Fractional Dimension Analysis of Constant-Pressure Well Tests

1991 ◽  
Author(s):  
T.W. Doe
Keyword(s):  
Constant Pressure ◽  
Fractional Dimension ◽  
Dimension Analysis ◽  
Well Tests

Well Test Analysis for a Well in a Constant Pressure Square

1972 ◽  
Author(s):  
Anil Kumar ◽  
H. J. Ramey
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Initial Pressure ◽  
Fluid Injection ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Water Influx ◽  
Mean Pressure ◽  
Well Tests

Abstract Very little information exists for analyzing well tests wherein a part of the drainage boundary is under pressure support from water influx or fluid injection. An idealization is the behavior of a well in the center of a square whose outer boundary remains at constant pressure. A study of this system indicated important differences from the behavior of a well in a closed outer boundary square, the conventional system. At infinite shut in, the constant- pressure boundary case well will reach the initial pressure of the system, rather than a mean pressure resulting from depletion. But it is possible to compute the mean pressure in the constant-pressure case at any time during shut in. Interpretative graphs for analyzing drawdown and buildup pressures are presented and discussed. This case is also of interest in analysis of well tests obtained from developed five-spot fluid injection patterns. Introduction Well-test analysis has become a widely used tool for reservoir engineers in the last twenty years. The initial theory was reported by Horner1 for unsteady flow of single phase fluids of small but constant compressibility to a well producing at a constant rate in -infinite and closed boundary reservoirs. Extension of the theory to the finite reservoir case involves specification of the outer boundary condition. The two most commonly observed conditions are: (1) no flow at the outer boundary corresponding to a closed or depletion reservoir, and (2) constant pressure at the outer boundary corresponding to complete water-drive.

Well-Test Analysis for a Well in a Constant-Pressure Square

1974 ◽  
Vol 14 (02) ◽  
pp. 107-116 ◽  
Author(s):  
Anil Kumar ◽  
Henry J. Ramey
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Fluid Injection ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Mean Pressure ◽  
Long Time ◽  
Single Well ◽  
Well Tests

Abstract Very little information exists for analyzing well tests wherein a part of the drainage boundary is under pressure support from water influx or fluid injection. An idealization is the behavior of a well in the center of a square whose outer boundary remains at constant pressure. A study of this system indicated important differences from the behavior of a well in a square with a closed outer boundary, the conventional system. At infinite shut-in, the well with a constant-pressure boundary will reach the initial pressure of the system, rather than a mean pressure resulting from depletion. It is possible to compute the mean pressure in the constant-pressure case at any time during shut-in. Interpretative graphs for analyzing drawdown and buildup pressures are presented and discussed. This case is also of interest in analyzing well tests obtained from developed five-spot fluid-injection patterns. Introduction Moore at. first demonstrated the application of transient flow theory to individual well behavior in 1931. Classic studies by Muskat, Elkins, and Arps in the 1930's and 1940's set the stage for two important papers in 1950 that clearly elucidated the basics of modern well-test analysis. One paper by Horner 5 summarized methods for analyzing transient pressure data from wells in infinite reservoirs (new wells in large reservoirs), and a well in a closed, circular reservoir under depletion (fully developed fields). The second paper by Miller, Dyes, and Hutchinsons considered two cases for wells assumed to have produced a long time before shut-in for pressure buildup. One case assumed a closed circular drainage boundary, and the other case assumed a circular drainage boundary at constant pressure. The former would represent annual well tests for fully developed fields, and the latter would represent wells under full water drive in single-well reservoirs. Since 1950, several hundred papers and a monograph have developed the behavior of a constant-rate well in a closed drainage shape of almost any geometry. Key in this development was a classic study by Matthews, Brons, and Hazebroek. The constant-pressure outer-boundary drainage region problem introduced by Miller-Dyes-Hutchinson was reviewed by Perrine in 1955, discussed by Hazekoek el al. in 1958 in connection with five-spot injection patterns, and mentioned briefly by Dietz in 1965. The only other studies dealing with water-drive conditions (constant-pressure outer boundaries) appear in Ref. 7 (Page 44) and in papers by Earlougher et al., published in 1968. It is clear that this case was eitherconsidered totally unimportant, orstudiously avoided. Almost all effort was expended on studying closed outer boundary (depletion) systems.Another problem concerned the conventional assumptions involved in developing well-test analysis method. Even for the common closed (depletion) systems, field applications raised the question of the importance of assumptions. Homer method of graphing assumed the well had been produced a short time, whereas the Miller-Dyes-Hutchinson method assumed that production was long enough to reach pseudosteady state -a long time in many cases. Engineers involved in applications were further confused by differences in methods, as well as by the importance of the assumptions required for analytical solutions that established welltest methods. Recently, Ramey and Cobb showed that an empirical approach could be used to avoid assumptions (which were sufficient but unnecessary) inherent in many previous analytical studies. It was decided to apply this method to the limiting case of a well in a full-water-drive, single-well reservoir - a well in a constant-pressure square. This case is a rarity not often seen in practice. It is closely approached by either an injector or a producer in a developed fluid-injection pattern, by a single injector in an aquifer gas-injection storage test, or by some single-well reservoirs in extensive aquifers.The main point is that a well in a constant-pressure square sets a limiting condition similar to a full water drive. The more common case of a well in a partial-water-drive reservoir should lie between this behavior and that of a closed square. SPEJ P. 107^

