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'''Hydraulic conductivity''', symbolically represented as <math>K</math>, is a property of vascular plants, soils and rocks, that describes the ease with which a fluid (usually water) can move through pore spaces or fractures. It depends on the [[intrinsic permeability]] of the material and on the degree of [[Saturation (chemistry)|saturation]], and on the [[density]] and [[viscosity]] of the fluid. Saturated hydraulic conductivity, ''K<sub>sat</sub>'', describes water movement through saturated media.
== the entire forest ==


Typical ranges of hydraulic conductivity for different soils can be found on [http://www.geotechdata.info/parameter/permeability.html Geotechdata.info database].
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</ul>


==Methods of determination==
== palm slowly recovered ==
[[File:HydrCondTable.GIF|thumb|450px|Overview of determination methods]]
There are two broad categories of determining hydraulic conductivity: 
*''Empirical'' approach by which the hydraulic conductivity is correlated to soil properties like [[Porosity|pore size]] and [[particle size (grain size)]] distributions, and [[soil texture]]
*''Experimental'' approach by which the hydraulic conductivity is determined from hydraulic experiments using [[Darcy's law]]


The experimental approach is broadly classified into:
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*[[Laboratory]] tests using soil samples subjected to hydraulic [[experiment]]s
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*''Field tests'' (on site, in situ) that are differentiated into:
<ul>
**small scale field tests, using observations of the water level in cavities in the soil
 
**large scale field tests, like [[pump test]]s in [[Water well|wells]] or by observing the functioning of existing horizontal [[drainage]] systems.
  <li>[http://www.musashiya-teikoku.com/aska/aska.cgi http://www.musashiya-teikoku.com/aska/aska.cgi]</li>
The small scale field tests are further subdivided into:
 
*[[Infiltration (hydrology)|infiltration]] tests in cavities ''above'' the [[water table]]
  <li>[http://1109525177a.a170.cnaaa9.com/forum.php?mod=viewthread&tid=308762 http://1109525177a.a170.cnaaa9.com/forum.php?mod=viewthread&tid=308762]</li>
*[[slug test]]s in cavities ''below'' the [[water table]]
 
  <li>[http://petro-offshore.com/plus/feedback.php?aid=477 http://petro-offshore.com/plus/feedback.php?aid=477]</li>
 
</ul>


==Estimation by empirical approach==
== but it is extremely difficult to practice more difficult ==


===Estimation from grain size===
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[[Allen Hazen]] derived an [[Empirical method|empirical]] formula for approximating hydraulic conductivity from grain size analyses:
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:<math>K = C (D_{10})^2</math>
<ul>
where
 
:<math>C</math> Hazen's empirical coefficient, which takes a value between 0.4 and 10.0 (depending on literatures), with an average value of 1.0. NB This should have units. A.F. Salarashayeri & M. Siosemarde give C as usually taken between 1.0 and 1.5, with D in mm and K in cm/s.
  <li>[http://www.bonkureshougatu.com/6/clip.cgi http://www.bonkureshougatu.com/6/clip.cgi]</li>
:<math>D_{10}</math> is the [[diameter]] of the 10 [[percentile]] grain size of the material
 
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</ul>


===Pedotransfer function===
== and get the sea flame ==
A [[pedotransfer function]] (PTF) is a specialized empirical estimation method, used primarily in the [[soil science]]s, however has increasing use in hydrogeology.<ref>{{cite journal |author=Wösten, J.H.M., Pachepsky, Y.A., and Rawls, W.J. |title=Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics |year=2001 |volume=251 |issue=3-4 |pages=123–150 |doi=10.1016/S0022-1694(01)00464-4 |journal=[[Journal of Hydrology]] |bibcode = 2001JHyd..251..123W }}</ref> There are many different PTF methods, however, they all attempt to determine soil properties, such as hydraulic conductivity, given several measured soil properties, such as soil [[particle size]], and [[bulk density]].


