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

The solute (contaminant) spreads

• ut from the flow path.

Mixing or spreading of the solute. Solute will not move as a “plug” Negligible at low flow rates & short distances of transport

x 2 4 6 8 10 12 0.0 0.5 1.0 x 2 4 6 8 10 12 0.0 0.5 1.0 x 2 4 6 8 10 12 0.0 0.5 1.0

Dispersion (thinning out/scattering/spreading)

Ct / C0

Pore size Path length Friction in pore

Slow Fast Long path Short path Slow Slow Fast Slow Slow Fast

Variation in velocity due to tortuous nature of flow path On larger scale, dispersion is caused by different flow rates resulting from heterogeneities encountered. This process is repeated millions

• f times by millions of water

particles.

Dispersion

Water with dissolved contaminants Solid particle Tortuous flow paths General direction

• f flow

Porous media

MD = aL.Vs

aL = dynamic dispersivity [L] Vs = Seepage velocity [LT-1] aL = 0.0175 L1.46 for L < 3500 m

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 DL = aL.Vs+Di DL = Coefficient of hydrodynamic dispersion [L2T-1] Concentration at distance, L, from the source at time, t, is given by: C = 0.5.Co [erfc{(L-Vs.t)/2(DL.t)0.5}+ exp(Vs.L/DL) x erfc {(L+Vs.t)/2(DL.t)0.5 }]

t C . η K . ρ z C v z C D t C

d dry s. 2 2 i.

          

C = f (t,z) Advection-Diffusion equation

• Combined advection-diffusion equation

Di: Diffusion coefficient Kd : 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

 

properties soil t, , l l, g, , ρ , T , V S, D, μ, f C

μ f f s



C : the concentration of contaminant in the pore water (ML-3)  : the dynamic viscosity of the fluid (ML-1T-1) D: the diffusion coefficient (L2T-1) S : the mass of the adsorbed contaminant/unit volume (ML-3) Vs: corresponds to the interstitial flow velocity (LT-1) Tf : 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].

Dimensionless Number Dimension Evaluation Concentration Number Ensures similarity of concentrations at homologous points in the model and prototype Advection Number Ensures kinematic similarity of motion in the model and prototype Diffusion Number Ensures similarity of diffusion process in the model and prototype Capillary Effects Number Ensures similarity of capillary effects in the model and prototype Adsorption Number Ensures similarity of adsorption process in the model and prototype Dynamic Effects Number Scaling is not done for contaminant flows. Significant in the case of dynamic events only.

f

C 

l t Vs.

2

l Dt

f f

T l l g

u

. . . 

f

 S

l gt2

Coefficients of Contaminant Transport Mechanisms

Reynolds Number (Re) It is N times higher in the model. Scaling is not required if Re<1 (i.e. for laminar flow) Peclet Number (Pe) It is N times higher in the model. For low velocities dispersion is dependent of velocity and can be modelled accurately (i.e. Pe<1)

 

u f

l Vs.

D l V

u

s.

Discrepancies Pe= /(fD) Re  : 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 Vs : the seepage velocity lu : the characteristic microscopic length (such as particle size) and is equal to either d10 (or d50) or the mean particle size of the soil.

The relation between Pe and Re numbers depends only on the contaminant.

0.01 0.1 1 10 0.1 1 10 100

advection advection-diffusion dispersion diffusion

Peclet number Reynolds number Sreedeep S., Berton, C., Moronnoz, T. and Singh, D. N., "Centrifuge and Numerical Modeling

• f 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.