow streams can naturally rearrange to form lubricated threads or stratified flows depending on the geometry and history of injection. An overview of two-fluid and three-fluid flow configurations in microchannels having square cross-sections is given for a variety of injection geometries. Miscible viscous fluid threads in confined microsystems can experience a range of viscous instabilities, such as folding and swirling. We show that microfluidics can be used to cause two or more instabilities to interact and co-evolve in diverging microchannels, thereby creating a variety of complex flow patterns.

Formation of capillary structures with highly viscous fluids in plane microchannels

A detailed experimental study of capillary structures made with high-viscosity fluids is conducted in plane microchannels. We examine the possibility to emulsify fluids via viscous folding instabilities using continuous microflows. Non-wetting capillary threads are formed in a sheath of immiscible liquids for a wide range of viscosity and flow rate ratios using symmetric hydrodynamic focusing sections. Downstream, threads are significantly deformed in a diverging channel connected to a long plane microchannel. Adjusting the residence time of thread structures in the plane channel allows us to produce various degrees of fold coalescence. Three typical regimes are identified: thread breakup, partial fold coalescence, and complete fold coalescence. The geometrical features of evolving folds are measured and related to material properties, flow parameters, and microgeometries. This study shows that folded structures offer the opportunity to examine novel interfacial configurations and provides a set of microfluidic techniques for improved manipulation of viscous materials with thin immiscible lubricants at the small scale.

Mobility control through spontaneous formation of nanoparticle stabilized emulsions

[1] We report on measurements of the flow pattern and in-situ saturations whenn-octane displaces a brine in which surface treated silica nanoparticles are dispersed. The nanoparticles are known to stabilize octane-in-water emulsions. We find that the displacement front is more spatially uniform, and with a later breakthrough when compared to a control displacement with no in-situ nanoparticles. Pressure measurements during the displacement are consistent with generation of a viscous phase such as an emulsion. These observations suggest that a nanoparticle stabilized emulsion is formed during the displacement which acts to suppress the viscous instability. We argue that generation of droplets of nonwetting phase occurs at the leading edge of all drainage displacements. The droplets rejoin the bulk phase in the absence of stabilizing agents, but are preserved when nanoparticles adhere to the fluid/fluid interface.

Interaction of viscous and inviscid instability modes in separation–bubble transition

This paper describes numerical simulations that are used to examine the interaction of viscous and inviscid instability modes in laminar-to-turbulent transition in a separation bubble. The results of a direct numerical simulation are presented in which separation of a laminar boundary-layer occurs in the presence of an adverse streamwise pressure gradient. The simulation is performed at low freestream-turbulence levels and at a flow Reynolds number and pressure distribution approximating those typically encountered on the suction side of low-pressure turbine blades in a gas-turbine engine. The simulation results reveal the development of a viscous instability upstream of the point of separation which produces streamwise-oriented vortices in the attached laminar boundary layer. These vortices remain embedded in the flow downstream of separation and are carried into the separated shear layer, where they are amplified by the local adverse pressure-gradient and contribute to the formation of coherent hairpin-like vortices. A strong interaction is observed between these vortices and the inviscid instability that typically dominates the shear layer in the separated zone. The interaction is noted to determine the spanwise extent of the vortical flow structures that periodically shed from the downstream end of the separated shear layer. The structure of the shed vortical flow structures is examined and compared with the coherent structures typically observed within turbulent boundary layers.

Viscous linear instability of a sheared liquid‐gas interface ‐ Effect of a velocity deficit near the interface

AbstractThe initial state of liquid atomization by a fast gas stream is considered by viscous linear spatial stability analysis for parallel two‐fluid flow. The unbounded basic velocity profile is characterized by different asymptotic velocities and a velocity deficit near the interface. We examine the influence of the velocity deficit on the spatial growth rates of two competing modes originating from the Kelvin‐Helmholtz and viscosity contrast mechanisms. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Inviscid and viscous vortex models for Richtmyer–Meshkov instability

We present simple inviscid and viscous vortex models for the Richtmyer–Meshkov (RM) instability, in the limit of fluids of the same densities. The evolution of the interface is driven by a row of alternating point vortices. A regularization method for the singular vortices is applied to the inviscid model for stable calculations. The regularized vortex model provides fine resolutions for the interface, improving previous results on the evolution of the RM instability. The point vortex model, for the inviscid fluid, is validated by comparing with the results of the full vortex sheet model. The viscous vortex model for the unstable interface is based on the multi-Lamb–Oseen vortices. We show that the viscous vortex model gives the main qualitative features of the evolution of the viscous RM instability.

Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks

We present results from a systematic study of relative permeability functions derived from two-phase lattice Boltzmann (LB) simulations on X-ray microtomography pore space images of Bentheimer and Berea sandstone. The simulations mimic both unsteady- and steady-state experiments for measuring relative permeability. For steady-state flow, we reproduce drainage and imbibition relative permeability curves that are in good agreement with available experimental steady-state data. Relative permeabilities from unsteady-state displacements are derived by explicit calculations using the Johnson, Bossler and Naumann method with input from simulated production and pressure profiles. We find that the nonwetting phase relative permeability for drainage is over-predicted compared to the steady-state data. This is due to transient dynamic effects causing viscous instabilities. Thus, the calculated unsteady-state relative permeabilities for the drainage is fundamentally different from the steady-state situation where transient effects have vanished. These effects have a larger impact on the invading nonwetting fluid than the defending wetting fluid. Unsteady-state imbibition relative permeabilities are comparable to the steady-state ones. However, the appearance of a piston-like front disguises most of the displacement and data can only be determined for a restricted range of saturations. Relative permeabilities derived from unsteady-state displacements exhibit clear rate effects, and residual saturations depend strongly on the capillary number. We conclude that the LB method can provide a versatile tool to compute multiphase flow properties from pore space images and to explore the effects of imposed flow and fluid conditions on these properties. Also, dynamic effects are properly captured by the method, giving the opportunity to examine differences between steady and unsteady-state setups.

Surface instability and primary atomization characteristics of straight liquid jet sprays

Using the detailed numerical simulation data of primary atomization, the liquid surface instability development that leads to atomization is characterized. The numerical results are compared with a theoretical analysis of liquid–gas layer for a parameter range close to high-speed Diesel jet fuel injection. For intermittent and short-duration Diesel injection, the aerodynamic surface interaction and transient head formation play an important role. The present numerical setting excludes nozzle disturbances to primarily investigate this interfacial instability mechanism and the role of jet head. The first disturbed area is the jet head region, and the generated disturbances are fed into the upstream region through the gas phase. This leads to the viscous boundary layer instability development on the liquid jet core. By temporal tracking of surface pattern development including the phase velocity and stability regime and by the visualization of vortex structures near the boundary layer region, it is suggested that the instability mode is the Tollmien–Schlichting (TS) mode similar to the turbulent transition of solid-wall boundary layer. It is also demonstrated that the jet head and the liquid core play an interacting role, thus the jet head cannot be neglected in Diesel injection. In this study, this type of boundary layer instability has been demonstrated as a possible mechanism of primary atomization, especially for high-speed straight liquid jets. The effect of nozzle turbulence is a challenging but important issue, and it should be examined in the future.

A mechanistic analysis of viscous fingering in low-tension polymer flooding in heavy-oil reservoirs

Modeling of the low tension polymer flooding (LTPF) in heavy oil reservoirs suffers from the paucity of detailed knowledge of viscous instability or fingering effects. Major limitations of previous approaches for studying viscous fingering in immiscible displacements are that the reported experiments have been conducted utilizing the linear displacements schemes in the media with high, single-phase permeabilities. Consequently, viscous instability has not been studied in low-permeability media and using the displacement schemes similar to the oil-field patterns (e.g., five-spot). To help understand viscous fingering in LTPF in heavy oil reservoirs and to overcome the limitations of previous studies, we conducted experiments in the low-permeability, one-quarter, five-spot patterns. New insights into the main driving mechanisms for viscous fingering are proposed. In summary, the mechanisms of spreading, splitting, coalescence, and microscopic crossflow drive the finger growth. In addition, the viscous fingers are readily initiated in the porous medium, but they can be damped out before traveling very far. This damping of the viscous fingers is due to the flow of the two phases in a direction transverse to the direction of bulk fluid movement as a result of dispersive processes such as stream splitting. Also, the initially-developed fingers may deteriorate over the time of displacement. This depends on the distance between the injector and producer and width of the porous medium. The presence of instabilities that look like fingers and stable displacements behind the unstable front were discovered. The results also indicate that a stable zone exists and progresses at varying velocities. Finally, we reveal three different types of displacements that occur in LTPF: stable displacements, displacement with macroscopic viscous fingering, and displacements with both macroscopic and microscopic viscous fingering.