==Determination by experimental approach==
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There are relatively simple and inexpensive laboratory tests that may be run to determine the hydraulic conductivity of a soil:  constant-head method and falling-head method.
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  <ul>
===Laboratory methods===
 
 
  <li>[http://www.greenfiltering.com/plus/feedback.php?aid=147 http://www.greenfiltering.com/plus/feedback.php?aid=147]</li>
====Constant-head method====
 
The [http://www.geotechdata.info/geotest/constant-head-permeability-test.html constant-head method] is typically used on granular soil. This procedure allows water to move through the soil under a steady state head condition while the quantity (volume) of water flowing through the soil specimen is measured over a period of time.  By knowing the quantity <math>Q</math> of water measured, length <math>L</math> of specimen, cross-sectional area <math>A</math> of the specimen, time <math>t</math> required for the quantity of water <math>Q</math> to be discharged, and head <math>h</math>, the hydraulic conductivity can be calculated:
  <li>[http://www.xingecm.com/home.php?mod=space&uid=25135 http://www.xingecm.com/home.php?mod=space&uid=25135]</li>
 
 
:<math>\frac{Q}{t} = Av\,</math>
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where <math>v</math> is the flow velocity. Using [[Darcy's Law]]:
 
:<math>v = Ki\,</math>
  </ul>
and expressing the hydraulic gradient <math>i</math> as:
:<math>i = \frac{h}{L}</math>
where <math>h</math> is the difference of hydraulic head over distance <math>L</math>, yields:
:<math>\frac{Q}{t} = \frac{AKh}{L}</math>
Solving for <math>K</math> gives:
:<math>K = \frac{QL}{Aht}</math>
 
====Falling-head method====
The [http://www.geotechdata.info/geotest/falling-head-permeability-test falling-head method] is  totally different than the constant head methods in its initial setup; however, the advantage to the falling-head method is that it can be used for both fine-grained and coarse-grained soils.  The soil sample is first saturated under a specific head condition.  The water is then allowed to flow through the soil without maintaining a constant pressure head.<ref>Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey:  Prentice Hall, 2001  ISBN 0-13-025517-3</ref>
 
:<math>K = \frac{2.3aL}{At}\log\left(\frac{h_1}{h_2}\right)</math>
 
===In-situ (field) methods===
 
====Augerhole method====
There are also in-situ methods for measuring the hydraulic conductivity in the field.<br>
When the water table is shallow, the augerhole method, a [[slug test]], can be used for determining the hydraulic conductivity below the water table. <br>
The method was developed by Hooghoudt (1934) <ref>S.B.Hooghoudt, 1934, in Dutch. Bijdrage tot de kennis van enige natuurkundige grootheden van de grond. Verslagen Landbouwkundig Onderzoek No. 40 B, p. 215-345.</ref> in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948).<ref>C.H.M. van Bavel and D. Kirkham, 1948. Field measurement of soil permeability using auger holes. Soil. Sci. Soc. Am. Proc 13:90-96.</ref> <br />
The method uses the following steps:
#an augerhole is perforated into the soil to below the water table
#water is bailed out from the augerhole
#the rate of rise of the water level in the hole is recorded
#the K-value is calculated from the data as:<ref name="Oost">Determination of the Saturated Hydraulic Conductivity. Chapter 12 in: H.P.Ritzema (ed., 1994) Drainage Principles and Applications, ILRI Publication 16, p.435-476. International Institute for Land Reclamation and Improvement, Wageningen (ILRI), The Netherlands. ISBN 90-70754-33-9. Free download from: [http://www.waterlog.info/articles.htm] , under nr. 6, or directly as PDF : [http://www.waterlog.info/pdf/chap12.pdf]</ref>
 
:K = F (Ho-Ht) <big>/</big> t
[[File:PANAZ1.JPG|thumb|200px|Cumulative frequency distribution (lognormal) of hydraulic conductivity (X-data)]]
 
where: K  = horizontal saturated hydraulic conductivity (m/day), H = depth of the waterlevel in the hole relative to the water table in the soil (cm), Ht = H at time t, Ho = H at time t = 0, t = time (in seconds) since the first measurement of H as Ho, and F is a factor depending on the geometry of the hole:
 
:F = 4000<math>r</math> <big>/</big> <math>h'</math>(20+D/<math>r</math>)(2&minus;<math>h'</math>/D)
 
where: <math>r</math> = radius of the cylindrical hole (cm), <math>h'</math> is the average depth of the water level in the hole relative to the water table in the soil (cm), found as <math>h'</math>=(Ho+Ht)/2, and D is the depth of the bottom of the hole relative to the water table in the soil (cm).
 
