Theory of Breakup of Core Fluids Surrounded by a Wetting Annulus in Sinusoidally Constricted Capillary Channels

Analysis of core-annular dynamics in the presence of base flow for arbitrary fluid viscosities leads to an equation describing the temporal evolution of the fluid/fluid interface. The equation follows from the conservation of mass in the small-slope approximation. Its useful applications occur, for example, in chemical engineering and petroleum recovery. The nonlinear equation allows inexpensive numerical analysis. For sinusoidally constricted pores, a purely geometric criterion exists that enables or prohibits the core-fluid breakup in the necks of the constrictions. The geometrically favoring condition sets up capillary-pressure gradients that ensure a continuous outflow of the core fluid from the necks into the crests of the profile. Such behavior is indeed observed in the numerical solutions of the evolution equation. For relatively large slopes of the initial configuration, setting up larger pressure gradients, the interface shape remains smooth, the evolution times are relatively fast, and the breakup is typically achieved by the growing film-fluid collar touching the axis of the channel at a single point. No satellite droplets are produced. Decreasing the slope lengthens the evolution times, allowing the formation and growth of wavy disturbances on the initial interface profile, which may touch the axis of the capillary in several places forming satellite drops. Thinner initial annuli also slow down the evolution process. Instability develops for the cases of the core both more and less viscous than the film. Finally, if the geometry prohibits the snap-off altogether, the initial interface configurations decay into steady-state solutions, and no breakup takes place. The solutions of the evolution equation validate well against two computational-fluid-dynamics codes

Viscosity Effects in Vibratory Mobilization of Residual Oil

The last decade has seen clarifications of the underlying capillary physics behind stimulation of oil production by seismic waves and vibrations. Computational studies have prevailed, however, and no viscous hydrodynamic theory of the phenomenon has been proposed. For a body of oil entrapped in a pore channel, viscosity effects are naturally incorporated through a model of two-phase core-annular flow. These effects are significant at the postmobilization stage, when the resistance of capillary forces is overcome and viscosity becomes the only force resisting an oil ganglion\u27s motion. A viscous equation of motion follows, and computational fluid dynamics (CFD) establishes the limits of its applicability. The theory allows inexpensive calculation of important geophysical parameters of reservoir stimulation for given pore geometries, such as the frequency and amplitude of vibrations needed to mobilize the residual oil. The theoretical mobilizing acceleration in seismic waves for a given frequency is accurate to within approximately 30% or better when checked against CFD. The advantages of the viscous theory over the inviscid one are twofold. The former can calculate complete time histories of forced displacement of an oil blob in a pore channel, including retardation by capillary forces, mobilization by vibrations, and an ensuing Haines jump. It also provides an approximately factor-of-two improvement in the calculation of the mobilizing acceleration needed to unplug a static ganglion

Direct pore‐level observation of permeability increase in two‐phase flow by shaking

Increases in permeability of natural reservoirs and aquifers by passing seismic waves have been well documented. If the physical causes of this phenomenon can be understood, technological applications would be possible for controlling the flow in hydrologic systems or enhancing production from oil reservoirs. The explanation of the dynamically increased mobility of underground fluids must lie at the pore level. The natural fluids can be viewed as two-phase systems, composed of water as the wetting phase and of dispersed non-wetting globules of gas or organic fluids, flowing through tortuous constricted channels. Capillary forces prevent free motion of the suspended non-wetting droplets, which tend to become immobilized in capillary constrictions. The capillary entrapment significantly reduces macroscopic permeability. In a controlled experiment with a constricted capillary channel, we immobilize the suspended ganglia and test the model of capillary entrapment: it agrees precisely with the experiment. We then demonstrate by direct optical pore-level observation that the vibrations applied to the wall of the channel liberate the trapped ganglia if a predictable critical acceleration is reached. When the droplet begins to progressively advance, the permeability is restored. The mobilizing acceleration in the elastic wave, needed to “unplug” an immobile flow, is theoretically calculated within a factor of 1–5 of the experimental value. Overcoming the capillary entrapment in porous channels is hypothesized to be one of the principal pore-scale mechanisms by which natural permeabilities are enhanced by the passage of elastic waves

Thickness of residual wetting film in liquid-liquid displacement

Core-annular flow is common in nature, representing, for example, how streams of oil, surrounded by water, move in petroleum reservoirs. Oil, typically a nonwetting fluid, tends to occupy the middle (core) part of a channel, while water forms a surrounding wall-wetting film. What is the thickness of the wetting film? A classic theory has been in existence for nearly 50 years offering a solution, although in a controversial manner, for moving gas bubbles. On the other hand, an acceptable, experimentally verified theory for a body of one liquid flowing in another has not been available. Here we develop a hydrodynamic, testable theory providing an explicit relationship between the thickness of the wetting film and fluid properties for a blob of one fluid moving in another, with neither phase being gas. In its relationship to the capillary number Ca, the thickness of the film is predicted to be proportional to Ca2 at lower Ca and to level off at a constant value of ∼20% the channel radius at higher Ca. The thickness of the film is deduced to be approximately unaffected by the viscosity ratio of the fluids. We have conducted our own laboratory experiments and compiled experimental data from other studies, all of which are mutually consistent and confirm the salient features of the theory. At the same time, the classic law, originally deduced for films surrounding moving gas bubbles but often believed to hold for liquids as well, fails to explain the observations

