Critical Perturbation Research Articles

Contact line friction and surface tension effects on seismic attenuation and effective bulk moduli in rock with a partially saturated crack

ABSTRACTThe effect of surface phenomena occurring at the interfaces between immiscible fluids and a solid on the seismic attributes of partially saturated rocks has not yet been fully studied. Meanwhile, over the past two decades considerable progress has been made in the physics of wetting to understand effects such as contact line friction, contact line pinning, contact angle hysteresis, and equilibrium contact angle. In this paper, we developed a new rock physics model considering the aforementioned effects on seismic properties of the rock with a partially saturated plane‐strain crack. We demonstrated that for small wave‐induced stress perturbations, the contact line of the interface meniscus will remain pinned, while the meniscus will bulge and change its shape through the change of the contact angles. When the stress perturbation is larger than a critical value, the contact line will move with advancing or receding contact angle depending on the direction of contact line motion. A critical stress perturbation predicted by our model can be in the range of ∼102−104 Pa, that is typical for linear seismic waves. Our model predicts strong seismic attenuation in the case when the contact line is moving. When the contact line is pinned, the attenuation is negligibly small. Seismic attenuation is associated with the hysteresis of loading and unloading bulk moduli, predicted by our model. The hysteresis is large when the contact line is moving and negligibly small when the contact line is pinned. Furthermore, we demonstrate that the bulk modulus of the rock with a partially saturated crack depends also on the surface tension and on the contact angle hysteresis. These parameters are typically neglected during calculation of the effecting fluid moduli by applying different averaging techniques. We demonstrate that contact line friction may be a dominant seismic attenuation mechanism in the low frequency limit (<∼10 Hz) when capillary forces dominate over viscous forces during wave‐induced two‐phase fluid flow.

PETROLEUM GEOLOGY: SCIENCE AND PRACTICE IN THE 21TH CENTURY. NEW IDEAS AND PARADIGMS

Nowadays, it is vitally necessary that conceptually new methods be used in petroleum geology. The aim of this paper is to outline new trends and approaches in petroleum geology; to substantiate the necessity for rehabilitation cycles in the process of oilfield development, especially at its active stage; to define the perturbation threshold for equilibrium of a fluid-saturated system. In this paper, an empirical estimation is given of the value of critical perturbation of an equilibrium fluid-saturated system during the oilfield development, equal to formation depression of 5-8 MPa.
 The author’s conclusion is that at present efforts should be focused on the efficient science-based development of the active oilfields in order to produce the residual (hard-to-extract) oil in a soft, sparing and non-damaging way, as well as on discovering new hydrocarbon accumulations, including secondary ones, throughout the whole stratigraphic section, with all depth horizons and various rock-fluid associations, in regions where a well-developed diversified infrastructure is already available. The use of rehabilitation cycles will make it possible to restore the energy potential of the stratum and filtration properties of the rock. In the long run, it will provide for an increased longevity of the object and higher final oil recovery.

Generalized Zermelo Navigation on Hermitian Manifolds with a Critical Wind

We study the Zermelo navigation problem on Hermitian manifolds (M, h) in the presence of a critical perturbation W determined by a complex velocity vector field such that \(0<||W(z)||_{h}=||u(z)||_{h}\le 1\), admitting space dependence of a ship’s relative speed \(||u(z)||_{h}\), with application of complex Finsler metric of complex Kropina type. We discuss the geodesics corresponding to the critical solutions to Zermelo’s problem and we find the necessary and sufficient conditions for the obtained locally projectively flat solutions.

Critical transitions and perturbation growth directions.

Critical transitions occur in a variety of dynamical systems. Here we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical transitions in several models of fast-slow systems, i.e., a network of coupled FitzHugh-Nagumo oscillators, models for Josephson junctions, and the Hindmarsh-Rose model, we find that tangencies between covariant Lyapunov vectors are a common and maybe generic feature during critical transitions. We further demonstrate that this deviation from hyperbolic dynamics is linked to the occurrence of critical transitions by using it as an indicator variable and evaluating the prediction success through receiver operating characteristic curves. In the presence of noise, we find the alignment of covariant Lyapunov vectors and changes in finite-time Lyapunov exponents to be more successful in announcing critical transitions than common indicator variables as, e.g., finite-time estimates of the variance. Additionally, we propose a new method for estimating approximations of covariant Lyapunov vectors without knowledge of the future trajectory of the system. We find that these approximated covariant Lyapunov vectors can also be applied to predict critical transitions.