The picture shows a large variation of K-values measured with the augerhole method in an area of 100 ha.<ref>Drainage research in farmers' fields: analysis of data. Contribution to the project “Liquid Gold” of the International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. Free download from : [http://www.waterlog.info/articles.htm] , under nr. 2, or directly as PDF : [http://www.waterlog.info/pdf/analysis.pdf]</ref> The ratio between the highest and lowest values is 25. The cumulative frequency distribution is [[lognormal]] and was made with the [[cumulative frequency analysis|CumFreq]] program.
 
==Related magnitudes==
 
===Transmissivity===
The transmissivity is a measure of how much water can be transmitted horizontally, such as to a pumping well. <br />
:<small>''Transmissivity'' should not be confused with the similar word [[transmittance]] used in [[optics]], meaning the fraction of incident light that passes through a sample.''</small>
An [[aquifer]] may consist of <math>n</math> soil layers. The transmissivity for horizontal flow <math>T_i</math> of the <math>i-th</math> soil layer with a ''saturated'' thickness <math>d_i</math> and horizontal hydraulic conductivity <math>K_i</math> is:
:<math>T_i = K_i d_i</math>
Transmissivity is directly proportional to horizontal hydraulic conductivity <math>K_i</math> and thickness <math>d_i</math>. Expressing <math>K_i</math> in m/day and <math>d_i</math> in m, the transmissivity <math>T_i</math> is found in units m<sup>2</sup>/day.<br/>
The total transmissivity <math>T_t</math> of the aquifer is:<ref name="Oost" />
:<math>T_t = \sum T_i</math> where <math>\sum</math> signifies the summation over all layers <math>i = 1, 2, 3, \cdots, n</math>.
 
The ''apparent'' horizontal hydraulic conductivity <math>K_A</math> of the aquifer is:
:<math>K_A = T_t / D_t</math>
where <math>D_t</math>, the total thickness of the aquifer, is <math>D_t = \sum d_i</math>, with <math>i = 1, 2, 3, \cdots, n</math>.
 
The transmissivity of an aquifer can be determined from [[pumping test]]s.<ref name="Boon">J.Boonstra and R.A.L.Kselik, SATEM 2002: Software for aquifer test evaluation, 2001. Publ. 57, International Institute for Land reclamation and Improvement (ILRI), Wageningen, The Netherlands. ISBN 90-70754-54-1 On line : [http://content.alterra.wur.nl/Internet/webdocs/ilri-publicaties/publicaties/Pub57/Pub57.pdf]</ref>
 
''Influence of the water table'' <br />
When a soil layer is above the [[water table]], it is not saturated and does not contribute to the transmissivity. When the soil layer is entirely below the water table, its saturated thickness corresponds to the thickness of the soil layer itself. When the water table is inside a soil layer, the saturated thickness corresponds to the distance of the water table to the bottom of the layer. As the water table may behave dynamically, this thickness may change from place to place or from time to time, so that the transmissivity may vary accordingly. <br >
In a semi-confined aquifer, the water table is found within a soil layer with a negligibly small transmissivity, so that changes of the total transmissivity (Dt) resulting from changes in the level of the water table are negligibly small. <br />
When pumping water from an unconfined aquifer, where the water table is inside a soil layer with a significant transmissivity, the water table may be drawn down whereby the transmissivity reduces and the flow of water to the well diminishes.
 
===Resistance===
The ''resistance'' to vertical flow (R<sub>i</sub>) of the <math>i-th</math> soil layer with a ''saturated'' thickness <math>d_i</math> and vertical hydraulic conductivity Kv<sub>i</sub> is:
: R<sub>i</sub>  = <math>d_i</math> / Kv<sub>i</sub>
Expressing Kv<sub>i</sub>  in m/day and <math>d_i</math> in m, the resistance (R<sub>i</sub>) is expressed in days. <br />
The total resistance (Rt) of the aquifer is:<ref name="Oost" />
:Rt = <big>Σ</big> R<sub>i</sub> = <big>Σ</big> <math>d_i</math> / Kv<sub>i</sub>
where  <big>Σ</big> signifies the summation over all layers: <math>i </math>= 1, 2, 3, . . .<math> n</math> <br />
The ''apparent'' vertical hydraulic conductivity (Kv<sub>A</sub>) of the aquifer is:
:Kv<sub>A</sub> = Dt / Rt
where Dt is the total thickness of the aquifer: Dt = <big>Σ</big> <math>d_i</math>, with <math>i</math>= 1, 2, 3, . . .<math> n</math>
 
