Characterization Methods – Hydraulic Conductivity - Revision history

Admin at 21:52, 26 April 2022

2022-04-26T21:52:07Z

Jhurley at 19:50, 11 November 2019

2019-11-11T19:50:04Z

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Debra Tabron at 20:52, 9 April 2019

2019-04-09T20:52:22Z

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Jhurley: /* Laboratory Grain Size Analyses on Core Samples */

2019-04-05T19:15:55Z

‎Laboratory Grain Size Analyses on Core Samples

Jhurley: /* Introduction */

2019-04-05T19:08:01Z

‎Introduction

Jhurley: /* Introduction */

2019-04-05T19:07:20Z

‎Introduction

Jhurley: /* DP Injection Logging */

2019-04-05T18:24:59Z

‎DP Injection Logging

Jhurley: /* Geophysical Methods */

2019-04-05T18:22:02Z

‎Geophysical Methods

Jhurley: /* Geophysical Methods */

2019-04-05T18:18:31Z

‎Geophysical Methods

Jhurley: /* Borehole Flowmeter Profiling */

2019-04-05T18:17:14Z

‎Borehole Flowmeter Profiling

@@ Line 9: / Line 9: @@
-'''CONTRIBUTOR(S):''' [[Dr. Gaisheng Liu]] and [[Dr. James Butler, Jr.]]
+'''Contributor(s):''' [[Dr. Gaisheng Liu]] and [[Dr. James Butler, Jr.]]
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 {|
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-| || [[File:Liu1w2 Eq5.png|330 px]]
+| ||[[File:Liu1w2 Eq5.png|330 px]]
 |-
 |where:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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 {|
 |-
-| || [[File:Liu1w2 Eq6.png|400 px]]
+| ||[[File:Liu1w2 Eq6.png|400 px]]
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 |where:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

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 Formation ''K'' can also be estimated from laboratory grain size analyses on sediment or core samples. A number of empirical and theoretical relationships have been developed for estimation of ''K'' from grain-size statistics. For example, ''K'' can be computed using the relationship developed by Hazen<ref name="Freeze1979" />,
-[[File:Liu1w2 Eq5.png|center|330 px]]
 {|
 |-
-|where:
+| || [[File:Liu1w2 Eq5.png|330 px]]
 |-
 |''d<sub>10</sub>''||is the particle diameter at which 10% of the sample’s mass is comprised of particles with a diameter smaller than this value, and
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 More theoretically-based relationships between grain sizes and ''K'' have been developed from the Kozeny-Carman equation that relates formation ''K'' with porosity and grain sizes assuming the porous space can be modeled as tortuous tubes of different diameters. For example, the following relationship can be used to estimate ''K''<ref>Bear, J., 1972. Dynamics of Fluids in Porous Media, Dover, 764 pp</ref>,
 {|
 |-
-|where:
+| || [[File:Liu1w2 Eq6.png|400 px]]
 |-
 |''n''||is porosity,

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 ==Introduction==
-[[File:Liu1w2 Fig1.png|thumb|70 px|Figure 1. Schematic of Darcy’s Law flow experiment.]]
+[[File:Liu1w2 Fig1.png|thumb|700 px|Figure 1. Schematic of Darcy’s Law flow experiment.]]
 Hydraulic conductivity is mathematically defined as the parameter ''K'' in Darcy’s Law<ref>Darcy, H. (1856). Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris. [https://doi.org/10.1029/2001wr000727 doi: 10.1029/2001WR000727]</ref> (see Fig. 1),

