Transient analysis for stimulated thermal scattering

1969 ◽  
Vol 47 (20) ◽  
pp. 2265-2268 ◽  
Author(s):  
R. H. Enns ◽  
I. P. Batra
Keyword(s):  
Steady State ◽  
Transient Analysis ◽  
Brillouin Scattering ◽  
Unit Length ◽  
State Theory ◽  
Nonlinear Gain ◽  
Thermal Scattering

In previous treatments, the nonlinear gain per unit length for stimulated thermal scattering has been calculated using a steady-state approach without examining the conditions under which such an approach is valid. Here we present a transient analysis and calculate the time which must elapse before the steady-state theory becomes applicable. We show that in both stimulated thermal Rayleigh and stimulated thermal Brillouin scattering it is the so-called Rayleigh lifetime τR which determines the onset of steady state.

Evaluation of Single-Hole Hydraulic Tests in Fractured Crystalline Rock by Steady-State and Transient Methods: A Comparison

1985 ◽  
Vol 50 ◽  
Author(s):  
J-E. Andersson ◽  
O. Persson
Keyword(s):  
Steady State ◽  
Hydraulic Conductivity ◽  
Flow Pattern ◽  
Transient Analysis ◽  
Crystalline Rock ◽  
Steady State Analysis ◽  
Single Hole ◽  
The Mean ◽  
Transient Methods ◽  
State Analysis

AbstractThe results from a large number of single-hole packer tests in crystalline rock from three test sites in Sweden have been analysed statistically. Average hydraulic conductivity values for 25 m long test intervals along boreholes with a maximal length of about 700 m are used in this study. A comparison between steady state and transient analysis of the same test data has been performed.The mean vaule of the hydraulic conductivity determined from steady state analysis was found to be about two to three times higher compared to transient analysis. However, in some cases the steady state analysis resulted in 10 to 20 times higher values compared to the transient analysis. Such divergence between the two analysis methods may be caused by deviations from the assumed flow pattern, borehole skin effects and influence of hydraulic boundaries.

Analytical Rate-Transient Analysis and Production Performance of Waterflooded Fields with Delayed Injection Support

2021 ◽  
pp. 1-23
Author(s):  
Daniel O'Reilly ◽  
Manouchehr Haghighi ◽  
Mohammad Sayyafzadeh ◽  
Matthew Flett
Keyword(s):  
Steady State ◽  
Transient Analysis ◽  
Water Injection ◽  
Data Interpretation ◽  
Production Performance ◽  
Production Data ◽  
Reservoir Properties ◽  
Two Phase ◽  
Production Forecasting ◽  
Rate Transient Analysis

Summary An approach to the analysis of production data from waterflooded oil fields is proposed in this paper. The method builds on the established techniques of rate-transient analysis (RTA) and extends the analysis period to include the transient- and steady-state effects caused by a water-injection well. This includes the initial rate transient during primary production, the depletion period of boundary-dominated flow (BDF), a transient period after injection starts and diffuses across the reservoir, and the steady-state production that follows. RTA will be applied to immiscible displacement using a graph that can be used to ascertain reservoir properties and evaluate performance aspects of the waterflood. The developed solutions can also be used for accurate and rapid forecasting of all production transience and boundary-dominated behavior at all stages of field life. Rigorous solutions are derived for the transient unit mobility displacement of a reservoir fluid, and for both constant-rate-injection and constant-pressure-injection after a period of reservoir depletion. A simple treatment of two-phase flow is given to extend this to the water/oil-displacement problem. The solutions are analytical and are validated using reservoir simulation and applied to field cases. Individual wells or total fields can be studied with this technique; several examples of both will be given. Practical cases are given for use of the new theory. The equations can be applied to production-data interpretation, production forecasting, injection-water allocation, and for the diagnosis of waterflood-performanceproblems. Correction Note: The y-axis of Fig. 8d was corrected to "Dimensionless Decline Rate Integral, qDdi". No other content was changed.

Non-steady-state stimulated scattering: a convenient solution in terms of convolution integrals

1977 ◽  
Vol 352 (1671) ◽  
pp. 539-555
Keyword(s):  
Steady State ◽  
Input Pulse ◽  
State Theory ◽  
Spatial Modulation ◽  
Bragg Angle ◽  
Stimulated Scattering ◽  
Scattering Spectrum ◽  
Convolution Integrals ◽  
Beam Incident ◽  
Scattered Beam

A non-steady-state theory of stimulated light scattering, which places particular emphasis on the effects induced in the scattering medium, is developed. It is shown that a spatial modulation of the dielectric constant is induced whose amplitude and phase can be expressed in terms of simple convolution integrals. These involve only the input pulse shape, the steady-state scattering spectrum and the frequency shift between the laser and scattered beams. The effect of the induced modulation on the scattered beam and on any weak independent beam incident at the Bragg angle is also considered.

Dynamic Instability in Quartering Seas: The Behavior of a Ship During Broaching

1996 ◽  
Vol 40 (01) ◽  
pp. 46-59 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Steady State ◽  
Transient Analysis ◽  
Dynamic Instability ◽  
Dynamical Analysis ◽  
Wave Excitation ◽  
Periodic Motions ◽  
Regular Waves ◽  
Limit Sets ◽  
Diffraction Wave ◽  
Surf Riding

The dynamic stability of ships encountering large regular waves from astern is analyzed, with focus on delineating the specific conditions leading to the uncontrolled turn identified as broaching. The problem's formulation takes into account motions of the actively steered or controls-fixed vessel in surge-sway-yaw-roll with consideration of Froude-Krylov and diffraction wave excitation. Dynamical analysis of surf-riding is carried out for the general case of quartering waves, exploring the route periodic motions—surf riding, loss of stationary stability, turn, capsize. Steady-state and transient analysis is carried out in the system's multidimensional state-space in order to identify all existing limit sets and locate attracting domains. Broaching from periodic motions is also a part of the investigation.

scholarly journals Alternating Strain Regimes for Failure Propagation in Flexural Systems

2019 ◽  
Vol 72 (3) ◽  
pp. 305-339 ◽  
Author(s):  
M Garau ◽  
M J Nieves ◽  
I S Jones
Keyword(s):  
Steady State ◽  
Transient Analysis ◽  
Fracture Process ◽  
Mechanical Load ◽  
Dynamic Features ◽  
Hopf Equation ◽  
Beam Structure ◽  
Numerical Studies ◽  
Failure Propagation ◽  
Discrete Mass

Summary We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler–Bernoulli beams. A fault inside the structure is assumed to propagate with a constant speed and this occurs as a result of the action of a remote sinusoidal, mechanical load. The established regime of fracture corresponds to the case of an alternating generalised strain regime. The model is reduced to a Wiener–Hopf equation and its solution is presented. We determine the minimum feeding wave energy required for the steady-state fracture process to occur. In addition, we identify the dynamic features of the structure during the steady-state fracture regime. A transient analysis of this problem is also presented, where the existence of steady-state fracture regimes, revealed by the analytical model, are verified and the associated transient features of this process are discussed.

Steady-state theory of thermal explosions

1978 ◽  
Vol 14 (5) ◽  
pp. 658-660 ◽  
Author(s):  
E. A. Eremin ◽  
A. K. Kolesnikov
Keyword(s):  
Steady State ◽  
State Theory ◽  
Thermal Explosions
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