The resistance plays a role in [[aquifer]]s where a sequence of layers occurs with varying horizontal permeability so that horizontal flow is found mainly in the layers with high horizontal permeability while the layers with low horizontal permeability transmit the water mainly in a vertical sense.
 
==Anisotropy==
When the horizontal and vertical hydraulic conductivity (Kh<sub>i</sub> and Kv<sub>i</sub>) of the <math>i-th</math> soil layer differ considerably, the layer is said to be [[anisotropy|anisotropic]] with respect to hydraulic conductivity.<br />
When the ''apparent'' horizontal and vertical hydraulic conductivity (Kh<sub>A</sub> and Kv<sub>A</sub>) differ considerably, the [[aquifer]] is said to be [[anisotropy|anisotropic]] with respect to hydraulic conductivity.<br />
An aquifer is called ''semi-confined'' when a saturated layer with a relatively small horizontal hydraulic conductivity (the semi-confining layer or [[aquitard]]) overlies a layer with a relatively high horizontal hydraulic conductivity so that the flow of groundwater in the first layer is mainly vertical and in the second layer mainly horizontal. <br>
The resistance of a semi-confining top layer of an aquifer can be determined from [[pumping test]]s.<ref name="Boon" /> <br />
When calculating flow to [[Drainage|drains]] <ref>The energy balance of groundwater flow applied to subsurface drainage in anisotropic soils by pipes or ditches with entrance resistance. International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands. On line : [http://www.waterlog.info/pdf/enerart.pdf] . Paper based on: R.J. Oosterbaan, J. Boonstra and K.V.G.K. Rao, 1996, “The energy balance of groundwater flow”. Published in V.P.Singh and B.Kumar (eds.), Subsurface-Water Hydrology, p. 153-160, Vol.2 of Proceedings of the International Conference on Hydrology and Water Resources, New Delhi, India, 1993. Kluwer Academic Publishers, Dordrecht, The Netherlands. ISBN 978-0-7923-3651-8 . On line : [http://www.waterlog.info/pdf/enerbal.pdf]. The corresponding free EnDrain program can be downloaded from: [http://www.waterlog.info/endrain.htm]</ref> or to a [[Water well|well]] field <ref>Subsurface drainage by (tube)wells, 9 pp. Explanation of equations used in the WellDrain model. International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. On line: [http://www.waterlog.info/pdf/wellspac.pdf] . The corresponding free WellDrain program can be downloaded from : [http://www.waterlog.info/weldrain.htm]</ref> in an aquifer with the aim to [[Watertable control|control the water table]], the anisotropy is to be taken into account, otherwise the result may be erroneous.
 
==Relative properties==
Because of their high porosity and permeability, [[sand]] and [[gravel]] [[aquifer]]s have higher hydraulic conductivity than [[clay]] or unfractured [[granite]] aquifers. Sand or gravel aquifers would thus be easier to extract water from (e.g., using a pumping [[Water well|well]]) because of their high transmissivity, compared to clay or unfractured bedrock aquifers.
 
Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and ([[gallon|gal]]/day)/ft² ); transmissivity then has units with dimensions of length squared per time. The following table gives some typical ranges (illustrating the many orders of magnitude which are likely) for ''K'' values.
 