Hybrid plasmonic mode converter: theoretical formulation and design with a graphical approach

The theoretical formulation based on rigorous transmission-line networks is developed for a general mode conversion problem and lays the groundwork for a simpler yet more efficient graphical design approach for hybrid plasmonic mode converters (HPMCs). The concurrence of co- and cross-polarization conversion to and among higher-order photonic and HP modes followed by subsequent power redistributions and losses over the course of the HPMC can lead to performance degradation and largely determines the silicon core thickness. Using gradient ascent of the TM polarization fraction incorporated with modal index contours sets critical perturbation parameters for required transverse structural asymmetry. Polarization reversal estimates are shown to be practically applicable for about 60% of the total device length. The mode conversion efficiency (MCE), insertion loss (IL), and the polarization conversion efficiency of the proposed HPMC (<7×0.4 μm2) at λ0=1550 nm are 90.04%, 0.4691 dB, and 99.96%, respectively. The 85%-bandwidth of the MCE is 135 nm, while the IL stays below 0.5 dB over a 68-nm spectral range.

The effects of large scale perturbation-generating obstacles on the propagation of detonation filled with methane–oxygen mixture

Orifice plates with large blockage ratios (BR=0.691, 0.826, 0.923 and 0.962) are placed in the entrance of the detonation transmission to investigate the artificially large-scale perturbations on the detonation propagation mechanism. Obstacles create large perturbations, thereby generating flow instability to affect the detonation transmission. In this study, stoichiometric methane–oxygen is examined because it has a wide application in the industry; therefore, its safety concerns must be addressed. Furthermore, the methane–oxygen mixture is characterized by a highly irregular cellular detonation front, and it is the representative of those potentially combustible mixtures used in practical aerospace application. Velocity behaviors after the detonation passes through the obstacles with different BR near the critical condition are analyzed; particular attention is paid to the cases for which BR is larger than 0.9 (i.e., 0.923 and 0.962), and the results are also compared with relatively smaller BR cases (BR=0.691 and 0.826). The effect of the diffraction, shock reflection and detonation instability on the propagation of detonation is examined. Finally, the analysis of critical length scale between the cell size (λ/d) and BR when the detonation fails or succeeds as it passes the obstacles is also performed, this work aims to explore the mechanism of critical perturbation scale on the detonation propagation.

Fault reactivation potential of an offshore CO2 storage site, Pohang Basin, South Korea

To estimate critical pore pressure perturbation (CPP) for evaluating the reactivation potential of faults existing within a pilot-scale offshore CO2 storage site, we used a semi-analytical solution in which poroelastic stressing caused by subsurface fluid injection was taken into account. CPP is defined as the difference between the initial reservoir pressure and the pressure in response to CO2 injection that results in the reactivation of a fault. Estimating the critical threshold pressure requires information about the fault configuration and friction coefficient, the orientation and magnitude of in-situ stresses, and the reservoir rock properties. The three-dimensional geometry of the faults was mapped by interpreting the seismic data obtained from the site. The friction coefficient was measured by running a set of direct shear tests on natural fault gouges obtained from a fault near the site. The pre-injection in-situ stress field was characterized by integrating data from core measurements on samples retrieved from an exploration borehole drilled at the pilot site, and from well logs and well tests carried out in neighboring boreholes. In-situ stress changes in response to CO2 injection were incorporated into the fault reactivation analysis that was performed using two friction coefficients μ=0.25 (lower bound) and μ=0.6 (upper bound). The results showed that CPP was ~3MPa for μ=0.25 at the WF2 and EF3 faults, and ~10MPa for μ=0.6 at the EF3 fault. However, the upper bound was reduced to a threshold pressure of ~6MPa, above which horizontal hydraulic fracturing would occur in the reservoir. Therefore, the pressure increase allowed at the site ranged from 3MPa to 6MPa.

