hydro section 1 - dispersion

Question 1

breakthrough

Answer 1

time taken for leachate to be detected at xxxx

breakthrough occurs over a finite interval of time, with concentrations gradually rising to 100% (if reactions are occurring, concentration may not reach 100%)

Question 2

Describe typical shape of a plume of solute moving down flow from a continuous source of pollution

Answer 2

Plume longitudinal, longitudinal dispersion zone approx 10to 100 times larger than transverse dispersion zone

Question 3

which two processes give rise to dispersion

Answer 3

mechanical dispersion - solute moving/separating outwards due to contact with grains (tortuosity) paths expand and become more varied

diffusion - caused by collision of atoms that are excited thermally

x = route[2Dt]

x = average distance travelled 
t = time
D = diffusion coefficient

Question 4

diffusion is important in..

Answer 4

• radioactive waste disposal
• natural, low flow systems
• landfill liners
• maintaining chemical homogeneity over pore scale/ lamination scale

Question 5

Describing diffusion quantitatively, what equation?

Fick’s (first) Law

Answer 5

F = -AD(dC / dx)

F= mass transferred by diffusion per unit time (M/T)
A = cross sectional area at right angles to direction of mass movement 
D = diffusion coefficient 
C = Concentration
X = distance

Question 6

diffusion coefficient value in water…

Answer 6

between 1 and 2 x10^-9 m2/s

dependant on species involved and temperature

in rocks the grains inhibit the movement of the diffusing solutes

therefore diffusion coefficients in rocks D* are < diffusion coefficients in open water: D* ~ 0.01D to 0.5D

Question 7

Calculating diffusive flux without knowing concentration gradient

Ficks (second) Law

Answer 7

combine conservation of mass(mass in - mass out = change in mass stored) with ficks law

end up with differential equation

> dC / dt = D(phi) x (d2C /dx2)

Question 8

C / Co

Answer 8

where Co is the concentration at the up-gradient boundary (see below), and erfc(β) is the ‘complementary error function’ of β. erfc(β) should be treated like any other function, e.g. sin(β) or log(β): β is the ‘argument’ of the complementary error function, and in the present case β = x/(2(D*t)^0.5 (remember also that x0.5 = the square root of x).