Hydraulic conductivity (''K'') is one of the most complex and important of the properties of aquifers in hydrogeology as the values found in nature:
* range over many [[orders of magnitude]] (the distribution is often considered to be [[lognormal distribution|lognormal]]),
* vary a large amount through space (sometimes considered to be [[random]]ly spatially distributed, or [[stochastic]] in nature),
* are directional (in general ''K'' is a symmetric second-rank [[tensor]]; e.g., vertical ''K'' values can be several orders of magnitude smaller than horizontal ''K'' values),
* are scale dependent (testing a m³ of aquifer will generally produce different results than a similar test on only a cm³ sample of the same aquifer),
* must be determined indirectly through field [[pumping test]]s, laboratory column flow tests or inverse computer simulation, (sometimes also from [[Particle size|grain size]] analyses), and
* are very dependent (in a [[nonlinearity|non-linear]] way) on the water content,  which makes solving the [[vadose zone|unsaturated flow]] equation difficult. In fact, the variably saturated ''K'' for a single material varies over a wider range than the saturated ''K'' values for all types of materials (see chart below for an illustrative range of the latter).
 
==Ranges of values for natural materials==
'''Table of saturated hydraulic conductivity (''K'') values found in nature'''
 
Values are for typical fresh [[groundwater]] conditions &mdash; using standard values of [[viscosity]] and [[specific gravity]] for water at 20°C and 1 atm.
See the similar table derived from the same source for [[permeability (fluid)|intrinsic permeability]] values.<ref>{{cite book |author=Bear, J. |year=1972 |title=Dynamics of Fluids in Porous Media |publisher=[[Dover Publications]] |isbn=0-486-65675-6}}</ref>
 
{|  border="1" width="600"
|  bgcolor="#FAEBD7" | ''K'' (cm/[[second|s]])
| 10²
| 10<sup>1</sup>
| 10<sup>0</sup>=1
| 10<sup>&minus;1</sup>
| 10<sup>&minus;2</sup>
| 10<sup>&minus;3</sup>
| 10<sup>&minus;4</sup>
| 10<sup>&minus;5</sup>
| 10<sup>&minus;6</sup>
| 10<sup>&minus;7</sup>
| 10<sup>&minus;8</sup>
| 10<sup>&minus;9</sup>
| 10<sup>&minus;10</sup>
|-
|  bgcolor="#FAEBD7" | ''K'' (ft/[[day]])
| 10<sup>5</sup>
| 10,000
| 1,000
| 100
| 10
| 1
| 0.1
| 0.01
| 0.001
| 0.0001
| 10<sup>&minus;5</sup>
| 10<sup>&minus;6</sup>
| 10<sup>&minus;7</sup>
|-
|  bgcolor="#FAEBD7" | Relative Permeability
|  colspan="4" align="center" | Pervious
|  colspan="4" align="center" | Semi-Pervious
|  colspan="5" align="center" | Impervious
|-
|  bgcolor="#FAEBD7" | [[Aquifer]]
|  colspan="5" align="center" | Good
|  colspan="4" align="center" | Poor
|  colspan="4" align="center" | None
|-
|  bgcolor="#FAEBD7" | Unconsolidated [[Sand]] & [[Gravel]]
|  colspan="2" align="center" | Well Sorted Gravel
|  colspan="3" align="center" | Well Sorted Sand or Sand & Gravel
|  colspan="4" align="center" | Very Fine Sand, Silt, [[Loess]], [[Loam]]
|  colspan="4" |
|-
|  bgcolor="#FAEBD7" | Unconsolidated Clay & Organic
|  colspan="4" |
|  colspan="2" align="center" | [[Peat]]
|  colspan="3" align="center" | Layered [[Clay]]
|  colspan="4" align="center" | Fat / Unweathered Clay
|-
|  bgcolor="#FAEBD7" | Consolidated Rocks
|  colspan="4" align="center" | Highly Fractured Rocks
|  colspan="3" align="center" | [[Petroleum geology|Oil Reservoir]] Rocks
| colspan="2" align="center" | Fresh [[Sandstone]]
|  colspan="2" align="center" | Fresh [[Limestone]], [[Dolomite]]
|  colspan="2" align="center" | Fresh [[Granite]]
|}
Source: modified from Bear, 1972
 
==Saturated Hydraulic Conductivity by Soil Texture==
 
==See also==
*[[Aquifer test]]
*[[Pedotransfer function]]–for estimating hydraulic conductivities given soil properties
 
==References==
<references/>
 
{{Aquiferproperties}}
{{Geotechnical engineering|state=collapsed}}
 
{{DEFAULTSORT:Hydraulic Conductivity}}
[[Category:Hydrology]]
[[Category:Hydraulic engineering]]
[[Category:Soil mechanics]]
[[Category:Soil physics]]

Revision as of 05:54, 26 February 2014

the entire forest

They now need to support freshmen team that arrogant, completely obliterate!

