Propagation Radius Research Articles

Improved Sweep in Bati Raman Heavy-Oil CO2 Flood: Bullhead Flowing Gel Treatments Plug Natural Fractures

Summary This paper covers the successful pilot field application of polymer gels for reservoir conformance improvement in the ongoing CO2 injection project at Bati Raman heavy-oil field in southeastern Turkey. Bati Raman is a naturally fractured carbonate reservoir in which the heterogeneities and the unfavorable mobility ratios between CO2 and the heavy oil cause inefficient sweep of the reservoir. These conditions prompted the pilot application of a conformance-improvement fracture-plugging (flowing) gel system in three wells in July 2002. Based on injection tests performed in the field, approximate treatment volumes were estimated to be on the order of 10,000 bbl for each well. Volumes actually pumped ranged from approximately 6,500 to 11,000 bbl. All three of the wells showed a gradual increase in injection pressure during treatment, indicating a decrease in injectivity index as treatment progressed. During one treatment, an offset producer experienced changes in fluid level consistent with rapid pressure transmission via the connecting fracture early in the treatment, with later loss of such communication. This behavior provides direct evidence of fracture plugging during treatment (Lane 2002). A mechanistic semianalytical model based on previously published laboratory work (Lane and Seright 2000) obtained a good match with the field data. The rate/pressure data were fed into the model, and effective fracture widths were backcalculated. Comparisons of results with the Formation MicroImager (FMI) log findings are explained. Gel-monitor well responses were scaled based on field data using a Fetkovich type decline-curve analysis. These studies enabled the incorporation of the effect of reservoir heterogeneities on the gel propagation radius so that future gel-treatment design parameters could be optimized. Pre and post-treatment CO2 injection pressures and the rates are as shown in Table 1. Sweep efficiency was increased as defined by produced oil/injected gas ratio. The 1-year average post-gel oil rate from 19 offset producers is 720 STB/D, as compared with apre-gel oil rate of 645 STB/D. The rate of increase from the treatments is thus 75 B/D, or 12%, which indicates a payout time of 12 months. Keeping this enlightened approach and seizing on the key concepts, four more CO2 injector wells were treated in 2004 to follow up on the encouraging results.

Dynamic characteristics of spherically converging detonation waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

On axisymmetric intrusive gravity currents in a stratified ambient – shallow-water theory and numerical results

The intrusion of a fixed volume of fluid, which is released from rest and then propagates horizontally-radially at the neutral buoyancy level in a stratified ambient fluid, in a cylindrical geometry with a vertical axis (either fully axisymmetric or a wedge), is investigated. It is assumed that the density change of the ambient fluid is linear with height. A closed one-layer shallow-water Boussinesq inviscid formulation is presented. In general, the solution of the resulting hyperbolic system is obtained by a finite-difference scheme. However, for the large-time developed motion an analytical similarity solutions is derived. The self-similar result indicates radial expansion with t 1 / 3 but the shape is peculiar: the intruding fluid propagates like a ring with a fixed ratio of inner to outer radii; the inner domain (between the axis and the inner radius of the ring) contains clear ambient fluid. It is verified that the initial-value lock-release finite-difference solution indeed approaches the similarity predictions after an initial spread of the outer radius to about 2.5 times the initial radius. The shallow-water results are corroborated by numerical solutions of the full axisymmetric Navier–Stokes formulation. It is concluded that the shallow-water model is a versatile and accurate predictive tool, and that the peculiar ring-shape prediction reproduces an interesting physical property of the axisymmetric intrusion. The interaction between the internal gravity waves and the head is less significant than in the two-dimensional geometry. However, a practical limitation on the applicability of the inviscid model is imposed by the prediction that the ratio of viscous to inertia forces increases like r N 7 (where r N is the radius of propagation, scaled with the initial value).

