The interaction of tube waves with borehole fractures, Part II: Analytical models

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 809-815 ◽  
Author(s):  
Sergio Kostek ◽  
David Linton Johnson ◽  
Kenneth W. Winkler ◽  
Brian E. Hornby
Keyword(s):  
Finite Difference ◽  
Analytical Models ◽  
Stoneley Wave ◽  
Single Fracture ◽  
Elastic Model ◽  
Formation Model ◽  
Wave Reflections ◽  
Fracture Width ◽  
Fracture Apertures

We develop a series of analytical models that can be used to interpret Stoneley‐wave reflections from fractures intersecting a borehole, thus facilitating the determination of effective fracture apertures from logs. The first model considers the combined effects of borehole enlargements (e.g., washouts) and fractures on the reflection coefficient of Stoneley waves. The result is expressed in terms of the washout volume, which can be obtained from a caliper log, as well as the fracture width. The predictions of this model are in excellent agreement with finite‐difference calculations. Next we develop an analytical elastic model that generalizes the rigid formation model. It also agrees with finite‐difference calculations. Finally, we establish the equivalence between a closely spaced multiple fracture and a permeable medium. In all the examples, the generalization of the result for the single fracture in a rigid formation can be accomplished with standard logging measurements.

Fracture apertures from electrical borehole scans

Geophysics ◽  
1990 ◽  
Vol 55 (7) ◽  
pp. 821-833 ◽  
Author(s):  
S. M. Luthi ◽  
P. Souhaité
Keyword(s):  
Detection Threshold ◽  
Three Dimensional ◽  
Stoneley Wave ◽  
Line Integral ◽  
Fracture Width ◽  
Dimensional Finite Element ◽  
Fracture Apertures ◽  
Three Dimensional Finite Element ◽  
The Relationship ◽  
Additional Current

Three-dimensional finite-element modeling was performed to investigate the response to fractures of the Formation MicroScanner (Mark of Schlumberger), which records high-resolution electrical scans of the borehole wall. It is found that the equation [Formula: see text] describes, over two orders of magnitude of resistivity contrasts between borehole mud and the formation, the relationship between fracture width W (in mm), formation sensitivity [Formula: see text], mud resistivity [Formula: see text], and the additional current flow A caused by the presence of the fracture. A is the additional current which can be injected into the formation divided by the voltage, integrated along a line perpendicular across the fracture trace. Coefficient c and exponent b are obtained numerically from forward modeling. Tool standoffs of up to 2.5 mm and fracture dips in the range from 0° to 40° were found to have an insignificant effect on the above relation. A three‐step approach to detect, trace,and quantify fractures is used. Potential fractures in Formation MicroScanner images are detected as locations where conductivity exceeds the local matrix conductivity by a statistically significant amount. Integration over a circular area is performed around these locations to gather all excessive currents; this integral is then geometrically reduced to approximate the line integral A. Line sharpening and neighborhood connectivity tests are done to trace the fractures, and apertures are computed for all fracture locations. Results from a well into basement in Moodus (Connecticut) show that the method successfully traces fractures seen on Formation MicroScanner images. The resulting fracture apertures range from 10 μm to 1 mm. For the wider fractures there is acceptable agreement with apertures obtained from Stoneley wave reflection measurements. This unique and novel technique for characterizing fractures in wellbores has a very low detection threshold of around 10 μm and resolves fractures as little as 1 cm apart. Furthermore, it provides azimuthal orientation of the fractures.

Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes

2001 ◽  
Vol 123 (6) ◽  
pp. 1159-1172 ◽  
Author(s):  
Mohammad B. Shafii ◽  
Amir Faghri ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Heat Pipes ◽  
Analytical Models ◽  
Charge Ratio ◽  
Sensible Heat ◽  
Governing Equations ◽  
Heating Wall ◽  
Heat Mode ◽  
Explicit Finite Difference

Analytical models for both unlooped and looped Pulsating Heat Pipes (PHPs) with multiple liquid slugs and vapor plugs are presented in this study. The governing equations are solved using an explicit finite difference scheme to predict the behavior of vapor plugs and liquid slugs. The results show that the effect of gravity on the performance of top heat mode unlooped PHP is insignificant. The effects of diameter, charge ratio, and heating wall temperature on the performance of looped and unlooped PHPs are also investigated. The results also show that heat transfer in both looped and unlooped PHPs is due mainly to the exchange of sensible heat.

A New Approach for Determining Joint Stiffness of Bolted Joints

2014 ◽  
Vol 670-671 ◽  
pp. 1041-1044 ◽  
Author(s):  
Xi Wang Wang ◽  
Xiao Yang Li ◽  
Lin Lin Zhang ◽  
Xiao Guang Wang
Keyword(s):  
Accurate Determination ◽  
Joint Stiffness ◽  
Fatigue Loading ◽  
Bolted Joints ◽  
Analytical Models ◽  
Bolted Connection ◽  
New Approach ◽  
Axisymmetric Model ◽  
Force Equilibrium

Joint member stiffness in a bolted connection directly influence the safety of a design in regard to both static and fatigue loading as well as in the prevention of separation in the connection. Thus, the accurate determination of the stiffness is of extreme importance to predict the behavior of bolted assemblies. In this paper, An analytical 3D axisymmetric model of bolted joints is proposed to obtain the joint stiffness of Bolted Joints. Considering many different analytical models have been proposed to calculate the joint stiffness, the expression based force equilibrium can be a easy way to choose the best expression for the joint stiffness as a judgment criteria.

