1_72_lecture_11地下水溶质运移

1.72, Groundwater Hydrology

Prof. Charles Harvey

Lecture Packet #11: Solute Transport in Groundwater

Importance of Solute Transport in Groundwater

• •

Geologic questions: ion migration, ore deposition.

Environmental problems: contamination of drinking water by organic compounds and metals, radioactive waste disposal, saltwater intrusion.

Drinking water standards

• Dissolved compounds can be toxic and carcinogenic.

• Typical values:

Contaminant MCL •

Immiscible compounds serve as a source of dissolved groundwater

contamination.

NAPLs – non-aqueous phase liquids

LNAPL – lighter-than-water NAPL (floaters)

• For example, fuels: gasoline, diesel fuel • Plume forms on surface of water table • Migrates in direction of water table • Must be skimmed

DNAPL – denser-than-water NAPL (sinkers)

• For example: chlorinated hydrocarbons – TCE (1.46 sg), TCA (1.34), carbon

tet (1.59)

• • • Can sink to bottom of aquifer to form pool Can migrate down dip on aquifer bottom Recovery difficult to impossible

The problem:

• Easy to contaminate

• Low concentrations are bad

• Substances can migrate with flowing groundwater • Hard to remove Dissolved Substances

A solute is a substance dissolved in a liquid

• Example: Chloride is a solute and water is the solvent • Concentrations measure in [Mass/Length3] (mg/L) Representing data involving dissolved substances, C(x,y,z,t)

2) Hydrodynamic dispersion – spread of a solute plume involving the mixing

of solute with native groundwater

• •

Molecular diffusion – spread of solute molecules due to thermal motion (function of temperature)

o o c

Lab experiments show:

• Spreading exists

• • • This is due to Mechanical Dispersion – the mixing that occurs because the porous media forces some solute molecules to move faster than others while following a tortuous path through pores of different sizes

dx

Velocity variations due to: for example –

Mechanical dispersion from lab fits: Dmech = α|V| Where α is the dispersivity with units of length [L] The Hydrodynamic Dispersion Coefficient consists of

Dh = Dhydrodynamic = Dmechanical + Dmolecular

NOT to be confused are:

Dispersion – the spreading or mixing process

Dispersion Coefficient – the D with units of [L2/T]

Dispersivity – spreading or mixing parameter, a length, [L] The flux of solute is due to:

• Advection (the main process)

• Dispersion (hydrodynamic dispersion)

Ftotal = VC + (− Dmech )

dcdx

Solute Transport Equation

Recall development of flow equation:

Conservation of mass + some empirical law

For transport of a nonreactive solute we use the above definition for flux as the empirical law giving in 1D:

∂ C ∂ 2C∂C

= Dh2−Vt∂ x∂ xChange in ∂

concentration with

time

dispersion advection

in uniform steady flow (one direction) the 2D transport equation is:

∂ CC∂ 2C ∂ ∂ 2C

V− D+ = D L Tx

x ∂ t ∂ x 2x 2∂ ∂

Where the longitudinal hydrodynamic dispersion coefficient is: DL = αL|V| and αL is the longitudinal dispersivity The transverse hydrodynamic dispersion coefficient is:

DT = αT|V| and αT is the transverse dispersivity (much smaller than longitudinal

dispersivity) Note: In 2D if flow is in two directions then you get 4 dispersion terms and two

advective terms and the form of the “D”s is more complex) From a pulse injection you get a plume (a cloud) of solute that migrates via advection and spreads longitudinally (mostly) and transversely (a bit) – Mass is

conserved. Map View

Longitudinal Dispersion

Concentration Profile

Distance

In reality:

• Plumes are not so perfectly shaped

• Even in homogeneous media they are distorted

• In heterogeneous media plumes can be complex, following high conductivity

lenses and even split into more than one plume

• There is a scale effect in which dispersivity is greater with greater travel

distance

Chemical Reaction During Transport

• • •

Homogeneous reactions – occurring in the aqueous phase Heterogeneous reactions – those involving a soli9 d surface or a phase conversion

Sorption – a type of surface reaction in which the solute spends some of its time stuck to solid surfaces thereby delaying its arrival in a process known as retardation. Equilibrium Isotherm – a relationship that is not a function of time showing the concentration in solution (C) versus that absorbed (S) on the solid surface.

Linear isotherm

S = KdC

Langmuir isotherm

S

Kd

C

Transport equation has two dependent variables, C and S

∂ C∂ S∂ 2C ∂ C+β = Dh 2 − V∂ t∂ t∂ x∂ xTwo unknowns and only one equation??? But we have a relation, the isotherm… S = KdC Æ need to get into a form showing Take derivative

S∂

∂ tK C ∂ S∂

= d ∂ t∂ t∂ CCS∂ 2C ∂ ∂

+β = Dh 2 − V∂ xtt∂ ∂ x∂ K dC ∂ ∂ CC∂ 2C ∂

+β = Dh 2 − V∂ x t t∂ ∂ x∂

∂ C C∂ 2C ∂

(1+β Kd = Dh 2 − V∂ xt∂ x∂

(1+β Kd ) = retardation factor

Retardation factor Æ the factor by which the non-reactive (nonsorbing) solute

migrates compared to the sorbing solute which is delayed.

R =

Velocitynonreactiv e Velocity

sorbing

C

One good thing about sorption

Some hazardous species haven’t migrated. Some spills involving plutonium indicate that it hasn’t migrated but a few meters at most (in unsaturated zone) One bad thing about sorption

Even if you pump out a contaminant plume, there will still be stuff stuck to the solids that will make its way back to the liquid. Therefore, it takes a long time to cleanup a contaminant plume if there is sorbed solute. Hot topics in Transport

• Complex chemical reaction modeling

• Coupled process models (T, Chemistry, High Conc.) • Theory of dispersion

• Rate Limited Mass Transfer

• Microbial activity to degrade VOCs • Optimal design of remedial systems