First-Passage-Time Modeling of Transport in Fractured Rock

1995 ◽  
Vol 412 ◽  
Author(s):  
M. W. Becker
Keyword(s):  
Time Domain ◽  
Breakthrough Curve ◽  
Fractured Rock ◽  
First Passage Time ◽  
Tracer Tests ◽  
Passage Time ◽  
Matrix Diffusion ◽  
Rock Matrix ◽  
Time Modeling ◽  
The Time Domain

AbstractThis paper presents theory intended for the design and interpretation of tracer tests in fractured rock. The objective is to provide an understanding of experiments in which particulate and solute tracers are injected simultaneously. In such experiments, it is expected that the solute tracer will diffuse into the rock matrix, while the particulates will be confined to the fractures. The theory allows information about matrix diffusion to be extracted from the breakthrough curve. Furthermore, it can accommodate tests in which a non-ideal source is used, and where some of the withdrawn fluid is re-injected. The solution is performed in Laplace space and transformed to the time domain using a commercial spreadsheet.

scholarly journals Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yuexiu Wu ◽  
Quansheng Liu ◽  
Andrew H. C. Chan ◽  
Hongyuan Liu
Keyword(s):  
Random Walk ◽  
Time Domain ◽  
Fractured Rock ◽  
Fracture Network ◽  
External Stress ◽  
Matrix Diffusion ◽  
Rock Masses ◽  
The Matrix ◽  
Nuclide Transport ◽  
Fractured Rock Masses

It is essential to study nuclide transport with underground water in fractured rock masses in order to evaluate potential radionuclide leakage in nuclear waste disposal. A time-domain random-walk (TDRW) method was firstly implemented into a discrete element method (DEM), that is, UDEC, in this paper to address the pressing challenges of modelling the nuclide transport in fractured rock masses such as massive fractures and coupled hydromechanical effect. The implementation was then validated against analytical solutions for nuclide transport in a single fracture and a simple fracture network. After that, the proposed implementation was applied to model the nuclide transport in a complex fracture network investigated in the DECOVALEX 2011 project to analyze the effect of matrix diffusion and stress on the nuclide transport in the fractured rock masses. It was concluded that the implementation of the TDRW method into UDEC provided a valuable tool to study the nuclide transport in the fractured rock masses. Moreover, it was found that the total travel time of the nuclide particles in the fractured rock masses with the matrix diffusion and external stress modelled was much longer than that without the matrix diffusion and external stress modelled.

Decomposition and Analysis of Non-Stationary Dynamic Signals Using the Hilbert Transform

2008 ◽  
Author(s):  
Michael Feldman
Keyword(s):  
Hilbert Transform ◽  
Time Domain ◽  
Instantaneous Frequency ◽  
Decomposition Method ◽  
Initial Signal ◽  
Time Modeling ◽  
Stationary Signals ◽  
A New Technique ◽  
The Time Domain ◽  
The Hilbert Transform

This paper describes a new technique, called the Hilbert Vibration Decomposition method, dedicated to decomposition of non-stationary wideband dynamic signals. Using the Hilbert transform in the time domain, we extract a number of elementary oscillating components of the initial signal, who’s both the instantaneous frequency and envelope can vary in time. Modeling examples of decomposition of non-stationary signals are included.

Apodisation in the time domain

1992 ◽  
Vol 2 (4) ◽  
pp. 615-620
Author(s):  
G. W. Series
Keyword(s):  
Time Domain ◽  
The Time Domain

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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