On the progenitors of millisecond pulsars by the recycling evolutionary channel

The recycling model suggested that low-mass X-ray binaries (LMXBs) could evolve into binary millisecond pulsars (BMSPs). In this work, we attempt to investigate the progenitor properties of BMSPs formed by the recycling evolutionary channel, and if sub-millisecond pulsars can be produced by this channel. Using Eggleton's stellar evolution code, considering that the dead pulsars can be spun up to a short spin period by the accreting material and angular momentum from the donor star, we have calculated the evolution of close binaries consisting of a neutron star and a low-mass main-sequence donor star, and the spin evolution of NSs. In calculation, some physical process such as the thermal and viscous instability of a accretion disk, propeller effect, and magnetic braking are included. Our calculated results indicate that, all LMXBs with a low-mass donor star of 1.0 - 2.0 $M_\odot$ and a short orbital period ($\la 3-4 \rm d$) can form millisecond pulsars with a spin period less than 10 ms. However, it is difficult to produce sub-millisecond pulsars by this evolutionary channel. In addition, our evolutionary scenario cannot account for the existence of BMSPs with a long orbital period ($P_{\rm orb}\ga 70-80\rm d$).

The progenitor of binary millisecond radio pulsar PSR J1713+0747

PSR J1713+0747 is a binary system comprising millisecond radio pulsar with a spin period of 4.57 ms, and a low-mass white dwarf (WD) companion orbiting the pulsar with a period of 67.8 days. Using the general relativistic Shapiro delay, the masses of the WD and pulsar components were previously found to be $0.28\pm 0.03 M_{\odot}$ and $1.3\pm 0.2 M_{\odot}$ (68% confidence), respectively. Standard binary evolution theory suggests that PSR J1713+0747 evolved from a low-mass X-ray binary (LMXB). Here, we test this hypothesis. We used a binary evolution code and a WD evolution code to calculate evolutionary sequences of LMXBs that could result in binary millisecond radio pulsars such as PSR J1713+0747. During the mass exchange, the mass transfer is nonconservative. Because of the thermal and viscous instabilities developing in the accretion disk, the neutron star accretes only a small part of the incoming material. We find that the progenitor of PSR J1713+0747 can be modelled as an LMXB including a donor star with mass $1.3-1.6 M_{\odot}$ and an initial orbital period ranging from 2.40 to 4.15 days. If the cooling timescale of the WD is 8 Gyr, its present effective temperature is between 3870 and 4120 K, slightly higher than the observed value. We estimate a surface gravity of ${\rm Log} (g) \approx 7.38 - 7.40$.

Viscous Linear Instability of an Incompressible Round Jet with Petrov-Galerkin Spectral Method and Truncated Boundary

Viscous Linear Instability of an Incompressible Round Jet with Petrov-Galerkin Spectral Method and Truncated Boundary

Experimental Investigation of Viscous Fingering Instabilities in Emulsions Displacements

Experiments were conducted to analyze the viscous fingering instability that develops during the displacement of oil-in-water (O/W) emulsions. For this purpose, a horizontal rectilinear Hele-Shaw cell, which is an analogue for a homogeneous porous media, was used. Different emulsion solutions were prepared by dispersing different volume fractions of mineral oil in water using non-ionic surfactants. These emulsions were characterized systematically by examining their droplets size distribution and shear viscosity. Flow displacement experiments involved displacing the O/W emulsions by injecting water at different rates. The developments of the instability were characterized qualitatively by identifying the main mechanisms of finger development and growth. These results and the correlations between the properties of the fluids and the flow patterns were used to examine the flow dynamics and its effects on the viscous fingering instability. It was found that the development of the flow instability can be corr...