On axisymmetric rotating gravity currents: two-layer shallow-water and numerical solutions

Axisymmetric gravity currents released from behind a lock over a solid horizontal bottom in a system rotating about a vertical axis are investigated. The major parameters are $\C$ , the ratio of Coriolis to inertia forces, and $H$ , the ratio of the total height of the ambient fluid into which propagation occurs to the initial height of the dense fluid inside the lock. We focus attention on the small $\C$ , almost inviscid case in which a significant radius of propagation is obtained. A two-layer shallow-water inviscid approximation is developed and it is shown that the angular velocities in the upper and lower layers are coupled by simple relationships which can be used to simplify both the time-dependent and the steady-state lens solutions. However, the major features predicted by the two-layer model differ only slightly from these obtained with a one-layer model. Finite-difference solutions of the full Navier–Stokes equations are also presented and compared with the shallow-water approximations.

Effect of phase change on shock wave attenuation in GeO2

Stress-wave profiles in vitreous GeO2 induced by planar and spherical projectile impact were measured using piezoresistance gauges in the 4 to 18 GPa shock pressure range. The planar experiments demonstrate the response of vitreous GeO2. This response can be divided into three regimes: (1) An elastic shock regime with ramp 4 GPa Hugoniot elastic limit (HEL) precursor. Shock propagation velocity decreases from an initial longitudinal elastic wave speed of 3.5 to 2.8 km/s at 4 GPa. (2) A transition wave regime where the ramp wave is superimposed on the precursor with an additional amplitude of 0 to 2 GPa followed by a sharp increase in shock pressure achieving peak loading pressures of 8 to 14 GPa. Above 4 GPa the ramp wave velocity decreases to a value below 2.5 km/s (the speed of the bulk wave, at the HEL). (3) A shock wave achieving the final shock state forms when peak pressure is >6 GPa specified by linear shock-particle velocity relation D=0.917+1.71 u (km/s) over the 6–40 GPa range for an initial density of 3.655 g/cm3. The Hugoniots of GeO2 and SiO2, both initially vitreous, are found to be virtually coincident if pressure in SiO2 is calculated by multiplying the GeO2 pressure by the ratio of the initial densities of vitreous GeO2 to fused SiO2. The volume axes are translated by aligning the specific volumes for onset and completion of the four- to six-fold coordination phase change. Although only limited spherical impactor spherically diverging shock experiments were conducted, our present results demonstrate (1) The supported elastic shock in fused SiO2 decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. A supported elastic precursor in vitreous GeO2 decays faster with radius than a linear elastic wave; (2) in GeO2 (vitreous) unsupported shock waves decay with peak pressure in a phase transition range (4–15 GPa) with propagation radius (r) as ∝r−3.35.

Axisymmetric gravity currents in a rotating system: experimental and numerical investigations

The propagation at high Reynolds number of a heavy, axisymmetric gravity current of given initial volume over a horizontal boundary is considered in both rotating and non-rotating situations. The investigation combines experiments with theoretical predictions by both shallow-water approximations and numerical solutions of the full axisymmetric equations. Attention is focused on cases when the initial ratio of Coriolis to inertia forces is small. The experiments were performed by quickly releasing a known cylindrical volume of dense salt water of 2 m diameter at the centre of a circular tank of diameter 13 m containing fresh ambient water of typical depth 80 cm. The propagation of the current was recorded for different initial values of the salt concentration, the volume of released fluid, the ratio of the initial height of the current to the ambient depth, and the rate of rotation. A major feature of the rotating currents was the attainment of a maximum radius of propagation. Thereafter a contraction–relaxation motion of the body of fluid and a regular series of outwardly propagating pulses was observed. The frequency of these pulses is slightly higher than inertial, and the amplitude is of the order of magnitude of half the maximum radius. Theoretical predictions of the corresponding gravity currents were also obtained by (i) previously developed shallow-water approximations (Ungarish & Huppert 1998) and (ii) a specially developed finite-difference code based on the full axisymmetric Navier–Stokes equations. The ‘numerical experiments’ provided by this code are needed to capture details of the flow field (such as the non-smooth shape of the interface, the vertical dependence of the velocity field) which are not reproduced by the shallow-water model and are very difficult for, or outside the range of, accurate experimental measurement. The comparisons and discussion provide insight into the flow field and indicate the advantages and limitations of the verified simulation tools.

