1.72, Groundwater Hydrology Prof. Charles Harvey Lecture Packet #11: Solute Transport in Groundwater

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1 1.72, Groundwater Hydrology Prof. harles Harvey Leture Paket #11: Solute Transport in Groundwater Importane of Solute Transport in Groundwater Geologi questions: ion migration, ore deposition. Environmental problems: ontamination of drinking water by organi ompounds and metals, radioative waste disposal, saltwater intrusion. Drinking water standards Dissolved ompounds an be toxi and arinogeni. Safe Drinking Water At direted EPA to establish MLs (maximum ontaminant levels) Typial values: ontaminant Trihloroethylene (TE) Tetrahloroethylene (PE) Vinyl hloride Benzene arbon Tetrahloride opper Lead Merury Arseni ML 5 µg/l 5 µg/l 2 µg/l 5 µg/l 5 µg/l 1 mg/l 0.05 mg/l 2 µg/l 10 µg/l Immisible ompounds serve as a soure of dissolved groundwater ontamination. Gasoline Immisible Ground Surfae Methanol Misible Ground Surfae Ethylene Glyol = PE Dissolved Impermeable Formation Impermeable Formation NAPLs non-aqueous phase liquids LNAPL lighter-than-water NAPL (floaters) For example, fuels: gasoline, diesel fuel Plume forms on surfae of water table Migrates in diretion of water table Must be skimmed DNAPL denser-than-water NAPL (sinkers) For example: hlorinated hydroarbons TE (1.46 sg), TA (1.34), arbon tet (1.59) Prof. harles Harvey Page 1 of 8

2 an sink to bottom of aquifer to form pool an migrate down dip on aquifer bottom Reovery diffiult to impossible The problem: Easy to ontaminate Low onentrations are bad Substanes an migrate with flowing groundwater Hard to remove Dissolved Substanes A solute is a substane dissolved in a liquid Example: hloride is a solute and water is the solvent onentrations measure in [Mass/Length 3 ] (mg/l) Representing data involving dissolved substanes, (x,y,z,t) onentration History onentration Profile Time Distane Proesses of Solute Migration 1) Advetion movement of the solute with the bulk fluid where it moves with the average veloity of the water (alone it is plug flow) Reall from Dary s law we have linear average veloity: K V = n e dh dl Advetive flux is simply veloity of water times the solute onentration F adve = V onentration History onentration Profile Time Distane Prof. harles Harvey Page 2 of 8

3 2) Hydrodynami dispersion spread of a solute plume involving the mixing of solute with native groundwater Moleular diffusion spread of solute moleules due to thermal motion (funtion of temperature) d Given by Fik s Law F diff = D mole dx o Where D mole is the diffusion oeffiient in porous media (value less than that in water); D units [L 2 /T] o d/dx is the onentration gradient onentration Profile Diffusion plus advetion Time Get a narrow mixing zone where onentrations are smeared out. Important Observation mixing zone seen in lab or field is muh, muh, muh bigger than an be explained by diffusion alone. Lab experiments show: Spreading exists Spreading is more intense than due to diffusion Spreading depends on groundwater veloity Fik s law applies, but the D is muh bigger F meh d = D meh dx This is due to Mehanial Dispersion the mixing that ours beause the porous media fores some solute moleules to move faster than others while following a tortuous path through pores of different sizes onentration Profile Mehanial dispersion plus advetion Time Prof. harles Harvey Page 3 of 8

4 Veloity variations due to: for example Measurement Loation Fluid veloity profile Short Path time Long Path time Mehanial dispersion from lab fits: D meh = α V Where α is the dispersivity with units of length [L] The Hydrodynami Dispersion oeffiient onsists of D h = D hydrodynami = D mehanial + D moleular NOT to be onfused are: Dispersion the spreading or mixing proess Dispersion oeffiient the D with units of [L 2 /T] Dispersivity spreading or mixing parameter, a length, [L] The flux of solute is due to: Advetion (the main proess) Dispersion (hydrodynami dispersion) d F total = V + ( D meh ) dx Solute Transport Equation Reall development of flow equation: onservation of mass + some empirial law For transport of a nonreative solute we use the above definition for flux as the empirial law giving in 1D: Prof. harles Harvey Page 4 of 8

5 = 2 D V h 2 t x x hange in onentration with dispersion advetion time in uniform steady flow (one diretion) the 2D transport equation is: t 2 = D L + x D 2 2 T x 2 V x x Where the longitudinal hydrodynami dispersion oeffiient is: D L = α L V and α L is the longitudinal dispersivity The transverse hydrodynami dispersion oeffiient is: D T = α T V and α T is the transverse dispersivity (muh smaller than longitudinal dispersivity) Note: In 2D if flow is in two diretions then you get 4 dispersion terms and two advetive terms and the form of the D s is more omplex) From a pulse injetion you get a plume (a loud) of solute that migrates via advetion and spreads longitudinally (mostly) and transversely (a bit) Mass is onserved. Map View Longitudinal Dispersion Advetion Transverse Dispersion onentration Profile Distane Prof. harles Harvey Page 5 of 8

6 In reality: Plumes are not so perfetly shaped Even in homogeneous media they are distorted In heterogeneous media plumes an be omplex, following high ondutivity lenses and even split into more than one plume There is a sale effet in whih dispersivity is greater with greater travel distane Prof. harles Harvey Page 6 of 8

7 hemial Reation During Transport Homogeneous reations ourring in the aqueous phase Heterogeneous reations those involving a soli9 d surfae or a phase onversion Sorption a type of surfae reation in whih the solute spends some of its time stuk to solid surfaes thereby delaying its arrival in a proess known as retardation. Equilibrium Isotherm a relationship that is not a funtion of time showing the onentration in solution () versus that absorbed (S) on the solid surfae. Linear isotherm S = K d S Langmuir isotherm K d Transport equation has two dependent variables, and S S 2 + β = D h V t t x 2 x Two unknowns and only one equation??? But we have a relation, the isotherm S S = K d Æ need to get into a form showing t S K d Take derivative = t t S 2 + β = D h V t t x 2 x K 2 d + β = D h V t t x 2 x 2 (1+ β K d ) = D h V t x 2 x (1+ β K d ) = retardation fator Retardation fator Æ the fator by whih the non-reative (nonsorbing) solute migrates ompared to the sorbing solute whih is delayed. Prof. harles Harvey Page 7 of 8

8 Veloity R = Veloity sorbing nonreativ e Retarded Speies Nonretarded Speies Distane One good thing about sorption Some hazardous speies haven t migrated. Some spills involving plutonium indiate 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 ontaminant plume, there will still be stuff stuk to the solids that will make its way bak to the liquid. Therefore, it takes a long time to leanup a ontaminant plume if there is sorbed solute. Hot topis in Transport omplex hemial reation modeling oupled proess models (T, hemistry, High on.) Theory of dispersion Rate Limited Mass Transfer Mirobial ativity to degrade VOs Optimal design of remedial systems Prof. harles Harvey Page 8 of 8