1. 19 Basics of Mass Transport
Advection, Diffusion, and Dispersion

2. Introduction Mass Transport: Mass moves and distributes by
Delivery/distribution problem
Dissolved mass: ions + molecules
Natural or contaminated: SOURCE
Iron in gw comes from iron silicate mineral or old car in a landfill
Mass moves and distributes by
Physical process (advection, dispersion)
Chemical process (reactions)
Biological process (redistribution of mass forms)

3. Key Elements of Mass Transfer

4. Physical and Chemical Mass Transport Processes operating in a groundwater flow system
Conceptualization of mass transport in a groundwater flow system

5. Introduction Topics: 19.1 Advection 19.2 Diffusion 19.3 Dispersion
19.8 Tracer and Tracer Tests

6. 19.1 Advection
Advection:
mass transport due simpley to the flow of water in which the mass is dissolved
It’s The main process
Direction and rate of transport = direction and rate of groundwater flow

7. 19.1 Advection
(a) advection alone (b) advection + dispersion

8. Mass spreading by advection in a shallow unconfined aquifer

9. Advection Velocity of advective transport (Darcy):
v: linear groundwater velocity
Kxx, Kyy, Kzz: Hydraulic conductivity along x,y, z
n: effective porosity
dh/dx, dh/dy, dh/dz: hydraulic gradient

10. Advection velocity
cases where velocity of groundwater and transported mass are different: 1- negatively charged ions vm>vgw 2-small voids (medium works as membrane) 3-Retardation

11. Advection, example Solution:
A small plume of tracer is added to an unconfined aquifer that has a hydraulic conductivity of 1 m/d and a porosity of the hydraulic gradient is
Calculate how far the center of mass of the tracer will move in one year.
Solution:
Assume advection only, use previous equation
v = -K/n * grad (h) = (1 m/d/0.35) x 0.07 = 0.2 m/d
Distance = d = v x t = 0.2 m/d x 365 d = 73 m

12. 19.2 Diffusion
Fick’s Law:
relates mass flux to gradient in concentration
(similar to Darcy’s)
Jdif: chemical mass flux [L2/T]
dC/dx concentration gradient [C: moles/L3]
Dm molecular diffusion coefficient [L2/T
Molecular diffusion: mixing caused by random molecular motions due to thermal kinetic energy of the solute
Coefficient is larger in gases than in liquids, in liquids than solids

13. 19.3 Dispersion Dispersion:
is a process of mixing that causes a zone of mixing to develop between a fluid of one composition that is adjacent to or being displaced by a fluid with a different composition
Dispersion spreads mass beyond the region it normally would occupy due to advection alone

14. Mixing caused by local variations in velocity
Advective process
Variations in K

15. Dispersion with time mixing zone size increases with time
Longitudinal & transverse dispersion

17. 19.3 Dispersion Dispersion: Occurs because of two processes
1. Diffusion:
mass transport by concentration gradient
2. Molecular Dispersion:
mixing due to local differences around some mean velocity of flow

19. “Rubber duckies” released in a river from the circle at point “a” will end up highly dispersed due to local variability in the flow velocity

20. (a) horizontal transverse dispersion (b) vertical transverse dispersion

21. Map view of Cl- ion distribution in a tracer test after 462 days

22. Mixing in Fractured Media

23. 19.8 Tracer and Tracer tests
Tracers:
Ions occuring naturally in groundwater systems: Br-, Cl-
Environmental isotopes: 2H, 3H, 18O
Contaminants of all kinds in the flow systems: radioisotopes 3H, 131I, 82Br…organic compounds
Ideal tracers: no reaction (conservative tracers)
Reactive tracers

24. 19.8 Tracer and Tracer tests
dfkd

25. Tracers and Tracer Tests
Natural Gradient Test
Single well pulse test
Two well tracer test
Single well injection or withdrawal with multiple observation wells

26. Cl- concentration distribution at various times after injection