Spatial instability of coflowing liquid-gas jets in capillary flow focusing

Considering both the first nonaxisymmetric (n=1) and the axisymmetric (n=0) disturbances, a viscous spatial instability analysis of coflowing liquid-gas jets in capillary flow focusing is carried out. A detailed parametric study is performed to explore characteristics of the spatially amplified branch in a convectively unstable regime. The numerical results show that the Weber number and the velocity at the interface have significant influences on the transition between axisymmetric and nonaxisymmetric instabilities, whereas the other parameters such as the Reynolds number, the slope of the liquid velocity profile at the interface, the density ratio, and the viscosity ratio hardly change the transition. Nonaxisymmetric disturbances grow faster than axisymmetric ones for relatively high Weber numbers. Particularly, the comparison of the theoretical prediction with the experimental results reported by Si et al. [J. Fluid Mech. 629, 1 (2009)] indicates that the spatial instability analysis is in better agreement with experiments than the temporal instability analysis for moderate and high Weber numbers.

Comment on “Viscous Rayleigh-Taylor Instability Experiments at High Pressure and Strain Rate”

A Comment on the Letter by Hye-Sook Park et al., Phys. Rev. Lett. 104, 135504 (2010). The authors of the Letter offer a Reply.

A new viscous instability in weakly ionised protoplanetary discs

AbstractLarge regions of protoplanetary discs are believed to be too weakly ionised to support magnetorotational instabilities, because abundant tiny dust grains soak up free electrons and reduce the conductivity of the gas. At the outer edge of this “dead zone”, the ionisation fraction increases gradually and the resistivity drops until the magnetorotational instability can develop turbulence. We identify a new viscous instability which operates in the semi-turbulent transition region between “dead” and “alive” zones. The strength of the saturated turbulence depends strongly on the local resistivity in this transition region. A slight increase (decrease) in dust density leads to a slight increase (decrease) in resistivity and a slight decrease (increase) in turbulent viscosity. Such spatial variation in the turbulence strength causes a mass pile-up where the turbulence is weak, leading to a run-away process where turbulence is weakened and mass continues to pile up. The final result is the appearance of high-amplitude pressure bumps and deep pressure valleys. Here we present a local linear stability analysis of weakly ionised accretion discs and identify the linear instability responsible for the pressure bumps. A paper in preparation concerns numerical results which confirm and expand the existence of the linear instability.

Instabilities in the Gamma Ray Burst central engine. What makes the jet variable?

AbstractBoth types of long and short gamma ray bursts involve a stage of a hyper-Eddington accretion of hot and dense plasma torus onto a newly born black hole. The prompt gamma ray emission originates in jets at some distance from this ‘central engine’ and in most events is rapidly variable, having a form of sipkes and subpulses. This indicates at the variable nature of the engine itself, for which a plausible mechanism is an internal instability in the accreting flow. We solve numerically the structure and evolution of the neutrino-cooled torus. We take into account the detailed treatment of the microphysics in the nuclear equation of state that includes the neutrino trapping effect. The models are calculated for both Schwarzschild and Kerr black holes. We find that for sufficiently large accretion rates (>~10M⊙ s−1 for non-rotating black hole, and >~1M⊙ s−1 for rotating black hole, depending on its spin), the inner regions of the disk become opaque, while the helium nuclei are being photodissociated. The sudden change of pressure in this region leads to the development of a viscous and thermal instability, and the neutrino pressure acts similarly to the radiation pressure in sub-Eddington disks. In the case of rapidly rotating black holes, the instability is enhanced and appears for much lower accretion rates. We also find the important and possibly further destabilizing role of the energy transfer from the rotating black hole to the torus via the magnetic coupling.

Finite element simulation of viscous fingering in miscible displacements at high mobility-ratios

Numerical simulations of viscous fingering instabilities in miscible displacements at high mobility-ratios are presented. Anisotropic dispersion and monotonic viscosity profiles are considered. The coupled set of partial differential equations is approximated by the semi-discrete SUPG stabilized finite element formulation plus a discontinuity capturing technique to improve stability around the moving sharp fronts. The pressure equation is discretized by the standard Galerkin method, and a post-processing scheme is used to improve the numerical evaluation of Darcy’s velocity. In the resulting scheme all variables (concentration, pressure and velocity) are approximated by equal order linear triangular elements. A homogeneous channel and a radial system were studied. Complex nonlinear viscous fingering mechanisms for high mobility-ratio miscible displacements were observed.