Conventional and fuzzy PODCs for DFIG‐based wind farms and their impact on inter‐area and torsional oscillation damping

Contribution to the damping of inter-area and torsional oscillation modes, in doubly fed induction generators (DFIG) based wind farms, by power oscillation damping controllers (PODCs) based on two conventional structures and a fuzzy control strategy is investigated in this study. In this regard, a PODC with no lead/lag compensation is designed first and then a PODC with one lead/lag block is developed using eigenvalue techniques and the application of an iterative process based on the bat optimisation algorithm (BOA). Moreover, a fuzzy PODC, based on a simple fuzzy controller and tuned with the BOA according to the system transient response under a critical perturbation, is also designed. Comparative performance of the three PODCs is evaluated on a multi-machine power system. It is observed that all three PODCs can contribute to improving the damping of inter-area oscillations. However, eigenvalue analysis and non-linear time domain simulations reveal that each of them may also impact to a lesser or greater extent the shaft torsional oscillation mode damping. Their relative impact in this regard is also investigated.

Resonant Robin problems with indefinite and unbounded potential

We study a semilinear Robin problem with an indefinite and unbounded potential and a reaction term which asymptotically at $ \pm \infty $ is resonant with respect to any nonprincipal nonnegative eigenvalue. We prove two multiplicity theorems producing three and four nontrivial solutions respectively. Our approach uses variational methods based on the critical point theory, truncation and perturbation techniques, and Morse theory (critical groups).

Nonlinear Nonhomogeneous Robin Problems with Superlinear Reaction Term

Abstract We consider a nonlinear Robin problem driven by a nonlinear, nonhomogeneous differential operator, and with a Carathéodory reaction term which is ( p - 1 ) ${{(p-1)}}$ -superlinear near ± ∞ ${\pm\infty}$ without satisfying the Ambrosetti–Rabinowitz condition and which does not have a standard subcritical polynomial growth. Using a combination of variational methods and Morse theoretic techniques, we prove a multiplicity theorem producing three nontrivial solutions (two of which have constant sign). In the process we establish some useful facts about the boundedness of the weak solutions of critical equations and the relation of Sobolev and Hölder local minimizers for functionals with a critical perturbation term.

Stability of stratified two-phase flows in inclined channels

Linear stability of the stratified gas-liquid and liquid-liquid plane-parallel flows in the inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict the parameter regions in which the stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in the inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of the non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of the steady state solutions are presented on the flow pattern map and are accompanied by the critical wavenumbers and the spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by the streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of two stable stratified flow configurations in a region of low flow rates in the countercurrent liquid-liquid flows. These configurations become unstable with respect to the shear mode of instability. It was revealed that in slightly upward inclined flows the lower and middle solutions for the holdup are stable in the part of the triple solution region, while the upper solution is always unstable. In the case of downward flows, in the triple solution region, none of the solutions are stable with respect to the short-wave perturbations. These flows are stable only in the single solution region at low flow rates of the heavy phase, and the long-wave perturbations are the most unstable ones.

Localization from Superselection Rules in Translationally Invariant Systems.

The cubic code model is studied in the presence of arbitrary extensive perturbations. Below a critical perturbation strength, we show that most states with finite energy are localized; the overwhelming majority of such states have energy concentrated around a finite number of defects, and remain so for a time that is near exponential in the distance between the defects. This phenomenon is due to an emergent superselection rule and does not require any disorder. Local integrals of motion for these finite energy sectors are identified as well. Our analysis extends more generally to systems with immobile topological excitations.

Возбуждение конвекции в слоях жидкости и насыщенной пористой среды в модулированном поле силы тяжести

The effect of periodic modulation of gravitational acceleration on convection excitation in a two-layer system that is heated from below and consists of a horizontal pure fluid layer and a homogeneous porous medium saturated with the same fluid is investigated. The linear stability problem for mechanical equilibrium of fluid in the layers is solved numerically by the Galerkin method and the shooting method. A rectangular modulation of gravitational acceleration is established. Boundaries for resonance regions of equilibrium instability with respect to perturbations of synchronous and subharmonic responses of the system to periodic vibrational actions are demined as modulation amplitude and frequency change for various critical perturbation wavelengths. A boundary of the main instability region with respect to synchronous perturbations is found. It is shown that the modulation amplitude corresponding to the threshold of convection excitation strongly depends on perturbation wavelength. Perturbations of shorter wavelength (short-wave perturbations) localized in the fluid layer are more susceptible to the gravity modulation effect than perturbations of larger wavelength (long-wave perturbations) penetrating the porous layer. The occurrence of narrow resonance stability regions as heat intensity increases for short-wave perturbations is much earlier than for long-wave perturbations.Received 22.10.2016; accepted 03.11.2016

