(Created page with "==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviatio...")
 
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
+
== Abstract ==
  
−
Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
+
Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic aquifer and under steady state flow conditions, drawdown <math>s</math> is directly related to the pumping rate <math>Q</math> through transmissivity <math>T</math>. In real, nonhomogeneous aquifers, <math>s</math> and <math>Q</math> are still directly related, now through a value called equivalent transmissivity <math>T_{eq}</math>. In this context, <math>T_{eq}</math> is defined as the value that best fits Thiem's equation and would, for example, be the transmissivity assigned to the well location in the classical interpretation of a steady state pumping test. This equivalent or upscaled transmissivity is clearly not a local value but is some representative value of a certain area surrounding the well. In this paper we present an analytical solution for upscaling transmissivities under radially convergent steady state flow conditions produced by constant pumping from a well of radius <math>r_w</math> in a heterogeneous aquifer based upon an extension of Thiem's equation. Using a perturbation expansion, we derive a second‐order expression for <math>T_{eq}</math> given as a weighted average of the fluctuations in log <math>T</math> throughout the domain. This expression is compared to other averaging formulae from the literature, and differences are pointed out. <math>T_{eq}</math> depends upon an infinite series which may be expressed in terms of coefficients of the finite Fourier transform of the log transmissivity function. Sufficient conditions for convergence of this series are examined. Finally, we show that our solution agrees with existing analytical ones to second order and test the solution with a numerical example
  
−
An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself. -->==
+
==Full Document==
  
−
 
+
<pdf>Media:Draft_Samper_895484853_6956_1998WR900056.pdf</pdf>
−
 
+
−
 
+
−
==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
+
−
 
+
−
Most of the documents in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific publications in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.
+
−
 
+
−
 
+
−
2.1 Subsections
+
−
 
+
−
Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
+
−
 
+
−
 
+
−
2.2 General guidelines
+
−
 
+
−
Some general guidelines that should be followed in your manuscripts are:
+
−
 
+
−
*  Avoid hyphenation at the end of a line.
+
−
 
+
−
*  Symbols denoting vectors and matrices should be indicated in bold type. Scalar variable names should normally be expressed using italics.
+
−
 
+
−
*  Use decimal points (not commas); use a space for thousands (10 000 and above).
+
−
 
+
−
*  Follow internationally accepted rules and conventions. In particular use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI.
+
−
 
+
−
 
+
−
2.3 Tables, figures, lists and equations
+
−
 
+
−
Please insert tables as editable text and not as images. Tables should be placed next to the relevant text in the article. Number tables consecutively in accordance with their appearance in the text and place any table notes below the table body. Be sparing in the use of tables and ensure that the data presented in them do not duplicate results described elsewhere in the article.
+
−
 
+
−
Graphics may be inserted directly in the document and positioned as they should appear in the final manuscript.
+
−
 
+
−
Number the figures according to their sequence in the text. Ensure that each illustration has a caption. A caption should comprise a brief title. Keep text in the illustrations themselves to a minimum but explain all symbols and abbreviations used. Try to keep the resolution of the figures to a minimum of 300 dpi. If a finer resolution is required, the figure can be inserted as supplementary material
+
−
 
+
−
For tabular summations that do not deserve to be presented as a table, lists are often used. Lists may be either numbered or bulleted. Below you see examples of both.
+
−
 
+
−
1. The first entry in this list
+
−
 
+
−
2. The second entry
+
−
 
+
−
2.1. A subentry
+
−
 
+
−
3. The last entry
+
−
 
+
−
* A bulleted list item
+
−
 
+
−
* Another one
+
−
 
+
−
You may choose to number equations for easy referencing. In that case they must be numbered consecutively with Arabic numerals in parentheses on the right hand side of the page. Below is an example of formulae that should be referenced as eq. (1].
+
−
 
+
−
 
+
−
2.4 Supplementary material
+
−
 
+
−
Supplementary material can be inserted to support and enhance your article. This includes video material, animation sequences, background datasets, computational models, sound clips and more. In order to ensure that your material is directly usable, please provide the files with a preferred maximum size of 50 MB. Please supply a concise and descriptive caption for each file. -->==
+
−
 
+
−
 
+
−
 
+
−
 
+
−
==3 Bibliography<!--
+
−
Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the document is [1], the second [2], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen
+
−
 
+
−
You should ensure that all references are cited in the text and that the reference list. References should preferably refer to documents published in Scipedia. Unpublished results should not be included in the reference list, but can be mentioned in the text. The reference data must be updated once publication is ready. Complete bibliographic information for all cited references must be given following the standards in the field (IEEE and ISO 690 standards are recommended). If possible, a hyperlink to the referenced publication should be given. See examples for Scipedia’s articles [1], other publication articles [2], books [3], book chapter [4], conference proceedings [5], and online documents [6], shown in references section below. -->==
+
−
 
+
−
 
+
−
 
+
−
 
+
−
==4 Acknowledgments<!-- Acknowledgments should be inserted at the end of the document, before the references section. -->==
+
−
 
+
−
 
+
−
 
+
−
 
+
−
==5 References<!--[1] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: http://www.scipedia.com/ucode.
+
−
 
+
−
[2] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Volume number, first page-last page.
+
−
 
+
−
[3] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.
+
−
 
+
−
[4] Author of Part, D. (Year). Title of chapter or part. In A. Editor & B. Editor (Eds.), Title: Subtitle of book (edition, inclusive page numbers). Place of publication: Publisher.
+
−
 
+
−
[5] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.
+
−
 
+
−
[6] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: http://www.scipedia.com/document.pdf.
+
−
-->==
+

Latest revision as of 09:48, 17 March 2020

Abstract

Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic aquifer and under steady state flow conditions, drawdown Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): s 

is directly related to the pumping rate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): Q
through transmissivity Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): T

. In real, nonhomogeneous aquifers, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): s 

and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): Q
are still directly related, now through a value called equivalent transmissivity Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): T_{eq}

. In this context, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): T_{eq} 

is defined as the value that best fits Thiem's equation and would, for example, be the transmissivity assigned to the well location in the classical interpretation of a steady state pumping test. This equivalent or upscaled transmissivity is clearly not a local value but is some representative value of a certain area surrounding the well. In this paper we present an analytical solution for upscaling transmissivities under radially convergent steady state flow conditions produced by constant pumping from a well of radius Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): r_w
in a heterogeneous aquifer based upon an extension of Thiem's equation. Using a perturbation expansion, we derive a second‐order expression for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): T_{eq}
given as a weighted average of the fluctuations in log Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): T
throughout the domain. This expression is compared to other averaging formulae from the literature, and differences are pointed out. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): T_{eq}
depends upon an infinite series which may be expressed in terms of coefficients of the finite Fourier transform of the log transmissivity function. Sufficient conditions for convergence of this series are examined. Finally, we show that our solution agrees with existing analytical ones to second order and test the solution with a numerical example

Full Document

The PDF file did not load properly or your web browser does not support viewing PDF files. Download directly to your device: Download PDF document
Back to Top
GET EPUB

Document information

Published on 01/01/1999

DOI: 10.1029/1998WR900056
Licence: CC BY-NC-SA license

Document Score

0

Views 3
Recommendations 0

Share this document

claim authorship

Are you one of the authors of this document?

I am an author