Contaminant Transport in Porous Media Flow of water through porous - PowerPoint PPT Presentation

IIT Bombay Slide 2 Contaminant Transport in Porous Media Flow of water through porous media is extensively studied (seepage, consolidation and stability) The concept of hydraulic conductivity are well established. Chemical flows in soils are of great importance. Some important examples are: waste storage, remediation of contaminated sites leaching phenomena, etc. Contaminants are basically dissolved inorganic or organic substances in the solvent (water or fluids). Various concentration units are used to define the relative amounts of contaminants in the solvent: Mass concentration: milligrams of contam. in 1 litre of water (mg/L) Parts per million (ppm): grams of solution/ million grams of solution Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 3 Types of Flow through Porous Media If flow does not change the fabric and stress state of the porous media, then flow rate J relates linearly to its corresponding driving force, X: J =  . X  : conductivity coefficient for flow Chemicals Electricity Heat Fluid H 1 T 1 >T 2 H 2  H C 1 C 2 V 1 V 2 T T 2 1 L L L L J D q q I J D = D  C/L I =  V/L = k  H/L q = K  T/L q Fick’s law Darcy’s law Ohm’s law Fourier’s law Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 4 Advection (or Convection) Solute (contaminant) gets transported (seepage velocity) t 0 along with the flowing fluid (water) in response to a gradient (hydraulic). V s = k.i/  t 1 If a mass of solute (non reactive) of a concentration C is placed at one end of a pipe, then in a t 2 given time it will travel a certain distance as a Plug due to advection. The transit time required for a non-reactive solute to migrate through a saturated soil of thickness L would be: t = L/V s =  .L/(k.i) Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 5 Representative values for effective porosity  Description Soils GC, GP, GM,GS 0.20 SW,SP,SM,SC - ML, MH 0.15 CL,OL, CH, OH, PT 0.01 Rocks Non fractured rocks 0.15 Fractured rocks 0.0001 The advective mass flux, J, (or the mass flowing through a unit cross sectional area in a unit of time) is: J =v.C=k.i.C C = concentration of the solute (i.e., the mass of solute per unit volume of the mixture). Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 6 Diffusion Contaminant at Contaminant • Solutes (contaminants) migrate due to concentration concentration = 0 C 0 at t 0 their chemical activity in the absence of at t 0 bulk fluid flow. • From higher concentration to lower concentration area. • Difference in contaminant concentration is the concentration gradient. Sample • Diffusion ceases when concentration gradient becomes negligible. 1.0 • Relative contaminant concentration C t /C 0 < 1.0 C t / C 0 0.5 =C t /C 0 • Time after introduction of contaminant 0 = t t o t Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 7 Diffusion • Add small amount of dye in a fluid • Pulse gets spread out Add continuous dye-- a sharp front Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 8 Types of Diffusion • Steady State Diffusion J D =-D.  .(  C/  x) • Diffusion flux constant with time • Fick’s First law applicable D = diffusion coefficient [L 2 /T]  = porosity  C/  x = concentration gradient (i.e., change in concentration with distance) • Non Steady-state Diffusion           • , , C x t C x t Concentration gradient non-uniform   D • Follows Fick’s second law      t x x Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 10 CONTAMINANT TRANSPORT MODELING THROUGH THE ROCK MASS Diffusion cells C 0 C t C t Intact Rock mass (IRM) C o C t Fractured Rock mass (FRM) Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 11 CONTAMINANT TRANSPORT MODELING THROUGH THE ROCK MASS Diffusion characteristics Diffusion cells N       2 C x, t C x, t 33 50 75 100  α D 40   i C 0 C t 2 C t x t Fractured rock mass Intact rock mass 30 -4 ) 0 (x10 Intact Rock mass (IRM) 20 t /C C   α C D a aL 10      t i t   C LV 6V 0 C o 0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 Time (s) s.L.V 6 D i  10 Diffusion time (s) Intact rock mass a C t 5 Fractured rock mass 10 y=1.8 4 10 Fractured Rock mass t m =t p .N -2 3 (FRM) 10 y=1.97 2 10 7 min. 50 days 6 m thick FRM 1 10 1 10 100 75 min. 520 days 0.3 m thick IRM N (D i ) m =(D i ) p Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 12 Modeling Diffusion in soils using impedance spectroscopy (IS) 60 A C U B B  60 A  30 70 Diffusion cell Impedance value of the soil is measured by using LCR meter Diffusion of contaminant can be monitored by determining the change in the impedance of the soil Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 13 • Break-through curve 40 (a) 30 -4 ) C t /C 0 (x10 20 10 453 0 0 100 200 300 400 500 t (h) • The slope of the break-through curve diffusion coefficient, D • Archie’s law ( D =  .  m ) porosity of the geomaterials Environmental Geomechanics Lecture No. 24 D N Singh

Dispersion IIT Bombay Slide 2 (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 Environmental Geomechanics Lecture No. 24 D N Singh

Dispersion IIT Bombay Slide 3 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 Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 4 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 }] Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 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 z t C = f (t,z) D i : Diffusion coefficient K d : Distribution coefficient Environmental Geomechanics Lecture No. 24 D N Singh

IIT Bombay Slide 6 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 Environmental Geomechanics Lecture No. 24 D N Singh