Generalisation of the concept of equivalent radius of thin cylindrical antennas

1984 ◽  
Vol 131 (3) ◽  
pp. 153 ◽  
Author(s):  
B.D. Popović ◽  
A. Nešić
SPE Journal ◽  
2021 ◽  
pp. 1-12
Author(s):  
Irfan Tai ◽  
Marie Ann Giddins ◽  
Ann Muggeridge

Summary The viability of any enhanced-oil-recovery project depends on the ability to inject the displacing fluid at an economic rate. This is typically evaluated using finite-volume numerical simulation. These simulators calculate injectivity using the Peaceman method (Peaceman 1978), which assumes that flow is Newtonian. Most polymer solutions exhibit some degree of non-Newtonian behavior resulting in a changing polymer viscosity with distance from the injection well. For shear-thinning polymer solutions, conventional simulations can overpredict injection-well bottomhole pressure (BHP) by several hundred psi, unless a computationally costly local grid refinement is used in the near-wellboreregion. We show theoretically and numerically that the Peaceman pressure-equivalent radius, based on Darcy flow, is not correct when fluids are shear thinning, and derive an analytical expression for calculating the correct radius. The expression does not depend on any particular functional relationship between polymer-solution viscosity and velocity. We test it using the relationship described by the Meter equation (Meter and Bird 1964) and the Cannella et al. (1988) correlation. Numerical tests indicate that the solution provides a significant improvement in the accuracy of BHP calculations for conventional numerical simulation, reducing or removing the need for expensive local grid refinement around the well when simulating the injection of fluids with shear-thinningnon-Newtonianrheology.


2017 ◽  
Vol 48 (2) ◽  
pp. 71 ◽  
Author(s):  
Vincenzo Bagarello ◽  
Andrea De Santis ◽  
Giuseppe Giordano ◽  
Massimo Iovino

Performing ponding infiltration runs with non-circular sources could represent a good means to sample completely an area of interest. Regardless of the shape of the source, predicting the expected reliability of the collected data by infiltrometers should facilitate soil hydraulic characterisation and also allow a more conscious use of the field data. The influence of the shape of the infiltration source (i.e., circular or square) and the analysis procedure of the steady-state infiltration data on the saturated hydraulic conductivity, Ks, of a sandy-loam soil was tested in this investigation. Circular and square surfaces sampled with the pressure infiltrometer (PI) yielded similar estimates of Ks (i.e., differing by a factor of 1.05-1.16, depending on the calculation method) when an equivalent radius was considered to geometrically describe the square source. With the simplified falling head (SFH) technique, the shape of the source was irrelevant (i.e., circular and square sources yielding Ks values that differed by a factor of 1.19), as theoretically expected. For the steady-state PI experiment, the twoponding depth approach yielded two times smaller Ks values than the one-ponding depth (OPD) approach, probably due to lower steady-state flow rates than those expected for the second phase of the two-level run. The conclusions were that: i) simple infiltrometer experiments (PI, SFH) can be carried out with square sources; and ii) the simplest PI run (OPD approach) is expected to yield the most reliable predictions of Ks. Sampling other soils is advisable in an attempt to make these conclusions of general validity.


2011 ◽  
Vol 312-315 ◽  
pp. 548-553 ◽  
Author(s):  
Yuan Wang ◽  
Khellil Sefiane

Single vapour bubble growth and heat transfer mechanism during flow boiling in a rectangular horizontal mini-channel were experimentally investigated. The hydraulic diameter of the channel was 1454 μm, with an aspect ratio (Win/din) of 10. Degassed FC-72 was used as the working liquid. In this paper, bubble equivalent radius was found to increase linearly till a critical time, beyond which the growth turned into exponential. Bubble growth rate increases with increasing heat flux. Heat transfer mechanisms of the bubble growth at different heat fluxes and mass fluxes were discussed. In addition, the relation between thermal and flow conditions with bubble temporal geometry was explored.


2013 ◽  
Vol 275-277 ◽  
pp. 1285-1291 ◽  
Author(s):  
Zheng Long Gao ◽  
Hong Fu Fan ◽  
Zhi Bin Gao

Unstable productivity analysis method was used to obtain the equivalent radius of 77 wells and the result shows that the equivalent radius ranges from 30 to 970m with an average value of 230m in McKittrick Hills. The difference range of the radius is mainly caused by varying formation properties, gas saturation, production time, etc. Permeability anisotropy changes the drainage from round to ellipse. The major axis and the minor axis of the ellipse are determined by the ratio of major and minor permeability. Current pressure distribution was obtained and was found to be consistent with the modified drainage results, which demonstrates that the unstable productivity analysis method is applicable in the study of gas well drainage radius. An interference well and an observation well’s model was constructed to study well interference quantitatively. When the well spacing is larger than 750m, the productivity will be reduced by 20%. The production rate of interference well is more sensitive to the cumulative production of observation well, when the production rate of interference well is below 16.8×104m3/d.


2015 ◽  
Vol 8 (5) ◽  
pp. 57-66
Author(s):  
H. T. Song ◽  
◽  
Y. P. Qin ◽  
J. S. Wu ◽  
S. Kong ◽  
...  

Radio Science ◽  
1966 ◽  
Vol 1 (7) ◽  
pp. 835-850 ◽  
Author(s):  
R. W. P. King ◽  
E. A. Aronson ◽  
C. W. Harrison

2021 ◽  
Author(s):  
Claudia Stephan ◽  
Alexis Mariaccia

<p>How convection couples to mesoscale vertical motion and what determines these motions is poorly understood. We diagnose profiles of area-averaged mesoscale divergence from measurements of horizontal winds collected by an extensive upper-air sounding network of a recent campaign over the western tropical North Atlantic, the Elucidating the Role of Clouds-Circulation Coupling in Climate (EUREC<sup>4</sup>A) campaign. Observed area-averaged divergence amplitudes scale approximately inversely with area equivalent radius. This functional dependence is also confirmed in reanalysis data and a global freely-evolving simulation run at 2.5 km horizontal resolution. Based on the numerical data it is demonstrated that the energy spectra of inertia gravity waves can explain the scaling of divergence amplitudes with area. At individual times, however, few waves can dominate the region. Nearly monochromatic tropospheric waves are diagnosed in the soundings by means of an optimized hodograph analysis. For one day, results suggest that an individual wave directly modulated the satellite observed cloud pattern. However, because such immediate wave impacts are rare, the systematic modulation of vertical motion due to inertia-gravity waves may be more relevant as a convection-modulating factor. We propose an analytic relationship between energy spectra and divergence amplitudes, which, if confirmed by future studies, could be used to design better external forcing methods for regional models.</p>


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