Source parameters of earthquakes in eastern and western North America based on finite–fault modeling,

Abstract The ground motion from large earthquakes is often predicted based on finite-fault modeling, in which the fault plane is discretized into small independently rupturing subfaults; the radiation from all subfaults is summed at the observation point. Despite the success of the method in matching observed ground-motion characteristics, the physical interpretation of the subfaults has remained largely unclear, and a rationale for the choice of the subfault attributes has been lacking. Two key parameters-the subfault size and the maximum slip velocity on the fault-govern the amplitude of the source spectrum at intermediate and high frequencies, respectively. We determined these key source parameters, on an event-by-event basis, for all well-recorded moderate to large earthquakes in western North America (WNA) by fitting simulated to observed response spectra. We compare the values of these source parameters with those obtained previously for eastern North America (ENA) and the Michoacan, Mexico, earthquakes (a total of 26 modeled events). We find that the characteristic subevent size increases linearly with moment magnitude in an apparently deterministic manner. The subevent size relationship obtained for WNA is not statistically different from that obtained for ENA. In both regions, the subevent size follows the trend of log Dl ‫ס‬ ‫2מ‬ ‫ם‬ 0.4 M (4 Յ M Յ 8), where Dl is the subfault size in km. This trend agrees well with independent studies by The slip velocities determined for all 26 earthquakes vary in a narrow range from about 0.25 to 0.60 m/sec, with a mean of 0.40 m/sec and standard deviation of 0.09 m/sec. The slip velocities for the ENA events are distributed randomly over this range, while those for the WNA region appear to exhibit a decreasing trend with increasing magnitude. Our results indicate that a generic, region-independent earthquake source model for engineering prediction of strong ground motions can be developed

Non-Newtonian effects in the peristaltic flow of a Maxwell fluid

We analyzed the effect of viscoelasticity on the dynamics of fluids in porous media by studying the flow of a Maxwell fluid in a circular tube, in which the flow is induced by a wave traveling on the tube wall. The present study investigates novelties brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. This problem has numerous applications in various branches of science, including stimulation of fluid flow in porous media under the effect of elastic waves. We have found that in the extreme non-Newtonian regime there is a possibility of a fluid flow in the direction {\it opposite} to the propagation of the wave traveling on the tube wall.Comment: to Appear in Phys. Rev. E., 01 September 2001 issu

Enhacement in the dymanic response of a viscoelastic fluid flowing through a longitudinally vibrating tube

We analyzed effects of elasticity on the dynamics of fluids in porous media by studying a flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to oscillatory pressure gradient. The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform and transforming the problem into the frequency domain, we calculated: (A) the dynamic permeability and (B) the function $F(\kappa)$ that measures the deviation from Poiseuille flow friction as a function of frequency parameter $\kappa$. This provides a more complete theory of flow of Maxwell fluid through the longitudinally oscillating cylindrical tube with the oscillating pressure gradient, which has important practical applications. This study has clearly shown transition from dissipative to elastic regime in which sharp enhancements (resonances) of the flow are found

Forced instability of core-annular flow in capillary constrictions

Instability of fluid cylinders and jets, a highly nonlinear hydrodynamic phenomenon, has fascinated researchers for nearly 150 years. A subset of the phenomenon is the core-annular flow, in which a non-wetting core fluid and a surrounding wall-wetting annulus flow through a solid channel. The model, for example, represents the flow of oil in petroleum reservoirs. The flow may be forced to break up when passing through a channel’s constriction. Although it has long been observed that the breakup occurs near the neck of the constriction, the exact conditions for the occurrence of the forced breakup and its dynamic theory have not been understood. Here, we test a simple geometric conjecture that the fluid will always break in the constrictions of all channels with sufficiently long wavelengths, regardless of the fluid properties. We also test a theory of the phenomenon. Four constricted glass tubes were fabricated above and below the critical wavelength required for the fluid disintegration. In a direct laboratory experiment, the breakup occurred according to the conjecture: the fluids were continuous in the shorter tubes but disintegrated in the longer tubes. The evolution of the interface to its pinch-off was recorded using high-speed digital photography. The experimentally observed core-annulus interface profiles agreed well with the theory, although the total durations of the process agreed less satisfactorily. Nonetheless, as the theory predicts, the ratio between the experimental and theoretical times of the breakup process tends to one with decreasing capillary number. The breakup condition and the dynamic theory of fluid disintegration in constricted channels can serve as quantitative models of this important natural and technical phenomenon

Elastic waves push organic fluids from reservoir rock

Elastic waves have been observed to increase productivity of oil wells, although the reason for the vibratory mobilization of the residual organic fluids has remained unclear. Residual oil is entrapped as ganglia in pore constrictions because of resisting capillary forces. An external pressure gradient exceeding an ‘‘unplugging’’ threshold is needed to carry the ganglia through. The vibrations help overcome this resistance by adding an oscillatory inertial forcing to the external gradient; when the vibratory forcing acts along the gradient and the threshold is exceeded, instant ‘‘unplugging’’ occurs. The mobilization effect is proportional to the amplitude and inversely proportional to the frequency of vibrations. We observe this dependence in a laboratory experiment, in which residual saturation is created in a glass micromodel, and mobilization of the dyed organic ganglia is monitored using digital photography.We also directly demonstrate the release of an entrapped ganglion by vibrations in a computational fluid-dynamics simulation