Groundwater Flow and Contaminant Transport
Groundwater Flow and Contaminant Transport BSysE 595
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This 5 page Class Notes was uploaded by Haylie Rowe on Thursday September 17, 2015. The Class Notes belongs to BSysE 595 at Washington State University taught by Staff in Fall. Since its upload, it has received 50 views. For similar materials see /class/205960/bsyse-595-washington-state-university in Bioengineering at Washington State University.
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Date Created: 09/17/15
Anisotropy and Heterogeneity of Porous Media 1 Practical Knowledge Studies show no possibility of finding a truly homogeneous geologic unit VS glass beads in nature Some observations by students Also most rocks have directional quality Sedimentary rocks horizontal stratification Metamorphic rocks schistosity Igneous basalts orientation of shrinkage cracks 2 Classical Definition in Terms of K A geologic formation is homogeneous if K is independent of position and heterogeneous if dependent on position is isotropic at the point of measurement if K is independent of the direction and anisotropic if it varies with the direction of measurement 1 3 Modern Definitions in Terms of K K has been found to have a lognormal distribution If all geologic formations show spatial variability there is no such a thing as a homogeneous formation Thus a formation is homogeneous if the K s probability density function pdf is monomodal and heterogeneous if multimodal The glass beads media is termed uniform 4 Layered Heterogeneity vs Anisotropy Relation A formation of n layers each being homogeneous and isotropic with K and thickness mi iln can be represented as a single equivalent anisotropic n homogeneous layer with total thickness m 2 ml i1 1 For flow perpendicular to the layering With specific discharge q and total head loss Ah let K2 be the equivalent K value KlAh1 KzAh2 KnAhn KzAh m1 m2 mquot m Hence 1 quot Im z E Ah1 Ah2 Ahn qm qmllK1 qm2K2 qmnKn K L 320 2 For ow parallel to the layering With specific discharge q total head loss Ah over distance Z assume unit Width and let Kx be the equivalent K value 2quot qi39mi39l 2n KiA lhmi i1 q 2 i1 Kxamp m39l ml m 1 Hence 2 Klml Kx 319 3 Similar approach can be used to derive the equivalent K for ow entering the layers With a nonzero 0r non9OO angle 5 K Averaging for Uniform Flow In a statistically homogeneous medium 1 2 or 3D under uniform or laminar flow condition the average K is between the harmonic and arithmetic means K H and K A N KH KA f 1Kl 11 N 2K 1 ZIH For some media the average K is best represented by the geometric mean KG KG KIKZKN N KG is between K H and K A
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