Transcript 19 Basics of Mass Transport Advection, Diffusion, and Dispersion

19
Basics of Mass Transport
Advection, Diffusion, and Dispersion
Introduction
 Mass Transport:
 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)
Key Elements of Mass Transfer
Physical and Chemical Mass Transport Processes
operating in a groundwater flow system
Conceptualization of mass transport in a groundwater flow system
Introduction
 Topics:
19.1 Advection
19.2 Diffusion
19.3 Dispersion
19.8 Tracer and Tracer Tests
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
19.1 Advection
 (a) advection alone (b) advection + dispersion
Mass spreading by advection in a shallow
unconfined aquifer
Advection
 Velocity of advective transport (Darcy):
Kxx h K yy h Kzz h
K
v  ( v x , v y , vz )  ( 
,
,
)   gradh
n x
n y
n z
n
 v:
linear groundwater velocity
 Kxx, Kyy, Kzz: Hydraulic conductivity along x,y, z
 n:
effective porosity
 dh/dx, dh/dy, dh/dz: hydraulic gradient
Advection velocity
K h
v 
ne l
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
Advection, example
A small plume of tracer is added to an unconfined aquifer that
has a hydraulic conductivity of 1 m/d and a porosity of 0.35.
the hydraulic gradient is 0.07.
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
19.2 Diffusion
Fick’s Law:
relates mass flux to gradient in concentration
(similar to Darcy’s)
J dif
dC
  Dm 
dx
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
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
 Mixing caused by local variations in velocity
 Advective process
 Variations in K
Dispersion with time
 mixing zone size
increases with time
 Longitudinal &
transverse dispersion
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
“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
(a) horizontal transverse dispersion
(b) vertical transverse dispersion
Map view of Cl- ion distribution in a tracer test after 462 days
Mixing in Fractured Media
19.8 Tracer and Tracer tests
 Tracers:
1. Ions occuring naturally in groundwater
systems: Br-, Cl2. Environmental isotopes: 2H, 3H, 18O
3. Contaminants of all kinds in the flow
systems: radioisotopes 3H, 131I,
82Br…organic compounds
 Ideal tracers: no reaction (conservative
tracers)
 Reactive tracers
19.8 Tracer and Tracer tests
dfkd
Tracers and Tracer Tests
 Natural Gradient Test
 Single well pulse test
 Two well tracer test
 Single well injection or withdrawal with multiple observation
wells
Cl- concentration
distribution at
various times after
injection