Ever since, the entire forest, a few pieces of older students teams are full of woods began churning, however, nearly a day after カシオ 腕時計 バンド their search time, but it is not found traces of Hsiao go far Bansi people, they may think XiaoYan five people have fled because of fear and open to far when this arrogant freshman team, but it is surprisingly emerged again.
On
open glade, yellow leaves on the ground covered カシオ 腕時計 ソーラー 電波 with a thick casio電波腕時計 layer, like a yellow 'color' carpet in general.

on the open space at this time, the five face 'color' covered with dirty 'mess' the dust of life, being Beikaozhuobei siege of a small circle, カシオ腕時計 g-shock his eyes filled with anger at them around five young on the chest that five young people are wearing 一枚 tower casio 腕時計 スタンダード badge.

'will' fire can 'pay out, lest 相关的主题文章:

palm slowly recovered

Venerable face 'color' suddenly taken aback and lay three thousand thunderous instant display to the extreme, a blur in the sky emerge.

'three thousand thunderous it.'

looked round after round blur, Xiao Yan is a faint smile, hands still gently Woxia.

'bang カシオ 時計 電波!'

accompanied by his palm Woxia, this space, suddenly completely collapse, far away, a blur suddenly casio 時計 solidified, rich flesh, splash 'shot' out of that mine Venerable even screams are never issued, pinch the meat is life and life is a ball.

palm slowly recovered, Xiao Yan even look fuzzy flesh never look at that group, his eyes swept away, not far from the stars fell Court カシオ 時計 has a 電波腕時計 カシオ rapidly swept to the elders, Gong Sheng said: 'Shao Gezhu, you have commanded inquire The Han is with the カシオ 時計 プロトレック news, I do not know the reason why they are often suppressed all these years seem to wind and thunder Court, and now the family's forces, is reduced Jiucheng, 相关的主题文章:

but it is extremely difficult to practice more difficult

Practice to the highest level, when the town was able to qualify to practice law Court Court of wind 時計 カシオ and thunder.

three thousand Lei Disillusionment!

storms Court has now capable Plains continent status, which Disillusionment thousand mine has a vital role, but it is extremely difficult to practice more difficult, one of カシオ 腕時計 チタン the conditions is to get the three thousand thunderous practice to the highest level, Over the years, even the entire wind and thunder Court, but also the practice casio 腕時計 デジタル few people can be successful.

can say is three thousand three thousand Lei Disillusionment Advanced thunderous law, therefore, for this shenfa fighting skills, wind and thunder was very tight conservative Court, unless the Cabinet core disciples, otherwise not qualified to practice, but now, but suddenly saw this shenfa fighting skills Xiao Yan cast out, it is no wonder that the カシオ腕時計 g-shock old guy would be so moved.

hear the words of Shen カシオ腕時計 g-shock Yun, Han Chi, who face 'color' is a change, looked at Xiao Yan eyes dismay, obviously, for he actually pregnant with thunder 相关的主题文章:

and get the sea flame

Laugh, can large revere captured, and get the sea flame, this line is very abundant harvest, but also destroyed the house of an important sub-temple of the soul, カシオ 腕時計 ソーラー 電波 such a loss, presumably even the soul of the house, they can not easily afford.

'The rest of those people, you easily pack it, do not leak a man' casio 電波時計 who Xiao Yan eyes glanced at a small medical cents and flee Harengula kill the soul of the house of the strong, then attention turned to the 'medicine' old bone with that quiet saints battle circle, at the moment of the latter, is the best they strive atmosphere are somewhat sluggish, although he mouth hard, but after all he is still only half the カシオ 時計 プロトレック holy senior, there is no way of As fighting holy 'medicine' old rival, has been resolved, it is only a matter of time.

'bone quiet note, the old devil, do not let him get away.'

'ah.' Purple research nodded, Jiaoqu a move, is Shanlue out, immediately rushed into カシオ ソーラー 腕時計 the flock is like a カシオ 時計 価格 dragon that general 相关的主题文章: