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

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

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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

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SLIDE 1

Flow of water through porous media is extensively studied (seepage, consolidation and stability) The concept of hydraulic conductivity are well established.

Contaminant Transport in Porous Media

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 2

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SLIDE 2

Types of Flow through Porous Media

Electricity

I = V/L

Ohm’s law

L I V1 V2 T

Heat

Fourier’s law

L

1

T2 q

T1 >T2

q = KT/L

Chemicals

Fick’s law

L

C1

JD

JD = DC/L

C2

Fluid

q

= kH/L

Darcy’s law

q L H

H1 H2

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

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

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SLIDE 3

Advection (or Convection)

Solute (contaminant) gets transported (seepage velocity) along with the flowing fluid (water) in response to a gradient (hydraulic).

t0 t1 t2 Vs = k.i/

If a mass of solute (non reactive)

  • f a concentration C is placed at
  • ne end of a pipe, then in a

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/Vs = .L/(k.i)

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

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SLIDE 4

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

Representative values for effective porosity

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

  • f the mixture).

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 5

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SLIDE 5
  • Solutes (contaminants) migrate due to

their chemical activity in the absence of bulk fluid flow.

  • From higher concentration to lower

concentration area.

  • Difference in contaminant concentration

is the concentration gradient.

  • Diffusion ceases when concentration

gradient becomes negligible.

Contaminant at concentration C0 at t0 Contaminant concentration = 0 at t0

Sample

  • Time after introduction of contaminant

= t

  • Relative contaminant concentration

=Ct/C0

Diffusion

1.0 0.5

to t Ct/C0 < 1.0 Ct / C0 Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 6

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SLIDE 6

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 7

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SLIDE 7

Types of Diffusion

  • Steady State Diffusion
  • Diffusion flux constant with time
  • Fick’s First law applicable
  • Non Steady-state Diffusion
  • Concentration gradient non-uniform
  • Follows Fick’s second law

   

            x t x C D x t t x C , ,

JD =-D..(C/x)

D = diffusion coefficient [L2/T] = porosity C/x = concentration gradient (i.e., change in concentration with distance)

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 8

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SLIDE 8

CONTAMINANT TRANSPORT MODELING THROUGH THE ROCK MASS

Fractured Rock mass (FRM) Co Ct Intact Rock mass (IRM) C0 Ct Ct

Diffusion cells

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 10

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SLIDE 9

7 min. 50 days 6 m thick FRM 75 min. 520 days 0.3 m thick IRM (Di)m=(Di)p

   

t t x, C α x t x, C D

2 2 i

    

         6V aL LV a D C C

i t

α t a s.L.V Di 

2000 4000 6000 8000 10000 10 20 30 40 Intact rock mass 2000 4000 6000 8000 10000

C

t/C 0 (x10

  • 4)

Fractured rock mass

N 33 50 75 100

Time (s)

1 10 100 10

1

10

2

10

3

10

4

10

5

10

6

y=1.8

Intact rock mass Fractured rock mass

y=1.97

Diffusion time (s)

N

tm=tp.N-2

Diffusion characteristics

Fractured Rock mass (FRM) Co Ct Intact Rock mass (IRM) C0 Ct Ct

Diffusion cells

CONTAMINANT TRANSPORT MODELING THROUGH THE ROCK MASS

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 11

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SLIDE 10

70 30 U C 60 A A B B 60 Modeling Diffusion in soils using impedance spectroscopy (IS)

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 12

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SLIDE 11
  • Break-through curve

100 200 300 400 500 10 20 30 40

(a)

453

Ct/C0 (x10

  • 4)

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 IIT Bombay Slide 13

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SLIDE 12

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

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

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SLIDE 13

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

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

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SLIDE 14

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 }]

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

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SLIDE 15

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

Environmental Geomechanics Lecture No. 24 D N Singh IIT Bombay Slide 5

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SLIDE 16

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 IIT Bombay Slide 6