19Basics 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):

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

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

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)

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

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-, 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

19.8 Tracer and Tracer tests

dfkd

Natural Gradient Test Single well pulse test Two well tracer test Single well injection or withdrawal with multiple observation

wells

Tracers and Tracer Tests

Cl- concentration distribution at various times after injection