Lecture 10
Measuring Permeability and Aquifer
Properties
Fetter 4.4.3
Return to Grain Size Distribution Curves |
Uniformity coefficient - a measure of how well or poorly sorted a sediment is.
 |
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| Cu = uniformity coefficient | ||
| d60 = grain size that is 60% finer by weight | ||
| d10 = grain size that is 10% finer by weight (effective grain size) | ||
for this
example  |
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Permeability from grain size
| 1) As median grain size increases, permeability increases à larger pore openings. | |
| 2) Permeability decreases for more poorly sorted sediments. | |
| 3) Coarser samples show greater decreases in permeability with increases in standard deviation of grain sizes than fine samples. |
Grain size distribution can be used to:
| 1.) Determine filter pack. | ||
| 2.) Determine screen slot size. | ||
| 3.) Estimate hydraulic conductivity | ||
| -designing aquifer tests | ||
| -computer flow modeling | ||
| 4.) Oil reservoir characterization | ||
| 5.) Geotechnical analysis | ||
Hazen Method (Hazen, 1911)
| - Empirical | |||
| - Use with sands where d10 is 0.1 to 3.0mm | |||
| - Uniform coefficient < 5 | |||
| K=C(d10)2 | |||
| K = Hydraulic Conductivity (L/T)(cm/s) | |||
| d10 = Effective grain size (L)(mm) | |||
C = is a coefficient based on
| Very fine sand, poorly sorted | 40-80 | |
| Fine sand with appreciable fines | 40-80 | |
| Medium sand, well sorted | 80-120 | |
| Coarse sand, poorly sorted | 80-120 | |
| Coarse sand, well sorted, clean | 120-150 |
| Other Techniques | ||
| 1.) Kruger, Justin and Hinds | ||
| 2.) Slichter | medium sand | |
| 3.) Kozeny | ||
| 4.) Terzaghi | coarse sand and gravel | |
| 5.) Masch and Denny | ||
| 6.) Shepard | ||
Most have a temperature correction and porosity correction.
K - typically varies two orders of magnitude within the same hydrogeologic unit.
| -because there is variation over orders of magnitude, an arithmetic mean is biased toward more permeable values. |
Use - Geometric mean = mean(ln(k)) - an unbiased estimator
Example -
| K (cm/s) | ln(k) | |
| 2.17 x 10-2 | -3.83 | |
| 2.58 x 10-2 | -3.66 | |
| 2.55 x 10-3 | -5.97 | |
| 1.67 x 10-1 | -1.79 | |
| 9.50 x 10-4 | -6.96 | |
| Sum | 2.18 x 10-1 | -22.21 |
| Geometric mean = mean ln(k) |  |
| e-4.44 = 1.18 x 10-2 cm/s | |
| Arithmetic mean |  |
| Measuring K | Fetter 4.5 | |
| 1.) Grain Size analyses - small sample | ||
| 2.) Permeameter - measure in lab, small sample | ||
| 3.) Pumping test - stress an aquifer | ||
| 4.) Injection test- (slug) - stress an aquifer | ||
| 5.) Flow nets - a large regional flow system is stressed | ||
Ranges in Permeability and Transmissivity
Properties of Aquifers |
Fetter 4.8 |
|
Porosity, intrinsic permeabilty and K describe properties of earth materials and their
ability to transmit water.
Transmissivity- The rate at which water of a specific density and viscosity is transmitted
through a unit width of an aquifer or confining bed under a unit hydraulic gradient. (1)
T = Kb |
|
(ft2/d) = (ft/d) (ft) |
|
(gal/d/ft) = (g/d/ft2) (ft) |
|
b = saturated thickness |
K = Hydraulic conductivity |
If an Aquifer has more than one Layer-
|
|
|
Where Ti = Transmissivity of each layer |
Schematic diagram showing the concepts of hydraulic conductivity and transmissivity.
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ENV 302 - Lectures