scholarly journals Constant pressure well tests in infinite radial reservoirs

1983 ◽  
Vol 4 (6) ◽  
pp. 589-603
Author(s):  
J. Kleppe ◽  
H.M. Cekirge
Keyword(s):  
Constant Pressure ◽  
Well Tests

FRACTIONAL DIMENSIONALITY ON SELF-TRAPPED FRENKEL EXCITONS IN MOLECULAR CRYSTALLITES

2000 ◽  
Vol 14 (11) ◽  
pp. 1209-1224
Author(s):  
MASUMI TAKESHIMA ◽  
ATSUO H. MATSUI
Keyword(s):  
Tight Binding ◽  
The Self ◽  
Molecular Chain ◽  
Fractional Dimension ◽  
High Threshold ◽  
Dimension Analysis ◽  
Self Trapping ◽  
Frenkel Excitons ◽  
2D And 3D

Self-trapped exciton characteristics in microcrystallites are discussed in terms of the fractional dimension. The concept of the fractional dimension is introduced since microcrystallites are formed with various side lengths where the concept of the integral dimensions (1D, 2D and 3D) are not significant. The theory is based on the tight-binding approach. Uniqueness in self-trapping appears in the magnitude of the fractional dimension. Exceptionally high threshold for self-trapping is found when (1) a thin crystallite is made of two layers, or (2) a crystallite is formed by two molecular chains, or (3) a linear molecular chain is made of four molecules. The fractional dimension analysis thus offers a wider overview of the self-trapped exciton character than the analysis that can be done using intergral dimensions only.

Fractional dimension analysis of self-trapped Frenkel excitons in molecular microcrystallites

2000 ◽  
Vol 87-89 ◽  
pp. 263-265
Author(s):  
Masumi Takeshima ◽  
Ken-ichi Mizuno ◽  
Atsuo H Matsui
Keyword(s):  
Fractional Dimension ◽  
Dimension Analysis ◽  
Frenkel Excitons

Using corpora in depth psychology: a trigram-based analysis of a corpus of fetish fantasies

Corpora ◽  
2012 ◽  
Vol 7 (1) ◽  
pp. 69-90 ◽  
Author(s):  
Andrew Wilson
Keyword(s):  
Depth Psychology ◽  
Constant Pressure ◽  
Psychological Theory ◽  
Evidence Base ◽  
Future Research ◽  
German Language ◽  
Alternative Theory ◽  
Depth Psychological ◽  
Psychological Constructs ◽  
Quantitative Linguistics

Contemporary depth psychology is under constant pressure to demonstrate and strengthen its evidence base. In this paper, I show how the analysis of large corpora can contribute to this goal of developing and testing depth-psychological theory. To provide a basis for evaluating statements about foot and shoe fetishism, I analyse the thirty-six most frequent three-word phrases (or trigrams) in a corpus of about 1.6 million words of amateur fetish stories written in the German language. Zipfian methods from quantitative linguistics are used to specify the number of phrases for analysis and I argue that these reflect the core themes of the corpus. The analysis reveals three main dimensions. First, it corroborates the observations of the early sexologists that foot and shoe fetishism is very closely intertwined with sadomasochism. Secondly, it shows that genitalia-related phrases are also common, but an examination of their contexts questions Freud's theory that fetishism results from an assumption of female castration. Thirdly, it reveals that the mouth also plays a key role; however, the frequent co-presence of genitalia references in the same texts does not seem to support straightforwardly the most common alternative theory of fetishism based on object relations. Future research could valuably extend this approach to other fetishes and, in due course, to other depth-psychological constructs.

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