High-Speed Imaging of Sustained Metabolic Target Patterns in Living Neutrophils during Adherence

Propagation of circular NAD(P)H autofluorescence and proton waves (target patterns) was detected in individual living human neutrophils using high-speed fluorescence microscopy. Waves were initiated at the point where a cell attached to the substrate followed by propagation to the cell's periphery. The time-dependence of wave propagation and critical radius are in reasonable agreement with theoretical expectations. We suggest that physical−chemical self-organization of metabolism is a fundamental aspect of cell function.

Simple models of Coriolis-influenced axisymmetric particle-driven gravity currents

Approximate analytical results are obtained for the propagation of an axisymmetric gravity current in a system rotating around a vertical axis, which occurs when a dense fluid intrudes horizontally under a lighter ambient fluid. Situations for which the density difference between the fluid is due either to compositional differences or to suspended particulate matter are considered; for the the latter, particle-driven cases, two models for the particle transport, turbulent remixing and laminar sedimentation are implemented. Attention is focused on situations in which the apparent importance of the Coriolis terms relative to the inertial terms, represented by the parameter C (the inverse of a Rossby number), is not large. A box-model approximation is used, in which the current is described as a control volume composed of a cylinder with a conical “roof” subject to global conservation conditions and simplifying assumptions. This leads to ordinary differential equations from which it is possible to calculate readily such essential features as the behaviour of the radius of propagation, height of the head (nose) and the amount of settled particles (when applicable). In particular, the limitation imposed by the Coriolis effects on the radius of propagation, the time of attainment of the maximal spread, and the appearance of an attached reverse motion are properly reflected. For the particle-driven case a parametric dependency between the settling and Coriolis influences is obtained, which allows for a stringent comparison to be made between the two different particle-transport models. The box model results are in good qualitative agreement with numerical solutions of the full shallow-water equations, for which a novel similarity transform is also presented.

Effect of irreversible phase change on shock-wave propagation

New release adiabat data for vitreous GeO 2 are reported up to ∼25 GPa using the VISAR technique. Numerical modeling of isentropic release wave induced dynamic states achieved from one dimensional strain–stress waves is consistent with a phase change that induce an increase in zero-pressure density from 3.7–6.3 Mg/m 3 starting at ∼8 GPa. The first release adiabat data for SiO 2 ( fused quartz) are presented (obtained with immersed foil technique) . Above 10 GPa, the SiO 2 release isentropes, in analogy with GeO 2, are steeper than the Hugoniot in the volume-pressure space, indicating the presence of an irreversible phase transition (to a stishovite-like phase) . We simulate propagation of shock-waves in GeO 2, in spherical and planar symmetries, and predict enhanced attenuation for shock pressures ( p) above the phase change initiation pressure (8 GPa) . The pressure from a spherical source decays with propagation radius r, p ∼ r x, where x is the decay coefficient. Modeling hysteresis of the phase change gives x = −2.71, whereas without the phase change, x = −1.15. An analytical model is also given.

Quantum stability of the vortex state in the Abelian Higgs model.

Treating the flux of the magnetic field penetrating the vortex as a dynamical variable, we consider the question of the stability of the quantum state of the vortex against the decay to the excitations which are present in the Abelian Higgs model. Specifically, the partial widths of the decay to a pair of the scalar field excitations possessing the Bogolyubov spectrum and to such a pair plus the quantum of the electromagnetic field with the finite radius of propagation implied by the finite London penetration depth are evaluated.

