14) Transport Processes

examples of point sources

leaky storage tanks
accidental spills
waste lagoons, landfills, dumps
septic systems
mine tailings
graveyards
injectionwells

examples of nonpoint sources

land applied manure/sewage/sludge
fertilizers and pesticides
air pollution fallout
urban runoff
military firing ranges

examples of linearly distributed sources

pipeline leakage
saltwater intrusion
road salt
losing streams
canal leakage

types and examples of contaminant types

chemical: inorganic, organic, metals, radionuclides

biological: bacteria, viruses

miscible/dissolved: cations and anions, organics

immiscible fluids: gasoline, chlorinated solvents

what are teh three key transport mechanisms

advection: transport due to bulk groundwater flow

diffusion: molecular transport due to solute concentration gradients (no water movement)

mechanical dispersion: spreading of solute mass due to groundwater velocity variations at the pore scale

details on advection

amount of solute transferred depends on
concentration in water and amount of water flowing

flux measurement (volume through cross-sectional area over time) mass per area per time

solutes move along with groundwater flow

advective mass flux = Ja = q C = ne v C

details on molecular diffusion

solutes move through stationary fluid due to random brownian motion

solutes move from high concentration to low concentration

spreads solutes in all directions but no water movement

how is diffusion affected in porous media?

value of diffusion coefficient is smaller than Dd because of tortuous flow paths that molecules have to travel

some molecules have longer path to follow, so diffusion coeff is smaller

true or false: tortuousity is always less than 1

true, it’s less than what it would be in free water (1)

what is mechanical dispersion

tendency for solutes to spread out from the path it would be expected to follow

multiple velocities in porous media causes spreading of solute in space

advective process that results from velocity variation

what is dispersion caused by?

some pores are larger than others, allowing fluid flowing through larger pores to move faster

some fluid particles will travel along longer flow paths in soil than others to go the same linear distance

as fluid moves through pores, it will more faster in the centre of the pores than along the edges (friction)

true or false: solute transport cannot occur with no advective water movement

false: solute transport can still happen (very slowly) even with no advective groundwater movement

what form of transport becomes dominant in very low hydraulic conductivity media

diffusion

longitudinal dispersion vs transverse dispersion

longitudinal: spreading parallel to the direction of groundwater flow

transverse: spreading in the direction perpendicular to groundwater flow, smaller than longitudinal, can be different horizontally than vertically

what are scale effects of dispersion

dispersion increases with scale until asymptote is reached

decrease in concentrations due to pore-scale mechanical dispersion and macro-scale heterogeneitywh

at is hydrodynamic dispersion

molecular diffusion and mechanical dispersion together

JH, subscript i refers to direction in which mass flux is being calculated (longitudinal or transverse)

under low flow velocities __ dominantes, and under high flow velocities __ dominantes

low flow = diffusion (D*) dominates

high flow = dispersion (av) dominates

what situations would you expect to see more dispersion? less?

more dispersion = high K materials like gravel and sand

less dispersion = low K materials like clay

explain this

shows how tracer progresses, the lines show zone of dispersion where 0<C/C0<1

important details about solute transport processes

advection moves the contaminants at the bulk average groundwater velocity

hydrodynamic dispersion spreads contaminants in all directions

spreading is greatest in parallel to flow (longitudinal)

dispersion is due to variations in flow velocity

transport is a transient process occurring within a steady groundwater flow system

what is the advection dispersion equation

solute mass flux in - solute mass flux out ± loss/gain of solute mass = net rate of change of solute mass within the element

what are the assumptions in the 2D advection dispersion equation

saturated porous medium

groundwater velocity is uniform and steady

flow is aligned with x-direction

dilute solution (no density effects)

what is the ogata-banks solution

assume v is known and steady

can solve for C at any point, x, along the column at any time t

solution reduces to the 1-D form of the diffusion equation when v=0

numerator: x-vt, how far are you along x relative to advective front vt

denominator: how much longitundinal dispersion is there about the centre of mass

what do variables mean in ogata-banks solution

C = concentration at location x and time t

C0 = boundary concentration at x=0

v = pore water velocity in +x direction (darcy/porosity)

DL = longitudinal dispersion coefficient

Erfc = complementary error function

what happens in ogata banks solution for the graphs>

more dispersion = flatter and longer

more advective flow = more vertical

what is assumed for 1D advection dispersion equation?

only moving water through pores of porous medium

uniform velocity and dispersion coefficient

what does ogatabanks solution mean

solute follows normal distribution about center of mass at x=vt

solute mass is conserved

plume spreading must cause peak concentrations to decline

peak concentration occurs at center of mass where x=vt and y=0

what things cause plume growth

advection

molecular diffusion

mechanical dispersion

what things limit plume growth

chemical:
sorption
precipitaiton/dissolution
volatilization
reactions
abiotic degradation

biological: degradation

what is adsorption

process where solute molecules attach to the surface of solid particles in a porous medium

clays are strong adsorbers because they have high surface area, platy structure, and electrical charge at surface

what is electrical conductivity

material’s ability to conduct/transport an electric charge which is directly related to concentration of ions in water
high EC = high salinity

specific conductivity is EC corrected to to 25°C

what is an isotherm

relationship between concentration of solute in aqueous solution to mass sorbed on solid surface

what is G in equations

source or sink for solute mass

during sorption, mass is lost from dissolved phase onto mineral surfaces, so we use sink term

G is adsorption term representing the rate of mass sorbed to solids per unit volume porous medium per unit time

what is retardation factor? what happens if its zero

measure of mean velocity of reactive contaminant relative to mean velocity of non-reactive contaminant

slows the advection of contaminant and reduces dispersion of contaminant

there is no slowing down of the plume

what are assumptions of Kd model

linear sorption isotherm
equilibrium
fast, reversible reaction
isothermal conditions

may not be valid for all concentrations, if other chemicals are present, different pH

what are effects of sorption on plumes

sorption may not be reversible

contaminants undergoing sorption will travel more slowly than non-reactive contaminants in a plume (retardation)

strong sorption can cause a contaminant to be immobile over a relevant time scale, such as many decades or centuries

each contaminant has its own particular sorption affinity, and will move at its own rate

how might ADE apply in landfill leachate

continuous space

ogata-banks equation for 1D best suited if source is large, otherwise need 2D or 3D solution

consider retardation

how might ADE apply in nuclear waste disposal

can use ogata-banks with v=0 (no flow)

slow diffussion

how might ADE apply in chemical spill

2-S slug input solution

consider retardation factor

most concentrated value in centre of plume

true or false: the greater the groundwater flow velocity, the greater the hydrodynamic dispersion

true

both equations (transverse and longitudinal) have velocity in them

hydrodynamic = mechanical dispersion + diffusion

true or false: dispersion, sorption, and diffusion are three transport processes that cause growth of groundwater contaminant plumes

false, sorption slows down, dispersion and diffusion do cause growth