Three-dimensional instabilities and optimal perturbations of a counter-rotating vortex pair in stratified flows

This paper investigates the three-dimensional instabilities and the optimal perturbations on a pair of horizontal counter-rotating Lamb-Oseen vortices in a vertically stably stratified flow. Two-dimensional (2D) simulations are first performed, showing that while the dipole moves vertically against the stratification the vortex parameters: the radius a∗, the separation distance b∗, and the circulation Γ∗ are solely function of the time rescaled by the Brunt-Väisälä frequency N, independently of the Froude number, when the Reynolds number is large enough. Here, the Froude number is Fr = W0/Nb0 with W0 the initial advection velocity of the dipole and b0 the initial separation distance between the two vortices. For weak and moderate stratifications (large Fr), the stratification acts on a long time scale compared to the advection time of the dipole implying that the 2D flow can be considered as quasi-steady. In that case, when three dimensional instabilities are added, a linear stability analysis of this 2D flow at different instants retrieves the instability peaks corresponding to the Crow instability for the long wavelengths and to the elliptic instability for the short wavelengths showing that the dynamics is almost unaffected by buoyancy effects. The Crow and elliptic instabilities scale with the instantaneous dipole parameters showing in particular that stratification promotes instability by reducing the distance b∗ between vortices [K. K. Nomura et al., “Short-wavelength instability and decay of a vortex pair in stratified fluid,” J. Fluid Mech. 553, 283-322 (2006)]. For strong stratifications (Froude numbers of order unity or smaller), the quasi-steady approximation is not valid, and the question of stability should be formulated in a different way, by, for example, searching for the transient growth of the energy of perturbation that may be computed for steady or unsteady base flow. Then, for each time horizon τ, we should determine the critical perturbation leading to the largest energy growth by the time τ. Presently, we compute the optimal perturbations at two time horizons τ = 4 and τ = 10 dimensionalized by 2πb02/Γ0 with a direct-adjoint technique which takes into account the evolution of the base flow. In the homogeneous case, this technique allows to investigate the effect of the weak unsteadiness of the flow due to viscous diffusion which induces a growth of the vortex core radius a∗. Both Crow and elliptic instabilities are retrieved in the optimal response and in the energy gain curves. Even if very slow, the viscous diffusion is found to increase the gain of the antisymmetric elliptic perturbation compared to the symmetric one. When the fluid is stratified, peaks at small wavenumber and at wavenumber of the order of the vortex core size are found for all Froude numbers with optimal responses strongly resembling, respectively, the Crow and the elliptic modes with optimal gains corresponding to mean growth rates larger than in the homogeneous case for both modes. However, as the strength of stratification increases (Froude numbers smaller than 2), optimal perturbations start departing from their homogeneous counterpart with large perturbation in the wake of the dipole associated with density effects.

Mechanisms of onset for moderate Mach number instabilities of viscoelastic flows around confined cylinders

An examination of the upstream and downstream instabilities that occur for highly confined and bounded viscoelastic flows around a cylinder is presented. An elasticity number-Mach number (El-Ma) phase space is used to demonstrate that the onset of downstream instabilities at Ma = 1; these instabilities are instigated by the disturbance of the base flow by traveling elastic waves. After the onset of the downstream instability, an upstream instability eventually occurs for Macrit ~ 10; however, this number is affected by both channel geometry and fluid properties. The upstream instability is instigated by perturbations of the flow field caused by the downstream instability and does not occur until a critical perturbation size at a given velocity is exceeded. The effects of these flow regimes on flow resistance are characterized by examining excess pressure drop; a significant increase in flow resistance is observed at the onset of the upstream instability.

Resonant Neumann equations with indefinite linear part

We consider aseminonlinear Neumann problem driven by the $p$-Laplacian plus an indefinite and unbounded potential. The reaction of the problem is resonant at $\pm \infty$ with respect to the higher parts of the spectrum. Using critical point theory, truncation and perturbation techniques, Morse theory and the reduction method, we prove two multiplicity theorems. One produces three nontrivial smooth solutions and the second four nontrivial smooth solutions.

