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# Class Note for BSysE 595 at WSU 12

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COURSE
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KARMA
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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Washington State University taught by a professor in Fall. Since its upload, it has received 29 views.

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Date Created: 02/06/15
Modeling Advection and Longitudinal Dispersivity 1 Combining ld Solutions to Form a 3d Solution If three ld solutions are of the form Cx t C0 2 F1 ax 35 t C CE F2 my y 065 Fm z then an approximate solution to a 3d problem may be given by C 9 9 9t w F10 xsxs t F2 y y F3az z 0 Q Describe the major mass transport processes in various directions implied in this problem 2 Solution to ld Advection and Longitudinal Dispersion problems For the ld advectiondispersion equation 2 D w z 181 6x2 6x at with BC and IC CO t C0 continuous source Cx 0 0 given by Ogata and Banks 1961 x vt m l erfc C0 2 12 vx x vt exp erfc D D t12 182 D dispersion coefficient in xdirection erfc the complementary error function erfB the error function v velocity of the tracer or pore velocity The second term in Eq 182 is often negligible Dt may be written as axvt if ignoring molecular diffusion so Eq 182 is simplified to m erfc 183 C0 2 2ocxvt 2 Values for erfc B and erf B are given in Table 181 and Fig 183 Useful relations erfc B 1 erf B erf 13 el fl3 erfc B 1 erfB 3 Physical Meaning of the Argument of erfc When x vt 0 or x vt the argument is zero erfc 0 1 and CC0 05 When x vtgtgt0 or xgtgtvt the argument B is positive as it a 00 erfcoo 0 and CC0 0 practically C s 0 when B 2 When x vtltlt0 or xltltvt the argument B is negative as it 6 oo erfc o 2 and CC0 1 practicallyC z C0 when B 2 The denominator 2ocxvt 2 has the units of length and can be regarded as the longitudinal spreading around the advective front Longitudinal dispersion moves mass ahead of the advective front as the advective front furthers away from source with time the spreading becomes larger

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