Three formations with thickness of 10 m, 5 m, and 2 m, for the 1 st , 2 nd , and
ID: 290926 • Letter: T
Question
Three formations with thickness of 10 m, 5 m, and 2 m, for the 1st, 2nd, and 3rd formations, respectively, overlie one another. The hydraulic conductivity of the 1st formation is 20 m/day, the 2nd formation is 5 m/day, and the 3rd formation is 50 m/day. If a constant total discharge per unit width of Q=100 m2/day flows horizontally through three formations,
(1) What are the percentages of those discharge Q going through the 1st, 2nd, and 3rd formations?
(2) If these formations contained groundwater contaminated with TCE (a common organic contaminants found in groundwater) with concentrations of 10 mg/L, 4 mg/L, and 1 mg/L in the 1st, 2nd, and 3rd formations, respectively, then what is the average concentration in discharge exiting these three formations?
Explanation / Answer
Formation 1
thickness=10m
hydraulic conductivity= 20m/day
transmissivity=200m2/day
Formation 2
thickness=5m
hydraulic conductivity= 5m/day
transmissivity=25m2/day
Formation 3
thickness=2m
hydraulic conductivity= 50m/day
transmissivity=100m2/day
Therfore total transmissivity= 325m2/day
Discharge per unit width =100m2/day
Therefore,
discharge through formation 1= ( transmissivity of formation 1/ total transmisivity)* total discharge
=(200/325)*100
=61.53%
discharge through formation 2= ( transmissivity of formation 2/ total transmisivity)* total discharge
=(25/325)*100
=7.69%
discharge through formation 3= ( transmissivity of formation 3/ total transmisivity)* total discharge
=(100/325)*100
=30.77%
Ans 2:
We know discharge passing through Formation 1= 61.53m2/day
TCE concentration for formation 1=10 mg/l
=10mg/l*6153 l/day (1m2=100l)
=61530 mg/day
We know discharge passing through Formation 2= 7.69 m2/day
TCE concentration for formation 2=4 mg/l
=4mg/l*769 l/day (1m2=100l)
=3076 mg/day
We know discharge passing through Formation 3= 30.77 m2/day
TCE concentration for formation 1=1 mg/l
=1 mg/l*3077 l/day (1m2=100l)
=3077 mg/day
Average concentration of TCE in the discharge exiting these three formation is (61530+3076+3077)mg/day= 67683mg/day
Since the discharge is 100m2/day or 10000l/day
Therefore the TCE concentration=67683mg/10000 l
=6.768mg/l