Probabilistic geomechanical analysis of compartmentalization at the Snøhvit CO2 sequestration project

AbstractPressure buildup caused by large‐scale CO2 injection is a key concern during a carbon sequestration project. Large overpressures can compromise seal integrity, reactivate faults, and induce seismicity. Furthermore, pressure buildup is directly related with storage capacity. In this work we study the geomechanical response to CO2 injection at Snøhvit, to understand the potential for fault reactivation, leakage, and contamination of the producing interval through bounding faults. Furthermore, we evaluate the potential contribution of a structural component to reservoir compartmentalization. We combine simplified analytical models, based on critically stressed fracture theory and a Mohr‐Coulomb failure criterion, with a rigorous sensitivity analysis. Large stress uncertainties are present and reflected in the modeling results. It was found that under the most likely stress state the faults are fairly stable and caprock hydrofracturing would be expected before fault reactivation. In most of the analyzed cases, the critical pressure perturbation needed for reactivation is above 13 MPa, which was the limiting pressure increase before reaching the fracture pressure. Faults were found to be ~ 20% less stable when considering variations in SHmax orientation. In those cases, fault reactivation could be expected before caprock failure if injection continued. However, if the pressure increase did reach the critical values for seal failure estimated under the worst case (and least likely) stress state, no indication of such failure can be observed in the measured pressure response. Finally, the potential role of a structural component in the compartmentalization and fluid migration is difficult to assess due to the stress state uncertainty.

The effects of variable fluid properties on thin film stability

A theoretical investigation has been conducted to study the impact of variable fluid properties on the stability of gravity-driven flow of a thin film down a heated incline. The incline is maintained at a uniform temperature which exceeds the temperature of the ambient gas above the fluid and is thus responsible for heating the thin fluid layer. The variable fluid properties are allowed to vary linearly with temperature. It is assumed that long-wave perturbations are most unstable. Based on this, a stability analysis was carried out whereby the governing linearized perturbation equations were expanded in powers of the wavenumber which is a small parameter. New interesting results illustrating how the critical Reynolds number and perturbation phase speed depend on the various dimensionless parameters have been obtained.

The bow shock, cold fronts and disintegrating cool core in the merging galaxy group RX J0751.3+5012

We present a new Chandra X-ray observation of the off-axis galaxy group merger RXJ0751.3+5012. The hot atmospheres of the two colliding groups appear highly distorted by the merger. The images reveal arc-like cold fronts around each group core, produced by the motion through the ambient medium, and the first detection of a group merger shock front. We detect a clear density and temperature jump associated with a bow shock of Mach number M=1.9+/-0.4 ahead of the northern group. Using galaxy redshifts and the shock velocity of 1100+/-300 km/s, we estimate that the merger axis is only 10deg from the plane of the sky. From the projected group separation of 90 kpc, this corresponds to a time since closest approach of 0.1 Gyr. The northern group hosts a dense, cool core with a ram pressure stripped tail of gas extending 100 kpc. The sheared sides of this tail appear distorted and broadened by Kelvin-Helmholtz instabilities. We use the presence of this substructure to place an upper limit on the magnetic field strength and, for Spitzer-like viscosity, show that the development of these structures is consistent with the critical perturbation length above which instabilities can grow in the intragroup medium. The northern group core also hosts a galaxy pair, UGC4052, with a surrounding IR and near-UV ring 40 kpc in diameter. The ring may have been produced by tidal stripping of a smaller galaxy by UGC4052 or it may be a collisional ring generated by a close encounter between the two large galaxies.

Uma introdução ao controle do caos em sistemas hamiltonianos quase integráveis

Sistemas Hamiltonianos quase integráveis são de grande interesse em diversos campos de pesquisa da física e da matemática. Nesses sistemas, o espaço de fase apresenta trajetórias regulares e caóticas. Essas trajetórias dependem, em parte, da amplitude da perturbação que quebra a integrabilidade do sistema. O valor da perturbação crítica responsável por esta transição é um elemento chave no controle do caos. No presente trabalho, exploramos um procedimento para o controle do caos em sistema hamiltoniano quase integrável baseado na alteração de um parâmetro (perturbação). Inicialmente, apresentamos as ferramentas básicas para este estudo: mapa hamiltoniano, linearização do mapa e critério de Chirikov. Posteriormente, investigamos o comportamento de uma interação do tipo onda-partícula frente a perturbação. Por fim, confrontamos os resultados analíticos com uma abordagem numérica (iteração do mapa), mostrando um bom acordo.