19 Basics of Mass Transport Advection, Diffusion, and Dispersion

Introduction Mass Transport: Mass moves and distributes by 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

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

Advection, example Solution: 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

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: Ions occuring naturally in groundwater systems: Br-, Cl- Environmental isotopes: 2H, 3H, 18O 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

Tracers and Tracer Tests Natural Gradient Test Single well pulse test Two well tracer test Single well injection or withdrawal with multiple observation wells

Cl- concentration distribution at various times after injection