Dynamic Fugacity Approach in Modeling Contaminant Fate and Transport in Rivers EWRI 2007

Transcription

1 Dynamic Fugacity Approach in Modeling Contaminant Fate and Transport in Rivers EWRI 2007 Sinem Gökgöz Kılıç May 17, 2007 Multimedia Environmental Simulations Laboratory School of Civil and Environmental Engineering Georgia Institute of Technology

2 Objective Development of a dynamic fugacity-based model to simulate concentration distribution of a contaminant in the water column as well as sediments of a river reach.

3 Outline Why Fugacity? Hydrodynamic model Contaminant Transport Solution of Governing Equations Hydrodynamics Contaminant Transport Application Future work

4 Why Fugacity? Linear relationship between concentration and fugacity C = F Z Continuous profile among different phases Decreases the number of coefficients used air water C 2 = 3 x Source: Mackay, 1980 C i = 7 x Ci = 70 x C 1 = 80 x f 2 = 3 x 10-9 f 2 = 7 x 10-9 f 2 = 8 x 10-9

5 Hydrodynamics of Rivers Characteristics of Channel Flow Free surface Gravity is the driving force Always unsteady Development of unsteady flow equations for open channels First published in 1871 by Saint Venant Still used

6 Derivation of Saint-Venant Equations for River Hydrodynamics Conservation of mass A t Q + = 0 x A cross-sectional area (L 2 ) Q volumetric flowrate (L 3 /T) t time (T) X distance along the river (L) Conservation of momentum Q ( Qu) h + = ga + ga( So S f ) t x x Q flowrate, L3/T u velocity, L/T t time, T A area, L2 x distance along the river, L h water surface elevation, L g gravitational accelaration,l/t 2 S o bed slope, L/L S f friction slope L/L

7 Solution of Saint-Venant Equations Coupled, non-linear, first order partial differential equations No analytical solution, so require numerical solution Numerical technique used in this study: Preissmann Weighted Four- Point Method Implicit scheme Flexible time steps and distance Unconditionally stable t φ = x (x, t + t) t (x, t) x (x + x, t + t) (x + x, t) (1 ) ( t t ) ( t + t t + θ φ t x+ x φx + θ φx+ x φx ) x t+ t t+ t t t φx + φx+ x φx + φ x+ x φ 2 2 = t t t t t+ t t+ t φx+ x + φ x φx+ x + φ x φ = (1 θ) + θ 2 2 x

8 Contaminant Transport: Advection Dispersion Equation is used C ( Cux ) C D + Hx = t x x x Reaction Reactions include: Volatilization Diffusion between air/water and water/sediment Deposition/resuspension of suspended particles Wet and dry deposition of aerosols from atmosphere Decay of the chemical in water column and sediments

9 Natural Processes in a River Reach Air particle deposition dry wet Air/water absorption volatilization Decay in water Advection and Dispersion Sediment resuspension Sediment deposition Sediment/water diffusive flux Decay in sediment Sediment Sediment burial

10 Contaminant Transport Contaminants are distributed among all media in the vicinity of water column Sediments and air are also considered as a compartment in the contaminant transport model Sediments are immobile Air concentration is assumed to be constant ( FwaterZbw) ( FwaterZbwux) FwaterZbw D + Hx = t x x x Reactions Water Phase ( F Z ) sed t sw = (Reactions + interactions with water) Sediment Phase

11 Water Phase Fugacity Model: 2 fw fw fw τ K b pρs Aw VZ w Bw = VZ w BwDH VZ 1 2 w BwU + fs M + t x x τ c H 1 1 H + K w K s K pρ s Diffusion Dispersion Advection Resuspension Decay Settling Diffusion Volatilization 2 HAw Aw QA w HAw kw gd ρs ρ K pρs Aw + fa + ud + ur fw Vw Kaw RT RT Kaw H 18 µ H 1 1 H + Dry and wet deposition K w K s K pρ s Diffusion f f ( uf ) = D + S f + S f f S t x x x w w w H 3 s 4 a w 5

12 Sediment Phase Fugacity Model: Settling Diffusion 2 fs gd ρs ρ K pρ s Aw VZ s Bs = fw + t 18 µ H 1 1 H + K w K s K pρ s Resuspension Diffusion τ K b p ρs A K w pρs ksk pρs fs M Vburial + Vs τ c H 1 1 H H H + K w K s K pρ s Burial Decay f t s = S f S f 6 w 7 s

13 Contaminant Transport Model: The final aqueous fugacity balance: f f ( Uf ) = D + S f + S f f S t x x x w w w H 3 s 4 a w 5 f f D f f U t x x x x x 2 w w H w w = DH + U f 2 w + S3fs + S4fa fws5 The final sediment fugacity balance: f t s = S f S f 6 w 7 s

14 Numerical Solution: Only water phase is mobile Sediment phase is immobile Air is assumed to be semi infinite (constant air concentration) Velocity input comes from hydrodynamics Dispersion coefficient calculated using velocity k 1 k df w f + w fw dt = i t k df w fw f = dx 2 x i+ 1 i 1 i k w + + = dx 2 ( x) ( x) 2 k+ 1 k+ 1 k+ 1 k k k d f w 1 fw 2fw fw fw 2fw fw i+ 1 i i 1 i+ 1 i i 1

15 Application: Q 2 1 Upstream Boundary Condition t Total simulation time = 1 week Number of nodes = 101 x = 100 m S0 = m/m n = km Downstream Boundary Condition 20 m 1.44 m

16 Application: Two application cases: Case 1 : Instantaneous spill of atrazine into water column (C 0 = 0.1 mg/l) Atrazine is the most commonly used agricultural herbicide Case 2: Sediment release of PCB as a result of dredging (C 0 = 0.1 mg/l) Although abandoned, PCBs are still existent in large amounts in the sediments of rivers

17 Results Case 1 (Atrazine Spill into Water Column) 0.1 Atrazine Concentration in Water Column Input into Water Atrazine Concentration in Sediments Input into Water Concentration (mg/l) Concentration (mg/l) Time (days) Time (days)

18 Results Case 1 (Atrazine Spill into Water Column) 0.1 Atrazine Concentration in Sediment Input into Water Atrazine Concentration in Sediments Input into Water Concentration (mg/l) Graph 1 Time = 0.01 days Time = 1 days Time = 2 days Time = 3 days Concentration (mg/l) Graph 1 Time = 0.01 days Time = 1 days Time = 2 days Time = 3 days Time = 4 days Time = 5 days Time = 6 days Distance (m) Distance (m)

19 Results Case 2 (PCB Release from Sediments) 2.4E-007 PCB Concentration in Water Column Input from Sediments PCB Concentration in Sediments Input from Sediments 2E E-007 Concentration (mg/l) 1.2E-007 Concentration (mg/l) E E Time (days) Time (days)

20 Results Case 2 (PCB Release from Sediments) PCB Concentration in Water Column Input from Sediments 0.16 PCB Concentration in Sediments Input from Sediments Concentration (mg/l) E-005 Graph 1 L= 5000 m L= 500 m L= 9500 m Concentration (mg/l) 0.08 Graph 1 L = 5000 m L = 500 m L = 9500 m 4E Time (days) Time (days)

21 Future Work A real case application Altamaha River