19 Basics of Mass Transport Advection, Diffusion, and Dispersion.
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Transcript of 19 Basics of Mass Transport Advection, Diffusion, and Dispersion.
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19Basics of Mass Transport
Advection, Diffusion, and Dispersion
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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)
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Key Elements of Mass Transfer
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Physical and Chemical Mass Transport Processes operating in a groundwater flow system
Conceptualization of mass transport in a groundwater flow system
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Introduction
Topics:
19.1 Advection
19.2 Diffusion
19.3 Dispersion
19.8 Tracer and Tracer Tests
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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
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19.1 Advection
(a) advection alone (b) advection + dispersion
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Mass spreading by advection in a shallow unconfined aquifer
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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
v v v vK
n
h
x
K
n
h
y
K
n
h
z
K
ngradx y z
xx yy zz
( , , ) ( , , ) h
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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
e
K hv
n l
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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
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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
J DdC
dxdif m
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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
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Mixing caused by local variations in velocity Advective process Variations in K
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Dispersion with time
mixing zone size increases with time
Longitudinal & transverse dispersion
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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
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“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
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(a) horizontal transverse dispersion(b) vertical transverse dispersion
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Map view of Cl- ion distribution in a tracer test after 462 days
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Mixing in Fractured Media
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19.8 Tracer and Tracer tests
Tracers:1. Ions occuring naturally in groundwater
systems: Br-, Cl-
2. Environmental isotopes: 2H, 3H, 18O3. Contaminants of all kinds in the flow
systems: radioisotopes 3H, 131I, 82Br…organic compounds
Ideal tracers: no reaction (conservative tracers)
Reactive tracers
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19.8 Tracer and Tracer tests
dfkd
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Natural Gradient Test Single well pulse test Two well tracer test Single well injection or withdrawal with multiple observation
wells
Tracers and Tracer Tests
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Cl- concentration distribution at various times after injection