Water quality of the Beli Lom river

1999 ◽  
Vol 39 (8) ◽  
pp. 55-62 ◽  
Author(s):  
Anastasios I. Stamou ◽  
Bogdana Koumanova ◽  
Stoyan Stoyanov ◽  
Georgy Atanasov ◽  
Konstantinos Pipilis
Keyword(s):  
Water Quality ◽  
Wastewater Treatment ◽  
Finite Difference ◽  
Treatment Plant ◽  
Quality Characteristics ◽  
Order Model ◽  
The Third ◽  
Do Concentration

A general methodology for the study of water quality in rivers is presented. The paper consists of four parts. In the first part the general characteristics of the area of study, which is the Beli Lom river, and its major pollution sources are presented. The effluent of the Razgrad Wastewater Treatment Plant (RWWTP) has been identified as the most significant pollution point source, due to the inadequate performance of the plant. The second part deals with data collection and processing. Four series of data have been collected, including physical, flow and water quality characteristics. In the third part a 1-d, finite-difference, second-order model is presented. In the fourth part, the model is calibrated, for the determination of its main coefficients, and is successfully verified by predicting the BOD and DO concentrations in the Beli Lom river for all series of data. Finally, the model has been applied to determine the maximum BOD and minimum DO effluent concentrations of the RWWTP, so that a minimum DO concentration is maintained throughout the river.

scholarly journals Multivariate Distributions in Hydrology and River Regulation

1976 ◽  
Vol 7 (5) ◽  
pp. 265-280
Author(s):  
N.A. Kartvelishvili ◽  
L.T. Gottschalk
Keyword(s):  
Markov Process ◽  
Finite Difference ◽  
Difference Scheme ◽  
River Runoff ◽  
Finite Difference Scheme ◽  
River Regulation ◽  
Distribution Functions ◽  
Multivariate Distributions ◽  
Model Order

It is assumed that the river runoff process can be approximated by a Markov process. The process is thus described by M distribution functions: Fn (qt, t ; qt-1; t-1;…;qt-n, t-n), t ≡ 1, 2, …, M where M is the number of time intervals within the year, n - the order of the Markov process and qt, in general, is a vector representing runoff at several sites in a river or neighbouring rivers. Fundamental hypothesis of relations between multivariate distributions and corresponding marginal distributions is given. A finite difference scheme for multisite and multilag generation of river runoff is derived. The derivation is based on the multivariate normal distribution. Different methods for determination of the order of the finite difference scheme are discussed as well as the influence of model order and method of parameter estimation on properties of the model.

scholarly journals Flow characteristics of fractal fracture with different fractal dimension and different fracture width

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4477-4484
Author(s):  
Jun-Jun Liu ◽  
Jing Xie ◽  
Yi-Ting Liu ◽  
Gui-Kang Liu ◽  
Rui-Feng Tang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Rock Mass ◽  
Flow Characteristics ◽  
Fracture Network ◽  
Basic Element ◽  
Single Fracture ◽  
Flow State ◽  
Complex Flow ◽  
Fracture Width ◽  
Fracture Models

Single fracture is the most basic element in complex fracture network of rock mass. Therefore, the study of flow characteristics of single fracture is an important way to reasonably predict the complex flow state in engineering rock mass. In order to study the flow characteristics of fractal single fracture, fracture models with dif?ferent fractal dimension and different fracture width are established in this paper. The results show that: the blocking effect of rough structure on fluid is obviously enhanced under high pressure. In addition, it is weakened and reaches a steady-state with the increase of fracture fractal dimension. The larger the fracture width is, the more obvious the phenomenon is. The hydraulic gradient index tends to 0.5 with the increase of fracture width when fractal dimension is greater than 1.3. It also could tend to 0.5 with the increase of fractal dimension when fracture width is greater than 1 mm.

scholarly journals Using Bayesian Model Selection to Advise Neutron Reflectometry Analysis from Langmuir-Blodgett Monolayers

2019 ◽  
Author(s):  
Andrew McCluskey ◽  
Tom Arnold ◽  
Joshaniel F. K. Cooper ◽  
Tim Snow
Keyword(s):  
Experimental Data ◽  
Soft Matter ◽  
General Framework ◽  
Neutron Reflectometry ◽  
Analytical Models ◽  
Colloid Interface ◽  
X Ray ◽  
Langmuir Blodgett ◽  
Generic Framework

The analysis of neutron and X-ray reflectometry data is important for the study of interfacial soft matter structures. However, there is still substantial discussion regarding the analytical models<br>that should be used to rationalise relflectometry data. In this work, we outline a robust and generic framework for the determination of the evidence for a particular model given experimental data, by<br>applying Bayesian logic. We apply this framework to the study of Langmuir-Blodgett monolayers by considering three possible analytical models from a recently published investigation [Campbell et al., J. Colloid Interface Sci, 2018, 531, 98]. From this, we can determine which model has the most evidence given the experimental data, and show the effect that different isotopic contrasts of neutron reflectometry will have on this. We believe that this general framework could become an important component of neutron and X-ray reflectometry data analysis, and hope others more regularly consider the relative evidence for their analytical models.<br>

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