Forge Pond project Continued discussion Update questions EPA - PDF document

CEE 577 Lecture #9 10/23/2017 Updated: 23 October 2017 Print version Lecture #9 (Diffusion) Chapra L8 David A. Reckhow CEE 577 #9 1 Forge Pond project  Continued discussion  Update  questions EPA 305(b) listing for Forge Pond David A. Reckhow CEE 577 #9 2 1

CEE 577 Lecture #9 10/23/2017 Liquid Water Transport  Advection: unidirectional flow  Diffusion: movement of mass that is not unidirectional flow; usually movement in an unorganized fashion  Dispersion  Eddy Diffusion  Molecular Diffusion David A. Reckhow CEE 577 #9 3 Incorporates molecular movement Mass Diffusion and interfacial area Bulk Diffusion T=0 (m 2 /yr) V 1 , c 1 V 2 , c 2 dc      1 V D c c 1 2 1 dt T=1 Concentration Gradient T=2 T=large David A. Reckhow CEE 577 #9 4 2

CEE 577 Lecture #9 10/23/2017 Fick’s First Law  Mass flux is proportional to the concentration gradient and a diffusion coefficient dc   J x D dx David A. Reckhow CEE 577 #9 5 Bulk Diffusion Coefficient The mixing dc   1 length V JA V 1 , c 1 V 2 , c 2 1 c dt  dc c c dc    2 1 J x D  dx dx dc DA And combining all three:   1 ( ) c V c c 1 2 1  dt D’ EA  E  Similar for Eddy Diffusion c  David A. Reckhow CEE 577 #9 6 3

CEE 577 Lecture #9 10/23/2017 Dispersion  Differences in velocities of parallel flow paths David A. Reckhow CEE 577 #9 7 Embayment Model Q 2 Main W 1 Bay Lake (2) (1) W 2 Q 1 dc        1 ( ) V W Q c k V c Q c E c c 1 1 1 1 1 1 1 2 2 2 1 dt dc       2 ( ) V W Q c k V c E c c 2 2 2 2 2 2 2 1 2 David A. Reckhow dt CEE 577 #9 8 4

CEE 577 Lecture #9 10/23/2017 Embayment Model with a Conservative Substance  Conservative substances (s) are those that do not undergo degradation, thus k=0  The mass balance on the bay (2), then becomes: ds      2 ( ) V W Q s E s s 2 2 2 2 1 2 dt And solving for the bulk diffusion coefficient:  W Q s   2 2 2 E  s s 2 1 David A. Reckhow CEE 577 #9 9 Map of Huron/Saginaw System Lake Huron Saginaw Bay David A. Reckhow CEE 577 #9 10 5

CEE 577 Lecture #9 10/23/2017 Parameters for Saginaw Bay Parameter Symbol Value Units 10 9 m 3 Volume V 2 8 Depth H 2 5.81 m 10 6 m 2 Surface Area A 2 1,376 10 9 m 3 /yr Outflow Q 2 7 Chloride Conc. s 2 15.2 mg/L 10 12 g/yr Chloride Loading W s2 0.353 10 12 mg/yr Phosphorus Loading W p2 1.42 David A. Reckhow CEE 577 #9 11 Parameters for Lake Huron Units Parameter Symbol Value 10 9 m 3 Volume V 1 3507 Depth H 1 60.3 m 10 6 m 2 Surface Area A 1 58,194 10 9 m 3 /yr Outflow Q 1 161 mg/L Chloride Conc. S 1 5.4 10 12 g/yr Chloride Loading W s1 ~0 10 12 mg/yr Phosphorus Loading W p1 4.05 David A. Reckhow CEE 577 #9 12 6

CEE 577 Lecture #9 10/23/2017 Chloride Tracer Model    W Q s     2 2 2 E 12  9 0 . 353 10 7 10 15 . 2 x x    s s E 2 1  15 . 2 5 . 4  9 3 25 . 2 10 / x m yr EA    E  c  9 3 2 . 52 10 10 10  E x x m    E 6 2 0 . 17 10 A x m c  9 2 1 . 48 10 / x m yr  4 . 7 10 5 2 / x cm s David A. Reckhow CEE 577 #9 13  To next lecture David A. Reckhow CEE 577 #9 14 7