Hydraulic Conductivity & Porosity

1 1 Hydraulic Conductivity & Porosity Today Hydraulic Conductivity Porosity Aquifer, Aquitard, etcnoise-to-signal photosDoes K change if we change theporous medium? Yes Hydraulic Conductivity is a property of theporous media It depends on the pore size, its distribution, and itsconnectivity In a clastic sediment this translates to a dependence on grain shape, size, and sorting K dependence on porous media isrepresented by a measurable property, theintrinsic permeability, k [L2]2 Intrinsic Permeability, k k !

2 L2 , where we could define L in terms of acharacteristic distance, say grain size. For perfectly sorted ( , uniform diameter)spherical glass beads, k can be predicted on thebasis of diameter, d alone k ! d2 If the grain size varies then use, , mediangrain size for d. What is the proportionality coeffcient? Lots of empirical and some theoretical models .. See text and other referencesEmpirical Intrinsic Permeability, k For real, mixed diameter and odd shaped grains,a proportionality constant, C, must be included toaccount for grain size distribution, grain shape,and packing: k = C d23 Relationship to Porosity Note that k typically cannot be correlatedwith Porosity .

3 For example, clay has a very high porositybut very low permeability, while well- sorted gravel, which also has highporosity, has a high permeability However, within a single lithologic type(such as sandstone), k typically increaseswith increasing Porosity , and Size Large grains: Small grains:4 Sorting and Size Well sorted grains: Poorly sorted grains:wikipediaSorting and Size Well sorted sandstone: This is an example of well-rounded,clean sandstone. The green areais open pore space. This rock hashigh Porosity and probably highpermeability also.

4 Poorly sorted sandstone: Poorly sorted coarse spaces between the large,well-rounded grains are filled bysmall angular fragments in adark clay-rich matrix. This rockhas very low Porosity andpermeability. ~jtoro/Petroleum/Review% 5 Does K change if we change thefluid in the porous medium? Yes! Hydraulic Conductivity is a property of the fluid Mainly the fluid dynamic viscosity, [M/LT] But also the fluid density, ! [M/L3] Often written instead in terms of Kinematic viscosity," = /! [L2/T] Specific weight, # = !

5 G [M/L2T2] Both ! and " depend on temperature and pressure Through an equation of state (EOS) How does K change with increasing & !? Decreases with Increases with ! 1!K!"K ! "#KK is a property of both the fluid &the porous medium We get:and we can also nowexpress Darcy s Lawin terms of thesequantities: !gkK =lllddhkgddhgkddhkAQq! " #$=$=$==6K is a property of both the fluid &the porous medium For example, usingthe empirical model,k = C d2 and !gCdK 2=lddhgCdAQq!2"==The basic units for Conductivity , K Units are [L/T] Commonly employed in current andhistorical literature and reports: SI (preferable): m/s Meinzer (old USGS): gal per day per square foot = gal d-1 ft-2 = [L3 T-1 L-2] = [L/T] USGS (recent) and most consultants: ft/d7 The basic units for permeability, k Units are [L2] Commonly employed in current and historicalliterature and reports: SI (preferable): m2, preferable but the numbers are very small !

6 Cm2, now commonly used ft2, now less common Darcy, common in oil, gas and deep basin work One darcy is the k which will permitq=1 cm/s for = 1 cP at g(dh/dl) = 1 atm/cm 1 darcy " 10-12 m2 = 10-8 cm2 Natural Variation of K Its huge! Over 13 orders of magnitude!Typical ranges of values: K (m/s)Gravel10-3 to 101 Sand10-7 to 10-2 Silt10-9 to 10-5 Clay & Shale10-12 to 10-9 Karst limestone10-5 to 10-1 Sandstone10-10 to 10-5 Igneous & Metamorphic rocks10-13 to 10-10 (unfractured)Use values in your text and cite them8 Natural Variation of K Its huge!

7 Over 13orders of magnitude!Miocene alluvial fan sedimentsin Southern a mixture of debris flow andchannel/ sheetflood : The wide variation in grainsize and in sorting suggesting widespatial variation of Conductivity injust this one Variation of K Its huge! Over 13 orders of magnitude!Typical ranges of values: K (m/s)Gravel10-3 to 101 Sand10-7 to 10-2 Silt10-9 to 10-5 Clay & Shale10-12 to 10-9 Karst limestone10-5 to 10-1 Sandstone10-10 to 10-5 Igneous & Metamorphic rocks10-13 to 10-10 (unfractured)Good aquifers: 10-5 < K < 10-3 m/sAquitards: 10-11 < K < 10-7 m/sTypical values9 Aquifers, Aquitards, and Aquicludes Aquifer.

8 A saturated permeable geologic unitthat can store & transmit significant quantities ofgroundwater under ordinary Hydraulic gradients&/or can yield economic quantities of water towells ( , store and transmit water) Aquitard: permeable geologic unit capable oftransmitting geologically significant amounts ofwater, but not economic quantities Aquiclude: a geologic unit that cannot transmitgeologically significant amounts of waterThese are relative terms; depend on local or regional : What is a Confined aquifer?

9 Phreatic aquifer? Perched aquifer? Water table? Capillary fringe?10 Natural Variation of Conductivity , K Its huge! In nature, over 13orders of magnitude!Typical ranges of values: K (m/s)Gravel10-3 to 101 Sand10-7 to 10-2 Silt10-9 to 10-5 Clay & Shale10-12 to 10-9 Karst limestone10-5 to 10-1 Sandstone10-10 to 10-5 Igneous & Metamorphic rocks10-13 to 10-10 (unfractured)Use values in your text and cite themSZ 2005 Natural Variation of Porosity , n Its varies much less,but the variation isstill important.

10 In nature, n varies over 3 orders of magnitude while ne varies n (%)Gravel25 - 40 Clay40 - 70 Karst Limestone5 - 50 Sandstone5 30 Crystalline Rock0 5 Normally, well- sorted sedimentary materials have a larger Porosity than poorlysorted ones, due to filling of the voids between larger grains by smaller ones.(Fetter, 2001)SZ 200511 Natural Variation of Conductivity , K,in a particular deposit Its still huge! In a particular depositnot unusual to be 7orders of magnitude!Miocene alluvial fan sedimentsin Southern a mixture of debris flow andchannel/ sheetflood : The wide variation in grain size and insorting suggesting wide spatial variation ofconductivity (& Porosity ) in just this measures Hydraulic properties at a point, not necessarily for awhole system.