Spiral Calcium Wave Propagation and Annihilation in Xenopus laevis Oocytes

Intracellular calcium (Ca2+) is a ubiquitous second messenger. Information is encoded in the magnitude, frequency, and spatial organization of changes in the concentration of cytosolic free Ca2+. Regenerative spiral waves of release of free Ca2+ were observed by confocal microscopy in Xenopus laevis oocytes expressing muscarinic acetylcholine receptor subtypes. This pattern of Ca2+ activity is characteristic of an intracellular milieu that behaves as a regenerative excitable medium. The minimal critical radius for propagation of focal Ca2+ waves (10.4 micrometers) and the effective diffusion constant for the excitation signal (2.3 x 10(-6) square centimeters per second) were estimated from measurements of velocity and curvature of circular wavefronts expanding from foci. By modeling Ca2+ release with cellular automata, the absolute refractory period for Ca2+ stores (4.7 seconds) was determined. Other phenomena expected of an excitable medium, such as wave propagation of undiminished amplitude and annihilation of colliding wavefronts, were observed.

Simple model of shock-wave attenuation in snow

AbstractA simple momentum model, assuming that snow compacts along a prescribed pressure–density curve, is used to calculate the pressure attenuation of shock waves in snow. Four shock-loading situations are examined: instantaneously applied pressure impulses for one-dimensional, cylindrical and spherical shock-wave geometries, and a one-dimensional pressure impulse of finite duration. Calculations show that for an instantaneously applied impulse the pressure attenuation for one-dimensional, cylindrical and spherical shock waves is determined by the pressure density (P–ρ) compaction curve of snow. The maximum attenuation for a one-dimensional shock wave is proportional to (Xf–X0)−1.5for the multi-stage (P–ρ) curve and (Xf–X0)−2when compaction occurs in a single step (single-stage compaction), where (Xf–X0) is the shock-wave propagation distance. Cylindrical waves have a maximum attenutation that varies from (R–R0)−2for single-stage compaction and (R–R0)−1.5for multi-stage compaction, when (R–R0) ≪R0, whereRis the propagation radius andR0is the interior radius over which a pressure impulse is applied, toR−4when (R–R0) ≫R0Spherical waves have a maximum attenuation that varies from (R–R0)−2for single-stage compaction and (R–R0)−1.5for multi-stage compaction toR−6when 〈R–R0〉 ≫R0.The shock-wave pressure in snow for a finite-duration pressure impulse is determined by the pressure impulse versus time profile during the time interval of the impulse. After the pressure impulse ends, shock-wave pressure attenuation is the same as for an instantaneously applied pressure impulse containing the same total momentum. Pressure attenuation near a shock-wave source, where the duration of the shock wave is relatively short, is greater than for a shock wave farther from a source where the shock wave has a relatively long duration. Shock-wave attenuation in snow can be delayed or reduced by increasing the duration of a finite-duration pressure impulse. A sufficiently long-duration impulse may result in no shock-wave pressure attenuation in a shallow snow cover.

Curvature and spiral geometry in aggregation patterns of Dictyostelium discoideum

ABSTRACT Aggregation patterns of the slime mould Dictyostelium discoideum were recorded using dark-field equipment combined with video techniques. Computerized image processing allowed the analysis of wave collision structures, expanding concentric circles and rotating spirals in terms of wave velocity and front geometry, as previously done in the Belousov-Zhabotinskii reaction, a chemical system showing similar patterns. We verified the linear relationship between the normal velocity and the curvature of wave fronts predicted by a reactiondiffusion model. The proportionality factor, which in this case is the diffusion coefficient of the chemical signal transmitter cAMP establishing communication between the cells, was determined to be 0.66×10−5cm2s-1. From measurements of positively curved circular waves, we could roughly estimate the critical radius of wave propagation (∽200//m); which means that up to 500 cells are necessary to form a center of an aggregation structure. Furthermore, we analyzed the geometrical parameters of spiral wave patterns and estimated the core radius ro to be ≈300 μm.

GEOELECTRIC RESISTIVITY ANOMALIES BEFORE EARTHQUAKES

Since geoelectric resistivity (ρ_x) measurements were started in 1967, the following phenomena have been observed before earthquakes: ⅰ) During 2-3 years before the great Tangshan earthquake, the anomaly of ρ_x propagated outwards from the epicenter with an apparent velocity of 100 km/year, and the radius of propagation reached about 150 km. (ⅱ) Before most of the earthquakes, the resistivity drops, but before a few earthquakes it may rise; all these are controlled by the stress conditions under the geoelectric station and the source mechanism of the earthquake. The relative variation of ρ_x is a magnified (up to about 1000 times) manifestation of rock strain. (ⅲ) Before an earthquake, geoelectric resistivity may exhibit both long-term and close-upon anomalies. The long-term anomaly reflects the accelerated accumulation of stress in the seismo-genotic region; its amplitude, duration and extent are logarithmically related to the earthquake magnitude. The close-upon anomaly may be a manifestation of premonitory slip on the fault. (ⅳ) The slippage on the fault during or after an earthquake may sometimes cause post-earthquake effect in the variation of ρ_x.

Precursor Ionization Fronts Ahead of Expanding Laser-Plasmas

Fast ionization fronts have been experimentally observed to propagate ahead of a laser-produced plasma expanding into low-density background gas. The ionizing wave has a velocity of 0.3-3×108 cm/sec and a thickness of 1-10 cm both quantities increasing with radius of propagation. Langmuir probe and microwave diagnostics indicate that the wave augments the initial photoionization density by a factor of ∼3; potential fluctuations exist within the wave which can accelerate electrons to energies above the ionization threshold. Equations describing a collisional ionizing electron wave are solved in an approximate manner to yield relations which agree with many features of the measured phenomena.

GaAs lasers utilizing light propagation along curved junctions

A junction laser in which the light propagation within the device is along curved-junction paths is reported here. Path curvatures with radii ranging from 0.25 to 1.00 mm were obtained by the intentional introduction of curved diffused junctions. It was found that for radii of curvature smaller than a critical value of about 0.4 mm, the threshold-current density increases very rapidly. This value is in good agreement with the theoretical value, which is obtained by assuming that the gradient of the refractive index across the GaAs junction determines the minimum bending radius for low-loss propagation. The design of these curved-junction devices is critically dependent on the suppression of lasing along undesired junction paths perpendicular to the desired direction by bending these paths through a smaller than critical radius.

Optimum size of the components of grouts for cementation of sand soils and for separate concreting

1. In order to increase the penetrating ability of grouts, to augment the radius of propagation, and to improve the effectiveness of grouting operations, the cements to be utilized in the grouts must be subjected to additional grinding. 2. The optimum degree of dispersion for which it is possible to achieve effective grouting of sandy soils may be established by determining the diameter of the penetrating particles by applying, Eq. (7). 3. The relationship derived here may be utilized for determining the diameters of the components of cementsand grouts in separate concreting of structures.

Effective Earth's Radius for Radiowave Propagation Beyond the Horizon

The geometrical optical arguments underlying the equivalent earth's radius approximation are extended to non-horizontal rays. The appropriate wave equation for a non-uniform, but spherically symmetric, region is derived in a natural way. The notion of a ``primary field'' with the form eikR/R at the source is dropped in favor of a solution to the wave equation in terms of a Green's Function. The formal solution thus obtained is seen to contain the known solutions for a uniform medium. For the non-uniform case, the solutions to the radial equation are found by a technique due to Langer. These functions account for the index variation near the earth without making unwarranted assumptions about the behavior at greater heights. The formal series obtained is summed by the Watson technique. The first term in this series (lowest mode) alone determines the field at large distances and indicates that one may account for standard atmospheric refraction by using an effective earth's radius.