← Older revision		Revision as of 19:07, 5 April 2019
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	==Introduction==		==Introduction==
		+	[[File:Liu1w2 Fig1.png\|thumb\|70 px\|Figure 1. Schematic of Darcy’s Law flow experiment.]]
	Hydraulic conductivity is mathematically defined as the parameter ''K'' in Darcy’s Law<ref>Darcy, H. (1856). Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris. [https://doi.org/10.1029/2001wr000727 doi: 10.1029/2001WR000727]</ref> (see Fig. 1),		Hydraulic conductivity is mathematically defined as the parameter ''K'' in Darcy’s Law<ref>Darcy, H. (1856). Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris. [https://doi.org/10.1029/2001wr000727 doi: 10.1029/2001WR000727]</ref> (see Fig. 1),
−	~~[[File:Liu1w2 Fig1.png\|left\|thumb\|600 px\|Figure 1. Schematic of Darcy’s Law flow experiment.]]~~

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 <div><ul>
-<li style="display: inline-block;">[[File:Liu1w2 Fig6A.png|thumb|Figure 6A. Schematic of the DPIL with a Screen Attached to the Probe Rod at its Lower End<ref name="Liu2012" />.]]</li>
+<li style="display: inline-block;">[[File:Liu1w2 Fig6A.png|thumb|200 px|Figure 6A. Schematic of the DPIL with a Screen Attached to the Probe Rod at its Lower End<ref name="Liu2012" />.]]</li>
 <li style="display: inline-block; middle:">[[File:Liu1w2 Fig6B.png|thumb|400 px|Figure 6B. Artistic Rendering of the HPT (continuous DPIL probe combined with an EC Wenner array) <ref name="Lessoff2010" />.]]</li>
 <li style="display: inline-block;">[[File:Liu1w2 Fig6C.png|thumb|600 px|Figure 6C. Six Example DPIL (red curve) ''K'' Profiles Calibrated by Collocated Direct Push Permeameter Tests (blue bars) at the MacroDispersion Experiment (MADE) Site, Columbus, MS. The dashed curves represent the upper ''K'' limit for continuous DPIL under the given tool operating procedure<ref name="Liu2009" />.]]</li>

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 <div><ul>
 <li style="display: inline-block;">[[File:Liu1w2 Fig9A.png|thumb|left|Figure 9A. Measurement Domain around a NMR Borehole Probe]]</li>
-<li style="display: inline-block;">[[File:Liu1w2 Fig9B.png|thumb|Figure 9B. NMR Responses as a Function of Pore Size, Where ''A'' is the Initial Magnetization, T<sub>2</sub> is NMR Relaxation Time<ref name="Walsh2011" />.]]</li>
+<li style="display: inline-block;">[[File:Liu1w2 Fig9B.png|thumb|450 px|Figure 9B. NMR Responses as a Function of Pore Size, Where ''A'' is the Initial Magnetization, T<sub>2</sub> is NMR Relaxation Time<ref name="Walsh2011" />.]]</li>
-<li style="display: inline-block;">[[File:Liu1w2 Fig9C.png|thumb|Figure 9C. Comparison of NMR and DPP ''K'' estimates at two GEMS locations. The dash lines show the range of the NMR ''K'' estimates due to the uncertainty in the empirical parameters used in the pore size - ''K'' relationship<ref name="Knight2016" />.]]</li>
+<li style="display: inline-block;">[[File:Liu1w2 Fig9C.png|thumb|550 px|Figure 9C. Comparison of NMR and DPP ''K'' estimates at two GEMS locations. The dash lines show the range of the NMR ''K'' estimates due to the uncertainty in the empirical parameters used in the pore size - ''K'' relationship<ref name="Knight2016" />.]]</li>
 </ul></div>

