Sub-topics Chemical characterization Sorption-Desorption - PowerPoint PPT Presentation

Geomaterial Characterization Sub-topics • Chemical characterization Sorption-Desorption (Contaminant Transport in Porous Media) • Thermal Characterization • Electrical Characterization

Dispersion (thinning out/scattering/spreading) The solute (contaminant) spreads out from the flow path. 0 2 4 6 8 10 12 Mixing or spreading of the solute. x 1.0 Solute will not move as a “plug” 0.5 0.0 Negligible at low flow rates & short distances of transport 0 2 4 6 8 10 12 C t / C 0 Pore Slow x 1.0 size 0.5 Fast 0.0 Long path Path length 0 2 4 6 8 10 12 Short path x 1.0 0.5 Friction Slow Slow Fast 0.0 Fast in pore Slow Slow

Dispersion Variation in velocity due to tortuous nature of flow path On larger scale, dispersion is caused by different flow rates resulting from heterogeneities encountered. Water with dissolved contaminants This process is repeated millions of times by millions of water particles. Solid particle M D = a L .V s Porous media Tortuous a L = dynamic dispersivity [L] flow paths V s = Seepage velocity [LT -1 ] a L = 0.0175 L 1.46 for L < 3500 m General direction of flow

Hydrodynamic Dispersion Processes of molecular diffusion and mechanical dispersivity cannot be separated in flowing groundwater Introduction of a factor which takes into account mixing and diffusion D L = a L .V s +D i D L = Coefficient of hydrodynamic dispersion [L 2 T -1 ] Concentration at distance, L, from the source at time, t, is given by: C = 0.5.C o [erfc{(L-V s .t)/2(D L .t) 0.5 }+ exp(V s .L/D L ) x erfc {(L+V s .t)/2(D L .t) 0.5 }]

Advection-Diffusion equation • Combined advection-diffusion equation     2 K C C C C    ρ d D v . . s.     i. dry η 2 t z t z C = f (t,z) D i : Diffusion coefficient K d : Distribution coefficient

Factors deciding type of Contaminant transport mechanism • Grain size • Density • Seepage velocity • Concentration • Viscosity • Hydraulic conductivity Factors affecting the behavior of contaminant • Contaminant • Soil condition • Mechanism

Concentration, C, of a contaminant in the porous media    μ, ρ C f D, S, V , T , , g, l, l , t, soil properties μ s f f C : the concentration of contaminant in the pore water (ML -3 )  : the dynamic viscosity of the fluid (ML -1 T -1 ) D: the diffusion coefficient (L 2 T -1 ) S : the mass of the adsorbed contaminant/unit volume (ML -3 ) V s : corresponds to the interstitial flow velocity (LT -1 ) T f : the surface tension of the fluid particle interface (MT -2 )  f : the fluid density (ML -3 ) g : the acceleration due to gravity [LT -2 ] l : the characteristic macroscopic length [L] l  : the characteristic microscopic length (particle size) [L] t: the time [T].

Coefficients of Contaminant Transport Mechanisms Dimensionless Number Dimension Evaluation Ensures similarity of C concentrations at homologous Concentration Number  points in the model and f prototype Ensures kinematic similarity of V s . t Advection Number motion in the model and l prototype Ensures similarity of diffusion Dt Diffusion Number process in the model and 2 l prototype Ensures similarity of capillary  . g . l . l u f Capillary Effects Number effects in the model and T prototype f Ensures similarity of adsorption S Adsorption Number process in the model and  f prototype gt 2 Scaling is not done for Dynamic Effects Number contaminant flows. Significant in l the case of dynamic events only.

Discrepancies  It is N times higher in the model. V s . l f u Reynolds Number (R e ) Scaling is not required if R e <1  (i.e. for laminar flow) It is N times higher in the model. For V l low velocities dispersion is s . u Peclet Number (P e ) dependent of velocity and can be D modelled accurately (i.e. P e <1) The relation between Pe and Re numbers depends only on the contaminant. P e =  /(  f D ) R e  : the viscosity of the contaminant (solution)  f : the density of the contaminant solution D : the coefficient of diffusion for the contaminant  f : the fluid density V s : the seepage velocity l u : the characteristic microscopic length (such as particle size) and is equal to either d 10 (or d 50 ) or the mean particle size of the soil.

100 10 Peclet number dispersion advection 1 advection-diffusion diffusion 0.1 0.01 0.1 1 10 Reynolds number Sreedeep S., Berton, C., Moronnoz, T. and Singh, D. N., "Centrifuge and Numerical Modeling of Contaminant Transport Through the Unsaturated Silty Soil", ISSMGE International Conference on From Experimental Evidence towards Numerical Modelling of Unsaturated Soils , September 18/19, 2003, Bauhaus-Universität Weimar. 2003.