Question

In the laboratory you set up an experiment as shown below. You maintain a constant reservoir so Water inflow that the driving force for water through the porous media column is constant. (a) Given that you used fine sand for your media in the column (K-104 m/s) and the column has a 20 cm diameter, what is the flow rate, Q, through the column? (b) If you added a chemical tracer (conservative) to the inflow at the top of the column, what would be the expected travel time through the column if the porosity was 0.2? (c) What is the expected arrival Constant water level reservoir connected by pipe to porous media 10 cm X-0 cm time of the tracer at a concentration of 10% of the initial concentration if D-104 m2/s? (d) How would the travel times change if the chemical retardation factor of the chemical was 5 X-50 cmm

Answer 1

Ans) Given,

Diameter of column = 20 cm or 0.20 m

Permeability(K) = 10^-4 m/s

a) We know,

Q = K i A

where, i = hydraulic gradient

A = cross sectional area of column

i = h/L = 0.1/0.5 = 0.20

=> Q = 10^-4 x 0.20 x ($\pi$/4) x 0.20 x 0.20

Q = 6.28 x 10^-7 m³/s

b) We know,

V = K x i / $\eta$

where, $\eta$ = porosity

=> V = 10^-4 x 0.20 / 0.20

=> V = 10^-4 m/s

Time taken to flow 50 cm or 0.50 m = 0.50 / 10^-4 sec

= 5000 sec or 83.33 min or 1.38 hour

c) According to Flick's law,

N = D x C

N = 10^-4 x 0.10 = 10^-5 mol m²/s

t = CA /N

= 0.01 x (0.785 x 0.2 x 0.2) / 10^-5

= 31.4 sec

d) New time = t x chemical retardation factor

= 31.4 x 5

= 157 sec