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 {|
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-| || [[File:Liu1w2 Eq1.png|310 px]]
+| ||[[File:Liu1w2 Eq1.png|310 px]]
 |-
 |where:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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 {|
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-| || [[File:Liu1w2 Eq2.png|290 px]]
+| ||[[File:Liu1w2 Eq2.png|290 px]]
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 |where:
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 {|
 |-
-|  || [[File:Liu1w2 Eq3.png|300 px]]
+| ||[[File:Liu1w2 Eq3.png|300 px]]
 |-
 |where:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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 {|
 |-
-| || [[File:Liu1w2 Eq4.png|290 px]]
+| ||[[File:Liu1w2 Eq4.png|290 px]]
 |-
 |where:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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 ==Indirect Approaches==
 ===Geophysical Methods===
-Estimates for formation ''K'' can also be inferred from the measurement of more readily evaluated geophysical properties using empirical, often site-specific, relationships. The geophysical properties that may be used for ''K'' estimation include, but are not limited to, electrical conductivity (EC) (or the reverse, electrical resistivity), the hydrogen response to nuclear magnetic resonance (NMR), and natural gamma radiation.  In addition to ''K'' estimation, geophysical methods have also been used for many purposes in environmental site investigation, assessment and monitoring (see related article –[http://www.enviro.wiki/index.php?title=Geophysical_Methods Geophysical Methods].
+Estimates for formation ''K'' can also be inferred from the measurement of more readily evaluated geophysical properties using empirical, often site-specific, relationships. The geophysical properties that may be used for ''K'' estimation include, but are not limited to, electrical conductivity (EC) (or the reverse, electrical resistivity), the hydrogen response to nuclear magnetic resonance (NMR), and natural gamma radiation.  In addition to ''K'' estimation, geophysical methods have also been used for many purposes in environmental site investigation, assessment and monitoring (see related article –[http://www.enviro.wiki/index.php?title=Geophysical_Methods Geophysical Methods]).
 Borehole EC logging measures vertical variations in the bulk EC of the surrounding formation, which can then be used to estimate ''K'' based on empirical relationships<ref>Purvance, D.T. and Andricevic, R., 2000. On the electrical‐hydraulic conductivity correlation in aquifers. Water Resources Research, 36(10), pp.2905-2913. [https://doi.org/10.1029/2000wr900165 doi: 10.1029/2000wr900165]</ref><ref>Slater, L. and Lesmes, D.P., 2002. Electrical‐hydraulic relationships observed for unconsolidated sediments. Water Resources Research, 38(10), pp.31-1. [https://doi.org/10.1029/2001wr001075 doi:10.1029/2001WR001075]</ref>. EC has been adapted to DP equipment for more efficient assessment of subsurface conditions than the approaches that rely on existing wells<ref>Christy, C.D., Christy, T.M. and Wittig, V., 1994, May. A percussion probing tool for the direct sensing of soil conductivity. In Proceedings of the 8th National Outdoor Action Conference (Vol. 38, pp. 1-394). Dublin, Ohio: National Ground Water Association.</ref>. Variations in the EC of saturated media are primarily a function of pore-fluid chemistry, clay content, and total porosity. If variations in pore-fluid chemistry can be neglected, EC profiling can be used to delineate the major hydrostratigraphic features, and thus large-scale variations in ''K''<ref name="Schulmeister2003">Schulmeister, M.K., Butler, J.J., Healey, J.M., Zheng, L., Wysocki, D.A. and McCall, G.W., 2003. Direct‐push electrical conductivity logging for high‐resolution hydrostratigraphic characterization. Groundwater Monitoring & Remediation, 23(3), pp.52-62. [http://dx.doi.org/10.1111/j.1745-6592.2003.tb00683.x doi: 10.1111/j.1745-6592.2003.tb00683.x]</ref>. However, when electrically-conductive clay is absent, EC profiling generally provides little information about vertical variations in ''K'' in silts, sands and gravels.

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 The most common method of estimating ''K'' from borehole flowmeter profiles is based on the assumption that the lateral flow rate of an interval (zone between flow-rate measurements) is proportional to the ''K'' and thickness of that interval in a well fully screened in a perfectly layered aquifer,
 {|
 |-
-|where:
+| || [[File:Liu1w2 Eq4.png|290 px]]
 |-
 |''K<sub>i</sub>''||is the ''K'' of test interval ''i'';