QUANTIFYING ECOSYSTEM SERVICES PROVIDED BY HYPORHEIC EXCHANGE Stanley B. Grant and Morvarid Azizian Civil and Environmental Engineering, University of California Irvine & Infrastructure Engineering, University of Melbourne Objectives •Present an analytical model of benthic exchange and reaction Pumping of solute across bedforms Advection-dominated mass transport First-order reaction in sediment •Evaluate model Compare to numerical solution Derive solution for solute flux into the sediment •Application Correlations for mass transfer coefficient Trade-off between volume of water processed in the sediment and extent of reaction streamline geometry J τ R ( ) = J MTL 1− C f τ R ( ) C 0 ⎡ ⎡ ⎡ ⎡ pressure head velocity field lliot and Brooks Velocity Model h x , y ( )=hh m =sin xe y normalize by wave number x =2πx λ y =2πx λ u x x , y ( )=u x u m =−cos xe y u y x , y ( )=u y u m =−sin xe y u m =−2πK h h m λ K h =hydrauλic conducτiviτy λ =bed form w avelength x =horizonτaλ disτance y =ve rτicaλ d isτan ce h m =m axim um πre ssure he ad u x =x - ve λociτy variable definitions u y = y - ve λociτy u m =m ax−ve λociτy predicted concentration field C f τ R ( ) =C 0 exπ − τ R x 0 π 2 cos x 0 ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ 0 π /2 ∫ sin x 0 d x 0 C x , y , τ R ( ) = C x , y , τ R ( ) C 0 =exπ − τ R cos −1 e y cos x ⎡ ⎡ ⎡ ⎡ − x ( ) 2π 2 e y cos x ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ , − π 2 < x < π 2 , y <0 predicted concentration field (analytical) Solution approach (neglect dispersion & diffusion) Numerical simulation results ∇⋅ u Cθ − D ⋅ ∇ C ( ) =−k r C C 0 =sτre am concenτraτion τ R = transit tim e reaction tim e = k r λθπ u m k r =1sτ- ord e r re acτion raτe θ =sedim ent porosity variable definitions C =se d im enτ concenτraτion C f =fλow-weighτed uπweλλing conc. J MTL =− C 0 u m θπ ( ) flux into sediment bed mass-transfer-limited flux D = u m e y θ a L cos 2 x + a T sin 2 x ( ) + ′ D m u m e y θ a L − a T ( ) sin 2 x 2 u m e y θ a L − a T ( ) sin2 x 2 u m e y θ a L sin 2 x + a T cos 2 x ( ) + ′ D m ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ ⎡ Numerical approach (governing equations) u =− u m cos xe y ˆ i − u m sin xe y ˆ j variable definitions a L = longitudinal dispersivity a T = transverse dispersivity advection/dispersion equation dispersion tensor predicted concentration field (numerical) Numerical and analytical solutions near-identical Numerical simulation carried out with COMSOL Mechanical dispersion & molecular diff. negligible Dirichlet b.c. at surface causes gradient artifact Applications Analytical model supports use of mass transfer coefficient J =− k m C 0 − C f ( ) k m =u m θπ ( ) Flux ~ conc. diff. in upwelling & downwelling zones Mass transfer coefficient = downwelling velocity Ecosystem services Flux into sediment = mass removal in sediment Mass removal in sediment = ecosystem service (N, P, C processing; CEC removal) Model identifies trade-off between volume of water processed by hyporheic zone and extent of reaction in sediment (hard to optimize both) Acknowledgements Funding by the National Science Foundation Partnerships for International Research and Education (PIRE) Award No. OISE- 1243543. A huge THANK YOU to Keith Stolzenbach (UCLA), Megan Rippy (UCI), Mike Stewardson (UoM), and Perran Cook (Monash Univ). ′ D m = τD m = diffusion/tortuosity